Properties

Label 336.2.s.d.155.2
Level $336$
Weight $2$
Character 336.155
Analytic conductor $2.683$
Analytic rank $0$
Dimension $48$
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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 155.2
Character \(\chi\) \(=\) 336.155
Dual form 336.2.s.d.323.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31976 - 0.508179i) q^{2} +(1.45100 - 0.945839i) q^{3} +(1.48351 + 1.34134i) q^{4} +(1.69539 - 1.69539i) q^{5} +(-2.39561 + 0.510910i) q^{6} +1.00000 q^{7} +(-1.27623 - 2.52413i) q^{8} +(1.21078 - 2.74482i) q^{9} +O(q^{10})\) \(q+(-1.31976 - 0.508179i) q^{2} +(1.45100 - 0.945839i) q^{3} +(1.48351 + 1.34134i) q^{4} +(1.69539 - 1.69539i) q^{5} +(-2.39561 + 0.510910i) q^{6} +1.00000 q^{7} +(-1.27623 - 2.52413i) q^{8} +(1.21078 - 2.74482i) q^{9} +(-3.09906 + 1.37594i) q^{10} +(0.445358 + 0.445358i) q^{11} +(3.42126 + 0.543124i) q^{12} +(-1.51259 + 1.51259i) q^{13} +(-1.31976 - 0.508179i) q^{14} +(0.856437 - 4.06356i) q^{15} +(0.401596 + 3.97979i) q^{16} -1.39276i q^{17} +(-2.99279 + 3.00719i) q^{18} +(0.965003 + 0.965003i) q^{19} +(4.78922 - 0.241025i) q^{20} +(1.45100 - 0.945839i) q^{21} +(-0.361442 - 0.814086i) q^{22} +6.04660i q^{23} +(-4.23922 - 2.45540i) q^{24} -0.748676i q^{25} +(2.76492 - 1.22759i) q^{26} +(-0.839319 - 5.12792i) q^{27} +(1.48351 + 1.34134i) q^{28} +(-4.93200 - 4.93200i) q^{29} +(-3.19530 + 4.92769i) q^{30} -0.470285i q^{31} +(1.49244 - 5.45643i) q^{32} +(1.06745 + 0.224976i) q^{33} +(-0.707773 + 1.83811i) q^{34} +(1.69539 - 1.69539i) q^{35} +(5.47794 - 2.44789i) q^{36} +(1.47646 + 1.47646i) q^{37} +(-0.783174 - 1.76396i) q^{38} +(-0.764098 + 3.62544i) q^{39} +(-6.44308 - 2.11569i) q^{40} -8.35300 q^{41} +(-2.39561 + 0.510910i) q^{42} +(8.97272 - 8.97272i) q^{43} +(0.0633144 + 1.25807i) q^{44} +(-2.60079 - 6.70626i) q^{45} +(3.07275 - 7.98003i) q^{46} -4.84660 q^{47} +(4.34695 + 5.39481i) q^{48} +1.00000 q^{49} +(-0.380461 + 0.988069i) q^{50} +(-1.31733 - 2.02089i) q^{51} +(-4.27286 + 0.215038i) q^{52} +(3.42232 - 3.42232i) q^{53} +(-1.49820 + 7.19412i) q^{54} +1.51011 q^{55} +(-1.27623 - 2.52413i) q^{56} +(2.31295 + 0.487478i) q^{57} +(4.00269 + 9.01537i) q^{58} +(6.61989 + 6.61989i) q^{59} +(6.72116 - 4.87955i) q^{60} +(-8.04415 + 8.04415i) q^{61} +(-0.238989 + 0.620661i) q^{62} +(1.21078 - 2.74482i) q^{63} +(-4.74249 + 6.44273i) q^{64} +5.12887i q^{65} +(-1.29445 - 0.839369i) q^{66} +(4.38159 + 4.38159i) q^{67} +(1.86817 - 2.06618i) q^{68} +(5.71911 + 8.77359i) q^{69} +(-3.09906 + 1.37594i) q^{70} +12.3448i q^{71} +(-8.47351 + 0.446841i) q^{72} -14.0195i q^{73} +(-1.19826 - 2.69887i) q^{74} +(-0.708126 - 1.08633i) q^{75} +(0.137190 + 2.72599i) q^{76} +(0.445358 + 0.445358i) q^{77} +(2.85079 - 4.39639i) q^{78} +16.5847i q^{79} +(7.42814 + 6.06642i) q^{80} +(-6.06803 - 6.64673i) q^{81} +(11.0239 + 4.24482i) q^{82} +(-9.24664 + 9.24664i) q^{83} +(3.42126 + 0.543124i) q^{84} +(-2.36127 - 2.36127i) q^{85} +(-16.4015 + 7.28205i) q^{86} +(-11.8212 - 2.49143i) q^{87} +(0.555766 - 1.69252i) q^{88} +5.25384 q^{89} +(0.0244230 + 10.1723i) q^{90} +(-1.51259 + 1.51259i) q^{91} +(-8.11057 + 8.97018i) q^{92} +(-0.444814 - 0.682381i) q^{93} +(6.39633 + 2.46294i) q^{94} +3.27211 q^{95} +(-2.99538 - 9.32886i) q^{96} +5.17660 q^{97} +(-1.31976 - 0.508179i) q^{98} +(1.76166 - 0.683197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31976 0.508179i −0.933208 0.359337i
\(3\) 1.45100 0.945839i 0.837733 0.546080i
\(4\) 1.48351 + 1.34134i 0.741754 + 0.670672i
\(5\) 1.69539 1.69539i 0.758200 0.758200i −0.217794 0.975995i \(-0.569886\pi\)
0.975995 + 0.217794i \(0.0698862\pi\)
\(6\) −2.39561 + 0.510910i −0.978006 + 0.208578i
\(7\) 1.00000 0.377964
\(8\) −1.27623 2.52413i −0.451214 0.892416i
\(9\) 1.21078 2.74482i 0.403593 0.914939i
\(10\) −3.09906 + 1.37594i −0.980008 + 0.435109i
\(11\) 0.445358 + 0.445358i 0.134281 + 0.134281i 0.771052 0.636772i \(-0.219731\pi\)
−0.636772 + 0.771052i \(0.719731\pi\)
\(12\) 3.42126 + 0.543124i 0.987633 + 0.156786i
\(13\) −1.51259 + 1.51259i −0.419518 + 0.419518i −0.885038 0.465519i \(-0.845868\pi\)
0.465519 + 0.885038i \(0.345868\pi\)
\(14\) −1.31976 0.508179i −0.352719 0.135816i
\(15\) 0.856437 4.06356i 0.221131 1.04921i
\(16\) 0.401596 + 3.97979i 0.100399 + 0.994947i
\(17\) 1.39276i 0.337795i −0.985634 0.168897i \(-0.945979\pi\)
0.985634 0.168897i \(-0.0540207\pi\)
\(18\) −2.99279 + 3.00719i −0.705407 + 0.708802i
\(19\) 0.965003 + 0.965003i 0.221387 + 0.221387i 0.809082 0.587695i \(-0.199965\pi\)
−0.587695 + 0.809082i \(0.699965\pi\)
\(20\) 4.78922 0.241025i 1.07090 0.0538948i
\(21\) 1.45100 0.945839i 0.316633 0.206399i
\(22\) −0.361442 0.814086i −0.0770598 0.173564i
\(23\) 6.04660i 1.26080i 0.776269 + 0.630402i \(0.217110\pi\)
−0.776269 + 0.630402i \(0.782890\pi\)
\(24\) −4.23922 2.45540i −0.865327 0.501207i
\(25\) 0.748676i 0.149735i
\(26\) 2.76492 1.22759i 0.542246 0.240749i
\(27\) −0.839319 5.12792i −0.161527 0.986868i
\(28\) 1.48351 + 1.34134i 0.280357 + 0.253490i
\(29\) −4.93200 4.93200i −0.915849 0.915849i 0.0808754 0.996724i \(-0.474228\pi\)
−0.996724 + 0.0808754i \(0.974228\pi\)
\(30\) −3.19530 + 4.92769i −0.583380 + 0.899668i
\(31\) 0.470285i 0.0844657i −0.999108 0.0422328i \(-0.986553\pi\)
0.999108 0.0422328i \(-0.0134471\pi\)
\(32\) 1.49244 5.45643i 0.263828 0.964570i
\(33\) 1.06745 + 0.224976i 0.185819 + 0.0391633i
\(34\) −0.707773 + 1.83811i −0.121382 + 0.315233i
\(35\) 1.69539 1.69539i 0.286573 0.286573i
\(36\) 5.47794 2.44789i 0.912990 0.407981i
\(37\) 1.47646 + 1.47646i 0.242729 + 0.242729i 0.817978 0.575249i \(-0.195095\pi\)
−0.575249 + 0.817978i \(0.695095\pi\)
\(38\) −0.783174 1.76396i −0.127048 0.286152i
\(39\) −0.764098 + 3.62544i −0.122354 + 0.580535i
\(40\) −6.44308 2.11569i −1.01874 0.334519i
\(41\) −8.35300 −1.30452 −0.652260 0.757996i \(-0.726179\pi\)
−0.652260 + 0.757996i \(0.726179\pi\)
\(42\) −2.39561 + 0.510910i −0.369651 + 0.0788352i
\(43\) 8.97272 8.97272i 1.36833 1.36833i 0.505500 0.862827i \(-0.331308\pi\)
0.862827 0.505500i \(-0.168692\pi\)
\(44\) 0.0633144 + 1.25807i 0.00954501 + 0.189661i
\(45\) −2.60079 6.70626i −0.387703 0.999711i
\(46\) 3.07275 7.98003i 0.453053 1.17659i
\(47\) −4.84660 −0.706949 −0.353475 0.935444i \(-0.615000\pi\)
−0.353475 + 0.935444i \(0.615000\pi\)
\(48\) 4.34695 + 5.39481i 0.627428 + 0.778674i
\(49\) 1.00000 0.142857
\(50\) −0.380461 + 0.988069i −0.0538053 + 0.139734i
\(51\) −1.31733 2.02089i −0.184463 0.282982i
\(52\) −4.27286 + 0.215038i −0.592538 + 0.0298204i
\(53\) 3.42232 3.42232i 0.470092 0.470092i −0.431852 0.901944i \(-0.642140\pi\)
0.901944 + 0.431852i \(0.142140\pi\)
\(54\) −1.49820 + 7.19412i −0.203880 + 0.978996i
\(55\) 1.51011 0.203623
\(56\) −1.27623 2.52413i −0.170543 0.337301i
\(57\) 2.31295 + 0.487478i 0.306358 + 0.0645681i
\(58\) 4.00269 + 9.01537i 0.525579 + 1.18378i
\(59\) 6.61989 + 6.61989i 0.861836 + 0.861836i 0.991551 0.129715i \(-0.0414064\pi\)
−0.129715 + 0.991551i \(0.541406\pi\)
\(60\) 6.72116 4.87955i 0.867699 0.629948i
\(61\) −8.04415 + 8.04415i −1.02995 + 1.02995i −0.0304110 + 0.999537i \(0.509682\pi\)
−0.999537 + 0.0304110i \(0.990318\pi\)
\(62\) −0.238989 + 0.620661i −0.0303516 + 0.0788240i
\(63\) 1.21078 2.74482i 0.152544 0.345814i
\(64\) −4.74249 + 6.44273i −0.592812 + 0.805341i
\(65\) 5.12887i 0.636158i
\(66\) −1.29445 0.839369i −0.159335 0.103319i
\(67\) 4.38159 + 4.38159i 0.535296 + 0.535296i 0.922144 0.386847i \(-0.126436\pi\)
−0.386847 + 0.922144i \(0.626436\pi\)
\(68\) 1.86817 2.06618i 0.226549 0.250561i
\(69\) 5.71911 + 8.77359i 0.688500 + 1.05622i
\(70\) −3.09906 + 1.37594i −0.370408 + 0.164456i
\(71\) 12.3448i 1.46506i 0.680737 + 0.732528i \(0.261660\pi\)
−0.680737 + 0.732528i \(0.738340\pi\)
\(72\) −8.47351 + 0.446841i −0.998612 + 0.0526607i
\(73\) 14.0195i 1.64086i −0.571750 0.820428i \(-0.693735\pi\)
0.571750 0.820428i \(-0.306265\pi\)
\(74\) −1.19826 2.69887i −0.139295 0.313738i
\(75\) −0.708126 1.08633i −0.0817674 0.125438i
\(76\) 0.137190 + 2.72599i 0.0157367 + 0.312693i
\(77\) 0.445358 + 0.445358i 0.0507533 + 0.0507533i
\(78\) 2.85079 4.39639i 0.322789 0.497794i
\(79\) 16.5847i 1.86592i 0.359974 + 0.932962i \(0.382786\pi\)
−0.359974 + 0.932962i \(0.617214\pi\)
\(80\) 7.42814 + 6.06642i 0.830492 + 0.678247i
\(81\) −6.06803 6.64673i −0.674226 0.738525i
\(82\) 11.0239 + 4.24482i 1.21739 + 0.468762i
\(83\) −9.24664 + 9.24664i −1.01495 + 1.01495i −0.0150642 + 0.999887i \(0.504795\pi\)
−0.999887 + 0.0150642i \(0.995205\pi\)
\(84\) 3.42126 + 0.543124i 0.373290 + 0.0592597i
\(85\) −2.36127 2.36127i −0.256116 0.256116i
\(86\) −16.4015 + 7.28205i −1.76862 + 0.785243i
\(87\) −11.8212 2.49143i −1.26736 0.267110i
\(88\) 0.555766 1.69252i 0.0592448 0.180423i
\(89\) 5.25384 0.556906 0.278453 0.960450i \(-0.410178\pi\)
0.278453 + 0.960450i \(0.410178\pi\)
\(90\) 0.0244230 + 10.1723i 0.00257441 + 1.07225i
\(91\) −1.51259 + 1.51259i −0.158563 + 0.158563i
\(92\) −8.11057 + 8.97018i −0.845585 + 0.935206i
\(93\) −0.444814 0.682381i −0.0461250 0.0707597i
\(94\) 6.39633 + 2.46294i 0.659731 + 0.254033i
\(95\) 3.27211 0.335711
\(96\) −2.99538 9.32886i −0.305715 0.952123i
\(97\) 5.17660 0.525604 0.262802 0.964850i \(-0.415353\pi\)
0.262802 + 0.964850i \(0.415353\pi\)
\(98\) −1.31976 0.508179i −0.133315 0.0513338i
\(99\) 1.76166 0.683197i 0.177053 0.0686638i
\(100\) 1.00423 1.11067i 0.100423 0.111067i
\(101\) −2.41310 + 2.41310i −0.240112 + 0.240112i −0.816896 0.576784i \(-0.804307\pi\)
0.576784 + 0.816896i \(0.304307\pi\)
\(102\) 0.711577 + 3.33653i 0.0704567 + 0.330365i
\(103\) −5.77249 −0.568780 −0.284390 0.958709i \(-0.591791\pi\)
−0.284390 + 0.958709i \(0.591791\pi\)
\(104\) 5.74840 + 1.88758i 0.563677 + 0.185092i
\(105\) 0.856437 4.06356i 0.0835797 0.396563i
\(106\) −6.25578 + 2.77748i −0.607615 + 0.269772i
\(107\) 11.2943 + 11.2943i 1.09186 + 1.09186i 0.995330 + 0.0965337i \(0.0307756\pi\)
0.0965337 + 0.995330i \(0.469224\pi\)
\(108\) 5.63316 8.73313i 0.542051 0.840345i
\(109\) −7.78278 + 7.78278i −0.745455 + 0.745455i −0.973622 0.228167i \(-0.926727\pi\)
0.228167 + 0.973622i \(0.426727\pi\)
\(110\) −1.99298 0.767406i −0.190023 0.0731693i
\(111\) 3.53883 + 0.745845i 0.335891 + 0.0707925i
\(112\) 0.401596 + 3.97979i 0.0379472 + 0.376055i
\(113\) 1.12705i 0.106024i −0.998594 0.0530119i \(-0.983118\pi\)
0.998594 0.0530119i \(-0.0168821\pi\)
\(114\) −2.80481 1.81875i −0.262694 0.170341i
\(115\) 10.2513 + 10.2513i 0.955941 + 0.955941i
\(116\) −0.701158 13.9322i −0.0651009 1.29357i
\(117\) 2.32038 + 5.98321i 0.214519 + 0.553148i
\(118\) −5.37254 12.1007i −0.494583 1.11396i
\(119\) 1.39276i 0.127674i
\(120\) −11.3500 + 3.02426i −1.03611 + 0.276076i
\(121\) 10.6033i 0.963937i
\(122\) 14.7042 6.52845i 1.33125 0.591058i
\(123\) −12.1202 + 7.90059i −1.09284 + 0.712372i
\(124\) 0.630814 0.697672i 0.0566487 0.0626528i
\(125\) 7.20764 + 7.20764i 0.644671 + 0.644671i
\(126\) −2.99279 + 3.00719i −0.266619 + 0.267902i
\(127\) 2.20449i 0.195617i −0.995205 0.0978084i \(-0.968817\pi\)
0.995205 0.0978084i \(-0.0311832\pi\)
\(128\) 9.53299 6.09279i 0.842605 0.538532i
\(129\) 4.53263 21.5061i 0.399076 1.89351i
\(130\) 2.60638 6.76885i 0.228595 0.593667i
\(131\) 10.5553 10.5553i 0.922222 0.922222i −0.0749639 0.997186i \(-0.523884\pi\)
0.997186 + 0.0749639i \(0.0238841\pi\)
\(132\) 1.28180 + 1.76557i 0.111567 + 0.153673i
\(133\) 0.965003 + 0.965003i 0.0836764 + 0.0836764i
\(134\) −3.55599 8.00926i −0.307191 0.691894i
\(135\) −10.1168 7.27084i −0.870714 0.625774i
\(136\) −3.51552 + 1.77748i −0.301453 + 0.152418i
\(137\) −11.4183 −0.975529 −0.487764 0.872975i \(-0.662187\pi\)
−0.487764 + 0.872975i \(0.662187\pi\)
\(138\) −3.08927 14.4853i −0.262976 1.23307i
\(139\) 6.59016 6.59016i 0.558970 0.558970i −0.370044 0.929014i \(-0.620658\pi\)
0.929014 + 0.370044i \(0.120658\pi\)
\(140\) 4.78922 0.241025i 0.404763 0.0203703i
\(141\) −7.03240 + 4.58410i −0.592235 + 0.386051i
\(142\) 6.27336 16.2921i 0.526448 1.36720i
\(143\) −1.34729 −0.112666
\(144\) 11.4100 + 3.71634i 0.950836 + 0.309695i
\(145\) −16.7233 −1.38879
\(146\) −7.12440 + 18.5023i −0.589620 + 1.53126i
\(147\) 1.45100 0.945839i 0.119676 0.0780115i
\(148\) 0.209901 + 4.17078i 0.0172538 + 0.342836i
\(149\) −7.72246 + 7.72246i −0.632649 + 0.632649i −0.948732 0.316083i \(-0.897632\pi\)
0.316083 + 0.948732i \(0.397632\pi\)
\(150\) 0.382506 + 1.79354i 0.0312315 + 0.146442i
\(151\) −20.3662 −1.65738 −0.828690 0.559709i \(-0.810913\pi\)
−0.828690 + 0.559709i \(0.810913\pi\)
\(152\) 1.20423 3.66736i 0.0976762 0.297462i
\(153\) −3.82288 1.68633i −0.309062 0.136332i
\(154\) −0.361442 0.814086i −0.0291259 0.0656009i
\(155\) −0.797315 0.797315i −0.0640419 0.0640419i
\(156\) −5.99650 + 4.35345i −0.480105 + 0.348555i
\(157\) 10.2467 10.2467i 0.817779 0.817779i −0.168007 0.985786i \(-0.553733\pi\)
0.985786 + 0.168007i \(0.0537331\pi\)
\(158\) 8.42800 21.8878i 0.670495 1.74130i
\(159\) 1.72881 8.20274i 0.137104 0.650520i
\(160\) −6.72050 11.7810i −0.531303 0.931371i
\(161\) 6.04660i 0.476539i
\(162\) 4.63059 + 11.8557i 0.363814 + 0.931472i
\(163\) 1.79718 + 1.79718i 0.140766 + 0.140766i 0.773978 0.633212i \(-0.218264\pi\)
−0.633212 + 0.773978i \(0.718264\pi\)
\(164\) −12.3917 11.2042i −0.967633 0.874904i
\(165\) 2.19116 1.42832i 0.170582 0.111195i
\(166\) 16.9023 7.50436i 1.31187 0.582451i
\(167\) 16.1405i 1.24899i −0.781028 0.624496i \(-0.785304\pi\)
0.781028 0.624496i \(-0.214696\pi\)
\(168\) −4.23922 2.45540i −0.327063 0.189438i
\(169\) 8.42412i 0.648009i
\(170\) 1.91635 + 4.31625i 0.146978 + 0.331041i
\(171\) 3.81716 1.48035i 0.291906 0.113205i
\(172\) 25.3466 1.27561i 1.93266 0.0972642i
\(173\) 9.68789 + 9.68789i 0.736557 + 0.736557i 0.971910 0.235353i \(-0.0756246\pi\)
−0.235353 + 0.971910i \(0.575625\pi\)
\(174\) 14.3350 + 9.29536i 1.08673 + 0.704679i
\(175\) 0.748676i 0.0565946i
\(176\) −1.59358 + 1.95129i −0.120120 + 0.147084i
\(177\) 15.8668 + 3.34408i 1.19262 + 0.251357i
\(178\) −6.93379 2.66989i −0.519709 0.200117i
\(179\) −5.28473 + 5.28473i −0.394999 + 0.394999i −0.876465 0.481466i \(-0.840105\pi\)
0.481466 + 0.876465i \(0.340105\pi\)
\(180\) 5.13711 13.4374i 0.382898 1.00156i
\(181\) −11.8638 11.8638i −0.881829 0.881829i 0.111892 0.993720i \(-0.464309\pi\)
−0.993720 + 0.111892i \(0.964309\pi\)
\(182\) 2.76492 1.22759i 0.204950 0.0909947i
\(183\) −4.06356 + 19.2805i −0.300387 + 1.42526i
\(184\) 15.2624 7.71683i 1.12516 0.568892i
\(185\) 5.00635 0.368074
\(186\) 0.240273 + 1.12662i 0.0176177 + 0.0826079i
\(187\) 0.620279 0.620279i 0.0453593 0.0453593i
\(188\) −7.18997 6.50096i −0.524383 0.474131i
\(189\) −0.839319 5.12792i −0.0610515 0.373001i
\(190\) −4.31838 1.66282i −0.313288 0.120633i
\(191\) −12.2503 −0.886404 −0.443202 0.896422i \(-0.646157\pi\)
−0.443202 + 0.896422i \(0.646157\pi\)
\(192\) −0.787556 + 13.8340i −0.0568370 + 0.998383i
\(193\) −10.1400 −0.729892 −0.364946 0.931029i \(-0.618913\pi\)
−0.364946 + 0.931029i \(0.618913\pi\)
\(194\) −6.83184 2.63064i −0.490498 0.188869i
\(195\) 4.85108 + 7.44196i 0.347393 + 0.532930i
\(196\) 1.48351 + 1.34134i 0.105965 + 0.0958102i
\(197\) 19.2804 19.2804i 1.37367 1.37367i 0.518741 0.854931i \(-0.326401\pi\)
0.854931 0.518741i \(-0.173599\pi\)
\(198\) −2.67214 + 0.00641564i −0.189901 + 0.000455940i
\(199\) 10.4170 0.738438 0.369219 0.929342i \(-0.379625\pi\)
0.369219 + 0.929342i \(0.379625\pi\)
\(200\) −1.88976 + 0.955479i −0.133626 + 0.0675626i
\(201\) 10.5019 + 2.21339i 0.740750 + 0.156121i
\(202\) 4.41098 1.95841i 0.310356 0.137793i
\(203\) −4.93200 4.93200i −0.346158 0.346158i
\(204\) 0.756443 4.76501i 0.0529616 0.333617i
\(205\) −14.1616 + 14.1616i −0.989087 + 0.989087i
\(206\) 7.61827 + 2.93346i 0.530790 + 0.204384i
\(207\) 16.5968 + 7.32109i 1.15356 + 0.508851i
\(208\) −6.62726 5.41236i −0.459518 0.375279i
\(209\) 0.859544i 0.0594559i
\(210\) −3.19530 + 4.92769i −0.220497 + 0.340043i
\(211\) 3.35351 + 3.35351i 0.230865 + 0.230865i 0.813054 0.582188i \(-0.197803\pi\)
−0.582188 + 0.813054i \(0.697803\pi\)
\(212\) 9.66756 0.486535i 0.663970 0.0334154i
\(213\) 11.6762 + 17.9122i 0.800038 + 1.22733i
\(214\) −9.16621 20.6453i −0.626589 1.41128i
\(215\) 30.4245i 2.07493i
\(216\) −11.8724 + 8.66294i −0.807814 + 0.589438i
\(217\) 0.470285i 0.0319250i
\(218\) 14.2264 6.31632i 0.963534 0.427795i
\(219\) −13.2602 20.3422i −0.896039 1.37460i
\(220\) 2.24026 + 2.02558i 0.151038 + 0.136564i
\(221\) 2.10669 + 2.10669i 0.141711 + 0.141711i
\(222\) −4.29137 2.78269i −0.288018 0.186762i
\(223\) 12.3063i 0.824088i −0.911164 0.412044i \(-0.864815\pi\)
0.911164 0.412044i \(-0.135185\pi\)
\(224\) 1.49244 5.45643i 0.0997176 0.364573i
\(225\) −2.05498 0.906480i −0.136998 0.0604320i
\(226\) −0.572743 + 1.48743i −0.0380983 + 0.0989423i
\(227\) −5.20817 + 5.20817i −0.345678 + 0.345678i −0.858497 0.512819i \(-0.828601\pi\)
0.512819 + 0.858497i \(0.328601\pi\)
\(228\) 2.77741 + 3.82564i 0.183938 + 0.253359i
\(229\) 12.4704 + 12.4704i 0.824068 + 0.824068i 0.986689 0.162620i \(-0.0519946\pi\)
−0.162620 + 0.986689i \(0.551995\pi\)
\(230\) −8.31974 18.7388i −0.548587 1.23560i
\(231\) 1.06745 + 0.224976i 0.0702331 + 0.0148023i
\(232\) −6.15467 + 18.7434i −0.404074 + 1.23056i
\(233\) −2.99215 −0.196022 −0.0980110 0.995185i \(-0.531248\pi\)
−0.0980110 + 0.995185i \(0.531248\pi\)
\(234\) −0.0217898 9.07554i −0.00142444 0.593287i
\(235\) −8.21687 + 8.21687i −0.536009 + 0.536009i
\(236\) 0.941117 + 18.7002i 0.0612615 + 1.21728i
\(237\) 15.6865 + 24.0643i 1.01894 + 1.56315i
\(238\) −0.707773 + 1.83811i −0.0458781 + 0.119147i
\(239\) 4.27730 0.276675 0.138338 0.990385i \(-0.455824\pi\)
0.138338 + 0.990385i \(0.455824\pi\)
\(240\) 16.5161 + 1.77653i 1.06611 + 0.114675i
\(241\) −25.2132 −1.62413 −0.812063 0.583569i \(-0.801656\pi\)
−0.812063 + 0.583569i \(0.801656\pi\)
\(242\) −5.38838 + 13.9938i −0.346378 + 0.899554i
\(243\) −15.0914 3.90500i −0.968115 0.250506i
\(244\) −22.7235 + 1.14360i −1.45473 + 0.0732114i
\(245\) 1.69539 1.69539i 0.108314 0.108314i
\(246\) 20.0106 4.26763i 1.27583 0.272094i
\(247\) −2.91932 −0.185752
\(248\) −1.18706 + 0.600190i −0.0753785 + 0.0381121i
\(249\) −4.67101 + 22.1627i −0.296013 + 1.40450i
\(250\) −5.84955 13.1751i −0.369958 0.833266i
\(251\) −11.5897 11.5897i −0.731533 0.731533i 0.239391 0.970923i \(-0.423052\pi\)
−0.970923 + 0.239391i \(0.923052\pi\)
\(252\) 5.47794 2.44789i 0.345078 0.154203i
\(253\) −2.69290 + 2.69290i −0.169301 + 0.169301i
\(254\) −1.12027 + 2.90939i −0.0702923 + 0.182551i
\(255\) −5.65958 1.19281i −0.354417 0.0746969i
\(256\) −15.6774 + 3.19653i −0.979840 + 0.199783i
\(257\) 18.3388i 1.14394i 0.820274 + 0.571970i \(0.193821\pi\)
−0.820274 + 0.571970i \(0.806179\pi\)
\(258\) −16.9109 + 26.0794i −1.05283 + 1.62363i
\(259\) 1.47646 + 1.47646i 0.0917428 + 0.0917428i
\(260\) −6.87957 + 7.60872i −0.426653 + 0.471873i
\(261\) −19.5090 + 7.56587i −1.20758 + 0.468316i
\(262\) −19.2944 + 8.56645i −1.19201 + 0.529237i
\(263\) 5.86015i 0.361352i 0.983543 + 0.180676i \(0.0578286\pi\)
−0.983543 + 0.180676i \(0.942171\pi\)
\(264\) −0.794439 2.98151i −0.0488943 0.183499i
\(265\) 11.6043i 0.712848i
\(266\) −0.783174 1.76396i −0.0480195 0.108155i
\(267\) 7.62330 4.96929i 0.466539 0.304115i
\(268\) 0.622909 + 12.3773i 0.0380502 + 0.756066i
\(269\) 1.15567 + 1.15567i 0.0704624 + 0.0704624i 0.741460 0.670997i \(-0.234134\pi\)
−0.670997 + 0.741460i \(0.734134\pi\)
\(270\) 9.65679 + 14.7369i 0.587693 + 0.896857i
\(271\) 6.87631i 0.417706i −0.977947 0.208853i \(-0.933027\pi\)
0.977947 0.208853i \(-0.0669731\pi\)
\(272\) 5.54291 0.559328i 0.336088 0.0339142i
\(273\) −0.764098 + 3.62544i −0.0462453 + 0.219422i
\(274\) 15.0693 + 5.80252i 0.910371 + 0.350543i
\(275\) 0.333429 0.333429i 0.0201065 0.0201065i
\(276\) −3.28405 + 20.6870i −0.197677 + 1.24521i
\(277\) 2.82011 + 2.82011i 0.169444 + 0.169444i 0.786735 0.617291i \(-0.211770\pi\)
−0.617291 + 0.786735i \(0.711770\pi\)
\(278\) −12.0464 + 5.34842i −0.722493 + 0.320777i
\(279\) −1.29085 0.569411i −0.0772809 0.0340897i
\(280\) −6.44308 2.11569i −0.385048 0.126436i
\(281\) −25.8107 −1.53974 −0.769868 0.638203i \(-0.779678\pi\)
−0.769868 + 0.638203i \(0.779678\pi\)
\(282\) 11.6106 2.47618i 0.691401 0.147454i
\(283\) 8.51014 8.51014i 0.505875 0.505875i −0.407383 0.913258i \(-0.633558\pi\)
0.913258 + 0.407383i \(0.133558\pi\)
\(284\) −16.5586 + 18.3136i −0.982572 + 1.08671i
\(285\) 4.74781 3.09489i 0.281236 0.183325i
\(286\) 1.77810 + 0.684666i 0.105141 + 0.0404851i
\(287\) −8.35300 −0.493062
\(288\) −13.1699 10.7030i −0.776043 0.630680i
\(289\) 15.0602 0.885895
\(290\) 22.0707 + 8.49842i 1.29603 + 0.499044i
\(291\) 7.51122 4.89623i 0.440316 0.287022i
\(292\) 18.8049 20.7980i 1.10048 1.21711i
\(293\) 8.85088 8.85088i 0.517074 0.517074i −0.399611 0.916685i \(-0.630855\pi\)
0.916685 + 0.399611i \(0.130855\pi\)
\(294\) −2.39561 + 0.510910i −0.139715 + 0.0297969i
\(295\) 22.4465 1.30689
\(296\) 1.84249 5.61108i 0.107092 0.326138i
\(297\) 1.90996 2.65756i 0.110827 0.154207i
\(298\) 14.1161 6.26737i 0.817727 0.363059i
\(299\) −9.14605 9.14605i −0.528930 0.528930i
\(300\) 0.406624 2.56141i 0.0234764 0.147883i
\(301\) 8.97272 8.97272i 0.517179 0.517179i
\(302\) 26.8784 + 10.3497i 1.54668 + 0.595557i
\(303\) −1.21899 + 5.78380i −0.0700293 + 0.332270i
\(304\) −3.45297 + 4.22805i −0.198041 + 0.242495i
\(305\) 27.2759i 1.56181i
\(306\) 4.18831 + 4.16825i 0.239430 + 0.238283i
\(307\) −14.6474 14.6474i −0.835971 0.835971i 0.152355 0.988326i \(-0.451314\pi\)
−0.988326 + 0.152355i \(0.951314\pi\)
\(308\) 0.0633144 + 1.25807i 0.00360767 + 0.0716853i
\(309\) −8.37586 + 5.45984i −0.476486 + 0.310600i
\(310\) 0.647082 + 1.45744i 0.0367518 + 0.0827770i
\(311\) 18.9809i 1.07631i −0.842846 0.538155i \(-0.819121\pi\)
0.842846 0.538155i \(-0.180879\pi\)
\(312\) 10.1263 2.69820i 0.573286 0.152755i
\(313\) 1.41725i 0.0801077i −0.999198 0.0400539i \(-0.987247\pi\)
0.999198 0.0400539i \(-0.0127529\pi\)
\(314\) −18.7304 + 8.31601i −1.05702 + 0.469300i
\(315\) −2.60079 6.70626i −0.146538 0.377855i
\(316\) −22.2458 + 24.6036i −1.25142 + 1.38406i
\(317\) 7.89489 + 7.89489i 0.443421 + 0.443421i 0.893160 0.449739i \(-0.148483\pi\)
−0.449739 + 0.893160i \(0.648483\pi\)
\(318\) −6.45007 + 9.94707i −0.361702 + 0.557804i
\(319\) 4.39301i 0.245961i
\(320\) 2.88256 + 18.9633i 0.161140 + 1.06008i
\(321\) 27.0706 + 5.70541i 1.51093 + 0.318445i
\(322\) 3.07275 7.98003i 0.171238 0.444710i
\(323\) 1.34402 1.34402i 0.0747833 0.0747833i
\(324\) −0.0864332 17.9998i −0.00480184 0.999988i
\(325\) 1.13244 + 1.13244i 0.0628166 + 0.0628166i
\(326\) −1.45855 3.28512i −0.0807813 0.181946i
\(327\) −3.93153 + 18.6540i −0.217414 + 1.03157i
\(328\) 10.6603 + 21.0841i 0.588618 + 1.16417i
\(329\) −4.84660 −0.267202
\(330\) −3.61764 + 0.771531i −0.199145 + 0.0424714i
\(331\) 12.2512 12.2512i 0.673384 0.673384i −0.285111 0.958495i \(-0.592030\pi\)
0.958495 + 0.285111i \(0.0920303\pi\)
\(332\) −26.1204 + 1.31455i −1.43354 + 0.0721453i
\(333\) 5.84028 2.26495i 0.320045 0.124118i
\(334\) −8.20228 + 21.3016i −0.448809 + 1.16557i
\(335\) 14.8570 0.811723
\(336\) 4.34695 + 5.39481i 0.237146 + 0.294311i
\(337\) 21.2205 1.15596 0.577978 0.816052i \(-0.303842\pi\)
0.577978 + 0.816052i \(0.303842\pi\)
\(338\) 4.28096 11.1178i 0.232853 0.604727i
\(339\) −1.06601 1.63534i −0.0578976 0.0888197i
\(340\) −0.335691 6.67025i −0.0182054 0.361745i
\(341\) 0.209445 0.209445i 0.0113421 0.0113421i
\(342\) −5.79000 + 0.0139014i −0.313087 + 0.000751703i
\(343\) 1.00000 0.0539949
\(344\) −34.0995 11.1971i −1.83852 0.603708i
\(345\) 24.5707 + 5.17853i 1.32284 + 0.278803i
\(346\) −7.86247 17.7088i −0.422689 0.952033i
\(347\) 5.77536 + 5.77536i 0.310038 + 0.310038i 0.844924 0.534886i \(-0.179646\pi\)
−0.534886 + 0.844924i \(0.679646\pi\)
\(348\) −14.1950 19.5523i −0.760929 1.04811i
\(349\) 23.8646 23.8646i 1.27744 1.27744i 0.335352 0.942093i \(-0.391145\pi\)
0.942093 0.335352i \(-0.108855\pi\)
\(350\) −0.380461 + 0.988069i −0.0203365 + 0.0528145i
\(351\) 9.02601 + 6.48691i 0.481773 + 0.346246i
\(352\) 3.09474 1.76540i 0.164950 0.0940960i
\(353\) 0.589919i 0.0313982i 0.999877 + 0.0156991i \(0.00499739\pi\)
−0.999877 + 0.0156991i \(0.995003\pi\)
\(354\) −19.2409 12.4765i −1.02264 0.663120i
\(355\) 20.9292 + 20.9292i 1.11081 + 1.11081i
\(356\) 7.79412 + 7.04721i 0.413088 + 0.373501i
\(357\) −1.31733 2.02089i −0.0697205 0.106957i
\(358\) 9.66014 4.28896i 0.510554 0.226679i
\(359\) 4.56354i 0.240855i −0.992722 0.120427i \(-0.961574\pi\)
0.992722 0.120427i \(-0.0384265\pi\)
\(360\) −13.6083 + 15.1234i −0.717221 + 0.797076i
\(361\) 17.1375i 0.901976i
\(362\) 9.62838 + 21.6862i 0.506056 + 1.13980i
\(363\) −10.0290 15.3854i −0.526387 0.807522i
\(364\) −4.27286 + 0.215038i −0.223958 + 0.0112711i
\(365\) −23.7684 23.7684i −1.24410 1.24410i
\(366\) 15.1609 23.3805i 0.792471 1.22212i
\(367\) 19.3900i 1.01215i −0.862489 0.506076i \(-0.831096\pi\)
0.862489 0.506076i \(-0.168904\pi\)
\(368\) −24.0642 + 2.42829i −1.25443 + 0.126583i
\(369\) −10.1136 + 22.9274i −0.526495 + 1.19356i
\(370\) −6.60715 2.54412i −0.343490 0.132262i
\(371\) 3.42232 3.42232i 0.177678 0.177678i
\(372\) 0.255423 1.60897i 0.0132431 0.0834210i
\(373\) −19.5876 19.5876i −1.01421 1.01421i −0.999898 0.0143107i \(-0.995445\pi\)
−0.0143107 0.999898i \(-0.504555\pi\)
\(374\) −1.13383 + 0.503404i −0.0586289 + 0.0260304i
\(375\) 17.2755 + 3.64099i 0.892104 + 0.188020i
\(376\) 6.18536 + 12.2335i 0.318986 + 0.630893i
\(377\) 14.9202 0.768431
\(378\) −1.49820 + 7.19412i −0.0770593 + 0.370026i
\(379\) −21.9568 + 21.9568i −1.12785 + 1.12785i −0.137320 + 0.990527i \(0.543849\pi\)
−0.990527 + 0.137320i \(0.956151\pi\)
\(380\) 4.85420 + 4.38902i 0.249015 + 0.225152i
\(381\) −2.08509 3.19870i −0.106822 0.163875i
\(382\) 16.1675 + 6.22536i 0.827199 + 0.318517i
\(383\) −33.3358 −1.70338 −0.851690 0.524046i \(-0.824422\pi\)
−0.851690 + 0.524046i \(0.824422\pi\)
\(384\) 8.06953 17.8573i 0.411797 0.911276i
\(385\) 1.51011 0.0769623
\(386\) 13.3823 + 5.15293i 0.681141 + 0.262277i
\(387\) −13.7645 35.4924i −0.699688 1.80418i
\(388\) 7.67953 + 6.94360i 0.389869 + 0.352508i
\(389\) 8.17897 8.17897i 0.414690 0.414690i −0.468679 0.883369i \(-0.655270\pi\)
0.883369 + 0.468679i \(0.155270\pi\)
\(390\) −2.62039 12.2868i −0.132689 0.622166i
\(391\) 8.42148 0.425893
\(392\) −1.27623 2.52413i −0.0644592 0.127488i
\(393\) 5.33209 25.2994i 0.268969 1.27618i
\(394\) −35.2433 + 15.6475i −1.77553 + 0.788311i
\(395\) 28.1175 + 28.1175i 1.41474 + 1.41474i
\(396\) 3.52983 + 1.34946i 0.177381 + 0.0678129i
\(397\) 10.0314 10.0314i 0.503462 0.503462i −0.409050 0.912512i \(-0.634140\pi\)
0.912512 + 0.409050i \(0.134140\pi\)
\(398\) −13.7478 5.29367i −0.689116 0.265348i
\(399\) 2.31295 + 0.487478i 0.115792 + 0.0244044i
\(400\) 2.97957 0.300665i 0.148979 0.0150332i
\(401\) 15.4592i 0.771993i −0.922500 0.385997i \(-0.873858\pi\)
0.922500 0.385997i \(-0.126142\pi\)
\(402\) −12.7352 8.25800i −0.635174 0.411872i
\(403\) 0.711350 + 0.711350i 0.0354349 + 0.0354349i
\(404\) −6.81664 + 0.343058i −0.339141 + 0.0170678i
\(405\) −21.5564 0.981113i −1.07115 0.0487519i
\(406\) 4.00269 + 9.01537i 0.198650 + 0.447425i
\(407\) 1.31511i 0.0651875i
\(408\) −3.41979 + 5.90423i −0.169305 + 0.292303i
\(409\) 12.5042i 0.618292i 0.951015 + 0.309146i \(0.100043\pi\)
−0.951015 + 0.309146i \(0.899957\pi\)
\(410\) 25.8864 11.4932i 1.27844 0.567609i
\(411\) −16.5679 + 10.7998i −0.817232 + 0.532717i
\(412\) −8.56354 7.74289i −0.421895 0.381465i
\(413\) 6.61989 + 6.61989i 0.325743 + 0.325743i
\(414\) −18.1833 18.0962i −0.893661 0.889380i
\(415\) 31.3533i 1.53907i
\(416\) 5.99592 + 10.5108i 0.293974 + 0.515335i
\(417\) 3.32906 15.7955i 0.163025 0.773510i
\(418\) 0.436802 1.13439i 0.0213647 0.0554847i
\(419\) 19.2109 19.2109i 0.938516 0.938516i −0.0597005 0.998216i \(-0.519015\pi\)
0.998216 + 0.0597005i \(0.0190146\pi\)
\(420\) 6.72116 4.87955i 0.327959 0.238098i
\(421\) 0.650536 + 0.650536i 0.0317052 + 0.0317052i 0.722782 0.691076i \(-0.242863\pi\)
−0.691076 + 0.722782i \(0.742863\pi\)
\(422\) −2.72163 6.13000i −0.132487 0.298404i
\(423\) −5.86816 + 13.3030i −0.285320 + 0.646815i
\(424\) −13.0061 4.27074i −0.631630 0.207405i
\(425\) −1.04273 −0.0505797
\(426\) −6.30708 29.5733i −0.305579 1.43283i
\(427\) −8.04415 + 8.04415i −0.389284 + 0.389284i
\(428\) 1.60566 + 31.9048i 0.0776125 + 1.54218i
\(429\) −1.95492 + 1.27432i −0.0943843 + 0.0615248i
\(430\) −15.4611 + 40.1528i −0.745599 + 1.93634i
\(431\) 9.29584 0.447765 0.223882 0.974616i \(-0.428127\pi\)
0.223882 + 0.974616i \(0.428127\pi\)
\(432\) 20.0710 5.39966i 0.965665 0.259791i
\(433\) 13.5879 0.652991 0.326495 0.945199i \(-0.394132\pi\)
0.326495 + 0.945199i \(0.394132\pi\)
\(434\) −0.238989 + 0.620661i −0.0114718 + 0.0297927i
\(435\) −24.2654 + 15.8175i −1.16344 + 0.758393i
\(436\) −21.9852 + 1.10644i −1.05290 + 0.0529889i
\(437\) −5.83499 + 5.83499i −0.279125 + 0.279125i
\(438\) 7.16270 + 33.5853i 0.342247 + 1.60477i
\(439\) −0.193033 −0.00921297 −0.00460649 0.999989i \(-0.501466\pi\)
−0.00460649 + 0.999989i \(0.501466\pi\)
\(440\) −1.92724 3.81172i −0.0918776 0.181716i
\(441\) 1.21078 2.74482i 0.0576561 0.130706i
\(442\) −1.70974 3.85088i −0.0813239 0.183168i
\(443\) −5.02164 5.02164i −0.238585 0.238585i 0.577679 0.816264i \(-0.303959\pi\)
−0.816264 + 0.577679i \(0.803959\pi\)
\(444\) 4.24946 + 5.85326i 0.201670 + 0.277783i
\(445\) 8.90730 8.90730i 0.422246 0.422246i
\(446\) −6.25378 + 16.2413i −0.296125 + 0.769046i
\(447\) −3.90106 + 18.5095i −0.184514 + 0.875467i
\(448\) −4.74249 + 6.44273i −0.224062 + 0.304390i
\(449\) 36.2149i 1.70909i −0.519379 0.854544i \(-0.673837\pi\)
0.519379 0.854544i \(-0.326163\pi\)
\(450\) 2.25141 + 2.24063i 0.106133 + 0.105624i
\(451\) −3.72008 3.72008i −0.175172 0.175172i
\(452\) 1.51176 1.67199i 0.0711072 0.0786437i
\(453\) −29.5513 + 19.2632i −1.38844 + 0.905062i
\(454\) 9.52019 4.22683i 0.446805 0.198375i
\(455\) 5.12887i 0.240445i
\(456\) −1.72139 6.46033i −0.0806115 0.302533i
\(457\) 28.6790i 1.34155i 0.741663 + 0.670773i \(0.234037\pi\)
−0.741663 + 0.670773i \(0.765963\pi\)
\(458\) −10.1207 22.7951i −0.472909 1.06514i
\(459\) −7.14198 + 1.16897i −0.333359 + 0.0545630i
\(460\) 1.45738 + 28.9585i 0.0679508 + 1.35020i
\(461\) −11.2373 11.2373i −0.523375 0.523375i 0.395214 0.918589i \(-0.370671\pi\)
−0.918589 + 0.395214i \(0.870671\pi\)
\(462\) −1.29445 0.839369i −0.0602230 0.0390510i
\(463\) 8.11410i 0.377094i 0.982064 + 0.188547i \(0.0603778\pi\)
−0.982064 + 0.188547i \(0.939622\pi\)
\(464\) 17.6476 21.6090i 0.819271 1.00317i
\(465\) −1.91103 0.402769i −0.0886220 0.0186780i
\(466\) 3.94890 + 1.52055i 0.182929 + 0.0704379i
\(467\) 11.8202 11.8202i 0.546973 0.546973i −0.378591 0.925564i \(-0.623591\pi\)
0.925564 + 0.378591i \(0.123591\pi\)
\(468\) −4.58324 + 11.9886i −0.211860 + 0.554172i
\(469\) 4.38159 + 4.38159i 0.202323 + 0.202323i
\(470\) 15.0199 6.66862i 0.692816 0.307600i
\(471\) 5.17621 24.5597i 0.238507 1.13165i
\(472\) 8.26100 25.1579i 0.380243 1.15799i
\(473\) 7.99215 0.367479
\(474\) −8.47330 39.7306i −0.389191 1.82489i
\(475\) 0.722474 0.722474i 0.0331494 0.0331494i
\(476\) 1.86817 2.06618i 0.0856276 0.0947031i
\(477\) −5.24997 13.5373i −0.240380 0.619831i
\(478\) −5.64499 2.17363i −0.258196 0.0994196i
\(479\) −28.2089 −1.28890 −0.644449 0.764647i \(-0.722913\pi\)
−0.644449 + 0.764647i \(0.722913\pi\)
\(480\) −20.8944 10.7377i −0.953693 0.490107i
\(481\) −4.46657 −0.203658
\(482\) 33.2753 + 12.8128i 1.51565 + 0.583608i
\(483\) 5.71911 + 8.77359i 0.260228 + 0.399212i
\(484\) 14.2227 15.7301i 0.646486 0.715005i
\(485\) 8.77634 8.77634i 0.398513 0.398513i
\(486\) 17.9325 + 12.8228i 0.813437 + 0.581653i
\(487\) 1.26539 0.0573402 0.0286701 0.999589i \(-0.490873\pi\)
0.0286701 + 0.999589i \(0.490873\pi\)
\(488\) 30.5707 + 10.0384i 1.38387 + 0.454415i
\(489\) 4.30753 + 0.907856i 0.194793 + 0.0410547i
\(490\) −3.09906 + 1.37594i −0.140001 + 0.0621585i
\(491\) 21.3825 + 21.3825i 0.964980 + 0.964980i 0.999407 0.0344277i \(-0.0109608\pi\)
−0.0344277 + 0.999407i \(0.510961\pi\)
\(492\) −28.5778 4.53671i −1.28839 0.204531i
\(493\) −6.86911 + 6.86911i −0.309369 + 0.309369i
\(494\) 3.85278 + 1.48353i 0.173345 + 0.0667474i
\(495\) 1.82841 4.14497i 0.0821808 0.186303i
\(496\) 1.87163 0.188864i 0.0840389 0.00848026i
\(497\) 12.3448i 0.553739i
\(498\) 17.4272 26.8756i 0.780931 1.20432i
\(499\) −9.37843 9.37843i −0.419836 0.419836i 0.465311 0.885147i \(-0.345943\pi\)
−0.885147 + 0.465311i \(0.845943\pi\)
\(500\) 1.02468 + 20.3605i 0.0458249 + 0.910550i
\(501\) −15.2664 23.4199i −0.682050 1.04632i
\(502\) 9.40590 + 21.1851i 0.419806 + 0.945539i
\(503\) 19.7856i 0.882195i −0.897459 0.441098i \(-0.854589\pi\)
0.897459 0.441098i \(-0.145411\pi\)
\(504\) −8.47351 + 0.446841i −0.377440 + 0.0199039i
\(505\) 8.18227i 0.364106i
\(506\) 4.92245 2.18550i 0.218830 0.0971572i
\(507\) 7.96786 + 12.2234i 0.353865 + 0.542858i
\(508\) 2.95698 3.27038i 0.131195 0.145100i
\(509\) −12.5552 12.5552i −0.556501 0.556501i 0.371809 0.928309i \(-0.378738\pi\)
−0.928309 + 0.371809i \(0.878738\pi\)
\(510\) 6.86310 + 4.45030i 0.303903 + 0.197063i
\(511\) 14.0195i 0.620185i
\(512\) 22.3148 + 3.74830i 0.986184 + 0.165653i
\(513\) 4.13851 5.75840i 0.182720 0.254240i
\(514\) 9.31937 24.2027i 0.411060 1.06753i
\(515\) −9.78660 + 9.78660i −0.431249 + 0.431249i
\(516\) 35.5713 25.8247i 1.56594 1.13687i
\(517\) −2.15847 2.15847i −0.0949296 0.0949296i
\(518\) −1.19826 2.69887i −0.0526486 0.118582i
\(519\) 23.2203 + 4.89391i 1.01926 + 0.214819i
\(520\) 12.9459 6.54559i 0.567717 0.287043i
\(521\) 7.36126 0.322503 0.161251 0.986913i \(-0.448447\pi\)
0.161251 + 0.986913i \(0.448447\pi\)
\(522\) 29.5919 0.0710483i 1.29520 0.00310970i
\(523\) −19.9496 + 19.9496i −0.872334 + 0.872334i −0.992726 0.120392i \(-0.961585\pi\)
0.120392 + 0.992726i \(0.461585\pi\)
\(524\) 29.8172 1.50060i 1.30257 0.0655539i
\(525\) −0.708126 1.08633i −0.0309052 0.0474111i
\(526\) 2.97800 7.73396i 0.129847 0.337217i
\(527\) −0.654996 −0.0285321
\(528\) −0.466674 + 4.33858i −0.0203094 + 0.188812i
\(529\) −13.5614 −0.589625
\(530\) −5.89707 + 15.3149i −0.256152 + 0.665235i
\(531\) 26.1856 10.1552i 1.13636 0.440696i
\(532\) 0.137190 + 2.72599i 0.00594793 + 0.118187i
\(533\) 12.6347 12.6347i 0.547270 0.547270i
\(534\) −12.5862 + 2.68424i −0.544657 + 0.116159i
\(535\) 38.2965 1.65570
\(536\) 5.46781 16.6516i 0.236174 0.719240i
\(537\) −2.66962 + 12.6666i −0.115203 + 0.546605i
\(538\) −0.937914 2.11249i −0.0404364 0.0910758i
\(539\) 0.445358 + 0.445358i 0.0191829 + 0.0191829i
\(540\) −5.25564 24.3564i −0.226167 1.04813i
\(541\) −19.1432 + 19.1432i −0.823032 + 0.823032i −0.986542 0.163509i \(-0.947719\pi\)
0.163509 + 0.986542i \(0.447719\pi\)
\(542\) −3.49440 + 9.07505i −0.150097 + 0.389807i
\(543\) −28.4355 5.99308i −1.22029 0.257188i
\(544\) −7.59952 2.07861i −0.325827 0.0891197i
\(545\) 26.3896i 1.13041i
\(546\) 2.85079 4.39639i 0.122003 0.188148i
\(547\) −23.1275 23.1275i −0.988862 0.988862i 0.0110764 0.999939i \(-0.496474\pi\)
−0.999939 + 0.0110764i \(0.996474\pi\)
\(548\) −16.9391 15.3158i −0.723603 0.654259i
\(549\) 12.3400 + 31.8194i 0.526660 + 1.35802i
\(550\) −0.609486 + 0.270603i −0.0259886 + 0.0115386i
\(551\) 9.51878i 0.405514i
\(552\) 14.8468 25.6329i 0.631923 1.09101i
\(553\) 16.5847i 0.705253i
\(554\) −2.28873 5.15497i −0.0972390 0.219014i
\(555\) 7.26419 4.73520i 0.308348 0.200998i
\(556\) 18.6162 0.936891i 0.789503 0.0397330i
\(557\) −7.81224 7.81224i −0.331015 0.331015i 0.521957 0.852972i \(-0.325202\pi\)
−0.852972 + 0.521957i \(0.825202\pi\)
\(558\) 1.41424 + 1.40746i 0.0598695 + 0.0595827i
\(559\) 27.1442i 1.14808i
\(560\) 7.42814 + 6.06642i 0.313896 + 0.256353i
\(561\) 0.313338 1.48671i 0.0132292 0.0627688i
\(562\) 34.0638 + 13.1164i 1.43689 + 0.553284i
\(563\) −5.29314 + 5.29314i −0.223079 + 0.223079i −0.809794 0.586715i \(-0.800421\pi\)
0.586715 + 0.809794i \(0.300421\pi\)
\(564\) −16.5815 2.63231i −0.698206 0.110840i
\(565\) −1.91079 1.91079i −0.0803873 0.0803873i
\(566\) −15.5560 + 6.90663i −0.653866 + 0.290307i
\(567\) −6.06803 6.64673i −0.254833 0.279136i
\(568\) 31.1599 15.7547i 1.30744 0.661054i
\(569\) 10.7397 0.450231 0.225115 0.974332i \(-0.427724\pi\)
0.225115 + 0.974332i \(0.427724\pi\)
\(570\) −7.83871 + 1.67175i −0.328327 + 0.0700220i
\(571\) −9.64927 + 9.64927i −0.403809 + 0.403809i −0.879573 0.475764i \(-0.842172\pi\)
0.475764 + 0.879573i \(0.342172\pi\)
\(572\) −1.99872 1.80718i −0.0835707 0.0755621i
\(573\) −17.7752 + 11.5868i −0.742569 + 0.484048i
\(574\) 11.0239 + 4.24482i 0.460129 + 0.177175i
\(575\) 4.52694 0.188787
\(576\) 11.9420 + 20.8180i 0.497583 + 0.867416i
\(577\) −38.6282 −1.60811 −0.804056 0.594554i \(-0.797329\pi\)
−0.804056 + 0.594554i \(0.797329\pi\)
\(578\) −19.8758 7.65328i −0.826724 0.318334i
\(579\) −14.7131 + 9.59079i −0.611455 + 0.398580i
\(580\) −24.8091 22.4317i −1.03014 0.931425i
\(581\) −9.24664 + 9.24664i −0.383615 + 0.383615i
\(582\) −12.4011 + 2.64478i −0.514044 + 0.109630i
\(583\) 3.04832 0.126249
\(584\) −35.3870 + 17.8920i −1.46433 + 0.740377i
\(585\) 14.0778 + 6.20992i 0.582045 + 0.256749i
\(586\) −16.1788 + 7.18317i −0.668341 + 0.296734i
\(587\) 9.36336 + 9.36336i 0.386467 + 0.386467i 0.873425 0.486958i \(-0.161894\pi\)
−0.486958 + 0.873425i \(0.661894\pi\)
\(588\) 3.42126 + 0.543124i 0.141090 + 0.0223981i
\(589\) 0.453826 0.453826i 0.0186996 0.0186996i
\(590\) −29.6239 11.4069i −1.21960 0.469613i
\(591\) 9.73964 46.2120i 0.400635 1.90091i
\(592\) −5.28306 + 6.46894i −0.217133 + 0.265872i
\(593\) 29.8401i 1.22539i −0.790320 0.612694i \(-0.790086\pi\)
0.790320 0.612694i \(-0.209914\pi\)
\(594\) −3.87120 + 2.53672i −0.158837 + 0.104083i
\(595\) −2.36127 2.36127i −0.0968028 0.0968028i
\(596\) −21.8148 + 1.09786i −0.893569 + 0.0449703i
\(597\) 15.1150 9.85276i 0.618614 0.403246i
\(598\) 7.42272 + 16.7184i 0.303538 + 0.683666i
\(599\) 8.61900i 0.352163i 0.984376 + 0.176081i \(0.0563422\pi\)
−0.984376 + 0.176081i \(0.943658\pi\)
\(600\) −1.83830 + 3.17380i −0.0750483 + 0.129570i
\(601\) 37.6975i 1.53771i 0.639421 + 0.768857i \(0.279174\pi\)
−0.639421 + 0.768857i \(0.720826\pi\)
\(602\) −16.4015 + 7.28205i −0.668477 + 0.296794i
\(603\) 17.3318 6.72152i 0.705805 0.273722i
\(604\) −30.2135 27.3181i −1.22937 1.11156i
\(605\) −17.9767 17.9767i −0.730858 0.730858i
\(606\) 4.54798 7.01373i 0.184749 0.284913i
\(607\) 9.27459i 0.376444i 0.982127 + 0.188222i \(0.0602724\pi\)
−0.982127 + 0.188222i \(0.939728\pi\)
\(608\) 6.70568 3.82527i 0.271951 0.155135i
\(609\) −11.8212 2.49143i −0.479018 0.100958i
\(610\) 13.8610 35.9975i 0.561217 1.45750i
\(611\) 7.33094 7.33094i 0.296578 0.296578i
\(612\) −3.40933 7.62948i −0.137814 0.308403i
\(613\) 23.9007 + 23.9007i 0.965339 + 0.965339i 0.999419 0.0340804i \(-0.0108502\pi\)
−0.0340804 + 0.999419i \(0.510850\pi\)
\(614\) 11.8875 + 26.7745i 0.479740 + 1.08053i
\(615\) −7.15382 + 33.9429i −0.288470 + 1.36871i
\(616\) 0.555766 1.69252i 0.0223924 0.0681936i
\(617\) −17.9544 −0.722817 −0.361409 0.932408i \(-0.617704\pi\)
−0.361409 + 0.932408i \(0.617704\pi\)
\(618\) 13.8287 2.94922i 0.556270 0.118635i
\(619\) −14.4355 + 14.4355i −0.580214 + 0.580214i −0.934962 0.354748i \(-0.884567\pi\)
0.354748 + 0.934962i \(0.384567\pi\)
\(620\) −0.113350 2.25230i −0.00455226 0.0904544i
\(621\) 31.0065 5.07503i 1.24425 0.203654i
\(622\) −9.64571 + 25.0502i −0.386758 + 1.00442i
\(623\) 5.25384 0.210491
\(624\) −14.7353 1.58499i −0.589886 0.0634503i
\(625\) 28.1829 1.12731
\(626\) −0.720216 + 1.87042i −0.0287856 + 0.0747572i
\(627\) 0.812990 + 1.24719i 0.0324677 + 0.0498082i
\(628\) 28.9455 1.45673i 1.15505 0.0581298i
\(629\) 2.05636 2.05636i 0.0819925 0.0819925i
\(630\) 0.0244230 + 10.1723i 0.000973037 + 0.405274i
\(631\) −12.7763 −0.508616 −0.254308 0.967123i \(-0.581848\pi\)
−0.254308 + 0.967123i \(0.581848\pi\)
\(632\) 41.8620 21.1658i 1.66518 0.841932i
\(633\) 8.03782 + 1.69405i 0.319475 + 0.0673325i
\(634\) −6.40731 14.4313i −0.254467 0.573142i
\(635\) −3.73746 3.73746i −0.148317 0.148317i
\(636\) 13.5674 9.84991i 0.537982 0.390574i
\(637\) −1.51259 + 1.51259i −0.0599312 + 0.0599312i
\(638\) −2.23244 + 5.79770i −0.0883830 + 0.229533i
\(639\) 33.8842 + 14.9468i 1.34044 + 0.591286i
\(640\) 5.83247 26.4917i 0.230549 1.04718i
\(641\) 1.57497i 0.0622075i 0.999516 + 0.0311038i \(0.00990224\pi\)
−0.999516 + 0.0311038i \(0.990098\pi\)
\(642\) −32.8272 21.2865i −1.29559 0.840110i
\(643\) −32.8549 32.8549i −1.29567 1.29567i −0.931225 0.364444i \(-0.881259\pi\)
−0.364444 0.931225i \(-0.618741\pi\)
\(644\) −8.11057 + 8.97018i −0.319601 + 0.353475i
\(645\) −28.7766 44.1458i −1.13308 1.73824i
\(646\) −2.45678 + 1.09078i −0.0966608 + 0.0429160i
\(647\) 28.8641i 1.13477i 0.823454 + 0.567383i \(0.192044\pi\)
−0.823454 + 0.567383i \(0.807956\pi\)
\(648\) −9.03304 + 23.7992i −0.354851 + 0.934923i
\(649\) 5.89644i 0.231456i
\(650\) −0.919064 2.07003i −0.0360487 0.0811933i
\(651\) −0.444814 0.682381i −0.0174336 0.0267446i
\(652\) 0.255496 + 5.07675i 0.0100060 + 0.198821i
\(653\) 11.3854 + 11.3854i 0.445546 + 0.445546i 0.893871 0.448325i \(-0.147979\pi\)
−0.448325 + 0.893871i \(0.647979\pi\)
\(654\) 14.6682 22.6208i 0.573573 0.884545i
\(655\) 35.7907i 1.39846i
\(656\) −3.35453 33.2432i −0.130972 1.29793i
\(657\) −38.4809 16.9745i −1.50128 0.662237i
\(658\) 6.39633 + 2.46294i 0.249355 + 0.0960154i
\(659\) −6.17983 + 6.17983i −0.240732 + 0.240732i −0.817153 0.576421i \(-0.804449\pi\)
0.576421 + 0.817153i \(0.304449\pi\)
\(660\) 5.16648 + 0.820177i 0.201105 + 0.0319253i
\(661\) −15.1242 15.1242i −0.588263 0.588263i 0.348898 0.937161i \(-0.386556\pi\)
−0.937161 + 0.348898i \(0.886556\pi\)
\(662\) −22.3943 + 9.94275i −0.870379 + 0.386436i
\(663\) 5.04938 + 1.06421i 0.196102 + 0.0413304i
\(664\) 35.1406 + 11.5389i 1.36372 + 0.447798i
\(665\) 3.27211 0.126887
\(666\) −8.85874 + 0.0212693i −0.343269 + 0.000824168i
\(667\) 29.8218 29.8218i 1.15471 1.15471i
\(668\) 21.6500 23.9446i 0.837664 0.926446i
\(669\) −11.6397 17.8563i −0.450018 0.690366i
\(670\) −19.6076 7.55000i −0.757507 0.291682i
\(671\) −7.16506 −0.276604
\(672\) −2.99538 9.32886i −0.115549 0.359869i
\(673\) −10.6946 −0.412248 −0.206124 0.978526i \(-0.566085\pi\)
−0.206124 + 0.978526i \(0.566085\pi\)
\(674\) −28.0059 10.7838i −1.07875 0.415377i
\(675\) −3.83915 + 0.628378i −0.147769 + 0.0241863i
\(676\) −11.2996 + 12.4972i −0.434601 + 0.480663i
\(677\) 8.78670 8.78670i 0.337700 0.337700i −0.517801 0.855501i \(-0.673249\pi\)
0.855501 + 0.517801i \(0.173249\pi\)
\(678\) 0.575821 + 2.69998i 0.0221143 + 0.103692i
\(679\) 5.17660 0.198660
\(680\) −2.94665 + 8.97369i −0.112999 + 0.344125i
\(681\) −2.63095 + 12.4831i −0.100818 + 0.478354i
\(682\) −0.382852 + 0.169981i −0.0146602 + 0.00650890i
\(683\) 12.9374 + 12.9374i 0.495037 + 0.495037i 0.909889 0.414852i \(-0.136167\pi\)
−0.414852 + 0.909889i \(0.636167\pi\)
\(684\) 7.64845 + 2.92401i 0.292446 + 0.111802i
\(685\) −19.3584 + 19.3584i −0.739646 + 0.739646i
\(686\) −1.31976 0.508179i −0.0503885 0.0194024i
\(687\) 29.8895 + 6.29952i 1.14036 + 0.240342i
\(688\) 39.3129 + 32.1061i 1.49879 + 1.22403i
\(689\) 10.3532i 0.394424i
\(690\) −29.7957 19.3207i −1.13430 0.735527i
\(691\) 10.0400 + 10.0400i 0.381940 + 0.381940i 0.871801 0.489861i \(-0.162952\pi\)
−0.489861 + 0.871801i \(0.662952\pi\)
\(692\) 1.37728 + 27.3669i 0.0523564 + 1.04033i
\(693\) 1.76166 0.683197i 0.0669198 0.0259525i
\(694\) −4.68715 10.5570i −0.177922 0.400737i
\(695\) 22.3457i 0.847622i
\(696\) 8.79779 + 33.0179i 0.333479 + 1.25154i
\(697\) 11.6338i 0.440660i
\(698\) −43.6230 + 19.3680i −1.65115 + 0.733089i
\(699\) −4.34159 + 2.83009i −0.164214 + 0.107044i
\(700\) 1.00423 1.11067i 0.0379564 0.0419793i
\(701\) 25.2156 + 25.2156i 0.952381 + 0.952381i 0.998917 0.0465357i \(-0.0148181\pi\)
−0.0465357 + 0.998917i \(0.514818\pi\)
\(702\) −8.61561 13.1480i −0.325175 0.496238i
\(703\) 2.84958i 0.107474i
\(704\) −4.98143 + 0.757214i −0.187745 + 0.0285386i
\(705\) −4.15081 + 19.6945i −0.156328 + 0.741737i
\(706\) 0.299784 0.778549i 0.0112825 0.0293011i
\(707\) −2.41310 + 2.41310i −0.0907539 + 0.0907539i
\(708\) 19.0529 + 26.2438i 0.716053 + 0.986301i
\(709\) −18.4484 18.4484i −0.692844 0.692844i 0.270013 0.962857i \(-0.412972\pi\)
−0.962857 + 0.270013i \(0.912972\pi\)
\(710\) −16.9856 38.2572i −0.637460 1.43577i
\(711\) 45.5220 + 20.0804i 1.70721 + 0.753074i
\(712\) −6.70509 13.2614i −0.251284 0.496992i
\(713\) 2.84362 0.106495
\(714\) 0.711577 + 3.33653i 0.0266301 + 0.124866i
\(715\) −2.28418 + 2.28418i −0.0854236 + 0.0854236i
\(716\) −14.9286 + 0.751305i −0.557907 + 0.0280776i
\(717\) 6.20634 4.04563i 0.231780 0.151087i
\(718\) −2.31910 + 6.02276i −0.0865479 + 0.224767i
\(719\) 30.2998 1.12999 0.564996 0.825094i \(-0.308878\pi\)
0.564996 + 0.825094i \(0.308878\pi\)
\(720\) 25.6451 13.0438i 0.955735 0.486114i
\(721\) −5.77249 −0.214979
\(722\) −8.70893 + 22.6174i −0.324113 + 0.841731i
\(723\) −36.5843 + 23.8476i −1.36058 + 0.886904i
\(724\) −1.68662 33.5135i −0.0626827 1.24552i
\(725\) −3.69247 + 3.69247i −0.137135 + 0.137135i
\(726\) 5.41734 + 25.4015i 0.201056 + 0.942736i
\(727\) −14.0577 −0.521373 −0.260686 0.965424i \(-0.583949\pi\)
−0.260686 + 0.965424i \(0.583949\pi\)
\(728\) 5.74840 + 1.88758i 0.213050 + 0.0699582i
\(729\) −25.5911 + 8.60792i −0.947818 + 0.318812i
\(730\) 19.2899 + 43.4471i 0.713952 + 1.60805i
\(731\) −12.4969 12.4969i −0.462214 0.462214i
\(732\) −31.8901 + 23.1522i −1.17869 + 0.855729i
\(733\) 32.7566 32.7566i 1.20989 1.20989i 0.238831 0.971061i \(-0.423236\pi\)
0.971061 0.238831i \(-0.0767642\pi\)
\(734\) −9.85361 + 25.5901i −0.363703 + 0.944548i
\(735\) 0.856437 4.06356i 0.0315902 0.149887i
\(736\) 32.9929 + 9.02417i 1.21613 + 0.332635i
\(737\) 3.90275i 0.143760i
\(738\) 24.9988 25.1191i 0.920217 0.924646i
\(739\) −1.60188 1.60188i −0.0589260 0.0589260i 0.677030 0.735956i \(-0.263267\pi\)
−0.735956 + 0.677030i \(0.763267\pi\)
\(740\) 7.42696 + 6.71523i 0.273020 + 0.246857i
\(741\) −4.23592 + 2.76120i −0.155610 + 0.101435i
\(742\) −6.25578 + 2.77748i −0.229657 + 0.101964i
\(743\) 31.9687i 1.17282i 0.810015 + 0.586409i \(0.199459\pi\)
−0.810015 + 0.586409i \(0.800541\pi\)
\(744\) −1.15474 + 1.99364i −0.0423348 + 0.0730905i
\(745\) 26.1851i 0.959349i
\(746\) 15.8969 + 35.8049i 0.582025 + 1.31091i
\(747\) 14.1847 + 36.5760i 0.518991 + 1.33824i
\(748\) 1.75220 0.0881820i 0.0640666 0.00322425i
\(749\) 11.2943 + 11.2943i 0.412686 + 0.412686i
\(750\) −20.9492 13.5843i −0.764956 0.496028i
\(751\) 15.0201i 0.548093i 0.961716 + 0.274046i \(0.0883622\pi\)
−0.961716 + 0.274046i \(0.911638\pi\)
\(752\) −1.94637 19.2884i −0.0709769 0.703377i
\(753\) −27.7785 5.85460i −1.01230 0.213353i
\(754\) −19.6910 7.58214i −0.717106 0.276125i
\(755\) −34.5286 + 34.5286i −1.25663 + 1.25663i
\(756\) 5.63316 8.73313i 0.204876 0.317621i
\(757\) 5.17499 + 5.17499i 0.188088 + 0.188088i 0.794869 0.606781i \(-0.207539\pi\)
−0.606781 + 0.794869i \(0.707539\pi\)
\(758\) 40.1356 17.8196i 1.45779 0.647239i
\(759\) −1.36034 + 6.45445i −0.0493772 + 0.234282i
\(760\) −4.17595 8.25923i −0.151478 0.299594i
\(761\) −11.6404 −0.421966 −0.210983 0.977490i \(-0.567666\pi\)
−0.210983 + 0.977490i \(0.567666\pi\)
\(762\) 1.12630 + 5.28111i 0.0408014 + 0.191314i
\(763\) −7.78278 + 7.78278i −0.281755 + 0.281755i
\(764\) −18.1735 16.4319i −0.657494 0.594486i
\(765\) −9.34024 + 3.62228i −0.337697 + 0.130964i
\(766\) 43.9951 + 16.9405i 1.58961 + 0.612087i
\(767\) −20.0264 −0.723112
\(768\) −19.7245 + 19.4665i −0.711747 + 0.702436i
\(769\) 40.3055 1.45345 0.726726 0.686927i \(-0.241041\pi\)
0.726726 + 0.686927i \(0.241041\pi\)
\(770\) −1.99298 0.767406i −0.0718218 0.0276554i
\(771\) 17.3455 + 26.6095i 0.624683 + 0.958317i
\(772\) −15.0428 13.6012i −0.541401 0.489518i
\(773\) 17.0980 17.0980i 0.614971 0.614971i −0.329266 0.944237i \(-0.606801\pi\)
0.944237 + 0.329266i \(0.106801\pi\)
\(774\) 0.129257 + 53.8361i 0.00464605 + 1.93510i
\(775\) −0.352091 −0.0126475
\(776\) −6.60651 13.0664i −0.237160 0.469057i
\(777\) 3.53883 + 0.745845i 0.126955 + 0.0267570i
\(778\) −14.9506 + 6.63786i −0.536006 + 0.237979i
\(779\) −8.06067 8.06067i −0.288803 0.288803i
\(780\) −2.78561 + 17.5472i −0.0997409 + 0.628290i
\(781\) −5.49785 + 5.49785i −0.196729 + 0.196729i
\(782\) −11.1143 4.27962i −0.397447 0.153039i
\(783\) −21.1514 + 29.4304i −0.755888 + 1.05176i
\(784\) 0.401596 + 3.97979i 0.0143427 + 0.142135i
\(785\) 34.7444i 1.24008i
\(786\) −19.8937 + 30.6793i −0.709583 + 1.09429i
\(787\) 26.8062 + 26.8062i 0.955536 + 0.955536i 0.999053 0.0435165i \(-0.0138561\pi\)
−0.0435165 + 0.999053i \(0.513856\pi\)
\(788\) 54.4643 2.74100i 1.94021 0.0976442i
\(789\) 5.54276 + 8.50305i 0.197327 + 0.302717i
\(790\) −22.8195 51.3969i −0.811881 1.82862i
\(791\) 1.12705i 0.0400733i
\(792\) −3.97275 3.57474i −0.141166 0.127023i
\(793\) 24.3351i 0.864164i
\(794\) −18.3368 + 8.14126i −0.650747 + 0.288922i
\(795\) −10.9758 16.8378i −0.389272 0.597176i
\(796\) 15.4536 + 13.9727i 0.547740 + 0.495250i
\(797\) −30.6309 30.6309i −1.08500 1.08500i −0.996035 0.0889663i \(-0.971644\pi\)
−0.0889663 0.996035i \(-0.528356\pi\)
\(798\) −2.80481 1.81875i −0.0992890 0.0643829i
\(799\) 6.75017i 0.238804i
\(800\) −4.08510 1.11735i −0.144430 0.0395043i
\(801\) 6.36124 14.4208i 0.224763 0.509535i
\(802\) −7.85601 + 20.4023i −0.277405 + 0.720430i
\(803\) 6.24369 6.24369i 0.220335 0.220335i
\(804\) 12.6108 + 17.3703i 0.444749 + 0.612603i
\(805\) 10.2513 + 10.2513i 0.361312 + 0.361312i
\(806\) −0.577315 1.30030i −0.0203351 0.0458012i
\(807\) 2.76995 + 0.583795i 0.0975068 + 0.0205506i
\(808\) 9.17064 + 3.01132i 0.322622 + 0.105938i
\(809\) −5.88033 −0.206742 −0.103371 0.994643i \(-0.532963\pi\)
−0.103371 + 0.994643i \(0.532963\pi\)
\(810\) 27.9506 + 12.2494i 0.982086 + 0.430398i
\(811\) −18.5431 + 18.5431i −0.651137 + 0.651137i −0.953267 0.302130i \(-0.902302\pi\)
0.302130 + 0.953267i \(0.402302\pi\)
\(812\) −0.701158 13.9322i −0.0246058 0.488923i
\(813\) −6.50388 9.97750i −0.228101 0.349926i
\(814\) 0.668310 1.73562i 0.0234243 0.0608335i
\(815\) 6.09382 0.213457
\(816\) 7.51370 6.05428i 0.263032 0.211942i
\(817\) 17.3174 0.605859
\(818\) 6.35436 16.5025i 0.222175 0.576995i
\(819\) 2.32038 + 5.98321i 0.0810805 + 0.209070i
\(820\) −40.0043 + 2.01328i −1.39701 + 0.0703068i
\(821\) −17.7928 + 17.7928i −0.620972 + 0.620972i −0.945780 0.324808i \(-0.894700\pi\)
0.324808 + 0.945780i \(0.394700\pi\)
\(822\) 27.3538 5.83371i 0.954073 0.203474i
\(823\) −3.21292 −0.111995 −0.0559977 0.998431i \(-0.517834\pi\)
−0.0559977 + 0.998431i \(0.517834\pi\)
\(824\) 7.36700 + 14.5705i 0.256642 + 0.507588i
\(825\) 0.168434 0.799174i 0.00586412 0.0278237i
\(826\) −5.37254 12.1007i −0.186935 0.421038i
\(827\) 7.63626 + 7.63626i 0.265539 + 0.265539i 0.827300 0.561761i \(-0.189876\pi\)
−0.561761 + 0.827300i \(0.689876\pi\)
\(828\) 14.8014 + 33.1229i 0.514384 + 1.15110i
\(829\) 17.7711 17.7711i 0.617217 0.617217i −0.327600 0.944817i \(-0.606240\pi\)
0.944817 + 0.327600i \(0.106240\pi\)
\(830\) 15.9331 41.3787i 0.553045 1.43627i
\(831\) 6.75933 + 1.42460i 0.234479 + 0.0494187i
\(832\) −2.57177 16.9187i −0.0891600 0.586551i
\(833\) 1.39276i 0.0482564i
\(834\) −12.4205 + 19.1545i −0.430087 + 0.663265i
\(835\) −27.3645 27.3645i −0.946987 0.946987i
\(836\) −1.15294 + 1.27514i −0.0398754 + 0.0441017i
\(837\) −2.41158 + 0.394719i −0.0833565 + 0.0136435i
\(838\) −35.1163 + 15.5911i −1.21307 + 0.538587i
\(839\) 8.70592i 0.300562i −0.988643 0.150281i \(-0.951982\pi\)
0.988643 0.150281i \(-0.0480178\pi\)
\(840\) −11.3500 + 3.02426i −0.391612 + 0.104347i
\(841\) 19.6492i 0.677558i
\(842\) −0.527960 1.18914i −0.0181947 0.0409804i
\(843\) −37.4512 + 24.4127i −1.28989 + 0.840820i
\(844\) 0.476753 + 9.47318i 0.0164105 + 0.326080i
\(845\) 14.2821 + 14.2821i 0.491321 + 0.491321i
\(846\) 14.5049 14.5747i 0.498687 0.501087i
\(847\) 10.6033i 0.364334i
\(848\) 14.9945 + 12.2457i 0.514914 + 0.420520i
\(849\) 4.29896 20.3974i 0.147540 0.700037i
\(850\) 1.37615 + 0.529892i 0.0472014 + 0.0181752i
\(851\) −8.92757 + 8.92757i −0.306033 + 0.306033i
\(852\) −6.70475 + 42.2347i −0.229701 + 1.44694i
\(853\) −19.8103 19.8103i −0.678291 0.678291i 0.281323 0.959613i \(-0.409227\pi\)
−0.959613 + 0.281323i \(0.909227\pi\)
\(854\) 14.7042 6.52845i 0.503167 0.223399i
\(855\) 3.96180 8.98133i 0.135491 0.307155i
\(856\) 14.0943 42.9225i 0.481732 1.46706i
\(857\) −51.7656 −1.76828 −0.884139 0.467224i \(-0.845254\pi\)
−0.884139 + 0.467224i \(0.845254\pi\)
\(858\) 3.22760 0.688346i 0.110188 0.0234997i
\(859\) 1.55742 1.55742i 0.0531386 0.0531386i −0.680038 0.733177i \(-0.738037\pi\)
0.733177 + 0.680038i \(0.238037\pi\)
\(860\) 40.8096 45.1349i 1.39160 1.53909i
\(861\) −12.1202 + 7.90059i −0.413054 + 0.269251i
\(862\) −12.2682 4.72395i −0.417858 0.160898i
\(863\) 19.0224 0.647530 0.323765 0.946138i \(-0.395051\pi\)
0.323765 + 0.946138i \(0.395051\pi\)
\(864\) −29.2328 3.07341i −0.994519 0.104559i
\(865\) 32.8495 1.11692
\(866\) −17.9326 6.90506i −0.609376 0.234644i
\(867\) 21.8523 14.2445i 0.742143 0.483770i
\(868\) 0.630814 0.697672i 0.0214112 0.0236805i
\(869\) −7.38614 + 7.38614i −0.250557 + 0.250557i
\(870\) 40.0626 8.54410i 1.35825 0.289672i
\(871\) −13.2551 −0.449133
\(872\) 29.5773 + 9.71218i 1.00162 + 0.328896i
\(873\) 6.26771 14.2088i 0.212130 0.480895i
\(874\) 10.6660 4.73554i 0.360782 0.160182i
\(875\) 7.20764 + 7.20764i 0.243663 + 0.243663i
\(876\) 7.61431 47.9643i 0.257264 1.62056i
\(877\) 8.86901 8.86901i 0.299485 0.299485i −0.541327 0.840812i \(-0.682078\pi\)
0.840812 + 0.541327i \(0.182078\pi\)
\(878\) 0.254757 + 0.0980954i 0.00859762 + 0.00331056i
\(879\) 4.47109 21.2141i 0.150806 0.715534i
\(880\) 0.606453 + 6.00992i 0.0204435 + 0.202594i
\(881\) 30.7009i 1.03434i 0.855883 + 0.517170i \(0.173014\pi\)
−0.855883 + 0.517170i \(0.826986\pi\)
\(882\) −2.99279 + 3.00719i −0.100772 + 0.101257i
\(883\) −22.6512 22.6512i −0.762275 0.762275i 0.214458 0.976733i \(-0.431201\pi\)
−0.976733 + 0.214458i \(0.931201\pi\)
\(884\) 0.299497 + 5.95108i 0.0100732 + 0.200156i
\(885\) 32.5698 21.2308i 1.09482 0.713666i
\(886\) 4.07544 + 9.17923i 0.136917 + 0.308382i
\(887\) 11.9499i 0.401239i −0.979669 0.200620i \(-0.935704\pi\)
0.979669 0.200620i \(-0.0642955\pi\)
\(888\) −2.63374 9.88435i −0.0883825 0.331697i
\(889\) 2.20449i 0.0739362i
\(890\) −16.2820 + 7.22895i −0.545772 + 0.242315i
\(891\) 0.257727 5.66262i 0.00863418 0.189705i
\(892\) 16.5069 18.2565i 0.552693 0.611271i
\(893\) −4.67698 4.67698i −0.156509 0.156509i
\(894\) 14.5546 22.4455i 0.486777 0.750691i
\(895\) 17.9193i 0.598977i
\(896\) 9.53299 6.09279i 0.318475 0.203546i
\(897\) −21.9216 4.62020i −0.731940 0.154264i
\(898\) −18.4037 + 47.7948i −0.614138 + 1.59493i
\(899\) −2.31944 + 2.31944i −0.0773578 + 0.0773578i
\(900\) −1.83267 4.10120i −0.0610892 0.136707i
\(901\) −4.76649 4.76649i −0.158795 0.158795i
\(902\) 3.01913 + 6.80006i 0.100526 + 0.226417i
\(903\) 4.53263 21.5061i 0.150837 0.715679i
\(904\) −2.84482 + 1.43837i −0.0946174 + 0.0478395i
\(905\) −40.2274 −1.33721
\(906\) 48.7896 10.4053i 1.62093 0.345693i
\(907\) 41.0833 41.0833i 1.36415 1.36415i 0.495595 0.868554i \(-0.334950\pi\)
0.868554 0.495595i \(-0.165050\pi\)
\(908\) −14.7123 + 0.740421i −0.488245 + 0.0245717i
\(909\) 3.70178 + 9.54523i 0.122780 + 0.316595i
\(910\) 2.60638 6.76885i 0.0864007 0.224385i
\(911\) 21.3664 0.707902 0.353951 0.935264i \(-0.384838\pi\)
0.353951 + 0.935264i \(0.384838\pi\)
\(912\) −1.01119 + 9.40083i −0.0334838 + 0.311293i
\(913\) −8.23614 −0.272576
\(914\) 14.5740 37.8492i 0.482067 1.25194i
\(915\) 25.7986 + 39.5772i 0.852876 + 1.30838i
\(916\) 1.77286 + 35.2271i 0.0585769 + 1.16394i
\(917\) 10.5553 10.5553i 0.348567 0.348567i
\(918\) 10.0197 + 2.08664i 0.330700 + 0.0688695i
\(919\) 29.4386 0.971090 0.485545 0.874212i \(-0.338621\pi\)
0.485545 + 0.874212i \(0.338621\pi\)
\(920\) 12.7927 38.9587i 0.421763 1.28443i
\(921\) −35.1074 7.39924i −1.15683 0.243813i
\(922\) 9.11997 + 20.5411i 0.300350 + 0.676486i
\(923\) −18.6727 18.6727i −0.614618 0.614618i
\(924\) 1.28180 + 1.76557i 0.0421682 + 0.0580830i
\(925\) 1.10539 1.10539i 0.0363450 0.0363450i
\(926\) 4.12341 10.7086i 0.135504 0.351907i
\(927\) −6.98920 + 15.8444i −0.229556 + 0.520399i
\(928\) −34.2718 + 19.5504i −1.12503 + 0.641774i
\(929\) 16.0304i 0.525940i −0.964804 0.262970i \(-0.915298\pi\)
0.964804 0.262970i \(-0.0847021\pi\)
\(930\) 2.31742 + 1.50270i 0.0759911 + 0.0492756i
\(931\) 0.965003 + 0.965003i 0.0316267 + 0.0316267i
\(932\) −4.43887 4.01350i −0.145400 0.131466i
\(933\) −17.9529 27.5413i −0.587752 0.901660i
\(934\) −21.6065 + 9.59299i −0.706987 + 0.313892i
\(935\) 2.10323i 0.0687828i
\(936\) 12.1411 13.4929i 0.396844 0.441028i
\(937\) 10.2290i 0.334167i −0.985943 0.167084i \(-0.946565\pi\)
0.985943 0.167084i \(-0.0534350\pi\)
\(938\) −3.55599 8.00926i −0.116107 0.261511i
\(939\) −1.34049 2.05642i −0.0437452 0.0671089i
\(940\) −23.2114 + 1.16815i −0.757073 + 0.0381009i
\(941\) −13.7787 13.7787i −0.449172 0.449172i 0.445907 0.895079i \(-0.352881\pi\)
−0.895079 + 0.445907i \(0.852881\pi\)
\(942\) −19.3121 + 29.7824i −0.629221 + 0.970363i
\(943\) 50.5073i 1.64474i
\(944\) −23.6872 + 29.0043i −0.770954 + 0.944009i
\(945\) −10.1168 7.27084i −0.329099 0.236520i
\(946\) −10.5477 4.06144i −0.342935 0.132049i
\(947\) −18.3826 + 18.3826i −0.597354 + 0.597354i −0.939608 0.342253i \(-0.888810\pi\)
0.342253 + 0.939608i \(0.388810\pi\)
\(948\) −9.00755 + 56.7406i −0.292552 + 1.84285i
\(949\) 21.2058 + 21.2058i 0.688369 + 0.688369i
\(950\) −1.32064 + 0.586343i −0.0428471 + 0.0190235i
\(951\) 18.9228 + 3.98816i 0.613612 + 0.129325i
\(952\) −3.51552 + 1.77748i −0.113939 + 0.0576085i
\(953\) 32.8708 1.06479 0.532394 0.846497i \(-0.321292\pi\)
0.532394 + 0.846497i \(0.321292\pi\)
\(954\) 0.0493005 + 20.5339i 0.00159616 + 0.664809i
\(955\) −20.7691 + 20.7691i −0.672071 + 0.672071i
\(956\) 6.34541 + 5.73732i 0.205225 + 0.185558i
\(957\) −4.15508 6.37424i −0.134315 0.206050i
\(958\) 37.2289 + 14.3352i 1.20281 + 0.463149i
\(959\) −11.4183 −0.368715
\(960\) 22.1188 + 24.7892i 0.713881 + 0.800068i
\(961\) 30.7788 0.992866
\(962\) 5.89479 + 2.26982i 0.190055 + 0.0731819i
\(963\) 44.6758 17.3259i 1.43966 0.558320i
\(964\) −37.4040 33.8196i −1.20470 1.08926i
\(965\) −17.1912 + 17.1912i −0.553404 + 0.553404i
\(966\) −3.08927 14.4853i −0.0993957 0.466058i
\(967\) −55.1646 −1.77398 −0.886988 0.461793i \(-0.847206\pi\)
−0.886988 + 0.461793i \(0.847206\pi\)
\(968\) −26.7642 + 13.5322i −0.860233 + 0.434942i
\(969\) 0.678942 3.22140i 0.0218108 0.103486i
\(970\) −16.0426 + 7.12267i −0.515096 + 0.228695i
\(971\) 7.89937 + 7.89937i 0.253503 + 0.253503i 0.822405 0.568902i \(-0.192632\pi\)
−0.568902 + 0.822405i \(0.692632\pi\)
\(972\) −17.1503 26.0359i −0.550097 0.835101i
\(973\) 6.59016 6.59016i 0.211271 0.211271i
\(974\) −1.67000 0.643044i −0.0535104 0.0206044i
\(975\) 2.71428 + 0.572062i 0.0869264 + 0.0183206i
\(976\) −35.2445 28.7835i −1.12815 0.921339i
\(977\) 13.4649i 0.430780i 0.976528 + 0.215390i \(0.0691023\pi\)
−0.976528 + 0.215390i \(0.930898\pi\)
\(978\) −5.22353 3.38714i −0.167030 0.108309i
\(979\) 2.33984 + 2.33984i 0.0747817 + 0.0747817i
\(980\) 4.78922 0.241025i 0.152986 0.00769926i
\(981\) 11.9391 + 30.7855i 0.381185 + 0.982906i
\(982\) −17.3536 39.0858i −0.553774 1.24728i
\(983\) 2.38464i 0.0760581i −0.999277 0.0380291i \(-0.987892\pi\)
0.999277 0.0380291i \(-0.0121079\pi\)
\(984\) 35.4102 + 20.5100i 1.12884 + 0.653834i
\(985\) 65.3755i 2.08304i
\(986\) 12.5563 5.57481i 0.399873 0.177538i
\(987\) −7.03240 + 4.58410i −0.223844 + 0.145914i
\(988\) −4.33083 3.91581i −0.137782 0.124578i
\(989\) 54.2544 + 54.2544i 1.72519 + 1.72519i
\(990\) −4.51944 + 4.54119i −0.143637 + 0.144329i
\(991\) 42.9802i 1.36531i −0.730741 0.682655i \(-0.760825\pi\)
0.730741 0.682655i \(-0.239175\pi\)
\(992\) −2.56608 0.701870i −0.0814730 0.0222844i
\(993\) 6.18876 29.3640i 0.196394 0.931838i
\(994\) 6.27336 16.2921i 0.198979 0.516754i
\(995\) 17.6608 17.6608i 0.559884 0.559884i
\(996\) −36.6572 + 26.6131i −1.16153 + 0.843268i
\(997\) −1.43276 1.43276i −0.0453761 0.0453761i 0.684055 0.729431i \(-0.260215\pi\)
−0.729431 + 0.684055i \(0.760215\pi\)
\(998\) 7.61132 + 17.1432i 0.240932 + 0.542657i
\(999\) 6.33195 8.81039i 0.200334 0.278749i
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.d.155.2 48
3.2 odd 2 inner 336.2.s.d.155.23 yes 48
4.3 odd 2 1344.2.s.d.911.4 48
12.11 even 2 1344.2.s.d.911.17 48
16.3 odd 4 inner 336.2.s.d.323.23 yes 48
16.13 even 4 1344.2.s.d.239.17 48
48.29 odd 4 1344.2.s.d.239.4 48
48.35 even 4 inner 336.2.s.d.323.2 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.s.d.155.2 48 1.1 even 1 trivial
336.2.s.d.155.23 yes 48 3.2 odd 2 inner
336.2.s.d.323.2 yes 48 48.35 even 4 inner
336.2.s.d.323.23 yes 48 16.3 odd 4 inner
1344.2.s.d.239.4 48 48.29 odd 4
1344.2.s.d.239.17 48 16.13 even 4
1344.2.s.d.911.4 48 4.3 odd 2
1344.2.s.d.911.17 48 12.11 even 2