Properties

Label 429.2.t.a.296.7
Level $429$
Weight $2$
Character 429.296
Analytic conductor $3.426$
Analytic rank $0$
Dimension $104$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(296,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.296");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(104\)
Relative dimension: \(52\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 296.7
Character \(\chi\) \(=\) 429.296
Dual form 429.2.t.a.329.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.92182 + 1.10956i) q^{2} +(-1.59672 + 0.671171i) q^{3} +(1.46227 - 2.53272i) q^{4} +1.97176 q^{5} +(2.32391 - 3.06154i) q^{6} +(0.477966 - 0.827861i) q^{7} +2.05166i q^{8} +(2.09906 - 2.14335i) q^{9} +O(q^{10})\) \(q+(-1.92182 + 1.10956i) q^{2} +(-1.59672 + 0.671171i) q^{3} +(1.46227 - 2.53272i) q^{4} +1.97176 q^{5} +(2.32391 - 3.06154i) q^{6} +(0.477966 - 0.827861i) q^{7} +2.05166i q^{8} +(2.09906 - 2.14335i) q^{9} +(-3.78937 + 2.18779i) q^{10} +(-3.31597 - 0.0657479i) q^{11} +(-0.634948 + 5.02549i) q^{12} +(-3.43390 + 1.09923i) q^{13} +2.12134i q^{14} +(-3.14836 + 1.32339i) q^{15} +(0.648086 + 1.12252i) q^{16} +(1.09581 - 1.89800i) q^{17} +(-1.65583 + 6.44818i) q^{18} +(-2.70718 + 4.68897i) q^{19} +(2.88324 - 4.99391i) q^{20} +(-0.207543 + 1.64266i) q^{21} +(6.44566 - 3.55293i) q^{22} +(-5.88960 + 3.40036i) q^{23} +(-1.37701 - 3.27593i) q^{24} -1.11217 q^{25} +(5.37969 - 5.92265i) q^{26} +(-1.91306 + 4.83117i) q^{27} +(-1.39783 - 2.42111i) q^{28} +(-3.45995 - 5.99282i) q^{29} +(4.58220 - 6.03662i) q^{30} -9.45661i q^{31} +(-6.04459 - 3.48984i) q^{32} +(5.33882 - 2.12060i) q^{33} +4.86348i q^{34} +(0.942433 - 1.63234i) q^{35} +(-2.35913 - 8.45048i) q^{36} +(-3.85093 + 2.22334i) q^{37} -12.0152i q^{38} +(4.74523 - 4.05990i) q^{39} +4.04538i q^{40} +(7.34788 - 4.24230i) q^{41} +(-1.42378 - 3.38719i) q^{42} +(3.90995 + 2.25741i) q^{43} +(-5.01536 + 8.30229i) q^{44} +(4.13884 - 4.22617i) q^{45} +(7.54584 - 13.0698i) q^{46} -8.69313 q^{47} +(-1.78822 - 1.35737i) q^{48} +(3.04310 + 5.27080i) q^{49} +(2.13739 - 1.23402i) q^{50} +(-0.475824 + 3.76605i) q^{51} +(-2.23725 + 10.3045i) q^{52} -0.387082i q^{53} +(-1.68393 - 11.4073i) q^{54} +(-6.53830 - 0.129639i) q^{55} +(1.69849 + 0.980623i) q^{56} +(1.17552 - 9.30397i) q^{57} +(13.2988 + 7.67808i) q^{58} +(1.10758 - 1.91839i) q^{59} +(-1.25196 + 9.90905i) q^{60} +(-8.44034 - 4.87303i) q^{61} +(10.4927 + 18.1739i) q^{62} +(-0.771119 - 2.76218i) q^{63} +12.8965 q^{64} +(-6.77083 + 2.16741i) q^{65} +(-7.90732 + 9.99919i) q^{66} +(-9.08197 + 5.24348i) q^{67} +(-3.20473 - 5.55075i) q^{68} +(7.12184 - 9.38236i) q^{69} +4.18276i q^{70} +(-2.05660 + 3.56214i) q^{71} +(4.39743 + 4.30655i) q^{72} -2.33785 q^{73} +(4.93387 - 8.54572i) q^{74} +(1.77582 - 0.746454i) q^{75} +(7.91723 + 13.7130i) q^{76} +(-1.63935 + 2.71374i) q^{77} +(-4.61477 + 13.0675i) q^{78} -8.16220i q^{79} +(1.27787 + 2.21333i) q^{80} +(-0.187909 - 8.99804i) q^{81} +(-9.41421 + 16.3059i) q^{82} +2.78415i q^{83} +(3.85692 + 2.92766i) q^{84} +(2.16067 - 3.74239i) q^{85} -10.0190 q^{86} +(9.54680 + 7.24665i) q^{87} +(0.134892 - 6.80325i) q^{88} +(-2.83303 - 4.90695i) q^{89} +(-3.26490 + 12.7143i) q^{90} +(-0.731283 + 3.36819i) q^{91} +19.8889i q^{92} +(6.34701 + 15.0996i) q^{93} +(16.7067 - 9.64559i) q^{94} +(-5.33790 + 9.24552i) q^{95} +(11.9938 + 1.51537i) q^{96} +(-16.4548 - 9.50019i) q^{97} +(-11.6966 - 6.75303i) q^{98} +(-7.10134 + 6.96929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9} - 4 q^{12} - 36 q^{15} - 44 q^{16} - 12 q^{22} + 64 q^{25} + 4 q^{27} + 12 q^{33} + 28 q^{36} - 12 q^{37} + 50 q^{42} - 66 q^{45} + 16 q^{48} - 24 q^{49} - 8 q^{55} - 24 q^{58} - 104 q^{64} - 60 q^{66} - 60 q^{67} - 42 q^{69} - 42 q^{75} + 16 q^{78} - 22 q^{81} - 16 q^{82} + 92 q^{88} - 84 q^{91} + 126 q^{93} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92182 + 1.10956i −1.35893 + 0.784581i −0.989480 0.144669i \(-0.953788\pi\)
−0.369453 + 0.929249i \(0.620455\pi\)
\(3\) −1.59672 + 0.671171i −0.921869 + 0.387501i
\(4\) 1.46227 2.53272i 0.731133 1.26636i
\(5\) 1.97176 0.881797 0.440899 0.897557i \(-0.354660\pi\)
0.440899 + 0.897557i \(0.354660\pi\)
\(6\) 2.32391 3.06154i 0.948733 1.24987i
\(7\) 0.477966 0.827861i 0.180654 0.312902i −0.761449 0.648224i \(-0.775512\pi\)
0.942103 + 0.335322i \(0.108845\pi\)
\(8\) 2.05166i 0.725371i
\(9\) 2.09906 2.14335i 0.699686 0.714450i
\(10\) −3.78937 + 2.18779i −1.19830 + 0.691841i
\(11\) −3.31597 0.0657479i −0.999803 0.0198237i
\(12\) −0.634948 + 5.02549i −0.183294 + 1.45073i
\(13\) −3.43390 + 1.09923i −0.952394 + 0.304870i
\(14\) 2.12134i 0.566951i
\(15\) −3.14836 + 1.32339i −0.812902 + 0.341697i
\(16\) 0.648086 + 1.12252i 0.162021 + 0.280629i
\(17\) 1.09581 1.89800i 0.265773 0.460331i −0.701993 0.712184i \(-0.747706\pi\)
0.967766 + 0.251852i \(0.0810397\pi\)
\(18\) −1.65583 + 6.44818i −0.390283 + 1.51985i
\(19\) −2.70718 + 4.68897i −0.621069 + 1.07572i 0.368218 + 0.929740i \(0.379968\pi\)
−0.989287 + 0.145984i \(0.953365\pi\)
\(20\) 2.88324 4.99391i 0.644711 1.11667i
\(21\) −0.207543 + 1.64266i −0.0452896 + 0.358458i
\(22\) 6.44566 3.55293i 1.37422 0.757487i
\(23\) −5.88960 + 3.40036i −1.22807 + 0.709024i −0.966625 0.256196i \(-0.917531\pi\)
−0.261441 + 0.965220i \(0.584198\pi\)
\(24\) −1.37701 3.27593i −0.281082 0.668697i
\(25\) −1.11217 −0.222433
\(26\) 5.37969 5.92265i 1.05504 1.16153i
\(27\) −1.91306 + 4.83117i −0.368169 + 0.929759i
\(28\) −1.39783 2.42111i −0.264164 0.457546i
\(29\) −3.45995 5.99282i −0.642497 1.11284i −0.984874 0.173275i \(-0.944565\pi\)
0.342376 0.939563i \(-0.388768\pi\)
\(30\) 4.58220 6.03662i 0.836591 1.10213i
\(31\) 9.45661i 1.69846i −0.528025 0.849229i \(-0.677067\pi\)
0.528025 0.849229i \(-0.322933\pi\)
\(32\) −6.04459 3.48984i −1.06854 0.616923i
\(33\) 5.33882 2.12060i 0.929370 0.369150i
\(34\) 4.86348i 0.834080i
\(35\) 0.942433 1.63234i 0.159300 0.275916i
\(36\) −2.35913 8.45048i −0.393188 1.40841i
\(37\) −3.85093 + 2.22334i −0.633090 + 0.365515i −0.781948 0.623344i \(-0.785774\pi\)
0.148858 + 0.988859i \(0.452440\pi\)
\(38\) 12.0152i 1.94912i
\(39\) 4.74523 4.05990i 0.759845 0.650104i
\(40\) 4.04538i 0.639630i
\(41\) 7.34788 4.24230i 1.14755 0.662536i 0.199258 0.979947i \(-0.436147\pi\)
0.948288 + 0.317411i \(0.102814\pi\)
\(42\) −1.42378 3.38719i −0.219694 0.522654i
\(43\) 3.90995 + 2.25741i 0.596261 + 0.344252i 0.767569 0.640966i \(-0.221466\pi\)
−0.171308 + 0.985218i \(0.554799\pi\)
\(44\) −5.01536 + 8.30229i −0.756094 + 1.25162i
\(45\) 4.13884 4.22617i 0.616981 0.630001i
\(46\) 7.54584 13.0698i 1.11257 1.92703i
\(47\) −8.69313 −1.26802 −0.634012 0.773323i \(-0.718593\pi\)
−0.634012 + 0.773323i \(0.718593\pi\)
\(48\) −1.78822 1.35737i −0.258107 0.195920i
\(49\) 3.04310 + 5.27080i 0.434728 + 0.752971i
\(50\) 2.13739 1.23402i 0.302272 0.174517i
\(51\) −0.475824 + 3.76605i −0.0666287 + 0.527353i
\(52\) −2.23725 + 10.3045i −0.310251 + 1.42897i
\(53\) 0.387082i 0.0531699i −0.999647 0.0265849i \(-0.991537\pi\)
0.999647 0.0265849i \(-0.00846324\pi\)
\(54\) −1.68393 11.4073i −0.229154 1.55234i
\(55\) −6.53830 0.129639i −0.881624 0.0174805i
\(56\) 1.69849 + 0.980623i 0.226970 + 0.131041i
\(57\) 1.17552 9.30397i 0.155701 1.23234i
\(58\) 13.2988 + 7.67808i 1.74622 + 1.00818i
\(59\) 1.10758 1.91839i 0.144195 0.249753i −0.784877 0.619651i \(-0.787274\pi\)
0.929072 + 0.369898i \(0.120607\pi\)
\(60\) −1.25196 + 9.90905i −0.161628 + 1.27925i
\(61\) −8.44034 4.87303i −1.08067 0.623928i −0.149596 0.988747i \(-0.547797\pi\)
−0.931078 + 0.364820i \(0.881131\pi\)
\(62\) 10.4927 + 18.1739i 1.33258 + 2.30809i
\(63\) −0.771119 2.76218i −0.0971518 0.348002i
\(64\) 12.8965 1.61206
\(65\) −6.77083 + 2.16741i −0.839818 + 0.268834i
\(66\) −7.90732 + 9.99919i −0.973324 + 1.23082i
\(67\) −9.08197 + 5.24348i −1.10954 + 0.640593i −0.938710 0.344708i \(-0.887978\pi\)
−0.170829 + 0.985301i \(0.554645\pi\)
\(68\) −3.20473 5.55075i −0.388630 0.673127i
\(69\) 7.12184 9.38236i 0.857369 1.12950i
\(70\) 4.18276i 0.499936i
\(71\) −2.05660 + 3.56214i −0.244074 + 0.422748i −0.961871 0.273504i \(-0.911817\pi\)
0.717797 + 0.696252i \(0.245151\pi\)
\(72\) 4.39743 + 4.30655i 0.518242 + 0.507532i
\(73\) −2.33785 −0.273624 −0.136812 0.990597i \(-0.543686\pi\)
−0.136812 + 0.990597i \(0.543686\pi\)
\(74\) 4.93387 8.54572i 0.573551 0.993420i
\(75\) 1.77582 0.746454i 0.205054 0.0861931i
\(76\) 7.91723 + 13.7130i 0.908169 + 1.57299i
\(77\) −1.63935 + 2.71374i −0.186821 + 0.309259i
\(78\) −4.61477 + 13.0675i −0.522520 + 1.47961i
\(79\) 8.16220i 0.918320i −0.888354 0.459160i \(-0.848151\pi\)
0.888354 0.459160i \(-0.151849\pi\)
\(80\) 1.27787 + 2.21333i 0.142870 + 0.247458i
\(81\) −0.187909 8.99804i −0.0208787 0.999782i
\(82\) −9.41421 + 16.3059i −1.03963 + 1.80068i
\(83\) 2.78415i 0.305601i 0.988257 + 0.152800i \(0.0488291\pi\)
−0.988257 + 0.152800i \(0.951171\pi\)
\(84\) 3.85692 + 2.92766i 0.420825 + 0.319434i
\(85\) 2.16067 3.74239i 0.234358 0.405919i
\(86\) −10.0190 −1.08037
\(87\) 9.54680 + 7.24665i 1.02352 + 0.776923i
\(88\) 0.134892 6.80325i 0.0143796 0.725228i
\(89\) −2.83303 4.90695i −0.300301 0.520136i 0.675903 0.736990i \(-0.263754\pi\)
−0.976204 + 0.216854i \(0.930420\pi\)
\(90\) −3.26490 + 12.7143i −0.344150 + 1.34020i
\(91\) −0.731283 + 3.36819i −0.0766593 + 0.353082i
\(92\) 19.8889i 2.07356i
\(93\) 6.34701 + 15.0996i 0.658154 + 1.56576i
\(94\) 16.7067 9.64559i 1.72316 0.994867i
\(95\) −5.33790 + 9.24552i −0.547657 + 0.948570i
\(96\) 11.9938 + 1.51537i 1.22411 + 0.154661i
\(97\) −16.4548 9.50019i −1.67073 0.964598i −0.967229 0.253907i \(-0.918284\pi\)
−0.703504 0.710691i \(-0.748382\pi\)
\(98\) −11.6966 6.75303i −1.18153 0.682159i
\(99\) −7.10134 + 6.96929i −0.713712 + 0.700440i
\(100\) −1.62628 + 2.81681i −0.162628 + 0.281681i
\(101\) 3.56582 + 6.17618i 0.354812 + 0.614553i 0.987086 0.160192i \(-0.0512115\pi\)
−0.632274 + 0.774745i \(0.717878\pi\)
\(102\) −3.26423 7.76564i −0.323207 0.768913i
\(103\) 2.25242 0.221937 0.110969 0.993824i \(-0.464605\pi\)
0.110969 + 0.993824i \(0.464605\pi\)
\(104\) −2.25524 7.04520i −0.221144 0.690839i
\(105\) −0.409225 + 3.23893i −0.0399363 + 0.316088i
\(106\) 0.429493 + 0.743903i 0.0417160 + 0.0722543i
\(107\) −0.896452 1.55270i −0.0866633 0.150105i 0.819435 0.573171i \(-0.194287\pi\)
−0.906099 + 0.423066i \(0.860954\pi\)
\(108\) 9.43859 + 11.9097i 0.908229 + 1.14601i
\(109\) −5.26402 −0.504201 −0.252101 0.967701i \(-0.581121\pi\)
−0.252101 + 0.967701i \(0.581121\pi\)
\(110\) 12.7093 7.00552i 1.21178 0.667950i
\(111\) 4.65664 6.13469i 0.441989 0.582279i
\(112\) 1.23905 0.117079
\(113\) 10.9465 + 6.31996i 1.02976 + 0.594531i 0.916916 0.399081i \(-0.130671\pi\)
0.112843 + 0.993613i \(0.464004\pi\)
\(114\) 8.06423 + 19.1849i 0.755284 + 1.79683i
\(115\) −11.6129 + 6.70469i −1.08291 + 0.625216i
\(116\) −20.2375 −1.87900
\(117\) −4.85194 + 9.66740i −0.448562 + 0.893752i
\(118\) 4.91574i 0.452531i
\(119\) −1.04752 1.81435i −0.0960258 0.166322i
\(120\) −2.71514 6.45935i −0.247857 0.589655i
\(121\) 10.9914 + 0.436037i 0.999214 + 0.0396397i
\(122\) 21.6278 1.95809
\(123\) −8.88523 + 11.7055i −0.801154 + 1.05545i
\(124\) −23.9510 13.8281i −2.15086 1.24180i
\(125\) −12.0517 −1.07794
\(126\) 4.54677 + 4.45281i 0.405058 + 0.396688i
\(127\) 8.60329 4.96711i 0.763419 0.440760i −0.0671031 0.997746i \(-0.521376\pi\)
0.830522 + 0.556986i \(0.188042\pi\)
\(128\) −12.6956 + 7.32980i −1.12214 + 0.647868i
\(129\) −7.75822 0.980216i −0.683073 0.0863032i
\(130\) 10.6075 11.6780i 0.930336 1.02423i
\(131\) 3.72037 0.325050 0.162525 0.986704i \(-0.448036\pi\)
0.162525 + 0.986704i \(0.448036\pi\)
\(132\) 2.43589 16.6226i 0.212017 1.44681i
\(133\) 2.58788 + 4.48233i 0.224397 + 0.388668i
\(134\) 11.6360 20.1541i 1.00519 1.74105i
\(135\) −3.77210 + 9.52590i −0.324650 + 0.819859i
\(136\) 3.89404 + 2.24822i 0.333911 + 0.192784i
\(137\) 4.60457 7.97534i 0.393395 0.681380i −0.599500 0.800375i \(-0.704634\pi\)
0.992895 + 0.118995i \(0.0379673\pi\)
\(138\) −3.27657 + 25.9334i −0.278920 + 2.20760i
\(139\) 1.52965 + 0.883145i 0.129743 + 0.0749073i 0.563467 0.826139i \(-0.309467\pi\)
−0.433724 + 0.901046i \(0.642801\pi\)
\(140\) −2.75618 4.77384i −0.232940 0.403463i
\(141\) 13.8805 5.83458i 1.16895 0.491360i
\(142\) 9.12773i 0.765982i
\(143\) 11.4590 3.41923i 0.958250 0.285930i
\(144\) 3.76632 + 0.967154i 0.313860 + 0.0805962i
\(145\) −6.82219 11.8164i −0.566552 0.981298i
\(146\) 4.49293 2.59399i 0.371837 0.214680i
\(147\) −8.39660 6.37358i −0.692540 0.525684i
\(148\) 13.0045i 1.06896i
\(149\) 4.66973 + 2.69607i 0.382559 + 0.220870i 0.678931 0.734202i \(-0.262444\pi\)
−0.296372 + 0.955073i \(0.595777\pi\)
\(150\) −2.58458 + 3.40494i −0.211030 + 0.278012i
\(151\) −19.7352 −1.60603 −0.803013 0.595962i \(-0.796771\pi\)
−0.803013 + 0.595962i \(0.796771\pi\)
\(152\) −9.62017 5.55421i −0.780299 0.450506i
\(153\) −1.76791 6.33270i −0.142927 0.511969i
\(154\) 0.139473 7.03429i 0.0112391 0.566839i
\(155\) 18.6462i 1.49770i
\(156\) −3.34379 17.9550i −0.267718 1.43755i
\(157\) 15.3245 1.22303 0.611513 0.791234i \(-0.290561\pi\)
0.611513 + 0.791234i \(0.290561\pi\)
\(158\) 9.05649 + 15.6863i 0.720496 + 1.24794i
\(159\) 0.259799 + 0.618064i 0.0206034 + 0.0490157i
\(160\) −11.9185 6.88113i −0.942238 0.544001i
\(161\) 6.50102i 0.512352i
\(162\) 10.3450 + 17.0841i 0.812782 + 1.34226i
\(163\) −7.54306 4.35499i −0.590818 0.341109i 0.174603 0.984639i \(-0.444136\pi\)
−0.765421 + 0.643530i \(0.777469\pi\)
\(164\) 24.8135i 1.93761i
\(165\) 10.5269 4.18132i 0.819516 0.325515i
\(166\) −3.08920 5.35065i −0.239768 0.415291i
\(167\) −10.6863 + 6.16976i −0.826934 + 0.477430i −0.852802 0.522235i \(-0.825098\pi\)
0.0258680 + 0.999665i \(0.491765\pi\)
\(168\) −3.37018 0.425808i −0.260015 0.0328518i
\(169\) 10.5834 7.54927i 0.814108 0.580713i
\(170\) 9.58961i 0.735489i
\(171\) 4.36758 + 15.6449i 0.333998 + 1.19639i
\(172\) 11.4348 6.60187i 0.871893 0.503388i
\(173\) −10.4906 + 18.1703i −0.797587 + 1.38146i 0.123597 + 0.992332i \(0.460557\pi\)
−0.921184 + 0.389128i \(0.872776\pi\)
\(174\) −26.3879 3.33399i −2.00046 0.252749i
\(175\) −0.531577 + 0.920719i −0.0401835 + 0.0695998i
\(176\) −2.07523 3.76485i −0.156426 0.283786i
\(177\) −0.480937 + 3.80652i −0.0361494 + 0.286116i
\(178\) 10.8892 + 6.28686i 0.816177 + 0.471220i
\(179\) 1.78408 1.03004i 0.133348 0.0769887i −0.431842 0.901949i \(-0.642136\pi\)
0.565190 + 0.824961i \(0.308803\pi\)
\(180\) −4.65163 16.6623i −0.346712 1.24194i
\(181\) −1.33526 −0.0992493 −0.0496246 0.998768i \(-0.515803\pi\)
−0.0496246 + 0.998768i \(0.515803\pi\)
\(182\) −2.33183 7.28446i −0.172846 0.539960i
\(183\) 16.7475 + 2.11598i 1.23801 + 0.156417i
\(184\) −6.97638 12.0834i −0.514305 0.890803i
\(185\) −7.59311 + 4.38389i −0.558257 + 0.322310i
\(186\) −28.9518 21.9763i −2.12285 1.61138i
\(187\) −3.75846 + 6.22165i −0.274846 + 0.454972i
\(188\) −12.7117 + 22.0173i −0.927094 + 1.60577i
\(189\) 3.08516 + 3.89288i 0.224412 + 0.283166i
\(190\) 23.6910i 1.71873i
\(191\) 7.90490 + 4.56389i 0.571978 + 0.330232i 0.757939 0.652325i \(-0.226206\pi\)
−0.185961 + 0.982557i \(0.559540\pi\)
\(192\) −20.5921 + 8.65575i −1.48611 + 0.624675i
\(193\) 6.32294 + 10.9516i 0.455135 + 0.788317i 0.998696 0.0510529i \(-0.0162577\pi\)
−0.543561 + 0.839370i \(0.682924\pi\)
\(194\) 42.1643 3.02722
\(195\) 9.35645 8.00514i 0.670030 0.573260i
\(196\) 17.7993 1.27138
\(197\) 17.8039 10.2791i 1.26847 0.732353i 0.293774 0.955875i \(-0.405089\pi\)
0.974699 + 0.223522i \(0.0717554\pi\)
\(198\) 5.91464 21.2731i 0.420335 1.51182i
\(199\) −3.35659 + 5.81378i −0.237942 + 0.412128i −0.960124 0.279576i \(-0.909806\pi\)
0.722181 + 0.691704i \(0.243140\pi\)
\(200\) 2.28179i 0.161347i
\(201\) 10.9821 14.4679i 0.774620 1.02049i
\(202\) −13.7057 7.91301i −0.964332 0.556757i
\(203\) −6.61496 −0.464279
\(204\) 8.84257 + 6.71210i 0.619104 + 0.469941i
\(205\) 14.4882 8.36479i 1.01190 0.584222i
\(206\) −4.32875 + 2.49920i −0.301598 + 0.174128i
\(207\) −5.07444 + 19.7610i −0.352698 + 1.37349i
\(208\) −3.45936 3.14223i −0.239864 0.217874i
\(209\) 9.28522 15.3705i 0.642272 1.06320i
\(210\) −2.80735 6.67872i −0.193726 0.460875i
\(211\) 8.20832 4.73908i 0.565084 0.326251i −0.190099 0.981765i \(-0.560881\pi\)
0.755184 + 0.655513i \(0.227548\pi\)
\(212\) −0.980371 0.566018i −0.0673322 0.0388743i
\(213\) 0.893022 7.06809i 0.0611888 0.484298i
\(214\) 3.44564 + 1.98934i 0.235539 + 0.135989i
\(215\) 7.70947 + 4.45107i 0.525782 + 0.303560i
\(216\) −9.91191 3.92495i −0.674420 0.267059i
\(217\) −7.82876 4.51994i −0.531451 0.306833i
\(218\) 10.1165 5.84077i 0.685176 0.395587i
\(219\) 3.73290 1.56910i 0.252246 0.106030i
\(220\) −9.88908 + 16.3701i −0.666721 + 1.10367i
\(221\) −1.67658 + 7.72208i −0.112779 + 0.519443i
\(222\) −2.14240 + 16.9566i −0.143788 + 1.13805i
\(223\) −0.307378 + 0.177465i −0.0205835 + 0.0118839i −0.510256 0.860022i \(-0.670450\pi\)
0.489673 + 0.871906i \(0.337116\pi\)
\(224\) −5.77821 + 3.33605i −0.386073 + 0.222899i
\(225\) −2.33450 + 2.38376i −0.155633 + 0.158918i
\(226\) −28.0496 −1.86583
\(227\) −18.7464 10.8232i −1.24424 0.718362i −0.274285 0.961648i \(-0.588441\pi\)
−0.969954 + 0.243287i \(0.921774\pi\)
\(228\) −21.8454 16.5821i −1.44675 1.09818i
\(229\) 5.36210i 0.354338i 0.984180 + 0.177169i \(0.0566938\pi\)
−0.984180 + 0.177169i \(0.943306\pi\)
\(230\) 14.8786 25.7704i 0.981064 1.69925i
\(231\) 0.796209 5.43338i 0.0523867 0.357490i
\(232\) 12.2952 7.09864i 0.807220 0.466049i
\(233\) −1.04207 −0.0682685 −0.0341343 0.999417i \(-0.510867\pi\)
−0.0341343 + 0.999417i \(0.510867\pi\)
\(234\) −1.40204 23.9626i −0.0916542 1.56648i
\(235\) −17.1408 −1.11814
\(236\) −3.23917 5.61040i −0.210852 0.365206i
\(237\) 5.47824 + 13.0328i 0.355850 + 0.846571i
\(238\) 4.02628 + 2.32458i 0.260985 + 0.150680i
\(239\) 12.0549i 0.779766i 0.920864 + 0.389883i \(0.127484\pi\)
−0.920864 + 0.389883i \(0.872516\pi\)
\(240\) −3.52593 2.67642i −0.227598 0.172762i
\(241\) −6.92345 + 11.9918i −0.445979 + 0.772458i −0.998120 0.0612929i \(-0.980478\pi\)
0.552141 + 0.833751i \(0.313811\pi\)
\(242\) −21.6072 + 11.3576i −1.38897 + 0.730096i
\(243\) 6.33926 + 14.2413i 0.406664 + 0.913578i
\(244\) −24.6840 + 14.2513i −1.58023 + 0.912349i
\(245\) 6.00025 + 10.3927i 0.383342 + 0.663968i
\(246\) 4.08785 32.3546i 0.260632 2.06285i
\(247\) 4.14196 19.0773i 0.263546 1.21386i
\(248\) 19.4017 1.23201
\(249\) −1.86864 4.44553i −0.118420 0.281724i
\(250\) 23.1613 13.3722i 1.46485 0.845730i
\(251\) 7.76115 + 4.48090i 0.489879 + 0.282832i 0.724524 0.689249i \(-0.242059\pi\)
−0.234645 + 0.972081i \(0.575393\pi\)
\(252\) −8.12340 2.08601i −0.511726 0.131406i
\(253\) 19.7533 10.8883i 1.24188 0.684540i
\(254\) −11.0227 + 19.0918i −0.691623 + 1.19793i
\(255\) −0.938210 + 7.42574i −0.0587530 + 0.465018i
\(256\) 3.36927 5.83575i 0.210580 0.364735i
\(257\) −7.99043 + 4.61328i −0.498430 + 0.287768i −0.728065 0.685508i \(-0.759580\pi\)
0.229635 + 0.973277i \(0.426247\pi\)
\(258\) 15.9975 6.72444i 0.995962 0.418645i
\(259\) 4.25072i 0.264127i
\(260\) −4.41133 + 20.3180i −0.273579 + 1.26007i
\(261\) −20.1074 5.16337i −1.24461 0.319605i
\(262\) −7.14988 + 4.12799i −0.441721 + 0.255028i
\(263\) −5.58664 9.67634i −0.344487 0.596669i 0.640774 0.767730i \(-0.278614\pi\)
−0.985260 + 0.171061i \(0.945280\pi\)
\(264\) 4.35076 + 10.9534i 0.267771 + 0.674138i
\(265\) 0.763233i 0.0468850i
\(266\) −9.94688 5.74283i −0.609882 0.352116i
\(267\) 7.81698 + 5.93361i 0.478391 + 0.363131i
\(268\) 30.6695i 1.87343i
\(269\) −15.4577 8.92453i −0.942475 0.544138i −0.0517394 0.998661i \(-0.516477\pi\)
−0.890735 + 0.454523i \(0.849810\pi\)
\(270\) −3.32030 22.4925i −0.202067 1.36885i
\(271\) −0.989728 1.71426i −0.0601217 0.104134i 0.834398 0.551162i \(-0.185816\pi\)
−0.894520 + 0.447029i \(0.852482\pi\)
\(272\) 2.84071 0.172243
\(273\) −1.09297 5.86888i −0.0661498 0.355201i
\(274\) 20.4363i 1.23460i
\(275\) 3.68791 + 0.0731227i 0.222390 + 0.00440946i
\(276\) −13.3489 31.7571i −0.803508 1.91156i
\(277\) −19.8682 11.4709i −1.19377 0.689222i −0.234608 0.972090i \(-0.575381\pi\)
−0.959159 + 0.282869i \(0.908714\pi\)
\(278\) −3.91962 −0.235083
\(279\) −20.2688 19.8500i −1.21346 1.18839i
\(280\) 3.34901 + 1.93355i 0.200142 + 0.115552i
\(281\) 16.6033i 0.990469i 0.868759 + 0.495234i \(0.164918\pi\)
−0.868759 + 0.495234i \(0.835082\pi\)
\(282\) −20.2021 + 26.6144i −1.20302 + 1.58486i
\(283\) −2.54009 + 1.46652i −0.150993 + 0.0871758i −0.573593 0.819140i \(-0.694451\pi\)
0.422600 + 0.906316i \(0.361118\pi\)
\(284\) 6.01460 + 10.4176i 0.356901 + 0.618171i
\(285\) 2.31783 18.3452i 0.137297 1.08668i
\(286\) −18.2283 + 19.2857i −1.07786 + 1.14038i
\(287\) 8.11069i 0.478759i
\(288\) −20.1679 + 5.63029i −1.18841 + 0.331768i
\(289\) 6.09841 + 10.5628i 0.358730 + 0.621339i
\(290\) 26.2221 + 15.1393i 1.53981 + 0.889012i
\(291\) 32.6501 + 4.12519i 1.91398 + 0.241823i
\(292\) −3.41856 + 5.92112i −0.200056 + 0.346507i
\(293\) 2.52360 + 1.45700i 0.147430 + 0.0851190i 0.571901 0.820323i \(-0.306206\pi\)
−0.424470 + 0.905442i \(0.639540\pi\)
\(294\) 23.2087 + 2.93231i 1.35356 + 0.171016i
\(295\) 2.18389 3.78261i 0.127151 0.220232i
\(296\) −4.56153 7.90080i −0.265134 0.459225i
\(297\) 6.66130 15.8942i 0.386528 0.922278i
\(298\) −11.9658 −0.693163
\(299\) 16.4865 18.1505i 0.953442 1.04967i
\(300\) 0.706168 5.58918i 0.0407706 0.322691i
\(301\) 3.73764 2.15793i 0.215434 0.124381i
\(302\) 37.9275 21.8974i 2.18248 1.26006i
\(303\) −9.83890 7.46838i −0.565230 0.429047i
\(304\) −7.01793 −0.402506
\(305\) −16.6423 9.60844i −0.952936 0.550178i
\(306\) 10.4241 + 10.2087i 0.595909 + 0.583594i
\(307\) 19.3061 1.10186 0.550928 0.834553i \(-0.314274\pi\)
0.550928 + 0.834553i \(0.314274\pi\)
\(308\) 4.47597 + 8.12023i 0.255042 + 0.462693i
\(309\) −3.59649 + 1.51176i −0.204597 + 0.0860009i
\(310\) 20.6891 + 35.8346i 1.17506 + 2.03527i
\(311\) 34.2031i 1.93948i 0.244138 + 0.969741i \(0.421495\pi\)
−0.244138 + 0.969741i \(0.578505\pi\)
\(312\) 8.32953 + 9.73560i 0.471567 + 0.551170i
\(313\) 32.2284 1.82166 0.910828 0.412786i \(-0.135444\pi\)
0.910828 + 0.412786i \(0.135444\pi\)
\(314\) −29.4509 + 17.0035i −1.66201 + 0.959562i
\(315\) −1.52046 5.44635i −0.0856682 0.306867i
\(316\) −20.6726 11.9353i −1.16292 0.671414i
\(317\) −16.4465 −0.923728 −0.461864 0.886951i \(-0.652819\pi\)
−0.461864 + 0.886951i \(0.652819\pi\)
\(318\) −1.18507 0.899546i −0.0664553 0.0504440i
\(319\) 11.0791 + 20.0995i 0.620310 + 1.12536i
\(320\) 25.4288 1.42151
\(321\) 2.47351 + 1.87756i 0.138058 + 0.104795i
\(322\) −7.21330 12.4938i −0.401982 0.696253i
\(323\) 5.93310 + 10.2764i 0.330126 + 0.571795i
\(324\) −23.0643 12.6816i −1.28135 0.704534i
\(325\) 3.81907 1.22252i 0.211844 0.0678133i
\(326\) 19.3286 1.07051
\(327\) 8.40519 3.53306i 0.464808 0.195379i
\(328\) 8.70375 + 15.0753i 0.480584 + 0.832396i
\(329\) −4.15502 + 7.19670i −0.229074 + 0.396767i
\(330\) −15.5913 + 19.7160i −0.858275 + 1.08533i
\(331\) 18.1116 + 10.4568i 0.995506 + 0.574756i 0.906916 0.421313i \(-0.138430\pi\)
0.0885904 + 0.996068i \(0.471764\pi\)
\(332\) 7.05148 + 4.07117i 0.387000 + 0.223435i
\(333\) −3.31794 + 12.9208i −0.181822 + 0.708057i
\(334\) 13.6915 23.7144i 0.749165 1.29759i
\(335\) −17.9075 + 10.3389i −0.978389 + 0.564873i
\(336\) −1.97842 + 0.831615i −0.107932 + 0.0453683i
\(337\) 24.0626i 1.31077i −0.755293 0.655387i \(-0.772505\pi\)
0.755293 0.655387i \(-0.227495\pi\)
\(338\) −11.9630 + 26.2513i −0.650703 + 1.42788i
\(339\) −21.7203 2.74426i −1.17968 0.149048i
\(340\) −6.31895 10.9447i −0.342693 0.593562i
\(341\) −0.621753 + 31.3579i −0.0336698 + 1.69812i
\(342\) −25.7527 25.2205i −1.39255 1.36377i
\(343\) 12.5095 0.675450
\(344\) −4.63143 + 8.02188i −0.249710 + 0.432511i
\(345\) 14.0425 18.4998i 0.756025 0.995994i
\(346\) 46.5600i 2.50308i
\(347\) −3.14172 + 5.44163i −0.168657 + 0.292122i −0.937948 0.346777i \(-0.887276\pi\)
0.769291 + 0.638898i \(0.220610\pi\)
\(348\) 32.3137 13.5828i 1.73220 0.728116i
\(349\) 7.28946 + 12.6257i 0.390196 + 0.675839i 0.992475 0.122446i \(-0.0390740\pi\)
−0.602279 + 0.798285i \(0.705741\pi\)
\(350\) 2.35928i 0.126109i
\(351\) 1.25873 18.6927i 0.0671860 0.997740i
\(352\) 19.8142 + 11.9696i 1.05610 + 0.637984i
\(353\) 9.02808 + 15.6371i 0.480516 + 0.832278i 0.999750 0.0223539i \(-0.00711608\pi\)
−0.519234 + 0.854632i \(0.673783\pi\)
\(354\) −3.29931 7.84909i −0.175356 0.417174i
\(355\) −4.05512 + 7.02368i −0.215224 + 0.372778i
\(356\) −16.5706 −0.878240
\(357\) 2.89034 + 2.19396i 0.152973 + 0.116117i
\(358\) −2.28579 + 3.95910i −0.120808 + 0.209245i
\(359\) 18.9379i 0.999504i −0.866169 0.499752i \(-0.833425\pi\)
0.866169 0.499752i \(-0.166575\pi\)
\(360\) 8.67066 + 8.49148i 0.456984 + 0.447540i
\(361\) −5.15763 8.93327i −0.271454 0.470172i
\(362\) 2.56614 1.48156i 0.134873 0.0778691i
\(363\) −17.8428 + 6.68085i −0.936505 + 0.350654i
\(364\) 7.46135 + 6.77732i 0.391081 + 0.355228i
\(365\) −4.60967 −0.241281
\(366\) −34.5336 + 14.5159i −1.80510 + 0.758760i
\(367\) 2.20927 + 3.82658i 0.115323 + 0.199746i 0.917909 0.396791i \(-0.129876\pi\)
−0.802586 + 0.596537i \(0.796543\pi\)
\(368\) −7.63393 4.40745i −0.397946 0.229754i
\(369\) 6.33089 24.6539i 0.329573 1.28343i
\(370\) 9.72841 16.8501i 0.505756 0.875995i
\(371\) −0.320450 0.185012i −0.0166370 0.00960535i
\(372\) 47.5241 + 6.00446i 2.46401 + 0.311317i
\(373\) 29.9388 + 17.2852i 1.55017 + 0.894993i 0.998127 + 0.0611798i \(0.0194863\pi\)
0.552047 + 0.833813i \(0.313847\pi\)
\(374\) 0.319764 16.1272i 0.0165346 0.833916i
\(375\) 19.2433 8.08877i 0.993718 0.417702i
\(376\) 17.8353i 0.919787i
\(377\) 18.4686 + 16.7755i 0.951182 + 0.863982i
\(378\) −10.2485 4.05825i −0.527127 0.208734i
\(379\) −12.3499 + 7.13023i −0.634373 + 0.366255i −0.782444 0.622721i \(-0.786027\pi\)
0.148071 + 0.988977i \(0.452694\pi\)
\(380\) 15.6109 + 27.0388i 0.800821 + 1.38706i
\(381\) −10.4033 + 13.7054i −0.532977 + 0.702149i
\(382\) −20.2557 −1.03637
\(383\) 17.9515 31.0929i 0.917277 1.58877i 0.113744 0.993510i \(-0.463716\pi\)
0.803533 0.595260i \(-0.202951\pi\)
\(384\) 15.3518 20.2246i 0.783418 1.03208i
\(385\) −3.23241 + 5.35084i −0.164739 + 0.272704i
\(386\) −24.3031 14.0314i −1.23700 0.714180i
\(387\) 13.0456 3.64196i 0.663146 0.185131i
\(388\) −48.1226 + 27.7836i −2.44306 + 1.41050i
\(389\) 19.2009i 0.973524i 0.873535 + 0.486762i \(0.161822\pi\)
−0.873535 + 0.486762i \(0.838178\pi\)
\(390\) −9.09922 + 25.7660i −0.460757 + 1.30471i
\(391\) 14.9046i 0.753756i
\(392\) −10.8139 + 6.24340i −0.546184 + 0.315339i
\(393\) −5.94040 + 2.49700i −0.299654 + 0.125957i
\(394\) −22.8106 + 39.5091i −1.14918 + 1.99044i
\(395\) 16.0939i 0.809772i
\(396\) 7.26720 + 28.1767i 0.365190 + 1.41593i
\(397\) 7.80104 + 4.50393i 0.391523 + 0.226046i 0.682820 0.730587i \(-0.260753\pi\)
−0.291297 + 0.956633i \(0.594087\pi\)
\(398\) 14.8974i 0.746740i
\(399\) −7.14054 5.42014i −0.357474 0.271347i
\(400\) −0.720779 1.24843i −0.0360390 0.0624213i
\(401\) −15.8865 27.5163i −0.793336 1.37410i −0.923890 0.382658i \(-0.875009\pi\)
0.130554 0.991441i \(-0.458324\pi\)
\(402\) −5.05258 + 39.9902i −0.252000 + 1.99453i
\(403\) 10.3949 + 32.4731i 0.517809 + 1.61760i
\(404\) 20.8567 1.03766
\(405\) −0.370510 17.7420i −0.0184108 0.881605i
\(406\) 12.7128 7.33972i 0.630924 0.364264i
\(407\) 12.9158 7.11934i 0.640211 0.352892i
\(408\) −7.72665 0.976228i −0.382526 0.0483305i
\(409\) −4.32366 + 7.48880i −0.213791 + 0.370297i −0.952898 0.303291i \(-0.901915\pi\)
0.739107 + 0.673588i \(0.235248\pi\)
\(410\) −18.5625 + 32.1513i −0.916739 + 1.58784i
\(411\) −1.99940 + 15.8249i −0.0986233 + 0.780584i
\(412\) 3.29364 5.70475i 0.162266 0.281053i
\(413\) −1.05877 1.83385i −0.0520989 0.0902379i
\(414\) −12.1740 43.6076i −0.598318 2.14320i
\(415\) 5.48968i 0.269478i
\(416\) 24.5927 + 5.33943i 1.20575 + 0.261787i
\(417\) −3.03517 0.383481i −0.148633 0.0187791i
\(418\) −0.789972 + 39.8419i −0.0386388 + 1.94873i
\(419\) −4.33374 + 2.50209i −0.211717 + 0.122235i −0.602109 0.798414i \(-0.705673\pi\)
0.390392 + 0.920649i \(0.372339\pi\)
\(420\) 7.60492 + 5.77264i 0.371082 + 0.281676i
\(421\) 6.12367i 0.298450i 0.988803 + 0.149225i \(0.0476778\pi\)
−0.988803 + 0.149225i \(0.952322\pi\)
\(422\) −10.5166 + 18.2153i −0.511941 + 0.886708i
\(423\) −18.2474 + 18.6324i −0.887219 + 0.905940i
\(424\) 0.794161 0.0385679
\(425\) −1.21872 + 2.11089i −0.0591167 + 0.102393i
\(426\) 6.12627 + 14.5745i 0.296819 + 0.706136i
\(427\) −8.06838 + 4.65828i −0.390456 + 0.225430i
\(428\) −5.24341 −0.253450
\(429\) −16.0020 + 13.1505i −0.772583 + 0.634913i
\(430\) −19.7550 −0.952670
\(431\) −23.9044 + 13.8012i −1.15144 + 0.664782i −0.949237 0.314563i \(-0.898142\pi\)
−0.202199 + 0.979344i \(0.564809\pi\)
\(432\) −6.66290 + 0.983566i −0.320569 + 0.0473218i
\(433\) −5.09682 + 8.82795i −0.244938 + 0.424244i −0.962114 0.272647i \(-0.912101\pi\)
0.717176 + 0.696892i \(0.245434\pi\)
\(434\) 20.0606 0.962942
\(435\) 18.8240 + 14.2887i 0.902541 + 0.685089i
\(436\) −7.69740 + 13.3323i −0.368638 + 0.638501i
\(437\) 36.8215i 1.76141i
\(438\) −5.43295 + 7.15742i −0.259597 + 0.341995i
\(439\) −29.8701 + 17.2455i −1.42562 + 0.823083i −0.996771 0.0802924i \(-0.974415\pi\)
−0.428850 + 0.903376i \(0.641081\pi\)
\(440\) 0.265975 13.4144i 0.0126799 0.639504i
\(441\) 17.6848 + 4.54129i 0.842134 + 0.216252i
\(442\) −5.34606 16.7007i −0.254286 0.794372i
\(443\) 31.8029i 1.51100i −0.655148 0.755501i \(-0.727394\pi\)
0.655148 0.755501i \(-0.272606\pi\)
\(444\) −8.72821 20.7645i −0.414223 0.985441i
\(445\) −5.58606 9.67533i −0.264804 0.458655i
\(446\) 0.393817 0.682111i 0.0186478 0.0322989i
\(447\) −9.26579 1.17069i −0.438257 0.0553718i
\(448\) 6.16408 10.6765i 0.291225 0.504417i
\(449\) 6.75458 11.6993i 0.318768 0.552123i −0.661463 0.749978i \(-0.730064\pi\)
0.980231 + 0.197855i \(0.0633975\pi\)
\(450\) 1.84156 7.17145i 0.0868119 0.338065i
\(451\) −24.6443 + 13.5842i −1.16045 + 0.639657i
\(452\) 32.0134 18.4829i 1.50578 0.869364i
\(453\) 31.5116 13.2457i 1.48055 0.622336i
\(454\) 48.0362 2.25445
\(455\) −1.44191 + 6.64125i −0.0675980 + 0.311347i
\(456\) 19.0886 + 2.41176i 0.893905 + 0.112941i
\(457\) −12.3507 21.3920i −0.577741 1.00068i −0.995738 0.0922285i \(-0.970601\pi\)
0.417997 0.908449i \(-0.362732\pi\)
\(458\) −5.94960 10.3050i −0.278006 0.481521i
\(459\) 7.07319 + 8.92502i 0.330148 + 0.416584i
\(460\) 39.2162i 1.82846i
\(461\) 2.65199 + 1.53112i 0.123515 + 0.0713116i 0.560485 0.828165i \(-0.310615\pi\)
−0.436969 + 0.899476i \(0.643948\pi\)
\(462\) 4.49851 + 11.3254i 0.209290 + 0.526907i
\(463\) 15.9359i 0.740602i −0.928912 0.370301i \(-0.879255\pi\)
0.928912 0.370301i \(-0.120745\pi\)
\(464\) 4.48469 7.76772i 0.208197 0.360607i
\(465\) 12.5148 + 29.7728i 0.580358 + 1.38068i
\(466\) 2.00268 1.15625i 0.0927724 0.0535622i
\(467\) 38.5307i 1.78299i −0.453032 0.891494i \(-0.649658\pi\)
0.453032 0.891494i \(-0.350342\pi\)
\(468\) 17.3900 + 26.4249i 0.803853 + 1.22149i
\(469\) 10.0248i 0.462903i
\(470\) 32.9415 19.0188i 1.51948 0.877271i
\(471\) −24.4690 + 10.2853i −1.12747 + 0.473924i
\(472\) 3.93588 + 2.27238i 0.181164 + 0.104595i
\(473\) −12.8169 7.74258i −0.589320 0.356004i
\(474\) −24.9889 18.9683i −1.14778 0.871241i
\(475\) 3.01083 5.21492i 0.138146 0.239277i
\(476\) −6.12700 −0.280831
\(477\) −0.829653 0.812508i −0.0379872 0.0372022i
\(478\) −13.3757 23.1673i −0.611789 1.05965i
\(479\) 35.0623 20.2432i 1.60204 0.924938i 0.610960 0.791662i \(-0.290784\pi\)
0.991079 0.133276i \(-0.0425497\pi\)
\(480\) 23.6489 + 2.98794i 1.07942 + 0.136380i
\(481\) 10.7798 11.8678i 0.491516 0.541124i
\(482\) 30.7281i 1.39963i
\(483\) −4.36330 10.3803i −0.198537 0.472322i
\(484\) 17.1767 27.2004i 0.780757 1.23638i
\(485\) −32.4449 18.7321i −1.47325 0.850580i
\(486\) −27.9845 20.3354i −1.26940 0.922431i
\(487\) 23.3931 + 13.5060i 1.06004 + 0.612015i 0.925444 0.378886i \(-0.123693\pi\)
0.134597 + 0.990900i \(0.457026\pi\)
\(488\) 9.99779 17.3167i 0.452579 0.783890i
\(489\) 14.9671 + 1.89103i 0.676837 + 0.0855154i
\(490\) −23.0628 13.3153i −1.04187 0.601526i
\(491\) 7.35437 + 12.7381i 0.331898 + 0.574864i 0.982884 0.184226i \(-0.0589777\pi\)
−0.650986 + 0.759090i \(0.725644\pi\)
\(492\) 16.6541 + 39.6203i 0.750825 + 1.78622i
\(493\) −15.1658 −0.683032
\(494\) 13.2074 + 41.2589i 0.594227 + 1.85633i
\(495\) −14.0021 + 13.7418i −0.629349 + 0.617646i
\(496\) 10.6152 6.12870i 0.476637 0.275187i
\(497\) 1.96597 + 3.40516i 0.0881859 + 0.152742i
\(498\) 8.52380 + 6.47013i 0.381960 + 0.289933i
\(499\) 34.8438i 1.55982i −0.625889 0.779912i \(-0.715264\pi\)
0.625889 0.779912i \(-0.284736\pi\)
\(500\) −17.6228 + 30.5236i −0.788117 + 1.36506i
\(501\) 12.9222 17.0238i 0.577320 0.760566i
\(502\) −19.8874 −0.887618
\(503\) −3.73934 + 6.47672i −0.166729 + 0.288783i −0.937268 0.348610i \(-0.886654\pi\)
0.770539 + 0.637393i \(0.219987\pi\)
\(504\) 5.66704 1.58207i 0.252430 0.0704711i
\(505\) 7.03093 + 12.1779i 0.312872 + 0.541911i
\(506\) −25.8811 + 42.8429i −1.15056 + 1.90460i
\(507\) −11.8319 + 19.1574i −0.525474 + 0.850809i
\(508\) 29.0530i 1.28902i
\(509\) −10.6676 18.4769i −0.472835 0.818974i 0.526682 0.850062i \(-0.323436\pi\)
−0.999517 + 0.0310888i \(0.990103\pi\)
\(510\) −6.43627 15.3120i −0.285003 0.678025i
\(511\) −1.11741 + 1.93541i −0.0494314 + 0.0856176i
\(512\) 14.3655i 0.634870i
\(513\) −17.4742 22.0491i −0.771505 0.973493i
\(514\) 10.2375 17.7318i 0.451555 0.782116i
\(515\) 4.44123 0.195704
\(516\) −13.8272 + 18.2161i −0.608708 + 0.801917i
\(517\) 28.8262 + 0.571556i 1.26777 + 0.0251370i
\(518\) −4.71645 8.16912i −0.207229 0.358931i
\(519\) 4.55525 36.0539i 0.199953 1.58259i
\(520\) −4.44678 13.8914i −0.195004 0.609180i
\(521\) 0.873932i 0.0382877i 0.999817 + 0.0191438i \(0.00609404\pi\)
−0.999817 + 0.0191438i \(0.993906\pi\)
\(522\) 44.3718 12.3873i 1.94210 0.542178i
\(523\) 0.174774 0.100906i 0.00764234 0.00441231i −0.496174 0.868223i \(-0.665262\pi\)
0.503816 + 0.863811i \(0.331929\pi\)
\(524\) 5.44017 9.42265i 0.237655 0.411630i
\(525\) 0.230823 1.82691i 0.0100739 0.0797331i
\(526\) 21.4730 + 12.3975i 0.936269 + 0.540555i
\(527\) −17.9486 10.3626i −0.781854 0.451403i
\(528\) 5.84043 + 4.61859i 0.254172 + 0.200998i
\(529\) 11.6249 20.1349i 0.505430 0.875430i
\(530\) 0.846856 + 1.46680i 0.0367851 + 0.0637136i
\(531\) −1.78690 6.40076i −0.0775450 0.277769i
\(532\) 15.1367 0.656258
\(533\) −20.5687 + 22.6446i −0.890928 + 0.980848i
\(534\) −21.6066 2.72989i −0.935007 0.118134i
\(535\) −1.76759 3.06155i −0.0764194 0.132362i
\(536\) −10.7578 18.6331i −0.464667 0.804827i
\(537\) −2.15735 + 2.84211i −0.0930966 + 0.122646i
\(538\) 39.6093 1.70768
\(539\) −9.74429 17.6779i −0.419716 0.761441i
\(540\) 18.6106 + 23.4831i 0.800874 + 1.01055i
\(541\) −21.2779 −0.914810 −0.457405 0.889259i \(-0.651221\pi\)
−0.457405 + 0.889259i \(0.651221\pi\)
\(542\) 3.80416 + 2.19633i 0.163403 + 0.0943407i
\(543\) 2.13205 0.896190i 0.0914949 0.0384592i
\(544\) −13.2474 + 7.64840i −0.567978 + 0.327922i
\(545\) −10.3794 −0.444604
\(546\) 8.61241 + 10.0662i 0.368577 + 0.430795i
\(547\) 44.8648i 1.91828i −0.282933 0.959140i \(-0.591307\pi\)
0.282933 0.959140i \(-0.408693\pi\)
\(548\) −13.4662 23.3242i −0.575248 0.996359i
\(549\) −28.1614 + 7.86183i −1.20190 + 0.335535i
\(550\) −7.16865 + 3.95145i −0.305672 + 0.168490i
\(551\) 37.4668 1.59614
\(552\) 19.2494 + 14.6116i 0.819309 + 0.621910i
\(553\) −6.75717 3.90125i −0.287344 0.165898i
\(554\) 50.9110 2.16300
\(555\) 9.18177 12.0961i 0.389745 0.513453i
\(556\) 4.47352 2.58279i 0.189719 0.109535i
\(557\) −36.5225 + 21.0863i −1.54751 + 0.893453i −0.549175 + 0.835707i \(0.685058\pi\)
−0.998331 + 0.0577463i \(0.981609\pi\)
\(558\) 60.9779 + 15.6585i 2.58140 + 0.662879i
\(559\) −15.9078 3.45381i −0.672828 0.146081i
\(560\) 2.44311 0.103240
\(561\) 1.82543 12.4568i 0.0770697 0.525928i
\(562\) −18.4224 31.9086i −0.777102 1.34598i
\(563\) −5.60831 + 9.71388i −0.236362 + 0.409391i −0.959668 0.281137i \(-0.909289\pi\)
0.723305 + 0.690528i \(0.242622\pi\)
\(564\) 5.51969 43.6872i 0.232421 1.83956i
\(565\) 21.5838 + 12.4614i 0.908039 + 0.524256i
\(566\) 3.25441 5.63680i 0.136793 0.236932i
\(567\) −7.53894 4.14519i −0.316606 0.174082i
\(568\) −7.30830 4.21945i −0.306649 0.177044i
\(569\) −17.6304 30.5367i −0.739103 1.28016i −0.952900 0.303286i \(-0.901916\pi\)
0.213797 0.976878i \(-0.431417\pi\)
\(570\) 15.9007 + 37.8280i 0.666007 + 1.58444i
\(571\) 10.3174i 0.431769i −0.976419 0.215884i \(-0.930737\pi\)
0.976419 0.215884i \(-0.0692634\pi\)
\(572\) 8.09617 34.0223i 0.338518 1.42254i
\(573\) −15.6851 1.98174i −0.655254 0.0827885i
\(574\) 8.99934 + 15.5873i 0.375625 + 0.650602i
\(575\) 6.55021 3.78177i 0.273163 0.157711i
\(576\) 27.0705 27.6417i 1.12794 1.15174i
\(577\) 39.9664i 1.66382i −0.554907 0.831912i \(-0.687246\pi\)
0.554907 0.831912i \(-0.312754\pi\)
\(578\) −23.4401 13.5332i −0.974980 0.562905i
\(579\) −17.4464 13.2430i −0.725048 0.550360i
\(580\) −39.9035 −1.65690
\(581\) 2.30489 + 1.33073i 0.0956230 + 0.0552080i
\(582\) −67.3248 + 28.2995i −2.79070 + 1.17305i
\(583\) −0.0254499 + 1.28355i −0.00105403 + 0.0531594i
\(584\) 4.79647i 0.198479i
\(585\) −9.56686 + 19.0618i −0.395541 + 0.788108i
\(586\) −6.46655 −0.267131
\(587\) 9.99810 + 17.3172i 0.412666 + 0.714758i 0.995180 0.0980623i \(-0.0312644\pi\)
−0.582515 + 0.812820i \(0.697931\pi\)
\(588\) −28.4205 + 11.9464i −1.17204 + 0.492660i
\(589\) 44.3418 + 25.6007i 1.82707 + 1.05486i
\(590\) 9.69266i 0.399041i
\(591\) −21.5289 + 28.3623i −0.885579 + 1.16667i
\(592\) −4.99147 2.88183i −0.205148 0.118442i
\(593\) 44.2238i 1.81605i 0.418913 + 0.908026i \(0.362411\pi\)
−0.418913 + 0.908026i \(0.637589\pi\)
\(594\) 4.83385 + 37.9371i 0.198335 + 1.55658i
\(595\) −2.06545 3.57747i −0.0846753 0.146662i
\(596\) 13.6568 7.88474i 0.559403 0.322971i
\(597\) 1.45750 11.5359i 0.0596517 0.472131i
\(598\) −11.5451 + 53.1749i −0.472113 + 2.17448i
\(599\) 9.30853i 0.380336i −0.981752 0.190168i \(-0.939097\pi\)
0.981752 0.190168i \(-0.0609033\pi\)
\(600\) 1.53147 + 3.64338i 0.0625220 + 0.148741i
\(601\) 11.2432 6.49125i 0.458619 0.264784i −0.252844 0.967507i \(-0.581366\pi\)
0.711463 + 0.702723i \(0.248033\pi\)
\(602\) −4.78872 + 8.29431i −0.195174 + 0.338051i
\(603\) −7.82497 + 30.4722i −0.318657 + 1.24092i
\(604\) −28.8581 + 49.9837i −1.17422 + 2.03381i
\(605\) 21.6723 + 0.859759i 0.881104 + 0.0349542i
\(606\) 27.1953 + 3.43600i 1.10473 + 0.139578i
\(607\) 23.9591 + 13.8328i 0.972470 + 0.561456i 0.899988 0.435914i \(-0.143575\pi\)
0.0724818 + 0.997370i \(0.476908\pi\)
\(608\) 32.7276 18.8953i 1.32728 0.766304i
\(609\) 10.5623 4.43977i 0.428005 0.179909i
\(610\) 42.6447 1.72664
\(611\) 29.8514 9.55571i 1.20766 0.386583i
\(612\) −18.6241 4.78249i −0.752835 0.193321i
\(613\) 0.701404 + 1.21487i 0.0283295 + 0.0490681i 0.879843 0.475265i \(-0.157648\pi\)
−0.851513 + 0.524333i \(0.824315\pi\)
\(614\) −37.1028 + 21.4213i −1.49735 + 0.864494i
\(615\) −17.5195 + 23.0804i −0.706455 + 0.930690i
\(616\) −5.56767 3.36339i −0.224328 0.135515i
\(617\) −12.0256 + 20.8289i −0.484132 + 0.838541i −0.999834 0.0182270i \(-0.994198\pi\)
0.515702 + 0.856768i \(0.327531\pi\)
\(618\) 5.23442 6.89587i 0.210559 0.277393i
\(619\) 27.0977i 1.08915i 0.838713 + 0.544574i \(0.183309\pi\)
−0.838713 + 0.544574i \(0.816691\pi\)
\(620\) −47.2255 27.2657i −1.89662 1.09502i
\(621\) −5.16055 34.9587i −0.207086 1.40285i
\(622\) −37.9506 65.7323i −1.52168 2.63563i
\(623\) −5.41637 −0.217002
\(624\) 7.63262 + 2.69544i 0.305549 + 0.107904i
\(625\) −18.2023 −0.728090
\(626\) −61.9372 + 35.7595i −2.47551 + 1.42924i
\(627\) −4.50970 + 30.7744i −0.180100 + 1.22901i
\(628\) 22.4085 38.8126i 0.894195 1.54879i
\(629\) 9.74541i 0.388575i
\(630\) 8.96513 + 8.77986i 0.357179 + 0.349798i
\(631\) −28.2667 16.3198i −1.12528 0.649681i −0.182537 0.983199i \(-0.558431\pi\)
−0.942744 + 0.333517i \(0.891764\pi\)
\(632\) 16.7461 0.666122
\(633\) −9.92569 + 13.0762i −0.394511 + 0.519732i
\(634\) 31.6073 18.2485i 1.25528 0.724739i
\(635\) 16.9636 9.79395i 0.673181 0.388661i
\(636\) 1.94528 + 0.245777i 0.0771353 + 0.00974570i
\(637\) −16.2435 14.7544i −0.643591 0.584590i
\(638\) −43.5937 26.3347i −1.72589 1.04260i
\(639\) 3.31799 + 11.8852i 0.131258 + 0.470170i
\(640\) −25.0326 + 14.4526i −0.989501 + 0.571289i
\(641\) −21.8328 12.6052i −0.862345 0.497875i 0.00245202 0.999997i \(-0.499219\pi\)
−0.864797 + 0.502122i \(0.832553\pi\)
\(642\) −6.83693 0.863816i −0.269832 0.0340921i
\(643\) 0.598409 + 0.345491i 0.0235989 + 0.0136249i 0.511753 0.859133i \(-0.328996\pi\)
−0.488154 + 0.872757i \(0.662330\pi\)
\(644\) 16.4653 + 9.50623i 0.648822 + 0.374598i
\(645\) −15.2973 1.93275i −0.602332 0.0761020i
\(646\) −22.8047 13.1663i −0.897239 0.518021i
\(647\) −1.37109 + 0.791601i −0.0539032 + 0.0311211i −0.526709 0.850045i \(-0.676574\pi\)
0.472806 + 0.881166i \(0.343241\pi\)
\(648\) 18.4609 0.385524i 0.725213 0.0151448i
\(649\) −3.79885 + 6.28851i −0.149118 + 0.246846i
\(650\) −5.98311 + 6.58698i −0.234677 + 0.258363i
\(651\) 15.5340 + 1.96266i 0.608826 + 0.0769225i
\(652\) −22.0599 + 12.7363i −0.863934 + 0.498793i
\(653\) −3.20106 + 1.84813i −0.125267 + 0.0723230i −0.561324 0.827596i \(-0.689708\pi\)
0.436057 + 0.899919i \(0.356375\pi\)
\(654\) −12.2331 + 16.1160i −0.478353 + 0.630186i
\(655\) 7.33567 0.286628
\(656\) 9.52411 + 5.49875i 0.371854 + 0.214690i
\(657\) −4.90728 + 5.01083i −0.191451 + 0.195491i
\(658\) 18.4410i 0.718907i
\(659\) −7.75247 + 13.4277i −0.301993 + 0.523068i −0.976587 0.215121i \(-0.930985\pi\)
0.674594 + 0.738189i \(0.264319\pi\)
\(660\) 4.80298 32.7758i 0.186956 1.27580i
\(661\) −0.385420 + 0.222522i −0.0149911 + 0.00865512i −0.507477 0.861665i \(-0.669422\pi\)
0.492486 + 0.870321i \(0.336088\pi\)
\(662\) −46.4098 −1.80377
\(663\) −2.50581 13.4553i −0.0973174 0.522560i
\(664\) −5.71213 −0.221674
\(665\) 5.10267 + 8.83808i 0.197873 + 0.342726i
\(666\) −7.95999 28.5130i −0.308443 1.10486i
\(667\) 40.7555 + 23.5302i 1.57806 + 0.911092i
\(668\) 36.0873i 1.39626i
\(669\) 0.371688 0.489665i 0.0143703 0.0189316i
\(670\) 22.9433 39.7390i 0.886377 1.53525i
\(671\) 27.6675 + 16.7138i 1.06809 + 0.645228i
\(672\) 6.98715 9.20493i 0.269535 0.355088i
\(673\) −40.4168 + 23.3347i −1.55795 + 0.899485i −0.560501 + 0.828154i \(0.689391\pi\)
−0.997453 + 0.0713312i \(0.977275\pi\)
\(674\) 26.6990 + 46.2441i 1.02841 + 1.78126i
\(675\) 2.12764 5.37306i 0.0818930 0.206809i
\(676\) −3.64443 37.8439i −0.140170 1.45553i
\(677\) −18.6397 −0.716382 −0.358191 0.933648i \(-0.616606\pi\)
−0.358191 + 0.933648i \(0.616606\pi\)
\(678\) 44.7875 18.8261i 1.72005 0.723011i
\(679\) −15.7297 + 9.08153i −0.603649 + 0.348517i
\(680\) 7.67811 + 4.43296i 0.294442 + 0.169996i
\(681\) 37.1970 + 4.69968i 1.42539 + 0.180092i
\(682\) −33.5987 60.9541i −1.28656 2.33405i
\(683\) −15.0046 + 25.9887i −0.574133 + 0.994428i 0.422002 + 0.906595i \(0.361328\pi\)
−0.996135 + 0.0878331i \(0.972006\pi\)
\(684\) 46.0106 + 11.8151i 1.75926 + 0.451761i
\(685\) 9.07910 15.7255i 0.346894 0.600839i
\(686\) −24.0410 + 13.8801i −0.917891 + 0.529945i
\(687\) −3.59889 8.56180i −0.137306 0.326653i
\(688\) 5.85198i 0.223105i
\(689\) 0.425491 + 1.32920i 0.0162099 + 0.0506386i
\(690\) −6.46060 + 51.1344i −0.245951 + 1.94665i
\(691\) 6.97257 4.02561i 0.265249 0.153142i −0.361478 0.932381i \(-0.617728\pi\)
0.626727 + 0.779239i \(0.284394\pi\)
\(692\) 30.6801 + 53.1396i 1.16628 + 2.02006i
\(693\) 2.37540 + 9.21000i 0.0902340 + 0.349859i
\(694\) 13.9438i 0.529299i
\(695\) 3.01610 + 1.74135i 0.114407 + 0.0660531i
\(696\) −14.8677 + 19.5868i −0.563557 + 0.742435i
\(697\) 18.5950i 0.704335i
\(698\) −28.0181 16.1762i −1.06050 0.612280i
\(699\) 1.66391 0.699410i 0.0629347 0.0264541i
\(700\) 1.55462 + 2.69267i 0.0587590 + 0.101774i
\(701\) 24.7407 0.934442 0.467221 0.884141i \(-0.345255\pi\)
0.467221 + 0.884141i \(0.345255\pi\)
\(702\) 18.3217 + 37.3206i 0.691506 + 1.40858i
\(703\) 24.0759i 0.908039i
\(704\) −42.7644 0.847917i −1.61174 0.0319571i
\(705\) 27.3691 11.5044i 1.03078 0.433280i
\(706\) −34.7007 20.0345i −1.30598 0.754007i
\(707\) 6.81735 0.256393
\(708\) 8.93760 + 6.78423i 0.335895 + 0.254967i
\(709\) −0.770952 0.445109i −0.0289537 0.0167164i 0.485453 0.874263i \(-0.338655\pi\)
−0.514407 + 0.857546i \(0.671988\pi\)
\(710\) 17.9977i 0.675441i
\(711\) −17.4945 17.1329i −0.656094 0.642536i
\(712\) 10.0674 5.81241i 0.377292 0.217829i
\(713\) 32.1559 + 55.6956i 1.20425 + 2.08582i
\(714\) −7.98906 1.00938i −0.298983 0.0377752i
\(715\) 22.5944 6.74190i 0.844983 0.252133i
\(716\) 6.02477i 0.225156i
\(717\) −8.09089 19.2483i −0.302160 0.718842i
\(718\) 21.0128 + 36.3953i 0.784191 + 1.35826i
\(719\) −32.6474 18.8490i −1.21754 0.702948i −0.253151 0.967427i \(-0.581467\pi\)
−0.964392 + 0.264478i \(0.914800\pi\)
\(720\) 7.42627 + 1.90699i 0.276761 + 0.0710695i
\(721\) 1.07658 1.86469i 0.0400939 0.0694447i
\(722\) 19.8241 + 11.4454i 0.737776 + 0.425955i
\(723\) 3.00631 23.7944i 0.111806 0.884922i
\(724\) −1.95251 + 3.38185i −0.0725645 + 0.125685i
\(725\) 3.84804 + 6.66501i 0.142913 + 0.247532i
\(726\) 26.8779 32.6372i 0.997532 1.21128i
\(727\) −12.5075 −0.463877 −0.231938 0.972730i \(-0.574507\pi\)
−0.231938 + 0.972730i \(0.574507\pi\)
\(728\) −6.91037 1.50034i −0.256115 0.0556064i
\(729\) −19.6804 18.4847i −0.728903 0.684617i
\(730\) 8.85897 5.11473i 0.327885 0.189305i
\(731\) 8.56910 4.94737i 0.316940 0.182985i
\(732\) 29.8485 39.3227i 1.10323 1.45341i
\(733\) −28.5101 −1.05304 −0.526522 0.850161i \(-0.676504\pi\)
−0.526522 + 0.850161i \(0.676504\pi\)
\(734\) −8.49166 4.90266i −0.313433 0.180961i
\(735\) −16.5561 12.5672i −0.610680 0.463546i
\(736\) 47.4669 1.74965
\(737\) 30.4603 16.7901i 1.12202 0.618472i
\(738\) 15.1883 + 54.4050i 0.559088 + 2.00267i
\(739\) 14.3761 + 24.9002i 0.528835 + 0.915968i 0.999435 + 0.0336218i \(0.0107042\pi\)
−0.470600 + 0.882347i \(0.655963\pi\)
\(740\) 25.6416i 0.942606i
\(741\) 6.19056 + 33.2411i 0.227416 + 1.22114i
\(742\) 0.821131 0.0301447
\(743\) 22.6209 13.0602i 0.829879 0.479131i −0.0239320 0.999714i \(-0.507619\pi\)
0.853811 + 0.520583i \(0.174285\pi\)
\(744\) −30.9792 + 13.0219i −1.13575 + 0.477406i
\(745\) 9.20757 + 5.31599i 0.337339 + 0.194763i
\(746\) −76.7161 −2.80878
\(747\) 5.96742 + 5.84410i 0.218336 + 0.213824i
\(748\) 10.2618 + 18.6168i 0.375210 + 0.680699i
\(749\) −1.71389 −0.0626243
\(750\) −28.0071 + 36.8968i −1.02268 + 1.34728i
\(751\) −10.9343 18.9388i −0.398999 0.691086i 0.594604 0.804019i \(-0.297309\pi\)
−0.993603 + 0.112933i \(0.963976\pi\)
\(752\) −5.63389 9.75819i −0.205447 0.355845i
\(753\) −15.3999 1.94571i −0.561202 0.0709054i
\(754\) −54.1069 11.7474i −1.97046 0.427815i
\(755\) −38.9130 −1.41619
\(756\) 14.3709 2.12141i 0.522665 0.0771549i
\(757\) 9.56102 + 16.5602i 0.347501 + 0.601890i 0.985805 0.167895i \(-0.0536969\pi\)
−0.638304 + 0.769785i \(0.720364\pi\)
\(758\) 15.8229 27.4061i 0.574714 0.995433i
\(759\) −24.2327 + 30.6434i −0.879591 + 1.11229i
\(760\) −18.9686 10.9516i −0.688065 0.397255i
\(761\) 27.6886 + 15.9860i 1.00371 + 0.579493i 0.909344 0.416045i \(-0.136584\pi\)
0.0943666 + 0.995538i \(0.469917\pi\)
\(762\) 4.78628 37.8825i 0.173389 1.37234i
\(763\) −2.51602 + 4.35787i −0.0910860 + 0.157766i
\(764\) 23.1181 13.3473i 0.836385 0.482887i
\(765\) −3.48588 12.4866i −0.126032 0.451453i
\(766\) 79.6732i 2.87871i
\(767\) −1.69459 + 7.80506i −0.0611882 + 0.281824i
\(768\) −1.46301 + 11.5794i −0.0527919 + 0.417837i
\(769\) −18.2288 31.5733i −0.657349 1.13856i −0.981299 0.192488i \(-0.938344\pi\)
0.323950 0.946074i \(-0.394989\pi\)
\(770\) 0.275008 13.8699i 0.00991060 0.499837i
\(771\) 9.66222 12.7291i 0.347976 0.458427i
\(772\) 36.9833 1.33106
\(773\) 10.1061 17.5043i 0.363492 0.629587i −0.625041 0.780592i \(-0.714918\pi\)
0.988533 + 0.151005i \(0.0482510\pi\)
\(774\) −21.0304 + 21.4742i −0.755922 + 0.771873i
\(775\) 10.5173i 0.377794i
\(776\) 19.4911 33.7597i 0.699691 1.21190i
\(777\) −2.85296 6.78722i −0.102349 0.243490i
\(778\) −21.3046 36.9007i −0.763808 1.32295i
\(779\) 45.9386i 1.64592i
\(780\) −6.59315 35.4029i −0.236073 1.26763i
\(781\) 7.05384 11.6767i 0.252406 0.417827i
\(782\) −16.5376 28.6439i −0.591383 1.02430i
\(783\) 35.5714 5.25099i 1.27122 0.187655i
\(784\) −3.94438 + 6.83186i −0.140871 + 0.243995i
\(785\) 30.2162 1.07846
\(786\) 8.64581 11.3901i 0.308386 0.406270i
\(787\) 5.32454 9.22237i 0.189799 0.328742i −0.755384 0.655282i \(-0.772550\pi\)
0.945183 + 0.326540i \(0.105883\pi\)
\(788\) 60.1229i 2.14179i
\(789\) 15.4148 + 11.7009i 0.548782 + 0.416562i
\(790\) 17.8572 + 30.9296i 0.635331 + 1.10043i
\(791\) 10.4641 6.04144i 0.372060 0.214809i
\(792\) −14.2986 14.5695i −0.508078 0.517706i
\(793\) 34.3399 + 7.45569i 1.21944 + 0.264759i
\(794\) −19.9896 −0.709405
\(795\) 0.512260 + 1.21867i 0.0181680 + 0.0432219i
\(796\) 9.81646 + 17.0026i 0.347935 + 0.602641i
\(797\) −26.3888 15.2356i −0.934739 0.539672i −0.0464317 0.998921i \(-0.514785\pi\)
−0.888307 + 0.459250i \(0.848118\pi\)
\(798\) 19.7368 + 2.49366i 0.698677 + 0.0882747i
\(799\) −9.52601 + 16.4995i −0.337006 + 0.583711i
\(800\) 6.72259 + 3.88129i 0.237679 + 0.137224i
\(801\) −16.4640 4.22780i −0.581728 0.149382i
\(802\) 61.0622 + 35.2543i 2.15618 + 1.24487i
\(803\) 7.75224 + 0.153709i 0.273571 + 0.00542426i
\(804\) −20.5845 48.9707i −0.725958 1.72706i
\(805\) 12.8184i 0.451791i
\(806\) −56.0083 50.8737i −1.97281 1.79195i
\(807\) 30.6716 + 3.87522i 1.07969 + 0.136414i
\(808\) −12.6714 + 7.31584i −0.445779 + 0.257370i
\(809\) 8.54272 + 14.7964i 0.300346 + 0.520215i 0.976214 0.216808i \(-0.0695645\pi\)
−0.675868 + 0.737022i \(0.736231\pi\)
\(810\) 20.3979 + 33.6858i 0.716709 + 1.18360i
\(811\) 24.3459 0.854901 0.427450 0.904039i \(-0.359412\pi\)
0.427450 + 0.904039i \(0.359412\pi\)
\(812\) −9.67283 + 16.7538i −0.339450 + 0.587944i
\(813\) 2.73089 + 2.07292i 0.0957763 + 0.0727006i
\(814\) −16.9225 + 28.0130i −0.593132 + 0.981855i
\(815\) −14.8731 8.58699i −0.520982 0.300789i
\(816\) −4.53583 + 1.90660i −0.158786 + 0.0667445i
\(817\) −21.1698 + 12.2224i −0.740639 + 0.427608i
\(818\) 19.1895i 0.670945i
\(819\) 5.68420 + 8.63742i 0.198622 + 0.301816i
\(820\) 48.9262i 1.70858i
\(821\) 4.76317 2.75002i 0.166236 0.0959763i −0.414574 0.910016i \(-0.636069\pi\)
0.580810 + 0.814039i \(0.302736\pi\)
\(822\) −13.7162 32.6311i −0.478408 1.13814i
\(823\) 19.6095 33.9646i 0.683543 1.18393i −0.290349 0.956921i \(-0.593771\pi\)
0.973892 0.227011i \(-0.0728953\pi\)
\(824\) 4.62119i 0.160987i
\(825\) −5.93766 + 2.35847i −0.206723 + 0.0821112i
\(826\) 4.06955 + 2.34956i 0.141598 + 0.0817515i
\(827\) 3.99661i 0.138976i 0.997583 + 0.0694879i \(0.0221365\pi\)
−0.997583 + 0.0694879i \(0.977863\pi\)
\(828\) 42.6290 + 41.7480i 1.48146 + 1.45084i
\(829\) −10.0608 17.4258i −0.349426 0.605223i 0.636722 0.771094i \(-0.280290\pi\)
−0.986148 + 0.165870i \(0.946957\pi\)
\(830\) −6.09115 10.5502i −0.211427 0.366202i
\(831\) 39.4231 + 4.98093i 1.36757 + 0.172787i
\(832\) −44.2853 + 14.1761i −1.53532 + 0.491469i
\(833\) 13.3386 0.462155
\(834\) 6.25856 2.63074i 0.216716 0.0910950i
\(835\) −21.0709 + 12.1653i −0.729188 + 0.420997i
\(836\) −25.3517 45.9926i −0.876808 1.59069i
\(837\) 45.6865 + 18.0911i 1.57916 + 0.625319i
\(838\) 5.55246 9.61714i 0.191806 0.332218i
\(839\) 6.49242 11.2452i 0.224143 0.388228i −0.731919 0.681392i \(-0.761375\pi\)
0.956062 + 0.293164i \(0.0947083\pi\)
\(840\) −6.64519 0.839590i −0.229281 0.0289686i
\(841\) −9.44255 + 16.3550i −0.325605 + 0.563965i
\(842\) −6.79461 11.7686i −0.234158 0.405573i
\(843\) −11.1436 26.5109i −0.383808 0.913083i
\(844\) 27.7192i 0.954133i
\(845\) 20.8679 14.8853i 0.717879 0.512071i
\(846\) 14.3944 56.0549i 0.494888 1.92721i
\(847\) 5.61447 8.89090i 0.192915 0.305495i
\(848\) 0.434507 0.250863i 0.0149210 0.00861465i
\(849\) 3.07154 4.04647i 0.105415 0.138875i
\(850\) 5.40900i 0.185527i
\(851\) 15.1203 26.1891i 0.518317 0.897752i
\(852\) −16.5957 12.5972i −0.568558 0.431573i
\(853\) −29.8292 −1.02133 −0.510666 0.859779i \(-0.670601\pi\)
−0.510666 + 0.859779i \(0.670601\pi\)
\(854\) 10.3373 17.9048i 0.353736 0.612689i
\(855\) 8.61182 + 30.8479i 0.294518 + 1.05498i
\(856\) 3.18561 1.83921i 0.108882 0.0628630i
\(857\) 7.98798 0.272864 0.136432 0.990649i \(-0.456436\pi\)
0.136432 + 0.990649i \(0.456436\pi\)
\(858\) 16.1616 43.0282i 0.551749 1.46896i
\(859\) −17.7875 −0.606900 −0.303450 0.952847i \(-0.598139\pi\)
−0.303450 + 0.952847i \(0.598139\pi\)
\(860\) 22.5466 13.0173i 0.768833 0.443886i
\(861\) 5.44366 + 12.9505i 0.185520 + 0.441353i
\(862\) 30.6267 53.0470i 1.04315 1.80679i
\(863\) 31.1502 1.06037 0.530183 0.847883i \(-0.322123\pi\)
0.530183 + 0.847883i \(0.322123\pi\)
\(864\) 28.4237 22.5261i 0.966994 0.766355i
\(865\) −20.6850 + 35.8274i −0.703310 + 1.21817i
\(866\) 22.6210i 0.768693i
\(867\) −16.8269 12.7727i −0.571471 0.433785i
\(868\) −22.8955 + 13.2187i −0.777123 + 0.448672i
\(869\) −0.536648 + 27.0657i −0.0182045 + 0.918139i
\(870\) −52.0305 6.57383i −1.76400 0.222874i
\(871\) 25.4229 27.9887i 0.861421 0.948362i
\(872\) 10.8000i 0.365733i
\(873\) −54.9018 + 15.3270i −1.85815 + 0.518740i
\(874\) 40.8558 + 70.7644i 1.38197 + 2.39364i
\(875\) −5.76031 + 9.97715i −0.194734 + 0.337289i
\(876\) 1.48441 11.7488i 0.0501536 0.396956i
\(877\) 11.2319 19.4542i 0.379274 0.656922i −0.611683 0.791103i \(-0.709507\pi\)
0.990957 + 0.134181i \(0.0428405\pi\)
\(878\) 38.2700 66.2856i 1.29155 2.23703i
\(879\) −5.00740 0.632662i −0.168895 0.0213392i
\(880\) −4.09186 7.42337i −0.137936 0.250242i
\(881\) −4.24725 + 2.45215i −0.143094 + 0.0826151i −0.569838 0.821757i \(-0.692994\pi\)
0.426744 + 0.904372i \(0.359661\pi\)
\(882\) −39.0259 + 10.8949i −1.31407 + 0.366850i
\(883\) −8.70611 −0.292984 −0.146492 0.989212i \(-0.546798\pi\)
−0.146492 + 0.989212i \(0.546798\pi\)
\(884\) 17.1063 + 15.5380i 0.575346 + 0.522601i
\(885\) −0.948292 + 7.50554i −0.0318765 + 0.252296i
\(886\) 35.2874 + 61.1195i 1.18550 + 2.05335i
\(887\) −7.63792 13.2293i −0.256456 0.444195i 0.708834 0.705376i \(-0.249222\pi\)
−0.965290 + 0.261180i \(0.915888\pi\)
\(888\) 12.5863 + 9.55384i 0.422369 + 0.320606i
\(889\) 9.49644i 0.318500i
\(890\) 21.4708 + 12.3962i 0.719703 + 0.415521i
\(891\) 0.0314971 + 29.8496i 0.00105519 + 0.999999i
\(892\) 1.03800i 0.0347549i
\(893\) 23.5339 40.7618i 0.787531 1.36404i
\(894\) 19.1062 8.03113i 0.639005 0.268601i
\(895\) 3.51778 2.03099i 0.117586 0.0678885i
\(896\) 14.0136i 0.468160i
\(897\) −14.1424 + 40.0467i −0.472200 + 1.33712i
\(898\) 29.9786i 1.00040i
\(899\) −56.6717 + 32.7194i −1.89011 + 1.09125i
\(900\) 2.62374 + 9.39834i 0.0874580 + 0.313278i
\(901\) −0.734680 0.424168i −0.0244758 0.0141311i
\(902\) 32.2893 53.4509i 1.07512 1.77972i
\(903\) −4.51964 + 5.95421i −0.150404 + 0.198144i
\(904\) −12.9664 + 22.4585i −0.431256 + 0.746957i
\(905\) −2.63282 −0.0875178
\(906\) −45.8628 + 60.4200i −1.52369 + 2.00732i
\(907\) 11.9712 + 20.7348i 0.397499 + 0.688488i 0.993417 0.114557i \(-0.0365449\pi\)
−0.595918 + 0.803045i \(0.703212\pi\)
\(908\) −54.8243 + 31.6529i −1.81941 + 1.05044i
\(909\) 20.7226 + 5.32136i 0.687324 + 0.176498i
\(910\) −4.59780 14.3632i −0.152416 0.476136i
\(911\) 8.04747i 0.266624i −0.991074 0.133312i \(-0.957439\pi\)
0.991074 0.133312i \(-0.0425613\pi\)
\(912\) 11.2057 4.71024i 0.371058 0.155971i
\(913\) 0.183052 9.23218i 0.00605815 0.305540i
\(914\) 47.4717 + 27.4078i 1.57022 + 0.906569i
\(915\) 33.0221 + 4.17219i 1.09168 + 0.137928i
\(916\) 13.5807 + 7.84082i 0.448719 + 0.259068i
\(917\) 1.77821 3.07995i 0.0587216 0.101709i
\(918\) −23.4963 9.30414i −0.775493 0.307082i
\(919\) −21.0124 12.1315i −0.693135 0.400181i 0.111651 0.993748i \(-0.464386\pi\)
−0.804785 + 0.593566i \(0.797720\pi\)
\(920\) −13.7557 23.8256i −0.453513 0.785508i
\(921\) −30.8265 + 12.9577i −1.01577 + 0.426970i
\(922\) −6.79553 −0.223799
\(923\) 3.14658 14.4927i 0.103571 0.477034i
\(924\) −12.5970 9.96162i −0.414410 0.327713i
\(925\) 4.28288 2.47272i 0.140820 0.0813026i
\(926\) 17.6819 + 30.6259i 0.581062 + 1.00643i
\(927\) 4.72796 4.82772i 0.155286 0.158563i
\(928\) 48.2988i 1.58549i
\(929\) −3.26981 + 5.66349i −0.107279 + 0.185813i −0.914667 0.404208i \(-0.867547\pi\)
0.807388 + 0.590021i \(0.200881\pi\)
\(930\) −57.0860 43.3320i −1.87192 1.42091i
\(931\) −32.9528 −1.07999
\(932\) −1.52379 + 2.63928i −0.0499134 + 0.0864526i
\(933\) −22.9562 54.6130i −0.751551 1.78795i
\(934\) 42.7523 + 74.0492i 1.39890 + 2.42296i
\(935\) −7.41078 + 12.2676i −0.242358 + 0.401193i
\(936\) −19.8342 9.95453i −0.648301 0.325374i
\(937\) 50.8866i 1.66239i 0.555979 + 0.831196i \(0.312343\pi\)
−0.555979 + 0.831196i \(0.687657\pi\)
\(938\) −11.1232 19.2659i −0.363185 0.629054i
\(939\) −51.4599 + 21.6308i −1.67933 + 0.705893i
\(940\) −25.0644 + 43.4128i −0.817509 + 1.41597i
\(941\) 9.85705i 0.321331i 0.987009 + 0.160665i \(0.0513640\pi\)
−0.987009 + 0.160665i \(0.948636\pi\)
\(942\) 35.6127 46.9165i 1.16033 1.52862i
\(943\) −28.8507 + 49.9708i −0.939507 + 1.62727i
\(944\) 2.87124 0.0934508
\(945\) 6.08319 + 7.67583i 0.197886 + 0.249695i
\(946\) 33.2226 + 0.658726i 1.08016 + 0.0214170i
\(947\) −9.91084 17.1661i −0.322059 0.557823i 0.658854 0.752271i \(-0.271042\pi\)
−0.980913 + 0.194448i \(0.937708\pi\)
\(948\) 41.0191 + 5.18258i 1.33224 + 0.168322i
\(949\) 8.02795 2.56982i 0.260598 0.0834200i
\(950\) 13.3629i 0.433548i
\(951\) 26.2605 11.0384i 0.851557 0.357945i
\(952\) 3.72243 2.14915i 0.120645 0.0696543i
\(953\) 25.9105 44.8783i 0.839324 1.45375i −0.0511362 0.998692i \(-0.516284\pi\)
0.890460 0.455061i \(-0.150382\pi\)
\(954\) 2.49598 + 0.640943i 0.0808102 + 0.0207513i
\(955\) 15.5866 + 8.99890i 0.504369 + 0.291198i
\(956\) 30.5316 + 17.6275i 0.987464 + 0.570113i
\(957\) −31.1805 24.6574i −1.00792 0.797060i
\(958\) −44.9224 + 77.8078i −1.45138 + 2.51386i
\(959\) −4.40165 7.62388i −0.142137 0.246188i
\(960\) −40.6027 + 17.0671i −1.31045 + 0.550837i
\(961\) −58.4275 −1.88476
\(962\) −7.54878 + 34.7686i −0.243382 + 1.12099i
\(963\) −5.20969 1.33780i −0.167880 0.0431099i
\(964\) 20.2479 + 35.0703i 0.652140 + 1.12954i
\(965\) 12.4673 + 21.5940i 0.401337 + 0.695136i
\(966\) 19.9031 + 15.1078i 0.640373 + 0.486086i
\(967\) −9.43118 −0.303286 −0.151643 0.988435i \(-0.548456\pi\)
−0.151643 + 0.988435i \(0.548456\pi\)
\(968\) −0.894599 + 22.5505i −0.0287535 + 0.724801i
\(969\) −16.3708 12.4265i −0.525905 0.399196i
\(970\) 83.1378 2.66939
\(971\) 34.5687 + 19.9583i 1.10936 + 0.640491i 0.938664 0.344832i \(-0.112064\pi\)
0.170698 + 0.985323i \(0.445398\pi\)
\(972\) 45.3388 + 4.76895i 1.45424 + 0.152964i
\(973\) 1.46224 0.844226i 0.0468773 0.0270646i
\(974\) −59.9431 −1.92070
\(975\) −5.27749 + 4.51528i −0.169015 + 0.144605i
\(976\) 12.6326i 0.404359i
\(977\) −2.95283 5.11445i −0.0944694 0.163626i 0.814918 0.579577i \(-0.196782\pi\)
−0.909387 + 0.415951i \(0.863449\pi\)
\(978\) −30.8624 + 12.9728i −0.986871 + 0.414824i
\(979\) 9.07163 + 16.4576i 0.289931 + 0.525987i
\(980\) 35.0959 1.12110
\(981\) −11.0495 + 11.2826i −0.352783 + 0.360227i
\(982\) −28.2676 16.3203i −0.902054 0.520801i
\(983\) −11.0187 −0.351442 −0.175721 0.984440i \(-0.556226\pi\)
−0.175721 + 0.984440i \(0.556226\pi\)
\(984\) −24.0156 18.2295i −0.765590 0.581134i
\(985\) 35.1049 20.2678i 1.11854 0.645787i
\(986\) 29.1459 16.8274i 0.928195 0.535894i
\(987\) 1.80420 14.2799i 0.0574283 0.454534i
\(988\) −42.2608 38.3865i −1.34449 1.22124i
\(989\) −30.7040 −0.976331
\(990\) 11.6623 41.9455i 0.370651 1.33311i
\(991\) −0.257650 0.446263i −0.00818452 0.0141760i 0.861904 0.507071i \(-0.169272\pi\)
−0.870089 + 0.492895i \(0.835939\pi\)
\(992\) −33.0021 + 57.1613i −1.04782 + 1.81487i
\(993\) −35.9376 4.54055i −1.14044 0.144090i
\(994\) −7.55649 4.36274i −0.239677 0.138378i
\(995\) −6.61839 + 11.4634i −0.209817 + 0.363414i
\(996\) −13.9917 1.76779i −0.443345 0.0560147i
\(997\) 9.52856 + 5.50132i 0.301773 + 0.174229i 0.643239 0.765665i \(-0.277590\pi\)
−0.341466 + 0.939894i \(0.610924\pi\)
\(998\) 38.6615 + 66.9636i 1.22381 + 2.11970i
\(999\) −3.37424 22.8579i −0.106756 0.723192i
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 429.2.t.a.296.7 104
3.2 odd 2 inner 429.2.t.a.296.46 yes 104
11.10 odd 2 inner 429.2.t.a.296.45 yes 104
13.4 even 6 inner 429.2.t.a.329.8 yes 104
33.32 even 2 inner 429.2.t.a.296.8 yes 104
39.17 odd 6 inner 429.2.t.a.329.45 yes 104
143.43 odd 6 inner 429.2.t.a.329.46 yes 104
429.329 even 6 inner 429.2.t.a.329.7 yes 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.t.a.296.7 104 1.1 even 1 trivial
429.2.t.a.296.8 yes 104 33.32 even 2 inner
429.2.t.a.296.45 yes 104 11.10 odd 2 inner
429.2.t.a.296.46 yes 104 3.2 odd 2 inner
429.2.t.a.329.7 yes 104 429.329 even 6 inner
429.2.t.a.329.8 yes 104 13.4 even 6 inner
429.2.t.a.329.45 yes 104 39.17 odd 6 inner
429.2.t.a.329.46 yes 104 143.43 odd 6 inner