Properties

Label 315.2.bx.a.2.10
Level $315$
Weight $2$
Character 315.2
Analytic conductor $2.515$
Analytic rank $0$
Dimension $176$
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] = [315,2,Mod(2,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bx (of order \(12\), degree \(4\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(176\)
Relative dimension: \(44\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 2.10
Character \(\chi\) \(=\) 315.2
Dual form 315.2.bx.a.158.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.62572 - 0.435610i) q^{2} +(0.558438 - 1.63956i) q^{3} +(0.721151 + 0.416356i) q^{4} +(1.01641 + 1.99171i) q^{5} +(-1.62207 + 2.42220i) q^{6} +(-2.57976 + 0.587246i) q^{7} +(1.38920 + 1.38920i) q^{8} +(-2.37629 - 1.83118i) q^{9} +O(q^{10})\) \(q+(-1.62572 - 0.435610i) q^{2} +(0.558438 - 1.63956i) q^{3} +(0.721151 + 0.416356i) q^{4} +(1.01641 + 1.99171i) q^{5} +(-1.62207 + 2.42220i) q^{6} +(-2.57976 + 0.587246i) q^{7} +(1.38920 + 1.38920i) q^{8} +(-2.37629 - 1.83118i) q^{9} +(-0.784783 - 3.68072i) q^{10} -5.77995i q^{11} +(1.08536 - 0.949858i) q^{12} +(-4.95511 - 1.32772i) q^{13} +(4.44976 + 0.169071i) q^{14} +(3.83313 - 0.554211i) q^{15} +(-2.48601 - 4.30589i) q^{16} +(-2.70643 - 0.725185i) q^{17} +(3.06550 + 4.01212i) q^{18} +(-3.19812 - 1.84643i) q^{19} +(-0.0962789 + 1.85951i) q^{20} +(-0.477810 + 4.55760i) q^{21} +(-2.51780 + 9.39656i) q^{22} +(2.75969 + 2.75969i) q^{23} +(3.05345 - 1.50189i) q^{24} +(-2.93383 + 4.04878i) q^{25} +(7.47724 + 4.31699i) q^{26} +(-4.32934 + 2.87347i) q^{27} +(-2.10490 - 0.650605i) q^{28} +(0.300752 - 0.520917i) q^{29} +(-6.47300 - 0.768756i) q^{30} +(2.14479 - 3.71489i) q^{31} +(1.14889 + 4.28773i) q^{32} +(-9.47655 - 3.22774i) q^{33} +(4.08399 + 2.35789i) q^{34} +(-3.79171 - 4.54125i) q^{35} +(-0.951241 - 2.30994i) q^{36} +(-6.58701 + 1.76498i) q^{37} +(4.39491 + 4.39491i) q^{38} +(-4.94399 + 7.38274i) q^{39} +(-1.35489 + 4.17887i) q^{40} +(0.0402002 - 0.0232096i) q^{41} +(2.76212 - 7.20123i) q^{42} +(-0.636185 - 2.37427i) q^{43} +(2.40652 - 4.16821i) q^{44} +(1.23190 - 6.59412i) q^{45} +(-3.28433 - 5.68862i) q^{46} +(4.27999 + 1.14682i) q^{47} +(-8.44804 + 1.67138i) q^{48} +(6.31028 - 3.02990i) q^{49} +(6.53327 - 5.30417i) q^{50} +(-2.70035 + 4.03237i) q^{51} +(-3.02058 - 3.02058i) q^{52} +(2.68751 - 10.0299i) q^{53} +(8.28999 - 2.78554i) q^{54} +(11.5120 - 5.87478i) q^{55} +(-4.39959 - 2.76799i) q^{56} +(-4.81328 + 4.21238i) q^{57} +(-0.715854 + 0.715854i) q^{58} +(-2.99060 + 5.17987i) q^{59} +(2.99501 + 1.19628i) q^{60} +(0.130166 + 0.225454i) q^{61} +(-5.10507 + 5.10507i) q^{62} +(7.20561 + 3.32853i) q^{63} +2.47292i q^{64} +(-2.39198 - 11.2187i) q^{65} +(14.0002 + 9.37547i) q^{66} +(3.68051 - 0.986190i) q^{67} +(-1.64981 - 1.64981i) q^{68} +(6.06578 - 2.98355i) q^{69} +(4.18604 + 9.03449i) q^{70} +4.98768i q^{71} +(-0.757268 - 5.84501i) q^{72} +(-9.64567 - 2.58455i) q^{73} +11.4775 q^{74} +(4.99985 + 7.07118i) q^{75} +(-1.53755 - 2.66311i) q^{76} +(3.39425 + 14.9108i) q^{77} +(11.2535 - 9.84859i) q^{78} +(11.7918 - 6.80798i) q^{79} +(6.04930 - 9.32795i) q^{80} +(2.29355 + 8.70285i) q^{81} +(-0.0754645 + 0.0202207i) q^{82} +(-5.20761 + 1.39537i) q^{83} +(-2.24216 + 3.08777i) q^{84} +(-1.30648 - 6.12751i) q^{85} +4.13703i q^{86} +(-0.686123 - 0.784000i) q^{87} +(8.02948 - 8.02948i) q^{88} +(-0.475414 + 0.823442i) q^{89} +(-4.87519 + 10.1835i) q^{90} +(13.5627 + 0.515319i) q^{91} +(0.841137 + 3.13917i) q^{92} +(-4.89304 - 5.59104i) q^{93} +(-6.45848 - 3.72881i) q^{94} +(0.426972 - 8.24646i) q^{95} +(7.67157 + 0.510755i) q^{96} +(8.57351 - 2.29726i) q^{97} +(-11.5786 + 2.17695i) q^{98} +(-10.5841 + 13.7348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176 q - 6 q^{2} - 2 q^{3} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 176 q - 6 q^{2} - 2 q^{3} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 22 q^{12} - 4 q^{13} - 14 q^{15} + 68 q^{16} - 18 q^{17} - 10 q^{18} - 12 q^{20} + 20 q^{21} + 4 q^{22} - 4 q^{25} - 32 q^{27} - 4 q^{28} - 20 q^{30} + 4 q^{31} - 90 q^{32} + 32 q^{33} + 8 q^{36} - 4 q^{37} - 36 q^{40} - 36 q^{41} + 14 q^{42} - 4 q^{43} - 68 q^{45} + 4 q^{46} - 6 q^{47} + 38 q^{48} + 36 q^{50} + 20 q^{51} - 52 q^{52} + 4 q^{55} - 96 q^{56} + 32 q^{57} - 12 q^{58} - 74 q^{60} - 8 q^{61} + 14 q^{63} - 78 q^{65} - 92 q^{66} + 2 q^{67} - 42 q^{70} - 46 q^{72} - 4 q^{73} + 54 q^{75} - 24 q^{76} + 42 q^{77} + 54 q^{78} + 36 q^{80} + 20 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 28 q^{87} + 12 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} + 4 q^{93} - 66 q^{95} - 4 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.62572 0.435610i −1.14956 0.308023i −0.366769 0.930312i \(-0.619536\pi\)
−0.782787 + 0.622290i \(0.786203\pi\)
\(3\) 0.558438 1.63956i 0.322414 0.946599i
\(4\) 0.721151 + 0.416356i 0.360575 + 0.208178i
\(5\) 1.01641 + 1.99171i 0.454551 + 0.890720i
\(6\) −1.62207 + 2.42220i −0.662207 + 0.988857i
\(7\) −2.57976 + 0.587246i −0.975056 + 0.221958i
\(8\) 1.38920 + 1.38920i 0.491155 + 0.491155i
\(9\) −2.37629 1.83118i −0.792098 0.610394i
\(10\) −0.784783 3.68072i −0.248170 1.16395i
\(11\) 5.77995i 1.74272i −0.490645 0.871360i \(-0.663239\pi\)
0.490645 0.871360i \(-0.336761\pi\)
\(12\) 1.08536 0.949858i 0.313316 0.274200i
\(13\) −4.95511 1.32772i −1.37430 0.368243i −0.505253 0.862971i \(-0.668601\pi\)
−0.869047 + 0.494729i \(0.835267\pi\)
\(14\) 4.44976 + 0.169071i 1.18925 + 0.0451860i
\(15\) 3.83313 0.554211i 0.989709 0.143097i
\(16\) −2.48601 4.30589i −0.621502 1.07647i
\(17\) −2.70643 0.725185i −0.656405 0.175883i −0.0847821 0.996400i \(-0.527019\pi\)
−0.571623 + 0.820516i \(0.693686\pi\)
\(18\) 3.06550 + 4.01212i 0.722546 + 0.945666i
\(19\) −3.19812 1.84643i −0.733699 0.423601i 0.0860751 0.996289i \(-0.472567\pi\)
−0.819774 + 0.572688i \(0.805901\pi\)
\(20\) −0.0962789 + 1.85951i −0.0215286 + 0.415800i
\(21\) −0.477810 + 4.55760i −0.104267 + 0.994549i
\(22\) −2.51780 + 9.39656i −0.536797 + 2.00335i
\(23\) 2.75969 + 2.75969i 0.575435 + 0.575435i 0.933642 0.358207i \(-0.116612\pi\)
−0.358207 + 0.933642i \(0.616612\pi\)
\(24\) 3.05345 1.50189i 0.623283 0.306572i
\(25\) −2.93383 + 4.04878i −0.586766 + 0.809757i
\(26\) 7.47724 + 4.31699i 1.46641 + 0.846631i
\(27\) −4.32934 + 2.87347i −0.833182 + 0.552999i
\(28\) −2.10490 0.650605i −0.397788 0.122953i
\(29\) 0.300752 0.520917i 0.0558482 0.0967319i −0.836750 0.547586i \(-0.815547\pi\)
0.892598 + 0.450854i \(0.148880\pi\)
\(30\) −6.47300 0.768756i −1.18180 0.140355i
\(31\) 2.14479 3.71489i 0.385216 0.667214i −0.606583 0.795020i \(-0.707460\pi\)
0.991799 + 0.127806i \(0.0407936\pi\)
\(32\) 1.14889 + 4.28773i 0.203098 + 0.757971i
\(33\) −9.47655 3.22774i −1.64966 0.561878i
\(34\) 4.08399 + 2.35789i 0.700398 + 0.404375i
\(35\) −3.79171 4.54125i −0.640916 0.767611i
\(36\) −0.951241 2.30994i −0.158540 0.384991i
\(37\) −6.58701 + 1.76498i −1.08290 + 0.290162i −0.755782 0.654823i \(-0.772743\pi\)
−0.327115 + 0.944984i \(0.606077\pi\)
\(38\) 4.39491 + 4.39491i 0.712949 + 0.712949i
\(39\) −4.94399 + 7.38274i −0.791672 + 1.18218i
\(40\) −1.35489 + 4.17887i −0.214227 + 0.660738i
\(41\) 0.0402002 0.0232096i 0.00627822 0.00362473i −0.496858 0.867832i \(-0.665513\pi\)
0.503136 + 0.864207i \(0.332180\pi\)
\(42\) 2.76212 7.20123i 0.426204 1.11117i
\(43\) −0.636185 2.37427i −0.0970173 0.362073i 0.900300 0.435269i \(-0.143347\pi\)
−0.997318 + 0.0731959i \(0.976680\pi\)
\(44\) 2.40652 4.16821i 0.362796 0.628381i
\(45\) 1.23190 6.59412i 0.183641 0.982993i
\(46\) −3.28433 5.68862i −0.484248 0.838742i
\(47\) 4.27999 + 1.14682i 0.624300 + 0.167281i 0.557082 0.830458i \(-0.311921\pi\)
0.0672183 + 0.997738i \(0.478588\pi\)
\(48\) −8.44804 + 1.67138i −1.21937 + 0.241243i
\(49\) 6.31028 3.02990i 0.901469 0.432843i
\(50\) 6.53327 5.30417i 0.923944 0.750123i
\(51\) −2.70035 + 4.03237i −0.378125 + 0.564645i
\(52\) −3.02058 3.02058i −0.418879 0.418879i
\(53\) 2.68751 10.0299i 0.369158 1.37772i −0.492539 0.870291i \(-0.663931\pi\)
0.861696 0.507425i \(-0.169402\pi\)
\(54\) 8.28999 2.78554i 1.12813 0.379065i
\(55\) 11.5120 5.87478i 1.55228 0.792155i
\(56\) −4.39959 2.76799i −0.587920 0.369888i
\(57\) −4.81328 + 4.21238i −0.637535 + 0.557943i
\(58\) −0.715854 + 0.715854i −0.0939963 + 0.0939963i
\(59\) −2.99060 + 5.17987i −0.389343 + 0.674361i −0.992361 0.123366i \(-0.960631\pi\)
0.603019 + 0.797727i \(0.293964\pi\)
\(60\) 2.99501 + 1.19628i 0.386654 + 0.154439i
\(61\) 0.130166 + 0.225454i 0.0166660 + 0.0288664i 0.874238 0.485497i \(-0.161361\pi\)
−0.857572 + 0.514364i \(0.828028\pi\)
\(62\) −5.10507 + 5.10507i −0.648344 + 0.648344i
\(63\) 7.20561 + 3.32853i 0.907822 + 0.419356i
\(64\) 2.47292i 0.309115i
\(65\) −2.39198 11.2187i −0.296689 1.39150i
\(66\) 14.0002 + 9.37547i 1.72330 + 1.15404i
\(67\) 3.68051 0.986190i 0.449646 0.120482i −0.0268877 0.999638i \(-0.508560\pi\)
0.476534 + 0.879156i \(0.341893\pi\)
\(68\) −1.64981 1.64981i −0.200068 0.200068i
\(69\) 6.06578 2.98355i 0.730234 0.359177i
\(70\) 4.18604 + 9.03449i 0.500327 + 1.07983i
\(71\) 4.98768i 0.591929i 0.955199 + 0.295965i \(0.0956410\pi\)
−0.955199 + 0.295965i \(0.904359\pi\)
\(72\) −0.757268 5.84501i −0.0892449 0.688842i
\(73\) −9.64567 2.58455i −1.12894 0.302499i −0.354444 0.935077i \(-0.615330\pi\)
−0.774496 + 0.632578i \(0.781997\pi\)
\(74\) 11.4775 1.33423
\(75\) 4.99985 + 7.07118i 0.577333 + 0.816509i
\(76\) −1.53755 2.66311i −0.176369 0.305480i
\(77\) 3.39425 + 14.9108i 0.386811 + 1.69925i
\(78\) 11.2535 9.84859i 1.27421 1.11513i
\(79\) 11.7918 6.80798i 1.32668 0.765958i 0.341893 0.939739i \(-0.388932\pi\)
0.984784 + 0.173781i \(0.0555985\pi\)
\(80\) 6.04930 9.32795i 0.676332 1.04290i
\(81\) 2.29355 + 8.70285i 0.254838 + 0.966984i
\(82\) −0.0754645 + 0.0202207i −0.00833366 + 0.00223300i
\(83\) −5.20761 + 1.39537i −0.571609 + 0.153162i −0.533035 0.846093i \(-0.678948\pi\)
−0.0385748 + 0.999256i \(0.512282\pi\)
\(84\) −2.24216 + 3.08777i −0.244640 + 0.336904i
\(85\) −1.30648 6.12751i −0.141707 0.664622i
\(86\) 4.13703i 0.446107i
\(87\) −0.686123 0.784000i −0.0735601 0.0840536i
\(88\) 8.02948 8.02948i 0.855946 0.855946i
\(89\) −0.475414 + 0.823442i −0.0503938 + 0.0872846i −0.890122 0.455722i \(-0.849381\pi\)
0.839728 + 0.543007i \(0.182714\pi\)
\(90\) −4.87519 + 10.1835i −0.513890 + 1.07344i
\(91\) 13.5627 + 0.515319i 1.42175 + 0.0540201i
\(92\) 0.841137 + 3.13917i 0.0876946 + 0.327281i
\(93\) −4.89304 5.59104i −0.507385 0.579764i
\(94\) −6.45848 3.72881i −0.666142 0.384597i
\(95\) 0.426972 8.24646i 0.0438064 0.846069i
\(96\) 7.67157 + 0.510755i 0.782976 + 0.0521287i
\(97\) 8.57351 2.29726i 0.870508 0.233252i 0.204201 0.978929i \(-0.434541\pi\)
0.666307 + 0.745677i \(0.267874\pi\)
\(98\) −11.5786 + 2.17695i −1.16961 + 0.219905i
\(99\) −10.5841 + 13.7348i −1.06375 + 1.38040i
\(100\) −3.80147 + 1.69826i −0.380147 + 0.169826i
\(101\) 6.05894i 0.602887i −0.953484 0.301444i \(-0.902531\pi\)
0.953484 0.301444i \(-0.0974685\pi\)
\(102\) 6.14655 5.37920i 0.608600 0.532620i
\(103\) 9.89409 9.89409i 0.974893 0.974893i −0.0247990 0.999692i \(-0.507895\pi\)
0.999692 + 0.0247990i \(0.00789458\pi\)
\(104\) −5.03916 8.72809i −0.494131 0.855859i
\(105\) −9.56307 + 3.68072i −0.933260 + 0.359201i
\(106\) −8.73826 + 15.1351i −0.848735 + 1.47005i
\(107\) 0.607225 + 2.26620i 0.0587027 + 0.219081i 0.989046 0.147609i \(-0.0471576\pi\)
−0.930343 + 0.366690i \(0.880491\pi\)
\(108\) −4.31849 + 0.269654i −0.415547 + 0.0259475i
\(109\) −0.0677925 + 0.0391400i −0.00649334 + 0.00374893i −0.503243 0.864145i \(-0.667860\pi\)
0.496750 + 0.867894i \(0.334527\pi\)
\(110\) −21.2743 + 4.53600i −2.02843 + 0.432491i
\(111\) −0.784645 + 11.7854i −0.0744752 + 1.11862i
\(112\) 8.94191 + 9.64825i 0.844931 + 0.911674i
\(113\) −0.841853 + 3.14184i −0.0791949 + 0.295559i −0.994152 0.107992i \(-0.965558\pi\)
0.914957 + 0.403552i \(0.132224\pi\)
\(114\) 9.65999 4.75142i 0.904741 0.445011i
\(115\) −2.69153 + 8.30147i −0.250987 + 0.774116i
\(116\) 0.433775 0.250440i 0.0402750 0.0232528i
\(117\) 9.34350 + 12.2288i 0.863807 + 1.13055i
\(118\) 7.11827 7.11827i 0.655290 0.655290i
\(119\) 7.40779 + 0.281462i 0.679071 + 0.0258015i
\(120\) 6.09488 + 4.55506i 0.556384 + 0.415818i
\(121\) −22.4078 −2.03707
\(122\) −0.113403 0.423226i −0.0102670 0.0383171i
\(123\) −0.0156041 0.0788716i −0.00140698 0.00711162i
\(124\) 3.09344 1.78600i 0.277799 0.160387i
\(125\) −11.0460 1.72813i −0.987982 0.154568i
\(126\) −10.2644 8.55009i −0.914421 0.761703i
\(127\) −7.99553 7.99553i −0.709489 0.709489i 0.256939 0.966428i \(-0.417286\pi\)
−0.966428 + 0.256939i \(0.917286\pi\)
\(128\) 3.37502 12.5957i 0.298312 1.11332i
\(129\) −4.24803 0.282824i −0.374018 0.0249012i
\(130\) −0.998266 + 19.2803i −0.0875537 + 1.69100i
\(131\) 11.7087i 1.02300i −0.859284 0.511499i \(-0.829090\pi\)
0.859284 0.511499i \(-0.170910\pi\)
\(132\) −5.49013 6.27331i −0.477854 0.546022i
\(133\) 9.33468 + 2.88527i 0.809419 + 0.250184i
\(134\) −6.41307 −0.554005
\(135\) −10.1235 5.70218i −0.871292 0.490766i
\(136\) −2.75234 4.76719i −0.236011 0.408783i
\(137\) 9.44890 9.44890i 0.807274 0.807274i −0.176946 0.984220i \(-0.556622\pi\)
0.984220 + 0.176946i \(0.0566219\pi\)
\(138\) −11.1609 + 2.20810i −0.950080 + 0.187966i
\(139\) −5.41128 + 3.12420i −0.458978 + 0.264991i −0.711615 0.702570i \(-0.752036\pi\)
0.252636 + 0.967561i \(0.418702\pi\)
\(140\) −0.843615 4.85363i −0.0712985 0.410206i
\(141\) 4.27038 6.37685i 0.359631 0.537028i
\(142\) 2.17268 8.10856i 0.182327 0.680455i
\(143\) −7.67413 + 28.6403i −0.641743 + 2.39502i
\(144\) −1.97739 + 14.7844i −0.164782 + 1.23203i
\(145\) 1.34320 + 0.0695463i 0.111547 + 0.00577550i
\(146\) 14.5553 + 8.40350i 1.20460 + 0.695478i
\(147\) −1.44380 12.0381i −0.119082 0.992884i
\(148\) −5.48509 1.46972i −0.450871 0.120811i
\(149\) 8.98476 0.736060 0.368030 0.929814i \(-0.380032\pi\)
0.368030 + 0.929814i \(0.380032\pi\)
\(150\) −5.04807 13.6737i −0.412173 1.11645i
\(151\) 0.804270 0.0654506 0.0327253 0.999464i \(-0.489581\pi\)
0.0327253 + 0.999464i \(0.489581\pi\)
\(152\) −1.87776 7.00788i −0.152306 0.568414i
\(153\) 5.10332 + 6.67922i 0.412579 + 0.539983i
\(154\) 0.977218 25.7194i 0.0787465 2.07253i
\(155\) 9.57897 + 0.495965i 0.769402 + 0.0398369i
\(156\) −6.63921 + 3.26560i −0.531562 + 0.261457i
\(157\) −19.8113 + 5.30842i −1.58111 + 0.423658i −0.939270 0.343178i \(-0.888497\pi\)
−0.641843 + 0.766836i \(0.721830\pi\)
\(158\) −22.1357 + 5.93125i −1.76102 + 0.471865i
\(159\) −14.9438 10.0074i −1.18512 0.793639i
\(160\) −7.37218 + 6.64635i −0.582822 + 0.525440i
\(161\) −8.73994 5.49871i −0.688804 0.433359i
\(162\) 0.0623893 15.1475i 0.00490177 1.19010i
\(163\) 3.73310 + 13.9321i 0.292399 + 1.09125i 0.943261 + 0.332052i \(0.107741\pi\)
−0.650862 + 0.759196i \(0.725592\pi\)
\(164\) 0.0386539 0.00301836
\(165\) −3.20331 22.1553i −0.249377 1.72478i
\(166\) 9.07394 0.704274
\(167\) 8.78402 + 2.35367i 0.679728 + 0.182133i 0.582133 0.813094i \(-0.302218\pi\)
0.0975951 + 0.995226i \(0.468885\pi\)
\(168\) −6.99518 + 5.66763i −0.539690 + 0.437267i
\(169\) 11.5319 + 6.65797i 0.887073 + 0.512152i
\(170\) −0.545242 + 10.5307i −0.0418182 + 0.807669i
\(171\) 4.21851 + 10.2440i 0.322598 + 0.783379i
\(172\) 0.529759 1.97709i 0.0403938 0.150752i
\(173\) −5.43521 + 20.2845i −0.413231 + 1.54220i 0.375121 + 0.926976i \(0.377601\pi\)
−0.788352 + 0.615224i \(0.789066\pi\)
\(174\) 0.773923 + 1.57344i 0.0586710 + 0.119282i
\(175\) 5.19093 12.1678i 0.392398 0.919796i
\(176\) −24.8878 + 14.3690i −1.87599 + 1.08310i
\(177\) 6.82262 + 7.79589i 0.512820 + 0.585975i
\(178\) 1.13159 1.13159i 0.0848161 0.0848161i
\(179\) −3.62325 6.27565i −0.270814 0.469064i 0.698256 0.715848i \(-0.253960\pi\)
−0.969071 + 0.246784i \(0.920626\pi\)
\(180\) 3.63389 4.24244i 0.270854 0.316213i
\(181\) −7.42740 −0.552075 −0.276037 0.961147i \(-0.589021\pi\)
−0.276037 + 0.961147i \(0.589021\pi\)
\(182\) −21.8246 6.74579i −1.61775 0.500031i
\(183\) 0.442334 0.0875123i 0.0326983 0.00646910i
\(184\) 7.66751i 0.565256i
\(185\) −10.2104 11.3255i −0.750686 0.832666i
\(186\) 5.51919 + 11.2209i 0.404686 + 0.822757i
\(187\) −4.19153 + 15.6430i −0.306515 + 1.14393i
\(188\) 2.60903 + 2.60903i 0.190283 + 0.190283i
\(189\) 9.48121 9.95523i 0.689656 0.724137i
\(190\) −4.28637 + 13.2204i −0.310966 + 0.959110i
\(191\) 23.3890 13.5036i 1.69237 0.977088i 0.739764 0.672867i \(-0.234937\pi\)
0.952601 0.304221i \(-0.0983962\pi\)
\(192\) 4.05449 + 1.38097i 0.292607 + 0.0996630i
\(193\) 1.82752 + 6.82039i 0.131548 + 0.490943i 0.999988 0.00485068i \(-0.00154402\pi\)
−0.868441 + 0.495793i \(0.834877\pi\)
\(194\) −14.9388 −1.07254
\(195\) −19.7294 2.34313i −1.41285 0.167795i
\(196\) 5.81218 + 0.442311i 0.415156 + 0.0315936i
\(197\) 17.3124 17.3124i 1.23346 1.23346i 0.270831 0.962627i \(-0.412701\pi\)
0.962627 0.270831i \(-0.0872986\pi\)
\(198\) 23.1898 17.7184i 1.64803 1.25919i
\(199\) 4.51831 2.60865i 0.320295 0.184922i −0.331229 0.943550i \(-0.607463\pi\)
0.651524 + 0.758628i \(0.274130\pi\)
\(200\) −9.70023 + 1.54889i −0.685910 + 0.109523i
\(201\) 0.438423 6.58513i 0.0309240 0.464480i
\(202\) −2.63933 + 9.85013i −0.185703 + 0.693053i
\(203\) −0.469960 + 1.52046i −0.0329847 + 0.106715i
\(204\) −3.62627 + 1.78364i −0.253889 + 0.124880i
\(205\) 0.0870866 + 0.0564768i 0.00608239 + 0.00394451i
\(206\) −20.3950 + 11.7750i −1.42098 + 0.820405i
\(207\) −1.50434 11.6113i −0.104559 0.807043i
\(208\) 6.60143 + 24.6369i 0.457727 + 1.70826i
\(209\) −10.6723 + 18.4849i −0.738218 + 1.27863i
\(210\) 17.1502 1.81804i 1.18348 0.125457i
\(211\) −8.18572 14.1781i −0.563528 0.976059i −0.997185 0.0749813i \(-0.976110\pi\)
0.433657 0.901078i \(-0.357223\pi\)
\(212\) 6.11412 6.11412i 0.419919 0.419919i
\(213\) 8.17759 + 2.78531i 0.560319 + 0.190846i
\(214\) 3.94871i 0.269928i
\(215\) 4.08225 3.68033i 0.278407 0.250996i
\(216\) −10.0061 2.02249i −0.680830 0.137613i
\(217\) −3.35149 + 10.8430i −0.227514 + 0.736073i
\(218\) 0.127261 0.0340995i 0.00861921 0.00230951i
\(219\) −9.62403 + 14.3713i −0.650332 + 0.971124i
\(220\) 10.7479 + 0.556487i 0.724622 + 0.0375183i
\(221\) 12.4478 + 7.18674i 0.837330 + 0.483433i
\(222\) 6.40945 18.8180i 0.430174 1.26298i
\(223\) −4.79865 17.9088i −0.321341 1.19926i −0.917939 0.396721i \(-0.870148\pi\)
0.596598 0.802540i \(-0.296519\pi\)
\(224\) −5.48182 10.3866i −0.366270 0.693985i
\(225\) 14.3857 4.24872i 0.959047 0.283248i
\(226\) 2.73723 4.74102i 0.182078 0.315368i
\(227\) −13.9460 + 13.9460i −0.925631 + 0.925631i −0.997420 0.0717885i \(-0.977129\pi\)
0.0717885 + 0.997420i \(0.477129\pi\)
\(228\) −5.22495 + 1.03372i −0.346031 + 0.0684595i
\(229\) 24.7606i 1.63623i 0.575057 + 0.818113i \(0.304980\pi\)
−0.575057 + 0.818113i \(0.695020\pi\)
\(230\) 7.99188 12.3234i 0.526969 0.812580i
\(231\) 26.3427 + 2.76172i 1.73322 + 0.181708i
\(232\) 1.14146 0.305854i 0.0749406 0.0200803i
\(233\) 9.80067 2.62608i 0.642064 0.172040i 0.0769256 0.997037i \(-0.475490\pi\)
0.565138 + 0.824996i \(0.308823\pi\)
\(234\) −9.86293 23.9506i −0.644760 1.56570i
\(235\) 2.06608 + 9.69014i 0.134776 + 0.632115i
\(236\) −4.31334 + 2.49031i −0.280775 + 0.162105i
\(237\) −4.57710 23.1351i −0.297315 1.50279i
\(238\) −11.9204 3.68448i −0.772682 0.238829i
\(239\) −2.63822 4.56953i −0.170652 0.295578i 0.767996 0.640455i \(-0.221254\pi\)
−0.938648 + 0.344877i \(0.887921\pi\)
\(240\) −11.9156 15.1272i −0.769146 0.976460i
\(241\) 3.63556 0.234187 0.117094 0.993121i \(-0.462642\pi\)
0.117094 + 0.993121i \(0.462642\pi\)
\(242\) 36.4287 + 9.76104i 2.34173 + 0.627463i
\(243\) 15.5496 + 1.09960i 0.997509 + 0.0705397i
\(244\) 0.216782i 0.0138780i
\(245\) 12.4485 + 9.48865i 0.795307 + 0.606207i
\(246\) −0.00898934 + 0.135020i −0.000573139 + 0.00860858i
\(247\) 13.3955 + 13.3955i 0.852334 + 0.852334i
\(248\) 8.14025 2.18117i 0.516907 0.138505i
\(249\) −0.620331 + 9.31740i −0.0393119 + 0.590466i
\(250\) 17.2048 + 7.62118i 1.08813 + 0.482006i
\(251\) 10.0487i 0.634268i 0.948381 + 0.317134i \(0.102720\pi\)
−0.948381 + 0.317134i \(0.897280\pi\)
\(252\) 3.81048 + 5.40048i 0.240037 + 0.340198i
\(253\) 15.9509 15.9509i 1.00282 1.00282i
\(254\) 9.51554 + 16.4814i 0.597058 + 1.03414i
\(255\) −10.7760 1.27979i −0.674818 0.0801438i
\(256\) −8.50073 + 14.7237i −0.531296 + 0.920231i
\(257\) 9.83080 9.83080i 0.613228 0.613228i −0.330557 0.943786i \(-0.607237\pi\)
0.943786 + 0.330557i \(0.107237\pi\)
\(258\) 6.78289 + 2.31027i 0.422284 + 0.143831i
\(259\) 15.9564 8.42142i 0.991482 0.523282i
\(260\) 2.94598 9.08625i 0.182702 0.563506i
\(261\) −1.66857 + 0.687122i −0.103282 + 0.0425318i
\(262\) −5.10044 + 19.0351i −0.315106 + 1.17599i
\(263\) 6.04934 + 6.04934i 0.373018 + 0.373018i 0.868575 0.495557i \(-0.165036\pi\)
−0.495557 + 0.868575i \(0.665036\pi\)
\(264\) −8.68083 17.6488i −0.534268 1.08621i
\(265\) 22.7083 4.84175i 1.39496 0.297426i
\(266\) −13.9187 8.75691i −0.853410 0.536920i
\(267\) 1.08459 + 1.23931i 0.0663758 + 0.0758445i
\(268\) 3.06481 + 0.821213i 0.187213 + 0.0501636i
\(269\) 6.48075 + 11.2250i 0.395138 + 0.684399i 0.993119 0.117111i \(-0.0373634\pi\)
−0.597981 + 0.801511i \(0.704030\pi\)
\(270\) 13.9740 + 13.6800i 0.850432 + 0.832540i
\(271\) −8.50968 + 14.7392i −0.516926 + 0.895342i 0.482881 + 0.875686i \(0.339590\pi\)
−0.999807 + 0.0196561i \(0.993743\pi\)
\(272\) 3.60563 + 13.4564i 0.218624 + 0.815914i
\(273\) 8.41881 21.9490i 0.509529 1.32841i
\(274\) −19.4773 + 11.2452i −1.17667 + 0.679348i
\(275\) 23.4017 + 16.9574i 1.41118 + 1.02257i
\(276\) 5.61656 + 0.373938i 0.338077 + 0.0225084i
\(277\) −18.3199 18.3199i −1.10074 1.10074i −0.994322 0.106417i \(-0.966062\pi\)
−0.106417 0.994322i \(-0.533938\pi\)
\(278\) 10.1581 2.72187i 0.609245 0.163247i
\(279\) −11.8993 + 4.90016i −0.712392 + 0.293365i
\(280\) 1.04126 11.5761i 0.0622271 0.691806i
\(281\) −25.6887 14.8314i −1.53246 0.884767i −0.999247 0.0387873i \(-0.987651\pi\)
−0.533215 0.845980i \(-0.679016\pi\)
\(282\) −9.72026 + 8.50674i −0.578833 + 0.506569i
\(283\) −1.71860 6.41388i −0.102160 0.381266i 0.895848 0.444361i \(-0.146569\pi\)
−0.998007 + 0.0630955i \(0.979903\pi\)
\(284\) −2.07665 + 3.59687i −0.123227 + 0.213435i
\(285\) −13.2821 5.30518i −0.786764 0.314252i
\(286\) 24.9519 43.2180i 1.47544 2.55554i
\(287\) −0.0900770 + 0.0834825i −0.00531708 + 0.00492782i
\(288\) 5.12151 12.2928i 0.301788 0.724357i
\(289\) −7.92357 4.57468i −0.466092 0.269099i
\(290\) −2.15337 0.698175i −0.126451 0.0409983i
\(291\) 1.02128 15.3396i 0.0598683 0.899225i
\(292\) −5.87989 5.87989i −0.344094 0.344094i
\(293\) −1.20343 + 4.49127i −0.0703052 + 0.262383i −0.992128 0.125229i \(-0.960033\pi\)
0.921823 + 0.387612i \(0.126700\pi\)
\(294\) −2.89670 + 20.1995i −0.168939 + 1.17806i
\(295\) −13.3565 0.691550i −0.777644 0.0402636i
\(296\) −11.6026 6.69875i −0.674386 0.389357i
\(297\) 16.6085 + 25.0233i 0.963722 + 1.45200i
\(298\) −14.6067 3.91385i −0.846143 0.226723i
\(299\) −10.0105 17.3386i −0.578921 1.00272i
\(300\) 0.661513 + 7.18110i 0.0381925 + 0.414601i
\(301\) 3.03548 + 5.75145i 0.174962 + 0.331508i
\(302\) −1.30752 0.350348i −0.0752391 0.0201602i
\(303\) −9.93398 3.38354i −0.570692 0.194380i
\(304\) 18.3610i 1.05308i
\(305\) −0.316737 + 0.488406i −0.0181363 + 0.0279660i
\(306\) −5.38703 13.0816i −0.307956 0.747824i
\(307\) −3.42180 3.42180i −0.195292 0.195292i 0.602686 0.797978i \(-0.294097\pi\)
−0.797978 + 0.602686i \(0.794097\pi\)
\(308\) −3.76046 + 12.1662i −0.214272 + 0.693233i
\(309\) −10.6967 21.7472i −0.608513 1.23715i
\(310\) −15.3567 4.97899i −0.872199 0.282788i
\(311\) 21.7248 + 12.5428i 1.23190 + 0.711239i 0.967426 0.253154i \(-0.0814679\pi\)
0.264475 + 0.964392i \(0.414801\pi\)
\(312\) −17.1243 + 3.38790i −0.969470 + 0.191802i
\(313\) −25.8953 6.93863i −1.46369 0.392195i −0.562927 0.826506i \(-0.690325\pi\)
−0.900763 + 0.434312i \(0.856992\pi\)
\(314\) 34.5200 1.94807
\(315\) 0.694364 + 17.7347i 0.0391230 + 0.999234i
\(316\) 11.3382 0.637823
\(317\) −24.5981 6.59104i −1.38157 0.370189i −0.509876 0.860248i \(-0.670309\pi\)
−0.871690 + 0.490058i \(0.836975\pi\)
\(318\) 19.9351 + 22.7789i 1.11790 + 1.27738i
\(319\) −3.01087 1.73833i −0.168577 0.0973277i
\(320\) −4.92534 + 2.51349i −0.275335 + 0.140508i
\(321\) 4.05465 + 0.269949i 0.226309 + 0.0150671i
\(322\) 11.8134 + 12.7465i 0.658334 + 0.710337i
\(323\) 7.31647 + 7.31647i 0.407099 + 0.407099i
\(324\) −1.96950 + 7.23100i −0.109417 + 0.401722i
\(325\) 19.9131 16.1669i 1.10458 0.896776i
\(326\) 24.2759i 1.34452i
\(327\) 0.0263144 + 0.133007i 0.00145519 + 0.00735530i
\(328\) 0.0880887 + 0.0236033i 0.00486389 + 0.00130327i
\(329\) −11.7148 0.445108i −0.645857 0.0245396i
\(330\) −4.44337 + 37.4136i −0.244599 + 2.05955i
\(331\) 7.91445 + 13.7082i 0.435017 + 0.753472i 0.997297 0.0734750i \(-0.0234089\pi\)
−0.562280 + 0.826947i \(0.690076\pi\)
\(332\) −4.33644 1.16195i −0.237993 0.0637701i
\(333\) 18.8847 + 7.86789i 1.03487 + 0.431158i
\(334\) −13.2551 7.65281i −0.725284 0.418743i
\(335\) 5.70511 + 6.32815i 0.311703 + 0.345744i
\(336\) 20.8124 9.27282i 1.13541 0.505874i
\(337\) 5.89322 21.9938i 0.321024 1.19808i −0.597225 0.802074i \(-0.703730\pi\)
0.918249 0.396004i \(-0.129603\pi\)
\(338\) −15.8474 15.8474i −0.861985 0.861985i
\(339\) 4.68110 + 3.13479i 0.254243 + 0.170258i
\(340\) 1.60906 4.96282i 0.0872637 0.269146i
\(341\) −21.4719 12.3968i −1.16277 0.671323i
\(342\) −2.39572 18.4915i −0.129546 0.999905i
\(343\) −14.4997 + 11.5221i −0.782910 + 0.622135i
\(344\) 2.41455 4.18212i 0.130184 0.225485i
\(345\) 12.1077 + 9.04878i 0.651856 + 0.487170i
\(346\) 17.6722 30.6092i 0.950064 1.64556i
\(347\) −3.09853 11.5639i −0.166338 0.620782i −0.997866 0.0652987i \(-0.979200\pi\)
0.831528 0.555483i \(-0.187467\pi\)
\(348\) −0.168374 0.851054i −0.00902581 0.0456213i
\(349\) 9.21413 + 5.31978i 0.493221 + 0.284761i 0.725910 0.687790i \(-0.241419\pi\)
−0.232689 + 0.972551i \(0.574752\pi\)
\(350\) −13.7394 + 17.5201i −0.734401 + 0.936489i
\(351\) 25.2675 8.49021i 1.34868 0.453174i
\(352\) 24.7829 6.64055i 1.32093 0.353942i
\(353\) −0.402327 0.402327i −0.0214137 0.0214137i 0.696319 0.717733i \(-0.254820\pi\)
−0.717733 + 0.696319i \(0.754820\pi\)
\(354\) −7.69569 15.6459i −0.409022 0.831571i
\(355\) −9.93402 + 5.06952i −0.527243 + 0.269062i
\(356\) −0.685691 + 0.395884i −0.0363415 + 0.0209818i
\(357\) 4.59826 11.9883i 0.243366 0.634489i
\(358\) 3.15665 + 11.7808i 0.166834 + 0.622633i
\(359\) −14.6803 + 25.4271i −0.774798 + 1.34199i 0.160110 + 0.987099i \(0.448815\pi\)
−0.934908 + 0.354890i \(0.884518\pi\)
\(360\) 10.8719 7.44918i 0.572999 0.392606i
\(361\) −2.68136 4.64425i −0.141124 0.244434i
\(362\) 12.0749 + 3.23545i 0.634641 + 0.170051i
\(363\) −12.5133 + 36.7388i −0.656781 + 1.92829i
\(364\) 9.56617 + 6.01853i 0.501404 + 0.315457i
\(365\) −4.65626 21.8384i −0.243720 1.14307i
\(366\) −0.757231 0.0504147i −0.0395811 0.00263522i
\(367\) −23.2628 23.2628i −1.21431 1.21431i −0.969595 0.244714i \(-0.921306\pi\)
−0.244714 0.969595i \(-0.578694\pi\)
\(368\) 5.02231 18.7435i 0.261806 0.977074i
\(369\) −0.138028 0.0184611i −0.00718548 0.000961044i
\(370\) 11.6658 + 22.8598i 0.606475 + 1.18842i
\(371\) −1.04309 + 27.4530i −0.0541543 + 1.42529i
\(372\) −1.20075 6.06923i −0.0622560 0.314675i
\(373\) 13.7523 13.7523i 0.712067 0.712067i −0.254900 0.966967i \(-0.582043\pi\)
0.966967 + 0.254900i \(0.0820426\pi\)
\(374\) 13.6285 23.6052i 0.704712 1.22060i
\(375\) −9.00186 + 17.1455i −0.464854 + 0.885387i
\(376\) 4.35259 + 7.53890i 0.224468 + 0.388789i
\(377\) −2.18189 + 2.18189i −0.112373 + 0.112373i
\(378\) −19.7504 + 12.0543i −1.01585 + 0.620006i
\(379\) 11.3129i 0.581104i 0.956859 + 0.290552i \(0.0938390\pi\)
−0.956859 + 0.290552i \(0.906161\pi\)
\(380\) 3.74138 5.76917i 0.191929 0.295952i
\(381\) −17.5741 + 8.64412i −0.900350 + 0.442852i
\(382\) −43.9061 + 11.7646i −2.24643 + 0.601930i
\(383\) 2.43811 + 2.43811i 0.124582 + 0.124582i 0.766649 0.642067i \(-0.221923\pi\)
−0.642067 + 0.766649i \(0.721923\pi\)
\(384\) −18.7667 12.5675i −0.957683 0.641331i
\(385\) −26.2482 + 21.9159i −1.33773 + 1.11694i
\(386\) 11.8841i 0.604886i
\(387\) −2.83597 + 6.80694i −0.144160 + 0.346016i
\(388\) 7.13927 + 1.91296i 0.362442 + 0.0971159i
\(389\) −25.1775 −1.27655 −0.638274 0.769809i \(-0.720351\pi\)
−0.638274 + 0.769809i \(0.720351\pi\)
\(390\) 31.0537 + 12.4036i 1.57247 + 0.628080i
\(391\) −5.46761 9.47019i −0.276509 0.478928i
\(392\) 12.9754 + 4.55710i 0.655355 + 0.230168i
\(393\) −19.1972 6.53861i −0.968368 0.329829i
\(394\) −35.6865 + 20.6036i −1.79786 + 1.03800i
\(395\) 25.5448 + 16.5661i 1.28530 + 0.833532i
\(396\) −13.3513 + 5.49812i −0.670930 + 0.276291i
\(397\) 14.4004 3.85859i 0.722738 0.193657i 0.121345 0.992610i \(-0.461279\pi\)
0.601393 + 0.798953i \(0.294613\pi\)
\(398\) −8.48186 + 2.27271i −0.425157 + 0.113920i
\(399\) 9.94340 13.6935i 0.497793 0.685532i
\(400\) 24.7271 + 2.56745i 1.23636 + 0.128372i
\(401\) 10.1707i 0.507900i −0.967217 0.253950i \(-0.918270\pi\)
0.967217 0.253950i \(-0.0817299\pi\)
\(402\) −3.58130 + 10.5146i −0.178619 + 0.524420i
\(403\) −15.5600 + 15.5600i −0.775099 + 0.775099i
\(404\) 2.52268 4.36941i 0.125508 0.217386i
\(405\) −15.0024 + 13.4137i −0.745475 + 0.666534i
\(406\) 1.42635 2.26711i 0.0707884 0.112515i
\(407\) 10.2015 + 38.0726i 0.505670 + 1.88719i
\(408\) −9.35309 + 1.85043i −0.463047 + 0.0916102i
\(409\) 9.91700 + 5.72558i 0.490364 + 0.283112i 0.724726 0.689038i \(-0.241967\pi\)
−0.234361 + 0.972150i \(0.575300\pi\)
\(410\) −0.116976 0.129751i −0.00577705 0.00640795i
\(411\) −10.2154 20.7686i −0.503888 1.02444i
\(412\) 11.2546 3.01566i 0.554474 0.148571i
\(413\) 4.67316 15.1190i 0.229951 0.743958i
\(414\) −2.61237 + 19.5320i −0.128391 + 0.959947i
\(415\) −8.07224 8.95379i −0.396251 0.439524i
\(416\) 22.7716i 1.11647i
\(417\) 2.10044 + 10.6168i 0.102859 + 0.519905i
\(418\) 25.4023 25.4023i 1.24247 1.24247i
\(419\) −14.8220 25.6724i −0.724100 1.25418i −0.959343 0.282242i \(-0.908922\pi\)
0.235243 0.971937i \(-0.424411\pi\)
\(420\) −8.42890 1.32729i −0.411288 0.0647653i
\(421\) −5.47489 + 9.48279i −0.266830 + 0.462163i −0.968041 0.250790i \(-0.919310\pi\)
0.701211 + 0.712953i \(0.252643\pi\)
\(422\) 7.13156 + 26.6153i 0.347159 + 1.29561i
\(423\) −8.07047 10.5626i −0.392400 0.513572i
\(424\) 17.6670 10.2001i 0.857986 0.495359i
\(425\) 10.8763 8.83017i 0.527579 0.428326i
\(426\) −12.0811 8.09037i −0.585333 0.391980i
\(427\) −0.468193 0.505177i −0.0226574 0.0244472i
\(428\) −0.505644 + 1.88709i −0.0244412 + 0.0912160i
\(429\) 42.6718 + 28.5760i 2.06021 + 1.37966i
\(430\) −8.23976 + 4.20491i −0.397357 + 0.202779i
\(431\) −1.68217 + 0.971200i −0.0810271 + 0.0467810i −0.539966 0.841687i \(-0.681563\pi\)
0.458939 + 0.888468i \(0.348230\pi\)
\(432\) 23.1356 + 11.4982i 1.11311 + 0.553208i
\(433\) −18.4087 + 18.4087i −0.884664 + 0.884664i −0.994004 0.109341i \(-0.965126\pi\)
0.109341 + 0.994004i \(0.465126\pi\)
\(434\) 10.1719 16.1678i 0.488267 0.776077i
\(435\) 0.864121 2.16342i 0.0414314 0.103728i
\(436\) −0.0651848 −0.00312178
\(437\) −3.73023 13.9214i −0.178441 0.665951i
\(438\) 21.9062 19.1714i 1.04672 0.916044i
\(439\) −11.9970 + 6.92649i −0.572587 + 0.330583i −0.758182 0.652043i \(-0.773912\pi\)
0.185595 + 0.982626i \(0.440579\pi\)
\(440\) 24.1536 + 7.83119i 1.15148 + 0.373337i
\(441\) −20.5434 4.35534i −0.978257 0.207397i
\(442\) −17.1060 17.1060i −0.813649 0.813649i
\(443\) 7.64150 28.5185i 0.363059 1.35495i −0.506975 0.861961i \(-0.669236\pi\)
0.870034 0.492992i \(-0.164097\pi\)
\(444\) −5.47278 + 8.17236i −0.259727 + 0.387843i
\(445\) −2.12327 0.109935i −0.100653 0.00521144i
\(446\) 31.2050i 1.47760i
\(447\) 5.01743 14.7310i 0.237316 0.696754i
\(448\) −1.45221 6.37952i −0.0686105 0.301404i
\(449\) −16.2033 −0.764681 −0.382340 0.924022i \(-0.624882\pi\)
−0.382340 + 0.924022i \(0.624882\pi\)
\(450\) −25.2379 + 0.640671i −1.18972 + 0.0302015i
\(451\) −0.134150 0.232355i −0.00631689 0.0109412i
\(452\) −1.91523 + 1.91523i −0.0900848 + 0.0900848i
\(453\) 0.449135 1.31865i 0.0211022 0.0619554i
\(454\) 28.7474 16.5973i 1.34918 0.778950i
\(455\) 12.7588 + 27.5367i 0.598144 + 1.29094i
\(456\) −12.5384 0.834779i −0.587166 0.0390921i
\(457\) 4.03576 15.0617i 0.188785 0.704555i −0.805004 0.593270i \(-0.797837\pi\)
0.993789 0.111285i \(-0.0354966\pi\)
\(458\) 10.7860 40.2537i 0.503995 1.88093i
\(459\) 13.8008 4.63726i 0.644168 0.216449i
\(460\) −5.39737 + 4.86597i −0.251654 + 0.226877i
\(461\) 20.9053 + 12.0697i 0.973658 + 0.562142i 0.900349 0.435168i \(-0.143311\pi\)
0.0733083 + 0.997309i \(0.476644\pi\)
\(462\) −41.6227 15.9649i −1.93646 0.742754i
\(463\) 32.8113 + 8.79175i 1.52487 + 0.408587i 0.921341 0.388755i \(-0.127095\pi\)
0.603527 + 0.797342i \(0.293761\pi\)
\(464\) −2.99069 −0.138839
\(465\) 6.16242 15.4283i 0.285776 0.715470i
\(466\) −17.0771 −0.791080
\(467\) 0.169822 + 0.633783i 0.00785841 + 0.0293280i 0.969744 0.244125i \(-0.0785008\pi\)
−0.961885 + 0.273453i \(0.911834\pi\)
\(468\) 1.64655 + 12.7090i 0.0761119 + 0.587474i
\(469\) −8.91569 + 4.70550i −0.411688 + 0.217280i
\(470\) 0.862255 16.6534i 0.0397728 0.768165i
\(471\) −2.35992 + 35.4462i −0.108740 + 1.63327i
\(472\) −11.3504 + 3.04133i −0.522444 + 0.139988i
\(473\) −13.7232 + 3.67711i −0.630992 + 0.169074i
\(474\) −2.63681 + 39.6050i −0.121113 + 1.81912i
\(475\) 16.8585 7.53136i 0.773523 0.345563i
\(476\) 5.22494 + 3.28726i 0.239485 + 0.150671i
\(477\) −24.7529 + 18.9127i −1.13336 + 0.865954i
\(478\) 2.29847 + 8.57799i 0.105129 + 0.392348i
\(479\) −2.65985 −0.121532 −0.0607659 0.998152i \(-0.519354\pi\)
−0.0607659 + 0.998152i \(0.519354\pi\)
\(480\) 6.78017 + 15.7987i 0.309471 + 0.721108i
\(481\) 34.9828 1.59508
\(482\) −5.91040 1.58369i −0.269211 0.0721349i
\(483\) −13.8962 + 11.2589i −0.632297 + 0.512300i
\(484\) −16.1594 9.32962i −0.734517 0.424074i
\(485\) 13.2897 + 14.7410i 0.603453 + 0.669354i
\(486\) −24.8003 8.56121i −1.12496 0.388345i
\(487\) 0.768573 2.86836i 0.0348274 0.129978i −0.946323 0.323221i \(-0.895234\pi\)
0.981151 + 0.193244i \(0.0619008\pi\)
\(488\) −0.132374 + 0.494026i −0.00599228 + 0.0223635i
\(489\) 24.9272 + 1.65960i 1.12725 + 0.0750495i
\(490\) −16.1044 20.8486i −0.727524 0.941842i
\(491\) −7.73296 + 4.46462i −0.348983 + 0.201486i −0.664237 0.747522i \(-0.731244\pi\)
0.315254 + 0.949007i \(0.397910\pi\)
\(492\) 0.0215858 0.0633752i 0.000973163 0.00285718i
\(493\) −1.19172 + 1.19172i −0.0536726 + 0.0536726i
\(494\) −15.9421 27.6125i −0.717267 1.24234i
\(495\) −38.1137 7.12033i −1.71308 0.320035i
\(496\) −21.3279 −0.957650
\(497\) −2.92900 12.8670i −0.131383 0.577164i
\(498\) 5.06723 14.8772i 0.227068 0.666665i
\(499\) 26.4915i 1.18592i −0.805231 0.592961i \(-0.797959\pi\)
0.805231 0.592961i \(-0.202041\pi\)
\(500\) −7.24629 5.84530i −0.324064 0.261410i
\(501\) 8.76431 13.0875i 0.391560 0.584707i
\(502\) 4.37731 16.3363i 0.195369 0.729126i
\(503\) 1.46414 + 1.46414i 0.0652830 + 0.0652830i 0.738994 0.673711i \(-0.235301\pi\)
−0.673711 + 0.738994i \(0.735301\pi\)
\(504\) 5.38603 + 14.6340i 0.239913 + 0.651851i
\(505\) 12.0677 6.15836i 0.537004 0.274043i
\(506\) −32.8799 + 18.9832i −1.46169 + 0.843908i
\(507\) 17.3560 15.1892i 0.770807 0.674577i
\(508\) −2.43699 9.09497i −0.108124 0.403524i
\(509\) 3.67812 0.163030 0.0815148 0.996672i \(-0.474024\pi\)
0.0815148 + 0.996672i \(0.474024\pi\)
\(510\) 16.9612 + 6.77470i 0.751055 + 0.299989i
\(511\) 26.4013 + 1.00313i 1.16792 + 0.0443757i
\(512\) 1.79213 1.79213i 0.0792019 0.0792019i
\(513\) 19.1514 1.19585i 0.845555 0.0527979i
\(514\) −20.2645 + 11.6997i −0.893829 + 0.516052i
\(515\) 29.7626 + 9.64974i 1.31150 + 0.425218i
\(516\) −2.94571 1.97265i −0.129678 0.0868412i
\(517\) 6.62855 24.7381i 0.291523 1.08798i
\(518\) −29.6090 + 6.74009i −1.30095 + 0.296143i
\(519\) 30.2223 + 20.2389i 1.32661 + 0.888391i
\(520\) 12.2620 18.9079i 0.537724 0.829164i
\(521\) 9.81608 5.66732i 0.430050 0.248290i −0.269318 0.963051i \(-0.586798\pi\)
0.699368 + 0.714762i \(0.253465\pi\)
\(522\) 3.01194 0.390221i 0.131829 0.0170795i
\(523\) −5.30960 19.8157i −0.232173 0.866480i −0.979403 0.201915i \(-0.935283\pi\)
0.747230 0.664565i \(-0.231383\pi\)
\(524\) 4.87501 8.44377i 0.212966 0.368868i
\(525\) −17.0509 15.3058i −0.744163 0.667998i
\(526\) −7.19937 12.4697i −0.313907 0.543704i
\(527\) −8.49871 + 8.49871i −0.370210 + 0.370210i
\(528\) 9.66047 + 48.8292i 0.420418 + 2.12502i
\(529\) 7.76823i 0.337749i
\(530\) −39.0264 2.02065i −1.69520 0.0877713i
\(531\) 16.5918 6.83256i 0.720024 0.296508i
\(532\) 5.53041 + 5.96727i 0.239774 + 0.258714i
\(533\) −0.230012 + 0.0616316i −0.00996293 + 0.00266956i
\(534\) −1.22338 2.48723i −0.0529409 0.107633i
\(535\) −3.89642 + 3.51280i −0.168457 + 0.151871i
\(536\) 6.48297 + 3.74294i 0.280022 + 0.161671i
\(537\) −12.3127 + 2.43596i −0.531330 + 0.105120i
\(538\) −5.64615 21.0717i −0.243423 0.908467i
\(539\) −17.5127 36.4731i −0.754324 1.57101i
\(540\) −4.92642 8.32711i −0.212000 0.358342i
\(541\) 6.49741 11.2538i 0.279346 0.483841i −0.691877 0.722016i \(-0.743216\pi\)
0.971222 + 0.238175i \(0.0765492\pi\)
\(542\) 20.2549 20.2549i 0.870021 0.870021i
\(543\) −4.14774 + 12.1777i −0.177997 + 0.522593i
\(544\) 12.4376i 0.533258i
\(545\) −0.146860 0.0952408i −0.00629081 0.00407967i
\(546\) −23.2478 + 32.0156i −0.994914 + 1.37014i
\(547\) 7.26209 1.94587i 0.310505 0.0831995i −0.100202 0.994967i \(-0.531949\pi\)
0.410706 + 0.911768i \(0.365282\pi\)
\(548\) 10.7482 2.87997i 0.459140 0.123026i
\(549\) 0.103535 0.774102i 0.00441875 0.0330379i
\(550\) −30.6578 37.7619i −1.30725 1.61017i
\(551\) −1.92368 + 1.11064i −0.0819515 + 0.0473147i
\(552\) 12.5713 + 4.28183i 0.535071 + 0.182247i
\(553\) −26.4219 + 24.4876i −1.12357 + 1.04132i
\(554\) 21.8027 + 37.7634i 0.926308 + 1.60441i
\(555\) −24.2707 + 10.4160i −1.03023 + 0.442135i
\(556\) −5.20313 −0.220662
\(557\) −19.3115 5.17450i −0.818254 0.219251i −0.174671 0.984627i \(-0.555886\pi\)
−0.643583 + 0.765376i \(0.722553\pi\)
\(558\) 21.4795 2.78283i 0.909298 0.117807i
\(559\) 12.6095i 0.533323i
\(560\) −10.1279 + 27.6163i −0.427982 + 1.16700i
\(561\) 23.3069 + 15.6079i 0.984018 + 0.658966i
\(562\) 35.3019 + 35.3019i 1.48912 + 1.48912i
\(563\) 0.975092 0.261275i 0.0410952 0.0110114i −0.238213 0.971213i \(-0.576562\pi\)
0.279308 + 0.960202i \(0.409895\pi\)
\(564\) 5.73463 2.82067i 0.241472 0.118772i
\(565\) −7.11330 + 1.51666i −0.299259 + 0.0638064i
\(566\) 11.1758i 0.469754i
\(567\) −11.0275 21.1044i −0.463112 0.886300i
\(568\) −6.92888 + 6.92888i −0.290729 + 0.290729i
\(569\) 14.7365 + 25.5244i 0.617786 + 1.07004i 0.989889 + 0.141846i \(0.0453037\pi\)
−0.372102 + 0.928192i \(0.621363\pi\)
\(570\) 19.2820 + 14.4105i 0.807632 + 0.603591i
\(571\) 4.40154 7.62369i 0.184199 0.319041i −0.759108 0.650965i \(-0.774364\pi\)
0.943306 + 0.331924i \(0.107698\pi\)
\(572\) −17.4588 + 17.4588i −0.729988 + 0.729988i
\(573\) −9.07867 45.8885i −0.379267 1.91702i
\(574\) 0.182806 0.0964806i 0.00763015 0.00402702i
\(575\) −19.2698 + 3.07692i −0.803608 + 0.128317i
\(576\) 4.52836 5.87638i 0.188682 0.244849i
\(577\) −4.96336 + 18.5235i −0.206627 + 0.771144i 0.782320 + 0.622877i \(0.214036\pi\)
−0.988947 + 0.148267i \(0.952630\pi\)
\(578\) 10.8887 + 10.8887i 0.452911 + 0.452911i
\(579\) 12.2030 + 0.812446i 0.507138 + 0.0337641i
\(580\) 0.939696 + 0.609405i 0.0390188 + 0.0253042i
\(581\) 12.6149 6.65787i 0.523356 0.276215i
\(582\) −8.34240 + 24.4930i −0.345804 + 1.01527i
\(583\) −57.9724 15.5337i −2.40097 0.643338i
\(584\) −9.80929 16.9902i −0.405911 0.703059i
\(585\) −14.8593 + 31.0390i −0.614358 + 1.28330i
\(586\) 3.91288 6.77730i 0.161640 0.279968i
\(587\) −8.22432 30.6936i −0.339454 1.26686i −0.898959 0.438032i \(-0.855676\pi\)
0.559505 0.828827i \(-0.310991\pi\)
\(588\) 3.97094 9.28240i 0.163759 0.382800i
\(589\) −13.7186 + 7.92044i −0.565265 + 0.326356i
\(590\) 21.4126 + 6.94247i 0.881543 + 0.285817i
\(591\) −18.7168 38.0526i −0.769905 1.56527i
\(592\) 23.9752 + 23.9752i 0.985374 + 0.985374i
\(593\) 18.9385 5.07456i 0.777712 0.208387i 0.151936 0.988390i \(-0.451449\pi\)
0.625776 + 0.780003i \(0.284782\pi\)
\(594\) −16.1003 47.9157i −0.660603 1.96601i
\(595\) 6.96874 + 15.0403i 0.285691 + 0.616590i
\(596\) 6.47937 + 3.74086i 0.265405 + 0.153232i
\(597\) −1.75383 8.86480i −0.0717796 0.362812i
\(598\) 8.72132 + 32.5484i 0.356641 + 1.33100i
\(599\) −11.9813 + 20.7522i −0.489543 + 0.847914i −0.999928 0.0120326i \(-0.996170\pi\)
0.510384 + 0.859946i \(0.329503\pi\)
\(600\) −2.87748 + 16.7690i −0.117473 + 0.684593i
\(601\) −17.9459 + 31.0833i −0.732030 + 1.26791i 0.223985 + 0.974593i \(0.428093\pi\)
−0.956014 + 0.293320i \(0.905240\pi\)
\(602\) −2.42945 10.6725i −0.0990171 0.434979i
\(603\) −10.5519 4.39621i −0.429705 0.179027i
\(604\) 0.580000 + 0.334863i 0.0235999 + 0.0136254i
\(605\) −22.7754 44.6298i −0.925953 1.81446i
\(606\) 14.6759 + 9.82802i 0.596169 + 0.399236i
\(607\) −3.78919 3.78919i −0.153798 0.153798i 0.626014 0.779812i \(-0.284685\pi\)
−0.779812 + 0.626014i \(0.784685\pi\)
\(608\) 4.24272 15.8340i 0.172065 0.642155i
\(609\) 2.23043 + 1.61961i 0.0903816 + 0.0656297i
\(610\) 0.727680 0.656036i 0.0294629 0.0265621i
\(611\) −19.6852 11.3652i −0.796376 0.459788i
\(612\) 0.899330 + 6.94152i 0.0363532 + 0.280594i
\(613\) −37.4975 10.0474i −1.51451 0.405812i −0.596580 0.802554i \(-0.703474\pi\)
−0.917930 + 0.396742i \(0.870141\pi\)
\(614\) 4.07231 + 7.05345i 0.164345 + 0.284654i
\(615\) 0.141229 0.111245i 0.00569492 0.00448582i
\(616\) −15.9988 + 25.4294i −0.644611 + 1.02458i
\(617\) 29.4318 + 7.88624i 1.18488 + 0.317488i 0.796861 0.604163i \(-0.206492\pi\)
0.388020 + 0.921651i \(0.373159\pi\)
\(618\) 7.91652 + 40.0143i 0.318449 + 1.60961i
\(619\) 13.7469i 0.552533i −0.961081 0.276266i \(-0.910903\pi\)
0.961081 0.276266i \(-0.0890972\pi\)
\(620\) 6.70138 + 4.34593i 0.269134 + 0.174537i
\(621\) −19.8775 4.01775i −0.797657 0.161227i
\(622\) −29.8546 29.8546i −1.19706 1.19706i
\(623\) 0.742890 2.40346i 0.0297633 0.0962928i
\(624\) 44.0801 + 2.93475i 1.76461 + 0.117484i
\(625\) −7.78528 23.7569i −0.311411 0.950275i
\(626\) 39.0759 + 22.5605i 1.56179 + 0.901699i
\(627\) 24.3473 + 27.8205i 0.972338 + 1.11104i
\(628\) −16.4971 4.42039i −0.658307 0.176393i
\(629\) 19.1072 0.761854
\(630\) 6.59655 29.1340i 0.262813 1.16073i
\(631\) 48.8664 1.94534 0.972670 0.232192i \(-0.0745897\pi\)
0.972670 + 0.232192i \(0.0745897\pi\)
\(632\) 25.8387 + 6.92347i 1.02781 + 0.275401i
\(633\) −27.8170 + 5.50337i −1.10563 + 0.218739i
\(634\) 37.1184 + 21.4303i 1.47416 + 0.851107i
\(635\) 7.79807 24.0515i 0.309457 0.954455i
\(636\) −6.61009 13.4388i −0.262107 0.532883i
\(637\) −35.2910 + 6.63523i −1.39828 + 0.262897i
\(638\) 4.13760 + 4.13760i 0.163809 + 0.163809i
\(639\) 9.13335 11.8522i 0.361310 0.468866i
\(640\) 28.5175 6.08034i 1.12725 0.240347i
\(641\) 8.31450i 0.328403i 0.986427 + 0.164202i \(0.0525047\pi\)
−0.986427 + 0.164202i \(0.947495\pi\)
\(642\) −6.47413 2.20511i −0.255514 0.0870287i
\(643\) −13.2363 3.54665i −0.521988 0.139866i −0.0118018 0.999930i \(-0.503757\pi\)
−0.510186 + 0.860064i \(0.670423\pi\)
\(644\) −4.01339 7.60433i −0.158150 0.299652i
\(645\) −3.75442 8.74831i −0.147830 0.344464i
\(646\) −8.70739 15.0816i −0.342588 0.593379i
\(647\) 26.8036 + 7.18200i 1.05376 + 0.282354i 0.743804 0.668398i \(-0.233020\pi\)
0.309954 + 0.950751i \(0.399686\pi\)
\(648\) −8.90379 + 15.2762i −0.349774 + 0.600105i
\(649\) 29.9394 + 17.2855i 1.17522 + 0.678515i
\(650\) −39.4155 + 17.6084i −1.54600 + 0.690659i
\(651\) 15.9062 + 11.5501i 0.623412 + 0.452685i
\(652\) −3.10860 + 11.6015i −0.121742 + 0.454348i
\(653\) 20.8214 + 20.8214i 0.814806 + 0.814806i 0.985350 0.170544i \(-0.0545525\pi\)
−0.170544 + 0.985350i \(0.554552\pi\)
\(654\) 0.0151594 0.227694i 0.000592778 0.00890355i
\(655\) 23.3204 11.9009i 0.911205 0.465005i
\(656\) −0.199876 0.115398i −0.00780385 0.00450555i
\(657\) 18.1882 + 23.8046i 0.709588 + 0.928707i
\(658\) 18.8510 + 5.82669i 0.734890 + 0.227148i
\(659\) 10.3246 17.8827i 0.402190 0.696613i −0.591800 0.806085i \(-0.701583\pi\)
0.993990 + 0.109472i \(0.0349160\pi\)
\(660\) 6.91441 17.3110i 0.269143 0.673830i
\(661\) 1.15797 2.00567i 0.0450399 0.0780114i −0.842627 0.538498i \(-0.818992\pi\)
0.887667 + 0.460487i \(0.152325\pi\)
\(662\) −6.89522 25.7333i −0.267990 1.00015i
\(663\) 18.7344 16.3955i 0.727584 0.636750i
\(664\) −9.17285 5.29595i −0.355976 0.205523i
\(665\) 3.74122 + 21.5246i 0.145078 + 0.834688i
\(666\) −27.2738 21.0173i −1.05684 0.814405i
\(667\) 2.26755 0.607589i 0.0878000 0.0235259i
\(668\) 5.35464 + 5.35464i 0.207177 + 0.207177i
\(669\) −32.0422 2.13330i −1.23882 0.0824780i
\(670\) −6.51829 12.7730i −0.251824 0.493463i
\(671\) 1.30311 0.752351i 0.0503060 0.0290442i
\(672\) −20.0907 + 3.18748i −0.775016 + 0.122960i
\(673\) 4.69845 + 17.5349i 0.181112 + 0.675919i 0.995429 + 0.0954995i \(0.0304448\pi\)
−0.814317 + 0.580420i \(0.802889\pi\)
\(674\) −19.1614 + 33.1886i −0.738070 + 1.27838i
\(675\) 1.06750 25.9588i 0.0410881 0.999156i
\(676\) 5.54418 + 9.60280i 0.213238 + 0.369338i
\(677\) −19.2800 5.16605i −0.740989 0.198547i −0.131471 0.991320i \(-0.541970\pi\)
−0.609518 + 0.792773i \(0.708637\pi\)
\(678\) −6.24460 7.13541i −0.239823 0.274034i
\(679\) −20.7685 + 10.9611i −0.797022 + 0.420650i
\(680\) 6.69737 10.3273i 0.256832 0.396033i
\(681\) 15.0773 + 30.6533i 0.577765 + 1.17464i
\(682\) 29.5070 + 29.5070i 1.12988 + 1.12988i
\(683\) 1.07869 4.02574i 0.0412751 0.154041i −0.942213 0.335015i \(-0.891259\pi\)
0.983488 + 0.180975i \(0.0579252\pi\)
\(684\) −1.22298 + 9.14388i −0.0467617 + 0.349625i
\(685\) 28.4234 + 9.21555i 1.08600 + 0.352108i
\(686\) 28.5915 12.4155i 1.09163 0.474025i
\(687\) 40.5964 + 13.8273i 1.54885 + 0.527543i
\(688\) −8.64180 + 8.64180i −0.329466 + 0.329466i
\(689\) −26.6338 + 46.1311i −1.01467 + 1.75745i
\(690\) −15.7419 19.9850i −0.599285 0.760816i
\(691\) −3.42870 5.93869i −0.130434 0.225918i 0.793410 0.608688i \(-0.208304\pi\)
−0.923844 + 0.382769i \(0.874970\pi\)
\(692\) −12.3652 + 12.3652i −0.470053 + 0.470053i
\(693\) 19.2387 41.6481i 0.730819 1.58208i
\(694\) 20.1494i 0.764859i
\(695\) −11.7226 7.60224i −0.444663 0.288369i
\(696\) 0.135971 2.04229i 0.00515396 0.0774128i
\(697\) −0.125630 + 0.0336625i −0.00475858 + 0.00127506i
\(698\) −12.6622 12.6622i −0.479272 0.479272i
\(699\) 1.16746 17.5353i 0.0441573 0.663245i
\(700\) 8.80957 6.61350i 0.332970 0.249967i
\(701\) 13.3434i 0.503972i 0.967731 + 0.251986i \(0.0810837\pi\)
−0.967731 + 0.251986i \(0.918916\pi\)
\(702\) −44.7762 + 2.79591i −1.68997 + 0.105525i
\(703\) 24.3250 + 6.51785i 0.917433 + 0.245826i
\(704\) 14.2933 0.538700
\(705\) 17.0413 + 2.02388i 0.641813 + 0.0762239i
\(706\) 0.478812 + 0.829327i 0.0180203 + 0.0312121i
\(707\) 3.55809 + 15.6306i 0.133816 + 0.587849i
\(708\) 1.67427 + 8.46265i 0.0629229 + 0.318046i
\(709\) −12.2000 + 7.04367i −0.458180 + 0.264530i −0.711279 0.702910i \(-0.751884\pi\)
0.253099 + 0.967440i \(0.418550\pi\)
\(710\) 18.3582 3.91425i 0.688973 0.146899i
\(711\) −40.4874 5.41511i −1.51839 0.203082i
\(712\) −1.80437 + 0.483479i −0.0676215 + 0.0181191i
\(713\) 16.1709 4.33298i 0.605605 0.162271i
\(714\) −12.6977 + 17.4866i −0.475199 + 0.654418i
\(715\) −64.8432 + 13.8255i −2.42500 + 0.517045i
\(716\) 6.03426i 0.225511i
\(717\) −8.96528 + 1.77371i −0.334815 + 0.0662404i
\(718\) 34.9423 34.9423i 1.30404 1.30404i
\(719\) 22.2556 38.5479i 0.829995 1.43759i −0.0680454 0.997682i \(-0.521676\pi\)
0.898041 0.439912i \(-0.144990\pi\)
\(720\) −31.4561 + 11.0886i −1.17230 + 0.413248i
\(721\) −19.7141 + 31.3346i −0.734190 + 1.16696i
\(722\) 2.33605 + 8.71827i 0.0869389 + 0.324460i
\(723\) 2.03024 5.96071i 0.0755053 0.221681i
\(724\) −5.35628 3.09245i −0.199064 0.114930i
\(725\) 1.22673 + 2.74596i 0.0455595 + 0.101982i
\(726\) 36.3470 54.2760i 1.34896 2.01437i
\(727\) −3.75157 + 1.00523i −0.139138 + 0.0372819i −0.327716 0.944776i \(-0.606279\pi\)
0.188578 + 0.982058i \(0.439612\pi\)
\(728\) 18.1253 + 19.5571i 0.671770 + 0.724835i
\(729\) 10.4864 24.8804i 0.388384 0.921498i
\(730\) −1.94324 + 37.5313i −0.0719224 + 1.38910i
\(731\) 6.88715i 0.254731i
\(732\) 0.355426 + 0.121059i 0.0131369 + 0.00447447i
\(733\) 2.40923 2.40923i 0.0889868 0.0889868i −0.661212 0.750199i \(-0.729958\pi\)
0.750199 + 0.661212i \(0.229958\pi\)
\(734\) 27.6853 + 47.9523i 1.02188 + 1.76995i
\(735\) 22.5089 15.1112i 0.830253 0.557386i
\(736\) −8.66222 + 15.0034i −0.319294 + 0.553033i
\(737\) −5.70013 21.2732i −0.209967 0.783607i
\(738\) 0.216354 + 0.0901390i 0.00796408 + 0.00331806i
\(739\) −0.421830 + 0.243543i −0.0155173 + 0.00895889i −0.507739 0.861511i \(-0.669518\pi\)
0.492221 + 0.870470i \(0.336185\pi\)
\(740\) −2.64782 12.4186i −0.0973358 0.456515i
\(741\) 29.4432 14.4821i 1.08162 0.532014i
\(742\) 13.6545 44.1764i 0.501274 1.62177i
\(743\) 2.85872 10.6689i 0.104876 0.391404i −0.893455 0.449153i \(-0.851726\pi\)
0.998331 + 0.0577492i \(0.0183924\pi\)
\(744\) 0.969668 14.5645i 0.0355497 0.533959i
\(745\) 9.13218 + 17.8951i 0.334577 + 0.655624i
\(746\) −28.3480 + 16.3667i −1.03789 + 0.599228i
\(747\) 14.9300 + 6.22026i 0.546260 + 0.227587i
\(748\) −9.53579 + 9.53579i −0.348663 + 0.348663i
\(749\) −2.89731 5.48964i −0.105865 0.200587i
\(750\) 22.1032 23.9524i 0.807095 0.874617i
\(751\) 22.0136 0.803287 0.401643 0.915796i \(-0.368439\pi\)
0.401643 + 0.915796i \(0.368439\pi\)
\(752\) −5.70200 21.2802i −0.207931 0.776008i
\(753\) 16.4754 + 5.61157i 0.600397 + 0.204497i
\(754\) 4.49759 2.59668i 0.163792 0.0945656i
\(755\) 0.817466 + 1.60187i 0.0297506 + 0.0582982i
\(756\) 10.9823 3.23166i 0.399423 0.117534i
\(757\) −7.72069 7.72069i −0.280613 0.280613i 0.552740 0.833354i \(-0.313582\pi\)
−0.833354 + 0.552740i \(0.813582\pi\)
\(758\) 4.92801 18.3916i 0.178993 0.668012i
\(759\) −17.2448 35.0599i −0.625945 1.27259i
\(760\) 12.0491 10.8628i 0.437067 0.394036i
\(761\) 30.7854i 1.11597i 0.829851 + 0.557985i \(0.188425\pi\)
−0.829851 + 0.557985i \(0.811575\pi\)
\(762\) 32.3360 6.39743i 1.17141 0.231754i
\(763\) 0.151903 0.140783i 0.00549927 0.00509667i
\(764\) 22.4893 0.813633
\(765\) −8.11601 + 16.9532i −0.293435 + 0.612943i
\(766\) −2.90162 5.02575i −0.104840 0.181588i
\(767\) 21.6961 21.6961i 0.783402 0.783402i
\(768\) 19.3932 + 22.1597i 0.699792 + 0.799619i
\(769\) −23.4329 + 13.5290i −0.845011 + 0.487867i −0.858964 0.512035i \(-0.828892\pi\)
0.0139534 + 0.999903i \(0.495558\pi\)
\(770\) 52.2189 24.1951i 1.88184 0.871929i
\(771\) −10.6283 21.6081i −0.382768 0.778195i
\(772\) −1.52180 + 5.67943i −0.0547707 + 0.204407i
\(773\) 3.10421 11.5851i 0.111651 0.416686i −0.887364 0.461070i \(-0.847466\pi\)
0.999015 + 0.0443838i \(0.0141325\pi\)
\(774\) 7.57565 9.83079i 0.272301 0.353360i
\(775\) 8.74832 + 19.5827i 0.314249 + 0.703430i
\(776\) 15.1017 + 8.71894i 0.542118 + 0.312992i
\(777\) −4.89674 30.8643i −0.175670 1.10725i
\(778\) 40.9314 + 10.9675i 1.46746 + 0.393206i
\(779\) −0.171420 −0.00614176
\(780\) −13.2523 9.90421i −0.474508 0.354628i
\(781\) 28.8285 1.03157
\(782\) 4.76349 + 17.7776i 0.170342 + 0.635725i
\(783\) 0.194783 + 3.11943i 0.00696096 + 0.111479i
\(784\) −28.7338 19.6390i −1.02621 0.701394i
\(785\) −30.7092 34.0629i −1.09606 1.21576i
\(786\) 28.3609 + 18.9924i 1.01160 + 0.677436i
\(787\) 10.8833 2.91618i 0.387948 0.103950i −0.0595724 0.998224i \(-0.518974\pi\)
0.447521 + 0.894274i \(0.352307\pi\)
\(788\) 19.6930 5.27672i 0.701534 0.187975i
\(789\) 13.2964 6.54006i 0.473365 0.232832i
\(790\) −34.3122 38.0594i −1.22077 1.35409i
\(791\) 0.326743 8.59956i 0.0116177 0.305765i
\(792\) −33.7839 + 4.37697i −1.20046 + 0.155529i
\(793\) −0.345647 1.28997i −0.0122743 0.0458082i
\(794\) −25.0919 −0.890478
\(795\) 4.74286 39.9354i 0.168212 1.41636i
\(796\) 4.34451 0.153987
\(797\) −36.2663 9.71753i −1.28462 0.344212i −0.449004 0.893530i \(-0.648221\pi\)
−0.835614 + 0.549317i \(0.814888\pi\)
\(798\) −22.1302 + 17.9303i −0.783400 + 0.634726i
\(799\) −10.7518 6.20757i −0.380372 0.219608i
\(800\) −20.7308 7.92786i −0.732943 0.280292i
\(801\) 2.63760 1.08617i 0.0931949 0.0383779i
\(802\) −4.43045 + 16.5347i −0.156445 + 0.583860i
\(803\) −14.9386 + 55.7515i −0.527170 + 1.96743i
\(804\) 3.05793 4.56633i 0.107845 0.161042i
\(805\) 2.06849 22.9964i 0.0729049 0.810516i
\(806\) 32.0743 18.5181i 1.12977 0.652272i
\(807\) 22.0231 4.35710i 0.775250 0.153377i
\(808\) 8.41707 8.41707i 0.296111 0.296111i
\(809\) 1.38873 + 2.40535i 0.0488251 + 0.0845675i 0.889405 0.457120i \(-0.151119\pi\)
−0.840580 + 0.541687i \(0.817786\pi\)
\(810\) 30.2328 15.2717i 1.06227 0.536594i
\(811\) −25.3407 −0.889834 −0.444917 0.895572i \(-0.646767\pi\)
−0.444917 + 0.895572i \(0.646767\pi\)
\(812\) −0.971963 + 0.900807i −0.0341092 + 0.0316121i
\(813\) 19.4136 + 22.1830i 0.680865 + 0.777993i
\(814\) 66.3391i 2.32518i
\(815\) −23.9544 + 21.5960i −0.839087 + 0.756474i
\(816\) 24.0761 + 1.60293i 0.842831 + 0.0561137i
\(817\) −2.34935 + 8.76788i −0.0821932 + 0.306749i
\(818\) −13.6281 13.6281i −0.476496 0.476496i
\(819\) −31.2853 26.0603i −1.09320 0.910619i
\(820\) 0.0392881 + 0.0769874i 0.00137200 + 0.00268851i
\(821\) −2.30068 + 1.32830i −0.0802942 + 0.0463579i −0.539610 0.841915i \(-0.681428\pi\)
0.459315 + 0.888273i \(0.348095\pi\)
\(822\) 7.56031 + 38.2139i 0.263696 + 1.33286i
\(823\) 3.73451 + 13.9374i 0.130177 + 0.485827i 0.999971 0.00758776i \(-0.00241528\pi\)
−0.869794 + 0.493414i \(0.835749\pi\)
\(824\) 27.4897 0.957648
\(825\) 40.8710 28.8988i 1.42295 1.00613i
\(826\) −14.1832 + 22.5436i −0.493497 + 0.784391i
\(827\) −21.3382 + 21.3382i −0.742001 + 0.742001i −0.972963 0.230962i \(-0.925813\pi\)
0.230962 + 0.972963i \(0.425813\pi\)
\(828\) 3.74959 8.99985i 0.130307 0.312767i
\(829\) 23.1488 13.3650i 0.803990 0.464184i −0.0408744 0.999164i \(-0.513014\pi\)
0.844864 + 0.534980i \(0.179681\pi\)
\(830\) 9.22282 + 18.0727i 0.320129 + 0.627312i
\(831\) −40.2671 + 19.8060i −1.39685 + 0.687064i
\(832\) 3.28334 12.2536i 0.113829 0.424816i
\(833\) −19.2756 + 3.62409i −0.667859 + 0.125567i
\(834\) 1.21004 18.1748i 0.0419002 0.629343i
\(835\) 4.24031 + 19.8875i 0.146742 + 0.688236i
\(836\) −15.3927 + 8.88695i −0.532366 + 0.307362i
\(837\) 1.38908 + 22.2460i 0.0480136 + 0.768935i
\(838\) 12.9132 + 48.1926i 0.446078 + 1.66479i
\(839\) 7.24965 12.5568i 0.250286 0.433508i −0.713319 0.700840i \(-0.752809\pi\)
0.963604 + 0.267332i \(0.0861421\pi\)
\(840\) −18.3982 8.17175i −0.634799 0.281952i
\(841\) 14.3191 + 24.8014i 0.493762 + 0.855221i
\(842\) 13.0314 13.0314i 0.449093 0.449093i
\(843\) −38.6625 + 33.8357i −1.33161 + 1.16536i
\(844\) 13.6327i 0.469257i
\(845\) −1.53960 + 29.7355i −0.0529638 + 1.02293i
\(846\) 8.51913 + 20.6874i 0.292894 + 0.711248i
\(847\) 57.8066 13.1589i 1.98626 0.452144i
\(848\) −49.8689 + 13.3623i −1.71251 + 0.458864i
\(849\) −11.4757 0.764022i −0.393844 0.0262212i
\(850\) −21.5283 + 9.61753i −0.738415 + 0.329879i
\(851\) −23.0489 13.3073i −0.790106 0.456168i
\(852\) 4.73759 + 5.41342i 0.162307 + 0.185461i
\(853\) 5.16052 + 19.2593i 0.176693 + 0.659426i 0.996257 + 0.0864391i \(0.0275488\pi\)
−0.819564 + 0.572987i \(0.805785\pi\)
\(854\) 0.541090 + 1.02522i 0.0185157 + 0.0350824i
\(855\) −16.1154 + 18.8141i −0.551134 + 0.643430i
\(856\) −2.30464 + 3.99175i −0.0787709 + 0.136435i
\(857\) −15.8490 + 15.8490i −0.541390 + 0.541390i −0.923936 0.382546i \(-0.875047\pi\)
0.382546 + 0.923936i \(0.375047\pi\)
\(858\) −56.9243 65.0447i −1.94336 2.22059i
\(859\) 36.6814i 1.25155i −0.780003 0.625776i \(-0.784782\pi\)
0.780003 0.625776i \(-0.215218\pi\)
\(860\) 4.47624 0.954401i 0.152639 0.0325448i
\(861\) 0.0865719 + 0.194306i 0.00295036 + 0.00662194i
\(862\) 3.15779 0.846128i 0.107555 0.0288192i
\(863\) −40.0009 + 10.7182i −1.36165 + 0.364852i −0.864421 0.502768i \(-0.832315\pi\)
−0.497227 + 0.867621i \(0.665648\pi\)
\(864\) −17.2946 15.2617i −0.588375 0.519215i
\(865\) −45.9252 + 9.79193i −1.56150 + 0.332936i
\(866\) 37.9463 21.9083i 1.28947 0.744474i
\(867\) −11.9253 + 10.4365i −0.405003 + 0.354441i
\(868\) −6.93149 + 6.42404i −0.235270 + 0.218046i
\(869\) −39.3498 68.1558i −1.33485 2.31203i
\(870\) −2.34722 + 3.14069i −0.0795784 + 0.106479i
\(871\) −19.5467 −0.662315
\(872\) −0.148550 0.0398039i −0.00503055 0.00134793i
\(873\) −24.5799 10.2407i −0.831903 0.346594i
\(874\) 24.2572i 0.820511i
\(875\) 29.5108 2.02856i 0.997646 0.0685777i
\(876\) −12.9240 + 6.35686i −0.436660 + 0.214778i
\(877\) 22.4304 + 22.4304i 0.757422 + 0.757422i 0.975852 0.218431i \(-0.0700937\pi\)
−0.218431 + 0.975852i \(0.570094\pi\)
\(878\) 22.5210 6.03449i 0.760048 0.203654i
\(879\) 6.69165 + 4.48119i 0.225704 + 0.151147i
\(880\) −53.9151 34.9646i −1.81748 1.17866i
\(881\) 26.6329i 0.897286i 0.893711 + 0.448643i \(0.148092\pi\)
−0.893711 + 0.448643i \(0.851908\pi\)
\(882\) 31.5005 + 16.0294i 1.06068 + 0.539740i
\(883\) 11.9623 11.9623i 0.402563 0.402563i −0.476572 0.879135i \(-0.658121\pi\)
0.879135 + 0.476572i \(0.158121\pi\)
\(884\) 5.98449 + 10.3654i 0.201280 + 0.348628i
\(885\) −8.59260 + 21.5125i −0.288837 + 0.723135i
\(886\) −24.8458 + 43.0342i −0.834712 + 1.44576i
\(887\) −2.74179 + 2.74179i −0.0920603 + 0.0920603i −0.751637 0.659577i \(-0.770736\pi\)
0.659577 + 0.751637i \(0.270736\pi\)
\(888\) −17.4623 + 15.2822i −0.585996 + 0.512838i
\(889\) 25.3219 + 15.9312i 0.849268 + 0.534314i
\(890\) 3.40395 + 1.10364i 0.114101 + 0.0369942i
\(891\) 50.3020 13.2566i 1.68518 0.444112i
\(892\) 3.99589 14.9129i 0.133792 0.499320i
\(893\) −11.5704 11.5704i −0.387188 0.387188i
\(894\) −14.5739 + 21.7629i −0.487424 + 0.727859i
\(895\) 8.81659 13.5951i 0.294706 0.454434i
\(896\) −1.30992 + 34.4759i −0.0437615 + 1.15176i
\(897\) −34.0179 + 6.73018i −1.13583 + 0.224714i
\(898\) 26.3420 + 7.05831i 0.879043 + 0.235539i
\(899\) −1.29010 2.23452i −0.0430273 0.0745254i
\(900\) 12.1432 + 2.92561i 0.404775 + 0.0975204i
\(901\) −14.5471 + 25.1963i −0.484634 + 0.839411i
\(902\) 0.116874 + 0.436181i 0.00389149 + 0.0145232i
\(903\) 11.1250 1.76502i 0.370215 0.0587362i
\(904\) −5.53414 + 3.19513i −0.184063 + 0.106269i
\(905\) −7.54927 14.7932i −0.250946 0.491744i
\(906\) −1.30458 + 1.94810i −0.0433418 + 0.0647212i
\(907\) 6.93324 + 6.93324i 0.230215 + 0.230215i 0.812782 0.582568i \(-0.197952\pi\)
−0.582568 + 0.812782i \(0.697952\pi\)
\(908\) −15.8637 + 4.25067i −0.526456 + 0.141063i
\(909\) −11.0950 + 14.3978i −0.367999 + 0.477546i
\(910\) −8.74701 50.3248i −0.289961 1.66825i
\(911\) −37.0302 21.3794i −1.22686 0.708330i −0.260491 0.965476i \(-0.583885\pi\)
−0.966373 + 0.257146i \(0.917218\pi\)
\(912\) 30.1039 + 10.2535i 0.996840 + 0.339527i
\(913\) 8.06519 + 30.0997i 0.266919 + 0.996155i
\(914\) −13.1220 + 22.7280i −0.434037 + 0.751775i
\(915\) 0.623891 + 0.792054i 0.0206252 + 0.0261845i
\(916\) −10.3092 + 17.8561i −0.340627 + 0.589983i
\(917\) 6.87592 + 30.2057i 0.227063 + 0.997480i
\(918\) −24.4563 + 1.52709i −0.807178 + 0.0504016i
\(919\) 10.2115 + 5.89559i 0.336845 + 0.194478i 0.658876 0.752252i \(-0.271032\pi\)
−0.322031 + 0.946729i \(0.604365\pi\)
\(920\) −15.2715 + 7.79331i −0.503485 + 0.256938i
\(921\) −7.52110 + 3.69937i −0.247829 + 0.121898i
\(922\) −28.7285 28.7285i −0.946122 0.946122i
\(923\) 6.62223 24.7145i 0.217973 0.813488i
\(924\) 17.8472 + 12.9596i 0.587129 + 0.426338i
\(925\) 12.1791 31.8475i 0.400447 1.04714i
\(926\) −49.5121 28.5858i −1.62707 0.939388i
\(927\) −41.6291 + 5.39339i −1.36728 + 0.177142i
\(928\) 2.57909 + 0.691064i 0.0846627 + 0.0226853i
\(929\) 11.0927 + 19.2131i 0.363940 + 0.630362i 0.988605 0.150530i \(-0.0480981\pi\)
−0.624666 + 0.780892i \(0.714765\pi\)
\(930\) −16.7391 + 22.3977i −0.548896 + 0.734448i
\(931\) −25.7755 1.96154i −0.844760 0.0642867i
\(932\) 8.16115 + 2.18677i 0.267327 + 0.0716301i
\(933\) 32.6966 28.6147i 1.07044 0.936803i
\(934\) 1.10433i 0.0361347i
\(935\) −35.4167 + 7.55135i −1.15825 + 0.246956i
\(936\) −4.00818 + 29.9681i −0.131011 + 0.979539i
\(937\) 30.7803 + 30.7803i 1.00555 + 1.00555i 0.999985 + 0.00556508i \(0.00177143\pi\)
0.00556508 + 0.999985i \(0.498229\pi\)
\(938\) 16.5441 3.76605i 0.540186 0.122966i
\(939\) −25.8372 + 38.5821i −0.843166 + 1.25908i
\(940\) −2.54460 + 7.84827i −0.0829956 + 0.255982i
\(941\) −39.0671 22.5554i −1.27355 0.735285i −0.297896 0.954598i \(-0.596285\pi\)
−0.975654 + 0.219314i \(0.929618\pi\)
\(942\) 19.2773 56.5975i 0.628087 1.84404i
\(943\) 0.174991 + 0.0468888i 0.00569850 + 0.00152691i
\(944\) 29.7386 0.967909
\(945\) 29.4647 + 8.76525i 0.958488 + 0.285134i
\(946\) 23.9118 0.777439
\(947\) −56.5670 15.1571i −1.83818 0.492539i −0.839475 0.543398i \(-0.817137\pi\)
−0.998706 + 0.0508592i \(0.983804\pi\)
\(948\) 6.33168 18.5896i 0.205643 0.603762i
\(949\) 44.3638 + 25.6135i 1.44011 + 0.831448i
\(950\) −30.6880 + 4.90012i −0.995649 + 0.158981i
\(951\) −24.5429 + 36.6493i −0.795858 + 1.18843i
\(952\) 9.89987 + 10.6819i 0.320857 + 0.346202i
\(953\) 3.24815 + 3.24815i 0.105218 + 0.105218i 0.757756 0.652538i \(-0.226296\pi\)
−0.652538 + 0.757756i \(0.726296\pi\)
\(954\) 48.4798 19.9641i 1.56959 0.646362i
\(955\) 50.6680 + 32.8589i 1.63958 + 1.06329i
\(956\) 4.39376i 0.142104i
\(957\) −4.53148 + 3.96575i −0.146482 + 0.128195i
\(958\) 4.32417 + 1.15866i 0.139708 + 0.0374345i
\(959\) −18.8270 + 29.9247i −0.607957 + 0.966319i
\(960\) 1.37052 + 9.47900i 0.0442333 + 0.305933i
\(961\) 6.29973 + 10.9115i 0.203217 + 0.351982i
\(962\) −56.8721 15.2388i −1.83363 0.491319i
\(963\) 2.70687 6.49709i 0.0872277 0.209366i
\(964\) 2.62179 + 1.51369i 0.0844421 + 0.0487527i
\(965\) −11.7268 + 10.5722i −0.377497 + 0.340331i
\(966\) 27.4957 12.2506i 0.884661 0.394155i
\(967\) 14.4423 53.8993i 0.464432 1.73329i −0.194332 0.980936i \(-0.562254\pi\)
0.658764 0.752350i \(-0.271080\pi\)
\(968\) −31.1288 31.1288i −1.00052 1.00052i
\(969\) 16.0816 7.90997i 0.516614 0.254105i
\(970\) −15.1839 29.7538i −0.487527 0.955337i
\(971\) −9.60350 5.54459i −0.308191 0.177934i 0.337926 0.941173i \(-0.390275\pi\)
−0.646117 + 0.763239i \(0.723608\pi\)
\(972\) 10.7558 + 7.26717i 0.344992 + 0.233095i
\(973\) 12.1251 11.2374i 0.388713 0.360255i
\(974\) −2.49897 + 4.32834i −0.0800721 + 0.138689i
\(975\) −15.3863 41.6768i −0.492755 1.33473i
\(976\) 0.647187 1.12096i 0.0207159 0.0358811i
\(977\) −1.54327 5.75956i −0.0493736 0.184265i 0.936835 0.349771i \(-0.113741\pi\)
−0.986209 + 0.165507i \(0.947074\pi\)
\(978\) −39.8017 13.5566i −1.27272 0.433491i
\(979\) 4.75945 + 2.74787i 0.152113 + 0.0878223i
\(980\) 5.02659 + 12.0258i 0.160569 + 0.384149i
\(981\) 0.232767 + 0.0311322i 0.00743169 + 0.000993974i
\(982\) 14.5164 3.88967i 0.463238 0.124124i
\(983\) 42.4890 + 42.4890i 1.35519 + 1.35519i 0.879747 + 0.475443i \(0.157712\pi\)
0.475443 + 0.879747i \(0.342288\pi\)
\(984\) 0.0878911 0.131246i 0.00280186 0.00418395i
\(985\) 52.0778 + 16.8849i 1.65934 + 0.537996i
\(986\) 2.45653 1.41828i 0.0782320 0.0451673i
\(987\) −7.27176 + 18.9585i −0.231463 + 0.603456i
\(988\) 4.08286 + 15.2375i 0.129893 + 0.484768i
\(989\) 4.79658 8.30793i 0.152523 0.264177i
\(990\) 58.8603 + 28.1783i 1.87070 + 0.895566i
\(991\) −3.47124 6.01236i −0.110268 0.190989i 0.805611 0.592445i \(-0.201837\pi\)
−0.915878 + 0.401456i \(0.868504\pi\)
\(992\) 18.3926 + 4.92828i 0.583966 + 0.156473i
\(993\) 26.8951 5.32099i 0.853491 0.168857i
\(994\) −0.843270 + 22.1940i −0.0267469 + 0.703951i
\(995\) 9.78813 + 6.34773i 0.310305 + 0.201236i
\(996\) −4.32671 + 6.46097i −0.137097 + 0.204724i
\(997\) −15.8613 15.8613i −0.502333 0.502333i 0.409829 0.912162i \(-0.365588\pi\)
−0.912162 + 0.409829i \(0.865588\pi\)
\(998\) −11.5399 + 43.0677i −0.365291 + 1.36328i
\(999\) 23.4458 26.5688i 0.741792 0.840599i
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 315.2.bx.a.2.10 yes 176
3.2 odd 2 945.2.ca.a.737.35 176
5.3 odd 4 inner 315.2.bx.a.128.10 yes 176
7.4 even 3 315.2.bv.a.137.35 yes 176
9.4 even 3 945.2.by.a.422.35 176
9.5 odd 6 315.2.bv.a.212.10 yes 176
15.8 even 4 945.2.ca.a.548.35 176
21.11 odd 6 945.2.by.a.872.10 176
35.18 odd 12 315.2.bv.a.263.10 yes 176
45.13 odd 12 945.2.by.a.233.10 176
45.23 even 12 315.2.bv.a.23.35 176
63.4 even 3 945.2.ca.a.557.35 176
63.32 odd 6 inner 315.2.bx.a.32.10 yes 176
105.53 even 12 945.2.by.a.683.35 176
315.158 even 12 inner 315.2.bx.a.158.10 yes 176
315.193 odd 12 945.2.ca.a.368.35 176
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bv.a.23.35 176 45.23 even 12
315.2.bv.a.137.35 yes 176 7.4 even 3
315.2.bv.a.212.10 yes 176 9.5 odd 6
315.2.bv.a.263.10 yes 176 35.18 odd 12
315.2.bx.a.2.10 yes 176 1.1 even 1 trivial
315.2.bx.a.32.10 yes 176 63.32 odd 6 inner
315.2.bx.a.128.10 yes 176 5.3 odd 4 inner
315.2.bx.a.158.10 yes 176 315.158 even 12 inner
945.2.by.a.233.10 176 45.13 odd 12
945.2.by.a.422.35 176 9.4 even 3
945.2.by.a.683.35 176 105.53 even 12
945.2.by.a.872.10 176 21.11 odd 6
945.2.ca.a.368.35 176 315.193 odd 12
945.2.ca.a.548.35 176 15.8 even 4
945.2.ca.a.557.35 176 63.4 even 3
945.2.ca.a.737.35 176 3.2 odd 2