Properties

Label 336.2.s.c.155.1
Level $336$
Weight $2$
Character 336.155
Analytic conductor $2.683$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(155,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.s (of order \(4\), 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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 155.1
Character \(\chi\) \(=\) 336.155
Dual form 336.2.s.c.323.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41409 + 0.0184003i) q^{2} +(0.827739 - 1.52146i) q^{3} +(1.99932 - 0.0520394i) q^{4} +(-1.23935 + 1.23935i) q^{5} +(-1.14250 + 2.16672i) q^{6} -1.00000 q^{7} +(-2.82627 + 0.110377i) q^{8} +(-1.62970 - 2.51875i) q^{9} +O(q^{10})\) \(q+(-1.41409 + 0.0184003i) q^{2} +(0.827739 - 1.52146i) q^{3} +(1.99932 - 0.0520394i) q^{4} +(-1.23935 + 1.23935i) q^{5} +(-1.14250 + 2.16672i) q^{6} -1.00000 q^{7} +(-2.82627 + 0.110377i) q^{8} +(-1.62970 - 2.51875i) q^{9} +(1.72975 - 1.77536i) q^{10} +(-3.57267 - 3.57267i) q^{11} +(1.57574 - 3.08497i) q^{12} +(1.58965 - 1.58965i) q^{13} +(1.41409 - 0.0184003i) q^{14} +(0.859765 + 2.91147i) q^{15} +(3.99458 - 0.208087i) q^{16} -2.20802i q^{17} +(2.35089 + 3.53176i) q^{18} +(-3.76716 - 3.76716i) q^{19} +(-2.41336 + 2.54235i) q^{20} +(-0.827739 + 1.52146i) q^{21} +(5.11782 + 4.98635i) q^{22} -3.97123i q^{23} +(-2.17148 + 4.39143i) q^{24} +1.92804i q^{25} +(-2.21866 + 2.27716i) q^{26} +(-5.18114 + 0.394660i) q^{27} +(-1.99932 + 0.0520394i) q^{28} +(4.75337 + 4.75337i) q^{29} +(-1.26936 - 4.10128i) q^{30} -1.24630i q^{31} +(-5.64489 + 0.367756i) q^{32} +(-8.39291 + 2.47844i) q^{33} +(0.0406281 + 3.12234i) q^{34} +(1.23935 - 1.23935i) q^{35} +(-3.38937 - 4.95098i) q^{36} +(-6.39946 - 6.39946i) q^{37} +(5.39644 + 5.25780i) q^{38} +(-1.10278 - 3.73440i) q^{39} +(3.36594 - 3.63953i) q^{40} -3.93566 q^{41} +(1.14250 - 2.16672i) q^{42} +(1.19053 - 1.19053i) q^{43} +(-7.32883 - 6.95699i) q^{44} +(5.14136 + 1.10184i) q^{45} +(0.0730718 + 5.61569i) q^{46} +8.26073 q^{47} +(2.98987 - 6.24985i) q^{48} +1.00000 q^{49} +(-0.0354765 - 2.72643i) q^{50} +(-3.35941 - 1.82766i) q^{51} +(3.09549 - 3.26094i) q^{52} +(2.18249 - 2.18249i) q^{53} +(7.31936 - 0.653421i) q^{54} +8.85554 q^{55} +(2.82627 - 0.110377i) q^{56} +(-8.84982 + 2.61337i) q^{57} +(-6.80917 - 6.63425i) q^{58} +(5.45245 + 5.45245i) q^{59} +(1.87046 + 5.77624i) q^{60} +(-5.10830 + 5.10830i) q^{61} +(0.0229323 + 1.76239i) q^{62} +(1.62970 + 2.51875i) q^{63} +(7.97563 - 0.623910i) q^{64} +3.94024i q^{65} +(11.8228 - 3.65918i) q^{66} +(-7.23888 - 7.23888i) q^{67} +(-0.114904 - 4.41454i) q^{68} +(-6.04208 - 3.28714i) q^{69} +(-1.72975 + 1.77536i) q^{70} +6.13227i q^{71} +(4.88398 + 6.93878i) q^{72} +10.2246i q^{73} +(9.16719 + 8.93169i) q^{74} +(2.93344 + 1.59591i) q^{75} +(-7.72781 - 7.33573i) q^{76} +(3.57267 + 3.57267i) q^{77} +(1.62814 + 5.26050i) q^{78} +6.53910i q^{79} +(-4.69278 + 5.20857i) q^{80} +(-3.68817 + 8.20959i) q^{81} +(5.56539 - 0.0724172i) q^{82} +(12.3619 - 12.3619i) q^{83} +(-1.57574 + 3.08497i) q^{84} +(2.73650 + 2.73650i) q^{85} +(-1.66162 + 1.70543i) q^{86} +(11.1666 - 3.29753i) q^{87} +(10.4917 + 9.70299i) q^{88} +9.15394 q^{89} +(-7.29064 - 1.46350i) q^{90} +(-1.58965 + 1.58965i) q^{91} +(-0.206661 - 7.93977i) q^{92} +(-1.89620 - 1.03161i) q^{93} +(-11.6814 + 0.152000i) q^{94} +9.33763 q^{95} +(-4.11296 + 8.89289i) q^{96} +7.67756 q^{97} +(-1.41409 + 0.0184003i) q^{98} +(-3.17628 + 14.8210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41409 + 0.0184003i −0.999915 + 0.0130110i
\(3\) 0.827739 1.52146i 0.477895 0.878417i
\(4\) 1.99932 0.0520394i 0.999661 0.0260197i
\(5\) −1.23935 + 1.23935i −0.554253 + 0.554253i −0.927665 0.373413i \(-0.878188\pi\)
0.373413 + 0.927665i \(0.378188\pi\)
\(6\) −1.14250 + 2.16672i −0.466426 + 0.884560i
\(7\) −1.00000 −0.377964
\(8\) −2.82627 + 0.110377i −0.999238 + 0.0390241i
\(9\) −1.62970 2.51875i −0.543233 0.839582i
\(10\) 1.72975 1.77536i 0.546994 0.561417i
\(11\) −3.57267 3.57267i −1.07720 1.07720i −0.996759 0.0804398i \(-0.974368\pi\)
−0.0804398 0.996759i \(-0.525632\pi\)
\(12\) 1.57574 3.08497i 0.454877 0.890554i
\(13\) 1.58965 1.58965i 0.440888 0.440888i −0.451422 0.892310i \(-0.649083\pi\)
0.892310 + 0.451422i \(0.149083\pi\)
\(14\) 1.41409 0.0184003i 0.377932 0.00491768i
\(15\) 0.859765 + 2.91147i 0.221990 + 0.751740i
\(16\) 3.99458 0.208087i 0.998646 0.0520218i
\(17\) 2.20802i 0.535523i −0.963485 0.267761i \(-0.913716\pi\)
0.963485 0.267761i \(-0.0862839\pi\)
\(18\) 2.35089 + 3.53176i 0.554110 + 0.832443i
\(19\) −3.76716 3.76716i −0.864246 0.864246i 0.127582 0.991828i \(-0.459278\pi\)
−0.991828 + 0.127582i \(0.959278\pi\)
\(20\) −2.41336 + 2.54235i −0.539643 + 0.568486i
\(21\) −0.827739 + 1.52146i −0.180627 + 0.332010i
\(22\) 5.11782 + 4.98635i 1.09112 + 1.06309i
\(23\) 3.97123i 0.828059i −0.910264 0.414029i \(-0.864121\pi\)
0.910264 0.414029i \(-0.135879\pi\)
\(24\) −2.17148 + 4.39143i −0.443252 + 0.896397i
\(25\) 1.92804i 0.385608i
\(26\) −2.21866 + 2.27716i −0.435115 + 0.446587i
\(27\) −5.18114 + 0.394660i −0.997111 + 0.0759524i
\(28\) −1.99932 + 0.0520394i −0.377837 + 0.00983453i
\(29\) 4.75337 + 4.75337i 0.882679 + 0.882679i 0.993806 0.111128i \(-0.0354462\pi\)
−0.111128 + 0.993806i \(0.535446\pi\)
\(30\) −1.26936 4.10128i −0.231752 0.748788i
\(31\) 1.24630i 0.223842i −0.993717 0.111921i \(-0.964300\pi\)
0.993717 0.111921i \(-0.0357004\pi\)
\(32\) −5.64489 + 0.367756i −0.997885 + 0.0650108i
\(33\) −8.39291 + 2.47844i −1.46102 + 0.431442i
\(34\) 0.0406281 + 3.12234i 0.00696766 + 0.535477i
\(35\) 1.23935 1.23935i 0.209488 0.209488i
\(36\) −3.38937 4.95098i −0.564894 0.825163i
\(37\) −6.39946 6.39946i −1.05206 1.05206i −0.998568 0.0534969i \(-0.982963\pi\)
−0.0534969 0.998568i \(-0.517037\pi\)
\(38\) 5.39644 + 5.25780i 0.875417 + 0.852928i
\(39\) −1.10278 3.73440i −0.176585 0.597982i
\(40\) 3.36594 3.63953i 0.532201 0.575460i
\(41\) −3.93566 −0.614646 −0.307323 0.951605i \(-0.599433\pi\)
−0.307323 + 0.951605i \(0.599433\pi\)
\(42\) 1.14250 2.16672i 0.176292 0.334332i
\(43\) 1.19053 1.19053i 0.181554 0.181554i −0.610479 0.792033i \(-0.709023\pi\)
0.792033 + 0.610479i \(0.209023\pi\)
\(44\) −7.32883 6.95699i −1.10486 1.04881i
\(45\) 5.14136 + 1.10184i 0.766429 + 0.164253i
\(46\) 0.0730718 + 5.61569i 0.0107738 + 0.827989i
\(47\) 8.26073 1.20495 0.602476 0.798137i \(-0.294181\pi\)
0.602476 + 0.798137i \(0.294181\pi\)
\(48\) 2.98987 6.24985i 0.431551 0.902088i
\(49\) 1.00000 0.142857
\(50\) −0.0354765 2.72643i −0.00501713 0.385575i
\(51\) −3.35941 1.82766i −0.470412 0.255924i
\(52\) 3.09549 3.26094i 0.429267 0.452211i
\(53\) 2.18249 2.18249i 0.299788 0.299788i −0.541143 0.840931i \(-0.682008\pi\)
0.840931 + 0.541143i \(0.182008\pi\)
\(54\) 7.31936 0.653421i 0.996039 0.0889193i
\(55\) 8.85554 1.19408
\(56\) 2.82627 0.110377i 0.377677 0.0147497i
\(57\) −8.84982 + 2.61337i −1.17219 + 0.346149i
\(58\) −6.80917 6.63425i −0.894088 0.871119i
\(59\) 5.45245 + 5.45245i 0.709849 + 0.709849i 0.966503 0.256654i \(-0.0826202\pi\)
−0.256654 + 0.966503i \(0.582620\pi\)
\(60\) 1.87046 + 5.77624i 0.241475 + 0.745709i
\(61\) −5.10830 + 5.10830i −0.654051 + 0.654051i −0.953966 0.299915i \(-0.903042\pi\)
0.299915 + 0.953966i \(0.403042\pi\)
\(62\) 0.0229323 + 1.76239i 0.00291241 + 0.223824i
\(63\) 1.62970 + 2.51875i 0.205323 + 0.317332i
\(64\) 7.97563 0.623910i 0.996954 0.0779887i
\(65\) 3.94024i 0.488727i
\(66\) 11.8228 3.65918i 1.45528 0.450415i
\(67\) −7.23888 7.23888i −0.884371 0.884371i 0.109605 0.993975i \(-0.465041\pi\)
−0.993975 + 0.109605i \(0.965041\pi\)
\(68\) −0.114904 4.41454i −0.0139341 0.535341i
\(69\) −6.04208 3.28714i −0.727381 0.395725i
\(70\) −1.72975 + 1.77536i −0.206744 + 0.212196i
\(71\) 6.13227i 0.727766i 0.931445 + 0.363883i \(0.118549\pi\)
−0.931445 + 0.363883i \(0.881451\pi\)
\(72\) 4.88398 + 6.93878i 0.575583 + 0.817744i
\(73\) 10.2246i 1.19670i 0.801237 + 0.598348i \(0.204176\pi\)
−0.801237 + 0.598348i \(0.795824\pi\)
\(74\) 9.16719 + 8.93169i 1.06566 + 1.03829i
\(75\) 2.93344 + 1.59591i 0.338725 + 0.184280i
\(76\) −7.72781 7.33573i −0.886441 0.841466i
\(77\) 3.57267 + 3.57267i 0.407143 + 0.407143i
\(78\) 1.62814 + 5.26050i 0.184351 + 0.595634i
\(79\) 6.53910i 0.735706i 0.929884 + 0.367853i \(0.119907\pi\)
−0.929884 + 0.367853i \(0.880093\pi\)
\(80\) −4.69278 + 5.20857i −0.524669 + 0.582335i
\(81\) −3.68817 + 8.20959i −0.409797 + 0.912177i
\(82\) 5.56539 0.0724172i 0.614594 0.00799714i
\(83\) 12.3619 12.3619i 1.35690 1.35690i 0.479183 0.877715i \(-0.340933\pi\)
0.877715 0.479183i \(-0.159067\pi\)
\(84\) −1.57574 + 3.08497i −0.171927 + 0.336598i
\(85\) 2.73650 + 2.73650i 0.296815 + 0.296815i
\(86\) −1.66162 + 1.70543i −0.179177 + 0.183901i
\(87\) 11.1666 3.29753i 1.19719 0.353532i
\(88\) 10.4917 + 9.70299i 1.11842 + 1.03434i
\(89\) 9.15394 0.970316 0.485158 0.874427i \(-0.338762\pi\)
0.485158 + 0.874427i \(0.338762\pi\)
\(90\) −7.29064 1.46350i −0.768501 0.154267i
\(91\) −1.58965 + 1.58965i −0.166640 + 0.166640i
\(92\) −0.206661 7.93977i −0.0215459 0.827778i
\(93\) −1.89620 1.03161i −0.196627 0.106973i
\(94\) −11.6814 + 0.152000i −1.20485 + 0.0156776i
\(95\) 9.33763 0.958021
\(96\) −4.11296 + 8.89289i −0.419778 + 0.907627i
\(97\) 7.67756 0.779538 0.389769 0.920913i \(-0.372555\pi\)
0.389769 + 0.920913i \(0.372555\pi\)
\(98\) −1.41409 + 0.0184003i −0.142845 + 0.00185871i
\(99\) −3.17628 + 14.8210i −0.319228 + 1.48957i
\(100\) 0.100334 + 3.85477i 0.0100334 + 0.385477i
\(101\) −5.10294 + 5.10294i −0.507761 + 0.507761i −0.913839 0.406077i \(-0.866896\pi\)
0.406077 + 0.913839i \(0.366896\pi\)
\(102\) 4.78416 + 2.52267i 0.473702 + 0.249781i
\(103\) 17.2234 1.69707 0.848535 0.529139i \(-0.177485\pi\)
0.848535 + 0.529139i \(0.177485\pi\)
\(104\) −4.31731 + 4.66823i −0.423347 + 0.457758i
\(105\) −0.859765 2.91147i −0.0839044 0.284131i
\(106\) −3.04608 + 3.12640i −0.295862 + 0.303663i
\(107\) −8.98275 8.98275i −0.868396 0.868396i 0.123899 0.992295i \(-0.460460\pi\)
−0.992295 + 0.123899i \(0.960460\pi\)
\(108\) −10.3382 + 1.05868i −0.994798 + 0.101871i
\(109\) 9.91151 9.91151i 0.949350 0.949350i −0.0494277 0.998778i \(-0.515740\pi\)
0.998778 + 0.0494277i \(0.0157397\pi\)
\(110\) −12.5226 + 0.162944i −1.19398 + 0.0155361i
\(111\) −15.0336 + 4.43946i −1.42693 + 0.421375i
\(112\) −3.99458 + 0.208087i −0.377453 + 0.0196624i
\(113\) 14.2233i 1.33801i −0.743256 0.669007i \(-0.766720\pi\)
0.743256 0.669007i \(-0.233280\pi\)
\(114\) 12.4664 3.85839i 1.16758 0.361371i
\(115\) 4.92173 + 4.92173i 0.458954 + 0.458954i
\(116\) 9.75088 + 9.25616i 0.905347 + 0.859413i
\(117\) −6.59455 1.41327i −0.609667 0.130657i
\(118\) −7.81061 7.60995i −0.719025 0.700553i
\(119\) 2.20802i 0.202409i
\(120\) −2.75129 8.13372i −0.251157 0.742504i
\(121\) 14.5279i 1.32072i
\(122\) 7.12962 7.31761i 0.645486 0.662506i
\(123\) −3.25770 + 5.98796i −0.293737 + 0.539916i
\(124\) −0.0648569 2.49176i −0.00582432 0.223767i
\(125\) −8.58624 8.58624i −0.767977 0.767977i
\(126\) −2.35089 3.53176i −0.209434 0.314634i
\(127\) 2.23296i 0.198143i −0.995080 0.0990717i \(-0.968413\pi\)
0.995080 0.0990717i \(-0.0315873\pi\)
\(128\) −11.2668 + 1.02902i −0.995855 + 0.0909534i
\(129\) −0.825900 2.79680i −0.0727164 0.246244i
\(130\) −0.0725016 5.57187i −0.00635881 0.488686i
\(131\) 4.97791 4.97791i 0.434922 0.434922i −0.455377 0.890299i \(-0.650495\pi\)
0.890299 + 0.455377i \(0.150495\pi\)
\(132\) −16.6512 + 5.39197i −1.44930 + 0.469311i
\(133\) 3.76716 + 3.76716i 0.326654 + 0.326654i
\(134\) 10.3697 + 10.1033i 0.895802 + 0.872789i
\(135\) 5.93211 6.91035i 0.510555 0.594748i
\(136\) 0.243714 + 6.24046i 0.0208983 + 0.535115i
\(137\) 5.14127 0.439248 0.219624 0.975585i \(-0.429517\pi\)
0.219624 + 0.975585i \(0.429517\pi\)
\(138\) 8.60455 + 4.53715i 0.732468 + 0.386228i
\(139\) 13.3617 13.3617i 1.13332 1.13332i 0.143702 0.989621i \(-0.454099\pi\)
0.989621 0.143702i \(-0.0459006\pi\)
\(140\) 2.41336 2.54235i 0.203966 0.214868i
\(141\) 6.83772 12.5684i 0.575840 1.05845i
\(142\) −0.112835 8.67160i −0.00946894 0.727705i
\(143\) −11.3585 −0.949849
\(144\) −7.03408 9.72223i −0.586174 0.810185i
\(145\) −11.7821 −0.978454
\(146\) −0.188135 14.4585i −0.0155702 1.19659i
\(147\) 0.827739 1.52146i 0.0682707 0.125488i
\(148\) −13.1276 12.4616i −1.07908 1.02433i
\(149\) −14.3514 + 14.3514i −1.17571 + 1.17571i −0.194886 + 0.980826i \(0.562434\pi\)
−0.980826 + 0.194886i \(0.937566\pi\)
\(150\) −4.17753 2.20279i −0.341094 0.179857i
\(151\) −17.5454 −1.42782 −0.713911 0.700236i \(-0.753078\pi\)
−0.713911 + 0.700236i \(0.753078\pi\)
\(152\) 11.0628 + 10.2312i 0.897314 + 0.829861i
\(153\) −5.56143 + 3.59840i −0.449615 + 0.290913i
\(154\) −5.11782 4.98635i −0.412406 0.401811i
\(155\) 1.54460 + 1.54460i 0.124065 + 0.124065i
\(156\) −2.39914 7.40888i −0.192085 0.593185i
\(157\) 9.29740 9.29740i 0.742014 0.742014i −0.230952 0.972965i \(-0.574184\pi\)
0.972965 + 0.230952i \(0.0741839\pi\)
\(158\) −0.120321 9.24690i −0.00957225 0.735644i
\(159\) −1.51404 5.12710i −0.120071 0.406606i
\(160\) 6.54019 7.45175i 0.517048 0.589113i
\(161\) 3.97123i 0.312977i
\(162\) 5.06436 11.6770i 0.397894 0.917431i
\(163\) −11.6109 11.6109i −0.909434 0.909434i 0.0867928 0.996226i \(-0.472338\pi\)
−0.996226 + 0.0867928i \(0.972338\pi\)
\(164\) −7.86865 + 0.204809i −0.614438 + 0.0159929i
\(165\) 7.33007 13.4734i 0.570645 1.04890i
\(166\) −17.2535 + 17.7084i −1.33913 + 1.37444i
\(167\) 4.92377i 0.381013i 0.981686 + 0.190507i \(0.0610130\pi\)
−0.981686 + 0.190507i \(0.938987\pi\)
\(168\) 2.17148 4.39143i 0.167533 0.338806i
\(169\) 7.94606i 0.611235i
\(170\) −3.92002 3.81931i −0.300652 0.292928i
\(171\) −3.34919 + 15.6279i −0.256119 + 1.19509i
\(172\) 2.31830 2.44221i 0.176769 0.186217i
\(173\) 1.92511 + 1.92511i 0.146363 + 0.146363i 0.776491 0.630128i \(-0.216998\pi\)
−0.630128 + 0.776491i \(0.716998\pi\)
\(174\) −15.7300 + 4.86848i −1.19249 + 0.369079i
\(175\) 1.92804i 0.145746i
\(176\) −15.0147 13.5279i −1.13178 1.01970i
\(177\) 12.8089 3.78250i 0.962777 0.284310i
\(178\) −12.9445 + 0.168435i −0.970233 + 0.0126247i
\(179\) 3.30607 3.30607i 0.247107 0.247107i −0.572675 0.819782i \(-0.694094\pi\)
0.819782 + 0.572675i \(0.194094\pi\)
\(180\) 10.3366 + 1.93538i 0.770443 + 0.144255i
\(181\) 14.1503 + 14.1503i 1.05178 + 1.05178i 0.998584 + 0.0531972i \(0.0169412\pi\)
0.0531972 + 0.998584i \(0.483059\pi\)
\(182\) 2.21866 2.27716i 0.164458 0.168794i
\(183\) 3.54375 + 12.0004i 0.261962 + 0.887097i
\(184\) 0.438332 + 11.2238i 0.0323142 + 0.827428i
\(185\) 15.8623 1.16622
\(186\) 2.70039 + 1.42391i 0.198002 + 0.104406i
\(187\) −7.88850 + 7.88850i −0.576865 + 0.576865i
\(188\) 16.5159 0.429884i 1.20454 0.0313525i
\(189\) 5.18114 0.394660i 0.376873 0.0287073i
\(190\) −13.2043 + 0.171815i −0.957940 + 0.0124648i
\(191\) −8.46813 −0.612732 −0.306366 0.951914i \(-0.599113\pi\)
−0.306366 + 0.951914i \(0.599113\pi\)
\(192\) 5.65248 12.6511i 0.407933 0.913012i
\(193\) −17.2773 −1.24365 −0.621823 0.783158i \(-0.713608\pi\)
−0.621823 + 0.783158i \(0.713608\pi\)
\(194\) −10.8568 + 0.141269i −0.779472 + 0.0101425i
\(195\) 5.99493 + 3.26149i 0.429306 + 0.233560i
\(196\) 1.99932 0.0520394i 0.142809 0.00371710i
\(197\) 16.4452 16.4452i 1.17167 1.17167i 0.189864 0.981810i \(-0.439195\pi\)
0.981810 0.189864i \(-0.0608047\pi\)
\(198\) 4.21884 21.0167i 0.299820 1.49359i
\(199\) 8.20937 0.581947 0.290973 0.956731i \(-0.406021\pi\)
0.290973 + 0.956731i \(0.406021\pi\)
\(200\) −0.212811 5.44917i −0.0150480 0.385314i
\(201\) −17.0056 + 5.02179i −1.19948 + 0.354210i
\(202\) 7.12214 7.30993i 0.501112 0.514325i
\(203\) −4.75337 4.75337i −0.333621 0.333621i
\(204\) −6.81166 3.47926i −0.476912 0.243597i
\(205\) 4.87764 4.87764i 0.340669 0.340669i
\(206\) −24.3555 + 0.316915i −1.69693 + 0.0220805i
\(207\) −10.0025 + 6.47190i −0.695223 + 0.449828i
\(208\) 6.01919 6.68076i 0.417355 0.463227i
\(209\) 26.9176i 1.86193i
\(210\) 1.26936 + 4.10128i 0.0875941 + 0.283015i
\(211\) −15.5340 15.5340i −1.06940 1.06940i −0.997405 0.0719974i \(-0.977063\pi\)
−0.0719974 0.997405i \(-0.522937\pi\)
\(212\) 4.24992 4.47707i 0.291886 0.307487i
\(213\) 9.33002 + 5.07591i 0.639282 + 0.347796i
\(214\) 12.8677 + 12.5372i 0.879621 + 0.857024i
\(215\) 2.95096i 0.201254i
\(216\) 14.5998 1.68730i 0.993388 0.114806i
\(217\) 1.24630i 0.0846045i
\(218\) −13.8334 + 14.1982i −0.936918 + 0.961622i
\(219\) 15.5563 + 8.46327i 1.05120 + 0.571895i
\(220\) 17.7051 0.460837i 1.19368 0.0310697i
\(221\) −3.50996 3.50996i −0.236106 0.236106i
\(222\) 21.1773 6.55444i 1.42132 0.439905i
\(223\) 4.58037i 0.306724i 0.988170 + 0.153362i \(0.0490101\pi\)
−0.988170 + 0.153362i \(0.950990\pi\)
\(224\) 5.64489 0.367756i 0.377165 0.0245718i
\(225\) 4.85624 3.14212i 0.323750 0.209475i
\(226\) 0.261712 + 20.1130i 0.0174088 + 1.33790i
\(227\) −15.9988 + 15.9988i −1.06188 + 1.06188i −0.0639247 + 0.997955i \(0.520362\pi\)
−0.997955 + 0.0639247i \(0.979638\pi\)
\(228\) −17.5576 + 5.68551i −1.16278 + 0.376532i
\(229\) −4.16743 4.16743i −0.275392 0.275392i 0.555875 0.831266i \(-0.312383\pi\)
−0.831266 + 0.555875i \(0.812383\pi\)
\(230\) −7.05035 6.86923i −0.464886 0.452943i
\(231\) 8.39291 2.47844i 0.552213 0.163070i
\(232\) −13.9590 12.9097i −0.916452 0.847560i
\(233\) −7.47847 −0.489931 −0.244966 0.969532i \(-0.578777\pi\)
−0.244966 + 0.969532i \(0.578777\pi\)
\(234\) 9.35132 + 1.87716i 0.611315 + 0.122714i
\(235\) −10.2379 + 10.2379i −0.667847 + 0.667847i
\(236\) 11.1850 + 10.6175i 0.728079 + 0.691139i
\(237\) 9.94900 + 5.41267i 0.646257 + 0.351590i
\(238\) −0.0406281 3.12234i −0.00263353 0.202391i
\(239\) −3.99993 −0.258734 −0.129367 0.991597i \(-0.541295\pi\)
−0.129367 + 0.991597i \(0.541295\pi\)
\(240\) 4.04024 + 11.4512i 0.260797 + 0.739173i
\(241\) 3.26993 0.210635 0.105317 0.994439i \(-0.466414\pi\)
0.105317 + 0.994439i \(0.466414\pi\)
\(242\) −0.267317 20.5438i −0.0171838 1.32060i
\(243\) 9.43775 + 12.4068i 0.605432 + 0.795897i
\(244\) −9.94731 + 10.4790i −0.636811 + 0.670848i
\(245\) −1.23935 + 1.23935i −0.0791789 + 0.0791789i
\(246\) 4.49651 8.52747i 0.286687 0.543692i
\(247\) −11.9769 −0.762072
\(248\) 0.137563 + 3.52239i 0.00873525 + 0.223672i
\(249\) −8.57577 29.0407i −0.543467 1.84038i
\(250\) 12.2997 + 11.9838i 0.777904 + 0.757920i
\(251\) −3.56566 3.56566i −0.225062 0.225062i 0.585564 0.810626i \(-0.300873\pi\)
−0.810626 + 0.585564i \(0.800873\pi\)
\(252\) 3.38937 + 4.95098i 0.213510 + 0.311882i
\(253\) −14.1879 + 14.1879i −0.891984 + 0.891984i
\(254\) 0.0410872 + 3.15762i 0.00257804 + 0.198127i
\(255\) 6.42858 1.89837i 0.402573 0.118881i
\(256\) 15.9134 1.66244i 0.994587 0.103903i
\(257\) 17.0440i 1.06318i −0.847002 0.531589i \(-0.821595\pi\)
0.847002 0.531589i \(-0.178405\pi\)
\(258\) 1.21936 + 3.93974i 0.0759142 + 0.245277i
\(259\) 6.39946 + 6.39946i 0.397643 + 0.397643i
\(260\) 0.205048 + 7.87782i 0.0127165 + 0.488562i
\(261\) 4.22598 19.7191i 0.261582 1.22058i
\(262\) −6.94764 + 7.13083i −0.429227 + 0.440544i
\(263\) 26.4446i 1.63064i 0.579009 + 0.815321i \(0.303440\pi\)
−0.579009 + 0.815321i \(0.696560\pi\)
\(264\) 23.4471 7.93114i 1.44307 0.488128i
\(265\) 5.40972i 0.332316i
\(266\) −5.39644 5.25780i −0.330877 0.322376i
\(267\) 7.57707 13.9274i 0.463709 0.852342i
\(268\) −14.8496 14.0962i −0.907082 0.861060i
\(269\) −11.5967 11.5967i −0.707061 0.707061i 0.258855 0.965916i \(-0.416655\pi\)
−0.965916 + 0.258855i \(0.916655\pi\)
\(270\) −8.26141 + 9.88104i −0.502773 + 0.601341i
\(271\) 7.02845i 0.426948i −0.976949 0.213474i \(-0.931522\pi\)
0.976949 0.213474i \(-0.0684778\pi\)
\(272\) −0.459460 8.82011i −0.0278589 0.534797i
\(273\) 1.10278 + 3.73440i 0.0667430 + 0.226016i
\(274\) −7.27023 + 0.0946008i −0.439211 + 0.00571504i
\(275\) 6.88824 6.88824i 0.415377 0.415377i
\(276\) −12.2511 6.25763i −0.737431 0.376665i
\(277\) 3.04438 + 3.04438i 0.182919 + 0.182919i 0.792627 0.609707i \(-0.208713\pi\)
−0.609707 + 0.792627i \(0.708713\pi\)
\(278\) −18.6488 + 19.1405i −1.11848 + 1.14797i
\(279\) −3.13912 + 2.03110i −0.187934 + 0.121599i
\(280\) −3.36594 + 3.63953i −0.201153 + 0.217503i
\(281\) 9.56982 0.570887 0.285444 0.958395i \(-0.407859\pi\)
0.285444 + 0.958395i \(0.407859\pi\)
\(282\) −9.43792 + 17.8987i −0.562020 + 1.06585i
\(283\) −15.9451 + 15.9451i −0.947839 + 0.947839i −0.998705 0.0508666i \(-0.983802\pi\)
0.0508666 + 0.998705i \(0.483802\pi\)
\(284\) 0.319120 + 12.2604i 0.0189363 + 0.727520i
\(285\) 7.72912 14.2069i 0.457834 0.841542i
\(286\) 16.0620 0.209000i 0.949769 0.0123584i
\(287\) 3.93566 0.232315
\(288\) 10.1257 + 13.6187i 0.596665 + 0.802490i
\(289\) 12.1247 0.713216
\(290\) 16.6611 0.216795i 0.978371 0.0127306i
\(291\) 6.35501 11.6811i 0.372537 0.684759i
\(292\) 0.532081 + 20.4422i 0.0311377 + 1.19629i
\(293\) 1.28702 1.28702i 0.0751886 0.0751886i −0.668512 0.743701i \(-0.733069\pi\)
0.743701 + 0.668512i \(0.233069\pi\)
\(294\) −1.14250 + 2.16672i −0.0666322 + 0.126366i
\(295\) −13.5150 −0.786871
\(296\) 18.7930 + 17.3803i 1.09232 + 1.01021i
\(297\) 19.9205 + 17.1005i 1.15590 + 0.992272i
\(298\) 20.0301 20.5583i 1.16031 1.19091i
\(299\) −6.31285 6.31285i −0.365081 0.365081i
\(300\) 5.94795 + 3.03809i 0.343405 + 0.175404i
\(301\) −1.19053 + 1.19053i −0.0686211 + 0.0686211i
\(302\) 24.8108 0.322840i 1.42770 0.0185773i
\(303\) 3.54003 + 11.9878i 0.203369 + 0.688683i
\(304\) −15.8321 14.2643i −0.908035 0.818116i
\(305\) 12.6619i 0.725019i
\(306\) 7.79818 5.19081i 0.445792 0.296739i
\(307\) 6.52035 + 6.52035i 0.372136 + 0.372136i 0.868255 0.496119i \(-0.165242\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(308\) 7.32883 + 6.95699i 0.417599 + 0.396411i
\(309\) 14.2565 26.2047i 0.811022 1.49074i
\(310\) −2.21263 2.15579i −0.125669 0.122441i
\(311\) 17.8276i 1.01091i 0.862852 + 0.505456i \(0.168676\pi\)
−0.862852 + 0.505456i \(0.831324\pi\)
\(312\) 3.52893 + 10.4327i 0.199787 + 0.590635i
\(313\) 4.87439i 0.275517i −0.990466 0.137758i \(-0.956010\pi\)
0.990466 0.137758i \(-0.0439897\pi\)
\(314\) −12.9763 + 13.3185i −0.732296 + 0.751605i
\(315\) −5.14136 1.10184i −0.289683 0.0620817i
\(316\) 0.340291 + 13.0738i 0.0191429 + 0.735457i
\(317\) 4.97157 + 4.97157i 0.279231 + 0.279231i 0.832802 0.553571i \(-0.186735\pi\)
−0.553571 + 0.832802i \(0.686735\pi\)
\(318\) 2.23534 + 7.22234i 0.125352 + 0.405009i
\(319\) 33.9644i 1.90164i
\(320\) −9.11133 + 10.6578i −0.509339 + 0.595790i
\(321\) −21.1023 + 6.23155i −1.17782 + 0.347811i
\(322\) −0.0730718 5.61569i −0.00407213 0.312950i
\(323\) −8.31795 + 8.31795i −0.462823 + 0.462823i
\(324\) −6.94662 + 16.6056i −0.385923 + 0.922531i
\(325\) 3.06490 + 3.06490i 0.170010 + 0.170010i
\(326\) 16.6325 + 16.2052i 0.921189 + 0.897524i
\(327\) −6.87585 23.2841i −0.380235 1.28761i
\(328\) 11.1232 0.434405i 0.614178 0.0239860i
\(329\) −8.26073 −0.455429
\(330\) −10.1175 + 19.1875i −0.556950 + 1.05624i
\(331\) 9.97563 9.97563i 0.548310 0.548310i −0.377642 0.925952i \(-0.623265\pi\)
0.925952 + 0.377642i \(0.123265\pi\)
\(332\) 24.0722 25.3588i 1.32113 1.39174i
\(333\) −5.68944 + 26.5478i −0.311779 + 1.45481i
\(334\) −0.0905988 6.96268i −0.00495735 0.380981i
\(335\) 17.9430 0.980329
\(336\) −2.98987 + 6.24985i −0.163111 + 0.340957i
\(337\) 7.16141 0.390107 0.195054 0.980793i \(-0.437512\pi\)
0.195054 + 0.980793i \(0.437512\pi\)
\(338\) −0.146210 11.2365i −0.00795276 0.611183i
\(339\) −21.6402 11.7732i −1.17533 0.639430i
\(340\) 5.61355 + 5.32874i 0.304437 + 0.288991i
\(341\) −4.45262 + 4.45262i −0.241123 + 0.241123i
\(342\) 4.44851 22.1609i 0.240548 1.19832i
\(343\) −1.00000 −0.0539949
\(344\) −3.23336 + 3.49617i −0.174331 + 0.188501i
\(345\) 11.5621 3.41432i 0.622485 0.183821i
\(346\) −2.75770 2.68686i −0.148255 0.144446i
\(347\) −7.59346 7.59346i −0.407638 0.407638i 0.473276 0.880914i \(-0.343071\pi\)
−0.880914 + 0.473276i \(0.843071\pi\)
\(348\) 22.1541 7.17393i 1.18758 0.384563i
\(349\) −7.63248 + 7.63248i −0.408557 + 0.408557i −0.881235 0.472678i \(-0.843287\pi\)
0.472678 + 0.881235i \(0.343287\pi\)
\(350\) 0.0354765 + 2.72643i 0.00189630 + 0.145734i
\(351\) −7.60881 + 8.86355i −0.406128 + 0.473101i
\(352\) 21.4812 + 18.8534i 1.14495 + 1.00489i
\(353\) 18.8358i 1.00253i −0.865294 0.501265i \(-0.832868\pi\)
0.865294 0.501265i \(-0.167132\pi\)
\(354\) −18.0434 + 5.58450i −0.958996 + 0.296813i
\(355\) −7.60000 7.60000i −0.403366 0.403366i
\(356\) 18.3017 0.476366i 0.969987 0.0252473i
\(357\) 3.35941 + 1.82766i 0.177799 + 0.0967300i
\(358\) −4.61426 + 4.73592i −0.243871 + 0.250301i
\(359\) 15.8207i 0.834984i −0.908681 0.417492i \(-0.862909\pi\)
0.908681 0.417492i \(-0.137091\pi\)
\(360\) −14.6525 2.54661i −0.772255 0.134218i
\(361\) 9.38299i 0.493842i
\(362\) −20.2702 19.7494i −1.06538 1.03801i
\(363\) 22.1036 + 12.0253i 1.16014 + 0.631164i
\(364\) −3.09549 + 3.26094i −0.162248 + 0.170920i
\(365\) −12.6718 12.6718i −0.663271 0.663271i
\(366\) −5.23201 16.9045i −0.273482 0.883614i
\(367\) 25.6082i 1.33674i −0.743831 0.668368i \(-0.766993\pi\)
0.743831 0.668368i \(-0.233007\pi\)
\(368\) −0.826363 15.8634i −0.0430771 0.826938i
\(369\) 6.41393 + 9.91292i 0.333896 + 0.516046i
\(370\) −22.4308 + 0.291871i −1.16612 + 0.0151736i
\(371\) −2.18249 + 2.18249i −0.113309 + 0.113309i
\(372\) −3.84480 1.96385i −0.199344 0.101821i
\(373\) −20.8264 20.8264i −1.07835 1.07835i −0.996658 0.0816898i \(-0.973968\pi\)
−0.0816898 0.996658i \(-0.526032\pi\)
\(374\) 11.0099 11.3002i 0.569310 0.584321i
\(375\) −20.1708 + 5.95648i −1.04162 + 0.307592i
\(376\) −23.3471 + 0.911792i −1.20403 + 0.0470221i
\(377\) 15.1123 0.778325
\(378\) −7.31936 + 0.653421i −0.376467 + 0.0336084i
\(379\) 7.30890 7.30890i 0.375433 0.375433i −0.494018 0.869451i \(-0.664472\pi\)
0.869451 + 0.494018i \(0.164472\pi\)
\(380\) 18.6689 0.485925i 0.957697 0.0249274i
\(381\) −3.39737 1.84831i −0.174053 0.0946918i
\(382\) 11.9747 0.155816i 0.612681 0.00797224i
\(383\) 15.8671 0.810769 0.405384 0.914146i \(-0.367138\pi\)
0.405384 + 0.914146i \(0.367138\pi\)
\(384\) −7.76036 + 17.9938i −0.396019 + 0.918242i
\(385\) −8.85554 −0.451320
\(386\) 24.4317 0.317907i 1.24354 0.0161810i
\(387\) −4.93885 1.05844i −0.251056 0.0538036i
\(388\) 15.3499 0.399536i 0.779274 0.0202834i
\(389\) −2.42160 + 2.42160i −0.122780 + 0.122780i −0.765827 0.643047i \(-0.777670\pi\)
0.643047 + 0.765827i \(0.277670\pi\)
\(390\) −8.53741 4.50175i −0.432309 0.227955i
\(391\) −8.76854 −0.443444
\(392\) −2.82627 + 0.110377i −0.142748 + 0.00557487i
\(393\) −3.45330 11.6941i −0.174196 0.589890i
\(394\) −22.9525 + 23.5577i −1.15633 + 1.18682i
\(395\) −8.10421 8.10421i −0.407767 0.407767i
\(396\) −5.57912 + 29.7973i −0.280362 + 1.49737i
\(397\) −2.29467 + 2.29467i −0.115166 + 0.115166i −0.762341 0.647175i \(-0.775950\pi\)
0.647175 + 0.762341i \(0.275950\pi\)
\(398\) −11.6088 + 0.151055i −0.581897 + 0.00757169i
\(399\) 8.84982 2.61337i 0.443045 0.130832i
\(400\) 0.401201 + 7.70172i 0.0200600 + 0.385086i
\(401\) 4.57856i 0.228642i −0.993444 0.114321i \(-0.963531\pi\)
0.993444 0.114321i \(-0.0364693\pi\)
\(402\) 23.9551 7.41419i 1.19477 0.369786i
\(403\) −1.98118 1.98118i −0.0986895 0.0986895i
\(404\) −9.93687 + 10.4680i −0.494378 + 0.520801i
\(405\) −5.60361 14.7455i −0.278445 0.732707i
\(406\) 6.80917 + 6.63425i 0.337934 + 0.329252i
\(407\) 45.7263i 2.26657i
\(408\) 9.69635 + 4.79466i 0.480041 + 0.237371i
\(409\) 34.4670i 1.70428i −0.523312 0.852141i \(-0.675304\pi\)
0.523312 0.852141i \(-0.324696\pi\)
\(410\) −6.80770 + 6.98720i −0.336208 + 0.345073i
\(411\) 4.25563 7.82225i 0.209915 0.385843i
\(412\) 34.4351 0.896295i 1.69650 0.0441573i
\(413\) −5.45245 5.45245i −0.268298 0.268298i
\(414\) 14.0254 9.33593i 0.689312 0.458836i
\(415\) 30.6414i 1.50413i
\(416\) −8.38877 + 9.55797i −0.411293 + 0.468618i
\(417\) −9.26932 31.3893i −0.453921 1.53714i
\(418\) −0.495292 38.0640i −0.0242255 1.86177i
\(419\) −19.6092 + 19.6092i −0.957971 + 0.957971i −0.999152 0.0411805i \(-0.986888\pi\)
0.0411805 + 0.999152i \(0.486888\pi\)
\(420\) −1.87046 5.77624i −0.0912690 0.281851i
\(421\) 20.9601 + 20.9601i 1.02153 + 1.02153i 0.999763 + 0.0217712i \(0.00693054\pi\)
0.0217712 + 0.999763i \(0.493069\pi\)
\(422\) 22.2523 + 21.6807i 1.08323 + 1.05540i
\(423\) −13.4625 20.8067i −0.654569 1.01166i
\(424\) −5.92741 + 6.40920i −0.287860 + 0.311258i
\(425\) 4.25714 0.206502
\(426\) −13.2869 7.00614i −0.643753 0.339449i
\(427\) 5.10830 5.10830i 0.247208 0.247208i
\(428\) −18.4269 17.4920i −0.890697 0.845506i
\(429\) −9.40190 + 17.2816i −0.453928 + 0.834363i
\(430\) −0.0542985 4.17294i −0.00261851 0.201237i
\(431\) −28.8191 −1.38817 −0.694083 0.719895i \(-0.744190\pi\)
−0.694083 + 0.719895i \(0.744190\pi\)
\(432\) −20.6144 + 2.65463i −0.991810 + 0.127721i
\(433\) 29.7649 1.43041 0.715205 0.698915i \(-0.246333\pi\)
0.715205 + 0.698915i \(0.246333\pi\)
\(434\) −0.0229323 1.76239i −0.00110079 0.0845973i
\(435\) −9.75254 + 17.9261i −0.467598 + 0.859490i
\(436\) 19.3005 20.3321i 0.924327 0.973730i
\(437\) −14.9603 + 14.9603i −0.715646 + 0.715646i
\(438\) −22.1538 11.6816i −1.05855 0.558169i
\(439\) −10.4581 −0.499137 −0.249568 0.968357i \(-0.580289\pi\)
−0.249568 + 0.968357i \(0.580289\pi\)
\(440\) −25.0282 + 0.977446i −1.19317 + 0.0465979i
\(441\) −1.62970 2.51875i −0.0776046 0.119940i
\(442\) 5.02800 + 4.89883i 0.239158 + 0.233014i
\(443\) 19.0958 + 19.0958i 0.907268 + 0.907268i 0.996051 0.0887831i \(-0.0282978\pi\)
−0.0887831 + 0.996051i \(0.528298\pi\)
\(444\) −29.8260 + 9.65826i −1.41548 + 0.458361i
\(445\) −11.3449 + 11.3449i −0.537800 + 0.537800i
\(446\) −0.0842801 6.47708i −0.00399078 0.306698i
\(447\) 9.95590 + 33.7143i 0.470898 + 1.59463i
\(448\) −7.97563 + 0.623910i −0.376813 + 0.0294770i
\(449\) 26.5991i 1.25529i −0.778500 0.627645i \(-0.784019\pi\)
0.778500 0.627645i \(-0.215981\pi\)
\(450\) −6.80937 + 4.53261i −0.320997 + 0.213669i
\(451\) 14.0608 + 14.0608i 0.662097 + 0.662097i
\(452\) −0.740171 28.4369i −0.0348147 1.33756i
\(453\) −14.5230 + 26.6946i −0.682349 + 1.25422i
\(454\) 22.3295 22.9182i 1.04797 1.07561i
\(455\) 3.94024i 0.184721i
\(456\) 24.7235 8.36291i 1.15779 0.391629i
\(457\) 5.10142i 0.238634i −0.992856 0.119317i \(-0.961929\pi\)
0.992856 0.119317i \(-0.0380705\pi\)
\(458\) 5.96982 + 5.81646i 0.278951 + 0.271785i
\(459\) 0.871416 + 11.4400i 0.0406742 + 0.533976i
\(460\) 10.0963 + 9.58400i 0.470740 + 0.446857i
\(461\) 7.89211 + 7.89211i 0.367572 + 0.367572i 0.866591 0.499019i \(-0.166306\pi\)
−0.499019 + 0.866591i \(0.666306\pi\)
\(462\) −11.8228 + 3.65918i −0.550045 + 0.170241i
\(463\) 11.5271i 0.535708i 0.963460 + 0.267854i \(0.0863145\pi\)
−0.963460 + 0.267854i \(0.913686\pi\)
\(464\) 19.9768 + 17.9986i 0.927402 + 0.835565i
\(465\) 3.62858 1.07153i 0.168271 0.0496908i
\(466\) 10.5753 0.137606i 0.489890 0.00637448i
\(467\) 17.4574 17.4574i 0.807833 0.807833i −0.176472 0.984306i \(-0.556469\pi\)
0.984306 + 0.176472i \(0.0564687\pi\)
\(468\) −13.2582 2.48241i −0.612860 0.114750i
\(469\) 7.23888 + 7.23888i 0.334261 + 0.334261i
\(470\) 14.2890 14.6657i 0.659101 0.676480i
\(471\) −6.44983 21.8415i −0.297193 1.00640i
\(472\) −16.0119 14.8083i −0.737009 0.681607i
\(473\) −8.50674 −0.391140
\(474\) −14.1684 7.47095i −0.650777 0.343152i
\(475\) 7.26324 7.26324i 0.333260 0.333260i
\(476\) 0.114904 + 4.41454i 0.00526661 + 0.202340i
\(477\) −9.05393 1.94034i −0.414551 0.0888420i
\(478\) 5.65628 0.0735999i 0.258712 0.00336638i
\(479\) −2.12141 −0.0969295 −0.0484648 0.998825i \(-0.515433\pi\)
−0.0484648 + 0.998825i \(0.515433\pi\)
\(480\) −5.92399 16.1188i −0.270392 0.735718i
\(481\) −20.3457 −0.927686
\(482\) −4.62399 + 0.0601676i −0.210617 + 0.00274056i
\(483\) 6.04208 + 3.28714i 0.274924 + 0.149570i
\(484\) 0.756023 + 29.0459i 0.0343647 + 1.32027i
\(485\) −9.51515 + 9.51515i −0.432061 + 0.432061i
\(486\) −13.5741 17.3707i −0.615736 0.787953i
\(487\) 34.1205 1.54615 0.773073 0.634316i \(-0.218718\pi\)
0.773073 + 0.634316i \(0.218718\pi\)
\(488\) 13.8736 15.0013i 0.628029 0.679077i
\(489\) −27.2763 + 8.05474i −1.23348 + 0.364248i
\(490\) 1.72975 1.77536i 0.0781421 0.0802024i
\(491\) −2.32777 2.32777i −0.105051 0.105051i 0.652628 0.757679i \(-0.273666\pi\)
−0.757679 + 0.652628i \(0.773666\pi\)
\(492\) −6.20158 + 12.1414i −0.279589 + 0.547376i
\(493\) 10.4955 10.4955i 0.472694 0.472694i
\(494\) 16.9365 0.220378i 0.762007 0.00991529i
\(495\) −14.4319 22.3049i −0.648664 1.00253i
\(496\) −0.259340 4.97846i −0.0116447 0.223539i
\(497\) 6.13227i 0.275070i
\(498\) 12.6613 + 40.9084i 0.567366 + 1.83315i
\(499\) 16.4946 + 16.4946i 0.738401 + 0.738401i 0.972269 0.233867i \(-0.0751381\pi\)
−0.233867 + 0.972269i \(0.575138\pi\)
\(500\) −17.6135 16.7198i −0.787699 0.747734i
\(501\) 7.49134 + 4.07560i 0.334688 + 0.182084i
\(502\) 5.10779 + 4.97657i 0.227972 + 0.222115i
\(503\) 21.0199i 0.937231i −0.883402 0.468616i \(-0.844753\pi\)
0.883402 0.468616i \(-0.155247\pi\)
\(504\) −4.88398 6.93878i −0.217550 0.309078i
\(505\) 12.6486i 0.562856i
\(506\) 19.8019 20.3241i 0.880303 0.903514i
\(507\) 12.0896 + 6.57726i 0.536919 + 0.292106i
\(508\) −0.116202 4.46442i −0.00515564 0.198076i
\(509\) 15.8208 + 15.8208i 0.701244 + 0.701244i 0.964678 0.263433i \(-0.0848549\pi\)
−0.263433 + 0.964678i \(0.584855\pi\)
\(510\) −9.05569 + 2.80277i −0.400993 + 0.124109i
\(511\) 10.2246i 0.452308i
\(512\) −22.4725 + 2.64366i −0.993151 + 0.116835i
\(513\) 21.0049 + 18.0314i 0.927391 + 0.796108i
\(514\) 0.313615 + 24.1019i 0.0138330 + 1.06309i
\(515\) −21.3457 + 21.3457i −0.940606 + 0.940606i
\(516\) −1.79678 5.54872i −0.0790990 0.244269i
\(517\) −29.5128 29.5128i −1.29797 1.29797i
\(518\) −9.16719 8.93169i −0.402783 0.392436i
\(519\) 4.52246 1.33549i 0.198514 0.0586216i
\(520\) −0.434911 11.1362i −0.0190721 0.488355i
\(521\) 9.99923 0.438074 0.219037 0.975717i \(-0.429708\pi\)
0.219037 + 0.975717i \(0.429708\pi\)
\(522\) −5.61309 + 27.9624i −0.245678 + 1.22388i
\(523\) −17.9456 + 17.9456i −0.784708 + 0.784708i −0.980621 0.195913i \(-0.937233\pi\)
0.195913 + 0.980621i \(0.437233\pi\)
\(524\) 9.69341 10.2115i 0.423458 0.446092i
\(525\) −2.93344 1.59591i −0.128026 0.0696514i
\(526\) −0.486588 37.3951i −0.0212162 1.63050i
\(527\) −2.75186 −0.119873
\(528\) −33.0105 + 11.6468i −1.43660 + 0.506862i
\(529\) 7.22933 0.314319
\(530\) −0.0995403 7.64984i −0.00432375 0.332288i
\(531\) 4.84750 22.6192i 0.210364 0.981590i
\(532\) 7.72781 + 7.33573i 0.335043 + 0.318044i
\(533\) −6.25630 + 6.25630i −0.270990 + 0.270990i
\(534\) −10.4584 + 19.8340i −0.452580 + 0.858303i
\(535\) 22.2655 0.962621
\(536\) 21.2581 + 19.6601i 0.918209 + 0.849185i
\(537\) −2.29350 7.76662i −0.0989718 0.335154i
\(538\) 16.6122 + 16.1854i 0.716201 + 0.697802i
\(539\) −3.57267 3.57267i −0.153886 0.153886i
\(540\) 11.5006 14.1247i 0.494907 0.607832i
\(541\) −19.7562 + 19.7562i −0.849384 + 0.849384i −0.990056 0.140672i \(-0.955074\pi\)
0.140672 + 0.990056i \(0.455074\pi\)
\(542\) 0.129325 + 9.93888i 0.00555500 + 0.426912i
\(543\) 33.2418 9.81638i 1.42654 0.421261i
\(544\) 0.812012 + 12.4640i 0.0348147 + 0.534390i
\(545\) 24.5676i 1.05236i
\(546\) −1.62814 5.26050i −0.0696780 0.225128i
\(547\) 13.7252 + 13.7252i 0.586847 + 0.586847i 0.936776 0.349929i \(-0.113794\pi\)
−0.349929 + 0.936776i \(0.613794\pi\)
\(548\) 10.2791 0.267549i 0.439099 0.0114291i
\(549\) 21.1915 + 4.54153i 0.904432 + 0.193828i
\(550\) −9.61388 + 9.86737i −0.409937 + 0.420746i
\(551\) 35.8134i 1.52570i
\(552\) 17.4394 + 8.62345i 0.742270 + 0.367038i
\(553\) 6.53910i 0.278071i
\(554\) −4.36106 4.24903i −0.185284 0.180524i
\(555\) 13.1298 24.1339i 0.557331 1.02443i
\(556\) 26.0190 27.4096i 1.10345 1.16243i
\(557\) −6.97099 6.97099i −0.295370 0.295370i 0.543827 0.839197i \(-0.316975\pi\)
−0.839197 + 0.543827i \(0.816975\pi\)
\(558\) 4.40164 2.92992i 0.186336 0.124033i
\(559\) 3.78504i 0.160090i
\(560\) 4.69278 5.20857i 0.198306 0.220102i
\(561\) 5.47245 + 18.5317i 0.231047 + 0.782408i
\(562\) −13.5326 + 0.176087i −0.570839 + 0.00742780i
\(563\) −12.0301 + 12.0301i −0.507009 + 0.507009i −0.913607 0.406598i \(-0.866715\pi\)
0.406598 + 0.913607i \(0.366715\pi\)
\(564\) 13.0168 25.4841i 0.548105 1.07307i
\(565\) 17.6276 + 17.6276i 0.741597 + 0.741597i
\(566\) 22.2545 22.8413i 0.935426 0.960091i
\(567\) 3.68817 8.20959i 0.154889 0.344770i
\(568\) −0.676860 17.3315i −0.0284004 0.727212i
\(569\) 5.33785 0.223774 0.111887 0.993721i \(-0.464310\pi\)
0.111887 + 0.993721i \(0.464310\pi\)
\(570\) −10.6683 + 20.2321i −0.446846 + 0.847428i
\(571\) 29.1035 29.1035i 1.21795 1.21795i 0.249595 0.968350i \(-0.419703\pi\)
0.968350 0.249595i \(-0.0802974\pi\)
\(572\) −22.7094 + 0.591092i −0.949527 + 0.0247148i
\(573\) −7.00940 + 12.8839i −0.292822 + 0.538235i
\(574\) −5.56539 + 0.0724172i −0.232295 + 0.00302264i
\(575\) 7.65669 0.319306
\(576\) −14.5693 19.0718i −0.607056 0.794659i
\(577\) −8.17753 −0.340435 −0.170217 0.985407i \(-0.554447\pi\)
−0.170217 + 0.985407i \(0.554447\pi\)
\(578\) −17.1454 + 0.223097i −0.713155 + 0.00927962i
\(579\) −14.3011 + 26.2867i −0.594332 + 1.09244i
\(580\) −23.5563 + 0.613136i −0.978123 + 0.0254591i
\(581\) −12.3619 + 12.3619i −0.512859 + 0.512859i
\(582\) −8.77164 + 16.6351i −0.363596 + 0.689548i
\(583\) −15.5946 −0.645862
\(584\) −1.12855 28.8974i −0.0466999 1.19578i
\(585\) 9.92447 6.42140i 0.410327 0.265492i
\(586\) −1.79629 + 1.84365i −0.0742040 + 0.0761605i
\(587\) −25.8580 25.8580i −1.06727 1.06727i −0.997568 0.0697047i \(-0.977794\pi\)
−0.0697047 0.997568i \(-0.522206\pi\)
\(588\) 1.57574 3.08497i 0.0649824 0.127222i
\(589\) −4.69502 + 4.69502i −0.193455 + 0.193455i
\(590\) 19.1114 0.248679i 0.786805 0.0102380i
\(591\) −11.4085 38.6332i −0.469281 1.58916i
\(592\) −26.8948 24.2315i −1.10537 0.995910i
\(593\) 18.1350i 0.744714i 0.928090 + 0.372357i \(0.121450\pi\)
−0.928090 + 0.372357i \(0.878550\pi\)
\(594\) −28.4841 23.8152i −1.16872 0.977148i
\(595\) −2.73650 2.73650i −0.112185 0.112185i
\(596\) −27.9462 + 29.4399i −1.14472 + 1.20591i
\(597\) 6.79521 12.4902i 0.278109 0.511192i
\(598\) 9.04312 + 8.81080i 0.369801 + 0.360300i
\(599\) 4.71552i 0.192671i −0.995349 0.0963354i \(-0.969288\pi\)
0.995349 0.0963354i \(-0.0307122\pi\)
\(600\) −8.46686 4.18670i −0.345658 0.170921i
\(601\) 14.1554i 0.577413i −0.957418 0.288706i \(-0.906775\pi\)
0.957418 0.288706i \(-0.0932251\pi\)
\(602\) 1.66162 1.70543i 0.0677224 0.0695081i
\(603\) −6.43572 + 30.0301i −0.262083 + 1.22292i
\(604\) −35.0789 + 0.913052i −1.42734 + 0.0371515i
\(605\) −18.0051 18.0051i −0.732011 0.732011i
\(606\) −5.22652 16.8868i −0.212313 0.685978i
\(607\) 7.96072i 0.323116i −0.986863 0.161558i \(-0.948348\pi\)
0.986863 0.161558i \(-0.0516518\pi\)
\(608\) 22.6506 + 19.8798i 0.918603 + 0.806232i
\(609\) −11.1666 + 3.29753i −0.452494 + 0.133623i
\(610\) 0.232983 + 17.9051i 0.00943320 + 0.724958i
\(611\) 13.1316 13.1316i 0.531249 0.531249i
\(612\) −10.9318 + 7.48377i −0.441894 + 0.302514i
\(613\) 17.7697 + 17.7697i 0.717713 + 0.717713i 0.968136 0.250423i \(-0.0805697\pi\)
−0.250423 + 0.968136i \(0.580570\pi\)
\(614\) −9.34037 9.10041i −0.376947 0.367263i
\(615\) −3.38374 11.4586i −0.136446 0.462054i
\(616\) −10.4917 9.70299i −0.422721 0.390945i
\(617\) 21.7284 0.874752 0.437376 0.899279i \(-0.355908\pi\)
0.437376 + 0.899279i \(0.355908\pi\)
\(618\) −19.6778 + 37.3183i −0.791557 + 1.50116i
\(619\) −19.6253 + 19.6253i −0.788807 + 0.788807i −0.981299 0.192491i \(-0.938343\pi\)
0.192491 + 0.981299i \(0.438343\pi\)
\(620\) 3.16853 + 3.00777i 0.127251 + 0.120795i
\(621\) 1.56729 + 20.5755i 0.0628930 + 0.825667i
\(622\) −0.328033 25.2099i −0.0131529 1.01083i
\(623\) −9.15394 −0.366745
\(624\) −5.18221 14.6879i −0.207454 0.587986i
\(625\) 11.6425 0.465698
\(626\) 0.0896901 + 6.89284i 0.00358474 + 0.275493i
\(627\) 40.9541 + 22.2807i 1.63555 + 0.889807i
\(628\) 18.1047 19.0723i 0.722455 0.761069i
\(629\) −14.1301 + 14.1301i −0.563405 + 0.563405i
\(630\) 7.29064 + 1.46350i 0.290466 + 0.0583073i
\(631\) −26.1699 −1.04181 −0.520904 0.853616i \(-0.674405\pi\)
−0.520904 + 0.853616i \(0.674405\pi\)
\(632\) −0.721765 18.4813i −0.0287103 0.735146i
\(633\) −36.4924 + 10.7763i −1.45044 + 0.428319i
\(634\) −7.12174 6.93879i −0.282841 0.275574i
\(635\) 2.76742 + 2.76742i 0.109822 + 0.109822i
\(636\) −3.29387 10.1719i −0.130611 0.403344i
\(637\) 1.58965 1.58965i 0.0629840 0.0629840i
\(638\) 0.624954 + 48.0288i 0.0247422 + 1.90148i
\(639\) 15.4456 9.99374i 0.611020 0.395346i
\(640\) 12.6882 15.2388i 0.501544 0.602367i
\(641\) 19.6364i 0.775592i 0.921745 + 0.387796i \(0.126763\pi\)
−0.921745 + 0.387796i \(0.873237\pi\)
\(642\) 29.7260 9.20029i 1.17319 0.363106i
\(643\) 8.37406 + 8.37406i 0.330241 + 0.330241i 0.852678 0.522437i \(-0.174977\pi\)
−0.522437 + 0.852678i \(0.674977\pi\)
\(644\) 0.206661 + 7.93977i 0.00814357 + 0.312871i
\(645\) 4.48978 + 2.44262i 0.176785 + 0.0961782i
\(646\) 11.6093 11.9154i 0.456762 0.468806i
\(647\) 15.9115i 0.625544i −0.949828 0.312772i \(-0.898742\pi\)
0.949828 0.312772i \(-0.101258\pi\)
\(648\) 9.51763 23.6096i 0.373888 0.927474i
\(649\) 38.9596i 1.52930i
\(650\) −4.39045 4.27766i −0.172208 0.167784i
\(651\) 1.89620 + 1.03161i 0.0743180 + 0.0404321i
\(652\) −23.8181 22.6097i −0.932789 0.885462i
\(653\) −7.56494 7.56494i −0.296039 0.296039i 0.543421 0.839460i \(-0.317129\pi\)
−0.839460 + 0.543421i \(0.817129\pi\)
\(654\) 10.1515 + 32.7994i 0.396956 + 1.28256i
\(655\) 12.3387i 0.482114i
\(656\) −15.7213 + 0.818960i −0.613814 + 0.0319750i
\(657\) 25.7531 16.6630i 1.00472 0.650084i
\(658\) 11.6814 0.152000i 0.455390 0.00592557i
\(659\) 21.0236 21.0236i 0.818963 0.818963i −0.166995 0.985958i \(-0.553406\pi\)
0.985958 + 0.166995i \(0.0534063\pi\)
\(660\) 13.9540 27.3191i 0.543160 1.06339i
\(661\) 18.6305 + 18.6305i 0.724643 + 0.724643i 0.969547 0.244904i \(-0.0787565\pi\)
−0.244904 + 0.969547i \(0.578756\pi\)
\(662\) −13.9229 + 14.2900i −0.541130 + 0.555398i
\(663\) −8.24561 + 2.43495i −0.320233 + 0.0945655i
\(664\) −33.5737 + 36.3027i −1.30291 + 1.40882i
\(665\) −9.33763 −0.362098
\(666\) 7.55691 37.6458i 0.292824 1.45874i
\(667\) 18.8767 18.8767i 0.730910 0.730910i
\(668\) 0.256230 + 9.84421i 0.00991385 + 0.380884i
\(669\) 6.96887 + 3.79135i 0.269432 + 0.146582i
\(670\) −25.3730 + 0.330156i −0.980246 + 0.0127550i
\(671\) 36.5005 1.40909
\(672\) 4.11296 8.89289i 0.158661 0.343051i
\(673\) 48.8310 1.88230 0.941148 0.337995i \(-0.109749\pi\)
0.941148 + 0.337995i \(0.109749\pi\)
\(674\) −10.1269 + 0.131772i −0.390074 + 0.00507567i
\(675\) −0.760921 9.98945i −0.0292879 0.384494i
\(676\) 0.413508 + 15.8867i 0.0159042 + 0.611028i
\(677\) −17.2859 + 17.2859i −0.664352 + 0.664352i −0.956403 0.292051i \(-0.905662\pi\)
0.292051 + 0.956403i \(0.405662\pi\)
\(678\) 30.8179 + 16.2502i 1.18355 + 0.624084i
\(679\) −7.67756 −0.294638
\(680\) −8.03613 7.43204i −0.308172 0.285006i
\(681\) 11.0988 + 37.5845i 0.425306 + 1.44024i
\(682\) 6.21449 6.37835i 0.237965 0.244240i
\(683\) −18.1722 18.1722i −0.695338 0.695338i 0.268063 0.963401i \(-0.413616\pi\)
−0.963401 + 0.268063i \(0.913616\pi\)
\(684\) −5.88285 + 31.4194i −0.224936 + 1.20135i
\(685\) −6.37181 + 6.37181i −0.243454 + 0.243454i
\(686\) 1.41409 0.0184003i 0.0539904 0.000702526i
\(687\) −9.79014 + 2.89105i −0.373517 + 0.110300i
\(688\) 4.50794 5.00341i 0.171864 0.190753i
\(689\) 6.93876i 0.264346i
\(690\) −16.2871 + 5.04092i −0.620040 + 0.191905i
\(691\) 28.3836 + 28.3836i 1.07976 + 1.07976i 0.996530 + 0.0832314i \(0.0265241\pi\)
0.0832314 + 0.996530i \(0.473476\pi\)
\(692\) 3.94909 + 3.74873i 0.150122 + 0.142505i
\(693\) 3.17628 14.8210i 0.120657 0.563003i
\(694\) 10.8776 + 10.5981i 0.412907 + 0.402300i
\(695\) 33.1195i 1.25629i
\(696\) −31.1959 + 10.5522i −1.18248 + 0.399982i
\(697\) 8.69000i 0.329157i
\(698\) 10.6526 10.9335i 0.403207 0.413838i
\(699\) −6.19022 + 11.3782i −0.234136 + 0.430364i
\(700\) −0.100334 3.85477i −0.00379227 0.145697i
\(701\) 8.31473 + 8.31473i 0.314043 + 0.314043i 0.846474 0.532431i \(-0.178721\pi\)
−0.532431 + 0.846474i \(0.678721\pi\)
\(702\) 10.5965 12.6739i 0.399938 0.478345i
\(703\) 48.2156i 1.81849i
\(704\) −30.7233 26.2653i −1.15793 0.989909i
\(705\) 7.10228 + 24.0509i 0.267487 + 0.905809i
\(706\) 0.346584 + 26.6356i 0.0130439 + 1.00244i
\(707\) 5.10294 5.10294i 0.191916 0.191916i
\(708\) 25.4123 8.22900i 0.955053 0.309265i
\(709\) −34.8067 34.8067i −1.30719 1.30719i −0.923434 0.383757i \(-0.874630\pi\)
−0.383757 0.923434i \(-0.625370\pi\)
\(710\) 10.8870 + 10.6073i 0.408580 + 0.398084i
\(711\) 16.4703 10.6568i 0.617686 0.399660i
\(712\) −25.8715 + 1.01038i −0.969576 + 0.0378657i
\(713\) −4.94935 −0.185355
\(714\) −4.78416 2.52267i −0.179043 0.0944085i
\(715\) 14.0772 14.0772i 0.526456 0.526456i
\(716\) 6.43785 6.78194i 0.240594 0.253453i
\(717\) −3.31090 + 6.08575i −0.123648 + 0.227276i
\(718\) 0.291105 + 22.3719i 0.0108639 + 0.834914i
\(719\) −7.90389 −0.294765 −0.147383 0.989080i \(-0.547085\pi\)
−0.147383 + 0.989080i \(0.547085\pi\)
\(720\) 20.7669 + 3.33154i 0.773936 + 0.124159i
\(721\) −17.2234 −0.641432
\(722\) −0.172650 13.2684i −0.00642536 0.493800i
\(723\) 2.70665 4.97507i 0.100661 0.185025i
\(724\) 29.0273 + 27.5546i 1.07879 + 1.02406i
\(725\) −9.16469 + 9.16469i −0.340368 + 0.340368i
\(726\) −31.4779 16.5982i −1.16825 0.616016i
\(727\) −28.1472 −1.04392 −0.521960 0.852970i \(-0.674799\pi\)
−0.521960 + 0.852970i \(0.674799\pi\)
\(728\) 4.31731 4.66823i 0.160010 0.173016i
\(729\) 26.6885 4.08958i 0.988462 0.151466i
\(730\) 18.1523 + 17.6859i 0.671845 + 0.654586i
\(731\) −2.62871 2.62871i −0.0972264 0.0972264i
\(732\) 7.70960 + 23.8083i 0.284955 + 0.879981i
\(733\) 28.6742 28.6742i 1.05911 1.05911i 0.0609673 0.998140i \(-0.480581\pi\)
0.998140 0.0609673i \(-0.0194185\pi\)
\(734\) 0.471198 + 36.2124i 0.0173922 + 1.33662i
\(735\) 0.859765 + 2.91147i 0.0317129 + 0.107391i
\(736\) 1.46045 + 22.4171i 0.0538327 + 0.826307i
\(737\) 51.7242i 1.90529i
\(738\) −9.25230 13.8998i −0.340582 0.511658i
\(739\) 1.83024 + 1.83024i 0.0673263 + 0.0673263i 0.739968 0.672642i \(-0.234841\pi\)
−0.672642 + 0.739968i \(0.734841\pi\)
\(740\) 31.7139 0.825465i 1.16582 0.0303447i
\(741\) −9.91374 + 18.2224i −0.364190 + 0.669417i
\(742\) 3.04608 3.12640i 0.111825 0.114774i
\(743\) 1.62576i 0.0596432i 0.999555 + 0.0298216i \(0.00949392\pi\)
−0.999555 + 0.0298216i \(0.990506\pi\)
\(744\) 5.47305 + 2.70632i 0.200652 + 0.0992185i
\(745\) 35.5727i 1.30328i
\(746\) 29.8336 + 29.0672i 1.09229 + 1.06423i
\(747\) −51.2828 10.9904i −1.87634 0.402116i
\(748\) −15.3612 + 16.1822i −0.561659 + 0.591679i
\(749\) 8.98275 + 8.98275i 0.328223 + 0.328223i
\(750\) 28.4138 8.79418i 1.03753 0.321118i
\(751\) 30.5920i 1.11632i 0.829734 + 0.558159i \(0.188492\pi\)
−0.829734 + 0.558159i \(0.811508\pi\)
\(752\) 32.9982 1.71895i 1.20332 0.0626838i
\(753\) −8.37645 + 2.47358i −0.305255 + 0.0901424i
\(754\) −21.3703 + 0.278071i −0.778259 + 0.0101268i
\(755\) 21.7448 21.7448i 0.791374 0.791374i
\(756\) 10.3382 1.05868i 0.375998 0.0385037i
\(757\) −11.0220 11.0220i −0.400602 0.400602i 0.477843 0.878445i \(-0.341419\pi\)
−0.878445 + 0.477843i \(0.841419\pi\)
\(758\) −10.2010 + 10.4700i −0.370517 + 0.380286i
\(759\) 9.84247 + 33.3302i 0.357259 + 1.20981i
\(760\) −26.3907 + 1.03066i −0.957291 + 0.0373859i
\(761\) 2.53536 0.0919066 0.0459533 0.998944i \(-0.485367\pi\)
0.0459533 + 0.998944i \(0.485367\pi\)
\(762\) 4.83821 + 2.55117i 0.175270 + 0.0924192i
\(763\) −9.91151 + 9.91151i −0.358821 + 0.358821i
\(764\) −16.9305 + 0.440677i −0.612525 + 0.0159431i
\(765\) 2.43288 11.3522i 0.0879610 0.410440i
\(766\) −22.4375 + 0.291958i −0.810700 + 0.0105489i
\(767\) 17.3349 0.625928
\(768\) 10.6428 25.5877i 0.384039 0.923317i
\(769\) −1.37099 −0.0494393 −0.0247196 0.999694i \(-0.507869\pi\)
−0.0247196 + 0.999694i \(0.507869\pi\)
\(770\) 12.5226 0.162944i 0.451282 0.00587211i
\(771\) −25.9319 14.1080i −0.933914 0.508088i
\(772\) −34.5429 + 0.899100i −1.24322 + 0.0323593i
\(773\) 3.38228 3.38228i 0.121652 0.121652i −0.643660 0.765312i \(-0.722585\pi\)
0.765312 + 0.643660i \(0.222585\pi\)
\(774\) 7.00347 + 1.40586i 0.251735 + 0.0505325i
\(775\) 2.40292 0.0863154
\(776\) −21.6989 + 0.847424i −0.778944 + 0.0304207i
\(777\) 15.0336 4.43946i 0.539328 0.159265i
\(778\) 3.37981 3.46892i 0.121172 0.124367i
\(779\) 14.8263 + 14.8263i 0.531206 + 0.531206i
\(780\) 12.1555 + 6.20880i 0.435238 + 0.222311i
\(781\) 21.9085 21.9085i 0.783949 0.783949i
\(782\) 12.3995 0.161344i 0.443407 0.00576964i
\(783\) −26.5039 22.7519i −0.947170 0.813087i
\(784\) 3.99458 0.208087i 0.142664 0.00743169i
\(785\) 23.0454i 0.822526i
\(786\) 5.09846 + 16.4730i 0.181856 + 0.587574i
\(787\) 37.7087 + 37.7087i 1.34417 + 1.34417i 0.891862 + 0.452308i \(0.149399\pi\)
0.452308 + 0.891862i \(0.350601\pi\)
\(788\) 32.0235 33.7351i 1.14079 1.20176i
\(789\) 40.2344 + 21.8892i 1.43238 + 0.779276i
\(790\) 11.6092 + 11.3110i 0.413038 + 0.402427i
\(791\) 14.2233i 0.505721i
\(792\) 7.34113 42.2388i 0.260856 1.50089i
\(793\) 16.2408i 0.576727i
\(794\) 3.20266 3.28711i 0.113658 0.116655i
\(795\) 8.23068 + 4.47783i 0.291912 + 0.158812i
\(796\) 16.4132 0.427211i 0.581750 0.0151421i
\(797\) 11.4184 + 11.4184i 0.404459 + 0.404459i 0.879801 0.475342i \(-0.157676\pi\)
−0.475342 + 0.879801i \(0.657676\pi\)
\(798\) −12.4664 + 3.85839i −0.441305 + 0.136586i
\(799\) 18.2398i 0.645278i
\(800\) −0.709049 10.8836i −0.0250687 0.384792i
\(801\) −14.9182 23.0565i −0.527107 0.814660i
\(802\) 0.0842468 + 6.47451i 0.00297486 + 0.228623i
\(803\) 36.5290 36.5290i 1.28908 1.28908i
\(804\) −33.7383 + 10.9251i −1.18986 + 0.385300i
\(805\) −4.92173 4.92173i −0.173468 0.173468i
\(806\) 2.83803 + 2.76512i 0.0999652 + 0.0973971i
\(807\) −27.2429 + 8.04489i −0.958995 + 0.283193i
\(808\) 13.8590 14.9855i 0.487560 0.527189i
\(809\) −10.3878 −0.365216 −0.182608 0.983186i \(-0.558454\pi\)
−0.182608 + 0.983186i \(0.558454\pi\)
\(810\) 8.19535 + 20.7483i 0.287955 + 0.729023i
\(811\) 20.4489 20.4489i 0.718058 0.718058i −0.250149 0.968207i \(-0.580480\pi\)
0.968207 + 0.250149i \(0.0804797\pi\)
\(812\) −9.75088 9.25616i −0.342189 0.324827i
\(813\) −10.6935 5.81772i −0.375038 0.204036i
\(814\) −0.841376 64.6612i −0.0294902 2.26638i
\(815\) 28.7798 1.00811
\(816\) −13.7998 6.60169i −0.483089 0.231105i
\(817\) −8.96984 −0.313815
\(818\) 0.634202 + 48.7395i 0.0221743 + 1.70414i
\(819\) 6.59455 + 1.41327i 0.230432 + 0.0493837i
\(820\) 9.49815 10.0058i 0.331690 0.349418i
\(821\) 11.8610 11.8610i 0.413952 0.413952i −0.469161 0.883113i \(-0.655444\pi\)
0.883113 + 0.469161i \(0.155444\pi\)
\(822\) −5.87392 + 11.1397i −0.204877 + 0.388541i
\(823\) 4.69616 0.163698 0.0818490 0.996645i \(-0.473917\pi\)
0.0818490 + 0.996645i \(0.473917\pi\)
\(824\) −48.6780 + 1.90106i −1.69578 + 0.0662266i
\(825\) −4.77854 16.1819i −0.166367 0.563380i
\(826\) 7.81061 + 7.60995i 0.271766 + 0.264784i
\(827\) 13.0079 + 13.0079i 0.452329 + 0.452329i 0.896127 0.443798i \(-0.146369\pi\)
−0.443798 + 0.896127i \(0.646369\pi\)
\(828\) −19.6615 + 13.4600i −0.683284 + 0.467766i
\(829\) −20.0165 + 20.0165i −0.695203 + 0.695203i −0.963372 0.268169i \(-0.913582\pi\)
0.268169 + 0.963372i \(0.413582\pi\)
\(830\) −0.563811 43.3299i −0.0195702 1.50400i
\(831\) 7.15187 2.11196i 0.248096 0.0732632i
\(832\) 11.6866 13.6702i 0.405161 0.473930i
\(833\) 2.20802i 0.0765032i
\(834\) 13.6853 + 44.2168i 0.473882 + 1.53110i
\(835\) −6.10226 6.10226i −0.211177 0.211177i
\(836\) 1.40078 + 53.8170i 0.0484469 + 1.86130i
\(837\) 0.491866 + 6.45727i 0.0170014 + 0.223196i
\(838\) 27.3684 28.0900i 0.945426 0.970354i
\(839\) 35.4357i 1.22338i −0.791099 0.611688i \(-0.790491\pi\)
0.791099 0.611688i \(-0.209509\pi\)
\(840\) 2.75129 + 8.13372i 0.0949285 + 0.280640i
\(841\) 16.1890i 0.558243i
\(842\) −30.0253 29.2539i −1.03474 1.00816i
\(843\) 7.92131 14.5601i 0.272824 0.501477i
\(844\) −31.8658 30.2490i −1.09687 1.04121i
\(845\) −9.84792 9.84792i −0.338779 0.338779i
\(846\) 19.4201 + 29.1749i 0.667676 + 1.00305i
\(847\) 14.5279i 0.499184i
\(848\) 8.26398 9.17227i 0.283786 0.314977i
\(849\) 11.0615 + 37.4583i 0.379630 + 1.28557i
\(850\) −6.02000 + 0.0783326i −0.206484 + 0.00268679i
\(851\) −25.4137 + 25.4137i −0.871172 + 0.871172i
\(852\) 18.9179 + 9.66286i 0.648115 + 0.331044i
\(853\) 4.77904 + 4.77904i 0.163631 + 0.163631i 0.784173 0.620542i \(-0.213087\pi\)
−0.620542 + 0.784173i \(0.713087\pi\)
\(854\) −7.12962 + 7.31761i −0.243971 + 0.250404i
\(855\) −15.2175 23.5191i −0.520428 0.804338i
\(856\) 26.3792 + 24.3962i 0.901623 + 0.833846i
\(857\) 13.0169 0.444647 0.222324 0.974973i \(-0.428636\pi\)
0.222324 + 0.974973i \(0.428636\pi\)
\(858\) 12.9772 24.6108i 0.443034 0.840199i
\(859\) −13.5335 + 13.5335i −0.461758 + 0.461758i −0.899231 0.437473i \(-0.855873\pi\)
0.437473 + 0.899231i \(0.355873\pi\)
\(860\) 0.153566 + 5.89992i 0.00523657 + 0.201186i
\(861\) 3.25770 5.98796i 0.111022 0.204069i
\(862\) 40.7529 0.530279i 1.38805 0.0180614i
\(863\) −28.1516 −0.958293 −0.479146 0.877735i \(-0.659054\pi\)
−0.479146 + 0.877735i \(0.659054\pi\)
\(864\) 29.1018 4.13321i 0.990064 0.140615i
\(865\) −4.77175 −0.162244
\(866\) −42.0904 + 0.547683i −1.43029 + 0.0186110i
\(867\) 10.0361 18.4472i 0.340842 0.626501i
\(868\) 0.0648569 + 2.49176i 0.00220139 + 0.0845759i
\(869\) 23.3620 23.3620i 0.792502 0.792502i
\(870\) 13.4612 25.5286i 0.456376 0.865502i
\(871\) −23.0145 −0.779817
\(872\) −26.9186 + 29.1066i −0.911579 + 0.985674i
\(873\) −12.5121 19.3378i −0.423470 0.654486i
\(874\) 20.8799 21.4305i 0.706275 0.724897i
\(875\) 8.58624 + 8.58624i 0.290268 + 0.290268i
\(876\) 31.5425 + 16.1113i 1.06572 + 0.544349i
\(877\) −31.2389 + 31.2389i −1.05486 + 1.05486i −0.0564564 + 0.998405i \(0.517980\pi\)
−0.998405 + 0.0564564i \(0.982020\pi\)
\(878\) 14.7887 0.192431i 0.499094 0.00649425i
\(879\) −0.892838 3.02347i −0.0301147 0.101979i
\(880\) 35.3742 1.84273i 1.19246 0.0621183i
\(881\) 36.9138i 1.24366i −0.783154 0.621828i \(-0.786390\pi\)
0.783154 0.621828i \(-0.213610\pi\)
\(882\) 2.35089 + 3.53176i 0.0791586 + 0.118920i
\(883\) −14.6891 14.6891i −0.494329 0.494329i 0.415338 0.909667i \(-0.363663\pi\)
−0.909667 + 0.415338i \(0.863663\pi\)
\(884\) −7.20020 6.83489i −0.242169 0.229882i
\(885\) −11.1869 + 20.5625i −0.376042 + 0.691201i
\(886\) −27.3546 26.6519i −0.918996 0.895387i
\(887\) 8.84622i 0.297027i 0.988910 + 0.148514i \(0.0474488\pi\)
−0.988910 + 0.148514i \(0.952551\pi\)
\(888\) 41.9991 14.2065i 1.40940 0.476739i
\(889\) 2.23296i 0.0748912i
\(890\) 15.8340 16.2515i 0.530757 0.544752i
\(891\) 42.5067 16.1535i 1.42403 0.541163i
\(892\) 0.238360 + 9.15764i 0.00798088 + 0.306621i
\(893\) −31.1195 31.1195i −1.04137 1.04137i
\(894\) −14.6989 47.4920i −0.491606 1.58837i
\(895\) 8.19473i 0.273920i
\(896\) 11.2668 1.02902i 0.376398 0.0343772i
\(897\) −14.8301 + 4.37937i −0.495164 + 0.146223i
\(898\) 0.489431 + 37.6136i 0.0163325 + 1.25518i
\(899\) 5.92413 5.92413i 0.197581 0.197581i
\(900\) 9.54569 6.53483i 0.318190 0.217828i
\(901\) −4.81897 4.81897i −0.160543 0.160543i
\(902\) −20.1420 19.6246i −0.670655 0.653426i
\(903\) 0.825900 + 2.79680i 0.0274842 + 0.0930716i
\(904\) 1.56992 + 40.1989i 0.0522147 + 1.33699i
\(905\) −35.0742 −1.16591
\(906\) 20.0457 38.0159i 0.665973 1.26300i
\(907\) −26.6472 + 26.6472i −0.884804 + 0.884804i −0.994018 0.109214i \(-0.965167\pi\)
0.109214 + 0.994018i \(0.465167\pi\)
\(908\) −31.1542 + 32.8194i −1.03389 + 1.08915i
\(909\) 21.1693 + 4.53676i 0.702140 + 0.150475i
\(910\) 0.0725016 + 5.57187i 0.00240340 + 0.184706i
\(911\) −48.5784 −1.60947 −0.804737 0.593632i \(-0.797694\pi\)
−0.804737 + 0.593632i \(0.797694\pi\)
\(912\) −34.8075 + 12.2809i −1.15259 + 0.406660i
\(913\) −88.3301 −2.92330
\(914\) 0.0938675 + 7.21388i 0.00310486 + 0.238614i
\(915\) −19.2646 10.4808i −0.636869 0.346483i
\(916\) −8.54891 8.11517i −0.282464 0.268133i
\(917\) −4.97791 + 4.97791i −0.164385 + 0.164385i
\(918\) −1.44276 16.1613i −0.0476183 0.533401i
\(919\) 31.5660 1.04126 0.520632 0.853781i \(-0.325696\pi\)
0.520632 + 0.853781i \(0.325696\pi\)
\(920\) −14.4534 13.3669i −0.476514 0.440694i
\(921\) 15.3176 4.52333i 0.504733 0.149049i
\(922\) −11.3054 11.0150i −0.372324 0.362759i
\(923\) 9.74813 + 9.74813i 0.320864 + 0.320864i
\(924\) 16.6512 5.39197i 0.547783 0.177383i
\(925\) 12.3384 12.3384i 0.405685 0.405685i
\(926\) −0.212101 16.3003i −0.00697008 0.535663i
\(927\) −28.0689 43.3813i −0.921904 1.42483i
\(928\) −28.5803 25.0842i −0.938195 0.823428i
\(929\) 8.25723i 0.270911i 0.990783 + 0.135456i \(0.0432498\pi\)
−0.990783 + 0.135456i \(0.956750\pi\)
\(930\) −5.11143 + 1.58201i −0.167610 + 0.0518760i
\(931\) −3.76716 3.76716i −0.123464 0.123464i
\(932\) −14.9519 + 0.389176i −0.489765 + 0.0127479i
\(933\) 27.1241 + 14.7566i 0.888002 + 0.483110i
\(934\) −24.3652 + 25.0077i −0.797254 + 0.818275i
\(935\) 19.5532i 0.639457i
\(936\) 18.7940 + 3.26641i 0.614301 + 0.106766i
\(937\) 11.4367i 0.373620i −0.982396 0.186810i \(-0.940185\pi\)
0.982396 0.186810i \(-0.0598149\pi\)
\(938\) −10.3697 10.1033i −0.338581 0.329883i
\(939\) −7.41620 4.03472i −0.242018 0.131668i
\(940\) −19.9361 + 21.0017i −0.650244 + 0.684998i
\(941\) 38.7594 + 38.7594i 1.26352 + 1.26352i 0.949375 + 0.314144i \(0.101717\pi\)
0.314144 + 0.949375i \(0.398283\pi\)
\(942\) 9.52256 + 30.7672i 0.310262 + 1.00245i
\(943\) 15.6294i 0.508963i
\(944\) 22.9149 + 20.6457i 0.745815 + 0.671960i
\(945\) −5.93211 + 6.91035i −0.192972 + 0.224794i
\(946\) 12.0293 0.156526i 0.391107 0.00508911i
\(947\) 11.9692 11.9692i 0.388948 0.388948i −0.485364 0.874312i \(-0.661313\pi\)
0.874312 + 0.485364i \(0.161313\pi\)
\(948\) 20.1729 + 10.3039i 0.655186 + 0.334656i
\(949\) 16.2534 + 16.2534i 0.527609 + 0.527609i
\(950\) −10.1373 + 10.4045i −0.328896 + 0.337568i
\(951\) 11.6792 3.44890i 0.378725 0.111838i
\(952\) −0.243714 6.24046i −0.00789881 0.202254i
\(953\) −30.7222 −0.995190 −0.497595 0.867409i \(-0.665783\pi\)
−0.497595 + 0.867409i \(0.665783\pi\)
\(954\) 12.8388 + 2.57723i 0.415672 + 0.0834408i
\(955\) 10.4950 10.4950i 0.339609 0.339609i
\(956\) −7.99715 + 0.208154i −0.258646 + 0.00673219i
\(957\) −51.6756 28.1136i −1.67043 0.908785i
\(958\) 2.99987 0.0390345i 0.0969213 0.00126115i
\(959\) −5.14127 −0.166020
\(960\) 8.67366 + 22.6844i 0.279941 + 0.732137i
\(961\) 29.4467 0.949895
\(962\) 28.7708 0.374367i 0.927608 0.0120701i
\(963\) −7.98611 + 37.2645i −0.257349 + 1.20083i
\(964\) 6.53764 0.170165i 0.210563 0.00548065i
\(965\) 21.4125 21.4125i 0.689294 0.689294i
\(966\) −8.60455 4.53715i −0.276847 0.145980i
\(967\) −14.1286 −0.454346 −0.227173 0.973854i \(-0.572948\pi\)
−0.227173 + 0.973854i \(0.572948\pi\)
\(968\) −1.60354 41.0597i −0.0515397 1.31971i
\(969\) 5.77036 + 19.5405i 0.185371 + 0.627733i
\(970\) 13.2802 13.6304i 0.426403 0.437646i
\(971\) −3.35904 3.35904i −0.107797 0.107797i 0.651151 0.758948i \(-0.274286\pi\)
−0.758948 + 0.651151i \(0.774286\pi\)
\(972\) 19.5147 + 24.3141i 0.625936 + 0.779875i
\(973\) −13.3617 + 13.3617i −0.428356 + 0.428356i
\(974\) −48.2496 + 0.627827i −1.54602 + 0.0201169i
\(975\) 7.20007 2.12619i 0.230587 0.0680927i
\(976\) −19.3426 + 21.4685i −0.619141 + 0.687190i
\(977\) 15.4506i 0.494310i 0.968976 + 0.247155i \(0.0794957\pi\)
−0.968976 + 0.247155i \(0.920504\pi\)
\(978\) 38.4230 11.8921i 1.22863 0.380266i
\(979\) −32.7040 32.7040i −1.04522 1.04522i
\(980\) −2.41336 + 2.54235i −0.0770919 + 0.0812124i
\(981\) −41.1173 8.81182i −1.31278 0.281340i
\(982\) 3.33451 + 3.24885i 0.106409 + 0.103675i
\(983\) 24.7893i 0.790655i 0.918540 + 0.395327i \(0.129369\pi\)
−0.918540 + 0.395327i \(0.870631\pi\)
\(984\) 8.54620 17.2832i 0.272443 0.550967i
\(985\) 40.7627i 1.29881i
\(986\) −14.6485 + 15.0348i −0.466504 + 0.478804i
\(987\) −6.83772 + 12.5684i −0.217647 + 0.400056i
\(988\) −23.9457 + 0.623271i −0.761814 + 0.0198289i
\(989\) −4.72787 4.72787i −0.150338 0.150338i
\(990\) 20.8184 + 31.2756i 0.661653 + 0.994005i
\(991\) 6.86472i 0.218065i 0.994038 + 0.109033i \(0.0347753\pi\)
−0.994038 + 0.109033i \(0.965225\pi\)
\(992\) 0.458336 + 7.03524i 0.0145522 + 0.223369i
\(993\) −6.92033 23.4348i −0.219610 0.743680i
\(994\) 0.112835 + 8.67160i 0.00357892 + 0.275046i
\(995\) −10.1743 + 10.1743i −0.322545 + 0.322545i
\(996\) −18.6570 57.6154i −0.591169 1.82561i
\(997\) −42.8927 42.8927i −1.35842 1.35842i −0.875861 0.482563i \(-0.839706\pi\)
−0.482563 0.875861i \(-0.660294\pi\)
\(998\) −23.6285 23.0215i −0.747946 0.728732i
\(999\) 35.6821 + 30.6309i 1.12893 + 0.969119i
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 336.2.s.c.155.1 40
3.2 odd 2 inner 336.2.s.c.155.20 yes 40
4.3 odd 2 1344.2.s.c.911.8 40
12.11 even 2 1344.2.s.c.911.16 40
16.3 odd 4 inner 336.2.s.c.323.20 yes 40
16.13 even 4 1344.2.s.c.239.16 40
48.29 odd 4 1344.2.s.c.239.8 40
48.35 even 4 inner 336.2.s.c.323.1 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.s.c.155.1 40 1.1 even 1 trivial
336.2.s.c.155.20 yes 40 3.2 odd 2 inner
336.2.s.c.323.1 yes 40 48.35 even 4 inner
336.2.s.c.323.20 yes 40 16.3 odd 4 inner
1344.2.s.c.239.8 40 48.29 odd 4
1344.2.s.c.239.16 40 16.13 even 4
1344.2.s.c.911.8 40 4.3 odd 2
1344.2.s.c.911.16 40 12.11 even 2