Properties

Label 304.2.bg.a.147.31
Level $304$
Weight $2$
Character 304.147
Analytic conductor $2.427$
Analytic rank $0$
Dimension $456$
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] = [304,2,Mod(3,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 27, 26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.bg (of order \(36\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.42745222145\)
Analytic rank: \(0\)
Dimension: \(456\)
Relative dimension: \(38\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 147.31
Character \(\chi\) \(=\) 304.147
Dual form 304.2.bg.a.91.31

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.14176 + 0.834502i) q^{2} +(-2.74773 + 1.92398i) q^{3} +(0.607213 + 1.90560i) q^{4} +(-2.55312 + 0.223369i) q^{5} +(-4.74280 - 0.0962697i) q^{6} +(0.422963 + 0.732593i) q^{7} +(-0.896935 + 2.68244i) q^{8} +(2.82226 - 7.75408i) q^{9} +O(q^{10})\) \(q+(1.14176 + 0.834502i) q^{2} +(-2.74773 + 1.92398i) q^{3} +(0.607213 + 1.90560i) q^{4} +(-2.55312 + 0.223369i) q^{5} +(-4.74280 - 0.0962697i) q^{6} +(0.422963 + 0.732593i) q^{7} +(-0.896935 + 2.68244i) q^{8} +(2.82226 - 7.75408i) q^{9} +(-3.10144 - 1.87555i) q^{10} +(2.78517 - 0.746283i) q^{11} +(-5.33479 - 4.06780i) q^{12} +(-2.72627 - 1.90895i) q^{13} +(-0.128430 + 1.18941i) q^{14} +(6.58553 - 5.52591i) q^{15} +(-3.26259 + 2.31420i) q^{16} +(-2.19070 + 0.797351i) q^{17} +(9.69313 - 6.49809i) q^{18} +(-2.26747 + 3.72271i) q^{19} +(-1.97594 - 4.72958i) q^{20} +(-2.57168 - 1.19920i) q^{21} +(3.80276 + 1.47215i) q^{22} +(-1.34593 + 1.12937i) q^{23} +(-2.69644 - 9.09632i) q^{24} +(1.54449 - 0.272336i) q^{25} +(-1.51971 - 4.45464i) q^{26} +(4.55940 + 17.0159i) q^{27} +(-1.13920 + 1.25084i) q^{28} +(-5.32904 + 2.48497i) q^{29} +(12.1305 - 0.813607i) q^{30} +(0.770393 + 1.33436i) q^{31} +(-5.65628 - 0.0803808i) q^{32} +(-6.21705 + 7.40919i) q^{33} +(-3.16664 - 0.917767i) q^{34} +(-1.24351 - 1.77592i) q^{35} +(16.4899 + 0.669700i) q^{36} +(5.67745 + 5.67745i) q^{37} +(-5.69551 + 2.35821i) q^{38} +11.1638 q^{39} +(1.69081 - 7.04895i) q^{40} +(0.524850 - 2.97657i) q^{41} +(-1.93550 - 3.51526i) q^{42} +(-0.736056 - 8.41315i) q^{43} +(3.11330 + 4.85425i) q^{44} +(-5.47354 + 20.4275i) q^{45} +(-2.47918 + 0.166282i) q^{46} +(-4.19208 + 11.5176i) q^{47} +(4.51222 - 12.6360i) q^{48} +(3.14220 - 5.44246i) q^{49} +(1.99070 + 0.977942i) q^{50} +(4.48537 - 6.40578i) q^{51} +(1.98227 - 6.35431i) q^{52} +(-10.0930 - 0.883022i) q^{53} +(-8.99409 + 23.2328i) q^{54} +(-6.94417 + 2.52747i) q^{55} +(-2.34451 + 0.477486i) q^{56} +(-0.932016 - 14.5916i) q^{57} +(-8.15818 - 1.60986i) q^{58} +(-0.366210 + 0.785339i) q^{59} +(14.5290 + 9.19395i) q^{60} +(6.16343 + 0.539230i) q^{61} +(-0.233925 + 2.16641i) q^{62} +(6.87430 - 1.21212i) q^{63} +(-6.39102 - 4.81196i) q^{64} +(7.38690 + 4.26483i) q^{65} +(-13.2813 + 3.27135i) q^{66} +(6.56723 + 14.0835i) q^{67} +(-2.84965 - 3.69043i) q^{68} +(1.52536 - 5.69273i) q^{69} +(0.0622214 - 3.06539i) q^{70} +(-2.02770 + 2.41651i) q^{71} +(18.2685 + 14.5255i) q^{72} +(10.1300 + 1.78619i) q^{73} +(1.74442 + 11.2201i) q^{74} +(-3.71988 + 3.71988i) q^{75} +(-8.47081 - 2.06041i) q^{76} +(1.72474 + 1.72474i) q^{77} +(12.7464 + 9.31625i) q^{78} +(-0.680733 + 3.86063i) q^{79} +(7.81285 - 6.63720i) q^{80} +(-26.3027 - 22.0706i) q^{81} +(3.08321 - 2.96053i) q^{82} +(-1.45004 - 0.388536i) q^{83} +(0.723623 - 5.62876i) q^{84} +(5.41503 - 2.52507i) q^{85} +(6.18040 - 10.2200i) q^{86} +(9.86172 - 17.0810i) q^{87} +(-0.496250 + 8.14042i) q^{88} +(0.616105 + 3.49410i) q^{89} +(-23.2962 + 18.7556i) q^{90} +(0.245376 - 2.80466i) q^{91} +(-2.96938 - 1.87902i) q^{92} +(-4.68411 - 2.18424i) q^{93} +(-14.3978 + 9.65204i) q^{94} +(4.95760 - 10.0110i) q^{95} +(15.6966 - 10.6617i) q^{96} +(3.36588 + 9.24767i) q^{97} +(8.12937 - 3.59178i) q^{98} +(2.07371 - 23.7026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8} - 42 q^{10} - 6 q^{11} - 18 q^{12} - 12 q^{13} - 24 q^{16} - 24 q^{17} - 12 q^{19} - 24 q^{20} + 6 q^{21} - 12 q^{22} - 24 q^{23} - 12 q^{24} - 54 q^{26} - 18 q^{27} + 12 q^{28} - 12 q^{29} - 48 q^{30} + 18 q^{32} - 24 q^{33} + 48 q^{34} + 18 q^{35} - 60 q^{36} - 66 q^{38} - 48 q^{39} - 42 q^{40} + 144 q^{42} - 12 q^{43} + 54 q^{44} - 6 q^{45} - 108 q^{46} - 12 q^{48} - 168 q^{49} + 36 q^{50} + 12 q^{51} - 60 q^{52} - 12 q^{53} - 126 q^{54} - 24 q^{55} - 24 q^{58} - 12 q^{59} + 30 q^{60} - 12 q^{61} - 6 q^{64} - 36 q^{65} - 72 q^{66} - 12 q^{67} - 42 q^{68} + 126 q^{69} + 102 q^{70} - 24 q^{71} - 48 q^{72} + 72 q^{74} + 36 q^{76} + 60 q^{77} - 108 q^{78} + 48 q^{80} - 24 q^{81} - 72 q^{82} - 6 q^{83} - 18 q^{84} - 108 q^{85} - 12 q^{86} - 12 q^{87} - 18 q^{88} + 96 q^{90} + 30 q^{91} - 12 q^{92} + 6 q^{93} - 132 q^{96} - 24 q^{97} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14176 + 0.834502i 0.807343 + 0.590082i
\(3\) −2.74773 + 1.92398i −1.58640 + 1.11081i −0.649972 + 0.759958i \(0.725219\pi\)
−0.936431 + 0.350853i \(0.885892\pi\)
\(4\) 0.607213 + 1.90560i 0.303606 + 0.952798i
\(5\) −2.55312 + 0.223369i −1.14179 + 0.0998937i −0.642319 0.766437i \(-0.722028\pi\)
−0.499471 + 0.866331i \(0.666472\pi\)
\(6\) −4.74280 0.0962697i −1.93624 0.0393020i
\(7\) 0.422963 + 0.732593i 0.159865 + 0.276894i 0.934820 0.355122i \(-0.115561\pi\)
−0.774955 + 0.632017i \(0.782227\pi\)
\(8\) −0.896935 + 2.68244i −0.317114 + 0.948387i
\(9\) 2.82226 7.75408i 0.940752 2.58469i
\(10\) −3.10144 1.87555i −0.980762 0.593101i
\(11\) 2.78517 0.746283i 0.839759 0.225013i 0.186793 0.982399i \(-0.440191\pi\)
0.652967 + 0.757387i \(0.273524\pi\)
\(12\) −5.33479 4.06780i −1.54002 1.17427i
\(13\) −2.72627 1.90895i −0.756131 0.529449i 0.130767 0.991413i \(-0.458256\pi\)
−0.886898 + 0.461964i \(0.847145\pi\)
\(14\) −0.128430 + 1.18941i −0.0343244 + 0.317882i
\(15\) 6.58553 5.52591i 1.70038 1.42678i
\(16\) −3.26259 + 2.31420i −0.815646 + 0.578551i
\(17\) −2.19070 + 0.797351i −0.531324 + 0.193386i −0.593729 0.804665i \(-0.702345\pi\)
0.0624057 + 0.998051i \(0.480123\pi\)
\(18\) 9.69313 6.49809i 2.28469 1.53161i
\(19\) −2.26747 + 3.72271i −0.520194 + 0.854048i
\(20\) −1.97594 4.72958i −0.441833 1.05757i
\(21\) −2.57168 1.19920i −0.561188 0.261686i
\(22\) 3.80276 + 1.47215i 0.810750 + 0.313864i
\(23\) −1.34593 + 1.12937i −0.280645 + 0.235489i −0.772234 0.635338i \(-0.780861\pi\)
0.491589 + 0.870827i \(0.336416\pi\)
\(24\) −2.69644 9.09632i −0.550408 1.85678i
\(25\) 1.54449 0.272336i 0.308899 0.0544672i
\(26\) −1.51971 4.45464i −0.298039 0.873626i
\(27\) 4.55940 + 17.0159i 0.877457 + 3.27471i
\(28\) −1.13920 + 1.25084i −0.215288 + 0.236386i
\(29\) −5.32904 + 2.48497i −0.989578 + 0.461448i −0.848869 0.528603i \(-0.822716\pi\)
−0.140709 + 0.990051i \(0.544938\pi\)
\(30\) 12.1305 0.813607i 2.21471 0.148544i
\(31\) 0.770393 + 1.33436i 0.138367 + 0.239658i 0.926878 0.375362i \(-0.122481\pi\)
−0.788512 + 0.615020i \(0.789148\pi\)
\(32\) −5.65628 0.0803808i −0.999899 0.0142095i
\(33\) −6.21705 + 7.40919i −1.08225 + 1.28978i
\(34\) −3.16664 0.917767i −0.543074 0.157396i
\(35\) −1.24351 1.77592i −0.210192 0.300186i
\(36\) 16.4899 + 0.669700i 2.74831 + 0.111617i
\(37\) 5.67745 + 5.67745i 0.933367 + 0.933367i 0.997915 0.0645480i \(-0.0205605\pi\)
−0.0645480 + 0.997915i \(0.520561\pi\)
\(38\) −5.69551 + 2.35821i −0.923934 + 0.382553i
\(39\) 11.1638 1.78765
\(40\) 1.69081 7.04895i 0.267340 1.11454i
\(41\) 0.524850 2.97657i 0.0819678 0.464862i −0.916002 0.401174i \(-0.868602\pi\)
0.997970 0.0636888i \(-0.0202865\pi\)
\(42\) −1.93550 3.51526i −0.298655 0.542417i
\(43\) −0.736056 8.41315i −0.112247 1.28299i −0.818282 0.574817i \(-0.805073\pi\)
0.706035 0.708177i \(-0.250482\pi\)
\(44\) 3.11330 + 4.85425i 0.469348 + 0.731805i
\(45\) −5.47354 + 20.4275i −0.815947 + 3.04515i
\(46\) −2.47918 + 0.166282i −0.365535 + 0.0245169i
\(47\) −4.19208 + 11.5176i −0.611478 + 1.68002i 0.115455 + 0.993313i \(0.463167\pi\)
−0.726933 + 0.686709i \(0.759055\pi\)
\(48\) 4.51222 12.6360i 0.651283 1.82384i
\(49\) 3.14220 5.44246i 0.448886 0.777494i
\(50\) 1.99070 + 0.977942i 0.281527 + 0.138302i
\(51\) 4.48537 6.40578i 0.628078 0.896988i
\(52\) 1.98227 6.35431i 0.274891 0.881184i
\(53\) −10.0930 0.883022i −1.38638 0.121292i −0.630594 0.776113i \(-0.717189\pi\)
−0.755784 + 0.654821i \(0.772744\pi\)
\(54\) −8.99409 + 23.2328i −1.22394 + 3.16159i
\(55\) −6.94417 + 2.52747i −0.936352 + 0.340804i
\(56\) −2.34451 + 0.477486i −0.313299 + 0.0638068i
\(57\) −0.932016 14.5916i −0.123449 1.93270i
\(58\) −8.15818 1.60986i −1.07122 0.211385i
\(59\) −0.366210 + 0.785339i −0.0476764 + 0.102242i −0.928703 0.370824i \(-0.879075\pi\)
0.881027 + 0.473067i \(0.156853\pi\)
\(60\) 14.5290 + 9.19395i 1.87568 + 1.18693i
\(61\) 6.16343 + 0.539230i 0.789147 + 0.0690414i 0.474601 0.880201i \(-0.342592\pi\)
0.314545 + 0.949242i \(0.398148\pi\)
\(62\) −0.233925 + 2.16641i −0.0297085 + 0.275134i
\(63\) 6.87430 1.21212i 0.866081 0.152713i
\(64\) −6.39102 4.81196i −0.798877 0.601494i
\(65\) 7.38690 + 4.26483i 0.916232 + 0.528987i
\(66\) −13.2813 + 3.27135i −1.63482 + 0.402675i
\(67\) 6.56723 + 14.0835i 0.802315 + 1.72057i 0.686295 + 0.727323i \(0.259236\pi\)
0.116020 + 0.993247i \(0.462986\pi\)
\(68\) −2.84965 3.69043i −0.345571 0.447531i
\(69\) 1.52536 5.69273i 0.183632 0.685324i
\(70\) 0.0622214 3.06539i 0.00743688 0.366384i
\(71\) −2.02770 + 2.41651i −0.240643 + 0.286787i −0.872826 0.488032i \(-0.837715\pi\)
0.632182 + 0.774820i \(0.282159\pi\)
\(72\) 18.2685 + 14.5255i 2.15297 + 1.71184i
\(73\) 10.1300 + 1.78619i 1.18562 + 0.209058i 0.731475 0.681868i \(-0.238832\pi\)
0.454150 + 0.890925i \(0.349943\pi\)
\(74\) 1.74442 + 11.2201i 0.202784 + 1.30431i
\(75\) −3.71988 + 3.71988i −0.429535 + 0.429535i
\(76\) −8.47081 2.06041i −0.971669 0.236345i
\(77\) 1.72474 + 1.72474i 0.196553 + 0.196553i
\(78\) 12.7464 + 9.31625i 1.44324 + 1.05486i
\(79\) −0.680733 + 3.86063i −0.0765885 + 0.434355i 0.922268 + 0.386550i \(0.126334\pi\)
−0.998857 + 0.0478043i \(0.984778\pi\)
\(80\) 7.81285 6.63720i 0.873504 0.742061i
\(81\) −26.3027 22.0706i −2.92253 2.45229i
\(82\) 3.08321 2.96053i 0.340483 0.326936i
\(83\) −1.45004 0.388536i −0.159162 0.0426474i 0.178358 0.983966i \(-0.442921\pi\)
−0.337520 + 0.941318i \(0.609588\pi\)
\(84\) 0.723623 5.62876i 0.0789538 0.614148i
\(85\) 5.41503 2.52507i 0.587342 0.273882i
\(86\) 6.18040 10.2200i 0.666450 1.10205i
\(87\) 9.86172 17.0810i 1.05729 1.83128i
\(88\) −0.496250 + 8.14042i −0.0529004 + 0.867772i
\(89\) 0.616105 + 3.49410i 0.0653070 + 0.370374i 0.999893 + 0.0146368i \(0.00465920\pi\)
−0.934586 + 0.355738i \(0.884230\pi\)
\(90\) −23.2962 + 18.7556i −2.45564 + 1.97701i
\(91\) 0.245376 2.80466i 0.0257224 0.294009i
\(92\) −2.96938 1.87902i −0.309579 0.195902i
\(93\) −4.68411 2.18424i −0.485720 0.226495i
\(94\) −14.3978 + 9.65204i −1.48502 + 0.995532i
\(95\) 4.95760 10.0110i 0.508639 1.02711i
\(96\) 15.6966 10.6617i 1.60203 1.08816i
\(97\) 3.36588 + 9.24767i 0.341753 + 0.938958i 0.984886 + 0.173204i \(0.0554120\pi\)
−0.643133 + 0.765754i \(0.722366\pi\)
\(98\) 8.12937 3.59178i 0.821191 0.362825i
\(99\) 2.07371 23.7026i 0.208416 2.38220i
\(100\) 1.45680 + 2.77781i 0.145680 + 0.277781i
\(101\) −3.87174 2.71102i −0.385252 0.269756i 0.364866 0.931060i \(-0.381115\pi\)
−0.750118 + 0.661303i \(0.770004\pi\)
\(102\) 10.4668 3.57078i 1.03637 0.353560i
\(103\) −3.18957 1.84150i −0.314277 0.181448i 0.334562 0.942374i \(-0.391412\pi\)
−0.648839 + 0.760926i \(0.724745\pi\)
\(104\) 7.56595 5.60086i 0.741902 0.549209i
\(105\) 6.83368 + 2.48726i 0.666899 + 0.242731i
\(106\) −10.7868 9.43081i −1.04771 0.916002i
\(107\) −9.26508 2.48257i −0.895689 0.239999i −0.218525 0.975831i \(-0.570125\pi\)
−0.677164 + 0.735832i \(0.736791\pi\)
\(108\) −29.6569 + 19.0206i −2.85374 + 1.83026i
\(109\) 13.6732 1.19625i 1.30965 0.114580i 0.589144 0.808028i \(-0.299465\pi\)
0.720506 + 0.693448i \(0.243909\pi\)
\(110\) −10.0377 2.90917i −0.957060 0.277378i
\(111\) −26.5234 4.67679i −2.51749 0.443901i
\(112\) −3.07532 1.41133i −0.290591 0.133358i
\(113\) 0.434198i 0.0408459i −0.999791 0.0204230i \(-0.993499\pi\)
0.999791 0.0204230i \(-0.00650128\pi\)
\(114\) 11.1126 17.4378i 1.04079 1.63320i
\(115\) 3.18404 3.18404i 0.296914 0.296914i
\(116\) −7.97121 8.64609i −0.740108 0.802769i
\(117\) −22.4964 + 15.7522i −2.07980 + 1.45629i
\(118\) −1.07349 + 0.591063i −0.0988227 + 0.0544117i
\(119\) −1.51072 1.26764i −0.138488 0.116205i
\(120\) 8.91617 + 22.6217i 0.813931 + 2.06507i
\(121\) −2.32606 + 1.34295i −0.211460 + 0.122087i
\(122\) 6.58714 + 5.75907i 0.596372 + 0.521401i
\(123\) 4.28472 + 9.18862i 0.386340 + 0.828510i
\(124\) −2.07496 + 2.27830i −0.186337 + 0.204597i
\(125\) 8.49528 2.27630i 0.759841 0.203599i
\(126\) 8.86029 + 4.35267i 0.789338 + 0.387767i
\(127\) 1.41118 + 8.00321i 0.125222 + 0.710170i 0.981176 + 0.193117i \(0.0618599\pi\)
−0.855953 + 0.517053i \(0.827029\pi\)
\(128\) −3.28139 10.8274i −0.290037 0.957015i
\(129\) 18.2092 + 21.7009i 1.60323 + 1.91066i
\(130\) 4.87503 + 11.0338i 0.427568 + 0.967726i
\(131\) 6.28927 13.4874i 0.549496 1.17840i −0.413902 0.910322i \(-0.635834\pi\)
0.963398 0.268076i \(-0.0863880\pi\)
\(132\) −17.8940 7.34823i −1.55747 0.639581i
\(133\) −3.68629 0.0865683i −0.319642 0.00750643i
\(134\) −4.25451 + 21.5603i −0.367534 + 1.86252i
\(135\) −15.4415 42.4252i −1.32899 3.65138i
\(136\) −0.173931 6.59161i −0.0149145 0.565226i
\(137\) 12.7164 + 15.1548i 1.08643 + 1.29476i 0.952756 + 0.303736i \(0.0982341\pi\)
0.133677 + 0.991025i \(0.457321\pi\)
\(138\) 6.49218 5.22679i 0.552651 0.444934i
\(139\) 3.73281 5.33100i 0.316613 0.452170i −0.629028 0.777382i \(-0.716547\pi\)
0.945641 + 0.325213i \(0.105436\pi\)
\(140\) 2.62911 3.44800i 0.222201 0.291409i
\(141\) −10.6410 39.7129i −0.896136 3.34443i
\(142\) −4.33172 + 1.06695i −0.363510 + 0.0895366i
\(143\) −9.01774 3.28219i −0.754101 0.274470i
\(144\) 8.73667 + 31.8296i 0.728056 + 2.65247i
\(145\) 13.0506 7.53478i 1.08379 0.625729i
\(146\) 10.0754 + 10.4929i 0.833845 + 0.868397i
\(147\) 1.83726 + 20.9999i 0.151534 + 1.73205i
\(148\) −7.37150 + 14.2663i −0.605934 + 1.17269i
\(149\) −1.29641 1.85147i −0.106206 0.151678i 0.762531 0.646952i \(-0.223957\pi\)
−0.868737 + 0.495274i \(0.835068\pi\)
\(150\) −7.35144 + 1.14295i −0.600243 + 0.0933212i
\(151\) 21.1210i 1.71881i 0.511298 + 0.859403i \(0.329165\pi\)
−0.511298 + 0.859403i \(0.670835\pi\)
\(152\) −7.95218 9.42140i −0.645007 0.764176i
\(153\) 19.2372i 1.55524i
\(154\) 0.529934 + 3.40854i 0.0427033 + 0.274668i
\(155\) −2.26496 3.23470i −0.181926 0.259817i
\(156\) 6.77883 + 21.2738i 0.542740 + 1.70326i
\(157\) −0.825133 9.43131i −0.0658528 0.752701i −0.955295 0.295653i \(-0.904463\pi\)
0.889443 0.457047i \(-0.151093\pi\)
\(158\) −3.99894 + 3.83982i −0.318138 + 0.305480i
\(159\) 29.4317 16.9924i 2.33409 1.34759i
\(160\) 14.4591 1.05822i 1.14309 0.0836594i
\(161\) −1.39664 0.508336i −0.110071 0.0400625i
\(162\) −11.6133 47.1489i −0.912429 3.70437i
\(163\) 2.65791 + 9.91947i 0.208184 + 0.776953i 0.988455 + 0.151512i \(0.0484142\pi\)
−0.780272 + 0.625441i \(0.784919\pi\)
\(164\) 5.99084 0.807260i 0.467806 0.0630364i
\(165\) 14.2179 20.3053i 1.10686 1.58076i
\(166\) −1.33135 1.65367i −0.103333 0.128350i
\(167\) −11.7007 13.9443i −0.905424 1.07904i −0.996533 0.0832008i \(-0.973486\pi\)
0.0911093 0.995841i \(-0.470959\pi\)
\(168\) 5.52341 5.82280i 0.426140 0.449239i
\(169\) −0.657823 1.80735i −0.0506018 0.139027i
\(170\) 8.28981 + 1.63584i 0.635800 + 0.125463i
\(171\) 22.4668 + 28.0886i 1.71808 + 2.14799i
\(172\) 15.5851 6.51120i 1.18835 0.496474i
\(173\) −3.85065 + 8.25774i −0.292759 + 0.627824i −0.996587 0.0825461i \(-0.973695\pi\)
0.703828 + 0.710371i \(0.251473\pi\)
\(174\) 25.5138 11.2727i 1.93420 0.854582i
\(175\) 0.852775 + 1.01630i 0.0644637 + 0.0768249i
\(176\) −7.35980 + 8.88025i −0.554765 + 0.669374i
\(177\) −0.504732 2.86248i −0.0379380 0.215157i
\(178\) −2.21240 + 4.50356i −0.165826 + 0.337556i
\(179\) 9.19171 2.46291i 0.687021 0.184087i 0.101611 0.994824i \(-0.467600\pi\)
0.585410 + 0.810738i \(0.300934\pi\)
\(180\) −42.2502 + 1.97350i −3.14914 + 0.147096i
\(181\) −0.108959 0.233664i −0.00809889 0.0173681i 0.902217 0.431283i \(-0.141939\pi\)
−0.910316 + 0.413915i \(0.864161\pi\)
\(182\) 2.62066 2.99747i 0.194256 0.222188i
\(183\) −17.9729 + 10.3767i −1.32860 + 0.767065i
\(184\) −1.82225 4.62334i −0.134338 0.340837i
\(185\) −15.7634 13.2270i −1.15895 0.972472i
\(186\) −3.52536 6.40277i −0.258492 0.469474i
\(187\) −5.50642 + 3.85564i −0.402670 + 0.281952i
\(188\) −24.4935 0.994749i −1.78637 0.0725496i
\(189\) −10.5373 + 10.5373i −0.766475 + 0.766475i
\(190\) 14.0146 7.29300i 1.01672 0.529090i
\(191\) 20.6770i 1.49614i 0.663622 + 0.748068i \(0.269018\pi\)
−0.663622 + 0.748068i \(0.730982\pi\)
\(192\) 26.8189 + 0.925759i 1.93549 + 0.0668109i
\(193\) −0.0171284 0.00302020i −0.00123293 0.000217399i 0.173032 0.984916i \(-0.444644\pi\)
−0.174265 + 0.984699i \(0.555755\pi\)
\(194\) −3.87419 + 13.3674i −0.278151 + 0.959724i
\(195\) −28.5026 + 2.49366i −2.04112 + 0.178575i
\(196\) 12.2791 + 2.68304i 0.877079 + 0.191646i
\(197\) −7.77981 2.08459i −0.554289 0.148521i −0.0292076 0.999573i \(-0.509298\pi\)
−0.525081 + 0.851052i \(0.675965\pi\)
\(198\) 22.1476 25.3321i 1.57396 1.80027i
\(199\) −13.9433 5.07496i −0.988417 0.359754i −0.203310 0.979114i \(-0.565170\pi\)
−0.785107 + 0.619360i \(0.787392\pi\)
\(200\) −0.654784 + 4.38728i −0.0463002 + 0.310228i
\(201\) −45.1413 26.0624i −3.18402 1.83830i
\(202\) −2.15823 6.32629i −0.151852 0.445116i
\(203\) −4.07446 2.85297i −0.285971 0.200239i
\(204\) 14.9304 + 4.65764i 1.04534 + 0.326100i
\(205\) −0.675131 + 7.71678i −0.0471532 + 0.538963i
\(206\) −2.10497 4.76424i −0.146660 0.331940i
\(207\) 4.95865 + 13.6238i 0.344650 + 0.946918i
\(208\) 13.3124 0.0810115i 0.923049 0.00561714i
\(209\) −3.53710 + 12.0605i −0.244666 + 0.834245i
\(210\) 5.72678 + 8.54256i 0.395185 + 0.589493i
\(211\) 1.41491 + 0.659785i 0.0974067 + 0.0454215i 0.470711 0.882287i \(-0.343997\pi\)
−0.373304 + 0.927709i \(0.621775\pi\)
\(212\) −4.44591 19.7693i −0.305346 1.35776i
\(213\) 0.922233 10.5412i 0.0631904 0.722269i
\(214\) −8.50675 10.5662i −0.581509 0.722292i
\(215\) 3.75848 + 21.3154i 0.256326 + 1.45370i
\(216\) −49.7337 3.03183i −3.38395 0.206290i
\(217\) −0.651695 + 1.12877i −0.0442399 + 0.0766258i
\(218\) 16.6097 + 10.0445i 1.12495 + 0.680296i
\(219\) −31.2711 + 14.5819i −2.11310 + 0.985356i
\(220\) −9.03292 11.6981i −0.609000 0.788683i
\(221\) 7.49455 + 2.00816i 0.504138 + 0.135083i
\(222\) −26.3804 27.4736i −1.77054 1.84391i
\(223\) −10.2635 8.61213i −0.687298 0.576711i 0.230831 0.972994i \(-0.425856\pi\)
−0.918129 + 0.396283i \(0.870300\pi\)
\(224\) −2.33351 4.17775i −0.155914 0.279138i
\(225\) 2.24724 12.7447i 0.149816 0.849649i
\(226\) 0.362339 0.495748i 0.0241025 0.0329767i
\(227\) 10.2347 + 10.2347i 0.679304 + 0.679304i 0.959843 0.280539i \(-0.0905131\pi\)
−0.280539 + 0.959843i \(0.590513\pi\)
\(228\) 27.2397 10.6362i 1.80399 0.704402i
\(229\) 14.1318 14.1318i 0.933857 0.933857i −0.0640876 0.997944i \(-0.520414\pi\)
0.997944 + 0.0640876i \(0.0204137\pi\)
\(230\) 6.29249 0.978309i 0.414915 0.0645078i
\(231\) −8.05751 1.42076i −0.530145 0.0934789i
\(232\) −1.88600 16.5237i −0.123822 1.08483i
\(233\) 7.19360 8.57300i 0.471269 0.561636i −0.477082 0.878859i \(-0.658306\pi\)
0.948351 + 0.317222i \(0.102750\pi\)
\(234\) −38.8306 0.788187i −2.53844 0.0515254i
\(235\) 8.13020 30.3423i 0.530356 1.97931i
\(236\) −1.71891 0.220980i −0.111891 0.0143845i
\(237\) −5.55731 11.9177i −0.360986 0.774137i
\(238\) −0.667021 2.70804i −0.0432366 0.175536i
\(239\) −7.49317 4.32618i −0.484693 0.279837i 0.237677 0.971344i \(-0.423614\pi\)
−0.722370 + 0.691507i \(0.756947\pi\)
\(240\) −8.69777 + 33.2690i −0.561438 + 2.14751i
\(241\) 22.0438 3.88692i 1.41997 0.250378i 0.589644 0.807663i \(-0.299268\pi\)
0.830321 + 0.557285i \(0.188157\pi\)
\(242\) −3.77649 0.407780i −0.242762 0.0262131i
\(243\) 62.0888 + 5.43207i 3.98300 + 0.348467i
\(244\) 2.71496 + 12.0724i 0.173807 + 0.772858i
\(245\) −6.80675 + 14.5971i −0.434867 + 0.932576i
\(246\) −2.77581 + 14.0668i −0.176979 + 0.896864i
\(247\) 13.2882 5.82060i 0.845510 0.370356i
\(248\) −4.27034 + 0.869702i −0.271167 + 0.0552261i
\(249\) 4.73184 1.72225i 0.299868 0.109143i
\(250\) 11.5991 + 4.49035i 0.733593 + 0.283994i
\(251\) 0.939829 + 0.0822244i 0.0593215 + 0.00518996i 0.116778 0.993158i \(-0.462743\pi\)
−0.0574563 + 0.998348i \(0.518299\pi\)
\(252\) 6.48398 + 12.3636i 0.408452 + 0.778835i
\(253\) −2.90580 + 4.14991i −0.182686 + 0.260903i
\(254\) −5.06747 + 10.3154i −0.317962 + 0.647243i
\(255\) −10.0208 + 17.3566i −0.627530 + 1.08691i
\(256\) 5.28893 15.1006i 0.330558 0.943786i
\(257\) 0.368203 1.01163i 0.0229679 0.0631037i −0.927679 0.373379i \(-0.878199\pi\)
0.950647 + 0.310275i \(0.100421\pi\)
\(258\) 2.68103 + 39.9728i 0.166914 + 2.48860i
\(259\) −1.75791 + 6.56061i −0.109231 + 0.407657i
\(260\) −3.64162 + 16.6661i −0.225844 + 1.03359i
\(261\) 4.22877 + 48.3350i 0.261754 + 2.99186i
\(262\) 18.4361 10.1509i 1.13898 0.627124i
\(263\) 2.06382 11.7045i 0.127261 0.721731i −0.852679 0.522436i \(-0.825024\pi\)
0.979939 0.199295i \(-0.0638653\pi\)
\(264\) −14.2985 23.3225i −0.880009 1.43540i
\(265\) 25.9659 1.59507
\(266\) −4.13660 3.17506i −0.253631 0.194675i
\(267\) −8.41548 8.41548i −0.515019 0.515019i
\(268\) −22.8497 + 21.0661i −1.39577 + 1.28682i
\(269\) 7.77335 + 11.1015i 0.473949 + 0.676870i 0.982945 0.183899i \(-0.0588720\pi\)
−0.508996 + 0.860769i \(0.669983\pi\)
\(270\) 17.7735 61.3253i 1.08166 3.73214i
\(271\) −0.933121 + 1.11205i −0.0566831 + 0.0675522i −0.793641 0.608386i \(-0.791817\pi\)
0.736958 + 0.675939i \(0.236262\pi\)
\(272\) 5.30213 7.67116i 0.321489 0.465132i
\(273\) 4.72189 + 8.17856i 0.285782 + 0.494989i
\(274\) 1.87229 + 27.9149i 0.113109 + 1.68640i
\(275\) 4.09843 1.91113i 0.247145 0.115245i
\(276\) 11.7742 0.549973i 0.708727 0.0331045i
\(277\) −4.48317 16.7314i −0.269368 1.00529i −0.959522 0.281632i \(-0.909124\pi\)
0.690155 0.723662i \(-0.257542\pi\)
\(278\) 8.71069 2.97167i 0.522432 0.178229i
\(279\) 12.5210 2.20779i 0.749611 0.132177i
\(280\) 5.87917 1.74277i 0.351347 0.104151i
\(281\) 4.39806 3.69041i 0.262366 0.220151i −0.502109 0.864804i \(-0.667443\pi\)
0.764475 + 0.644653i \(0.222998\pi\)
\(282\) 20.9910 54.2224i 1.25000 3.22889i
\(283\) 16.1317 + 7.52234i 0.958930 + 0.447157i 0.838100 0.545517i \(-0.183667\pi\)
0.120830 + 0.992673i \(0.461444\pi\)
\(284\) −5.83614 2.39663i −0.346311 0.142214i
\(285\) 5.63886 + 37.0459i 0.334017 + 2.19441i
\(286\) −7.55706 11.2728i −0.446858 0.666573i
\(287\) 2.40261 0.874478i 0.141822 0.0516188i
\(288\) −16.5868 + 43.6324i −0.977384 + 2.57107i
\(289\) −8.85934 + 7.43387i −0.521138 + 0.437287i
\(290\) 21.1884 + 2.28789i 1.24423 + 0.134350i
\(291\) −27.0409 18.9342i −1.58516 1.10994i
\(292\) 2.74730 + 20.3882i 0.160774 + 1.19313i
\(293\) −5.81683 + 1.55861i −0.339823 + 0.0910552i −0.424695 0.905337i \(-0.639619\pi\)
0.0848720 + 0.996392i \(0.472952\pi\)
\(294\) −15.4268 + 25.5100i −0.899709 + 1.48777i
\(295\) 0.759557 2.08686i 0.0442231 0.121502i
\(296\) −20.3217 + 10.1371i −1.18118 + 0.589209i
\(297\) 25.3974 + 43.9895i 1.47371 + 2.55253i
\(298\) 0.0648681 3.19578i 0.00375771 0.185126i
\(299\) 5.82526 0.509644i 0.336884 0.0294735i
\(300\) −9.34734 4.82983i −0.539669 0.278850i
\(301\) 5.85210 4.09768i 0.337309 0.236186i
\(302\) −17.6256 + 24.1151i −1.01424 + 1.38767i
\(303\) 15.8544 0.910813
\(304\) −1.21727 17.3931i −0.0698154 0.997560i
\(305\) −15.8564 −0.907937
\(306\) −16.0535 + 21.9642i −0.917718 + 1.25561i
\(307\) −11.9267 + 8.35115i −0.680692 + 0.476625i −0.862071 0.506788i \(-0.830833\pi\)
0.181379 + 0.983413i \(0.441944\pi\)
\(308\) −2.23938 + 4.33395i −0.127600 + 0.246950i
\(309\) 12.3071 1.07673i 0.700125 0.0612530i
\(310\) 0.113331 5.58335i 0.00643678 0.317113i
\(311\) 7.67846 + 13.2995i 0.435406 + 0.754145i 0.997329 0.0730449i \(-0.0232716\pi\)
−0.561923 + 0.827190i \(0.689938\pi\)
\(312\) −10.0132 + 29.9464i −0.566888 + 1.69538i
\(313\) −0.656122 + 1.80268i −0.0370862 + 0.101893i −0.956854 0.290570i \(-0.906155\pi\)
0.919767 + 0.392464i \(0.128377\pi\)
\(314\) 6.92835 11.4568i 0.390989 0.646546i
\(315\) −17.2802 + 4.63021i −0.973627 + 0.260883i
\(316\) −7.77015 + 1.04702i −0.437105 + 0.0588995i
\(317\) 9.57345 + 6.70340i 0.537699 + 0.376501i 0.810653 0.585526i \(-0.199112\pi\)
−0.272955 + 0.962027i \(0.588001\pi\)
\(318\) 47.7840 + 5.15965i 2.67960 + 0.289339i
\(319\) −12.9878 + 10.8980i −0.727176 + 0.610173i
\(320\) 17.3919 + 10.8579i 0.972236 + 0.606978i
\(321\) 30.2344 11.0044i 1.68752 0.614206i
\(322\) −1.17042 1.74590i −0.0652248 0.0972950i
\(323\) 1.99906 9.96332i 0.111231 0.554374i
\(324\) 26.0863 63.5239i 1.44924 3.52911i
\(325\) −4.73058 2.20591i −0.262405 0.122362i
\(326\) −5.24313 + 13.5436i −0.290390 + 0.750113i
\(327\) −35.2686 + 29.5939i −1.95036 + 1.63654i
\(328\) 7.51373 + 4.07767i 0.414876 + 0.225152i
\(329\) −10.2108 + 1.80045i −0.562942 + 0.0992619i
\(330\) 33.1782 11.3188i 1.82640 0.623079i
\(331\) −1.55003 5.78477i −0.0851971 0.317960i 0.910154 0.414269i \(-0.135963\pi\)
−0.995351 + 0.0963094i \(0.969296\pi\)
\(332\) −0.140088 2.99911i −0.00768831 0.164597i
\(333\) 60.0466 28.0002i 3.29053 1.53440i
\(334\) −1.72274 25.6852i −0.0942644 1.40543i
\(335\) −19.9127 34.4899i −1.08795 1.88438i
\(336\) 11.1655 2.03892i 0.609129 0.111232i
\(337\) −1.28721 + 1.53403i −0.0701186 + 0.0835640i −0.799963 0.600049i \(-0.795148\pi\)
0.729845 + 0.683613i \(0.239592\pi\)
\(338\) 0.757168 2.61251i 0.0411845 0.142102i
\(339\) 0.835389 + 1.19306i 0.0453721 + 0.0647981i
\(340\) 8.09983 + 8.78559i 0.439275 + 0.476466i
\(341\) 3.14148 + 3.14148i 0.170121 + 0.170121i
\(342\) 2.21159 + 50.8189i 0.119589 + 2.74797i
\(343\) 11.2376 0.606775
\(344\) 23.2280 + 5.57162i 1.25237 + 0.300402i
\(345\) −2.62285 + 14.8749i −0.141210 + 0.800840i
\(346\) −11.2876 + 6.21495i −0.606825 + 0.334118i
\(347\) 0.860438 + 9.83485i 0.0461907 + 0.527962i 0.983677 + 0.179941i \(0.0575907\pi\)
−0.937487 + 0.348021i \(0.886854\pi\)
\(348\) 38.5376 + 8.42065i 2.06583 + 0.451394i
\(349\) −7.10989 + 26.5345i −0.380584 + 1.42036i 0.464429 + 0.885611i \(0.346260\pi\)
−0.845012 + 0.534747i \(0.820407\pi\)
\(350\) 0.125558 + 1.87201i 0.00671137 + 0.100063i
\(351\) 20.0524 55.0936i 1.07032 2.94068i
\(352\) −15.8137 + 3.99732i −0.842872 + 0.213058i
\(353\) −3.02078 + 5.23215i −0.160780 + 0.278479i −0.935149 0.354255i \(-0.884734\pi\)
0.774369 + 0.632735i \(0.218068\pi\)
\(354\) 1.81246 3.68945i 0.0963314 0.196092i
\(355\) 4.63718 6.62257i 0.246116 0.351490i
\(356\) −6.28424 + 3.29571i −0.333064 + 0.174672i
\(357\) 6.58998 + 0.576548i 0.348779 + 0.0305142i
\(358\) 12.5500 + 4.85846i 0.663288 + 0.256777i
\(359\) 7.44267 2.70891i 0.392809 0.142971i −0.138062 0.990424i \(-0.544087\pi\)
0.530871 + 0.847453i \(0.321865\pi\)
\(360\) −49.8863 33.0046i −2.62924 1.73950i
\(361\) −8.71712 16.8823i −0.458796 0.888542i
\(362\) 0.0705883 0.357714i 0.00371004 0.0188011i
\(363\) 3.80758 8.16538i 0.199846 0.428571i
\(364\) 5.49355 1.23544i 0.287940 0.0647546i
\(365\) −26.2621 2.29763i −1.37462 0.120264i
\(366\) −29.1800 3.15082i −1.52526 0.164696i
\(367\) 1.80211 0.317761i 0.0940696 0.0165870i −0.126415 0.991977i \(-0.540347\pi\)
0.220485 + 0.975390i \(0.429236\pi\)
\(368\) 1.77762 6.79940i 0.0926647 0.354443i
\(369\) −21.5993 12.4704i −1.12442 0.649182i
\(370\) −6.95993 28.2566i −0.361830 1.46899i
\(371\) −3.62206 7.76754i −0.188048 0.403271i
\(372\) 1.31802 10.2523i 0.0683362 0.531558i
\(373\) 4.90620 18.3102i 0.254034 0.948066i −0.714592 0.699541i \(-0.753388\pi\)
0.968626 0.248525i \(-0.0799457\pi\)
\(374\) −9.50453 0.192924i −0.491468 0.00997584i
\(375\) −18.9632 + 22.5994i −0.979254 + 1.16703i
\(376\) −27.1354 21.5756i −1.39940 1.11268i
\(377\) 19.2721 + 3.39819i 0.992564 + 0.175016i
\(378\) −20.8244 + 3.23762i −1.07109 + 0.166525i
\(379\) 16.6441 16.6441i 0.854951 0.854951i −0.135787 0.990738i \(-0.543356\pi\)
0.990738 + 0.135787i \(0.0433562\pi\)
\(380\) 22.0872 + 3.36836i 1.13305 + 0.172793i
\(381\) −19.2756 19.2756i −0.987518 0.987518i
\(382\) −17.2550 + 23.6081i −0.882843 + 1.20790i
\(383\) 1.11071 6.29916i 0.0567547 0.321872i −0.943191 0.332250i \(-0.892192\pi\)
0.999946 + 0.0103778i \(0.00330343\pi\)
\(384\) 29.8481 + 23.4374i 1.52318 + 1.19604i
\(385\) −4.78874 4.01823i −0.244057 0.204788i
\(386\) −0.0170361 0.0177420i −0.000867114 0.000903045i
\(387\) −67.3136 18.0366i −3.42174 0.916854i
\(388\) −15.5785 + 12.0293i −0.790879 + 0.610695i
\(389\) −20.2394 + 9.43779i −1.02618 + 0.478515i −0.861460 0.507826i \(-0.830449\pi\)
−0.164719 + 0.986341i \(0.552672\pi\)
\(390\) −34.6240 20.9384i −1.75326 1.06026i
\(391\) 2.04802 3.54728i 0.103573 0.179394i
\(392\) 11.7807 + 13.3103i 0.595017 + 0.672273i
\(393\) 8.66826 + 49.1601i 0.437256 + 2.47980i
\(394\) −7.14305 8.87237i −0.359862 0.446983i
\(395\) 0.875649 10.0087i 0.0440587 0.503593i
\(396\) 46.4268 10.4409i 2.33303 0.524674i
\(397\) −15.3277 7.14744i −0.769277 0.358720i −0.00196872 0.999998i \(-0.500627\pi\)
−0.767308 + 0.641278i \(0.778404\pi\)
\(398\) −11.6848 17.4301i −0.585707 0.873692i
\(399\) 10.2955 6.85449i 0.515419 0.343154i
\(400\) −4.40880 + 4.46279i −0.220440 + 0.223139i
\(401\) 1.98305 + 5.44838i 0.0990288 + 0.272079i 0.979308 0.202377i \(-0.0648668\pi\)
−0.880279 + 0.474457i \(0.842645\pi\)
\(402\) −29.7913 67.4274i −1.48585 3.36297i
\(403\) 0.446933 5.10847i 0.0222633 0.254471i
\(404\) 2.81514 9.02412i 0.140058 0.448967i
\(405\) 72.0839 + 50.4737i 3.58188 + 2.50806i
\(406\) −2.27123 6.65754i −0.112719 0.330408i
\(407\) 20.0496 + 11.5757i 0.993823 + 0.573784i
\(408\) 13.1601 + 17.7773i 0.651520 + 0.880109i
\(409\) 12.7538 + 4.64202i 0.630637 + 0.229533i 0.637509 0.770443i \(-0.279965\pi\)
−0.00687149 + 0.999976i \(0.502187\pi\)
\(410\) −7.21051 + 8.24728i −0.356102 + 0.407304i
\(411\) −64.0987 17.1752i −3.16176 0.847190i
\(412\) 1.57240 7.19620i 0.0774667 0.354531i
\(413\) −0.730227 + 0.0638866i −0.0359321 + 0.00314365i
\(414\) −5.70750 + 19.6930i −0.280508 + 0.967859i
\(415\) 3.78890 + 0.668086i 0.185990 + 0.0327950i
\(416\) 15.2671 + 11.0167i 0.748532 + 0.540139i
\(417\) 21.8300i 1.06902i
\(418\) −14.1031 + 10.8185i −0.689803 + 0.529149i
\(419\) −21.7483 + 21.7483i −1.06248 + 1.06248i −0.0645618 + 0.997914i \(0.520565\pi\)
−0.997914 + 0.0645618i \(0.979435\pi\)
\(420\) −0.590208 + 14.5325i −0.0287992 + 0.709115i
\(421\) −21.6363 + 15.1499i −1.05449 + 0.738362i −0.966216 0.257734i \(-0.917024\pi\)
−0.0882744 + 0.996096i \(0.528135\pi\)
\(422\) 1.06489 + 1.93406i 0.0518382 + 0.0941487i
\(423\) 77.4777 + 65.0115i 3.76709 + 3.16097i
\(424\) 11.4214 26.2819i 0.554673 1.27636i
\(425\) −3.16638 + 1.82811i −0.153592 + 0.0886763i
\(426\) 9.84960 11.2658i 0.477215 0.545832i
\(427\) 2.21187 + 4.74336i 0.107040 + 0.229547i
\(428\) −0.895098 19.1629i −0.0432662 0.926276i
\(429\) 31.0932 8.33139i 1.50119 0.402243i
\(430\) −13.4965 + 27.4734i −0.650858 + 1.32489i
\(431\) −2.66352 15.1055i −0.128297 0.727609i −0.979295 0.202439i \(-0.935113\pi\)
0.850998 0.525169i \(-0.175998\pi\)
\(432\) −54.2537 44.9645i −2.61028 2.16336i
\(433\) −2.65118 3.15956i −0.127408 0.151839i 0.698569 0.715542i \(-0.253820\pi\)
−0.825977 + 0.563704i \(0.809376\pi\)
\(434\) −1.68604 + 0.744938i −0.0809324 + 0.0357581i
\(435\) −21.3628 + 45.8127i −1.02427 + 2.19655i
\(436\) 10.5821 + 25.3291i 0.506789 + 1.21305i
\(437\) −1.15245 7.57129i −0.0551291 0.362184i
\(438\) −47.8726 9.44676i −2.28744 0.451383i
\(439\) −8.68926 23.8735i −0.414716 1.13942i −0.954654 0.297718i \(-0.903775\pi\)
0.539938 0.841705i \(-0.318448\pi\)
\(440\) −0.551333 20.8943i −0.0262838 0.996098i
\(441\) −33.3332 39.7249i −1.58729 1.89166i
\(442\) 6.88114 + 8.54705i 0.327302 + 0.406542i
\(443\) −4.62526 + 6.60555i −0.219753 + 0.313839i −0.913858 0.406034i \(-0.866911\pi\)
0.694105 + 0.719874i \(0.255800\pi\)
\(444\) −7.19327 53.3827i −0.341377 2.53343i
\(445\) −2.35347 8.78325i −0.111565 0.416366i
\(446\) −4.53161 18.3979i −0.214578 0.871166i
\(447\) 7.12437 + 2.59306i 0.336971 + 0.122647i
\(448\) 0.822044 6.71730i 0.0388379 0.317362i
\(449\) 9.71979 5.61172i 0.458705 0.264834i −0.252794 0.967520i \(-0.581350\pi\)
0.711500 + 0.702686i \(0.248016\pi\)
\(450\) 13.2013 12.6760i 0.622315 0.597554i
\(451\) −0.759571 8.68194i −0.0357668 0.408816i
\(452\) 0.827406 0.263651i 0.0389179 0.0124011i
\(453\) −40.6365 58.0349i −1.90927 2.72672i
\(454\) 3.14466 + 20.2265i 0.147586 + 0.949277i
\(455\) 7.21546i 0.338266i
\(456\) 39.9770 + 10.5876i 1.87210 + 0.495810i
\(457\) 16.8264i 0.787105i −0.919302 0.393553i \(-0.871246\pi\)
0.919302 0.393553i \(-0.128754\pi\)
\(458\) 27.9281 4.34205i 1.30500 0.202891i
\(459\) −23.5559 33.6414i −1.09950 1.57024i
\(460\) 8.00089 + 4.13411i 0.373043 + 0.192754i
\(461\) 0.367996 + 4.20622i 0.0171393 + 0.195903i 0.999937 + 0.0112181i \(0.00357091\pi\)
−0.982798 + 0.184685i \(0.940874\pi\)
\(462\) −8.01408 8.34617i −0.372849 0.388299i
\(463\) −15.4385 + 8.91340i −0.717486 + 0.414241i −0.813827 0.581108i \(-0.802620\pi\)
0.0963406 + 0.995348i \(0.469286\pi\)
\(464\) 11.6357 20.4399i 0.540175 0.948899i
\(465\) 12.4470 + 4.53034i 0.577216 + 0.210089i
\(466\) 15.3675 3.78520i 0.711887 0.175346i
\(467\) −8.27329 30.8763i −0.382842 1.42879i −0.841540 0.540195i \(-0.818351\pi\)
0.458698 0.888592i \(-0.348316\pi\)
\(468\) −43.6774 33.3042i −2.01899 1.53949i
\(469\) −7.53976 + 10.7679i −0.348154 + 0.497215i
\(470\) 34.6034 27.8589i 1.59614 1.28503i
\(471\) 20.4129 + 24.3272i 0.940577 + 1.12094i
\(472\) −1.77816 1.68673i −0.0818465 0.0776382i
\(473\) −8.32863 22.8827i −0.382951 1.05215i
\(474\) 3.60025 18.2447i 0.165365 0.838006i
\(475\) −2.48827 + 6.36721i −0.114170 + 0.292148i
\(476\) 1.49829 3.64855i 0.0686740 0.167231i
\(477\) −35.3320 + 75.7697i −1.61774 + 3.46926i
\(478\) −4.94516 11.1925i −0.226186 0.511933i
\(479\) 4.97020 + 5.92325i 0.227094 + 0.270640i 0.867545 0.497359i \(-0.165697\pi\)
−0.640451 + 0.767999i \(0.721252\pi\)
\(480\) −37.6938 + 30.7268i −1.72048 + 1.40248i
\(481\) −4.64026 26.3162i −0.211578 1.19992i
\(482\) 28.4123 + 13.9577i 1.29414 + 0.635755i
\(483\) 4.81563 1.29034i 0.219119 0.0587126i
\(484\) −3.97154 3.61708i −0.180525 0.164413i
\(485\) −10.6591 22.8586i −0.484006 1.03795i
\(486\) 66.3572 + 58.0154i 3.01002 + 2.63163i
\(487\) 13.2939 7.67523i 0.602403 0.347798i −0.167583 0.985858i \(-0.553596\pi\)
0.769986 + 0.638060i \(0.220263\pi\)
\(488\) −6.97465 + 16.0494i −0.315728 + 0.726523i
\(489\) −26.3881 22.1422i −1.19331 1.00131i
\(490\) −19.9530 + 10.9861i −0.901384 + 0.496302i
\(491\) 13.5892 9.51529i 0.613274 0.429419i −0.225237 0.974304i \(-0.572316\pi\)
0.838511 + 0.544885i \(0.183427\pi\)
\(492\) −14.9080 + 13.7444i −0.672107 + 0.619645i
\(493\) 9.69295 9.69295i 0.436549 0.436549i
\(494\) 20.0292 + 4.44335i 0.901157 + 0.199916i
\(495\) 60.9789i 2.74080i
\(496\) −5.60145 2.57062i −0.251512 0.115424i
\(497\) −2.62796 0.463381i −0.117880 0.0207855i
\(498\) 6.83983 + 1.98234i 0.306500 + 0.0888310i
\(499\) −7.24137 + 0.633538i −0.324168 + 0.0283611i −0.248079 0.968740i \(-0.579799\pi\)
−0.0760898 + 0.997101i \(0.524244\pi\)
\(500\) 9.49615 + 14.8064i 0.424681 + 0.662161i
\(501\) 58.9788 + 15.8033i 2.63498 + 0.706040i
\(502\) 1.00444 + 0.878170i 0.0448303 + 0.0391946i
\(503\) 1.17090 + 0.426172i 0.0522078 + 0.0190021i 0.367992 0.929829i \(-0.380045\pi\)
−0.315784 + 0.948831i \(0.602268\pi\)
\(504\) −2.91434 + 19.5271i −0.129815 + 0.869807i
\(505\) 10.4906 + 6.05673i 0.466824 + 0.269521i
\(506\) −6.78082 + 2.31329i −0.301444 + 0.102838i
\(507\) 5.28484 + 3.70048i 0.234708 + 0.164344i
\(508\) −14.3940 + 7.54879i −0.638630 + 0.334924i
\(509\) 2.33653 26.7067i 0.103565 1.18375i −0.749520 0.661982i \(-0.769716\pi\)
0.853085 0.521772i \(-0.174729\pi\)
\(510\) −25.9255 + 11.4546i −1.14800 + 0.507218i
\(511\) 2.97606 + 8.17665i 0.131653 + 0.361714i
\(512\) 18.6401 12.8275i 0.823785 0.566902i
\(513\) −73.6836 21.6098i −3.25321 0.954097i
\(514\) 1.26460 0.847767i 0.0557793 0.0373934i
\(515\) 8.55468 + 3.98911i 0.376964 + 0.175781i
\(516\) −30.2963 + 47.8765i −1.33372 + 2.10765i
\(517\) −3.08022 + 35.2070i −0.135468 + 1.54840i
\(518\) −7.48195 + 6.02364i −0.328738 + 0.264663i
\(519\) −5.30720 30.0986i −0.232960 1.32118i
\(520\) −18.0657 + 15.9897i −0.792234 + 0.701193i
\(521\) −22.4023 + 38.8018i −0.981460 + 1.69994i −0.324744 + 0.945802i \(0.605278\pi\)
−0.656717 + 0.754137i \(0.728055\pi\)
\(522\) −35.5075 + 58.7157i −1.55412 + 2.56992i
\(523\) 11.9812 5.58692i 0.523901 0.244299i −0.142630 0.989776i \(-0.545556\pi\)
0.666531 + 0.745477i \(0.267778\pi\)
\(524\) 29.5204 + 3.79509i 1.28961 + 0.165789i
\(525\) −4.29853 1.15179i −0.187603 0.0502682i
\(526\) 12.1238 11.6414i 0.528624 0.507590i
\(527\) −2.75165 2.30891i −0.119864 0.100578i
\(528\) 3.13729 38.5606i 0.136533 1.67814i
\(529\) −3.45786 + 19.6105i −0.150342 + 0.852630i
\(530\) 29.6467 + 21.6686i 1.28777 + 0.941222i
\(531\) 5.05605 + 5.05605i 0.219414 + 0.219414i
\(532\) −2.07340 7.07714i −0.0898932 0.306833i
\(533\) −7.11302 + 7.11302i −0.308099 + 0.308099i
\(534\) −2.58569 16.6312i −0.111894 0.719701i
\(535\) 24.2094 + 4.26877i 1.04666 + 0.184555i
\(536\) −43.6685 + 4.98428i −1.88619 + 0.215288i
\(537\) −20.5177 + 24.4521i −0.885406 + 1.05519i
\(538\) −0.388953 + 19.1621i −0.0167689 + 0.826135i
\(539\) 4.68995 17.5031i 0.202010 0.753913i
\(540\) 71.4691 55.1864i 3.07554 2.37485i
\(541\) 18.4992 + 39.6717i 0.795344 + 1.70562i 0.704443 + 0.709760i \(0.251197\pi\)
0.0909004 + 0.995860i \(0.471026\pi\)
\(542\) −1.99340 + 0.490998i −0.0856241 + 0.0210902i
\(543\) 0.748957 + 0.432410i 0.0321408 + 0.0185565i
\(544\) 12.4553 4.33395i 0.534018 0.185817i
\(545\) −34.6420 + 6.10832i −1.48390 + 0.261652i
\(546\) −1.43378 + 13.2783i −0.0613599 + 0.568261i
\(547\) −11.5663 1.01192i −0.494540 0.0432666i −0.162842 0.986652i \(-0.552066\pi\)
−0.331698 + 0.943386i \(0.607622\pi\)
\(548\) −21.1573 + 33.4344i −0.903797 + 1.42825i
\(549\) 21.5760 46.2699i 0.920842 1.97475i
\(550\) 6.27425 + 1.23811i 0.267535 + 0.0527930i
\(551\) 2.83263 25.4731i 0.120674 1.08519i
\(552\) 13.9023 + 9.19770i 0.591720 + 0.391480i
\(553\) −3.11620 + 1.13420i −0.132514 + 0.0482312i
\(554\) 8.84372 22.8444i 0.375734 0.970566i
\(555\) 68.7621 + 6.01590i 2.91879 + 0.255361i
\(556\) 12.4253 + 3.87617i 0.526952 + 0.164386i
\(557\) 15.3168 21.8747i 0.648994 0.926860i −0.350960 0.936390i \(-0.614145\pi\)
0.999955 + 0.00953034i \(0.00303365\pi\)
\(558\) 16.1383 + 7.92803i 0.683189 + 0.335620i
\(559\) −14.0536 + 24.3416i −0.594406 + 1.02954i
\(560\) 8.16692 + 2.91636i 0.345115 + 0.123239i
\(561\) 7.71199 21.1885i 0.325600 0.894580i
\(562\) 8.10116 0.543357i 0.341727 0.0229201i
\(563\) −2.16281 + 8.07171i −0.0911515 + 0.340182i −0.996408 0.0846836i \(-0.973012\pi\)
0.905256 + 0.424866i \(0.139679\pi\)
\(564\) 69.2153 44.3916i 2.91449 1.86923i
\(565\) 0.0969865 + 1.10856i 0.00408025 + 0.0466375i
\(566\) 12.1411 + 22.0506i 0.510327 + 0.926856i
\(567\) 5.04370 28.6043i 0.211816 1.20127i
\(568\) −4.66345 7.60663i −0.195674 0.319167i
\(569\) −18.9211 −0.793215 −0.396608 0.917988i \(-0.629813\pi\)
−0.396608 + 0.917988i \(0.629813\pi\)
\(570\) −24.4767 + 47.0030i −1.02521 + 1.96874i
\(571\) −7.43419 7.43419i −0.311111 0.311111i 0.534229 0.845340i \(-0.320602\pi\)
−0.845340 + 0.534229i \(0.820602\pi\)
\(572\) 0.778839 19.1771i 0.0325649 0.801837i
\(573\) −39.7822 56.8148i −1.66192 2.37347i
\(574\) 3.47295 + 1.00654i 0.144958 + 0.0420122i
\(575\) −1.77121 + 2.11084i −0.0738644 + 0.0880281i
\(576\) −55.3494 + 35.9759i −2.30622 + 1.49900i
\(577\) −19.7269 34.1681i −0.821244 1.42244i −0.904757 0.425929i \(-0.859947\pi\)
0.0835132 0.996507i \(-0.473386\pi\)
\(578\) −16.3188 + 1.09453i −0.678772 + 0.0455263i
\(579\) 0.0528750 0.0246560i 0.00219741 0.00102467i
\(580\) 22.2827 + 20.2940i 0.925240 + 0.842662i
\(581\) −0.328673 1.22662i −0.0136356 0.0508889i
\(582\) −15.0734 44.1839i −0.624813 1.83148i
\(583\) −28.7696 + 5.07286i −1.19152 + 0.210097i
\(584\) −13.8773 + 25.5710i −0.574246 + 1.05814i
\(585\) 53.9175 45.2422i 2.22922 1.87053i
\(586\) −7.94206 3.07460i −0.328084 0.127010i
\(587\) −12.0162 5.60326i −0.495963 0.231271i 0.158509 0.987358i \(-0.449331\pi\)
−0.654472 + 0.756086i \(0.727109\pi\)
\(588\) −38.9018 + 16.2525i −1.60428 + 0.670242i
\(589\) −6.71427 0.157677i −0.276657 0.00649697i
\(590\) 2.60872 1.74884i 0.107399 0.0719985i
\(591\) 25.3875 9.24031i 1.04430 0.380096i
\(592\) −31.6619 5.38440i −1.30130 0.221297i
\(593\) 12.4368 10.4357i 0.510718 0.428544i −0.350663 0.936502i \(-0.614044\pi\)
0.861382 + 0.507958i \(0.169599\pi\)
\(594\) −7.71177 + 71.4195i −0.316418 + 2.93038i
\(595\) 4.14020 + 2.89900i 0.169732 + 0.118848i
\(596\) 2.74095 3.59467i 0.112274 0.147243i
\(597\) 48.0767 12.8821i 1.96765 0.527229i
\(598\) 7.07633 + 4.27930i 0.289372 + 0.174994i
\(599\) 2.19721 6.03678i 0.0897755 0.246656i −0.886677 0.462390i \(-0.846992\pi\)
0.976452 + 0.215734i \(0.0692143\pi\)
\(600\) −6.64188 13.3149i −0.271154 0.543577i
\(601\) −4.87754 8.44815i −0.198959 0.344607i 0.749232 0.662308i \(-0.230423\pi\)
−0.948191 + 0.317700i \(0.897089\pi\)
\(602\) 10.1012 + 0.205035i 0.411694 + 0.00835659i
\(603\) 127.739 11.1757i 5.20193 0.455110i
\(604\) −40.2482 + 12.8250i −1.63767 + 0.521840i
\(605\) 5.63875 3.94829i 0.229248 0.160521i
\(606\) 18.1019 + 13.2306i 0.735339 + 0.537455i
\(607\) 1.45340 0.0589916 0.0294958 0.999565i \(-0.490610\pi\)
0.0294958 + 0.999565i \(0.490610\pi\)
\(608\) 13.1247 20.8744i 0.532277 0.846570i
\(609\) 16.6846 0.676093
\(610\) −18.1042 13.2322i −0.733017 0.535757i
\(611\) 33.4154 23.3977i 1.35184 0.946570i
\(612\) −36.6584 + 11.6811i −1.48183 + 0.472180i
\(613\) 37.0237 3.23915i 1.49537 0.130828i 0.690092 0.723722i \(-0.257570\pi\)
0.805281 + 0.592894i \(0.202015\pi\)
\(614\) −20.5864 0.417864i −0.830800 0.0168636i
\(615\) −12.9919 22.5026i −0.523883 0.907391i
\(616\) −6.17352 + 3.07955i −0.248738 + 0.124079i
\(617\) 6.06492 16.6632i 0.244164 0.670836i −0.755709 0.654908i \(-0.772707\pi\)
0.999873 0.0159284i \(-0.00507037\pi\)
\(618\) 14.9502 + 9.04091i 0.601385 + 0.363679i
\(619\) −23.6658 + 6.34123i −0.951209 + 0.254876i −0.700875 0.713284i \(-0.747207\pi\)
−0.250334 + 0.968160i \(0.580540\pi\)
\(620\) 4.78871 6.28025i 0.192319 0.252221i
\(621\) −25.3538 17.7529i −1.01741 0.712400i
\(622\) −2.33152 + 21.5925i −0.0934855 + 0.865779i
\(623\) −2.29917 + 1.92923i −0.0921143 + 0.0772930i
\(624\) −36.4230 + 25.8354i −1.45809 + 1.03424i
\(625\) −28.5497 + 10.3912i −1.14199 + 0.415650i
\(626\) −2.25347 + 1.51068i −0.0900668 + 0.0603791i
\(627\) −13.4853 39.9444i −0.538550 1.59523i
\(628\) 17.4712 7.29918i 0.697178 0.291269i
\(629\) −16.9645 7.91069i −0.676420 0.315420i
\(630\) −23.5937 9.13377i −0.939994 0.363898i
\(631\) −11.7341 + 9.84607i −0.467127 + 0.391966i −0.845745 0.533587i \(-0.820844\pi\)
0.378619 + 0.925553i \(0.376399\pi\)
\(632\) −9.74535 5.28876i −0.387649 0.210376i
\(633\) −5.15722 + 0.909357i −0.204981 + 0.0361437i
\(634\) 5.33654 + 15.6427i 0.211941 + 0.621252i
\(635\) −5.39059 20.1180i −0.213919 0.798357i
\(636\) 50.2520 + 45.7669i 1.99262 + 1.81478i
\(637\) −18.9559 + 8.83928i −0.751060 + 0.350225i
\(638\) −23.9233 + 1.60457i −0.947132 + 0.0635256i
\(639\) 13.0152 + 22.5429i 0.514872 + 0.891785i
\(640\) 10.7963 + 26.9107i 0.426761 + 1.06374i
\(641\) −9.49722 + 11.3184i −0.375118 + 0.447048i −0.920267 0.391291i \(-0.872029\pi\)
0.545149 + 0.838339i \(0.316473\pi\)
\(642\) 43.7035 + 12.6663i 1.72484 + 0.499899i
\(643\) 18.5350 + 26.4708i 0.730951 + 1.04391i 0.996804 + 0.0798922i \(0.0254576\pi\)
−0.265853 + 0.964014i \(0.585654\pi\)
\(644\) 0.120624 2.97010i 0.00475327 0.117038i
\(645\) −51.3377 51.3377i −2.02142 2.02142i
\(646\) 10.5968 9.70746i 0.416927 0.381935i
\(647\) 29.0955 1.14386 0.571932 0.820301i \(-0.306194\pi\)
0.571932 + 0.820301i \(0.306194\pi\)
\(648\) 82.7950 50.7597i 3.25250 1.99403i
\(649\) −0.433869 + 2.46060i −0.0170309 + 0.0965868i
\(650\) −3.56033 6.46629i −0.139648 0.253629i
\(651\) −0.381048 4.35540i −0.0149345 0.170702i
\(652\) −17.2886 + 11.0881i −0.677073 + 0.434245i
\(653\) 6.84755 25.5554i 0.267965 1.00006i −0.692445 0.721471i \(-0.743466\pi\)
0.960410 0.278590i \(-0.0898670\pi\)
\(654\) −64.9642 + 4.35725i −2.54030 + 0.170382i
\(655\) −13.0446 + 35.8397i −0.509695 + 1.40037i
\(656\) 5.17602 + 10.9259i 0.202090 + 0.426586i
\(657\) 42.4397 73.5077i 1.65573 2.86781i
\(658\) −13.1608 6.46530i −0.513060 0.252044i
\(659\) −5.03601 + 7.19217i −0.196175 + 0.280167i −0.905173 0.425044i \(-0.860259\pi\)
0.708998 + 0.705211i \(0.249148\pi\)
\(660\) 47.3269 + 14.7639i 1.84220 + 0.574686i
\(661\) −5.47190 0.478729i −0.212832 0.0186204i −0.0197590 0.999805i \(-0.506290\pi\)
−0.193073 + 0.981184i \(0.561845\pi\)
\(662\) 3.05765 7.89830i 0.118839 0.306976i
\(663\) −24.4567 + 8.90150i −0.949818 + 0.345706i
\(664\) 2.34281 3.54115i 0.0909188 0.137423i
\(665\) 9.43088 0.602384i 0.365714 0.0233594i
\(666\) 91.9248 + 18.1396i 3.56201 + 0.702897i
\(667\) 4.36605 9.36302i 0.169054 0.362538i
\(668\) 19.4674 30.7639i 0.753216 1.19029i
\(669\) 44.7710 + 3.91696i 1.73095 + 0.151438i
\(670\) 6.04639 55.9963i 0.233592 2.16332i
\(671\) 17.5686 3.09782i 0.678228 0.119590i
\(672\) 14.4498 + 6.98971i 0.557412 + 0.269634i
\(673\) −4.91601 2.83826i −0.189498 0.109407i 0.402249 0.915530i \(-0.368228\pi\)
−0.591748 + 0.806123i \(0.701562\pi\)
\(674\) −2.74983 + 0.677314i −0.105919 + 0.0260892i
\(675\) 11.6760 + 25.0393i 0.449410 + 0.963762i
\(676\) 3.04465 2.35099i 0.117102 0.0904228i
\(677\) 2.27069 8.47433i 0.0872697 0.325695i −0.908465 0.417962i \(-0.862745\pi\)
0.995734 + 0.0922669i \(0.0294113\pi\)
\(678\) −0.0418001 + 2.05932i −0.00160532 + 0.0790876i
\(679\) −5.35114 + 6.37724i −0.205358 + 0.244736i
\(680\) 1.91643 + 16.7903i 0.0734917 + 0.643880i
\(681\) −47.8138 8.43086i −1.83223 0.323071i
\(682\) 0.965232 + 6.20838i 0.0369606 + 0.237731i
\(683\) −26.9765 + 26.9765i −1.03223 + 1.03223i −0.0327626 + 0.999463i \(0.510431\pi\)
−0.999463 + 0.0327626i \(0.989569\pi\)
\(684\) −39.8834 + 59.8684i −1.52498 + 2.28913i
\(685\) −35.8516 35.8516i −1.36982 1.36982i
\(686\) 12.8306 + 9.37782i 0.489876 + 0.358047i
\(687\) −11.6411 + 66.0198i −0.444134 + 2.51881i
\(688\) 21.8712 + 25.7453i 0.833831 + 0.981529i
\(689\) 25.8306 + 21.6744i 0.984066 + 0.825729i
\(690\) −15.4078 + 14.7948i −0.586566 + 0.563227i
\(691\) 33.9275 + 9.09084i 1.29066 + 0.345832i 0.837912 0.545806i \(-0.183776\pi\)
0.452750 + 0.891637i \(0.350443\pi\)
\(692\) −18.0741 2.32357i −0.687073 0.0883290i
\(693\) 18.2415 8.50615i 0.692937 0.323122i
\(694\) −7.22479 + 11.9470i −0.274249 + 0.453503i
\(695\) −8.33953 + 14.4445i −0.316336 + 0.547911i
\(696\) 36.9735 + 41.7741i 1.40148 + 1.58344i
\(697\) 1.22358 + 6.93928i 0.0463465 + 0.262844i
\(698\) −30.2608 + 24.3627i −1.14539 + 0.922141i
\(699\) −3.27178 + 37.3967i −0.123750 + 1.41447i
\(700\) −1.41884 + 2.24215i −0.0536270 + 0.0847454i
\(701\) −13.3901 6.24392i −0.505739 0.235830i 0.152966 0.988231i \(-0.451117\pi\)
−0.658705 + 0.752402i \(0.728895\pi\)
\(702\) 68.8708 46.1697i 2.59936 1.74256i
\(703\) −34.0090 + 8.26202i −1.28267 + 0.311608i
\(704\) −21.3911 8.63259i −0.806208 0.325353i
\(705\) 36.0385 + 99.0149i 1.35729 + 3.72912i
\(706\) −7.81524 + 3.45299i −0.294130 + 0.129955i
\(707\) 0.348473 3.98307i 0.0131057 0.149799i
\(708\) 5.14825 2.69995i 0.193483 0.101470i
\(709\) 4.82778 + 3.38045i 0.181311 + 0.126955i 0.660709 0.750642i \(-0.270256\pi\)
−0.479397 + 0.877598i \(0.659145\pi\)
\(710\) 10.8211 3.69163i 0.406108 0.138544i
\(711\) 28.0144 + 16.1741i 1.05062 + 0.606578i
\(712\) −9.92535 1.48132i −0.371968 0.0555147i
\(713\) −2.54387 0.925893i −0.0952687 0.0346750i
\(714\) 7.04301 + 6.15763i 0.263578 + 0.230443i
\(715\) 23.7565 + 6.36554i 0.888443 + 0.238058i
\(716\) 10.2746 + 16.0202i 0.383981 + 0.598702i
\(717\) 28.9127 2.52953i 1.07976 0.0944671i
\(718\) 10.7583 + 3.11801i 0.401496 + 0.116363i
\(719\) 42.4296 + 7.48148i 1.58236 + 0.279012i 0.894579 0.446910i \(-0.147475\pi\)
0.687777 + 0.725922i \(0.258587\pi\)
\(720\) −29.4155 79.3134i −1.09625 2.95584i
\(721\) 3.11554i 0.116029i
\(722\) 4.13548 26.5499i 0.153907 0.988085i
\(723\) −53.0920 + 53.0920i −1.97451 + 1.97451i
\(724\) 0.379108 0.349517i 0.0140894 0.0129897i
\(725\) −7.55392 + 5.28931i −0.280545 + 0.196440i
\(726\) 11.1613 6.14543i 0.414236 0.228078i
\(727\) −1.04939 0.880539i −0.0389196 0.0326574i 0.623120 0.782126i \(-0.285865\pi\)
−0.662040 + 0.749469i \(0.730309\pi\)
\(728\) 7.30327 + 3.17381i 0.270677 + 0.117629i
\(729\) −91.8476 + 53.0282i −3.40176 + 1.96401i
\(730\) −28.0675 24.5391i −1.03882 0.908232i
\(731\) 8.32071 + 17.8438i 0.307753 + 0.659978i
\(732\) −30.6871 27.9483i −1.13423 1.03300i
\(733\) −43.7651 + 11.7268i −1.61650 + 0.433140i −0.949971 0.312338i \(-0.898888\pi\)
−0.666530 + 0.745478i \(0.732221\pi\)
\(734\) 2.32275 + 1.14106i 0.0857341 + 0.0421174i
\(735\) −9.38148 53.2050i −0.346041 1.96250i
\(736\) 7.70371 6.27982i 0.283963 0.231477i
\(737\) 28.8011 + 34.3238i 1.06090 + 1.26433i
\(738\) −14.2546 32.2628i −0.524719 1.18761i
\(739\) 16.2258 34.7963i 0.596875 1.28000i −0.343272 0.939236i \(-0.611535\pi\)
0.940148 0.340768i \(-0.110687\pi\)
\(740\) 15.6337 38.0702i 0.574705 1.39949i
\(741\) −25.3137 + 41.5597i −0.929923 + 1.52674i
\(742\) 2.34652 11.8913i 0.0861433 0.436542i
\(743\) 8.38701 + 23.0431i 0.307689 + 0.845370i 0.993106 + 0.117219i \(0.0373979\pi\)
−0.685417 + 0.728151i \(0.740380\pi\)
\(744\) 10.0604 10.6058i 0.368834 0.388826i
\(745\) 3.72345 + 4.43744i 0.136417 + 0.162575i
\(746\) 20.8816 16.8115i 0.764529 0.615514i
\(747\) −7.10511 + 10.1472i −0.259962 + 0.371265i
\(748\) −10.6909 8.15182i −0.390897 0.298060i
\(749\) −2.10007 7.83757i −0.0767349 0.286379i
\(750\) −40.5106 + 9.97822i −1.47924 + 0.364353i
\(751\) −26.0232 9.47168i −0.949601 0.345627i −0.179651 0.983730i \(-0.557497\pi\)
−0.769950 + 0.638104i \(0.779719\pi\)
\(752\) −12.9771 47.2786i −0.473228 1.72407i
\(753\) −2.74060 + 1.58228i −0.0998729 + 0.0576616i
\(754\) 19.1682 + 19.9625i 0.698066 + 0.726992i
\(755\) −4.71779 53.9246i −0.171698 1.96252i
\(756\) −26.4782 13.6814i −0.963002 0.497589i
\(757\) 14.6686 + 20.9490i 0.533141 + 0.761404i 0.991881 0.127167i \(-0.0405883\pi\)
−0.458741 + 0.888570i \(0.651699\pi\)
\(758\) 32.8931 5.11397i 1.19473 0.185748i
\(759\) 16.9935i 0.616827i
\(760\) 22.4073 + 22.2777i 0.812799 + 0.808097i
\(761\) 53.7453i 1.94826i 0.225979 + 0.974132i \(0.427442\pi\)
−0.225979 + 0.974132i \(0.572558\pi\)
\(762\) −5.92249 38.0935i −0.214549 1.37998i
\(763\) 6.65960 + 9.51090i 0.241094 + 0.344318i
\(764\) −39.4020 + 12.5553i −1.42551 + 0.454236i
\(765\) −4.29700 49.1150i −0.155358 1.77576i
\(766\) 6.52482 6.26521i 0.235751 0.226371i
\(767\) 2.49756 1.44197i 0.0901817 0.0520665i
\(768\) 14.5206 + 51.6681i 0.523969 + 1.86441i
\(769\) 5.21063 + 1.89651i 0.187900 + 0.0683901i 0.434257 0.900789i \(-0.357011\pi\)
−0.246356 + 0.969179i \(0.579233\pi\)
\(770\) −2.11435 8.58404i −0.0761958 0.309347i
\(771\) 0.934633 + 3.48810i 0.0336600 + 0.125621i
\(772\) −0.00464530 0.0344737i −0.000167188 0.00124074i
\(773\) −15.8072 + 22.5750i −0.568544 + 0.811965i −0.995741 0.0921936i \(-0.970612\pi\)
0.427197 + 0.904159i \(0.359501\pi\)
\(774\) −61.8041 76.7668i −2.22150 2.75933i
\(775\) 1.55326 + 1.85110i 0.0557947 + 0.0664936i
\(776\) −27.8253 + 0.734220i −0.998871 + 0.0263570i
\(777\) −7.79223 21.4090i −0.279545 0.768043i
\(778\) −30.9843 6.11418i −1.11084 0.219204i
\(779\) 9.89083 + 8.70316i 0.354376 + 0.311823i
\(780\) −22.0591 52.8003i −0.789841 1.89055i
\(781\) −3.84407 + 8.24363i −0.137552 + 0.294980i
\(782\) 5.29855 2.34105i 0.189476 0.0837157i
\(783\) −66.5813 79.3485i −2.37942 2.83568i
\(784\) 2.34324 + 25.0282i 0.0836870 + 0.893864i
\(785\) 4.21333 + 23.8950i 0.150380 + 0.852848i
\(786\) −31.1272 + 63.3625i −1.11027 + 2.26007i
\(787\) −10.5013 + 2.81381i −0.374331 + 0.100302i −0.441079 0.897468i \(-0.645404\pi\)
0.0667483 + 0.997770i \(0.478738\pi\)
\(788\) −0.751606 16.0910i −0.0267749 0.573217i
\(789\) 16.8484 + 36.1316i 0.599820 + 1.28632i
\(790\) 9.35207 10.6968i 0.332732 0.380574i
\(791\) 0.318091 0.183650i 0.0113100 0.00652983i
\(792\) 61.7210 + 26.8223i 2.19316 + 0.953090i
\(793\) −15.7738 13.2358i −0.560144 0.470017i
\(794\) −11.5360 20.9517i −0.409397 0.743547i
\(795\) −71.3471 + 49.9578i −2.53042 + 1.77182i
\(796\) 1.20425 29.6519i 0.0426835 1.05098i
\(797\) 34.5147 34.5147i 1.22257 1.22257i 0.255861 0.966713i \(-0.417641\pi\)
0.966713 0.255861i \(-0.0823591\pi\)
\(798\) 17.4750 + 0.765455i 0.618609 + 0.0270968i
\(799\) 28.5743i 1.01089i
\(800\) −8.75798 + 1.41626i −0.309641 + 0.0500724i
\(801\) 28.8324 + 5.08393i 1.01874 + 0.179632i
\(802\) −2.28253 + 7.87558i −0.0805989 + 0.278096i
\(803\) 29.5467 2.58500i 1.04268 0.0912227i
\(804\) 22.2539 101.846i 0.784835 3.59185i
\(805\) 3.67934 + 0.985877i 0.129680 + 0.0347476i
\(806\) 4.77331 5.45965i 0.168133 0.192308i
\(807\) −42.7181 15.5481i −1.50375 0.547320i
\(808\) 10.7449 7.95411i 0.378003 0.279825i
\(809\) 40.4202 + 23.3366i 1.42110 + 0.820472i 0.996393 0.0848586i \(-0.0270439\pi\)
0.424707 + 0.905331i \(0.360377\pi\)
\(810\) 40.1818 + 117.783i 1.41185 + 4.13847i
\(811\) −25.3228 17.7312i −0.889203 0.622627i 0.0371387 0.999310i \(-0.488176\pi\)
−0.926342 + 0.376683i \(0.877065\pi\)
\(812\) 2.96254 9.49663i 0.103965 0.333266i
\(813\) 0.424401 4.85092i 0.0148844 0.170129i
\(814\) 13.2319 + 29.9480i 0.463777 + 1.04968i
\(815\) −9.00168 24.7319i −0.315315 0.866321i
\(816\) 0.190349 + 31.2795i 0.00666353 + 1.09500i
\(817\) 32.9887 + 16.3365i 1.15413 + 0.571541i
\(818\) 10.6880 + 15.9432i 0.373697 + 0.557440i
\(819\) −21.0551 9.81815i −0.735724 0.343074i
\(820\) −15.1150 + 3.39920i −0.527839 + 0.118705i
\(821\) −1.09928 + 12.5648i −0.0383651 + 0.438515i 0.952584 + 0.304276i \(0.0984146\pi\)
−0.990949 + 0.134239i \(0.957141\pi\)
\(822\) −58.8523 73.1004i −2.05271 2.54967i
\(823\) 6.95641 + 39.4518i 0.242485 + 1.37520i 0.826261 + 0.563287i \(0.190464\pi\)
−0.583776 + 0.811915i \(0.698425\pi\)
\(824\) 7.80054 6.90413i 0.271745 0.240517i
\(825\) −7.58440 + 13.1366i −0.264055 + 0.457357i
\(826\) −0.887055 0.536433i −0.0308646 0.0186649i
\(827\) 4.76135 2.22025i 0.165568 0.0772057i −0.338067 0.941122i \(-0.609773\pi\)
0.503636 + 0.863916i \(0.331995\pi\)
\(828\) −22.9504 + 17.7217i −0.797583 + 0.615872i
\(829\) 3.82369 + 1.02455i 0.132802 + 0.0355842i 0.324608 0.945849i \(-0.394768\pi\)
−0.191806 + 0.981433i \(0.561434\pi\)
\(830\) 3.76848 + 3.92464i 0.130806 + 0.136226i
\(831\) 44.5095 + 37.3479i 1.54402 + 1.29558i
\(832\) 8.23783 + 25.3188i 0.285595 + 0.877773i
\(833\) −2.54409 + 14.4282i −0.0881475 + 0.499909i
\(834\) −18.2172 + 24.9245i −0.630810 + 0.863066i
\(835\) 32.9879 + 32.9879i 1.14159 + 1.14159i
\(836\) −25.1303 + 0.583036i −0.869149 + 0.0201647i
\(837\) −19.1928 + 19.1928i −0.663400 + 0.663400i
\(838\) −42.9803 + 6.68225i −1.48473 + 0.230835i
\(839\) 21.2832 + 3.75279i 0.734776 + 0.129561i 0.528500 0.848933i \(-0.322755\pi\)
0.206276 + 0.978494i \(0.433866\pi\)
\(840\) −12.8013 + 16.1001i −0.441687 + 0.555505i
\(841\) 3.58274 4.26974i 0.123543 0.147232i
\(842\) −37.3460 0.758053i −1.28703 0.0261242i
\(843\) −4.98440 + 18.6020i −0.171672 + 0.640688i
\(844\) −0.398130 + 3.09688i −0.0137042 + 0.106599i
\(845\) 2.08321 + 4.46746i 0.0716646 + 0.153685i
\(846\) 34.2084 + 138.883i 1.17611 + 4.77488i
\(847\) −1.96768 1.13604i −0.0676102 0.0390348i
\(848\) 34.9727 20.4763i 1.20097 0.703158i
\(849\) −58.7984 + 10.3677i −2.01796 + 0.355820i
\(850\) −5.14079 0.555095i −0.176328 0.0190396i
\(851\) −14.0533 1.22951i −0.481742 0.0421470i
\(852\) 20.6472 4.64333i 0.707361 0.159078i
\(853\) −22.5392 + 48.3354i −0.771726 + 1.65497i −0.0161859 + 0.999869i \(0.505152\pi\)
−0.755540 + 0.655102i \(0.772625\pi\)
\(854\) −1.43294 + 7.26157i −0.0490340 + 0.248486i
\(855\) −63.6346 66.6952i −2.17626 2.28093i
\(856\) 14.9695 22.6264i 0.511648 0.773353i
\(857\) 23.9735 8.72564i 0.818919 0.298062i 0.101616 0.994824i \(-0.467599\pi\)
0.717303 + 0.696762i \(0.245376\pi\)
\(858\) 42.4534 + 16.4349i 1.44933 + 0.561078i
\(859\) 51.2204 + 4.48121i 1.74762 + 0.152897i 0.915664 0.401946i \(-0.131666\pi\)
0.831955 + 0.554843i \(0.187221\pi\)
\(860\) −38.3363 + 20.1051i −1.30726 + 0.685578i
\(861\) −4.91924 + 7.02541i −0.167647 + 0.239425i
\(862\) 9.56453 19.4696i 0.325769 0.663136i
\(863\) 13.2756 22.9939i 0.451905 0.782722i −0.546599 0.837394i \(-0.684078\pi\)
0.998504 + 0.0546718i \(0.0174113\pi\)
\(864\) −24.4215 96.6133i −0.830836 3.28685i
\(865\) 7.98664 21.9431i 0.271554 0.746089i
\(866\) −0.390347 5.81986i −0.0132645 0.197767i
\(867\) 10.0405 37.4715i 0.340992 1.27260i
\(868\) −2.54669 0.556464i −0.0864404 0.0188876i
\(869\) 0.985168 + 11.2605i 0.0334195 + 0.381987i
\(870\) −62.6219 + 34.4796i −2.12308 + 1.16897i
\(871\) 8.98067 50.9319i 0.304298 1.72576i
\(872\) −9.05507 + 37.7504i −0.306643 + 1.27839i
\(873\) 81.2066 2.74843
\(874\) 5.00245 9.60629i 0.169210 0.324938i
\(875\) 5.26080 + 5.26080i 0.177847 + 0.177847i
\(876\) −46.7754 50.7356i −1.58040 1.71420i
\(877\) 30.0257 + 42.8811i 1.01390 + 1.44799i 0.890144 + 0.455680i \(0.150604\pi\)
0.123752 + 0.992313i \(0.460507\pi\)
\(878\) 10.0015 34.5090i 0.337535 1.16462i
\(879\) 12.9843 15.4741i 0.437951 0.521929i
\(880\) 16.8069 24.3163i 0.566560 0.819703i
\(881\) −3.01875 5.22862i −0.101704 0.176157i 0.810683 0.585486i \(-0.199096\pi\)
−0.912387 + 0.409329i \(0.865763\pi\)
\(882\) −4.90781 73.1728i −0.165254 2.46386i
\(883\) 27.4471 12.7988i 0.923667 0.430713i 0.0982024 0.995166i \(-0.468691\pi\)
0.825465 + 0.564453i \(0.190913\pi\)
\(884\) 0.724047 + 15.5010i 0.0243524 + 0.521354i
\(885\) 1.92803 + 7.19551i 0.0648101 + 0.241875i
\(886\) −10.7933 + 3.68214i −0.362607 + 0.123704i
\(887\) 49.0861 8.65520i 1.64815 0.290613i 0.728997 0.684517i \(-0.239987\pi\)
0.919152 + 0.393904i \(0.128876\pi\)
\(888\) 36.3350 66.9528i 1.21932 2.24679i
\(889\) −5.26622 + 4.41889i −0.176623 + 0.148205i
\(890\) 4.64256 11.9923i 0.155619 0.401983i
\(891\) −89.7284 41.8410i −3.00602 1.40173i
\(892\) 10.1791 24.7875i 0.340821 0.829949i
\(893\) −33.3714 41.7219i −1.11673 1.39617i
\(894\) 5.97038 + 8.90594i 0.199679 + 0.297859i
\(895\) −22.9174 + 8.34125i −0.766044 + 0.278817i
\(896\) 6.54417 6.98351i 0.218625 0.233303i
\(897\) −15.0257 + 12.6081i −0.501694 + 0.420971i
\(898\) 15.7806 + 1.70397i 0.526606 + 0.0568621i
\(899\) −7.42130 5.19645i −0.247514 0.173311i
\(900\) 25.6508 3.45643i 0.855028 0.115214i
\(901\) 22.8148 6.11321i 0.760072 0.203661i
\(902\) 6.37785 10.5465i 0.212359 0.351161i
\(903\) −8.19612 + 22.5187i −0.272750 + 0.749374i
\(904\) 1.16471 + 0.389447i 0.0387378 + 0.0129528i
\(905\) 0.330380 + 0.572235i 0.0109822 + 0.0190217i
\(906\) 2.03332 100.173i 0.0675525 3.32802i
\(907\) −31.8384 + 2.78550i −1.05718 + 0.0924911i −0.602464 0.798146i \(-0.705814\pi\)
−0.454714 + 0.890637i \(0.650259\pi\)
\(908\) −13.2886 + 25.7180i −0.440998 + 0.853480i
\(909\) −31.9485 + 22.3706i −1.05966 + 0.741985i
\(910\) −6.02131 + 8.23829i −0.199605 + 0.273097i
\(911\) 44.9611 1.48963 0.744814 0.667272i \(-0.232538\pi\)
0.744814 + 0.667272i \(0.232538\pi\)
\(912\) 36.8086 + 45.4494i 1.21886 + 1.50498i
\(913\) −4.32855 −0.143254
\(914\) 14.0417 19.2116i 0.464457 0.635464i
\(915\) 43.5692 30.5075i 1.44035 1.00855i
\(916\) 35.5105 + 18.3485i 1.17330 + 0.606252i
\(917\) 12.5409 1.09719i 0.414137 0.0362323i
\(918\) 1.17866 58.0677i 0.0389017 1.91652i
\(919\) −8.77704 15.2023i −0.289528 0.501477i 0.684169 0.729323i \(-0.260165\pi\)
−0.973697 + 0.227846i \(0.926832\pi\)
\(920\) 5.68514 + 11.3969i 0.187434 + 0.375745i
\(921\) 16.7038 45.8934i 0.550410 1.51224i
\(922\) −3.08993 + 5.10957i −0.101762 + 0.168275i
\(923\) 10.1411 2.71729i 0.333797 0.0894406i
\(924\) −2.18523 16.2171i −0.0718889 0.533502i
\(925\) 10.3150 + 7.22261i 0.339153 + 0.237478i
\(926\) −25.0652 2.70650i −0.823694 0.0889412i
\(927\) −23.2809 + 19.5350i −0.764645 + 0.641613i
\(928\) 30.3423 13.6274i 0.996035 0.447340i
\(929\) −7.05387 + 2.56740i −0.231430 + 0.0842336i −0.455132 0.890424i \(-0.650408\pi\)
0.223702 + 0.974658i \(0.428186\pi\)
\(930\) 10.4309 + 15.5596i 0.342041 + 0.510219i
\(931\) 13.1358 + 24.0381i 0.430509 + 0.787818i
\(932\) 20.7047 + 8.50246i 0.678206 + 0.278507i
\(933\) −46.6863 21.7702i −1.52844 0.712724i
\(934\) 16.3203 42.1573i 0.534016 1.37943i
\(935\) 13.1973 11.0739i 0.431599 0.362155i
\(936\) −22.0765 74.4741i −0.721592 2.43426i
\(937\) −30.2622 + 5.33605i −0.988625 + 0.174321i −0.644501 0.764603i \(-0.722935\pi\)
−0.344123 + 0.938924i \(0.611824\pi\)
\(938\) −17.5944 + 6.00236i −0.574478 + 0.195984i
\(939\) −1.66548 6.21564i −0.0543508 0.202840i
\(940\) 62.7569 2.93137i 2.04691 0.0956106i
\(941\) −43.3618 + 20.2199i −1.41355 + 0.659151i −0.971326 0.237753i \(-0.923589\pi\)
−0.442227 + 0.896903i \(0.645812\pi\)
\(942\) 3.00549 + 44.8103i 0.0979242 + 1.46000i
\(943\) 2.65523 + 4.59899i 0.0864661 + 0.149764i
\(944\) −0.622643 3.40972i −0.0202653 0.110977i
\(945\) 24.5493 29.2567i 0.798588 0.951720i
\(946\) 9.58642 33.0768i 0.311681 1.07542i
\(947\) 18.3813 + 26.2513i 0.597313 + 0.853052i 0.998003 0.0631621i \(-0.0201185\pi\)
−0.400690 + 0.916214i \(0.631230\pi\)
\(948\) 19.3358 17.8265i 0.627998 0.578979i
\(949\) −24.2073 24.2073i −0.785803 0.785803i
\(950\) −8.15445 + 5.19333i −0.264565 + 0.168494i
\(951\) −39.2025 −1.27123
\(952\) 4.75540 2.91543i 0.154124 0.0944896i
\(953\) −4.08232 + 23.1520i −0.132239 + 0.749967i 0.844503 + 0.535551i \(0.179896\pi\)
−0.976742 + 0.214416i \(0.931215\pi\)
\(954\) −103.571 + 57.0259i −3.35322 + 1.84628i
\(955\) −4.61861 52.7909i −0.149455 1.70827i
\(956\) 3.69401 16.9059i 0.119473 0.546774i
\(957\) 14.7193 54.9331i 0.475807 1.77573i
\(958\) 0.731786 + 10.9105i 0.0236429 + 0.352504i
\(959\) −5.72374 + 15.7259i −0.184829 + 0.507814i
\(960\) −68.6787 + 3.62694i −2.21659 + 0.117059i
\(961\) 14.3130 24.7908i 0.461709 0.799704i
\(962\) 16.6629 33.9190i 0.537234 1.09359i
\(963\) −45.3985 + 64.8358i −1.46295 + 2.08930i
\(964\) 20.7922 + 39.6464i 0.669670 + 1.27692i
\(965\) 0.0444055 + 0.00388498i 0.00142946 + 0.000125062i
\(966\) 6.57506 + 2.54539i 0.211549 + 0.0818967i
\(967\) 2.94943 1.07350i 0.0948473 0.0345216i −0.294161 0.955756i \(-0.595040\pi\)
0.389008 + 0.921234i \(0.372818\pi\)
\(968\) −1.51607 7.44408i −0.0487284 0.239262i
\(969\) 13.6764 + 31.2227i 0.439348 + 1.00302i
\(970\) 6.90541 34.9940i 0.221719 1.12359i
\(971\) −0.875568 + 1.87766i −0.0280983 + 0.0602570i −0.919856 0.392256i \(-0.871695\pi\)
0.891758 + 0.452513i \(0.149472\pi\)
\(972\) 27.3498 + 121.615i 0.877245 + 3.90079i
\(973\) 5.48430 + 0.479814i 0.175819 + 0.0153821i
\(974\) 21.5834 + 2.33054i 0.691575 + 0.0746753i
\(975\) 17.2425 3.04031i 0.552201 0.0973680i
\(976\) −21.3566 + 12.5041i −0.683609 + 0.400248i
\(977\) −21.1474 12.2094i −0.676564 0.390614i 0.121995 0.992531i \(-0.461071\pi\)
−0.798559 + 0.601916i \(0.794404\pi\)
\(978\) −11.6510 47.3020i −0.372558 1.51255i
\(979\) 4.32355 + 9.27188i 0.138181 + 0.296330i
\(980\) −31.9494 4.10736i −1.02058 0.131205i
\(981\) 29.3133 109.399i 0.935903 3.49284i
\(982\) 23.4561 + 0.476114i 0.748515 + 0.0151934i
\(983\) −31.0970 + 37.0599i −0.991839 + 1.18203i −0.00855278 + 0.999963i \(0.502722\pi\)
−0.983287 + 0.182065i \(0.941722\pi\)
\(984\) −28.4911 + 3.25194i −0.908262 + 0.103668i
\(985\) 20.3284 + 3.58445i 0.647718 + 0.114210i
\(986\) 19.1558 2.97819i 0.610044 0.0948450i
\(987\) 24.5926 24.5926i 0.782792 0.782792i
\(988\) 19.1605 + 21.7876i 0.609576 + 0.693157i
\(989\) 10.4922 + 10.4922i 0.333633 + 0.333633i
\(990\) −50.8870 + 69.6230i −1.61729 + 2.21276i
\(991\) −6.40250 + 36.3104i −0.203382 + 1.15344i 0.696584 + 0.717476i \(0.254703\pi\)
−0.899966 + 0.435961i \(0.856409\pi\)
\(992\) −4.25030 7.60944i −0.134947 0.241600i
\(993\) 15.3888 + 12.9128i 0.488350 + 0.409774i
\(994\) −2.61380 2.72211i −0.0829047 0.0863400i
\(995\) 36.7326 + 9.84247i 1.16450 + 0.312027i
\(996\) 6.15515 + 7.97121i 0.195033 + 0.252577i
\(997\) 41.2603 19.2400i 1.30673 0.609337i 0.360476 0.932768i \(-0.382614\pi\)
0.946252 + 0.323431i \(0.104836\pi\)
\(998\) −8.79657 5.31960i −0.278450 0.168389i
\(999\) −70.7212 + 122.493i −2.23752 + 3.87550i
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 304.2.bg.a.147.31 yes 456
16.11 odd 4 inner 304.2.bg.a.299.16 yes 456
19.15 odd 18 inner 304.2.bg.a.243.16 yes 456
304.91 even 36 inner 304.2.bg.a.91.31 456
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
304.2.bg.a.91.31 456 304.91 even 36 inner
304.2.bg.a.147.31 yes 456 1.1 even 1 trivial
304.2.bg.a.243.16 yes 456 19.15 odd 18 inner
304.2.bg.a.299.16 yes 456 16.11 odd 4 inner