Properties

Label 273.2.u.c.62.5
Level $273$
Weight $2$
Character 273.62
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(62,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.62");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.u (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 62.5
Character \(\chi\) \(=\) 273.62
Dual form 273.2.u.c.251.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.03726 - 1.79658i) q^{2} +(-1.69497 + 0.356466i) q^{3} +(-1.15180 + 1.99498i) q^{4} -4.16126i q^{5} +(2.39854 + 2.67541i) q^{6} +(1.87191 - 1.86974i) q^{7} +0.629840 q^{8} +(2.74586 - 1.20840i) q^{9} +O(q^{10})\) \(q+(-1.03726 - 1.79658i) q^{2} +(-1.69497 + 0.356466i) q^{3} +(-1.15180 + 1.99498i) q^{4} -4.16126i q^{5} +(2.39854 + 2.67541i) q^{6} +(1.87191 - 1.86974i) q^{7} +0.629840 q^{8} +(2.74586 - 1.20840i) q^{9} +(-7.47605 + 4.31630i) q^{10} +(-0.0676716 - 0.117211i) q^{11} +(1.24113 - 3.79202i) q^{12} +(-1.33588 - 3.34894i) q^{13} +(-5.30080 - 1.42364i) q^{14} +(1.48335 + 7.05323i) q^{15} +(1.65030 + 2.85841i) q^{16} +(-1.65037 + 2.85853i) q^{17} +(-5.01916 - 3.67975i) q^{18} +(-1.48799 + 2.57727i) q^{19} +(8.30165 + 4.79296i) q^{20} +(-2.50634 + 3.83644i) q^{21} +(-0.140386 + 0.243155i) q^{22} +(-2.78875 + 1.61009i) q^{23} +(-1.06756 + 0.224516i) q^{24} -12.3161 q^{25} +(-4.63100 + 5.87373i) q^{26} +(-4.22341 + 3.02701i) q^{27} +(1.57403 + 5.88802i) q^{28} +(5.45038 - 3.14678i) q^{29} +(11.1331 - 9.98097i) q^{30} +6.26358 q^{31} +(4.05342 - 7.02072i) q^{32} +(0.156483 + 0.174546i) q^{33} +6.84744 q^{34} +(-7.78049 - 7.78953i) q^{35} +(-0.751960 + 6.86979i) q^{36} +(3.35765 - 1.93854i) q^{37} +6.17370 q^{38} +(3.45807 + 5.20017i) q^{39} -2.62093i q^{40} +(-5.27438 + 3.04517i) q^{41} +(9.49219 + 0.523481i) q^{42} +(-1.24239 + 2.15189i) q^{43} +0.311778 q^{44} +(-5.02847 - 11.4263i) q^{45} +(5.78531 + 3.34015i) q^{46} -2.22423i q^{47} +(-3.81614 - 4.25665i) q^{48} +(0.00812450 - 7.00000i) q^{49} +(12.7750 + 22.1269i) q^{50} +(1.77837 - 5.43343i) q^{51} +(8.21976 + 1.19227i) q^{52} -5.66165i q^{53} +(9.81904 + 4.44791i) q^{54} +(-0.487745 + 0.281599i) q^{55} +(1.17901 - 1.17764i) q^{56} +(1.60339 - 4.89882i) q^{57} +(-11.3069 - 6.52804i) q^{58} +(7.34623 + 4.24135i) q^{59} +(-15.7796 - 5.16468i) q^{60} +(-5.49299 - 3.17138i) q^{61} +(-6.49694 - 11.2530i) q^{62} +(2.88062 - 7.39608i) q^{63} -10.2165 q^{64} +(-13.9358 + 5.55895i) q^{65} +(0.151273 - 0.462184i) q^{66} +(7.78682 - 4.49572i) q^{67} +(-3.80181 - 6.58493i) q^{68} +(4.15292 - 3.72315i) q^{69} +(-5.92416 + 22.0580i) q^{70} +(-2.70902 + 4.69216i) q^{71} +(1.72945 - 0.761099i) q^{72} -7.01030 q^{73} +(-6.96550 - 4.02153i) q^{74} +(20.8755 - 4.39028i) q^{75} +(-3.42774 - 5.93702i) q^{76} +(-0.345829 - 0.0928798i) q^{77} +(5.75563 - 11.6066i) q^{78} +0.180850 q^{79} +(11.8946 - 6.86735i) q^{80} +(6.07954 - 6.63620i) q^{81} +(10.9418 + 6.31724i) q^{82} -15.7501i q^{83} +(-4.76681 - 9.41894i) q^{84} +(11.8951 + 6.86763i) q^{85} +5.15472 q^{86} +(-8.11652 + 7.27658i) q^{87} +(-0.0426223 - 0.0738240i) q^{88} +(-4.55407 + 2.62930i) q^{89} +(-15.3124 + 20.8860i) q^{90} +(-8.76232 - 3.77118i) q^{91} -7.41802i q^{92} +(-10.6166 + 2.23275i) q^{93} +(-3.99601 + 2.30710i) q^{94} +(10.7247 + 6.19191i) q^{95} +(-4.36778 + 13.3448i) q^{96} +(0.256710 - 0.444635i) q^{97} +(-12.5845 + 7.24620i) q^{98} +(-0.327454 - 0.240070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 40 q^{4} - 6 q^{9} + 18 q^{15} - 32 q^{16} + 24 q^{22} - 80 q^{25} + 12 q^{28} + 20 q^{30} + 50 q^{36} - 36 q^{37} - 60 q^{39} + 48 q^{43} - 84 q^{46} - 16 q^{49} + 52 q^{51} - 48 q^{58} - 36 q^{63} + 176 q^{64} + 60 q^{67} - 66 q^{72} + 166 q^{78} - 104 q^{79} - 30 q^{81} + 60 q^{84} + 132 q^{85} - 8 q^{91} - 162 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03726 1.79658i −0.733451 1.27038i −0.955399 0.295317i \(-0.904575\pi\)
0.221948 0.975059i \(-0.428758\pi\)
\(3\) −1.69497 + 0.356466i −0.978593 + 0.205806i
\(4\) −1.15180 + 1.99498i −0.575902 + 0.997492i
\(5\) 4.16126i 1.86097i −0.366325 0.930487i \(-0.619384\pi\)
0.366325 0.930487i \(-0.380616\pi\)
\(6\) 2.39854 + 2.67541i 0.979201 + 1.09223i
\(7\) 1.87191 1.86974i 0.707517 0.706696i
\(8\) 0.629840 0.222682
\(9\) 2.74586 1.20840i 0.915288 0.402800i
\(10\) −7.47605 + 4.31630i −2.36414 + 1.36493i
\(11\) −0.0676716 0.117211i −0.0204038 0.0353403i 0.855643 0.517566i \(-0.173162\pi\)
−0.876047 + 0.482226i \(0.839829\pi\)
\(12\) 1.24113 3.79202i 0.358284 1.09466i
\(13\) −1.33588 3.34894i −0.370507 0.928830i
\(14\) −5.30080 1.42364i −1.41670 0.380485i
\(15\) 1.48335 + 7.05323i 0.382999 + 1.82114i
\(16\) 1.65030 + 2.85841i 0.412576 + 0.714602i
\(17\) −1.65037 + 2.85853i −0.400274 + 0.693295i −0.993759 0.111550i \(-0.964418\pi\)
0.593485 + 0.804845i \(0.297752\pi\)
\(18\) −5.01916 3.67975i −1.18303 0.867325i
\(19\) −1.48799 + 2.57727i −0.341368 + 0.591266i −0.984687 0.174332i \(-0.944223\pi\)
0.643319 + 0.765598i \(0.277557\pi\)
\(20\) 8.30165 + 4.79296i 1.85631 + 1.07174i
\(21\) −2.50634 + 3.83644i −0.546929 + 0.837179i
\(22\) −0.140386 + 0.243155i −0.0299303 + 0.0518409i
\(23\) −2.78875 + 1.61009i −0.581495 + 0.335726i −0.761727 0.647898i \(-0.775648\pi\)
0.180232 + 0.983624i \(0.442315\pi\)
\(24\) −1.06756 + 0.224516i −0.217915 + 0.0458292i
\(25\) −12.3161 −2.46322
\(26\) −4.63100 + 5.87373i −0.908214 + 1.15193i
\(27\) −4.22341 + 3.02701i −0.812796 + 0.582549i
\(28\) 1.57403 + 5.88802i 0.297463 + 1.11273i
\(29\) 5.45038 3.14678i 1.01211 0.584342i 0.100301 0.994957i \(-0.468019\pi\)
0.911809 + 0.410615i \(0.134686\pi\)
\(30\) 11.1331 9.98097i 2.03261 1.82227i
\(31\) 6.26358 1.12497 0.562486 0.826807i \(-0.309845\pi\)
0.562486 + 0.826807i \(0.309845\pi\)
\(32\) 4.05342 7.02072i 0.716549 1.24110i
\(33\) 0.156483 + 0.174546i 0.0272402 + 0.0303846i
\(34\) 6.84744 1.17433
\(35\) −7.78049 7.78953i −1.31514 1.31667i
\(36\) −0.751960 + 6.86979i −0.125327 + 1.14497i
\(37\) 3.35765 1.93854i 0.551995 0.318694i −0.197931 0.980216i \(-0.563422\pi\)
0.749926 + 0.661521i \(0.230089\pi\)
\(38\) 6.17370 1.00151
\(39\) 3.45807 + 5.20017i 0.553734 + 0.832694i
\(40\) 2.62093i 0.414405i
\(41\) −5.27438 + 3.04517i −0.823720 + 0.475575i −0.851698 0.524034i \(-0.824427\pi\)
0.0279776 + 0.999609i \(0.491093\pi\)
\(42\) 9.49219 + 0.523481i 1.46468 + 0.0807748i
\(43\) −1.24239 + 2.15189i −0.189463 + 0.328160i −0.945071 0.326864i \(-0.894008\pi\)
0.755608 + 0.655024i \(0.227341\pi\)
\(44\) 0.311778 0.0470023
\(45\) −5.02847 11.4263i −0.749600 1.70333i
\(46\) 5.78531 + 3.34015i 0.852997 + 0.492478i
\(47\) 2.22423i 0.324437i −0.986755 0.162219i \(-0.948135\pi\)
0.986755 0.162219i \(-0.0518650\pi\)
\(48\) −3.81614 4.25665i −0.550813 0.614394i
\(49\) 0.00812450 7.00000i 0.00116064 0.999999i
\(50\) 12.7750 + 22.1269i 1.80666 + 3.12922i
\(51\) 1.77837 5.43343i 0.249021 0.760832i
\(52\) 8.21976 + 1.19227i 1.13988 + 0.165338i
\(53\) 5.66165i 0.777688i −0.921304 0.388844i \(-0.872875\pi\)
0.921304 0.388844i \(-0.127125\pi\)
\(54\) 9.81904 + 4.44791i 1.33620 + 0.605284i
\(55\) −0.487745 + 0.281599i −0.0657675 + 0.0379709i
\(56\) 1.17901 1.17764i 0.157551 0.157369i
\(57\) 1.60339 4.89882i 0.212374 0.648864i
\(58\) −11.3069 6.52804i −1.48467 0.857173i
\(59\) 7.34623 + 4.24135i 0.956398 + 0.552177i 0.895063 0.445941i \(-0.147131\pi\)
0.0613354 + 0.998117i \(0.480464\pi\)
\(60\) −15.7796 5.16468i −2.03714 0.666758i
\(61\) −5.49299 3.17138i −0.703305 0.406053i 0.105272 0.994443i \(-0.466429\pi\)
−0.808577 + 0.588390i \(0.799762\pi\)
\(62\) −6.49694 11.2530i −0.825112 1.42914i
\(63\) 2.88062 7.39608i 0.362925 0.931819i
\(64\) −10.2165 −1.27707
\(65\) −13.9358 + 5.55895i −1.72853 + 0.689503i
\(66\) 0.151273 0.462184i 0.0186205 0.0568909i
\(67\) 7.78682 4.49572i 0.951311 0.549240i 0.0578232 0.998327i \(-0.481584\pi\)
0.893488 + 0.449087i \(0.148251\pi\)
\(68\) −3.80181 6.58493i −0.461037 0.798540i
\(69\) 4.15292 3.72315i 0.499953 0.448215i
\(70\) −5.92416 + 22.0580i −0.708072 + 2.63644i
\(71\) −2.70902 + 4.69216i −0.321501 + 0.556857i −0.980798 0.195026i \(-0.937521\pi\)
0.659297 + 0.751883i \(0.270854\pi\)
\(72\) 1.72945 0.761099i 0.203818 0.0896963i
\(73\) −7.01030 −0.820493 −0.410247 0.911975i \(-0.634557\pi\)
−0.410247 + 0.911975i \(0.634557\pi\)
\(74\) −6.96550 4.02153i −0.809723 0.467494i
\(75\) 20.8755 4.39028i 2.41049 0.506946i
\(76\) −3.42774 5.93702i −0.393189 0.681023i
\(77\) −0.345829 0.0928798i −0.0394109 0.0105846i
\(78\) 5.75563 11.6066i 0.651697 1.31419i
\(79\) 0.180850 0.0203472 0.0101736 0.999948i \(-0.496762\pi\)
0.0101736 + 0.999948i \(0.496762\pi\)
\(80\) 11.8946 6.86735i 1.32986 0.767793i
\(81\) 6.07954 6.63620i 0.675504 0.737356i
\(82\) 10.9418 + 6.31724i 1.20832 + 0.697622i
\(83\) 15.7501i 1.72879i −0.502810 0.864397i \(-0.667701\pi\)
0.502810 0.864397i \(-0.332299\pi\)
\(84\) −4.76681 9.41894i −0.520102 1.02769i
\(85\) 11.8951 + 6.86763i 1.29020 + 0.744900i
\(86\) 5.15472 0.555848
\(87\) −8.11652 + 7.27658i −0.870183 + 0.780131i
\(88\) −0.0426223 0.0738240i −0.00454355 0.00786966i
\(89\) −4.55407 + 2.62930i −0.482731 + 0.278705i −0.721554 0.692358i \(-0.756572\pi\)
0.238823 + 0.971063i \(0.423238\pi\)
\(90\) −15.3124 + 20.8860i −1.61407 + 2.20158i
\(91\) −8.76232 3.77118i −0.918540 0.395327i
\(92\) 7.41802i 0.773382i
\(93\) −10.6166 + 2.23275i −1.10089 + 0.231526i
\(94\) −3.99601 + 2.30710i −0.412157 + 0.237959i
\(95\) 10.7247 + 6.19191i 1.10033 + 0.635276i
\(96\) −4.36778 + 13.3448i −0.445785 + 1.36200i
\(97\) 0.256710 0.444635i 0.0260650 0.0451459i −0.852699 0.522403i \(-0.825036\pi\)
0.878764 + 0.477257i \(0.158369\pi\)
\(98\) −12.5845 + 7.24620i −1.27123 + 0.731977i
\(99\) −0.327454 0.240070i −0.0329104 0.0241280i
\(100\) 14.1858 24.5705i 1.41858 2.45705i
\(101\) 4.78076 + 8.28052i 0.475704 + 0.823943i 0.999613 0.0278314i \(-0.00886015\pi\)
−0.523909 + 0.851774i \(0.675527\pi\)
\(102\) −11.6062 + 2.44088i −1.14919 + 0.241683i
\(103\) 1.29232i 0.127336i 0.997971 + 0.0636680i \(0.0202799\pi\)
−0.997971 + 0.0636680i \(0.979720\pi\)
\(104\) −0.841391 2.10930i −0.0825052 0.206834i
\(105\) 15.9644 + 10.4296i 1.55797 + 1.01782i
\(106\) −10.1716 + 5.87259i −0.987955 + 0.570396i
\(107\) 3.75536 2.16816i 0.363044 0.209604i −0.307371 0.951590i \(-0.599449\pi\)
0.670415 + 0.741986i \(0.266116\pi\)
\(108\) −1.17430 11.9122i −0.112997 1.14625i
\(109\) 16.0503i 1.53734i −0.639643 0.768672i \(-0.720918\pi\)
0.639643 0.768672i \(-0.279082\pi\)
\(110\) 1.01183 + 0.584182i 0.0964745 + 0.0556996i
\(111\) −5.00011 + 4.48267i −0.474589 + 0.425476i
\(112\) 8.43371 + 2.26505i 0.796911 + 0.214027i
\(113\) 4.13455 + 2.38709i 0.388946 + 0.224558i 0.681703 0.731629i \(-0.261239\pi\)
−0.292757 + 0.956187i \(0.594573\pi\)
\(114\) −10.4643 + 2.20071i −0.980067 + 0.206116i
\(115\) 6.70000 + 11.6047i 0.624778 + 1.08215i
\(116\) 14.4979i 1.34610i
\(117\) −7.71501 7.58147i −0.713253 0.700907i
\(118\) 17.5975i 1.61998i
\(119\) 2.25536 + 8.43669i 0.206748 + 0.773390i
\(120\) 0.934272 + 4.44241i 0.0852870 + 0.405534i
\(121\) 5.49084 9.51042i 0.499167 0.864583i
\(122\) 13.1581i 1.19128i
\(123\) 7.85443 7.04161i 0.708210 0.634921i
\(124\) −7.21442 + 12.4957i −0.647874 + 1.12215i
\(125\) 30.4443i 2.72302i
\(126\) −16.2756 + 2.49636i −1.44995 + 0.222393i
\(127\) 6.09882 + 10.5635i 0.541183 + 0.937356i 0.998836 + 0.0482255i \(0.0153566\pi\)
−0.457654 + 0.889131i \(0.651310\pi\)
\(128\) 2.49033 + 4.31338i 0.220116 + 0.381253i
\(129\) 1.33875 4.09026i 0.117870 0.360127i
\(130\) 24.4422 + 19.2708i 2.14372 + 1.69016i
\(131\) −8.67577 −0.758005 −0.379003 0.925396i \(-0.623733\pi\)
−0.379003 + 0.925396i \(0.623733\pi\)
\(132\) −0.528455 + 0.111138i −0.0459961 + 0.00967334i
\(133\) 2.03345 + 7.60658i 0.176322 + 0.659574i
\(134\) −16.1539 9.32644i −1.39548 0.805681i
\(135\) 12.5962 + 17.5747i 1.08411 + 1.51259i
\(136\) −1.03947 + 1.80042i −0.0891338 + 0.154384i
\(137\) −1.04880 + 1.81657i −0.0896047 + 0.155200i −0.907344 0.420389i \(-0.861894\pi\)
0.817739 + 0.575589i \(0.195227\pi\)
\(138\) −10.9966 3.59920i −0.936092 0.306384i
\(139\) 13.7074 + 7.91397i 1.16265 + 0.671254i 0.951937 0.306294i \(-0.0990891\pi\)
0.210710 + 0.977549i \(0.432422\pi\)
\(140\) 24.5016 6.54994i 2.07076 0.553571i
\(141\) 0.792863 + 3.77001i 0.0667711 + 0.317492i
\(142\) 11.2398 0.943223
\(143\) −0.302131 + 0.383208i −0.0252654 + 0.0320455i
\(144\) 7.98561 + 5.85457i 0.665467 + 0.487881i
\(145\) −13.0946 22.6805i −1.08745 1.88351i
\(146\) 7.27148 + 12.5946i 0.601792 + 1.04233i
\(147\) 2.48149 + 11.8677i 0.204670 + 0.978831i
\(148\) 8.93129i 0.734147i
\(149\) −4.25366 + 7.36755i −0.348473 + 0.603573i −0.985978 0.166873i \(-0.946633\pi\)
0.637505 + 0.770446i \(0.279966\pi\)
\(150\) −29.5407 32.9507i −2.41199 2.69041i
\(151\) 18.7737i 1.52778i −0.645346 0.763891i \(-0.723287\pi\)
0.645346 0.763891i \(-0.276713\pi\)
\(152\) −0.937194 + 1.62327i −0.0760164 + 0.131664i
\(153\) −1.07745 + 9.84344i −0.0871068 + 0.795795i
\(154\) 0.191848 + 0.717651i 0.0154595 + 0.0578299i
\(155\) 26.0644i 2.09354i
\(156\) −14.3573 + 0.909204i −1.14950 + 0.0727946i
\(157\) 14.3222i 1.14304i −0.820590 0.571518i \(-0.806355\pi\)
0.820590 0.571518i \(-0.193645\pi\)
\(158\) −0.187588 0.324912i −0.0149237 0.0258486i
\(159\) 2.01819 + 9.59634i 0.160053 + 0.761039i
\(160\) −29.2151 16.8673i −2.30965 1.33348i
\(161\) −2.20986 + 8.22820i −0.174161 + 0.648473i
\(162\) −18.2285 4.03894i −1.43217 0.317329i
\(163\) −17.3437 10.0134i −1.35846 0.784309i −0.369047 0.929411i \(-0.620316\pi\)
−0.989417 + 0.145101i \(0.953649\pi\)
\(164\) 14.0297i 1.09554i
\(165\) 0.726333 0.651168i 0.0565450 0.0506933i
\(166\) −28.2963 + 16.3369i −2.19622 + 1.26799i
\(167\) 10.4689 6.04420i 0.810105 0.467714i −0.0368875 0.999319i \(-0.511744\pi\)
0.846992 + 0.531605i \(0.178411\pi\)
\(168\) −1.57860 + 2.41634i −0.121791 + 0.186425i
\(169\) −9.43084 + 8.94758i −0.725450 + 0.688275i
\(170\) 28.4940i 2.18539i
\(171\) −0.971438 + 8.87491i −0.0742877 + 0.678682i
\(172\) −2.86198 4.95710i −0.218224 0.377976i
\(173\) 4.43933 7.68914i 0.337516 0.584594i −0.646449 0.762957i \(-0.723747\pi\)
0.983965 + 0.178363i \(0.0570800\pi\)
\(174\) 21.4919 + 7.03432i 1.62930 + 0.533270i
\(175\) −23.0547 + 23.0280i −1.74277 + 1.74075i
\(176\) 0.223357 0.386866i 0.0168362 0.0291611i
\(177\) −13.9636 4.57029i −1.04957 0.343524i
\(178\) 9.44749 + 5.45451i 0.708119 + 0.408833i
\(179\) 0.390517 0.225465i 0.0291886 0.0168521i −0.485335 0.874328i \(-0.661302\pi\)
0.514523 + 0.857476i \(0.327969\pi\)
\(180\) 28.5870 + 3.12910i 2.13075 + 0.233230i
\(181\) 6.19316i 0.460334i −0.973151 0.230167i \(-0.926073\pi\)
0.973151 0.230167i \(-0.0739272\pi\)
\(182\) 2.31354 + 19.6539i 0.171491 + 1.45684i
\(183\) 10.4409 + 3.41733i 0.771817 + 0.252617i
\(184\) −1.75647 + 1.01410i −0.129489 + 0.0747602i
\(185\) −8.06679 13.9721i −0.593082 1.02725i
\(186\) 15.0235 + 16.7576i 1.10157 + 1.22873i
\(187\) 0.446733 0.0326684
\(188\) 4.43730 + 2.56188i 0.323624 + 0.186844i
\(189\) −2.24613 + 13.5630i −0.163382 + 0.986563i
\(190\) 25.6904i 1.86378i
\(191\) −14.5435 8.39669i −1.05233 0.607563i −0.129030 0.991641i \(-0.541186\pi\)
−0.923301 + 0.384077i \(0.874520\pi\)
\(192\) 17.3167 3.64184i 1.24973 0.262827i
\(193\) −9.09642 + 5.25182i −0.654774 + 0.378034i −0.790283 0.612742i \(-0.790066\pi\)
0.135509 + 0.990776i \(0.456733\pi\)
\(194\) −1.06510 −0.0764696
\(195\) 21.6393 14.3899i 1.54962 1.03048i
\(196\) 13.9555 + 8.07883i 0.996823 + 0.577059i
\(197\) −5.13352 8.89152i −0.365748 0.633494i 0.623148 0.782104i \(-0.285853\pi\)
−0.988896 + 0.148610i \(0.952520\pi\)
\(198\) −0.0916514 + 0.837313i −0.00651338 + 0.0595053i
\(199\) −3.64345 2.10355i −0.258278 0.149117i 0.365271 0.930901i \(-0.380976\pi\)
−0.623549 + 0.781785i \(0.714310\pi\)
\(200\) −7.75718 −0.548516
\(201\) −11.5959 + 10.3959i −0.817910 + 0.733267i
\(202\) 9.91776 17.1781i 0.697811 1.20864i
\(203\) 4.31898 16.0813i 0.303133 1.12869i
\(204\) 8.79127 + 9.80606i 0.615512 + 0.686561i
\(205\) 12.6717 + 21.9481i 0.885033 + 1.53292i
\(206\) 2.32176 1.34047i 0.161764 0.0933947i
\(207\) −5.71191 + 7.79101i −0.397005 + 0.541513i
\(208\) 7.36804 9.34526i 0.510882 0.647977i
\(209\) 0.402778 0.0278607
\(210\) 2.17834 39.4995i 0.150320 2.72573i
\(211\) −1.40807 2.43885i −0.0969358 0.167898i 0.813479 0.581594i \(-0.197571\pi\)
−0.910415 + 0.413696i \(0.864237\pi\)
\(212\) 11.2949 + 6.52111i 0.775737 + 0.447872i
\(213\) 2.91912 8.91876i 0.200015 0.611103i
\(214\) −7.79054 4.49787i −0.532551 0.307468i
\(215\) 8.95457 + 5.16992i 0.610696 + 0.352586i
\(216\) −2.66007 + 1.90653i −0.180995 + 0.129723i
\(217\) 11.7249 11.7113i 0.795937 0.795013i
\(218\) −28.8358 + 16.6483i −1.95300 + 1.12757i
\(219\) 11.8823 2.49893i 0.802929 0.168862i
\(220\) 1.29739i 0.0874700i
\(221\) 11.7777 + 1.70835i 0.792257 + 0.114916i
\(222\) 13.2399 + 4.33343i 0.888602 + 0.290841i
\(223\) 9.80561 + 16.9838i 0.656632 + 1.13732i 0.981482 + 0.191555i \(0.0613529\pi\)
−0.324850 + 0.945766i \(0.605314\pi\)
\(224\) −5.53930 20.7210i −0.370110 1.38448i
\(225\) −33.8184 + 14.8828i −2.25456 + 0.992187i
\(226\) 9.90408i 0.658810i
\(227\) −1.07376 0.619937i −0.0712681 0.0411467i 0.463942 0.885865i \(-0.346434\pi\)
−0.535211 + 0.844719i \(0.679768\pi\)
\(228\) 7.92627 + 8.84121i 0.524930 + 0.585524i
\(229\) 13.7271 0.907112 0.453556 0.891228i \(-0.350155\pi\)
0.453556 + 0.891228i \(0.350155\pi\)
\(230\) 13.8992 24.0742i 0.916489 1.58741i
\(231\) 0.619280 + 0.0341524i 0.0407456 + 0.00224706i
\(232\) 3.43287 1.98197i 0.225379 0.130122i
\(233\) 16.2961i 1.06759i 0.845614 + 0.533795i \(0.179235\pi\)
−0.845614 + 0.533795i \(0.820765\pi\)
\(234\) −5.61827 + 21.7246i −0.367278 + 1.42018i
\(235\) −9.25561 −0.603770
\(236\) −16.9228 + 9.77041i −1.10158 + 0.635999i
\(237\) −0.306536 + 0.0644669i −0.0199116 + 0.00418757i
\(238\) 12.8178 12.8030i 0.830856 0.829892i
\(239\) 0.406354 0.0262848 0.0131424 0.999914i \(-0.495817\pi\)
0.0131424 + 0.999914i \(0.495817\pi\)
\(240\) −17.7130 + 15.8800i −1.14337 + 1.02505i
\(241\) −4.63850 + 8.03412i −0.298792 + 0.517523i −0.975860 0.218398i \(-0.929917\pi\)
0.677068 + 0.735921i \(0.263250\pi\)
\(242\) −22.7817 −1.46446
\(243\) −7.93907 + 13.4153i −0.509292 + 0.860594i
\(244\) 12.6537 7.30561i 0.810069 0.467694i
\(245\) −29.1288 0.0338082i −1.86097 0.00215993i
\(246\) −20.7979 6.80717i −1.32603 0.434010i
\(247\) 10.6189 + 1.54026i 0.675665 + 0.0980044i
\(248\) 3.94505 0.250511
\(249\) 5.61436 + 26.6959i 0.355796 + 1.69179i
\(250\) 54.6957 31.5786i 3.45926 1.99720i
\(251\) −3.97968 + 6.89301i −0.251195 + 0.435083i −0.963855 0.266427i \(-0.914157\pi\)
0.712660 + 0.701510i \(0.247490\pi\)
\(252\) 11.4371 + 14.2656i 0.720472 + 0.898650i
\(253\) 0.377439 + 0.217914i 0.0237294 + 0.0137002i
\(254\) 12.6521 21.9141i 0.793863 1.37501i
\(255\) −22.6099 7.40026i −1.41589 0.463422i
\(256\) −5.05030 + 8.74737i −0.315644 + 0.546711i
\(257\) −9.17088 15.8844i −0.572064 0.990843i −0.996354 0.0853171i \(-0.972810\pi\)
0.424290 0.905526i \(-0.360524\pi\)
\(258\) −8.73711 + 1.83748i −0.543949 + 0.114397i
\(259\) 2.66066 9.90674i 0.165326 0.615575i
\(260\) 4.96134 34.2046i 0.307689 2.12128i
\(261\) 11.1634 15.2269i 0.690999 0.942519i
\(262\) 8.99900 + 15.5867i 0.555960 + 0.962951i
\(263\) 4.58741 2.64854i 0.282872 0.163316i −0.351851 0.936056i \(-0.614448\pi\)
0.634723 + 0.772740i \(0.281114\pi\)
\(264\) 0.0985593 + 0.109936i 0.00606591 + 0.00676611i
\(265\) −23.5596 −1.44726
\(266\) 11.5566 11.5432i 0.708583 0.707761i
\(267\) 6.78178 6.07996i 0.415038 0.372087i
\(268\) 20.7128i 1.26523i
\(269\) 4.55345 7.88680i 0.277628 0.480867i −0.693166 0.720778i \(-0.743785\pi\)
0.970795 + 0.239911i \(0.0771182\pi\)
\(270\) 18.5089 40.8596i 1.12642 2.48664i
\(271\) 0.696430 + 1.20625i 0.0423051 + 0.0732746i 0.886403 0.462915i \(-0.153197\pi\)
−0.844098 + 0.536190i \(0.819863\pi\)
\(272\) −10.8945 −0.660573
\(273\) 16.1962 + 3.26858i 0.980238 + 0.197824i
\(274\) 4.35149 0.262883
\(275\) 0.833452 + 1.44358i 0.0502590 + 0.0870512i
\(276\) 2.64427 + 12.5733i 0.159166 + 0.756826i
\(277\) 2.97135 5.14652i 0.178531 0.309225i −0.762847 0.646579i \(-0.776199\pi\)
0.941378 + 0.337355i \(0.109532\pi\)
\(278\) 32.8353i 1.96933i
\(279\) 17.1989 7.56891i 1.02967 0.453139i
\(280\) −4.90047 4.90616i −0.292859 0.293199i
\(281\) 26.9448 1.60739 0.803695 0.595042i \(-0.202865\pi\)
0.803695 + 0.595042i \(0.202865\pi\)
\(282\) 5.95073 5.33491i 0.354361 0.317689i
\(283\) −4.36194 + 2.51837i −0.259290 + 0.149701i −0.624011 0.781416i \(-0.714498\pi\)
0.364721 + 0.931117i \(0.381165\pi\)
\(284\) −6.24052 10.8089i −0.370307 0.641390i
\(285\) −20.3853 6.67212i −1.20752 0.395222i
\(286\) 1.00185 + 0.145317i 0.0592407 + 0.00859280i
\(287\) −4.17951 + 15.5620i −0.246709 + 0.918597i
\(288\) 2.64629 24.1761i 0.155934 1.42459i
\(289\) 3.05254 + 5.28716i 0.179561 + 0.311010i
\(290\) −27.1649 + 47.0510i −1.59518 + 2.76293i
\(291\) −0.276620 + 0.845153i −0.0162157 + 0.0495438i
\(292\) 8.07449 13.9854i 0.472524 0.818435i
\(293\) 16.0047 + 9.24029i 0.935002 + 0.539824i 0.888390 0.459089i \(-0.151824\pi\)
0.0466121 + 0.998913i \(0.485158\pi\)
\(294\) 18.7473 16.7680i 1.09337 0.977932i
\(295\) 17.6494 30.5696i 1.02759 1.77983i
\(296\) 2.11478 1.22097i 0.122919 0.0709675i
\(297\) 0.640603 + 0.290186i 0.0371716 + 0.0168383i
\(298\) 17.6485 1.02235
\(299\) 9.11753 + 7.18849i 0.527281 + 0.415721i
\(300\) −15.2859 + 46.7030i −0.882534 + 2.69640i
\(301\) 1.69782 + 6.35110i 0.0978608 + 0.366071i
\(302\) −33.7285 + 19.4731i −1.94086 + 1.12055i
\(303\) −11.0550 12.3311i −0.635092 0.708402i
\(304\) −9.82251 −0.563360
\(305\) −13.1969 + 22.8578i −0.755654 + 1.30883i
\(306\) 18.8021 8.27445i 1.07485 0.473019i
\(307\) −14.4260 −0.823334 −0.411667 0.911334i \(-0.635053\pi\)
−0.411667 + 0.911334i \(0.635053\pi\)
\(308\) 0.583621 0.582944i 0.0332549 0.0332163i
\(309\) −0.460668 2.19044i −0.0262065 0.124610i
\(310\) −46.8268 + 27.0355i −2.65959 + 1.53551i
\(311\) 21.1949 1.20185 0.600927 0.799304i \(-0.294798\pi\)
0.600927 + 0.799304i \(0.294798\pi\)
\(312\) 2.17803 + 3.27528i 0.123307 + 0.185426i
\(313\) 3.03904i 0.171777i 0.996305 + 0.0858883i \(0.0273728\pi\)
−0.996305 + 0.0858883i \(0.972627\pi\)
\(314\) −25.7310 + 14.8558i −1.45208 + 0.838361i
\(315\) −30.7770 11.9870i −1.73409 0.675393i
\(316\) −0.208304 + 0.360793i −0.0117180 + 0.0202962i
\(317\) 30.0895 1.68999 0.844996 0.534772i \(-0.179603\pi\)
0.844996 + 0.534772i \(0.179603\pi\)
\(318\) 15.1472 13.5797i 0.849415 0.761512i
\(319\) −0.737672 0.425895i −0.0413017 0.0238455i
\(320\) 42.5137i 2.37659i
\(321\) −5.59236 + 5.01362i −0.312135 + 0.279833i
\(322\) 17.0748 4.56457i 0.951542 0.254373i
\(323\) −4.91146 8.50691i −0.273281 0.473337i
\(324\) 6.23668 + 19.7722i 0.346482 + 1.09845i
\(325\) 16.4529 + 41.2460i 0.912641 + 2.28792i
\(326\) 41.5458i 2.30101i
\(327\) 5.72140 + 27.2049i 0.316394 + 1.50443i
\(328\) −3.32202 + 1.91797i −0.183428 + 0.105902i
\(329\) −4.15874 4.16357i −0.229279 0.229545i
\(330\) −1.92327 0.629489i −0.105873 0.0346522i
\(331\) 21.4884 + 12.4063i 1.18111 + 0.681913i 0.956270 0.292484i \(-0.0944818\pi\)
0.224837 + 0.974396i \(0.427815\pi\)
\(332\) 31.4211 + 18.1410i 1.72446 + 0.995616i
\(333\) 6.87713 9.38036i 0.376864 0.514041i
\(334\) −21.7178 12.5388i −1.18834 0.686091i
\(335\) −18.7079 32.4030i −1.02212 1.77037i
\(336\) −15.1023 0.832871i −0.823899 0.0454369i
\(337\) 11.4714 0.624886 0.312443 0.949937i \(-0.398853\pi\)
0.312443 + 0.949937i \(0.398853\pi\)
\(338\) 25.8573 + 7.66235i 1.40645 + 0.416777i
\(339\) −7.85887 2.57222i −0.426835 0.139704i
\(340\) −27.4016 + 15.8203i −1.48606 + 0.857978i
\(341\) −0.423866 0.734158i −0.0229537 0.0397569i
\(342\) 16.9521 7.46030i 0.916667 0.403407i
\(343\) −13.0730 13.1186i −0.705875 0.708337i
\(344\) −0.782508 + 1.35534i −0.0421900 + 0.0730752i
\(345\) −15.4930 17.2814i −0.834116 0.930399i
\(346\) −18.4189 −0.990206
\(347\) 3.14913 + 1.81815i 0.169054 + 0.0976034i 0.582140 0.813089i \(-0.302216\pi\)
−0.413086 + 0.910692i \(0.635549\pi\)
\(348\) −5.16800 24.5735i −0.277034 1.31728i
\(349\) −15.8325 27.4226i −0.847492 1.46790i −0.883439 0.468546i \(-0.844778\pi\)
0.0359467 0.999354i \(-0.488555\pi\)
\(350\) 65.2853 + 17.5338i 3.48965 + 0.937219i
\(351\) 15.7793 + 10.1002i 0.842235 + 0.539111i
\(352\) −1.09720 −0.0584812
\(353\) 17.5574 10.1368i 0.934487 0.539526i 0.0462589 0.998929i \(-0.485270\pi\)
0.888228 + 0.459403i \(0.151937\pi\)
\(354\) 6.27290 + 29.8272i 0.333401 + 1.58530i
\(355\) 19.5253 + 11.2729i 1.03630 + 0.598306i
\(356\) 12.1137i 0.642027i
\(357\) −6.83016 13.4960i −0.361491 0.714284i
\(358\) −0.810134 0.467731i −0.0428169 0.0247203i
\(359\) −3.41596 −0.180288 −0.0901439 0.995929i \(-0.528733\pi\)
−0.0901439 + 0.995929i \(0.528733\pi\)
\(360\) −3.16713 7.19672i −0.166923 0.379300i
\(361\) 5.07179 + 8.78460i 0.266936 + 0.462347i
\(362\) −11.1265 + 6.42390i −0.584797 + 0.337633i
\(363\) −5.91669 + 18.0772i −0.310545 + 0.948807i
\(364\) 17.6159 13.1370i 0.923325 0.688567i
\(365\) 29.1717i 1.52692i
\(366\) −4.69043 22.3027i −0.245172 1.16578i
\(367\) 2.16586 1.25046i 0.113057 0.0652735i −0.442405 0.896815i \(-0.645875\pi\)
0.555462 + 0.831542i \(0.312541\pi\)
\(368\) −9.20457 5.31426i −0.479822 0.277025i
\(369\) −10.8030 + 14.7352i −0.562379 + 0.767082i
\(370\) −16.7347 + 28.9853i −0.869994 + 1.50687i
\(371\) −10.5858 10.5981i −0.549589 0.550227i
\(372\) 7.77393 23.7516i 0.403060 1.23146i
\(373\) −16.1192 + 27.9193i −0.834620 + 1.44560i 0.0597194 + 0.998215i \(0.480979\pi\)
−0.894339 + 0.447389i \(0.852354\pi\)
\(374\) −0.463377 0.802593i −0.0239607 0.0415011i
\(375\) −10.8524 51.6023i −0.560414 2.66473i
\(376\) 1.40091i 0.0722464i
\(377\) −17.8194 14.0493i −0.917748 0.723575i
\(378\) 26.6968 10.0330i 1.37314 0.516040i
\(379\) −7.82909 + 4.52013i −0.402153 + 0.232183i −0.687413 0.726267i \(-0.741254\pi\)
0.285259 + 0.958450i \(0.407920\pi\)
\(380\) −24.7055 + 14.2637i −1.26737 + 0.731714i
\(381\) −14.1028 15.7308i −0.722511 0.805911i
\(382\) 34.8381i 1.78247i
\(383\) 28.0369 + 16.1871i 1.43262 + 0.827122i 0.997320 0.0731642i \(-0.0233097\pi\)
0.435298 + 0.900286i \(0.356643\pi\)
\(384\) −5.75862 6.42334i −0.293868 0.327790i
\(385\) −0.386497 + 1.43909i −0.0196977 + 0.0733427i
\(386\) 18.8706 + 10.8950i 0.960490 + 0.554539i
\(387\) −0.811100 + 7.41009i −0.0412305 + 0.376676i
\(388\) 0.591360 + 1.02427i 0.0300218 + 0.0519992i
\(389\) 27.2103i 1.37962i −0.723992 0.689809i \(-0.757695\pi\)
0.723992 0.689809i \(-0.242305\pi\)
\(390\) −48.2982 23.9507i −2.44567 1.21279i
\(391\) 10.6290i 0.537530i
\(392\) 0.00511714 4.40888i 0.000258454 0.222682i
\(393\) 14.7052 3.09262i 0.741779 0.156002i
\(394\) −10.6496 + 18.4456i −0.536517 + 0.929275i
\(395\) 0.752565i 0.0378656i
\(396\) 0.856099 0.376752i 0.0430206 0.0189325i
\(397\) −9.44286 + 16.3555i −0.473923 + 0.820859i −0.999554 0.0298533i \(-0.990496\pi\)
0.525631 + 0.850713i \(0.323829\pi\)
\(398\) 8.72768i 0.437479i
\(399\) −6.15812 12.1681i −0.308292 0.609166i
\(400\) −20.3253 35.2045i −1.01627 1.76022i
\(401\) −10.1429 17.5681i −0.506513 0.877307i −0.999972 0.00753736i \(-0.997601\pi\)
0.493458 0.869769i \(-0.335733\pi\)
\(402\) 30.7049 + 10.0498i 1.53142 + 0.501236i
\(403\) −8.36739 20.9764i −0.416810 1.04491i
\(404\) −22.0260 −1.09583
\(405\) −27.6150 25.2986i −1.37220 1.25710i
\(406\) −33.3713 + 8.92105i −1.65619 + 0.442744i
\(407\) −0.454436 0.262369i −0.0225255 0.0130051i
\(408\) 1.12009 3.42219i 0.0554526 0.169424i
\(409\) 17.3827 30.1077i 0.859519 1.48873i −0.0128703 0.999917i \(-0.504097\pi\)
0.872389 0.488813i \(-0.162570\pi\)
\(410\) 26.2877 45.5316i 1.29826 2.24865i
\(411\) 1.13014 3.45289i 0.0557455 0.170319i
\(412\) −2.57815 1.48850i −0.127017 0.0733330i
\(413\) 21.6817 5.79612i 1.06689 0.285209i
\(414\) 19.9219 + 2.18063i 0.979108 + 0.107172i
\(415\) −65.5402 −3.21724
\(416\) −28.9269 4.19581i −1.41826 0.205717i
\(417\) −26.0547 8.52774i −1.27591 0.417605i
\(418\) −0.417784 0.723623i −0.0204345 0.0353936i
\(419\) 9.83196 + 17.0295i 0.480323 + 0.831943i 0.999745 0.0225741i \(-0.00718618\pi\)
−0.519422 + 0.854518i \(0.673853\pi\)
\(420\) −39.1947 + 19.8360i −1.91250 + 0.967896i
\(421\) 4.45948i 0.217342i 0.994078 + 0.108671i \(0.0346595\pi\)
−0.994078 + 0.108671i \(0.965341\pi\)
\(422\) −2.92107 + 5.05944i −0.142195 + 0.246290i
\(423\) −2.68776 6.10744i −0.130683 0.296954i
\(424\) 3.56593i 0.173177i
\(425\) 20.3262 35.2060i 0.985965 1.70774i
\(426\) −19.0512 + 4.00661i −0.923031 + 0.194121i
\(427\) −16.2121 + 4.33392i −0.784556 + 0.209733i
\(428\) 9.98917i 0.482845i
\(429\) 0.375503 0.757226i 0.0181294 0.0365592i
\(430\) 21.4501i 1.03442i
\(431\) 9.16416 + 15.8728i 0.441422 + 0.764565i 0.997795 0.0663673i \(-0.0211409\pi\)
−0.556373 + 0.830932i \(0.687808\pi\)
\(432\) −15.6223 7.07675i −0.751630 0.340480i
\(433\) 16.7224 + 9.65465i 0.803625 + 0.463973i 0.844737 0.535181i \(-0.179757\pi\)
−0.0411122 + 0.999155i \(0.513090\pi\)
\(434\) −33.2020 8.91710i −1.59375 0.428034i
\(435\) 30.2798 + 33.7750i 1.45180 + 1.61939i
\(436\) 32.0202 + 18.4869i 1.53349 + 0.885360i
\(437\) 9.58316i 0.458425i
\(438\) −16.8145 18.7554i −0.803428 0.896169i
\(439\) −15.4742 + 8.93402i −0.738542 + 0.426397i −0.821539 0.570152i \(-0.806884\pi\)
0.0829970 + 0.996550i \(0.473551\pi\)
\(440\) −0.307201 + 0.177363i −0.0146452 + 0.00845543i
\(441\) −8.43649 19.2309i −0.401737 0.915755i
\(442\) −9.14736 22.9317i −0.435096 1.09075i
\(443\) 40.7368i 1.93546i 0.251985 + 0.967731i \(0.418917\pi\)
−0.251985 + 0.967731i \(0.581083\pi\)
\(444\) −3.18370 15.1383i −0.151092 0.718431i
\(445\) 10.9412 + 18.9507i 0.518662 + 0.898349i
\(446\) 20.3419 35.2332i 0.963216 1.66834i
\(447\) 4.58355 14.0041i 0.216795 0.662370i
\(448\) −19.1245 + 19.1023i −0.903546 + 0.902498i
\(449\) 7.33357 12.7021i 0.346093 0.599450i −0.639459 0.768825i \(-0.720842\pi\)
0.985552 + 0.169375i \(0.0541749\pi\)
\(450\) 61.8165 + 45.3202i 2.91406 + 2.13642i
\(451\) 0.713852 + 0.412143i 0.0336140 + 0.0194070i
\(452\) −9.52439 + 5.49891i −0.447990 + 0.258647i
\(453\) 6.69218 + 31.8209i 0.314426 + 1.49508i
\(454\) 2.57214i 0.120716i
\(455\) −15.6929 + 36.4623i −0.735694 + 1.70938i
\(456\) 1.00988 3.08547i 0.0472919 0.144490i
\(457\) 16.4569 9.50141i 0.769822 0.444457i −0.0629889 0.998014i \(-0.520063\pi\)
0.832811 + 0.553557i \(0.186730\pi\)
\(458\) −14.2385 24.6618i −0.665322 1.15237i
\(459\) −1.68260 17.0684i −0.0785370 0.796686i
\(460\) −30.8684 −1.43924
\(461\) 25.4386 + 14.6870i 1.18479 + 0.684040i 0.957118 0.289697i \(-0.0935546\pi\)
0.227674 + 0.973737i \(0.426888\pi\)
\(462\) −0.580995 1.14801i −0.0270303 0.0534103i
\(463\) 32.7022i 1.51980i 0.650040 + 0.759900i \(0.274752\pi\)
−0.650040 + 0.759900i \(0.725248\pi\)
\(464\) 17.9896 + 10.3863i 0.835144 + 0.482171i
\(465\) 9.29107 + 44.1785i 0.430863 + 2.04873i
\(466\) 29.2772 16.9032i 1.35624 0.783025i
\(467\) −20.1268 −0.931355 −0.465678 0.884954i \(-0.654189\pi\)
−0.465678 + 0.884954i \(0.654189\pi\)
\(468\) 24.0111 6.65895i 1.10991 0.307810i
\(469\) 6.17041 22.9750i 0.284923 1.06088i
\(470\) 9.60045 + 16.6285i 0.442836 + 0.767014i
\(471\) 5.10538 + 24.2757i 0.235243 + 1.11857i
\(472\) 4.62695 + 2.67137i 0.212973 + 0.122960i
\(473\) 0.336299 0.0154630
\(474\) 0.433776 + 0.483848i 0.0199240 + 0.0222239i
\(475\) 18.3262 31.7420i 0.840865 1.45642i
\(476\) −19.4288 5.21801i −0.890517 0.239167i
\(477\) −6.84154 15.5461i −0.313253 0.711808i
\(478\) −0.421493 0.730048i −0.0192787 0.0333916i
\(479\) −14.5400 + 8.39467i −0.664350 + 0.383562i −0.793932 0.608006i \(-0.791970\pi\)
0.129583 + 0.991569i \(0.458636\pi\)
\(480\) 55.5314 + 18.1755i 2.53465 + 0.829594i
\(481\) −10.9775 8.65493i −0.500531 0.394631i
\(482\) 19.2453 0.876598
\(483\) 0.812576 14.7343i 0.0369735 0.670434i
\(484\) 12.6487 + 21.9083i 0.574943 + 0.995831i
\(485\) −1.85025 1.06824i −0.0840153 0.0485063i
\(486\) 32.3366 + 0.348042i 1.46682 + 0.0157875i
\(487\) 4.85942 + 2.80559i 0.220201 + 0.127133i 0.606043 0.795432i \(-0.292756\pi\)
−0.385842 + 0.922565i \(0.626089\pi\)
\(488\) −3.45970 1.99746i −0.156613 0.0904207i
\(489\) 32.9665 + 10.7900i 1.49080 + 0.487940i
\(490\) 30.1533 + 52.3674i 1.36219 + 2.36572i
\(491\) −13.6357 + 7.87256i −0.615369 + 0.355284i −0.775064 0.631883i \(-0.782282\pi\)
0.159695 + 0.987166i \(0.448949\pi\)
\(492\) 5.00112 + 23.7800i 0.225468 + 1.07209i
\(493\) 20.7734i 0.935588i
\(494\) −8.24733 20.6754i −0.371065 0.930229i
\(495\) −0.998996 + 1.36262i −0.0449015 + 0.0612454i
\(496\) 10.3368 + 17.9039i 0.464136 + 0.803907i
\(497\) 3.70208 + 13.8485i 0.166061 + 0.621190i
\(498\) 42.1379 37.7772i 1.88824 1.69284i
\(499\) 20.1085i 0.900179i −0.892983 0.450090i \(-0.851392\pi\)
0.892983 0.450090i \(-0.148608\pi\)
\(500\) −60.7359 35.0659i −2.71619 1.56819i
\(501\) −15.5899 + 13.9765i −0.696504 + 0.624426i
\(502\) 16.5118 0.736958
\(503\) −10.3449 + 17.9180i −0.461259 + 0.798923i −0.999024 0.0441713i \(-0.985935\pi\)
0.537765 + 0.843094i \(0.319269\pi\)
\(504\) 1.81433 4.65835i 0.0808168 0.207499i
\(505\) 34.4574 19.8940i 1.53334 0.885272i
\(506\) 0.904133i 0.0401936i
\(507\) 12.7955 18.5277i 0.568269 0.822843i
\(508\) −28.0986 −1.24667
\(509\) 10.7770 6.22209i 0.477681 0.275789i −0.241769 0.970334i \(-0.577728\pi\)
0.719449 + 0.694545i \(0.244394\pi\)
\(510\) 10.1571 + 48.2966i 0.449766 + 2.13861i
\(511\) −13.1227 + 13.1075i −0.580513 + 0.579839i
\(512\) 30.9152 1.36627
\(513\) −1.51704 15.3890i −0.0669791 0.679442i
\(514\) −19.0251 + 32.9525i −0.839162 + 1.45347i
\(515\) 5.37768 0.236969
\(516\) 6.61802 + 7.38195i 0.291342 + 0.324972i
\(517\) −0.260704 + 0.150517i −0.0114657 + 0.00661974i
\(518\) −20.5581 + 5.49573i −0.903269 + 0.241468i
\(519\) −4.78362 + 14.6153i −0.209978 + 0.641543i
\(520\) −8.77735 + 3.50125i −0.384912 + 0.153540i
\(521\) 17.3820 0.761521 0.380761 0.924674i \(-0.375662\pi\)
0.380761 + 0.924674i \(0.375662\pi\)
\(522\) −38.9357 4.26185i −1.70417 0.186536i
\(523\) 12.6620 7.31041i 0.553671 0.319662i −0.196930 0.980417i \(-0.563097\pi\)
0.750601 + 0.660755i \(0.229764\pi\)
\(524\) 9.99278 17.3080i 0.436537 0.756104i
\(525\) 30.8684 47.2500i 1.34721 2.06216i
\(526\) −9.51665 5.49444i −0.414946 0.239569i
\(527\) −10.3372 + 17.9046i −0.450297 + 0.779937i
\(528\) −0.240680 + 0.735347i −0.0104742 + 0.0320019i
\(529\) −6.31524 + 10.9383i −0.274576 + 0.475579i
\(530\) 24.4374 + 42.3268i 1.06149 + 1.83856i
\(531\) 25.2970 + 2.76898i 1.09780 + 0.120164i
\(532\) −17.5171 4.70460i −0.759464 0.203970i
\(533\) 17.2440 + 13.5956i 0.746922 + 0.588892i
\(534\) −17.9576 5.87754i −0.777101 0.254346i
\(535\) −9.02228 15.6270i −0.390067 0.675616i
\(536\) 4.90445 2.83158i 0.211840 0.122306i
\(537\) −0.581545 + 0.521364i −0.0250955 + 0.0224985i
\(538\) −18.8924 −0.814508
\(539\) −0.821024 + 0.472749i −0.0353640 + 0.0203627i
\(540\) −49.5696 + 4.88656i −2.13314 + 0.210284i
\(541\) 21.0587i 0.905385i −0.891667 0.452692i \(-0.850464\pi\)
0.891667 0.452692i \(-0.149536\pi\)
\(542\) 1.44475 2.50239i 0.0620575 0.107487i
\(543\) 2.20765 + 10.4972i 0.0947393 + 0.450479i
\(544\) 13.3793 + 23.1736i 0.573632 + 0.993560i
\(545\) −66.7897 −2.86096
\(546\) −10.9273 32.4881i −0.467647 1.39036i
\(547\) −44.6507 −1.90913 −0.954564 0.298006i \(-0.903678\pi\)
−0.954564 + 0.298006i \(0.903678\pi\)
\(548\) −2.41602 4.18466i −0.103207 0.178760i
\(549\) −18.9153 2.07045i −0.807285 0.0883645i
\(550\) 1.72901 2.99473i 0.0737251 0.127696i
\(551\) 18.7295i 0.797902i
\(552\) 2.61567 2.34499i 0.111330 0.0998093i
\(553\) 0.338536 0.338143i 0.0143960 0.0143793i
\(554\) −12.3282 −0.523775
\(555\) 18.6536 + 20.8068i 0.791800 + 0.883198i
\(556\) −31.5765 + 18.2307i −1.33914 + 0.773154i
\(557\) −8.29174 14.3617i −0.351332 0.608525i 0.635151 0.772388i \(-0.280938\pi\)
−0.986483 + 0.163863i \(0.947605\pi\)
\(558\) −31.4379 23.0484i −1.33087 0.975716i
\(559\) 8.86623 + 1.28604i 0.375002 + 0.0543936i
\(560\) 9.42548 35.0949i 0.398299 1.48303i
\(561\) −0.757201 + 0.159245i −0.0319690 + 0.00672334i
\(562\) −27.9486 48.4085i −1.17894 2.04199i
\(563\) −15.2602 + 26.4314i −0.643141 + 1.11395i 0.341587 + 0.939850i \(0.389036\pi\)
−0.984728 + 0.174102i \(0.944298\pi\)
\(564\) −8.43433 2.76057i −0.355149 0.116241i
\(565\) 9.93329 17.2050i 0.417897 0.723818i
\(566\) 9.04890 + 5.22438i 0.380354 + 0.219597i
\(567\) −1.02762 23.7896i −0.0431560 0.999068i
\(568\) −1.70625 + 2.95531i −0.0715926 + 0.124002i
\(569\) 36.3777 21.0027i 1.52503 0.880479i 0.525474 0.850810i \(-0.323888\pi\)
0.999560 0.0296692i \(-0.00944540\pi\)
\(570\) 9.15775 + 43.5445i 0.383576 + 1.82388i
\(571\) 14.4809 0.606006 0.303003 0.952990i \(-0.402011\pi\)
0.303003 + 0.952990i \(0.402011\pi\)
\(572\) −0.416498 1.04413i −0.0174147 0.0436571i
\(573\) 27.6440 + 9.04790i 1.15484 + 0.377982i
\(574\) 32.2937 8.63298i 1.34791 0.360334i
\(575\) 34.3466 19.8300i 1.43235 0.826970i
\(576\) −28.0532 + 12.3456i −1.16888 + 0.514402i
\(577\) 35.3915 1.47337 0.736684 0.676237i \(-0.236391\pi\)
0.736684 + 0.676237i \(0.236391\pi\)
\(578\) 6.33255 10.9683i 0.263399 0.456221i
\(579\) 13.5461 12.1442i 0.562956 0.504698i
\(580\) 60.3295 2.50505
\(581\) −29.4486 29.4828i −1.22173 1.22315i
\(582\) 1.80531 0.379671i 0.0748326 0.0157379i
\(583\) −0.663606 + 0.383133i −0.0274837 + 0.0158677i
\(584\) −4.41536 −0.182709
\(585\) −31.5485 + 32.1042i −1.30437 + 1.32735i
\(586\) 38.3382i 1.58374i
\(587\) 13.4483 7.76440i 0.555072 0.320471i −0.196093 0.980585i \(-0.562826\pi\)
0.751165 + 0.660114i \(0.229492\pi\)
\(588\) −26.5340 8.71873i −1.09425 0.359554i
\(589\) −9.32012 + 16.1429i −0.384029 + 0.665158i
\(590\) −73.2278 −3.01474
\(591\) 11.8707 + 13.2410i 0.488295 + 0.544660i
\(592\) 11.0823 + 6.39836i 0.455479 + 0.262971i
\(593\) 11.5568i 0.474582i 0.971439 + 0.237291i \(0.0762594\pi\)
−0.971439 + 0.237291i \(0.923741\pi\)
\(594\) −0.143127 1.45189i −0.00587258 0.0595719i
\(595\) 35.1073 9.38514i 1.43926 0.384753i
\(596\) −9.79876 16.9719i −0.401373 0.695198i
\(597\) 6.92540 + 2.26669i 0.283438 + 0.0927695i
\(598\) 3.45749 23.8367i 0.141387 0.974756i
\(599\) 26.7007i 1.09096i −0.838124 0.545480i \(-0.816347\pi\)
0.838124 0.545480i \(-0.183653\pi\)
\(600\) 13.1482 2.76517i 0.536774 0.112888i
\(601\) −15.0608 + 8.69538i −0.614345 + 0.354692i −0.774664 0.632373i \(-0.782081\pi\)
0.160319 + 0.987065i \(0.448748\pi\)
\(602\) 9.64919 9.63800i 0.393272 0.392815i
\(603\) 15.9489 21.7542i 0.649490 0.885901i
\(604\) 37.4532 + 21.6236i 1.52395 + 0.879853i
\(605\) −39.5754 22.8488i −1.60897 0.928938i
\(606\) −10.6869 + 32.6517i −0.434127 + 1.32638i
\(607\) −18.9551 10.9437i −0.769362 0.444191i 0.0632848 0.997996i \(-0.479842\pi\)
−0.832647 + 0.553804i \(0.813176\pi\)
\(608\) 12.0629 + 20.8935i 0.489214 + 0.847343i
\(609\) −1.58811 + 28.7969i −0.0643534 + 1.16691i
\(610\) 54.7545 2.21694
\(611\) −7.44882 + 2.97131i −0.301347 + 0.120206i
\(612\) −18.3965 13.4872i −0.743634 0.545188i
\(613\) −23.2086 + 13.3995i −0.937388 + 0.541201i −0.889140 0.457634i \(-0.848697\pi\)
−0.0482473 + 0.998835i \(0.515364\pi\)
\(614\) 14.9635 + 25.9175i 0.603876 + 1.04594i
\(615\) −29.3020 32.6844i −1.18157 1.31796i
\(616\) −0.217817 0.0584994i −0.00877610 0.00235701i
\(617\) −10.6859 + 18.5085i −0.430197 + 0.745123i −0.996890 0.0788059i \(-0.974889\pi\)
0.566693 + 0.823929i \(0.308223\pi\)
\(618\) −3.45748 + 3.09968i −0.139080 + 0.124687i
\(619\) 20.7895 0.835600 0.417800 0.908539i \(-0.362801\pi\)
0.417800 + 0.908539i \(0.362801\pi\)
\(620\) 51.9981 + 30.0211i 2.08829 + 1.20568i
\(621\) 6.90430 15.2417i 0.277060 0.611626i
\(622\) −21.9846 38.0784i −0.881502 1.52681i
\(623\) −3.60873 + 13.4368i −0.144581 + 0.538332i
\(624\) −9.15736 + 18.4664i −0.366588 + 0.739248i
\(625\) 65.1062 2.60425
\(626\) 5.45988 3.15226i 0.218221 0.125990i
\(627\) −0.682698 + 0.143577i −0.0272643 + 0.00573390i
\(628\) 28.5725 + 16.4964i 1.14017 + 0.658277i
\(629\) 12.7973i 0.510260i
\(630\) 10.3880 + 67.7271i 0.413868 + 2.69831i
\(631\) 3.16741 + 1.82870i 0.126093 + 0.0727996i 0.561720 0.827328i \(-0.310140\pi\)
−0.435627 + 0.900127i \(0.643473\pi\)
\(632\) 0.113907 0.00453096
\(633\) 3.25601 + 3.63186i 0.129415 + 0.144354i
\(634\) −31.2105 54.0582i −1.23953 2.14692i
\(635\) 43.9574 25.3788i 1.74440 1.00713i
\(636\) −21.4691 7.02686i −0.851305 0.278633i
\(637\) −23.4534 + 9.32395i −0.929259 + 0.369428i
\(638\) 1.76705i 0.0699582i
\(639\) −1.76859 + 16.1576i −0.0699645 + 0.639185i
\(640\) 17.9491 10.3629i 0.709501 0.409631i
\(641\) −6.03872 3.48646i −0.238515 0.137707i 0.375979 0.926628i \(-0.377306\pi\)
−0.614494 + 0.788921i \(0.710640\pi\)
\(642\) 14.8081 + 4.84671i 0.584429 + 0.191284i
\(643\) 12.8122 22.1914i 0.505264 0.875143i −0.494717 0.869054i \(-0.664728\pi\)
0.999981 0.00608902i \(-0.00193821\pi\)
\(644\) −13.8698 13.8859i −0.546546 0.547181i
\(645\) −17.0206 5.57088i −0.670187 0.219353i
\(646\) −10.1889 + 17.6477i −0.400877 + 0.694339i
\(647\) −20.6305 35.7330i −0.811067 1.40481i −0.912118 0.409929i \(-0.865554\pi\)
0.101050 0.994881i \(-0.467780\pi\)
\(648\) 3.82914 4.17975i 0.150423 0.164196i
\(649\) 1.14808i 0.0450659i
\(650\) 57.0359 72.3416i 2.23713 2.83747i
\(651\) −15.6987 + 24.0298i −0.615280 + 0.941803i
\(652\) 39.9531 23.0669i 1.56468 0.903371i
\(653\) 3.39607 1.96072i 0.132899 0.0767291i −0.432077 0.901837i \(-0.642219\pi\)
0.564975 + 0.825108i \(0.308886\pi\)
\(654\) 42.9413 38.4974i 1.67914 1.50537i
\(655\) 36.1022i 1.41063i
\(656\) −17.4086 10.0509i −0.679694 0.392421i
\(657\) −19.2493 + 8.47124i −0.750988 + 0.330495i
\(658\) −3.16651 + 11.7902i −0.123443 + 0.459630i
\(659\) 1.76677 + 1.02005i 0.0688236 + 0.0397353i 0.534017 0.845474i \(-0.320682\pi\)
−0.465193 + 0.885209i \(0.654015\pi\)
\(660\) 0.462475 + 2.19904i 0.0180018 + 0.0855975i
\(661\) −15.4047 26.6817i −0.599173 1.03780i −0.992943 0.118590i \(-0.962163\pi\)
0.393770 0.919209i \(-0.371171\pi\)
\(662\) 51.4741i 2.00060i
\(663\) −20.5719 + 1.30276i −0.798948 + 0.0505950i
\(664\) 9.92002i 0.384971i
\(665\) 31.6530 8.46171i 1.22745 0.328131i
\(666\) −23.9859 2.62547i −0.929436 0.101735i
\(667\) −10.1332 + 17.5512i −0.392358 + 0.679584i
\(668\) 27.8469i 1.07743i
\(669\) −22.6744 25.2917i −0.876642 0.977835i
\(670\) −38.8098 + 67.2205i −1.49935 + 2.59695i
\(671\) 0.858449i 0.0331400i
\(672\) 16.7753 + 33.1470i 0.647121 + 1.27867i
\(673\) 3.34304 + 5.79031i 0.128865 + 0.223200i 0.923237 0.384231i \(-0.125533\pi\)
−0.794372 + 0.607431i \(0.792200\pi\)
\(674\) −11.8988 20.6093i −0.458323 0.793840i
\(675\) 52.0160 37.2810i 2.00210 1.43495i
\(676\) −6.98778 29.1202i −0.268761 1.12001i
\(677\) 26.3980 1.01456 0.507280 0.861782i \(-0.330651\pi\)
0.507280 + 0.861782i \(0.330651\pi\)
\(678\) 3.53047 + 16.7871i 0.135587 + 0.644707i
\(679\) −0.350814 1.31230i −0.0134630 0.0503615i
\(680\) 7.49200 + 4.32551i 0.287305 + 0.165876i
\(681\) 2.04099 + 0.668017i 0.0782107 + 0.0255985i
\(682\) −0.879317 + 1.52302i −0.0336708 + 0.0583195i
\(683\) −19.4470 + 33.6832i −0.744120 + 1.28885i 0.206486 + 0.978450i \(0.433797\pi\)
−0.950605 + 0.310403i \(0.899536\pi\)
\(684\) −16.5864 12.1602i −0.634197 0.464956i
\(685\) 7.55922 + 4.36432i 0.288823 + 0.166752i
\(686\) −10.0086 + 37.0940i −0.382129 + 1.41626i
\(687\) −23.2670 + 4.89324i −0.887693 + 0.186689i
\(688\) −8.20129 −0.312671
\(689\) −18.9605 + 7.56329i −0.722339 + 0.288138i
\(690\) −14.9772 + 45.7597i −0.570172 + 1.74204i
\(691\) 14.1406 + 24.4923i 0.537935 + 0.931730i 0.999015 + 0.0443717i \(0.0141286\pi\)
−0.461081 + 0.887358i \(0.652538\pi\)
\(692\) 10.2265 + 17.7128i 0.388752 + 0.673338i
\(693\) −1.06184 + 0.162865i −0.0403358 + 0.00618672i
\(694\) 7.54356i 0.286350i
\(695\) 32.9321 57.0401i 1.24919 2.16366i
\(696\) −5.11211 + 4.58308i −0.193774 + 0.173721i
\(697\) 20.1026i 0.761441i
\(698\) −32.8447 + 56.8886i −1.24319 + 2.15327i
\(699\) −5.80899 27.6214i −0.219716 1.04474i
\(700\) −19.3859 72.5175i −0.732719 2.74090i
\(701\) 21.1916i 0.800395i 0.916429 + 0.400198i \(0.131059\pi\)
−0.916429 + 0.400198i \(0.868941\pi\)
\(702\) 1.77875 38.8253i 0.0671346 1.46537i
\(703\) 11.5381i 0.435168i
\(704\) 0.691369 + 1.19749i 0.0260569 + 0.0451319i
\(705\) 15.6880 3.29931i 0.590845 0.124259i
\(706\) −36.4231 21.0289i −1.37080 0.791432i
\(707\) 24.4316 + 6.56163i 0.918846 + 0.246776i
\(708\) 25.2009 22.5930i 0.947109 0.849097i
\(709\) −12.9760 7.49170i −0.487324 0.281357i 0.236139 0.971719i \(-0.424118\pi\)
−0.723464 + 0.690362i \(0.757451\pi\)
\(710\) 46.7718i 1.75531i
\(711\) 0.496589 0.218539i 0.0186236 0.00819586i
\(712\) −2.86834 + 1.65604i −0.107495 + 0.0620625i
\(713\) −17.4676 + 10.0849i −0.654166 + 0.377683i
\(714\) −17.1620 + 26.2698i −0.642273 + 0.983121i
\(715\) 1.59463 + 1.25725i 0.0596358 + 0.0470183i
\(716\) 1.03877i 0.0388206i
\(717\) −0.688759 + 0.144851i −0.0257222 + 0.00540957i
\(718\) 3.54323 + 6.13706i 0.132232 + 0.229033i
\(719\) 4.52338 7.83472i 0.168694 0.292186i −0.769267 0.638927i \(-0.779379\pi\)
0.937961 + 0.346741i \(0.112712\pi\)
\(720\) 24.3624 33.2302i 0.907934 1.23842i
\(721\) 2.41630 + 2.41911i 0.0899878 + 0.0900923i
\(722\) 10.5215 18.2238i 0.391570 0.678219i
\(723\) 4.99824 15.2711i 0.185887 0.567937i
\(724\) 12.3552 + 7.13331i 0.459179 + 0.265107i
\(725\) −67.1275 + 38.7561i −2.49305 + 1.43937i
\(726\) 38.6143 8.12088i 1.43311 0.301394i
\(727\) 48.2879i 1.79090i 0.445163 + 0.895450i \(0.353146\pi\)
−0.445163 + 0.895450i \(0.646854\pi\)
\(728\) −5.51886 2.37524i −0.204542 0.0880323i
\(729\) 8.67440 25.5686i 0.321274 0.946986i
\(730\) 52.4093 30.2585i 1.93976 1.11992i
\(731\) −4.10082 7.10282i −0.151674 0.262707i
\(732\) −18.8435 + 16.8934i −0.696474 + 0.624399i
\(733\) −14.2320 −0.525672 −0.262836 0.964841i \(-0.584658\pi\)
−0.262836 + 0.964841i \(0.584658\pi\)
\(734\) −4.49311 2.59410i −0.165844 0.0957498i
\(735\) 49.3846 10.3261i 1.82158 0.380885i
\(736\) 26.1054i 0.962258i
\(737\) −1.05389 0.608465i −0.0388207 0.0224131i
\(738\) 37.6784 + 4.12423i 1.38696 + 0.151815i
\(739\) 21.8719 12.6277i 0.804571 0.464519i −0.0404963 0.999180i \(-0.512894\pi\)
0.845067 + 0.534661i \(0.179561\pi\)
\(740\) 37.1654 1.36623
\(741\) −18.5478 + 1.17458i −0.681370 + 0.0431492i
\(742\) −8.06017 + 30.0113i −0.295898 + 1.10175i
\(743\) −17.6281 30.5327i −0.646711 1.12014i −0.983904 0.178700i \(-0.942811\pi\)
0.337193 0.941436i \(-0.390523\pi\)
\(744\) −6.68675 + 1.40628i −0.245148 + 0.0515566i
\(745\) 30.6583 + 17.7006i 1.12323 + 0.648499i
\(746\) 66.8790 2.44861
\(747\) −19.0324 43.2475i −0.696358 1.58234i
\(748\) −0.514549 + 0.891226i −0.0188138 + 0.0325864i
\(749\) 2.97581 11.0802i 0.108734 0.404860i
\(750\) −81.4510 + 73.0220i −2.97417 + 2.66639i
\(751\) 2.27926 + 3.94779i 0.0831713 + 0.144057i 0.904610 0.426239i \(-0.140162\pi\)
−0.821439 + 0.570296i \(0.806828\pi\)
\(752\) 6.35776 3.67065i 0.231844 0.133855i
\(753\) 4.28833 13.1021i 0.156275 0.477467i
\(754\) −6.75737 + 46.5868i −0.246089 + 1.69659i
\(755\) −78.1223 −2.84316
\(756\) −24.4709 20.1029i −0.889996 0.731136i
\(757\) −14.6997 25.4607i −0.534271 0.925384i −0.999198 0.0400355i \(-0.987253\pi\)
0.464927 0.885349i \(-0.346080\pi\)
\(758\) 16.2416 + 9.37706i 0.589920 + 0.340590i
\(759\) −0.717428 0.234815i −0.0260410 0.00852324i
\(760\) 6.75484 + 3.89991i 0.245024 + 0.141465i
\(761\) −22.0452 12.7278i −0.799139 0.461383i 0.0440309 0.999030i \(-0.485980\pi\)
−0.843170 + 0.537647i \(0.819313\pi\)
\(762\) −13.6333 + 41.6538i −0.493883 + 1.50896i
\(763\) −30.0100 30.0449i −1.08644 1.08770i
\(764\) 33.5025 19.3427i 1.21208 0.699794i
\(765\) 40.9612 + 4.48356i 1.48095 + 0.162104i
\(766\) 67.1607i 2.42662i
\(767\) 4.39035 30.2681i 0.158526 1.09292i
\(768\) 5.44198 16.6268i 0.196370 0.599969i
\(769\) 4.30034 + 7.44842i 0.155074 + 0.268597i 0.933086 0.359653i \(-0.117105\pi\)
−0.778012 + 0.628250i \(0.783772\pi\)
\(770\) 2.98633 0.798329i 0.107620 0.0287698i
\(771\) 21.2066 + 23.6546i 0.763739 + 0.851898i
\(772\) 24.1963i 0.870843i
\(773\) 3.51062 + 2.02686i 0.126268 + 0.0729011i 0.561804 0.827271i \(-0.310108\pi\)
−0.435535 + 0.900172i \(0.643441\pi\)
\(774\) 14.1542 6.22896i 0.508761 0.223895i
\(775\) −77.1430 −2.77106
\(776\) 0.161686 0.280049i 0.00580420 0.0100532i
\(777\) −0.978340 + 17.7401i −0.0350977 + 0.636422i
\(778\) −48.8855 + 28.2241i −1.75263 + 1.01188i
\(779\) 18.1247i 0.649384i
\(780\) 3.78344 + 59.7444i 0.135469 + 2.13919i
\(781\) 0.733295 0.0262394
\(782\) −19.0958 + 11.0250i −0.682865 + 0.394252i
\(783\) −13.4939 + 29.7885i −0.482231 + 1.06455i
\(784\) 20.0222 11.5289i 0.715080 0.411746i
\(785\) −59.5984 −2.12716
\(786\) −20.8092 23.2112i −0.742239 0.827917i
\(787\) −5.14027 + 8.90321i −0.183231 + 0.317365i −0.942979 0.332852i \(-0.891989\pi\)
0.759748 + 0.650218i \(0.225322\pi\)
\(788\) 23.6512 0.842540
\(789\) −6.83142 + 6.12447i −0.243205 + 0.218037i
\(790\) −1.35204 + 0.780603i −0.0481036 + 0.0277726i
\(791\) 12.2028 3.26213i 0.433880 0.115988i
\(792\) −0.206244 0.151206i −0.00732856 0.00537286i
\(793\) −3.28279 + 22.6323i −0.116575 + 0.803696i
\(794\) 39.1787 1.39040
\(795\) 39.9329 8.39820i 1.41627 0.297854i
\(796\) 8.39309 4.84575i 0.297485 0.171753i
\(797\) 18.6331 32.2735i 0.660020 1.14319i −0.320590 0.947218i \(-0.603881\pi\)
0.980610 0.195970i \(-0.0627854\pi\)
\(798\) −15.4734 + 23.6850i −0.547753 + 0.838440i
\(799\) 6.35803 + 3.67081i 0.224931 + 0.129864i
\(800\) −49.9224 + 86.4681i −1.76502 + 3.05711i
\(801\) −9.32763 + 12.7228i −0.329575 + 0.449539i
\(802\) −21.0416 + 36.4452i −0.743006 + 1.28692i
\(803\) 0.474398 + 0.821682i 0.0167411 + 0.0289965i
\(804\) −7.38340 35.1076i −0.260392 1.23815i
\(805\) 34.2397 + 9.19580i 1.20679 + 0.324109i
\(806\) −29.0066 + 36.7906i −1.02171 + 1.29589i
\(807\) −4.90659 + 14.9911i −0.172720 + 0.527710i
\(808\) 3.01111 + 5.21540i 0.105931 + 0.183477i
\(809\) −10.7988 + 6.23469i −0.379666 + 0.219200i −0.677673 0.735363i \(-0.737011\pi\)
0.298007 + 0.954564i \(0.403678\pi\)
\(810\) −16.8071 + 75.8537i −0.590541 + 2.66523i
\(811\) 11.6976 0.410757 0.205378 0.978683i \(-0.434157\pi\)
0.205378 + 0.978683i \(0.434157\pi\)
\(812\) 27.1073 + 27.1388i 0.951280 + 0.952385i
\(813\) −1.61042 1.79631i −0.0564798 0.0629994i
\(814\) 1.08857i 0.0381545i
\(815\) −41.6684 + 72.1717i −1.45958 + 2.52807i
\(816\) 18.4658 3.88350i 0.646432 0.135950i
\(817\) −3.69733 6.40396i −0.129353 0.224046i
\(818\) −72.1213 −2.52166
\(819\) −28.6172 + 0.233233i −0.999967 + 0.00814982i
\(820\) −58.3814 −2.03877
\(821\) −13.4192 23.2427i −0.468333 0.811176i 0.531012 0.847364i \(-0.321812\pi\)
−0.999345 + 0.0361879i \(0.988479\pi\)
\(822\) −7.37565 + 1.55116i −0.257255 + 0.0541028i
\(823\) −5.70202 + 9.87618i −0.198760 + 0.344262i −0.948127 0.317893i \(-0.897025\pi\)
0.749367 + 0.662155i \(0.230358\pi\)
\(824\) 0.813954i 0.0283554i
\(825\) −1.92727 2.14973i −0.0670988 0.0748441i
\(826\) −32.9028 32.9410i −1.14483 1.14616i
\(827\) −40.7898 −1.41840 −0.709200 0.705007i \(-0.750944\pi\)
−0.709200 + 0.705007i \(0.750944\pi\)
\(828\) −8.96394 20.3689i −0.311518 0.707868i
\(829\) 21.8676 12.6252i 0.759492 0.438493i −0.0696215 0.997573i \(-0.522179\pi\)
0.829113 + 0.559081i \(0.188846\pi\)
\(830\) 67.9820 + 117.748i 2.35969 + 4.08710i
\(831\) −3.20179 + 9.78240i −0.111069 + 0.339348i
\(832\) 13.6481 + 34.2146i 0.473161 + 1.18618i
\(833\) 19.9963 + 11.5758i 0.692830 + 0.401078i
\(834\) 11.7047 + 55.6549i 0.405299 + 1.92717i
\(835\) −25.1515 43.5637i −0.870404 1.50758i
\(836\) −0.463921 + 0.803535i −0.0160451 + 0.0277908i
\(837\) −26.4537 + 18.9599i −0.914372 + 0.655351i
\(838\) 20.3965 35.3279i 0.704587 1.22038i
\(839\) 4.00176 + 2.31042i 0.138156 + 0.0797645i 0.567485 0.823384i \(-0.307917\pi\)
−0.429329 + 0.903148i \(0.641250\pi\)
\(840\) 10.0550 + 6.56895i 0.346932 + 0.226650i
\(841\) 5.30442 9.18753i 0.182911 0.316811i
\(842\) 8.01182 4.62563i 0.276106 0.159410i
\(843\) −45.6706 + 9.60489i −1.57298 + 0.330810i
\(844\) 6.48730 0.223302
\(845\) 37.2332 + 39.2442i 1.28086 + 1.35004i
\(846\) −8.18461 + 11.1638i −0.281393 + 0.383818i
\(847\) −7.50365 28.0691i −0.257828 0.964467i
\(848\) 16.1833 9.34344i 0.555737 0.320855i
\(849\) 6.49565 5.82344i 0.222930 0.199860i
\(850\) −84.3339 −2.89263
\(851\) −6.24245 + 10.8122i −0.213988 + 0.370639i
\(852\) 14.4305 + 16.0963i 0.494381 + 0.551449i
\(853\) 14.7098 0.503655 0.251827 0.967772i \(-0.418968\pi\)
0.251827 + 0.967772i \(0.418968\pi\)
\(854\) 24.6023 + 24.6309i 0.841874 + 0.842852i
\(855\) 36.9309 + 4.04241i 1.26301 + 0.138248i
\(856\) 2.36527 1.36559i 0.0808434 0.0466750i
\(857\) 8.04731 0.274891 0.137445 0.990509i \(-0.456111\pi\)
0.137445 + 0.990509i \(0.456111\pi\)
\(858\) −1.74991 + 0.110817i −0.0597410 + 0.00378322i
\(859\) 4.04679i 0.138075i −0.997614 0.0690373i \(-0.978007\pi\)
0.997614 0.0690373i \(-0.0219928\pi\)
\(860\) −20.6278 + 11.9095i −0.703403 + 0.406110i
\(861\) 1.53683 27.8671i 0.0523749 0.949707i
\(862\) 19.0112 32.9283i 0.647523 1.12154i
\(863\) 5.32323 0.181205 0.0906025 0.995887i \(-0.471121\pi\)
0.0906025 + 0.995887i \(0.471121\pi\)
\(864\) 4.13257 + 41.9211i 0.140593 + 1.42619i
\(865\) −31.9965 18.4732i −1.08792 0.628108i
\(866\) 40.0574i 1.36121i
\(867\) −7.05867 7.87347i −0.239725 0.267397i
\(868\) 9.85904 + 36.8800i 0.334638 + 1.25179i
\(869\) −0.0122384 0.0211975i −0.000415160 0.000719078i
\(870\) 29.2717 89.4334i 0.992402 3.03208i
\(871\) −25.4582 20.0719i −0.862617 0.680109i
\(872\) 10.1091i 0.342339i
\(873\) 0.167594 1.53112i 0.00567221 0.0518205i
\(874\) −17.2169 + 9.94020i −0.582371 + 0.336232i
\(875\) 56.9230 + 56.9891i 1.92435 + 1.92658i
\(876\) −8.70071 + 26.5832i −0.293970 + 0.898163i
\(877\) 25.3898 + 14.6588i 0.857352 + 0.494992i 0.863125 0.504991i \(-0.168504\pi\)
−0.00577255 + 0.999983i \(0.501837\pi\)
\(878\) 32.1014 + 18.5337i 1.08337 + 0.625484i
\(879\) −30.4213 9.95693i −1.02609 0.335839i
\(880\) −1.60985 0.929449i −0.0542681 0.0313317i
\(881\) −2.65204 4.59347i −0.0893495 0.154758i 0.817887 0.575379i \(-0.195145\pi\)
−0.907236 + 0.420621i \(0.861812\pi\)
\(882\) −25.7990 + 35.1042i −0.868697 + 1.18202i
\(883\) 50.0090 1.68294 0.841468 0.540307i \(-0.181692\pi\)
0.841468 + 0.540307i \(0.181692\pi\)
\(884\) −16.9738 + 21.5287i −0.570890 + 0.724090i
\(885\) −19.0182 + 58.1061i −0.639289 + 1.95321i
\(886\) 73.1869 42.2545i 2.45876 1.41957i
\(887\) −18.1438 31.4260i −0.609210 1.05518i −0.991371 0.131087i \(-0.958153\pi\)
0.382161 0.924096i \(-0.375180\pi\)
\(888\) −3.14927 + 2.82336i −0.105683 + 0.0947458i
\(889\) 31.1674 + 8.37068i 1.04532 + 0.280743i
\(890\) 22.6977 39.3135i 0.760827 1.31779i
\(891\) −1.18925 0.263504i −0.0398412 0.00882772i
\(892\) −45.1766 −1.51262
\(893\) 5.73244 + 3.30963i 0.191829 + 0.110752i
\(894\) −29.9138 + 6.29110i −1.00047 + 0.210406i
\(895\) −0.938221 1.62505i −0.0313613 0.0543193i
\(896\) 12.7266 + 3.41800i 0.425166 + 0.114187i
\(897\) −18.0164 8.93421i −0.601551 0.298304i
\(898\) −30.4272 −1.01537
\(899\) 34.1389 19.7101i 1.13860 0.657368i
\(900\) 9.26123 84.6092i 0.308708 2.82031i
\(901\) 16.1840 + 9.34383i 0.539167 + 0.311288i
\(902\) 1.70999i 0.0569365i
\(903\) −5.14171 10.1597i −0.171105 0.338094i
\(904\) 2.60411 + 1.50348i 0.0866113 + 0.0500051i
\(905\) −25.7714 −0.856669
\(906\) 50.2273 45.0295i 1.66869 1.49600i
\(907\) 20.1405 + 34.8843i 0.668754 + 1.15832i 0.978253 + 0.207416i \(0.0665053\pi\)
−0.309499 + 0.950900i \(0.600161\pi\)
\(908\) 2.47353 1.42809i 0.0820869 0.0473929i
\(909\) 23.1335 + 16.9601i 0.767290 + 0.562532i
\(910\) 81.7851 9.62725i 2.71115 0.319140i
\(911\) 32.8778i 1.08929i −0.838666 0.544646i \(-0.816664\pi\)
0.838666 0.544646i \(-0.183336\pi\)
\(912\) 16.6489 3.50139i 0.551300 0.115943i
\(913\) −1.84608 + 1.06583i −0.0610962 + 0.0352739i
\(914\) −34.1401 19.7108i −1.12925 0.651975i
\(915\) 14.2204 43.4475i 0.470113 1.43633i
\(916\) −15.8109 + 27.3853i −0.522408 + 0.904836i
\(917\) −16.2403 + 16.2215i −0.536302 + 0.535680i
\(918\) −28.9196 + 20.7273i −0.954487 + 0.684102i
\(919\) −9.23167 + 15.9897i −0.304525 + 0.527452i −0.977155 0.212526i \(-0.931831\pi\)
0.672631 + 0.739978i \(0.265164\pi\)
\(920\) 4.21993 + 7.30913i 0.139127 + 0.240975i
\(921\) 24.4516 5.14237i 0.805709 0.169447i
\(922\) 60.9366i 2.00684i
\(923\) 19.3327 + 2.80419i 0.636344 + 0.0923010i
\(924\) −0.781422 + 1.19612i −0.0257069 + 0.0393493i
\(925\) −41.3533 + 23.8753i −1.35969 + 0.785016i
\(926\) 58.7522 33.9206i 1.93072 1.11470i
\(927\) 1.56164 + 3.54853i 0.0512909 + 0.116549i
\(928\) 51.0208i 1.67484i
\(929\) −14.8047 8.54752i −0.485728 0.280435i 0.237073 0.971492i \(-0.423812\pi\)
−0.722800 + 0.691057i \(0.757145\pi\)
\(930\) 69.7330 62.5166i 2.28663 2.05000i
\(931\) 18.0288 + 10.4368i 0.590869 + 0.342054i
\(932\) −32.5104 18.7699i −1.06491 0.614827i
\(933\) −35.9248 + 7.55527i −1.17613 + 0.247348i
\(934\) 20.8766 + 36.1594i 0.683104 + 1.18317i
\(935\) 1.85898i 0.0607950i
\(936\) −4.85922 4.77511i −0.158829 0.156079i
\(937\) 39.3582i 1.28578i 0.765960 + 0.642888i \(0.222264\pi\)
−0.765960 + 0.642888i \(0.777736\pi\)
\(938\) −47.6767 + 12.7453i −1.55670 + 0.416148i
\(939\) −1.08331 5.15109i −0.0353526 0.168099i
\(940\) 10.6607 18.4648i 0.347712 0.602255i
\(941\) 12.4816i 0.406887i 0.979087 + 0.203444i \(0.0652133\pi\)
−0.979087 + 0.203444i \(0.934787\pi\)
\(942\) 38.3178 34.3524i 1.24846 1.11926i
\(943\) 9.80597 16.9844i 0.319326 0.553089i
\(944\) 27.9980i 0.911259i
\(945\) 56.4392 + 9.34674i 1.83597 + 0.304049i
\(946\) −0.348828 0.604188i −0.0113414 0.0196438i
\(947\) 24.2738 + 42.0434i 0.788792 + 1.36623i 0.926707 + 0.375784i \(0.122627\pi\)
−0.137915 + 0.990444i \(0.544040\pi\)
\(948\) 0.224459 0.685787i 0.00729009 0.0222733i
\(949\) 9.36492 + 23.4771i 0.303998 + 0.762098i
\(950\) −76.0360 −2.46693
\(951\) −51.0008 + 10.7259i −1.65381 + 0.347810i
\(952\) 1.42051 + 5.31376i 0.0460391 + 0.172220i
\(953\) 22.9526 + 13.2517i 0.743507 + 0.429264i 0.823343 0.567544i \(-0.192106\pi\)
−0.0798358 + 0.996808i \(0.525440\pi\)
\(954\) −20.8334 + 28.4167i −0.674508 + 0.920025i
\(955\) −34.9409 + 60.5193i −1.13066 + 1.95836i
\(956\) −0.468040 + 0.810669i −0.0151375 + 0.0262189i
\(957\) 1.40215 + 0.458926i 0.0453251 + 0.0148350i
\(958\) 30.1634 + 17.4149i 0.974536 + 0.562649i
\(959\) 1.43326 + 5.36144i 0.0462824 + 0.173130i
\(960\) −15.1547 72.0595i −0.489115 2.32571i
\(961\) 8.23241 0.265562
\(962\) −4.16281 + 28.6994i −0.134214 + 0.925305i
\(963\) 7.69170 10.4914i 0.247862 0.338082i
\(964\) −10.6853 18.5075i −0.344150 0.596085i
\(965\) 21.8542 + 37.8526i 0.703512 + 1.21852i
\(966\) −27.3142 + 13.8234i −0.878821 + 0.444761i
\(967\) 7.09303i 0.228097i 0.993475 + 0.114048i \(0.0363819\pi\)
−0.993475 + 0.114048i \(0.963618\pi\)
\(968\) 3.45835 5.99004i 0.111156 0.192527i
\(969\) 11.3572 + 12.6682i 0.364846 + 0.406961i
\(970\) 4.43216i 0.142308i
\(971\) 28.8163 49.9113i 0.924759 1.60173i 0.132811 0.991141i \(-0.457600\pi\)
0.791948 0.610588i \(-0.209067\pi\)
\(972\) −17.6191 31.2902i −0.565133 1.00363i
\(973\) 40.4562 10.8150i 1.29697 0.346714i
\(974\) 11.6405i 0.372984i
\(975\) −42.5900 64.0459i −1.36397 2.05111i
\(976\) 20.9349i 0.670111i
\(977\) −5.54648 9.60678i −0.177448 0.307348i 0.763558 0.645739i \(-0.223451\pi\)
−0.941006 + 0.338391i \(0.890117\pi\)
\(978\) −14.8097 70.4191i −0.473561 2.25175i
\(979\) 0.616363 + 0.355857i 0.0196990 + 0.0113732i
\(980\) 33.6182 58.0726i 1.07389 1.85506i
\(981\) −19.3952 44.0721i −0.619242 1.40711i
\(982\) 28.2874 + 16.3317i 0.902687 + 0.521167i
\(983\) 16.0491i 0.511885i −0.966692 0.255943i \(-0.917614\pi\)
0.966692 0.255943i \(-0.0823858\pi\)
\(984\) 4.94704 4.43509i 0.157706 0.141385i
\(985\) −36.9999 + 21.3619i −1.17892 + 0.680648i
\(986\) 37.3211 21.5474i 1.18855 0.686208i
\(987\) 8.53312 + 5.57469i 0.271612 + 0.177444i
\(988\) −15.3037 + 19.4105i −0.486875 + 0.617529i
\(989\) 8.00144i 0.254431i
\(990\) 3.48428 + 0.381386i 0.110738 + 0.0121212i
\(991\) −8.69946 15.0679i −0.276347 0.478648i 0.694127 0.719853i \(-0.255791\pi\)
−0.970474 + 0.241205i \(0.922457\pi\)
\(992\) 25.3889 43.9748i 0.806098 1.39620i
\(993\) −40.8446 13.3685i −1.29616 0.424236i
\(994\) 21.0399 21.0155i 0.667346 0.666572i
\(995\) −8.75342 + 15.1614i −0.277502 + 0.480648i
\(996\) −59.7246 19.5479i −1.89245 0.619399i
\(997\) 12.4651 + 7.19671i 0.394773 + 0.227922i 0.684226 0.729270i \(-0.260140\pi\)
−0.289453 + 0.957192i \(0.593474\pi\)
\(998\) −36.1265 + 20.8577i −1.14357 + 0.660238i
\(999\) −8.31276 + 18.3509i −0.263004 + 0.580598i
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 273.2.u.c.62.5 64
3.2 odd 2 inner 273.2.u.c.62.27 yes 64
7.6 odd 2 inner 273.2.u.c.62.6 yes 64
13.4 even 6 inner 273.2.u.c.251.28 yes 64
21.20 even 2 inner 273.2.u.c.62.28 yes 64
39.17 odd 6 inner 273.2.u.c.251.6 yes 64
91.69 odd 6 inner 273.2.u.c.251.27 yes 64
273.251 even 6 inner 273.2.u.c.251.5 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.u.c.62.5 64 1.1 even 1 trivial
273.2.u.c.62.6 yes 64 7.6 odd 2 inner
273.2.u.c.62.27 yes 64 3.2 odd 2 inner
273.2.u.c.62.28 yes 64 21.20 even 2 inner
273.2.u.c.251.5 yes 64 273.251 even 6 inner
273.2.u.c.251.6 yes 64 39.17 odd 6 inner
273.2.u.c.251.27 yes 64 91.69 odd 6 inner
273.2.u.c.251.28 yes 64 13.4 even 6 inner