Properties

Label 495.2.n.g.136.2
Level $495$
Weight $2$
Character 495.136
Analytic conductor $3.953$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), 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: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} - 172 x^{7} + 471 x^{6} - 430 x^{5} + 383 x^{4} + 70 x^{3} + 17 x^{2} + 4 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.2
Root \(0.0698401 + 0.214946i\) of defining polynomial
Character \(\chi\) \(=\) 495.136
Dual form 495.2.n.g.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.991861 - 0.720629i) q^{2} +(-0.153553 - 0.472586i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.139581 - 0.429587i) q^{7} +(-0.945971 + 2.91140i) q^{8} +O(q^{10})\) \(q+(-0.991861 - 0.720629i) q^{2} +(-0.153553 - 0.472586i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.139581 - 0.429587i) q^{7} +(-0.945971 + 2.91140i) q^{8} +1.22601 q^{10} +(1.55234 + 2.93091i) q^{11} +(3.91592 + 2.84508i) q^{13} +(-0.171128 + 0.526677i) q^{14} +(2.23230 - 1.62186i) q^{16} +(0.598736 - 0.435007i) q^{17} +(2.10247 - 6.47075i) q^{19} +(0.402006 + 0.292074i) q^{20} +(0.572395 - 4.02572i) q^{22} +0.00634166 q^{23} +(0.309017 - 0.951057i) q^{25} +(-1.83380 - 5.64385i) q^{26} +(-0.181584 + 0.131928i) q^{28} +(0.100091 + 0.308048i) q^{29} +(4.53521 + 3.29503i) q^{31} +2.73956 q^{32} -0.907341 q^{34} +(0.365429 + 0.265500i) q^{35} +(2.27713 + 7.00828i) q^{37} +(-6.74837 + 4.90298i) q^{38} +(-0.945971 - 2.91140i) q^{40} +(3.39006 - 10.4335i) q^{41} -1.80668 q^{43} +(1.14674 - 1.18366i) q^{44} +(-0.00629004 - 0.00456998i) q^{46} +(0.518988 - 1.59728i) q^{47} +(5.49806 - 3.99457i) q^{49} +(-0.991861 + 0.720629i) q^{50} +(0.743247 - 2.28748i) q^{52} +(6.98948 + 5.07816i) q^{53} +(-2.97862 - 1.45871i) q^{55} +1.38274 q^{56} +(0.122712 - 0.377669i) q^{58} +(0.463691 + 1.42709i) q^{59} +(-10.5540 + 7.66790i) q^{61} +(-2.12381 - 6.53641i) q^{62} +(-7.18186 - 5.21793i) q^{64} -4.84034 q^{65} +9.60773 q^{67} +(-0.297516 - 0.216158i) q^{68} +(-0.171128 - 0.526677i) q^{70} +(9.23296 - 6.70814i) q^{71} +(3.16430 + 9.73870i) q^{73} +(2.79178 - 8.59220i) q^{74} -3.38083 q^{76} +(1.04241 - 1.07597i) q^{77} +(1.69866 + 1.23415i) q^{79} +(-0.852662 + 2.62422i) q^{80} +(-10.8812 + 7.90563i) q^{82} +(-12.8589 + 9.34255i) q^{83} +(-0.228697 + 0.703856i) q^{85} +(1.79197 + 1.30194i) q^{86} +(-10.0015 + 1.74692i) q^{88} +9.36925 q^{89} +(0.675622 - 2.07935i) q^{91} +(-0.000973778 - 0.00299698i) q^{92} +(-1.66581 + 1.21028i) q^{94} +(2.10247 + 6.47075i) q^{95} +(-4.75689 - 3.45608i) q^{97} -8.33191 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.991861 0.720629i −0.701351 0.509562i 0.179021 0.983845i \(-0.442707\pi\)
−0.880372 + 0.474284i \(0.842707\pi\)
\(3\) 0 0
\(4\) −0.153553 0.472586i −0.0767763 0.236293i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) 0 0
\(7\) −0.139581 0.429587i −0.0527568 0.162369i 0.921207 0.389073i \(-0.127205\pi\)
−0.973964 + 0.226705i \(0.927205\pi\)
\(8\) −0.945971 + 2.91140i −0.334451 + 1.02933i
\(9\) 0 0
\(10\) 1.22601 0.387698
\(11\) 1.55234 + 2.93091i 0.468048 + 0.883703i
\(12\) 0 0
\(13\) 3.91592 + 2.84508i 1.08608 + 0.789084i 0.978733 0.205138i \(-0.0657643\pi\)
0.107348 + 0.994222i \(0.465764\pi\)
\(14\) −0.171128 + 0.526677i −0.0457358 + 0.140760i
\(15\) 0 0
\(16\) 2.23230 1.62186i 0.558074 0.405465i
\(17\) 0.598736 0.435007i 0.145215 0.105505i −0.512806 0.858505i \(-0.671394\pi\)
0.658021 + 0.753000i \(0.271394\pi\)
\(18\) 0 0
\(19\) 2.10247 6.47075i 0.482340 1.48449i −0.353456 0.935451i \(-0.614993\pi\)
0.835796 0.549040i \(-0.185007\pi\)
\(20\) 0.402006 + 0.292074i 0.0898912 + 0.0653098i
\(21\) 0 0
\(22\) 0.572395 4.02572i 0.122035 0.858286i
\(23\) 0.00634166 0.00132233 0.000661164 1.00000i \(-0.499790\pi\)
0.000661164 1.00000i \(0.499790\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) −1.83380 5.64385i −0.359637 1.10685i
\(27\) 0 0
\(28\) −0.181584 + 0.131928i −0.0343162 + 0.0249321i
\(29\) 0.100091 + 0.308048i 0.0185864 + 0.0572030i 0.959920 0.280276i \(-0.0904259\pi\)
−0.941333 + 0.337479i \(0.890426\pi\)
\(30\) 0 0
\(31\) 4.53521 + 3.29503i 0.814548 + 0.591804i 0.915146 0.403123i \(-0.132075\pi\)
−0.100597 + 0.994927i \(0.532075\pi\)
\(32\) 2.73956 0.484291
\(33\) 0 0
\(34\) −0.907341 −0.155608
\(35\) 0.365429 + 0.265500i 0.0617688 + 0.0448776i
\(36\) 0 0
\(37\) 2.27713 + 7.00828i 0.374358 + 1.15215i 0.943911 + 0.330200i \(0.107116\pi\)
−0.569553 + 0.821954i \(0.692884\pi\)
\(38\) −6.74837 + 4.90298i −1.09473 + 0.795368i
\(39\) 0 0
\(40\) −0.945971 2.91140i −0.149571 0.460332i
\(41\) 3.39006 10.4335i 0.529438 1.62944i −0.225931 0.974143i \(-0.572543\pi\)
0.755369 0.655299i \(-0.227457\pi\)
\(42\) 0 0
\(43\) −1.80668 −0.275516 −0.137758 0.990466i \(-0.543990\pi\)
−0.137758 + 0.990466i \(0.543990\pi\)
\(44\) 1.14674 1.18366i 0.172878 0.178444i
\(45\) 0 0
\(46\) −0.00629004 0.00456998i −0.000927416 0.000673807i
\(47\) 0.518988 1.59728i 0.0757022 0.232987i −0.906044 0.423184i \(-0.860912\pi\)
0.981746 + 0.190196i \(0.0609125\pi\)
\(48\) 0 0
\(49\) 5.49806 3.99457i 0.785437 0.570653i
\(50\) −0.991861 + 0.720629i −0.140270 + 0.101912i
\(51\) 0 0
\(52\) 0.743247 2.28748i 0.103070 0.317216i
\(53\) 6.98948 + 5.07816i 0.960079 + 0.697539i 0.953169 0.302438i \(-0.0978004\pi\)
0.00691024 + 0.999976i \(0.497800\pi\)
\(54\) 0 0
\(55\) −2.97862 1.45871i −0.401636 0.196693i
\(56\) 1.38274 0.184776
\(57\) 0 0
\(58\) 0.122712 0.377669i 0.0161129 0.0495903i
\(59\) 0.463691 + 1.42709i 0.0603674 + 0.185792i 0.976692 0.214643i \(-0.0688589\pi\)
−0.916325 + 0.400435i \(0.868859\pi\)
\(60\) 0 0
\(61\) −10.5540 + 7.66790i −1.35130 + 0.981774i −0.352350 + 0.935868i \(0.614617\pi\)
−0.998946 + 0.0459057i \(0.985383\pi\)
\(62\) −2.12381 6.53641i −0.269724 0.830125i
\(63\) 0 0
\(64\) −7.18186 5.21793i −0.897733 0.652241i
\(65\) −4.84034 −0.600371
\(66\) 0 0
\(67\) 9.60773 1.17377 0.586885 0.809670i \(-0.300354\pi\)
0.586885 + 0.809670i \(0.300354\pi\)
\(68\) −0.297516 0.216158i −0.0360791 0.0262130i
\(69\) 0 0
\(70\) −0.171128 0.526677i −0.0204537 0.0629500i
\(71\) 9.23296 6.70814i 1.09575 0.796110i 0.115390 0.993320i \(-0.463188\pi\)
0.980361 + 0.197211i \(0.0631883\pi\)
\(72\) 0 0
\(73\) 3.16430 + 9.73870i 0.370353 + 1.13983i 0.946561 + 0.322526i \(0.104532\pi\)
−0.576208 + 0.817303i \(0.695468\pi\)
\(74\) 2.79178 8.59220i 0.324537 0.998823i
\(75\) 0 0
\(76\) −3.38083 −0.387807
\(77\) 1.04241 1.07597i 0.118793 0.122618i
\(78\) 0 0
\(79\) 1.69866 + 1.23415i 0.191114 + 0.138852i 0.679228 0.733928i \(-0.262315\pi\)
−0.488114 + 0.872780i \(0.662315\pi\)
\(80\) −0.852662 + 2.62422i −0.0953305 + 0.293397i
\(81\) 0 0
\(82\) −10.8812 + 7.90563i −1.20162 + 0.873030i
\(83\) −12.8589 + 9.34255i −1.41145 + 1.02548i −0.418339 + 0.908291i \(0.637388\pi\)
−0.993110 + 0.117187i \(0.962612\pi\)
\(84\) 0 0
\(85\) −0.228697 + 0.703856i −0.0248056 + 0.0763439i
\(86\) 1.79197 + 1.30194i 0.193233 + 0.140392i
\(87\) 0 0
\(88\) −10.0015 + 1.74692i −1.06617 + 0.186223i
\(89\) 9.36925 0.993138 0.496569 0.867997i \(-0.334593\pi\)
0.496569 + 0.867997i \(0.334593\pi\)
\(90\) 0 0
\(91\) 0.675622 2.07935i 0.0708244 0.217975i
\(92\) −0.000973778 0.00299698i −0.000101523 0.000312457i
\(93\) 0 0
\(94\) −1.66581 + 1.21028i −0.171815 + 0.124831i
\(95\) 2.10247 + 6.47075i 0.215709 + 0.663885i
\(96\) 0 0
\(97\) −4.75689 3.45608i −0.482989 0.350912i 0.319493 0.947589i \(-0.396487\pi\)
−0.802482 + 0.596677i \(0.796487\pi\)
\(98\) −8.33191 −0.841650
\(99\) 0 0
\(100\) −0.496906 −0.0496906
\(101\) −1.78628 1.29781i −0.177742 0.129137i 0.495357 0.868689i \(-0.335037\pi\)
−0.673099 + 0.739552i \(0.735037\pi\)
\(102\) 0 0
\(103\) 2.99111 + 9.20568i 0.294723 + 0.907063i 0.983314 + 0.181914i \(0.0582292\pi\)
−0.688592 + 0.725149i \(0.741771\pi\)
\(104\) −11.9875 + 8.70944i −1.17547 + 0.854031i
\(105\) 0 0
\(106\) −3.27313 10.0736i −0.317914 0.978439i
\(107\) 3.63294 11.1810i 0.351210 1.08091i −0.606965 0.794729i \(-0.707613\pi\)
0.958175 0.286184i \(-0.0923869\pi\)
\(108\) 0 0
\(109\) −12.5091 −1.19816 −0.599078 0.800691i \(-0.704466\pi\)
−0.599078 + 0.800691i \(0.704466\pi\)
\(110\) 1.90318 + 3.59332i 0.181461 + 0.342609i
\(111\) 0 0
\(112\) −1.00832 0.732586i −0.0952771 0.0692228i
\(113\) −3.06115 + 9.42124i −0.287968 + 0.886276i 0.697525 + 0.716561i \(0.254285\pi\)
−0.985493 + 0.169715i \(0.945715\pi\)
\(114\) 0 0
\(115\) −0.00513051 + 0.00372753i −0.000478422 + 0.000347594i
\(116\) 0.130210 0.0946030i 0.0120897 0.00878367i
\(117\) 0 0
\(118\) 0.568489 1.74963i 0.0523336 0.161066i
\(119\) −0.270446 0.196491i −0.0247917 0.0180123i
\(120\) 0 0
\(121\) −6.18048 + 9.09954i −0.561862 + 0.827231i
\(122\) 15.9938 1.44801
\(123\) 0 0
\(124\) 0.860790 2.64924i 0.0773012 0.237909i
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) 0.454312 0.330077i 0.0403137 0.0292896i −0.567446 0.823411i \(-0.692068\pi\)
0.607760 + 0.794121i \(0.292068\pi\)
\(128\) 1.67007 + 5.13995i 0.147615 + 0.454312i
\(129\) 0 0
\(130\) 4.80095 + 3.48809i 0.421071 + 0.305926i
\(131\) −3.03500 −0.265170 −0.132585 0.991172i \(-0.542328\pi\)
−0.132585 + 0.991172i \(0.542328\pi\)
\(132\) 0 0
\(133\) −3.07322 −0.266482
\(134\) −9.52953 6.92361i −0.823226 0.598108i
\(135\) 0 0
\(136\) 0.700092 + 2.15466i 0.0600324 + 0.184761i
\(137\) −16.7469 + 12.1674i −1.43079 + 1.03953i −0.440918 + 0.897547i \(0.645347\pi\)
−0.989869 + 0.141981i \(0.954653\pi\)
\(138\) 0 0
\(139\) 1.09662 + 3.37504i 0.0930139 + 0.286267i 0.986731 0.162364i \(-0.0519117\pi\)
−0.893717 + 0.448631i \(0.851912\pi\)
\(140\) 0.0693589 0.213465i 0.00586190 0.0180411i
\(141\) 0 0
\(142\) −13.9919 −1.17417
\(143\) −2.25985 + 15.8937i −0.188978 + 1.32910i
\(144\) 0 0
\(145\) −0.262041 0.190384i −0.0217613 0.0158105i
\(146\) 3.87945 11.9397i 0.321065 0.988138i
\(147\) 0 0
\(148\) 2.96236 2.15228i 0.243504 0.176916i
\(149\) 5.10052 3.70575i 0.417851 0.303587i −0.358921 0.933368i \(-0.616855\pi\)
0.776773 + 0.629781i \(0.216855\pi\)
\(150\) 0 0
\(151\) −1.13852 + 3.50400i −0.0926512 + 0.285151i −0.986634 0.162949i \(-0.947899\pi\)
0.893983 + 0.448100i \(0.147899\pi\)
\(152\) 16.8500 + 12.2423i 1.36672 + 0.992980i
\(153\) 0 0
\(154\) −1.80929 + 0.316022i −0.145797 + 0.0254657i
\(155\) −5.60583 −0.450271
\(156\) 0 0
\(157\) 0.874113 2.69024i 0.0697618 0.214705i −0.910097 0.414394i \(-0.863993\pi\)
0.979859 + 0.199690i \(0.0639934\pi\)
\(158\) −0.795469 2.44820i −0.0632841 0.194768i
\(159\) 0 0
\(160\) −2.21635 + 1.61028i −0.175218 + 0.127303i
\(161\) −0.000885178 0.00272430i −6.97618e−5 0.000214705i
\(162\) 0 0
\(163\) −7.16094 5.20273i −0.560888 0.407509i 0.270896 0.962609i \(-0.412680\pi\)
−0.831784 + 0.555099i \(0.812680\pi\)
\(164\) −5.45129 −0.425674
\(165\) 0 0
\(166\) 19.4868 1.51247
\(167\) −15.9249 11.5701i −1.23230 0.895320i −0.235241 0.971937i \(-0.575588\pi\)
−0.997061 + 0.0766171i \(0.975588\pi\)
\(168\) 0 0
\(169\) 3.22271 + 9.91849i 0.247901 + 0.762961i
\(170\) 0.734054 0.533322i 0.0562994 0.0409039i
\(171\) 0 0
\(172\) 0.277420 + 0.853811i 0.0211531 + 0.0651025i
\(173\) 0.899661 2.76887i 0.0684000 0.210513i −0.911014 0.412375i \(-0.864699\pi\)
0.979414 + 0.201862i \(0.0646992\pi\)
\(174\) 0 0
\(175\) −0.451695 −0.0341449
\(176\) 8.21881 + 4.02499i 0.619516 + 0.303395i
\(177\) 0 0
\(178\) −9.29299 6.75175i −0.696539 0.506065i
\(179\) −1.94467 + 5.98508i −0.145352 + 0.447346i −0.997056 0.0766763i \(-0.975569\pi\)
0.851704 + 0.524022i \(0.175569\pi\)
\(180\) 0 0
\(181\) 9.03200 6.56213i 0.671343 0.487759i −0.199131 0.979973i \(-0.563812\pi\)
0.870475 + 0.492213i \(0.163812\pi\)
\(182\) −2.16856 + 1.57555i −0.160745 + 0.116788i
\(183\) 0 0
\(184\) −0.00599902 + 0.0184631i −0.000442254 + 0.00136112i
\(185\) −5.96160 4.33136i −0.438306 0.318448i
\(186\) 0 0
\(187\) 2.20441 + 1.07956i 0.161202 + 0.0789455i
\(188\) −0.834545 −0.0608655
\(189\) 0 0
\(190\) 2.57765 7.93318i 0.187002 0.575534i
\(191\) −6.30228 19.3964i −0.456017 1.40348i −0.869937 0.493163i \(-0.835841\pi\)
0.413920 0.910313i \(-0.364159\pi\)
\(192\) 0 0
\(193\) 2.40629 1.74827i 0.173208 0.125843i −0.497804 0.867290i \(-0.665860\pi\)
0.671012 + 0.741447i \(0.265860\pi\)
\(194\) 2.22762 + 6.85590i 0.159934 + 0.492225i
\(195\) 0 0
\(196\) −2.73202 1.98493i −0.195144 0.141781i
\(197\) 5.20127 0.370575 0.185288 0.982684i \(-0.440678\pi\)
0.185288 + 0.982684i \(0.440678\pi\)
\(198\) 0 0
\(199\) 8.10264 0.574381 0.287191 0.957873i \(-0.407279\pi\)
0.287191 + 0.957873i \(0.407279\pi\)
\(200\) 2.47658 + 1.79934i 0.175121 + 0.127233i
\(201\) 0 0
\(202\) 0.836505 + 2.57450i 0.0588563 + 0.181141i
\(203\) 0.118363 0.0859955i 0.00830743 0.00603570i
\(204\) 0 0
\(205\) 3.39006 + 10.4335i 0.236772 + 0.728709i
\(206\) 3.66712 11.2862i 0.255500 0.786349i
\(207\) 0 0
\(208\) 13.3558 0.926059
\(209\) 22.2289 3.88264i 1.53761 0.268568i
\(210\) 0 0
\(211\) 1.06252 + 0.771967i 0.0731470 + 0.0531444i 0.623758 0.781618i \(-0.285605\pi\)
−0.550611 + 0.834762i \(0.685605\pi\)
\(212\) 1.32661 4.08290i 0.0911122 0.280415i
\(213\) 0 0
\(214\) −11.6608 + 8.47204i −0.797113 + 0.579137i
\(215\) 1.46163 1.06194i 0.0996826 0.0724236i
\(216\) 0 0
\(217\) 0.782470 2.40820i 0.0531175 0.163479i
\(218\) 12.4073 + 9.01443i 0.840328 + 0.610534i
\(219\) 0 0
\(220\) −0.231994 + 1.63164i −0.0156411 + 0.110005i
\(221\) 3.58223 0.240967
\(222\) 0 0
\(223\) 8.84861 27.2332i 0.592547 1.82367i 0.0259701 0.999663i \(-0.491733\pi\)
0.566577 0.824009i \(-0.308267\pi\)
\(224\) −0.382392 1.17688i −0.0255497 0.0786338i
\(225\) 0 0
\(226\) 9.82545 7.13861i 0.653579 0.474853i
\(227\) −2.43074 7.48104i −0.161334 0.496534i 0.837414 0.546570i \(-0.184067\pi\)
−0.998747 + 0.0500354i \(0.984067\pi\)
\(228\) 0 0
\(229\) 13.0664 + 9.49331i 0.863453 + 0.627336i 0.928822 0.370526i \(-0.120822\pi\)
−0.0653689 + 0.997861i \(0.520822\pi\)
\(230\) 0.00777492 0.000512663
\(231\) 0 0
\(232\) −0.991532 −0.0650973
\(233\) −14.9138 10.8355i −0.977035 0.709858i −0.0199914 0.999800i \(-0.506364\pi\)
−0.957044 + 0.289942i \(0.906364\pi\)
\(234\) 0 0
\(235\) 0.518988 + 1.59728i 0.0338551 + 0.104195i
\(236\) 0.603224 0.438268i 0.0392665 0.0285288i
\(237\) 0 0
\(238\) 0.126648 + 0.389782i 0.00820937 + 0.0252658i
\(239\) 6.91081 21.2693i 0.447023 1.37579i −0.433227 0.901285i \(-0.642625\pi\)
0.880250 0.474510i \(-0.157375\pi\)
\(240\) 0 0
\(241\) −13.2213 −0.851662 −0.425831 0.904803i \(-0.640018\pi\)
−0.425831 + 0.904803i \(0.640018\pi\)
\(242\) 12.6876 4.57164i 0.815588 0.293876i
\(243\) 0 0
\(244\) 5.24433 + 3.81023i 0.335734 + 0.243925i
\(245\) −2.10007 + 6.46335i −0.134169 + 0.412928i
\(246\) 0 0
\(247\) 26.6429 19.3572i 1.69525 1.23167i
\(248\) −13.8833 + 10.0868i −0.881591 + 0.640513i
\(249\) 0 0
\(250\) 0.378857 1.16600i 0.0239610 0.0737444i
\(251\) 16.9919 + 12.3454i 1.07252 + 0.779232i 0.976364 0.216134i \(-0.0693450\pi\)
0.0961569 + 0.995366i \(0.469345\pi\)
\(252\) 0 0
\(253\) 0.00984441 + 0.0185868i 0.000618913 + 0.00116854i
\(254\) −0.688477 −0.0431989
\(255\) 0 0
\(256\) −3.43893 + 10.5839i −0.214933 + 0.661497i
\(257\) −1.04068 3.20289i −0.0649160 0.199791i 0.913338 0.407203i \(-0.133496\pi\)
−0.978254 + 0.207412i \(0.933496\pi\)
\(258\) 0 0
\(259\) 2.69283 1.95645i 0.167324 0.121568i
\(260\) 0.743247 + 2.28748i 0.0460942 + 0.141863i
\(261\) 0 0
\(262\) 3.01030 + 2.18711i 0.185977 + 0.135120i
\(263\) 21.0450 1.29769 0.648845 0.760920i \(-0.275252\pi\)
0.648845 + 0.760920i \(0.275252\pi\)
\(264\) 0 0
\(265\) −8.63948 −0.530719
\(266\) 3.04820 + 2.21465i 0.186897 + 0.135789i
\(267\) 0 0
\(268\) −1.47529 4.54048i −0.0901177 0.277354i
\(269\) −18.9161 + 13.7434i −1.15334 + 0.837947i −0.988921 0.148444i \(-0.952573\pi\)
−0.164415 + 0.986391i \(0.552573\pi\)
\(270\) 0 0
\(271\) −6.34951 19.5418i −0.385705 1.18708i −0.935967 0.352087i \(-0.885472\pi\)
0.550262 0.834992i \(-0.314528\pi\)
\(272\) 0.631036 1.94213i 0.0382622 0.117759i
\(273\) 0 0
\(274\) 25.3788 1.53319
\(275\) 3.26716 0.570661i 0.197017 0.0344122i
\(276\) 0 0
\(277\) 15.8420 + 11.5099i 0.951856 + 0.691564i 0.951245 0.308436i \(-0.0998055\pi\)
0.000611096 1.00000i \(0.499805\pi\)
\(278\) 1.34446 4.13783i 0.0806354 0.248170i
\(279\) 0 0
\(280\) −1.11866 + 0.812754i −0.0668527 + 0.0485714i
\(281\) −11.1585 + 8.10711i −0.665659 + 0.483630i −0.868569 0.495567i \(-0.834960\pi\)
0.202910 + 0.979197i \(0.434960\pi\)
\(282\) 0 0
\(283\) 9.73949 29.9751i 0.578953 1.78183i −0.0433533 0.999060i \(-0.513804\pi\)
0.622306 0.782774i \(-0.286196\pi\)
\(284\) −4.58792 3.33332i −0.272243 0.197796i
\(285\) 0 0
\(286\) 13.6949 14.1359i 0.809799 0.835872i
\(287\) −4.95530 −0.292502
\(288\) 0 0
\(289\) −5.08404 + 15.6471i −0.299061 + 0.920415i
\(290\) 0.122712 + 0.377669i 0.00720589 + 0.0221775i
\(291\) 0 0
\(292\) 4.11649 2.99080i 0.240899 0.175024i
\(293\) −7.20413 22.1720i −0.420870 1.29530i −0.906894 0.421359i \(-0.861553\pi\)
0.486024 0.873945i \(-0.338447\pi\)
\(294\) 0 0
\(295\) −1.21396 0.881993i −0.0706794 0.0513516i
\(296\) −22.5580 −1.31116
\(297\) 0 0
\(298\) −7.72948 −0.447757
\(299\) 0.0248334 + 0.0180425i 0.00143615 + 0.00104343i
\(300\) 0 0
\(301\) 0.252179 + 0.776126i 0.0145353 + 0.0447352i
\(302\) 3.65433 2.65503i 0.210283 0.152780i
\(303\) 0 0
\(304\) −5.80129 17.8545i −0.332727 1.02403i
\(305\) 4.03125 12.4069i 0.230829 0.710418i
\(306\) 0 0
\(307\) −10.0938 −0.576083 −0.288042 0.957618i \(-0.593004\pi\)
−0.288042 + 0.957618i \(0.593004\pi\)
\(308\) −0.668551 0.327409i −0.0380942 0.0186558i
\(309\) 0 0
\(310\) 5.56020 + 4.03972i 0.315798 + 0.229441i
\(311\) −4.11778 + 12.6732i −0.233498 + 0.718632i 0.763819 + 0.645430i \(0.223322\pi\)
−0.997317 + 0.0732020i \(0.976678\pi\)
\(312\) 0 0
\(313\) −18.7435 + 13.6180i −1.05945 + 0.769732i −0.973986 0.226609i \(-0.927236\pi\)
−0.0854599 + 0.996342i \(0.527236\pi\)
\(314\) −2.80566 + 2.03843i −0.158333 + 0.115036i
\(315\) 0 0
\(316\) 0.322407 0.992267i 0.0181368 0.0558194i
\(317\) −5.60802 4.07446i −0.314978 0.228845i 0.419052 0.907962i \(-0.362363\pi\)
−0.734029 + 0.679118i \(0.762363\pi\)
\(318\) 0 0
\(319\) −0.747485 + 0.771552i −0.0418512 + 0.0431986i
\(320\) 8.87727 0.496254
\(321\) 0 0
\(322\) −0.00108523 + 0.00334001i −6.04777e−5 + 0.000186131i
\(323\) −1.55599 4.78886i −0.0865779 0.266459i
\(324\) 0 0
\(325\) 3.91592 2.84508i 0.217216 0.157817i
\(326\) 3.35342 + 10.3208i 0.185729 + 0.571614i
\(327\) 0 0
\(328\) 27.1692 + 19.7396i 1.50017 + 1.08994i
\(329\) −0.758613 −0.0418237
\(330\) 0 0
\(331\) −10.5717 −0.581075 −0.290538 0.956864i \(-0.593834\pi\)
−0.290538 + 0.956864i \(0.593834\pi\)
\(332\) 6.38968 + 4.64237i 0.350679 + 0.254783i
\(333\) 0 0
\(334\) 7.45750 + 22.9518i 0.408056 + 1.25587i
\(335\) −7.77281 + 5.64728i −0.424674 + 0.308544i
\(336\) 0 0
\(337\) −1.96123 6.03605i −0.106835 0.328805i 0.883322 0.468767i \(-0.155302\pi\)
−0.990157 + 0.139963i \(0.955302\pi\)
\(338\) 3.95107 12.1601i 0.214910 0.661424i
\(339\) 0 0
\(340\) 0.367750 0.0199440
\(341\) −2.61724 + 18.4073i −0.141731 + 0.996811i
\(342\) 0 0
\(343\) −5.04145 3.66283i −0.272213 0.197774i
\(344\) 1.70906 5.25996i 0.0921466 0.283598i
\(345\) 0 0
\(346\) −2.88767 + 2.09801i −0.155242 + 0.112790i
\(347\) −20.4210 + 14.8367i −1.09626 + 0.796477i −0.980445 0.196794i \(-0.936947\pi\)
−0.115811 + 0.993271i \(0.536947\pi\)
\(348\) 0 0
\(349\) −3.43118 + 10.5601i −0.183667 + 0.565269i −0.999923 0.0124217i \(-0.996046\pi\)
0.816256 + 0.577691i \(0.196046\pi\)
\(350\) 0.448019 + 0.325504i 0.0239476 + 0.0173989i
\(351\) 0 0
\(352\) 4.25273 + 8.02942i 0.226672 + 0.427970i
\(353\) 18.8552 1.00356 0.501780 0.864996i \(-0.332679\pi\)
0.501780 + 0.864996i \(0.332679\pi\)
\(354\) 0 0
\(355\) −3.52668 + 10.8540i −0.187177 + 0.576070i
\(356\) −1.43867 4.42778i −0.0762494 0.234672i
\(357\) 0 0
\(358\) 6.24187 4.53498i 0.329893 0.239681i
\(359\) 6.57983 + 20.2506i 0.347270 + 1.06879i 0.960357 + 0.278773i \(0.0899276\pi\)
−0.613087 + 0.790016i \(0.710072\pi\)
\(360\) 0 0
\(361\) −22.0789 16.0412i −1.16205 0.844275i
\(362\) −13.6873 −0.719391
\(363\) 0 0
\(364\) −1.08642 −0.0569437
\(365\) −8.28423 6.01885i −0.433617 0.315041i
\(366\) 0 0
\(367\) −9.66781 29.7545i −0.504656 1.55317i −0.801349 0.598197i \(-0.795884\pi\)
0.296693 0.954973i \(-0.404116\pi\)
\(368\) 0.0141565 0.0102853i 0.000737957 0.000536157i
\(369\) 0 0
\(370\) 2.79178 + 8.59220i 0.145138 + 0.446687i
\(371\) 1.20591 3.71141i 0.0626078 0.192687i
\(372\) 0 0
\(373\) 9.39368 0.486386 0.243193 0.969978i \(-0.421805\pi\)
0.243193 + 0.969978i \(0.421805\pi\)
\(374\) −1.40850 2.65934i −0.0728319 0.137511i
\(375\) 0 0
\(376\) 4.15938 + 3.02196i 0.214503 + 0.155846i
\(377\) −0.484473 + 1.49106i −0.0249517 + 0.0767933i
\(378\) 0 0
\(379\) 6.63173 4.81823i 0.340649 0.247496i −0.404287 0.914632i \(-0.632480\pi\)
0.744936 + 0.667136i \(0.232480\pi\)
\(380\) 2.73515 1.98720i 0.140310 0.101941i
\(381\) 0 0
\(382\) −7.72664 + 23.7802i −0.395329 + 1.21670i
\(383\) 27.2501 + 19.7984i 1.39242 + 1.01165i 0.995596 + 0.0937524i \(0.0298862\pi\)
0.396820 + 0.917897i \(0.370114\pi\)
\(384\) 0 0
\(385\) −0.210886 + 1.48319i −0.0107478 + 0.0755901i
\(386\) −3.64656 −0.185605
\(387\) 0 0
\(388\) −0.902863 + 2.77873i −0.0458359 + 0.141069i
\(389\) 10.1771 + 31.3219i 0.515999 + 1.58808i 0.781456 + 0.623960i \(0.214477\pi\)
−0.265457 + 0.964123i \(0.585523\pi\)
\(390\) 0 0
\(391\) 0.00379698 0.00275867i 0.000192021 0.000139512i
\(392\) 6.42879 + 19.7858i 0.324703 + 0.999333i
\(393\) 0 0
\(394\) −5.15894 3.74819i −0.259904 0.188831i
\(395\) −2.09965 −0.105645
\(396\) 0 0
\(397\) −15.3865 −0.772228 −0.386114 0.922451i \(-0.626183\pi\)
−0.386114 + 0.922451i \(0.626183\pi\)
\(398\) −8.03669 5.83900i −0.402843 0.292683i
\(399\) 0 0
\(400\) −0.852662 2.62422i −0.0426331 0.131211i
\(401\) −5.37426 + 3.90463i −0.268378 + 0.194988i −0.713832 0.700317i \(-0.753042\pi\)
0.445455 + 0.895305i \(0.353042\pi\)
\(402\) 0 0
\(403\) 8.38491 + 25.8061i 0.417682 + 1.28549i
\(404\) −0.339039 + 1.04346i −0.0168678 + 0.0519138i
\(405\) 0 0
\(406\) −0.179370 −0.00890198
\(407\) −17.0058 + 17.5533i −0.842945 + 0.870085i
\(408\) 0 0
\(409\) −19.8088 14.3919i −0.979482 0.711636i −0.0218895 0.999760i \(-0.506968\pi\)
−0.957593 + 0.288125i \(0.906968\pi\)
\(410\) 4.15623 12.7916i 0.205262 0.631731i
\(411\) 0 0
\(412\) 3.89119 2.82711i 0.191705 0.139282i
\(413\) 0.548339 0.398392i 0.0269820 0.0196036i
\(414\) 0 0
\(415\) 4.91167 15.1166i 0.241104 0.742043i
\(416\) 10.7279 + 7.79428i 0.525979 + 0.382146i
\(417\) 0 0
\(418\) −24.8459 12.1678i −1.21526 0.595146i
\(419\) 20.8656 1.01935 0.509676 0.860367i \(-0.329765\pi\)
0.509676 + 0.860367i \(0.329765\pi\)
\(420\) 0 0
\(421\) −5.23200 + 16.1025i −0.254992 + 0.784785i 0.738839 + 0.673882i \(0.235374\pi\)
−0.993831 + 0.110903i \(0.964626\pi\)
\(422\) −0.497571 1.53137i −0.0242214 0.0745458i
\(423\) 0 0
\(424\) −21.3964 + 15.5454i −1.03910 + 0.754951i
\(425\) −0.228697 0.703856i −0.0110934 0.0341420i
\(426\) 0 0
\(427\) 4.76717 + 3.46355i 0.230700 + 0.167613i
\(428\) −5.84186 −0.282377
\(429\) 0 0
\(430\) −2.21500 −0.106817
\(431\) −21.1677 15.3792i −1.01961 0.740791i −0.0534080 0.998573i \(-0.517008\pi\)
−0.966203 + 0.257782i \(0.917008\pi\)
\(432\) 0 0
\(433\) −7.74375 23.8328i −0.372141 1.14533i −0.945387 0.325949i \(-0.894316\pi\)
0.573246 0.819383i \(-0.305684\pi\)
\(434\) −2.51152 + 1.82472i −0.120557 + 0.0875895i
\(435\) 0 0
\(436\) 1.92081 + 5.91163i 0.0919899 + 0.283116i
\(437\) 0.0133332 0.0410353i 0.000637812 0.00196298i
\(438\) 0 0
\(439\) 5.11234 0.243999 0.121999 0.992530i \(-0.461069\pi\)
0.121999 + 0.992530i \(0.461069\pi\)
\(440\) 7.06458 7.29203i 0.336791 0.347634i
\(441\) 0 0
\(442\) −3.55307 2.58146i −0.169003 0.122788i
\(443\) 8.67635 26.7031i 0.412226 1.26870i −0.502483 0.864587i \(-0.667580\pi\)
0.914709 0.404113i \(-0.132420\pi\)
\(444\) 0 0
\(445\) −7.57988 + 5.50711i −0.359321 + 0.261062i
\(446\) −28.4016 + 20.6350i −1.34486 + 0.977096i
\(447\) 0 0
\(448\) −1.23910 + 3.81356i −0.0585421 + 0.180174i
\(449\) −29.9297 21.7452i −1.41247 1.02622i −0.992958 0.118467i \(-0.962202\pi\)
−0.419510 0.907751i \(-0.637798\pi\)
\(450\) 0 0
\(451\) 35.8422 6.26041i 1.68775 0.294791i
\(452\) 4.92239 0.231530
\(453\) 0 0
\(454\) −2.98010 + 9.17181i −0.139863 + 0.430454i
\(455\) 0.675622 + 2.07935i 0.0316736 + 0.0974815i
\(456\) 0 0
\(457\) −29.8092 + 21.6576i −1.39441 + 1.01310i −0.399050 + 0.916929i \(0.630660\pi\)
−0.995365 + 0.0961719i \(0.969340\pi\)
\(458\) −6.11891 18.8321i −0.285918 0.879965i
\(459\) 0 0
\(460\) 0.00254938 + 0.00185224i 0.000118866 + 8.63609e-5i
\(461\) 23.0013 1.07128 0.535640 0.844447i \(-0.320071\pi\)
0.535640 + 0.844447i \(0.320071\pi\)
\(462\) 0 0
\(463\) −36.1571 −1.68036 −0.840181 0.542306i \(-0.817551\pi\)
−0.840181 + 0.542306i \(0.817551\pi\)
\(464\) 0.723042 + 0.525321i 0.0335664 + 0.0243874i
\(465\) 0 0
\(466\) 6.98403 + 21.4946i 0.323529 + 0.995720i
\(467\) 1.83240 1.33132i 0.0847935 0.0616061i −0.544581 0.838708i \(-0.683311\pi\)
0.629374 + 0.777102i \(0.283311\pi\)
\(468\) 0 0
\(469\) −1.34106 4.12736i −0.0619244 0.190584i
\(470\) 0.636283 1.95828i 0.0293496 0.0903287i
\(471\) 0 0
\(472\) −4.59348 −0.211432
\(473\) −2.80458 5.29521i −0.128955 0.243474i
\(474\) 0 0
\(475\) −5.50435 3.99914i −0.252557 0.183493i
\(476\) −0.0513310 + 0.157981i −0.00235275 + 0.00724103i
\(477\) 0 0
\(478\) −22.1818 + 16.1160i −1.01457 + 0.737130i
\(479\) 24.7000 17.9456i 1.12857 0.819954i 0.143084 0.989711i \(-0.454298\pi\)
0.985486 + 0.169756i \(0.0542981\pi\)
\(480\) 0 0
\(481\) −11.0221 + 33.9225i −0.502564 + 1.54673i
\(482\) 13.1137 + 9.52768i 0.597314 + 0.433974i
\(483\) 0 0
\(484\) 5.24935 + 1.52355i 0.238607 + 0.0692524i
\(485\) 5.87983 0.266989
\(486\) 0 0
\(487\) −4.99195 + 15.3636i −0.226207 + 0.696193i 0.771960 + 0.635671i \(0.219277\pi\)
−0.998167 + 0.0605221i \(0.980723\pi\)
\(488\) −12.3406 37.9804i −0.558632 1.71929i
\(489\) 0 0
\(490\) 6.74066 4.89737i 0.304512 0.221241i
\(491\) −3.60828 11.1051i −0.162839 0.501168i 0.836031 0.548682i \(-0.184870\pi\)
−0.998871 + 0.0475137i \(0.984870\pi\)
\(492\) 0 0
\(493\) 0.193931 + 0.140899i 0.00873420 + 0.00634577i
\(494\) −40.3754 −1.81658
\(495\) 0 0
\(496\) 15.4680 0.694534
\(497\) −4.17048 3.03003i −0.187072 0.135916i
\(498\) 0 0
\(499\) −12.6501 38.9330i −0.566296 1.74288i −0.664068 0.747672i \(-0.731171\pi\)
0.0977712 0.995209i \(-0.468829\pi\)
\(500\) 0.402006 0.292074i 0.0179782 0.0130620i
\(501\) 0 0
\(502\) −7.95720 24.4897i −0.355147 1.09303i
\(503\) −0.131171 + 0.403703i −0.00584863 + 0.0180002i −0.953938 0.300003i \(-0.903012\pi\)
0.948090 + 0.318003i \(0.103012\pi\)
\(504\) 0 0
\(505\) 2.20797 0.0982533
\(506\) 0.00362993 0.0255297i 0.000161370 0.00113493i
\(507\) 0 0
\(508\) −0.225751 0.164017i −0.0100161 0.00727710i
\(509\) −6.12017 + 18.8360i −0.271272 + 0.834889i 0.718910 + 0.695103i \(0.244641\pi\)
−0.990182 + 0.139786i \(0.955359\pi\)
\(510\) 0 0
\(511\) 3.74195 2.71868i 0.165534 0.120267i
\(512\) 19.7827 14.3729i 0.874278 0.635200i
\(513\) 0 0
\(514\) −1.27588 + 3.92677i −0.0562769 + 0.173202i
\(515\) −7.83082 5.68943i −0.345067 0.250706i
\(516\) 0 0
\(517\) 5.48714 0.958415i 0.241324 0.0421510i
\(518\) −4.08078 −0.179299
\(519\) 0 0
\(520\) 4.57882 14.0922i 0.200795 0.617982i
\(521\) 11.3748 + 35.0079i 0.498337 + 1.53372i 0.811690 + 0.584088i \(0.198548\pi\)
−0.313353 + 0.949637i \(0.601452\pi\)
\(522\) 0 0
\(523\) 8.49589 6.17262i 0.371499 0.269910i −0.386333 0.922359i \(-0.626258\pi\)
0.757832 + 0.652449i \(0.226258\pi\)
\(524\) 0.466033 + 1.43430i 0.0203587 + 0.0626577i
\(525\) 0 0
\(526\) −20.8737 15.1656i −0.910137 0.661253i
\(527\) 4.14875 0.180723
\(528\) 0 0
\(529\) −23.0000 −0.999998
\(530\) 8.56916 + 6.22586i 0.372220 + 0.270434i
\(531\) 0 0
\(532\) 0.471900 + 1.45236i 0.0204595 + 0.0629678i
\(533\) 42.9594 31.2118i 1.86078 1.35193i
\(534\) 0 0
\(535\) 3.63294 + 11.1810i 0.157066 + 0.483399i
\(536\) −9.08863 + 27.9719i −0.392569 + 1.20820i
\(537\) 0 0
\(538\) 28.6660 1.23588
\(539\) 20.2426 + 9.91338i 0.871910 + 0.427000i
\(540\) 0 0
\(541\) −0.529593 0.384772i −0.0227690 0.0165426i 0.576343 0.817208i \(-0.304479\pi\)
−0.599112 + 0.800666i \(0.704479\pi\)
\(542\) −7.78454 + 23.9584i −0.334375 + 1.02910i
\(543\) 0 0
\(544\) 1.64028 1.19173i 0.0703262 0.0510950i
\(545\) 10.1201 7.35267i 0.433497 0.314954i
\(546\) 0 0
\(547\) −4.14573 + 12.7592i −0.177259 + 0.545546i −0.999729 0.0232616i \(-0.992595\pi\)
0.822471 + 0.568807i \(0.192595\pi\)
\(548\) 8.32166 + 6.04604i 0.355484 + 0.258274i
\(549\) 0 0
\(550\) −3.65180 1.78839i −0.155713 0.0762574i
\(551\) 2.20374 0.0938823
\(552\) 0 0
\(553\) 0.293073 0.901985i 0.0124627 0.0383563i
\(554\) −7.41872 22.8325i −0.315191 0.970059i
\(555\) 0 0
\(556\) 1.42661 1.03649i 0.0605017 0.0439571i
\(557\) −4.09205 12.5940i −0.173386 0.533626i 0.826171 0.563420i \(-0.190515\pi\)
−0.999556 + 0.0297943i \(0.990515\pi\)
\(558\) 0 0
\(559\) −7.07481 5.14015i −0.299232 0.217405i
\(560\) 1.24635 0.0526679
\(561\) 0 0
\(562\) 16.9099 0.713300
\(563\) 17.2822 + 12.5562i 0.728356 + 0.529182i 0.889043 0.457824i \(-0.151371\pi\)
−0.160687 + 0.987005i \(0.551371\pi\)
\(564\) 0 0
\(565\) −3.06115 9.42124i −0.128783 0.396355i
\(566\) −31.2611 + 22.7125i −1.31400 + 0.954679i
\(567\) 0 0
\(568\) 10.7960 + 33.2265i 0.452988 + 1.39415i
\(569\) 14.0100 43.1185i 0.587332 1.80762i −0.00236662 0.999997i \(-0.500753\pi\)
0.589698 0.807624i \(-0.299247\pi\)
\(570\) 0 0
\(571\) −25.1544 −1.05268 −0.526339 0.850275i \(-0.676436\pi\)
−0.526339 + 0.850275i \(0.676436\pi\)
\(572\) 7.85817 1.37255i 0.328567 0.0573893i
\(573\) 0 0
\(574\) 4.91497 + 3.57093i 0.205147 + 0.149048i
\(575\) 0.00195968 0.00603127i 8.17243e−5 0.000251522i
\(576\) 0 0
\(577\) −6.16999 + 4.48276i −0.256860 + 0.186620i −0.708762 0.705448i \(-0.750746\pi\)
0.451902 + 0.892068i \(0.350746\pi\)
\(578\) 16.3184 11.8560i 0.678755 0.493144i
\(579\) 0 0
\(580\) −0.0497357 + 0.153071i −0.00206516 + 0.00635592i
\(581\) 5.80831 + 4.21998i 0.240969 + 0.175074i
\(582\) 0 0
\(583\) −4.03358 + 28.3686i −0.167054 + 1.17491i
\(584\) −31.3466 −1.29713
\(585\) 0 0
\(586\) −8.83232 + 27.1831i −0.364860 + 1.12292i
\(587\) −2.43760 7.50217i −0.100611 0.309648i 0.888065 0.459719i \(-0.152050\pi\)
−0.988675 + 0.150071i \(0.952050\pi\)
\(588\) 0 0
\(589\) 30.8564 22.4185i 1.27142 0.923739i
\(590\) 0.568489 + 1.74963i 0.0234043 + 0.0720310i
\(591\) 0 0
\(592\) 16.4497 + 11.9514i 0.676077 + 0.491199i
\(593\) 8.68507 0.356653 0.178327 0.983971i \(-0.442932\pi\)
0.178327 + 0.983971i \(0.442932\pi\)
\(594\) 0 0
\(595\) 0.334290 0.0137045
\(596\) −2.53448 1.84141i −0.103816 0.0754271i
\(597\) 0 0
\(598\) −0.0116293 0.0357914i −0.000475558 0.00146362i
\(599\) −11.3275 + 8.22991i −0.462829 + 0.336265i −0.794640 0.607081i \(-0.792340\pi\)
0.331811 + 0.943346i \(0.392340\pi\)
\(600\) 0 0
\(601\) −3.18091 9.78983i −0.129752 0.399335i 0.864985 0.501798i \(-0.167328\pi\)
−0.994737 + 0.102462i \(0.967328\pi\)
\(602\) 0.309173 0.951537i 0.0126010 0.0387817i
\(603\) 0 0
\(604\) 1.83076 0.0744927
\(605\) −0.348460 10.9945i −0.0141669 0.446989i
\(606\) 0 0
\(607\) −22.2282 16.1497i −0.902214 0.655497i 0.0368195 0.999322i \(-0.488277\pi\)
−0.939034 + 0.343825i \(0.888277\pi\)
\(608\) 5.75986 17.7270i 0.233593 0.718926i
\(609\) 0 0
\(610\) −12.9392 + 9.40090i −0.523894 + 0.380631i
\(611\) 6.57671 4.77826i 0.266065 0.193308i
\(612\) 0 0
\(613\) −3.35530 + 10.3266i −0.135519 + 0.417086i −0.995670 0.0929536i \(-0.970369\pi\)
0.860151 + 0.510039i \(0.170369\pi\)
\(614\) 10.0116 + 7.27388i 0.404037 + 0.293550i
\(615\) 0 0
\(616\) 2.14648 + 4.05269i 0.0864842 + 0.163287i
\(617\) −18.2404 −0.734330 −0.367165 0.930156i \(-0.619671\pi\)
−0.367165 + 0.930156i \(0.619671\pi\)
\(618\) 0 0
\(619\) 6.08144 18.7167i 0.244434 0.752289i −0.751295 0.659966i \(-0.770571\pi\)
0.995729 0.0923233i \(-0.0294293\pi\)
\(620\) 0.860790 + 2.64924i 0.0345701 + 0.106396i
\(621\) 0 0
\(622\) 13.2169 9.60267i 0.529951 0.385032i
\(623\) −1.30777 4.02491i −0.0523948 0.161255i
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 28.4044 1.13527
\(627\) 0 0
\(628\) −1.40559 −0.0560893
\(629\) 4.41205 + 3.20554i 0.175920 + 0.127813i
\(630\) 0 0
\(631\) −9.40181 28.9358i −0.374280 1.15192i −0.943963 0.330051i \(-0.892934\pi\)
0.569683 0.821865i \(-0.307066\pi\)
\(632\) −5.19997 + 3.77800i −0.206844 + 0.150281i
\(633\) 0 0
\(634\) 2.62619 + 8.08260i 0.104300 + 0.321001i
\(635\) −0.173532 + 0.534076i −0.00688640 + 0.0211942i
\(636\) 0 0
\(637\) 32.8948 1.30334
\(638\) 1.29740 0.226612i 0.0513647 0.00897166i
\(639\) 0 0
\(640\) −4.37230 3.17666i −0.172830 0.125569i
\(641\) −11.5427 + 35.5247i −0.455908 + 1.40314i 0.414159 + 0.910205i \(0.364076\pi\)
−0.870066 + 0.492935i \(0.835924\pi\)
\(642\) 0 0
\(643\) −0.861554 + 0.625956i −0.0339764 + 0.0246853i −0.604644 0.796496i \(-0.706685\pi\)
0.570667 + 0.821181i \(0.306685\pi\)
\(644\) −0.00115154 0.000836645i −4.53772e−5 3.29684e-5i
\(645\) 0 0
\(646\) −1.90766 + 5.87118i −0.0750559 + 0.230998i
\(647\) −12.7864 9.28987i −0.502686 0.365223i 0.307356 0.951595i \(-0.400556\pi\)
−0.810042 + 0.586372i \(0.800556\pi\)
\(648\) 0 0
\(649\) −3.46288 + 3.57437i −0.135930 + 0.140306i
\(650\) −5.93429 −0.232762
\(651\) 0 0
\(652\) −1.35916 + 4.18305i −0.0532287 + 0.163821i
\(653\) −10.9241 33.6210i −0.427495 1.31569i −0.900585 0.434679i \(-0.856862\pi\)
0.473091 0.881014i \(-0.343138\pi\)
\(654\) 0 0
\(655\) 2.45537 1.78393i 0.0959393 0.0697040i
\(656\) −9.35409 28.7889i −0.365216 1.12402i
\(657\) 0 0
\(658\) 0.752439 + 0.546679i 0.0293331 + 0.0213118i
\(659\) 28.4474 1.10815 0.554077 0.832465i \(-0.313071\pi\)
0.554077 + 0.832465i \(0.313071\pi\)
\(660\) 0 0
\(661\) 39.5989 1.54022 0.770110 0.637911i \(-0.220201\pi\)
0.770110 + 0.637911i \(0.220201\pi\)
\(662\) 10.4857 + 7.61830i 0.407538 + 0.296094i
\(663\) 0 0
\(664\) −15.0357 46.2752i −0.583499 1.79583i
\(665\) 2.48629 1.80639i 0.0964140 0.0700489i
\(666\) 0 0
\(667\) 0.000634741 0.00195353i 2.45773e−5 7.56411e-5i
\(668\) −3.02256 + 9.30248i −0.116946 + 0.359924i
\(669\) 0 0
\(670\) 11.7791 0.455068
\(671\) −38.8573 19.0295i −1.50007 0.734627i
\(672\) 0 0
\(673\) 14.2080 + 10.3227i 0.547679 + 0.397912i 0.826929 0.562306i \(-0.190086\pi\)
−0.279250 + 0.960218i \(0.590086\pi\)
\(674\) −2.40448 + 7.40024i −0.0926173 + 0.285047i
\(675\) 0 0
\(676\) 4.19248 3.04602i 0.161249 0.117155i
\(677\) −36.4616 + 26.4909i −1.40133 + 1.01813i −0.406819 + 0.913509i \(0.633362\pi\)
−0.994512 + 0.104619i \(0.966638\pi\)
\(678\) 0 0
\(679\) −0.820716 + 2.52590i −0.0314962 + 0.0969353i
\(680\) −1.83287 1.33165i −0.0702872 0.0510666i
\(681\) 0 0
\(682\) 15.8608 16.3714i 0.607340 0.626894i
\(683\) −15.7677 −0.603334 −0.301667 0.953413i \(-0.597543\pi\)
−0.301667 + 0.953413i \(0.597543\pi\)
\(684\) 0 0
\(685\) 6.39676 19.6872i 0.244408 0.752210i
\(686\) 2.36087 + 7.26603i 0.0901386 + 0.277418i
\(687\) 0 0
\(688\) −4.03304 + 2.93018i −0.153758 + 0.111712i
\(689\) 12.9225 + 39.7713i 0.492307 + 1.51517i
\(690\) 0 0
\(691\) −2.39970 1.74348i −0.0912889 0.0663253i 0.541205 0.840891i \(-0.317968\pi\)
−0.632493 + 0.774566i \(0.717968\pi\)
\(692\) −1.44668 −0.0549944
\(693\) 0 0
\(694\) 30.9465 1.17471
\(695\) −2.87098 2.08589i −0.108903 0.0791224i
\(696\) 0 0
\(697\) −2.50891 7.72162i −0.0950316 0.292477i
\(698\) 11.0132 8.00153i 0.416854 0.302862i
\(699\) 0 0
\(700\) 0.0693589 + 0.213465i 0.00262152 + 0.00806821i
\(701\) −11.4738 + 35.3128i −0.433360 + 1.33375i 0.461397 + 0.887194i \(0.347348\pi\)
−0.894757 + 0.446553i \(0.852652\pi\)
\(702\) 0 0
\(703\) 50.1364 1.89093
\(704\) 4.14459 29.1494i 0.156205 1.09861i
\(705\) 0 0
\(706\) −18.7017 13.5876i −0.703848 0.511375i
\(707\) −0.308191 + 0.948516i −0.0115907 + 0.0356726i
\(708\) 0 0
\(709\) 25.6867 18.6625i 0.964683 0.700883i 0.0104495 0.999945i \(-0.496674\pi\)
0.954234 + 0.299062i \(0.0966738\pi\)
\(710\) 11.3197 8.22423i 0.424820 0.308650i
\(711\) 0 0
\(712\) −8.86303 + 27.2776i −0.332156 + 1.02227i
\(713\) 0.0287608 + 0.0208959i 0.00107710 + 0.000782558i
\(714\) 0 0
\(715\) −7.51386 14.1866i −0.281002 0.530549i
\(716\) 3.12708 0.116864
\(717\) 0 0
\(718\) 8.06692 24.8274i 0.301055 0.926552i
\(719\) 9.85059 + 30.3170i 0.367365 + 1.13063i 0.948487 + 0.316816i \(0.102614\pi\)
−0.581122 + 0.813816i \(0.697386\pi\)
\(720\) 0 0
\(721\) 3.53714 2.56989i 0.131730 0.0957075i
\(722\) 10.3394 + 31.8213i 0.384792 + 1.18427i
\(723\) 0 0
\(724\) −4.48806 3.26077i −0.166797 0.121185i
\(725\) 0.323900 0.0120294
\(726\) 0 0
\(727\) 41.4129 1.53592 0.767959 0.640499i \(-0.221272\pi\)
0.767959 + 0.640499i \(0.221272\pi\)
\(728\) 5.41470 + 3.93401i 0.200682 + 0.145804i
\(729\) 0 0
\(730\) 3.87945 + 11.9397i 0.143585 + 0.441909i
\(731\) −1.08172 + 0.785918i −0.0400090 + 0.0290682i
\(732\) 0 0
\(733\) 14.7376 + 45.3578i 0.544347 + 1.67533i 0.722537 + 0.691333i \(0.242976\pi\)
−0.178189 + 0.983996i \(0.557024\pi\)
\(734\) −11.8528 + 36.4792i −0.437495 + 1.34647i
\(735\) 0 0
\(736\) 0.0173734 0.000640391
\(737\) 14.9145 + 28.1594i 0.549381 + 1.03726i
\(738\) 0 0
\(739\) 10.0777 + 7.32187i 0.370714 + 0.269339i 0.757507 0.652827i \(-0.226417\pi\)
−0.386793 + 0.922167i \(0.626417\pi\)
\(740\) −1.13152 + 3.48246i −0.0415955 + 0.128018i
\(741\) 0 0
\(742\) −3.87065 + 2.81219i −0.142096 + 0.103239i
\(743\) −22.1446 + 16.0890i −0.812407 + 0.590249i −0.914528 0.404524i \(-0.867437\pi\)
0.102120 + 0.994772i \(0.467437\pi\)
\(744\) 0 0
\(745\) −1.94823 + 5.99603i −0.0713775 + 0.219677i
\(746\) −9.31722 6.76936i −0.341128 0.247844i
\(747\) 0 0
\(748\) 0.171694 1.20754i 0.00627775 0.0441521i
\(749\) −5.31033 −0.194035
\(750\) 0 0
\(751\) −12.9393 + 39.8231i −0.472162 + 1.45317i 0.377585 + 0.925975i \(0.376755\pi\)
−0.849747 + 0.527191i \(0.823245\pi\)
\(752\) −1.43203 4.40733i −0.0522207 0.160719i
\(753\) 0 0
\(754\) 1.55503 1.12979i 0.0566308 0.0411447i
\(755\) −1.13852 3.50400i −0.0414349 0.127523i
\(756\) 0 0
\(757\) −13.0407 9.47464i −0.473973 0.344362i 0.325015 0.945709i \(-0.394631\pi\)
−0.798988 + 0.601347i \(0.794631\pi\)
\(758\) −10.0499 −0.365029
\(759\) 0 0
\(760\) −20.8278 −0.755504
\(761\) 8.83760 + 6.42090i 0.320363 + 0.232757i 0.736330 0.676622i \(-0.236557\pi\)
−0.415967 + 0.909380i \(0.636557\pi\)
\(762\) 0 0
\(763\) 1.74604 + 5.37376i 0.0632109 + 0.194543i
\(764\) −8.19875 + 5.95674i −0.296620 + 0.215507i
\(765\) 0 0
\(766\) −12.7610 39.2744i −0.461075 1.41904i
\(767\) −2.24442 + 6.90762i −0.0810414 + 0.249420i
\(768\) 0 0
\(769\) −34.2074 −1.23355 −0.616775 0.787139i \(-0.711561\pi\)
−0.616775 + 0.787139i \(0.711561\pi\)
\(770\) 1.27800 1.31914i 0.0460558 0.0475386i
\(771\) 0 0
\(772\) −1.19570 0.868727i −0.0430342 0.0312662i
\(773\) 2.66894 8.21416i 0.0959952 0.295443i −0.891517 0.452988i \(-0.850358\pi\)
0.987512 + 0.157545i \(0.0503580\pi\)
\(774\) 0 0
\(775\) 4.53521 3.29503i 0.162910 0.118361i
\(776\) 14.5619 10.5798i 0.522742 0.379794i
\(777\) 0 0
\(778\) 12.4772 38.4009i 0.447329 1.37674i
\(779\) −60.3852 43.8724i −2.16352 1.57189i
\(780\) 0 0
\(781\) 33.9937 + 16.6477i 1.21639 + 0.595701i
\(782\) −0.00575405 −0.000205764
\(783\) 0 0
\(784\) 5.79466 17.8341i 0.206952 0.636934i
\(785\) 0.874113 + 2.69024i 0.0311984 + 0.0960189i
\(786\) 0 0
\(787\) 18.6918 13.5804i 0.666291 0.484089i −0.202491 0.979284i \(-0.564904\pi\)
0.868781 + 0.495196i \(0.164904\pi\)
\(788\) −0.798669 2.45805i −0.0284514 0.0875644i
\(789\) 0 0
\(790\) 2.08256 + 1.51307i 0.0740943 + 0.0538327i
\(791\) 4.47453 0.159096
\(792\) 0 0
\(793\) −63.1443 −2.24232
\(794\) 15.2613 + 11.0880i 0.541603 + 0.393498i
\(795\) 0 0
\(796\) −1.24418 3.82920i −0.0440988 0.135722i
\(797\) 32.1449 23.3547i 1.13863 0.827265i 0.151704 0.988426i \(-0.451524\pi\)
0.986928 + 0.161161i \(0.0515238\pi\)
\(798\) 0 0
\(799\) −0.384092 1.18211i −0.0135882 0.0418202i
\(800\) 0.846572 2.60548i 0.0299308 0.0921176i
\(801\) 0 0
\(802\) 8.14430 0.287585
\(803\) −23.6312 + 24.3920i −0.833927 + 0.860776i
\(804\) 0 0
\(805\) 0.00231743 + 0.00168371i 8.16785e−5 + 5.93429e-5i
\(806\) 10.2800 31.6385i 0.362096 1.11442i
\(807\) 0 0
\(808\) 5.46822 3.97289i 0.192371 0.139766i
\(809\) 25.0908 18.2296i 0.882147 0.640917i −0.0516716 0.998664i \(-0.516455\pi\)
0.933819 + 0.357747i \(0.116455\pi\)
\(810\) 0 0
\(811\) 2.30503 7.09414i 0.0809404 0.249109i −0.902395 0.430910i \(-0.858193\pi\)
0.983335 + 0.181801i \(0.0581927\pi\)
\(812\) −0.0588151 0.0427317i −0.00206401 0.00149959i
\(813\) 0 0
\(814\) 29.5168 5.15557i 1.03456 0.180703i
\(815\) 8.85141 0.310051
\(816\) 0 0
\(817\) −3.79849 + 11.6906i −0.132892 + 0.409001i
\(818\) 9.27633 + 28.5496i 0.324339 + 0.998213i
\(819\) 0 0
\(820\) 4.41019 3.20419i 0.154010 0.111895i
\(821\) −3.91079 12.0362i −0.136488 0.420065i 0.859331 0.511420i \(-0.170880\pi\)
−0.995818 + 0.0913546i \(0.970880\pi\)
\(822\) 0 0
\(823\) 22.0772 + 16.0401i 0.769564 + 0.559121i 0.901829 0.432093i \(-0.142225\pi\)
−0.132265 + 0.991214i \(0.542225\pi\)
\(824\) −29.6309 −1.03224
\(825\) 0 0
\(826\) −0.830969 −0.0289131
\(827\) 13.7164 + 9.96556i 0.476966 + 0.346536i 0.800150 0.599800i \(-0.204753\pi\)
−0.323184 + 0.946336i \(0.604753\pi\)
\(828\) 0 0
\(829\) 6.11217 + 18.8113i 0.212284 + 0.653344i 0.999335 + 0.0364562i \(0.0116069\pi\)
−0.787051 + 0.616888i \(0.788393\pi\)
\(830\) −15.7651 + 11.4540i −0.547215 + 0.397575i
\(831\) 0 0
\(832\) −13.2782 40.8660i −0.460337 1.41677i
\(833\) 1.55422 4.78339i 0.0538504 0.165735i
\(834\) 0 0
\(835\) 19.6842 0.681200
\(836\) −5.24819 9.90890i −0.181512 0.342706i
\(837\) 0 0
\(838\) −20.6958 15.0364i −0.714923 0.519422i
\(839\) −1.53882 + 4.73601i −0.0531261 + 0.163505i −0.974099 0.226121i \(-0.927396\pi\)
0.920973 + 0.389626i \(0.127396\pi\)
\(840\) 0 0
\(841\) 23.3766 16.9841i 0.806090 0.585659i
\(842\) 16.7933 12.2011i 0.578736 0.420476i
\(843\) 0 0
\(844\) 0.201668 0.620670i 0.00694170 0.0213643i
\(845\) −8.43717 6.12996i −0.290247 0.210877i
\(846\) 0 0
\(847\) 4.77173 + 1.38493i 0.163959 + 0.0475868i
\(848\) 23.8387 0.818623
\(849\) 0 0
\(850\) −0.280384 + 0.862933i −0.00961709 + 0.0295983i
\(851\) 0.0144408 + 0.0444441i 0.000495023 + 0.00152353i
\(852\) 0 0
\(853\) 18.8068 13.6639i 0.643931 0.467843i −0.217267 0.976112i \(-0.569714\pi\)
0.861199 + 0.508269i \(0.169714\pi\)
\(854\) −2.23243 6.87072i −0.0763923 0.235111i
\(855\) 0 0
\(856\) 29.1158 + 21.1539i 0.995158 + 0.723025i
\(857\) −30.6976 −1.04861 −0.524306 0.851530i \(-0.675675\pi\)
−0.524306 + 0.851530i \(0.675675\pi\)
\(858\) 0 0
\(859\) −11.1830 −0.381560 −0.190780 0.981633i \(-0.561102\pi\)
−0.190780 + 0.981633i \(0.561102\pi\)
\(860\) −0.726295 0.527684i −0.0247665 0.0179939i
\(861\) 0 0
\(862\) 9.91268 + 30.5081i 0.337627 + 1.03911i
\(863\) 2.96371 2.15326i 0.100886 0.0732980i −0.536199 0.844092i \(-0.680140\pi\)
0.637085 + 0.770794i \(0.280140\pi\)
\(864\) 0 0
\(865\) 0.899661 + 2.76887i 0.0305894 + 0.0941445i
\(866\) −9.49389 + 29.2192i −0.322616 + 0.992909i
\(867\) 0 0
\(868\) −1.25823 −0.0427071
\(869\) −0.980280 + 6.89442i −0.0332537 + 0.233877i
\(870\) 0 0
\(871\) 37.6231 + 27.3348i 1.27481 + 0.926203i
\(872\) 11.8333 36.4190i 0.400725 1.23330i
\(873\) 0 0
\(874\) −0.0427958 + 0.0310930i −0.00144759 + 0.00105174i
\(875\) 0.365429 0.265500i 0.0123538 0.00897553i
\(876\) 0 0
\(877\) 2.27520 7.00235i 0.0768281 0.236453i −0.905265 0.424846i \(-0.860328\pi\)
0.982094 + 0.188394i \(0.0603281\pi\)
\(878\) −5.07073 3.68410i −0.171129 0.124332i
\(879\) 0 0
\(880\) −9.01498 + 1.57461i −0.303895 + 0.0530801i
\(881\) 6.07165 0.204559 0.102280 0.994756i \(-0.467386\pi\)
0.102280 + 0.994756i \(0.467386\pi\)
\(882\) 0 0
\(883\) 9.63412 29.6508i 0.324214 0.997828i −0.647580 0.761997i \(-0.724219\pi\)
0.971794 0.235830i \(-0.0757810\pi\)
\(884\) −0.550061 1.69291i −0.0185005 0.0569388i
\(885\) 0 0
\(886\) −27.8487 + 20.2333i −0.935596 + 0.679750i
\(887\) −1.75830 5.41150i −0.0590380 0.181700i 0.917188 0.398454i \(-0.130453\pi\)
−0.976226 + 0.216754i \(0.930453\pi\)
\(888\) 0 0
\(889\) −0.205210 0.149094i −0.00688254 0.00500046i
\(890\) 11.4868 0.385037
\(891\) 0 0
\(892\) −14.2288 −0.476414
\(893\) −9.24445 6.71648i −0.309354 0.224759i
\(894\) 0 0
\(895\) −1.94467 5.98508i −0.0650032 0.200059i
\(896\) 1.97495 1.43488i 0.0659784 0.0479361i
\(897\) 0 0
\(898\) 14.0159 + 43.1364i 0.467715 + 1.43948i
\(899\) −0.561092 + 1.72686i −0.0187135 + 0.0575941i
\(900\) 0 0
\(901\) 6.39389 0.213011
\(902\) −40.0620 19.6195i −1.33392 0.653258i
\(903\) 0 0
\(904\) −24.5332 17.8244i −0.815963 0.592832i
\(905\) −3.44992 + 10.6178i −0.114679 + 0.352946i
\(906\) 0 0
\(907\) −34.3765 + 24.9760i −1.14145 + 0.829313i −0.987321 0.158737i \(-0.949258\pi\)
−0.154131 + 0.988050i \(0.549258\pi\)
\(908\) −3.16219 + 2.29747i −0.104941 + 0.0762441i
\(909\) 0 0
\(910\) 0.828317 2.54930i 0.0274585 0.0845084i
\(911\) 1.73457 + 1.26024i 0.0574690 + 0.0417537i 0.616149 0.787630i \(-0.288692\pi\)
−0.558680 + 0.829383i \(0.688692\pi\)
\(912\) 0 0
\(913\) −47.3436 23.1855i −1.56684 0.767329i
\(914\) 45.1737 1.49421
\(915\) 0 0
\(916\) 2.48002 7.63273i 0.0819423 0.252193i
\(917\) 0.423630 + 1.30380i 0.0139895 + 0.0430553i
\(918\) 0 0
\(919\) −12.9995 + 9.44470i −0.428815 + 0.311552i −0.781175 0.624312i \(-0.785379\pi\)
0.352360 + 0.935864i \(0.385379\pi\)
\(920\) −0.00599902 0.0184631i −0.000197782 0.000608710i
\(921\) 0 0
\(922\) −22.8141 16.5754i −0.751343 0.545883i
\(923\) 55.2407 1.81827
\(924\) 0 0
\(925\) 7.36894 0.242289
\(926\) 35.8628 + 26.0558i 1.17852 + 0.856248i
\(927\) 0 0
\(928\) 0.274205 + 0.843916i 0.00900122 + 0.0277029i
\(929\) 30.3196 22.0285i 0.994753 0.722730i 0.0337960 0.999429i \(-0.489240\pi\)
0.960957 + 0.276699i \(0.0892403\pi\)
\(930\) 0 0
\(931\) −14.2883 43.9750i −0.468282 1.44122i
\(932\) −2.83066 + 8.71187i −0.0927213 + 0.285367i
\(933\) 0 0
\(934\) −2.77688 −0.0908621
\(935\) −2.41796 + 0.422334i −0.0790756 + 0.0138118i
\(936\) 0 0
\(937\) 21.0388 + 15.2856i 0.687308 + 0.499359i 0.875774 0.482721i \(-0.160351\pi\)
−0.188466 + 0.982080i \(0.560351\pi\)
\(938\) −1.64415 + 5.06017i −0.0536834 + 0.165220i
\(939\) 0 0
\(940\) 0.675161 0.490533i 0.0220213 0.0159994i
\(941\) −6.94527 + 5.04603i −0.226409 + 0.164496i −0.695207 0.718810i \(-0.744687\pi\)
0.468798 + 0.883306i \(0.344687\pi\)
\(942\) 0 0
\(943\) 0.0214986 0.0661658i 0.000700090 0.00215466i
\(944\) 3.34964 + 2.43366i 0.109022 + 0.0792088i
\(945\) 0 0
\(946\) −1.03413 + 7.27318i −0.0336226 + 0.236471i
\(947\) −36.0304 −1.17083 −0.585416 0.810733i \(-0.699069\pi\)
−0.585416 + 0.810733i \(0.699069\pi\)
\(948\) 0 0
\(949\) −15.3163 + 47.1386i −0.497187 + 1.53019i
\(950\) 2.57765 + 7.93318i 0.0836299 + 0.257386i
\(951\) 0 0
\(952\) 0.827896 0.601502i 0.0268323 0.0194948i
\(953\) −13.5512 41.7062i −0.438965 1.35100i −0.888968 0.457969i \(-0.848577\pi\)
0.450003 0.893027i \(-0.351423\pi\)
\(954\) 0 0
\(955\) 16.4996 + 11.9876i 0.533914 + 0.387911i
\(956\) −11.1127 −0.359412
\(957\) 0 0
\(958\) −37.4310 −1.20934
\(959\) 7.56451 + 5.49594i 0.244271 + 0.177473i
\(960\) 0 0
\(961\) 0.131439 + 0.404529i 0.00423998 + 0.0130493i
\(962\) 35.3779 25.7035i 1.14063 0.828716i
\(963\) 0 0
\(964\) 2.03017 + 6.24822i 0.0653874 + 0.201242i
\(965\) −0.919120 + 2.82876i −0.0295875 + 0.0910610i
\(966\) 0 0
\(967\) −48.1271 −1.54766 −0.773831 0.633392i \(-0.781662\pi\)
−0.773831 + 0.633392i \(0.781662\pi\)
\(968\) −20.6458 26.6017i −0.663582 0.855012i
\(969\) 0 0
\(970\) −5.83198 4.23718i −0.187253 0.136048i
\(971\) 9.80617 30.1803i 0.314695 0.968531i −0.661185 0.750223i \(-0.729946\pi\)
0.975880 0.218308i \(-0.0700539\pi\)
\(972\) 0 0
\(973\) 1.29681 0.942187i 0.0415738 0.0302051i
\(974\) 16.0228 11.6413i 0.513404 0.373010i
\(975\) 0 0
\(976\) −11.1233 + 34.2341i −0.356049 + 1.09581i
\(977\) −34.8913 25.3500i −1.11627 0.811018i −0.132631 0.991166i \(-0.542342\pi\)
−0.983640 + 0.180148i \(0.942342\pi\)
\(978\) 0 0
\(979\) 14.5443 + 27.4604i 0.464836 + 0.877639i
\(980\) 3.37696 0.107873
\(981\) 0 0
\(982\) −4.42378 + 13.6150i −0.141168 + 0.434472i
\(983\) 13.8106 + 42.5048i 0.440491 + 1.35569i 0.887354 + 0.461089i \(0.152541\pi\)
−0.446863 + 0.894602i \(0.647459\pi\)
\(984\) 0 0
\(985\) −4.20792 + 3.05723i −0.134075 + 0.0974115i
\(986\) −0.0908164 0.279504i −0.00289218 0.00890123i
\(987\) 0 0
\(988\) −13.2390 9.61873i −0.421190 0.306012i
\(989\) −0.0114573 −0.000364322
\(990\) 0 0
\(991\) 13.7657 0.437282 0.218641 0.975805i \(-0.429838\pi\)
0.218641 + 0.975805i \(0.429838\pi\)
\(992\) 12.4245 + 9.02693i 0.394479 + 0.286605i
\(993\) 0 0
\(994\) 1.95301 + 6.01074i 0.0619457 + 0.190649i
\(995\) −6.55518 + 4.76261i −0.207813 + 0.150985i
\(996\) 0 0
\(997\) 1.51297 + 4.65646i 0.0479164 + 0.147471i 0.972152 0.234351i \(-0.0752965\pi\)
−0.924236 + 0.381823i \(0.875297\pi\)
\(998\) −15.5091 + 47.7322i −0.490933 + 1.51094i
\(999\) 0 0
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 495.2.n.g.136.2 yes 16
3.2 odd 2 495.2.n.h.136.3 yes 16
11.3 even 5 inner 495.2.n.g.91.2 16
11.5 even 5 5445.2.a.cd.1.6 8
11.6 odd 10 5445.2.a.cb.1.3 8
33.5 odd 10 5445.2.a.ca.1.3 8
33.14 odd 10 495.2.n.h.91.3 yes 16
33.17 even 10 5445.2.a.cc.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
495.2.n.g.91.2 16 11.3 even 5 inner
495.2.n.g.136.2 yes 16 1.1 even 1 trivial
495.2.n.h.91.3 yes 16 33.14 odd 10
495.2.n.h.136.3 yes 16 3.2 odd 2
5445.2.a.ca.1.3 8 33.5 odd 10
5445.2.a.cb.1.3 8 11.6 odd 10
5445.2.a.cc.1.6 8 33.17 even 10
5445.2.a.cd.1.6 8 11.5 even 5