Properties

Label 825.2.cv.a.608.8
Level $825$
Weight $2$
Character 825.608
Analytic conductor $6.588$
Analytic rank $0$
Dimension $928$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(38,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 19, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.38");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.cv (of order \(20\), degree \(8\), 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: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(928\)
Relative dimension: \(116\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 608.8
Character \(\chi\) \(=\) 825.608
Dual form 825.2.cv.a.422.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.395170 - 2.49501i) q^{2} +(-1.66780 + 0.467371i) q^{3} +(-4.16679 + 1.35387i) q^{4} +(-0.105290 + 2.23359i) q^{5} +(1.82516 + 3.97649i) q^{6} +(0.988634 + 1.94030i) q^{7} +(2.73085 + 5.35960i) q^{8} +(2.56313 - 1.55896i) q^{9} +O(q^{10})\) \(q+(-0.395170 - 2.49501i) q^{2} +(-1.66780 + 0.467371i) q^{3} +(-4.16679 + 1.35387i) q^{4} +(-0.105290 + 2.23359i) q^{5} +(1.82516 + 3.97649i) q^{6} +(0.988634 + 1.94030i) q^{7} +(2.73085 + 5.35960i) q^{8} +(2.56313 - 1.55896i) q^{9} +(5.61442 - 0.619949i) q^{10} +(-3.23766 + 0.719398i) q^{11} +(6.31662 - 4.20542i) q^{12} +(-1.07948 + 2.11860i) q^{13} +(4.45039 - 3.23340i) q^{14} +(-0.868311 - 3.77439i) q^{15} +(5.20412 - 3.78102i) q^{16} +(2.22285 - 4.36258i) q^{17} +(-4.90250 - 5.77897i) q^{18} +(-1.10263 - 0.358267i) q^{19} +(-2.58527 - 9.44943i) q^{20} +(-2.55569 - 2.77398i) q^{21} +(3.07433 + 7.79371i) q^{22} +(-4.95313 - 2.52374i) q^{23} +(-7.05944 - 7.66243i) q^{24} +(-4.97783 - 0.470347i) q^{25} +(5.71251 + 1.85611i) q^{26} +(-3.54618 + 3.79798i) q^{27} +(-6.74635 - 6.74635i) q^{28} +(-2.17558 - 6.69574i) q^{29} +(-9.07400 + 3.65797i) q^{30} +9.76449 q^{31} +(-2.98337 - 2.98337i) q^{32} +(5.06356 - 2.71300i) q^{33} +(-11.7631 - 3.82206i) q^{34} +(-4.43793 + 2.00391i) q^{35} +(-8.56938 + 9.96602i) q^{36} +(-3.96161 + 0.627457i) q^{37} +(-0.458151 + 2.89265i) q^{38} +(0.810189 - 4.03793i) q^{39} +(-12.2587 + 5.53529i) q^{40} -7.61370i q^{41} +(-5.91118 + 7.47266i) q^{42} +(-8.42050 - 8.42050i) q^{43} +(12.5167 - 7.38096i) q^{44} +(3.21221 + 5.88912i) q^{45} +(-4.33943 + 13.3554i) q^{46} +(1.82458 + 11.5199i) q^{47} +(-6.91231 + 8.73824i) q^{48} +(1.32712 - 1.82662i) q^{49} +(0.793571 + 12.6056i) q^{50} +(-1.66833 + 8.31482i) q^{51} +(1.62966 - 10.2892i) q^{52} +(3.28243 + 6.44214i) q^{53} +(10.8773 + 7.34689i) q^{54} +(-1.26595 - 7.30735i) q^{55} +(-7.69944 + 10.5974i) q^{56} +(2.00641 + 0.0821803i) q^{57} +(-15.8462 + 8.07404i) q^{58} +(-1.40880 - 1.02355i) q^{59} +(8.72811 + 14.5515i) q^{60} +(1.41589 - 4.35765i) q^{61} +(-3.85864 - 24.3625i) q^{62} +(5.55886 + 3.43200i) q^{63} +(1.29743 - 1.78577i) q^{64} +(-4.61843 - 2.63418i) q^{65} +(-8.76993 - 11.5615i) q^{66} +(2.80979 - 0.445027i) q^{67} +(-3.35576 + 21.1874i) q^{68} +(9.44036 + 1.89416i) q^{69} +(6.75350 + 10.2808i) q^{70} -0.232686i q^{71} +(15.3549 + 9.48004i) q^{72} +(-7.21050 - 7.21050i) q^{73} +(3.13102 + 9.63629i) q^{74} +(8.52186 - 1.54205i) q^{75} +5.07948 q^{76} +(-4.59672 - 5.57083i) q^{77} +(-10.3948 - 0.425759i) q^{78} +(-6.64089 - 2.15776i) q^{79} +(7.89729 + 12.0220i) q^{80} +(4.13926 - 7.99165i) q^{81} +(-18.9962 + 3.00871i) q^{82} +(-4.68065 - 2.38491i) q^{83} +(14.4046 + 8.09853i) q^{84} +(9.51017 + 5.42426i) q^{85} +(-17.6817 + 24.3367i) q^{86} +(6.75782 + 10.1504i) q^{87} +(-12.6973 - 15.3880i) q^{88} +(-0.0432300 - 0.133048i) q^{89} +(13.4240 - 10.3417i) q^{90} -5.17794 q^{91} +(24.0555 + 3.81001i) q^{92} +(-16.2852 + 4.56364i) q^{93} +(28.0213 - 9.10466i) q^{94} +(0.916316 - 2.42510i) q^{95} +(6.37002 + 3.58134i) q^{96} +(-7.21489 - 14.1600i) q^{97} +(-5.08186 - 2.58934i) q^{98} +(-7.17703 + 6.89131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9} - 8 q^{12} - 24 q^{13} + 26 q^{15} + 204 q^{16} + 2 q^{18} - 40 q^{19} - 12 q^{21} - 40 q^{22} + 40 q^{24} - 8 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 24 q^{31} - 12 q^{33} - 40 q^{34} - 34 q^{36} + 16 q^{37} - 60 q^{39} - 28 q^{40} - 26 q^{42} - 40 q^{43} - 28 q^{45} - 4 q^{46} - 36 q^{48} + 60 q^{49} - 12 q^{51} - 68 q^{52} - 80 q^{54} - 32 q^{55} + 30 q^{57} + 112 q^{58} - 80 q^{60} - 4 q^{61} - 14 q^{63} + 100 q^{64} - 30 q^{66} - 12 q^{67} - 110 q^{69} + 60 q^{70} - 138 q^{72} + 140 q^{73} - 86 q^{75} - 128 q^{76} + 20 q^{78} - 20 q^{79} + 18 q^{81} + 52 q^{82} - 10 q^{84} + 28 q^{85} + 44 q^{87} - 36 q^{88} - 184 q^{90} - 24 q^{91} - 98 q^{93} - 300 q^{94} + 14 q^{96} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{3}{20}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.395170 2.49501i −0.279428 1.76424i −0.584006 0.811749i \(-0.698516\pi\)
0.304579 0.952487i \(-0.401484\pi\)
\(3\) −1.66780 + 0.467371i −0.962906 + 0.269837i
\(4\) −4.16679 + 1.35387i −2.08339 + 0.676936i
\(5\) −0.105290 + 2.23359i −0.0470869 + 0.998891i
\(6\) 1.82516 + 3.97649i 0.745118 + 1.62339i
\(7\) 0.988634 + 1.94030i 0.373669 + 0.733366i 0.998891 0.0470806i \(-0.0149918\pi\)
−0.625222 + 0.780447i \(0.714992\pi\)
\(8\) 2.73085 + 5.35960i 0.965502 + 1.89490i
\(9\) 2.56313 1.55896i 0.854376 0.519655i
\(10\) 5.61442 0.619949i 1.77544 0.196045i
\(11\) −3.23766 + 0.719398i −0.976192 + 0.216907i
\(12\) 6.31662 4.20542i 1.82345 1.21400i
\(13\) −1.07948 + 2.11860i −0.299394 + 0.587595i −0.990872 0.134803i \(-0.956960\pi\)
0.691478 + 0.722397i \(0.256960\pi\)
\(14\) 4.45039 3.23340i 1.18942 0.864162i
\(15\) −0.868311 3.77439i −0.224197 0.974544i
\(16\) 5.20412 3.78102i 1.30103 0.945254i
\(17\) 2.22285 4.36258i 0.539120 1.05808i −0.447384 0.894342i \(-0.647644\pi\)
0.986504 0.163740i \(-0.0523557\pi\)
\(18\) −4.90250 5.77897i −1.15553 1.36212i
\(19\) −1.10263 0.358267i −0.252961 0.0821920i 0.179792 0.983705i \(-0.442458\pi\)
−0.432753 + 0.901513i \(0.642458\pi\)
\(20\) −2.58527 9.44943i −0.578084 2.11296i
\(21\) −2.55569 2.77398i −0.557697 0.605333i
\(22\) 3.07433 + 7.79371i 0.655450 + 1.66162i
\(23\) −4.95313 2.52374i −1.03280 0.526237i −0.146432 0.989221i \(-0.546779\pi\)
−0.886367 + 0.462984i \(0.846779\pi\)
\(24\) −7.05944 7.66243i −1.44100 1.56409i
\(25\) −4.97783 0.470347i −0.995566 0.0940694i
\(26\) 5.71251 + 1.85611i 1.12031 + 0.364012i
\(27\) −3.54618 + 3.79798i −0.682462 + 0.730921i
\(28\) −6.74635 6.74635i −1.27494 1.27494i
\(29\) −2.17558 6.69574i −0.403995 1.24337i −0.921732 0.387828i \(-0.873226\pi\)
0.517737 0.855540i \(-0.326774\pi\)
\(30\) −9.07400 + 3.65797i −1.65668 + 0.667851i
\(31\) 9.76449 1.75375 0.876877 0.480714i \(-0.159623\pi\)
0.876877 + 0.480714i \(0.159623\pi\)
\(32\) −2.98337 2.98337i −0.527391 0.527391i
\(33\) 5.06356 2.71300i 0.881452 0.472273i
\(34\) −11.7631 3.82206i −2.01735 0.655477i
\(35\) −4.43793 + 2.00391i −0.750147 + 0.338722i
\(36\) −8.56938 + 9.96602i −1.42823 + 1.66100i
\(37\) −3.96161 + 0.627457i −0.651285 + 0.103153i −0.473330 0.880885i \(-0.656948\pi\)
−0.177955 + 0.984039i \(0.556948\pi\)
\(38\) −0.458151 + 2.89265i −0.0743219 + 0.469250i
\(39\) 0.810189 4.03793i 0.129734 0.646586i
\(40\) −12.2587 + 5.53529i −1.93826 + 0.875206i
\(41\) 7.61370i 1.18906i −0.804074 0.594530i \(-0.797338\pi\)
0.804074 0.594530i \(-0.202662\pi\)
\(42\) −5.91118 + 7.47266i −0.912115 + 1.15306i
\(43\) −8.42050 8.42050i −1.28411 1.28411i −0.938305 0.345809i \(-0.887604\pi\)
−0.345809 0.938305i \(-0.612396\pi\)
\(44\) 12.5167 7.38096i 1.88696 1.11272i
\(45\) 3.21221 + 5.88912i 0.478848 + 0.877898i
\(46\) −4.33943 + 13.3554i −0.639814 + 1.96915i
\(47\) 1.82458 + 11.5199i 0.266142 + 1.68035i 0.652331 + 0.757934i \(0.273791\pi\)
−0.386190 + 0.922419i \(0.626209\pi\)
\(48\) −6.91231 + 8.73824i −0.997706 + 1.26126i
\(49\) 1.32712 1.82662i 0.189588 0.260945i
\(50\) 0.793571 + 12.6056i 0.112228 + 1.78270i
\(51\) −1.66833 + 8.31482i −0.233612 + 1.16431i
\(52\) 1.62966 10.2892i 0.225993 1.42686i
\(53\) 3.28243 + 6.44214i 0.450877 + 0.884895i 0.998829 + 0.0483856i \(0.0154076\pi\)
−0.547952 + 0.836510i \(0.684592\pi\)
\(54\) 10.8773 + 7.34689i 1.48022 + 0.999786i
\(55\) −1.26595 7.30735i −0.170700 0.985323i
\(56\) −7.69944 + 10.5974i −1.02888 + 1.41613i
\(57\) 2.00641 + 0.0821803i 0.265756 + 0.0108850i
\(58\) −15.8462 + 8.07404i −2.08071 + 1.06017i
\(59\) −1.40880 1.02355i −0.183410 0.133255i 0.492292 0.870430i \(-0.336159\pi\)
−0.675702 + 0.737175i \(0.736159\pi\)
\(60\) 8.72811 + 14.5515i 1.12679 + 1.87859i
\(61\) 1.41589 4.35765i 0.181286 0.557940i −0.818579 0.574394i \(-0.805238\pi\)
0.999865 + 0.0164541i \(0.00523775\pi\)
\(62\) −3.85864 24.3625i −0.490047 3.09404i
\(63\) 5.55886 + 3.43200i 0.700351 + 0.432392i
\(64\) 1.29743 1.78577i 0.162179 0.223221i
\(65\) −4.61843 2.63418i −0.572845 0.326730i
\(66\) −8.76993 11.5615i −1.07950 1.42312i
\(67\) 2.80979 0.445027i 0.343271 0.0543687i 0.0175809 0.999845i \(-0.494404\pi\)
0.325690 + 0.945477i \(0.394404\pi\)
\(68\) −3.35576 + 21.1874i −0.406945 + 2.56935i
\(69\) 9.44036 + 1.89416i 1.13649 + 0.228030i
\(70\) 6.75350 + 10.2808i 0.807198 + 1.22879i
\(71\) 0.232686i 0.0276147i −0.999905 0.0138073i \(-0.995605\pi\)
0.999905 0.0138073i \(-0.00439515\pi\)
\(72\) 15.3549 + 9.48004i 1.80960 + 1.11723i
\(73\) −7.21050 7.21050i −0.843925 0.843925i 0.145442 0.989367i \(-0.453540\pi\)
−0.989367 + 0.145442i \(0.953540\pi\)
\(74\) 3.13102 + 9.63629i 0.363974 + 1.12020i
\(75\) 8.52186 1.54205i 0.984020 0.178060i
\(76\) 5.07948 0.582656
\(77\) −4.59672 5.57083i −0.523844 0.634855i
\(78\) −10.3948 0.425759i −1.17698 0.0482077i
\(79\) −6.64089 2.15776i −0.747159 0.242767i −0.0894006 0.995996i \(-0.528495\pi\)
−0.657758 + 0.753229i \(0.728495\pi\)
\(80\) 7.89729 + 12.0220i 0.882944 + 1.34410i
\(81\) 4.13926 7.99165i 0.459918 0.887961i
\(82\) −18.9962 + 3.00871i −2.09778 + 0.332256i
\(83\) −4.68065 2.38491i −0.513769 0.261778i 0.177829 0.984061i \(-0.443093\pi\)
−0.691597 + 0.722283i \(0.743093\pi\)
\(84\) 14.4046 + 8.09853i 1.57167 + 0.883622i
\(85\) 9.51017 + 5.42426i 1.03152 + 0.588343i
\(86\) −17.6817 + 24.3367i −1.90666 + 2.62430i
\(87\) 6.75782 + 10.1504i 0.724515 + 1.08823i
\(88\) −12.6973 15.3880i −1.35353 1.64037i
\(89\) −0.0432300 0.133048i −0.00458237 0.0141031i 0.948739 0.316060i \(-0.102360\pi\)
−0.953322 + 0.301957i \(0.902360\pi\)
\(90\) 13.4240 10.3417i 1.41502 1.09011i
\(91\) −5.17794 −0.542796
\(92\) 24.0555 + 3.81001i 2.50796 + 0.397221i
\(93\) −16.2852 + 4.56364i −1.68870 + 0.473227i
\(94\) 28.0213 9.10466i 2.89017 0.939074i
\(95\) 0.916316 2.42510i 0.0940120 0.248810i
\(96\) 6.37002 + 3.58134i 0.650137 + 0.365519i
\(97\) −7.21489 14.1600i −0.732561 1.43773i −0.892706 0.450639i \(-0.851196\pi\)
0.160145 0.987093i \(-0.448804\pi\)
\(98\) −5.08186 2.58934i −0.513345 0.261563i
\(99\) −7.17703 + 6.89131i −0.721319 + 0.692603i
\(100\) 21.3783 4.77950i 2.13783 0.477950i
\(101\) −1.40541 1.93438i −0.139844 0.192478i 0.733351 0.679851i \(-0.237955\pi\)
−0.873194 + 0.487372i \(0.837955\pi\)
\(102\) 21.4048 + 0.876715i 2.11939 + 0.0868077i
\(103\) −3.59235 + 7.05038i −0.353965 + 0.694694i −0.997496 0.0707253i \(-0.977469\pi\)
0.643531 + 0.765420i \(0.277469\pi\)
\(104\) −14.3028 −1.40250
\(105\) 6.46503 5.41628i 0.630922 0.528575i
\(106\) 14.7761 10.7354i 1.43518 1.04272i
\(107\) −0.315401 + 0.619009i −0.0304909 + 0.0598418i −0.905749 0.423814i \(-0.860691\pi\)
0.875259 + 0.483655i \(0.160691\pi\)
\(108\) 9.63420 20.6264i 0.927052 1.98478i
\(109\) 3.56169 + 1.15726i 0.341148 + 0.110846i 0.474580 0.880212i \(-0.342600\pi\)
−0.133432 + 0.991058i \(0.542600\pi\)
\(110\) −17.7316 + 6.04619i −1.69064 + 0.576482i
\(111\) 6.31393 2.89802i 0.599291 0.275067i
\(112\) 12.4813 + 6.35954i 1.17937 + 0.600920i
\(113\) −0.854684 + 0.854684i −0.0804019 + 0.0804019i −0.746164 0.665762i \(-0.768107\pi\)
0.665762 + 0.746164i \(0.268107\pi\)
\(114\) −0.587835 5.03849i −0.0550558 0.471898i
\(115\) 6.15852 10.7975i 0.574285 1.00687i
\(116\) 18.1303 + 24.9543i 1.68336 + 2.31695i
\(117\) 0.535974 + 7.11312i 0.0495508 + 0.657609i
\(118\) −1.99706 + 3.91945i −0.183844 + 0.360814i
\(119\) 10.6623 0.977413
\(120\) 17.8580 14.9611i 1.63020 1.36576i
\(121\) 9.96493 4.65834i 0.905903 0.423485i
\(122\) −11.4319 1.81063i −1.03499 0.163927i
\(123\) 3.55842 + 12.6981i 0.320852 + 1.14495i
\(124\) −40.6866 + 13.2199i −3.65376 + 1.18718i
\(125\) 1.57467 11.0689i 0.140843 0.990032i
\(126\) 6.36618 15.2256i 0.567144 1.35641i
\(127\) −8.09611 15.8895i −0.718413 1.40997i −0.904085 0.427354i \(-0.859446\pi\)
0.185671 0.982612i \(-0.440554\pi\)
\(128\) −12.4867 6.36231i −1.10368 0.562354i
\(129\) 17.9792 + 10.1082i 1.58298 + 0.889980i
\(130\) −4.74724 + 12.5640i −0.416361 + 1.10193i
\(131\) 1.87821 2.58514i 0.164100 0.225865i −0.719046 0.694963i \(-0.755421\pi\)
0.883146 + 0.469098i \(0.155421\pi\)
\(132\) −17.4257 + 18.1599i −1.51671 + 1.58062i
\(133\) −0.394953 2.49364i −0.0342468 0.216226i
\(134\) −2.22069 6.83459i −0.191839 0.590418i
\(135\) −8.10974 8.32059i −0.697975 0.716122i
\(136\) 29.4520 2.52548
\(137\) −9.24642 1.46449i −0.789975 0.125120i −0.251607 0.967830i \(-0.580959\pi\)
−0.538368 + 0.842710i \(0.680959\pi\)
\(138\) 0.995392 24.3023i 0.0847334 2.06875i
\(139\) 14.1197i 1.19762i 0.800891 + 0.598810i \(0.204360\pi\)
−0.800891 + 0.598810i \(0.795640\pi\)
\(140\) 15.7789 14.3582i 1.33356 1.21349i
\(141\) −8.42711 18.3602i −0.709690 1.54621i
\(142\) −0.580552 + 0.0919504i −0.0487188 + 0.00771631i
\(143\) 1.97088 7.63590i 0.164813 0.638546i
\(144\) 7.44437 17.8043i 0.620364 1.48369i
\(145\) 15.1846 4.15435i 1.26101 0.345000i
\(146\) −15.1409 + 20.8396i −1.25307 + 1.72470i
\(147\) −1.35966 + 3.66669i −0.112143 + 0.302424i
\(148\) 15.6577 7.97799i 1.28705 0.655787i
\(149\) −0.445257 0.323498i −0.0364769 0.0265020i 0.569397 0.822062i \(-0.307177\pi\)
−0.605874 + 0.795560i \(0.707177\pi\)
\(150\) −7.21500 20.6527i −0.589102 1.68629i
\(151\) −0.857726 2.63981i −0.0698007 0.214825i 0.910071 0.414452i \(-0.136027\pi\)
−0.979872 + 0.199628i \(0.936027\pi\)
\(152\) −1.09096 6.88804i −0.0884884 0.558694i
\(153\) −1.10367 14.6472i −0.0892261 1.18416i
\(154\) −12.0828 + 13.6703i −0.973658 + 1.10158i
\(155\) −1.02810 + 21.8098i −0.0825789 + 1.75181i
\(156\) 2.09095 + 17.9221i 0.167410 + 1.43491i
\(157\) −20.5382 10.4648i −1.63913 0.835179i −0.997685 0.0680108i \(-0.978335\pi\)
−0.641446 0.767168i \(-0.721665\pi\)
\(158\) −2.75934 + 17.4218i −0.219521 + 1.38600i
\(159\) −8.48531 9.21010i −0.672929 0.730408i
\(160\) 6.97774 6.34951i 0.551639 0.501973i
\(161\) 12.1056i 0.954058i
\(162\) −21.5749 7.16942i −1.69509 0.563283i
\(163\) −5.08055 + 9.97114i −0.397939 + 0.781000i −0.999846 0.0175666i \(-0.994408\pi\)
0.601906 + 0.798567i \(0.294408\pi\)
\(164\) 10.3080 + 31.7247i 0.804917 + 2.47728i
\(165\) 5.52659 + 11.5956i 0.430244 + 0.902712i
\(166\) −4.10072 + 12.6207i −0.318277 + 0.979557i
\(167\) 14.0411 + 14.0411i 1.08653 + 1.08653i 0.995883 + 0.0906497i \(0.0288944\pi\)
0.0906497 + 0.995883i \(0.471106\pi\)
\(168\) 7.88824 21.2728i 0.608591 1.64123i
\(169\) 4.31801 + 5.94324i 0.332155 + 0.457172i
\(170\) 9.77543 25.8714i 0.749741 1.98425i
\(171\) −3.38471 + 0.800679i −0.258835 + 0.0612295i
\(172\) 46.4867 + 23.6862i 3.54458 + 1.80605i
\(173\) −2.50470 + 15.8141i −0.190429 + 1.20232i 0.688452 + 0.725282i \(0.258291\pi\)
−0.878881 + 0.477041i \(0.841709\pi\)
\(174\) 22.6547 20.8719i 1.71745 1.58230i
\(175\) −4.00864 10.1235i −0.303024 0.765265i
\(176\) −14.1291 + 15.9855i −1.06502 + 1.20495i
\(177\) 2.82798 + 1.04865i 0.212564 + 0.0788216i
\(178\) −0.314873 + 0.160436i −0.0236007 + 0.0120252i
\(179\) −10.6937 7.76945i −0.799287 0.580716i 0.111418 0.993774i \(-0.464461\pi\)
−0.910705 + 0.413058i \(0.864461\pi\)
\(180\) −21.3577 20.1898i −1.59191 1.50486i
\(181\) −1.70358 5.24308i −0.126626 0.389715i 0.867568 0.497319i \(-0.165682\pi\)
−0.994194 + 0.107604i \(0.965682\pi\)
\(182\) 2.04617 + 12.9190i 0.151672 + 0.957621i
\(183\) −0.324780 + 7.92944i −0.0240084 + 0.586161i
\(184\) 33.4388i 2.46514i
\(185\) −0.984365 8.91467i −0.0723720 0.655420i
\(186\) 17.8218 + 38.8284i 1.30675 + 2.84703i
\(187\) −4.05840 + 15.7237i −0.296779 + 1.14983i
\(188\) −23.1991 45.5308i −1.69197 3.32068i
\(189\) −10.8751 3.12586i −0.791047 0.227372i
\(190\) −6.41275 1.32789i −0.465230 0.0963350i
\(191\) 5.85179 8.05429i 0.423420 0.582788i −0.543007 0.839728i \(-0.682714\pi\)
0.966427 + 0.256940i \(0.0827143\pi\)
\(192\) −1.32925 + 3.58469i −0.0959303 + 0.258702i
\(193\) 1.70784 + 10.7829i 0.122933 + 0.776168i 0.969717 + 0.244231i \(0.0785356\pi\)
−0.846784 + 0.531937i \(0.821464\pi\)
\(194\) −32.4782 + 23.5968i −2.33180 + 1.69415i
\(195\) 8.93376 + 2.23478i 0.639760 + 0.160036i
\(196\) −3.05680 + 9.40787i −0.218343 + 0.671991i
\(197\) −4.18677 0.663119i −0.298295 0.0472453i 0.00549311 0.999985i \(-0.498251\pi\)
−0.303788 + 0.952740i \(0.598251\pi\)
\(198\) 20.0300 + 15.1835i 1.42347 + 1.07905i
\(199\) 3.36286i 0.238387i −0.992871 0.119193i \(-0.961969\pi\)
0.992871 0.119193i \(-0.0380308\pi\)
\(200\) −11.0728 27.9636i −0.782968 1.97733i
\(201\) −4.47818 + 2.05543i −0.315867 + 0.144979i
\(202\) −4.27092 + 4.27092i −0.300501 + 0.300501i
\(203\) 10.8409 10.8409i 0.760883 0.760883i
\(204\) −4.30564 36.9048i −0.301455 2.58385i
\(205\) 17.0059 + 0.801643i 1.18774 + 0.0559892i
\(206\) 19.0103 + 6.17683i 1.32451 + 0.430360i
\(207\) −16.6299 + 1.25307i −1.15586 + 0.0870940i
\(208\) 2.39271 + 15.1070i 0.165905 + 1.04748i
\(209\) 3.82769 + 0.366716i 0.264767 + 0.0253663i
\(210\) −16.0684 13.9899i −1.10883 0.965397i
\(211\) −8.53803 6.20324i −0.587782 0.427049i 0.253739 0.967273i \(-0.418340\pi\)
−0.841521 + 0.540224i \(0.818340\pi\)
\(212\) −22.3990 22.3990i −1.53837 1.53837i
\(213\) 0.108750 + 0.388073i 0.00745146 + 0.0265904i
\(214\) 1.66907 + 0.542313i 0.114095 + 0.0370718i
\(215\) 19.6945 17.9213i 1.34315 1.22222i
\(216\) −30.0397 8.63438i −2.04394 0.587495i
\(217\) 9.65351 + 18.9461i 0.655323 + 1.28614i
\(218\) 1.47990 9.34375i 0.100232 0.632838i
\(219\) 15.3957 + 8.65571i 1.04034 + 0.584899i
\(220\) 15.1681 + 28.7343i 1.02264 + 1.93726i
\(221\) 6.84305 + 9.41866i 0.460314 + 0.633567i
\(222\) −9.72565 14.6081i −0.652743 0.980430i
\(223\) 12.8324 + 2.03245i 0.859321 + 0.136103i 0.570518 0.821285i \(-0.306743\pi\)
0.288803 + 0.957388i \(0.406743\pi\)
\(224\) 2.83919 8.73812i 0.189701 0.583840i
\(225\) −13.4921 + 6.55470i −0.899471 + 0.436980i
\(226\) 2.47019 + 1.79470i 0.164315 + 0.119382i
\(227\) −7.85035 7.85035i −0.521046 0.521046i 0.396841 0.917887i \(-0.370106\pi\)
−0.917887 + 0.396841i \(0.870106\pi\)
\(228\) −8.47157 + 2.37400i −0.561043 + 0.157222i
\(229\) −5.34549 1.73686i −0.353240 0.114775i 0.127022 0.991900i \(-0.459458\pi\)
−0.480262 + 0.877125i \(0.659458\pi\)
\(230\) −29.3736 11.0987i −1.93684 0.731826i
\(231\) 10.2701 + 7.14267i 0.675720 + 0.469953i
\(232\) 29.9453 29.9453i 1.96600 1.96600i
\(233\) 8.14550 8.14550i 0.533630 0.533630i −0.388021 0.921651i \(-0.626841\pi\)
0.921651 + 0.388021i \(0.126841\pi\)
\(234\) 17.5355 4.14815i 1.14633 0.271173i
\(235\) −25.9229 + 2.86242i −1.69102 + 0.186724i
\(236\) 7.25594 + 2.35760i 0.472321 + 0.153467i
\(237\) 12.0842 + 0.494953i 0.784951 + 0.0321506i
\(238\) −4.21343 26.6026i −0.273116 1.72439i
\(239\) −10.5369 + 7.65552i −0.681577 + 0.495195i −0.873880 0.486141i \(-0.838404\pi\)
0.192304 + 0.981335i \(0.438404\pi\)
\(240\) −18.7898 16.3593i −1.21288 1.05599i
\(241\) 1.73938 5.35325i 0.112043 0.344833i −0.879276 0.476313i \(-0.841973\pi\)
0.991319 + 0.131480i \(0.0419729\pi\)
\(242\) −15.5604 23.0217i −1.00026 1.47989i
\(243\) −3.16841 + 15.2631i −0.203253 + 0.979126i
\(244\) 20.0743i 1.28513i
\(245\) 3.94018 + 3.15655i 0.251729 + 0.201665i
\(246\) 30.2758 13.8962i 1.93031 0.885990i
\(247\) 1.94930 1.94930i 0.124031 0.124031i
\(248\) 26.6654 + 52.3338i 1.69325 + 3.32320i
\(249\) 8.92104 + 1.78996i 0.565348 + 0.113434i
\(250\) −28.2392 + 0.445274i −1.78601 + 0.0281616i
\(251\) −5.44865 7.49943i −0.343916 0.473360i 0.601664 0.798749i \(-0.294505\pi\)
−0.945580 + 0.325390i \(0.894505\pi\)
\(252\) −27.8091 6.77445i −1.75181 0.426750i
\(253\) 17.8521 + 4.60777i 1.12235 + 0.289688i
\(254\) −36.4451 + 26.4789i −2.28677 + 1.66143i
\(255\) −18.3962 4.60182i −1.15202 0.288177i
\(256\) −9.57543 + 29.4701i −0.598464 + 1.84188i
\(257\) 17.1335 8.72996i 1.06876 0.544560i 0.171101 0.985253i \(-0.445267\pi\)
0.897658 + 0.440693i \(0.145267\pi\)
\(258\) 18.1153 48.8528i 1.12781 3.04144i
\(259\) −5.13404 7.06640i −0.319014 0.439085i
\(260\) 22.8103 + 4.72333i 1.41464 + 0.292929i
\(261\) −16.0147 13.7704i −0.991285 0.852366i
\(262\) −7.19215 3.66459i −0.444333 0.226399i
\(263\) 3.89423 + 7.64286i 0.240129 + 0.471279i 0.979347 0.202187i \(-0.0648048\pi\)
−0.739218 + 0.673466i \(0.764805\pi\)
\(264\) 28.3684 + 19.7298i 1.74596 + 1.21429i
\(265\) −14.7347 + 6.65331i −0.905144 + 0.408710i
\(266\) −6.06556 + 1.97082i −0.371904 + 0.120839i
\(267\) 0.134282 + 0.201694i 0.00821792 + 0.0123434i
\(268\) −11.1053 + 5.65843i −0.678364 + 0.345644i
\(269\) −0.789516 2.42988i −0.0481377 0.148153i 0.924098 0.382154i \(-0.124818\pi\)
−0.972236 + 0.234002i \(0.924818\pi\)
\(270\) −17.5552 + 23.5219i −1.06838 + 1.43150i
\(271\) −7.30064 22.4691i −0.443482 1.36490i −0.884140 0.467223i \(-0.845255\pi\)
0.440657 0.897675i \(-0.354745\pi\)
\(272\) −4.92703 31.1080i −0.298745 1.88620i
\(273\) 8.63579 2.42002i 0.522662 0.146466i
\(274\) 23.6486i 1.42866i
\(275\) 16.4549 2.05821i 0.992268 0.124115i
\(276\) −41.9004 + 4.88847i −2.52211 + 0.294252i
\(277\) 25.1855 3.98900i 1.51325 0.239676i 0.656074 0.754696i \(-0.272216\pi\)
0.857178 + 0.515021i \(0.172216\pi\)
\(278\) 35.2288 5.57970i 2.11288 0.334648i
\(279\) 25.0277 15.2225i 1.49837 0.911347i
\(280\) −22.8595 18.3132i −1.36611 1.09442i
\(281\) 3.58411 1.16455i 0.213810 0.0694711i −0.200154 0.979765i \(-0.564144\pi\)
0.413964 + 0.910293i \(0.364144\pi\)
\(282\) −42.4787 + 28.2811i −2.52957 + 1.68411i
\(283\) −2.74863 + 1.40050i −0.163389 + 0.0832510i −0.533773 0.845628i \(-0.679226\pi\)
0.370384 + 0.928879i \(0.379226\pi\)
\(284\) 0.315026 + 0.969551i 0.0186934 + 0.0575323i
\(285\) −0.394811 + 4.47285i −0.0233866 + 0.264949i
\(286\) −19.8305 1.89988i −1.17260 0.112342i
\(287\) 14.7729 7.52716i 0.872016 0.444314i
\(288\) −12.2977 2.99580i −0.724652 0.176529i
\(289\) −4.09873 5.64142i −0.241102 0.331848i
\(290\) −16.3656 36.2440i −0.961023 2.12832i
\(291\) 18.6510 + 20.2441i 1.09334 + 1.18673i
\(292\) 39.8067 + 20.2825i 2.32951 + 1.18695i
\(293\) 5.87904 + 11.5383i 0.343457 + 0.674073i 0.996531 0.0832213i \(-0.0265208\pi\)
−0.653074 + 0.757294i \(0.726521\pi\)
\(294\) 9.68572 + 1.94339i 0.564883 + 0.113341i
\(295\) 2.43453 3.03891i 0.141744 0.176932i
\(296\) −14.1815 19.5191i −0.824282 1.13453i
\(297\) 8.74908 14.8477i 0.507673 0.861550i
\(298\) −0.631178 + 1.23876i −0.0365631 + 0.0717592i
\(299\) 10.6936 7.76937i 0.618428 0.449314i
\(300\) −33.4211 + 17.9629i −1.92957 + 1.03709i
\(301\) 8.01353 24.6631i 0.461892 1.42156i
\(302\) −6.24739 + 3.18321i −0.359497 + 0.183173i
\(303\) 3.24802 + 2.56932i 0.186594 + 0.147603i
\(304\) −7.09284 + 2.30460i −0.406802 + 0.132178i
\(305\) 9.58411 + 3.62132i 0.548785 + 0.207356i
\(306\) −36.1087 + 8.54179i −2.06420 + 0.488302i
\(307\) 14.6574 14.6574i 0.836544 0.836544i −0.151859 0.988402i \(-0.548526\pi\)
0.988402 + 0.151859i \(0.0485258\pi\)
\(308\) 26.6957 + 16.9891i 1.52113 + 0.968044i
\(309\) 2.69618 13.4376i 0.153381 0.764438i
\(310\) 54.8220 6.05349i 3.11368 0.343815i
\(311\) 11.4926 + 15.8182i 0.651687 + 0.896970i 0.999171 0.0407162i \(-0.0129639\pi\)
−0.347484 + 0.937686i \(0.612964\pi\)
\(312\) 23.8542 6.68469i 1.35048 0.378446i
\(313\) 10.4367 + 1.65300i 0.589915 + 0.0934333i 0.444253 0.895901i \(-0.353469\pi\)
0.145661 + 0.989335i \(0.453469\pi\)
\(314\) −17.9935 + 55.3784i −1.01543 + 3.12519i
\(315\) −8.25097 + 12.0548i −0.464890 + 0.679214i
\(316\) 30.5925 1.72096
\(317\) 13.9809 + 13.9809i 0.785245 + 0.785245i 0.980711 0.195466i \(-0.0626218\pi\)
−0.195466 + 0.980711i \(0.562622\pi\)
\(318\) −19.6261 + 24.8105i −1.10058 + 1.39130i
\(319\) 11.8607 + 20.1134i 0.664071 + 1.12614i
\(320\) 3.85206 + 3.08596i 0.215337 + 0.172510i
\(321\) 0.236719 1.17979i 0.0132124 0.0658496i
\(322\) −30.2036 + 4.78379i −1.68318 + 0.266590i
\(323\) −4.01395 + 4.01395i −0.223342 + 0.223342i
\(324\) −6.42776 + 38.9035i −0.357098 + 2.16131i
\(325\) 6.36995 10.0383i 0.353341 0.556825i
\(326\) 26.8858 + 8.73571i 1.48906 + 0.483826i
\(327\) −6.48106 0.265456i −0.358403 0.0146798i
\(328\) 40.8064 20.7919i 2.25315 1.14804i
\(329\) −20.5483 + 14.9292i −1.13286 + 0.823075i
\(330\) 26.7470 18.3711i 1.47238 1.01130i
\(331\) −3.99322 2.90124i −0.219487 0.159467i 0.472609 0.881272i \(-0.343312\pi\)
−0.692096 + 0.721806i \(0.743312\pi\)
\(332\) 22.7322 + 3.60042i 1.24759 + 0.197599i
\(333\) −9.17594 + 7.78426i −0.502838 + 0.426575i
\(334\) 29.4840 40.5813i 1.61329 2.22051i
\(335\) 0.698166 + 6.32277i 0.0381449 + 0.345450i
\(336\) −23.7886 4.77306i −1.29777 0.260392i
\(337\) −26.5191 + 4.20021i −1.44459 + 0.228800i −0.828991 0.559262i \(-0.811085\pi\)
−0.615596 + 0.788062i \(0.711085\pi\)
\(338\) 13.1221 13.1221i 0.713746 0.713746i
\(339\) 1.02599 1.82490i 0.0557241 0.0991149i
\(340\) −46.9706 9.72619i −2.54734 0.527477i
\(341\) −31.6141 + 7.02456i −1.71200 + 0.380401i
\(342\) 3.33524 + 8.12848i 0.180349 + 0.439538i
\(343\) 19.9121 + 3.15377i 1.07515 + 0.170288i
\(344\) 22.1354 68.1256i 1.19346 3.67309i
\(345\) −5.22474 + 20.8864i −0.281291 + 1.12449i
\(346\) 40.4460 2.17439
\(347\) −12.1640 12.1640i −0.652998 0.652998i 0.300716 0.953714i \(-0.402774\pi\)
−0.953714 + 0.300716i \(0.902774\pi\)
\(348\) −41.9007 33.1452i −2.24611 1.77677i
\(349\) 14.6432 4.75787i 0.783834 0.254683i 0.110358 0.993892i \(-0.464800\pi\)
0.673476 + 0.739209i \(0.264800\pi\)
\(350\) −23.6741 + 14.0021i −1.26543 + 0.748443i
\(351\) −4.21836 11.6128i −0.225160 0.619845i
\(352\) 11.8054 + 7.51293i 0.629230 + 0.400440i
\(353\) 4.25674 26.8760i 0.226563 1.43047i −0.567872 0.823117i \(-0.692233\pi\)
0.794436 0.607348i \(-0.207767\pi\)
\(354\) 1.49886 7.47023i 0.0796637 0.397038i
\(355\) 0.519724 + 0.0244994i 0.0275841 + 0.00130029i
\(356\) 0.360260 + 0.495856i 0.0190937 + 0.0262803i
\(357\) −17.7826 + 4.98326i −0.941157 + 0.263742i
\(358\) −15.1590 + 29.7512i −0.801177 + 1.57240i
\(359\) 13.1392 + 9.54618i 0.693460 + 0.503828i 0.877796 0.479035i \(-0.159013\pi\)
−0.184336 + 0.982863i \(0.559013\pi\)
\(360\) −22.7912 + 33.2985i −1.20120 + 1.75498i
\(361\) −14.2839 10.3778i −0.751783 0.546202i
\(362\) −12.4083 + 6.32236i −0.652167 + 0.332296i
\(363\) −14.4424 + 12.4265i −0.758028 + 0.652222i
\(364\) 21.5754 7.01027i 1.13086 0.367438i
\(365\) 16.8645 15.3461i 0.882727 0.803251i
\(366\) 19.9124 2.32315i 1.04084 0.121433i
\(367\) −4.30623 + 27.1885i −0.224783 + 1.41923i 0.574614 + 0.818424i \(0.305152\pi\)
−0.799398 + 0.600802i \(0.794848\pi\)
\(368\) −35.3190 + 5.59398i −1.84113 + 0.291606i
\(369\) −11.8695 19.5149i −0.617900 1.01590i
\(370\) −21.8532 + 5.97881i −1.13609 + 0.310824i
\(371\) −9.25458 + 12.7378i −0.480474 + 0.661315i
\(372\) 61.6786 41.0638i 3.19788 2.12906i
\(373\) −2.92230 + 5.73533i −0.151311 + 0.296964i −0.954203 0.299160i \(-0.903294\pi\)
0.802892 + 0.596124i \(0.203294\pi\)
\(374\) 40.8345 + 3.91220i 2.11150 + 0.202295i
\(375\) 2.54703 + 19.1967i 0.131528 + 0.991312i
\(376\) −56.7595 + 41.2382i −2.92715 + 2.12670i
\(377\) 16.5341 + 2.61874i 0.851549 + 0.134872i
\(378\) −3.50151 + 28.3687i −0.180098 + 1.45913i
\(379\) 25.7060i 1.32043i 0.751078 + 0.660213i \(0.229534\pi\)
−0.751078 + 0.660213i \(0.770466\pi\)
\(380\) −0.534816 + 11.3455i −0.0274355 + 0.582010i
\(381\) 20.9290 + 22.7167i 1.07223 + 1.16381i
\(382\) −22.4080 11.4174i −1.14649 0.584167i
\(383\) −18.6767 + 18.6767i −0.954337 + 0.954337i −0.999002 0.0446648i \(-0.985778\pi\)
0.0446648 + 0.999002i \(0.485778\pi\)
\(384\) 23.7990 + 4.77514i 1.21449 + 0.243681i
\(385\) 12.9269 9.68062i 0.658817 0.493370i
\(386\) 26.2285 8.52214i 1.33499 0.433766i
\(387\) −34.7101 8.45557i −1.76441 0.429821i
\(388\) 49.2338 + 49.2338i 2.49947 + 2.49947i
\(389\) 18.5131 0.938653 0.469326 0.883025i \(-0.344497\pi\)
0.469326 + 0.883025i \(0.344497\pi\)
\(390\) 2.04544 23.1729i 0.103575 1.17341i
\(391\) −22.0201 + 15.9985i −1.11360 + 0.809081i
\(392\) 13.4141 + 2.12458i 0.677514 + 0.107308i
\(393\) −1.92427 + 5.18932i −0.0970666 + 0.261767i
\(394\) 10.7081i 0.539464i
\(395\) 5.51876 14.6058i 0.277679 0.734899i
\(396\) 20.5752 38.4314i 1.03394 1.93125i
\(397\) 0.180600 1.14026i 0.00906405 0.0572282i −0.982742 0.184983i \(-0.940777\pi\)
0.991806 + 0.127755i \(0.0407770\pi\)
\(398\) −8.39035 + 1.32890i −0.420570 + 0.0666118i
\(399\) 1.82416 + 3.97430i 0.0913220 + 0.198964i
\(400\) −27.6836 + 16.3735i −1.38418 + 0.818675i
\(401\) −10.8529 + 14.9377i −0.541968 + 0.745955i −0.988895 0.148615i \(-0.952518\pi\)
0.446927 + 0.894570i \(0.352518\pi\)
\(402\) 6.89796 + 10.3609i 0.344039 + 0.516752i
\(403\) −10.5406 + 20.6871i −0.525064 + 1.03050i
\(404\) 8.47495 + 6.15741i 0.421645 + 0.306343i
\(405\) 17.4142 + 10.0868i 0.865320 + 0.501219i
\(406\) −31.3322 22.7642i −1.55499 1.12977i
\(407\) 12.3750 4.88147i 0.613405 0.241966i
\(408\) −49.1200 + 13.7650i −2.43180 + 0.681468i
\(409\) −24.5250 + 7.96866i −1.21268 + 0.394025i −0.844412 0.535694i \(-0.820050\pi\)
−0.368271 + 0.929719i \(0.620050\pi\)
\(410\) −4.72011 42.7465i −0.233109 2.11110i
\(411\) 16.1057 1.87903i 0.794434 0.0926856i
\(412\) 5.42324 34.2410i 0.267184 1.68693i
\(413\) 0.593217 3.74542i 0.0291903 0.184300i
\(414\) 9.69806 + 40.9966i 0.476634 + 2.01487i
\(415\) 5.81974 10.2035i 0.285680 0.500872i
\(416\) 9.54108 3.10008i 0.467790 0.151994i
\(417\) −6.59915 23.5489i −0.323162 1.15320i
\(418\) −0.597628 9.69502i −0.0292310 0.474199i
\(419\) −22.4786 16.3317i −1.09815 0.797853i −0.117394 0.993085i \(-0.537454\pi\)
−0.980757 + 0.195232i \(0.937454\pi\)
\(420\) −19.6054 + 31.3213i −0.956647 + 1.52832i
\(421\) −8.99888 6.53807i −0.438579 0.318646i 0.346491 0.938053i \(-0.387373\pi\)
−0.785070 + 0.619407i \(0.787373\pi\)
\(422\) −12.1032 + 23.7538i −0.589173 + 1.15632i
\(423\) 22.6358 + 26.6826i 1.10059 + 1.29735i
\(424\) −25.5634 + 35.1850i −1.24147 + 1.70874i
\(425\) −13.1169 + 20.6707i −0.636262 + 1.00268i
\(426\) 0.925271 0.424688i 0.0448295 0.0205762i
\(427\) 9.85496 1.56087i 0.476915 0.0755359i
\(428\) 0.476149 3.00629i 0.0230156 0.145314i
\(429\) 0.281756 + 13.6563i 0.0136033 + 0.659332i
\(430\) −52.4965 42.0560i −2.53161 2.02812i
\(431\) 16.6908i 0.803968i 0.915647 + 0.401984i \(0.131679\pi\)
−0.915647 + 0.401984i \(0.868321\pi\)
\(432\) −4.09454 + 33.1733i −0.196999 + 1.59605i
\(433\) −23.2958 3.68969i −1.11953 0.177315i −0.430877 0.902411i \(-0.641796\pi\)
−0.688649 + 0.725095i \(0.741796\pi\)
\(434\) 43.4558 31.5725i 2.08595 1.51553i
\(435\) −23.3833 + 14.0255i −1.12114 + 0.672470i
\(436\) −16.4076 −0.785780
\(437\) 4.55730 + 4.55730i 0.218005 + 0.218005i
\(438\) 15.5121 41.8328i 0.741199 1.99885i
\(439\) −19.1220 + 6.21310i −0.912642 + 0.296535i −0.727445 0.686166i \(-0.759292\pi\)
−0.185197 + 0.982701i \(0.559292\pi\)
\(440\) 35.7074 26.7403i 1.70228 1.27479i
\(441\) 0.553937 6.75078i 0.0263779 0.321466i
\(442\) 20.7954 20.7954i 0.989138 0.989138i
\(443\) −33.5044 17.0713i −1.59184 0.811084i −0.999987 0.00503973i \(-0.998396\pi\)
−0.591855 0.806044i \(-0.701604\pi\)
\(444\) −22.3853 + 20.6237i −1.06236 + 0.978756i
\(445\) 0.301726 0.0825493i 0.0143032 0.00391321i
\(446\) 32.8201i 1.55408i
\(447\) 0.893794 + 0.331431i 0.0422750 + 0.0156761i
\(448\) 4.74762 + 0.751949i 0.224304 + 0.0355262i
\(449\) −2.46005 + 1.78733i −0.116097 + 0.0843492i −0.644319 0.764757i \(-0.722859\pi\)
0.528222 + 0.849106i \(0.322859\pi\)
\(450\) 21.6857 + 31.0726i 1.02227 + 1.46478i
\(451\) 5.47728 + 24.6506i 0.257915 + 1.16075i
\(452\) 2.40416 4.71842i 0.113082 0.221936i
\(453\) 2.66429 + 4.00180i 0.125179 + 0.188021i
\(454\) −16.4844 + 22.6889i −0.773653 + 1.06484i
\(455\) 0.545184 11.5654i 0.0255586 0.542194i
\(456\) 5.03877 + 10.9780i 0.235962 + 0.514092i
\(457\) 12.1525 1.92476i 0.568468 0.0900365i 0.134417 0.990925i \(-0.457084\pi\)
0.434051 + 0.900888i \(0.357084\pi\)
\(458\) −2.22109 + 14.0234i −0.103785 + 0.655270i
\(459\) 8.68637 + 23.9128i 0.405445 + 1.11615i
\(460\) −11.0428 + 53.3288i −0.514872 + 2.48647i
\(461\) −26.1581 + 8.49927i −1.21830 + 0.395850i −0.846463 0.532447i \(-0.821273\pi\)
−0.371839 + 0.928297i \(0.621273\pi\)
\(462\) 13.7626 28.4464i 0.640294 1.32345i
\(463\) −31.9034 + 16.2556i −1.48268 + 0.755462i −0.993185 0.116546i \(-0.962818\pi\)
−0.489492 + 0.872008i \(0.662818\pi\)
\(464\) −36.6387 26.6195i −1.70091 1.23578i
\(465\) −8.47862 36.8550i −0.393187 1.70911i
\(466\) −23.5420 17.1042i −1.09056 0.792338i
\(467\) −0.0428370 + 0.0840724i −0.00198226 + 0.00389041i −0.891996 0.452044i \(-0.850695\pi\)
0.890013 + 0.455935i \(0.150695\pi\)
\(468\) −11.8635 28.9132i −0.548393 1.33652i
\(469\) 3.64134 + 5.01188i 0.168142 + 0.231427i
\(470\) 17.3857 + 63.5466i 0.801943 + 2.93119i
\(471\) 39.1447 + 7.85417i 1.80369 + 0.361901i
\(472\) 1.63861 10.3458i 0.0754232 0.476203i
\(473\) 33.3204 + 21.2051i 1.53208 + 0.975009i
\(474\) −3.54039 30.3457i −0.162616 1.39382i
\(475\) 5.32020 + 2.30201i 0.244108 + 0.105623i
\(476\) −44.4276 + 14.4354i −2.03634 + 0.661646i
\(477\) 18.4564 + 11.3948i 0.845058 + 0.521733i
\(478\) 23.2645 + 23.2645i 1.06409 + 1.06409i
\(479\) 23.0811 1.05460 0.527301 0.849679i \(-0.323204\pi\)
0.527301 + 0.849679i \(0.323204\pi\)
\(480\) −8.66992 + 13.8509i −0.395726 + 0.632205i
\(481\) 2.94715 9.07041i 0.134379 0.413575i
\(482\) −14.0437 2.22431i −0.639675 0.101315i
\(483\) 5.65782 + 20.1898i 0.257440 + 0.918668i
\(484\) −35.2150 + 32.9015i −1.60068 + 1.49552i
\(485\) 32.3873 14.6242i 1.47063 0.664050i
\(486\) 39.3335 + 1.87368i 1.78420 + 0.0849920i
\(487\) −24.9130 + 24.9130i −1.12892 + 1.12892i −0.138564 + 0.990353i \(0.544249\pi\)
−0.990353 + 0.138564i \(0.955751\pi\)
\(488\) 27.2218 4.31151i 1.23227 0.195173i
\(489\) 3.81313 19.0044i 0.172436 0.859409i
\(490\) 6.31858 11.0782i 0.285444 0.500460i
\(491\) −1.85733 + 2.55639i −0.0838199 + 0.115368i −0.848868 0.528605i \(-0.822715\pi\)
0.765048 + 0.643973i \(0.222715\pi\)
\(492\) −32.0188 48.0928i −1.44352 2.16819i
\(493\) −34.0467 5.39246i −1.53339 0.242864i
\(494\) −5.63381 4.09320i −0.253477 0.184162i
\(495\) −14.6367 16.7561i −0.657870 0.753132i
\(496\) 50.8156 36.9197i 2.28169 1.65774i
\(497\) 0.451481 0.230041i 0.0202517 0.0103187i
\(498\) 0.940635 22.9654i 0.0421509 1.02910i
\(499\) 40.2224 + 13.0690i 1.80060 + 0.585050i 0.999902 0.0140173i \(-0.00446200\pi\)
0.800698 + 0.599068i \(0.204462\pi\)
\(500\) 8.42452 + 48.2536i 0.376756 + 2.15797i
\(501\) −29.9802 16.8554i −1.33942 0.753043i
\(502\) −16.5580 + 16.5580i −0.739019 + 0.739019i
\(503\) −34.6409 + 5.48658i −1.54456 + 0.244635i −0.869802 0.493402i \(-0.835753\pi\)
−0.674761 + 0.738036i \(0.735753\pi\)
\(504\) −3.21374 + 39.1656i −0.143151 + 1.74457i
\(505\) 4.46859 2.93544i 0.198849 0.130625i
\(506\) 4.44178 46.3621i 0.197461 2.06105i
\(507\) −9.97929 7.89403i −0.443196 0.350586i
\(508\) 55.2471 + 55.2471i 2.45119 + 2.45119i
\(509\) −45.0741 −1.99787 −0.998937 0.0460914i \(-0.985323\pi\)
−0.998937 + 0.0460914i \(0.985323\pi\)
\(510\) −4.21192 + 47.7172i −0.186507 + 2.11295i
\(511\) 6.86201 21.1191i 0.303558 0.934254i
\(512\) 49.6288 + 7.86043i 2.19330 + 0.347385i
\(513\) 5.27082 2.91729i 0.232712 0.128802i
\(514\) −28.5520 39.2984i −1.25937 1.73338i
\(515\) −15.3694 8.76615i −0.677257 0.386283i
\(516\) −88.6009 17.7773i −3.90043 0.782602i
\(517\) −14.1948 35.9850i −0.624285 1.58262i
\(518\) −15.6019 + 15.6019i −0.685508 + 0.685508i
\(519\) −3.21369 27.5454i −0.141065 1.20911i
\(520\) 1.50593 31.9465i 0.0660395 1.40095i
\(521\) −4.20552 + 1.36646i −0.184247 + 0.0598655i −0.399687 0.916652i \(-0.630881\pi\)
0.215440 + 0.976517i \(0.430881\pi\)
\(522\) −28.0287 + 45.3984i −1.22678 + 1.98704i
\(523\) −9.31279 + 4.74511i −0.407220 + 0.207489i −0.645588 0.763686i \(-0.723388\pi\)
0.238368 + 0.971175i \(0.423388\pi\)
\(524\) −4.32617 + 13.3146i −0.188990 + 0.581650i
\(525\) 11.4170 + 15.0105i 0.498280 + 0.655111i
\(526\) 17.5301 12.7364i 0.764349 0.555332i
\(527\) 21.7050 42.5984i 0.945483 1.85562i
\(528\) 16.0935 33.2642i 0.700378 1.44764i
\(529\) 4.64513 + 6.39347i 0.201962 + 0.277977i
\(530\) 22.4228 + 34.1339i 0.973983 + 1.48268i
\(531\) −5.20662 0.427231i −0.225948 0.0185402i
\(532\) 5.02175 + 9.85573i 0.217720 + 0.427300i
\(533\) 16.1304 + 8.21885i 0.698685 + 0.355998i
\(534\) 0.450163 0.414737i 0.0194804 0.0179474i
\(535\) −1.34940 0.769650i −0.0583397 0.0332749i
\(536\) 10.0583 + 13.8440i 0.434452 + 0.597972i
\(537\) 21.4662 + 7.95997i 0.926336 + 0.343498i
\(538\) −5.75058 + 2.93007i −0.247925 + 0.126324i
\(539\) −2.98269 + 6.86870i −0.128473 + 0.295856i
\(540\) 45.0566 + 23.6906i 1.93893 + 1.01948i
\(541\) −3.47834 10.7052i −0.149546 0.460254i 0.848022 0.529961i \(-0.177794\pi\)
−0.997567 + 0.0697072i \(0.977794\pi\)
\(542\) −53.1755 + 27.0942i −2.28408 + 1.16380i
\(543\) 5.29170 + 7.94822i 0.227089 + 0.341091i
\(544\) −19.6468 + 6.38363i −0.842349 + 0.273696i
\(545\) −2.95985 + 7.83349i −0.126786 + 0.335550i
\(546\) −9.45057 20.5900i −0.404447 0.881172i
\(547\) 29.3632 4.65067i 1.25548 0.198848i 0.506964 0.861967i \(-0.330768\pi\)
0.748514 + 0.663119i \(0.230768\pi\)
\(548\) 40.5106 6.41625i 1.73053 0.274089i
\(549\) −3.16432 13.3765i −0.135050 0.570897i
\(550\) −11.6377 40.2417i −0.496235 1.71591i
\(551\) 8.16237i 0.347729i
\(552\) 15.6283 + 55.7692i 0.665184 + 2.37370i
\(553\) −2.37871 15.0186i −0.101153 0.638655i
\(554\) −19.9052 61.2618i −0.845689 2.60276i
\(555\) 5.80818 + 14.4078i 0.246544 + 0.611579i
\(556\) −19.1163 58.8339i −0.810712 2.49511i
\(557\) 35.9787 18.3321i 1.52447 0.776755i 0.527138 0.849780i \(-0.323265\pi\)
0.997330 + 0.0730240i \(0.0232650\pi\)
\(558\) −47.8704 56.4287i −2.02652 2.38882i
\(559\) 26.9295 8.74991i 1.13899 0.370082i
\(560\) −15.5187 + 27.2085i −0.655786 + 1.14977i
\(561\) −0.580186 28.1208i −0.0244955 1.18726i
\(562\) −4.32189 8.48218i −0.182308 0.357799i
\(563\) −7.27962 3.70915i −0.306800 0.156322i 0.293812 0.955863i \(-0.405076\pi\)
−0.600611 + 0.799541i \(0.705076\pi\)
\(564\) 59.9713 + 65.0938i 2.52525 + 2.74094i
\(565\) −1.81902 1.99900i −0.0765269 0.0840986i
\(566\) 4.58043 + 6.30442i 0.192530 + 0.264995i
\(567\) 19.5985 + 0.130604i 0.823058 + 0.00548487i
\(568\) 1.24710 0.635430i 0.0523272 0.0266620i
\(569\) 8.81124 27.1182i 0.369386 1.13685i −0.577802 0.816177i \(-0.696090\pi\)
0.947189 0.320677i \(-0.103910\pi\)
\(570\) 11.3158 0.782481i 0.473967 0.0327745i
\(571\) −11.1297 + 8.08617i −0.465762 + 0.338396i −0.795787 0.605576i \(-0.792943\pi\)
0.330025 + 0.943972i \(0.392943\pi\)
\(572\) 2.12578 + 34.4855i 0.0888834 + 1.44191i
\(573\) −5.99528 + 16.1679i −0.250456 + 0.675425i
\(574\) −24.6181 33.8839i −1.02754 1.41429i
\(575\) 23.4688 + 14.8925i 0.978716 + 0.621058i
\(576\) 0.541548 6.59980i 0.0225645 0.274992i
\(577\) 9.32467 + 18.3007i 0.388191 + 0.761868i 0.999566 0.0294736i \(-0.00938311\pi\)
−0.611375 + 0.791341i \(0.709383\pi\)
\(578\) −12.4557 + 12.4557i −0.518088 + 0.518088i
\(579\) −7.88794 17.1855i −0.327812 0.714205i
\(580\) −57.6465 + 37.8683i −2.39364 + 1.57239i
\(581\) 11.4397i 0.474599i
\(582\) 43.1388 54.5342i 1.78816 2.26052i
\(583\) −15.2619 18.4961i −0.632082 0.766030i
\(584\) 18.9546 58.3362i 0.784346 2.41397i
\(585\) −15.9442 + 0.448207i −0.659212 + 0.0185311i
\(586\) 26.4648 19.2278i 1.09325 0.794295i
\(587\) 3.30237 + 20.8503i 0.136303 + 0.860586i 0.957183 + 0.289484i \(0.0934837\pi\)
−0.820879 + 0.571101i \(0.806516\pi\)
\(588\) 0.701178 17.1191i 0.0289161 0.705981i
\(589\) −10.7666 3.49829i −0.443632 0.144145i
\(590\) −8.54416 4.87328i −0.351758 0.200630i
\(591\) 7.29263 0.850822i 0.299979 0.0349981i
\(592\) −18.2443 + 18.2443i −0.749835 + 0.749835i
\(593\) −12.4175 + 12.4175i −0.509925 + 0.509925i −0.914503 0.404578i \(-0.867418\pi\)
0.404578 + 0.914503i \(0.367418\pi\)
\(594\) −40.5024 15.9616i −1.66184 0.654914i
\(595\) −1.12263 + 23.8152i −0.0460234 + 0.976329i
\(596\) 2.29327 + 0.745127i 0.0939358 + 0.0305216i
\(597\) 1.57170 + 5.60858i 0.0643254 + 0.229544i
\(598\) −23.6104 23.6104i −0.965503 0.965503i
\(599\) −12.6465 9.18819i −0.516720 0.375419i 0.298647 0.954364i \(-0.403465\pi\)
−0.815367 + 0.578944i \(0.803465\pi\)
\(600\) 31.5367 + 41.4627i 1.28748 + 1.69271i
\(601\) 9.18091 28.2559i 0.374497 1.15258i −0.569320 0.822116i \(-0.692794\pi\)
0.943817 0.330467i \(-0.107206\pi\)
\(602\) −64.7014 10.2477i −2.63703 0.417665i
\(603\) 6.50808 5.52103i 0.265029 0.224834i
\(604\) 7.14792 + 9.83827i 0.290845 + 0.400314i
\(605\) 9.35560 + 22.7480i 0.380359 + 0.924839i
\(606\) 5.12695 9.11915i 0.208268 0.370440i
\(607\) 1.81170 11.4386i 0.0735347 0.464280i −0.923253 0.384192i \(-0.874480\pi\)
0.996788 0.0800875i \(-0.0255200\pi\)
\(608\) 2.22072 + 4.35841i 0.0900620 + 0.176757i
\(609\) −13.0138 + 23.1472i −0.527345 + 0.937973i
\(610\) 5.24786 25.3435i 0.212480 1.02613i
\(611\) −26.3757 8.56999i −1.06705 0.346705i
\(612\) 24.4292 + 59.5376i 0.987491 + 2.40666i
\(613\) 26.4084 + 26.4084i 1.06662 + 1.06662i 0.997616 + 0.0690075i \(0.0219832\pi\)
0.0690075 + 0.997616i \(0.478017\pi\)
\(614\) −42.3626 30.7782i −1.70961 1.24211i
\(615\) −28.7371 + 6.61106i −1.15879 + 0.266584i
\(616\) 17.3045 39.8497i 0.697217 1.60559i
\(617\) 1.29447 + 8.17298i 0.0521135 + 0.329032i 0.999947 + 0.0102667i \(0.00326805\pi\)
−0.947834 + 0.318765i \(0.896732\pi\)
\(618\) −34.5924 1.41686i −1.39151 0.0569945i
\(619\) −29.2330 9.49836i −1.17497 0.381771i −0.344475 0.938795i \(-0.611943\pi\)
−0.830496 + 0.557024i \(0.811943\pi\)
\(620\) −25.2439 92.2689i −1.01382 3.70561i
\(621\) 27.1498 9.86221i 1.08948 0.395757i
\(622\) 34.9251 34.9251i 1.40037 1.40037i
\(623\) 0.215415 0.215415i 0.00863043 0.00863043i
\(624\) −11.0511 24.0772i −0.442400 0.963860i
\(625\) 24.5575 + 4.68261i 0.982302 + 0.187305i
\(626\) 26.6927i 1.06686i
\(627\) −6.55522 + 1.17734i −0.261790 + 0.0470184i
\(628\) 99.7465 + 15.7983i 3.98032 + 0.630420i
\(629\) −6.06872 + 18.6776i −0.241976 + 0.744724i
\(630\) 33.3375 + 15.8225i 1.32820 + 0.630384i
\(631\) −31.4208 + 22.8285i −1.25084 + 0.908789i −0.998270 0.0587889i \(-0.981276\pi\)
−0.252571 + 0.967578i \(0.581276\pi\)
\(632\) −6.57058 41.4850i −0.261364 1.65019i
\(633\) 17.1390 + 6.35536i 0.681213 + 0.252603i
\(634\) 29.3576 40.4072i 1.16594 1.60478i
\(635\) 36.3430 16.4104i 1.44223 0.651226i
\(636\) 47.8258 + 26.8885i 1.89642 + 1.06620i
\(637\) 2.43728 + 4.78343i 0.0965685 + 0.189526i
\(638\) 45.4962 37.5407i 1.80121 1.48625i
\(639\) −0.362748 0.596403i −0.0143501 0.0235933i
\(640\) 15.5255 27.2204i 0.613700 1.07598i
\(641\) 20.5476i 0.811582i −0.913966 0.405791i \(-0.866996\pi\)
0.913966 0.405791i \(-0.133004\pi\)
\(642\) −3.03714 0.124397i −0.119866 0.00490957i
\(643\) −3.44335 21.7405i −0.135792 0.857360i −0.957706 0.287748i \(-0.907094\pi\)
0.821914 0.569612i \(-0.192906\pi\)
\(644\) 16.3895 + 50.4416i 0.645836 + 1.98768i
\(645\) −24.4706 + 39.0939i −0.963531 + 1.53932i
\(646\) 11.6010 + 8.42864i 0.456436 + 0.331620i
\(647\) 2.71103 1.38134i 0.106582 0.0543060i −0.399887 0.916564i \(-0.630951\pi\)
0.506469 + 0.862258i \(0.330951\pi\)
\(648\) 54.1358 + 0.360762i 2.12665 + 0.0141721i
\(649\) 5.29757 + 2.30044i 0.207948 + 0.0903000i
\(650\) −27.5629 11.9262i −1.08110 0.467785i
\(651\) −24.9550 27.0865i −0.978063 1.06161i
\(652\) 7.66993 48.4261i 0.300378 1.89651i
\(653\) 5.27767 + 2.68911i 0.206531 + 0.105233i 0.554197 0.832386i \(-0.313026\pi\)
−0.347665 + 0.937619i \(0.613026\pi\)
\(654\) 1.89881 + 16.2752i 0.0742492 + 0.636410i
\(655\) 5.57638 + 4.46734i 0.217887 + 0.174554i
\(656\) −28.7875 39.6226i −1.12396 1.54700i
\(657\) −29.7223 7.24053i −1.15958 0.282480i
\(658\) 45.3686 + 45.3686i 1.76865 + 1.76865i
\(659\) −4.23443 + 13.0322i −0.164950 + 0.507664i −0.999033 0.0439759i \(-0.985998\pi\)
0.834083 + 0.551639i \(0.185998\pi\)
\(660\) −38.7270 40.8339i −1.50745 1.58946i
\(661\) 11.1752 + 34.3938i 0.434665 + 1.33776i 0.893429 + 0.449204i \(0.148292\pi\)
−0.458764 + 0.888558i \(0.651708\pi\)
\(662\) −5.66062 + 11.1096i −0.220006 + 0.431787i
\(663\) −15.8149 12.5102i −0.614199 0.485856i
\(664\) 31.5993i 1.22629i
\(665\) 5.61134 0.619608i 0.217598 0.0240274i
\(666\) 23.0478 + 19.8179i 0.893086 + 0.767929i
\(667\) −6.12242 + 38.6554i −0.237061 + 1.49674i
\(668\) −77.5161 39.4964i −2.99919 1.52816i
\(669\) −22.3518 + 2.60776i −0.864171 + 0.100822i
\(670\) 15.4995 4.24050i 0.598797 0.163825i
\(671\) −1.44928 + 15.1272i −0.0559488 + 0.583979i
\(672\) −0.651261 + 15.9004i −0.0251229 + 0.613371i
\(673\) −3.38276 21.3579i −0.130396 0.823288i −0.963016 0.269444i \(-0.913160\pi\)
0.832620 0.553844i \(-0.186840\pi\)
\(674\) 20.9591 + 64.5055i 0.807315 + 2.48466i
\(675\) 19.4386 17.2377i 0.748193 0.663481i
\(676\) −26.0386 18.9182i −1.00149 0.727622i
\(677\) −7.87312 + 4.01156i −0.302589 + 0.154177i −0.598692 0.800979i \(-0.704313\pi\)
0.296103 + 0.955156i \(0.404313\pi\)
\(678\) −4.95858 1.83871i −0.190433 0.0706151i
\(679\) 20.3419 27.9982i 0.780649 1.07447i
\(680\) −3.10098 + 65.7835i −0.118917 + 2.52268i
\(681\) 16.7618 + 9.42380i 0.642315 + 0.361121i
\(682\) 30.0193 + 76.1016i 1.14950 + 2.91408i
\(683\) 0.866555 0.137249i 0.0331578 0.00525168i −0.139834 0.990175i \(-0.544657\pi\)
0.172991 + 0.984923i \(0.444657\pi\)
\(684\) 13.0194 7.91873i 0.497808 0.302780i
\(685\) 4.24462 20.4985i 0.162178 0.783207i
\(686\) 50.9272i 1.94441i
\(687\) 9.72698 + 0.398405i 0.371107 + 0.0152001i
\(688\) −75.6593 11.9833i −2.88449 0.456858i
\(689\) −17.1916 −0.654950
\(690\) 54.1765 + 4.78207i 2.06246 + 0.182050i
\(691\) −0.302581 0.931249i −0.0115107 0.0354264i 0.945136 0.326677i \(-0.105929\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(692\) −10.9737 69.2850i −0.417156 2.63382i
\(693\) −20.4667 7.11264i −0.777466 0.270187i
\(694\) −25.5424 + 35.1561i −0.969577 + 1.33451i
\(695\) −31.5377 1.48666i −1.19629 0.0563922i
\(696\) −35.9473 + 63.9384i −1.36258 + 2.42358i
\(697\) −33.2154 16.9241i −1.25812 0.641045i
\(698\) −17.6575 34.6548i −0.668346 1.31170i
\(699\) −9.77812 + 17.3921i −0.369842 + 0.657828i
\(700\) 30.4091 + 36.7553i 1.14935 + 1.38922i
\(701\) −34.0135 + 11.0517i −1.28467 + 0.417416i −0.870224 0.492657i \(-0.836026\pi\)
−0.414449 + 0.910072i \(0.636026\pi\)
\(702\) −27.3070 + 15.1139i −1.03064 + 0.570437i
\(703\) 4.59299 + 0.727459i 0.173228 + 0.0274366i
\(704\) −2.91598 + 6.71508i −0.109900 + 0.253084i
\(705\) 41.8964 16.8895i 1.57791 0.636097i
\(706\) −68.7380 −2.58699
\(707\) 2.36385 4.63932i 0.0889018 0.174480i
\(708\) −13.2033 0.540793i −0.496212 0.0203242i
\(709\) 21.6292 + 29.7700i 0.812301 + 1.11804i 0.990964 + 0.134126i \(0.0428226\pi\)
−0.178664 + 0.983910i \(0.557177\pi\)
\(710\) −0.144253 1.30640i −0.00541373 0.0490281i
\(711\) −20.3853 + 4.82230i −0.764510 + 0.180851i
\(712\) 0.595030 0.595030i 0.0222997 0.0222997i
\(713\) −48.3648 24.6431i −1.81128 0.922891i
\(714\) 19.4604 + 42.3986i 0.728288 + 1.58673i
\(715\) 16.8479 + 5.20612i 0.630077 + 0.194698i
\(716\) 55.0773 + 17.8957i 2.05834 + 0.668794i
\(717\) 13.9955 17.6925i 0.522673 0.660740i
\(718\) 18.6256 36.5547i 0.695100 1.36421i
\(719\) 8.36713 6.07908i 0.312041 0.226711i −0.420731 0.907186i \(-0.638226\pi\)
0.732772 + 0.680474i \(0.238226\pi\)
\(720\) 38.9836 + 18.5023i 1.45283 + 0.689538i
\(721\) −17.2314 −0.641731
\(722\) −20.2482 + 39.7394i −0.753561 + 1.47895i
\(723\) −0.398983 + 9.74110i −0.0148384 + 0.362275i
\(724\) 14.1969 + 19.5404i 0.527625 + 0.726213i
\(725\) 7.68033 + 34.3535i 0.285240 + 1.27586i
\(726\) 36.7114 + 31.1232i 1.36249 + 1.15509i
\(727\) −44.7923 22.8228i −1.66125 0.846451i −0.994906 0.100809i \(-0.967857\pi\)
−0.666347 0.745641i \(-0.732143\pi\)
\(728\) −14.1402 27.7517i −0.524071 1.02855i
\(729\) −1.84924 26.9366i −0.0684903 0.997652i
\(730\) −44.9529 36.0127i −1.66378 1.33289i
\(731\) −55.4526 + 18.0176i −2.05099 + 0.666407i
\(732\) −9.38216 33.4800i −0.346774 1.23746i
\(733\) 41.0910 + 6.50818i 1.51773 + 0.240385i 0.858993 0.511987i \(-0.171091\pi\)
0.658738 + 0.752372i \(0.271091\pi\)
\(734\) 69.5371 2.56666
\(735\) −8.04672 3.42298i −0.296808 0.126259i
\(736\) 7.24776 + 22.3063i 0.267156 + 0.822221i
\(737\) −8.77701 + 3.46221i −0.323305 + 0.127532i
\(738\) −43.9993 + 37.3261i −1.61964 + 1.37399i
\(739\) 6.32395 8.70417i 0.232630 0.320188i −0.676703 0.736256i \(-0.736592\pi\)
0.909334 + 0.416068i \(0.136592\pi\)
\(740\) 16.1710 + 35.8128i 0.594456 + 1.31651i
\(741\) −2.34000 + 4.16208i −0.0859619 + 0.152898i
\(742\) 35.4381 + 18.0566i 1.30097 + 0.662879i
\(743\) 14.6881 2.32636i 0.538853 0.0853459i 0.118925 0.992903i \(-0.462055\pi\)
0.419928 + 0.907557i \(0.362055\pi\)
\(744\) −68.9319 74.8197i −2.52716 2.74302i
\(745\) 0.769442 0.960460i 0.0281902 0.0351885i
\(746\) 15.4645 + 5.02472i 0.566196 + 0.183968i
\(747\) −15.7151 + 1.18413i −0.574986 + 0.0433252i
\(748\) −4.37737 71.0118i −0.160052 2.59645i
\(749\) −1.51288 −0.0552795
\(750\) 46.8893 13.9408i 1.71216 0.509047i
\(751\) 1.13212 + 3.48430i 0.0413116 + 0.127144i 0.969585 0.244754i \(-0.0787072\pi\)
−0.928274 + 0.371898i \(0.878707\pi\)
\(752\) 53.0523 + 53.0523i 1.93462 + 1.93462i
\(753\) 12.5923 + 9.96102i 0.458889 + 0.363000i
\(754\) 42.2875i 1.54002i
\(755\) 5.98655 1.63786i 0.217873 0.0596079i
\(756\) 49.5462 1.69871i 1.80198 0.0617816i
\(757\) 6.45398 40.7488i 0.234574 1.48104i −0.536287 0.844036i \(-0.680173\pi\)
0.770860 0.637004i \(-0.219827\pi\)
\(758\) 64.1365 10.1582i 2.32954 0.368964i
\(759\) −31.9274 + 0.658724i −1.15889 + 0.0239102i
\(760\) 15.4999 1.71151i 0.562240 0.0620830i
\(761\) 1.88723 2.59755i 0.0684120 0.0941610i −0.773440 0.633870i \(-0.781466\pi\)
0.841852 + 0.539709i \(0.181466\pi\)
\(762\) 48.4077 61.1950i 1.75363 2.21686i
\(763\) 1.27576 + 8.05486i 0.0461858 + 0.291606i
\(764\) −13.4787 + 41.4831i −0.487641 + 1.50081i
\(765\) 32.8320 0.922938i 1.18704 0.0333689i
\(766\) 53.9791 + 39.2181i 1.95034 + 1.41701i
\(767\) 3.68928 1.87978i 0.133212 0.0678750i
\(768\) 2.19644 53.6256i 0.0792572 1.93505i
\(769\) 1.33418 1.83634i 0.0481118 0.0662202i −0.784283 0.620403i \(-0.786969\pi\)
0.832395 + 0.554183i \(0.186969\pi\)
\(770\) −29.2615 28.4273i −1.05451 1.02445i
\(771\) −24.4952 + 22.5676i −0.882172 + 0.812751i
\(772\) −21.7148 42.6178i −0.781534 1.53385i
\(773\) −2.53768 + 16.0223i −0.0912739 + 0.576281i 0.899087 + 0.437770i \(0.144232\pi\)
−0.990361 + 0.138511i \(0.955768\pi\)
\(774\) −7.38031 + 89.9433i −0.265280 + 3.23294i
\(775\) −48.6060 4.59270i −1.74598 0.164975i
\(776\) 56.1892 77.3378i 2.01708 2.77627i
\(777\) 11.8652 + 9.38586i 0.425662 + 0.336716i
\(778\) −7.31584 46.1904i −0.262286 1.65601i
\(779\) −2.72773 + 8.39510i −0.0977312 + 0.300786i
\(780\) −40.2507 + 2.78331i −1.44121 + 0.0996584i
\(781\) 0.167393 + 0.753357i 0.00598981 + 0.0269572i
\(782\) 48.6181 + 48.6181i 1.73858 + 1.73858i
\(783\) 33.1452 + 15.4815i 1.18451 + 0.553263i
\(784\) 14.5238i 0.518707i
\(785\) 25.5364 44.7722i 0.911434 1.59799i
\(786\) 13.7078 + 2.75040i 0.488941 + 0.0981036i
\(787\) −3.11864 + 19.6903i −0.111167 + 0.701884i 0.867654 + 0.497168i \(0.165627\pi\)
−0.978822 + 0.204715i \(0.934373\pi\)
\(788\) 18.3432 2.90527i 0.653448 0.103496i
\(789\) −10.0669 10.9267i −0.358390 0.389002i
\(790\) −38.6225 7.99755i −1.37413 0.284540i
\(791\) −2.50332 0.813377i −0.0890077 0.0289204i
\(792\) −56.5341 19.6469i −2.00885 0.698121i
\(793\) 7.70370 + 7.70370i 0.273567 + 0.273567i
\(794\) −2.91633 −0.103497
\(795\) 21.4650 17.9830i 0.761284 0.637790i
\(796\) 4.55288 + 14.0123i 0.161372 + 0.496653i
\(797\) −21.5397 21.5397i −0.762975 0.762975i 0.213884 0.976859i \(-0.431388\pi\)
−0.976859 + 0.213884i \(0.931388\pi\)
\(798\) 9.19506 6.12181i 0.325501 0.216710i
\(799\) 54.3124 + 17.6472i 1.92143 + 0.624312i
\(800\) 13.4475 + 16.2539i 0.475441 + 0.574664i
\(801\) −0.318221 0.273626i −0.0112438 0.00966809i
\(802\) 41.5585 + 21.1751i 1.46748 + 0.747719i
\(803\) 28.5324 + 18.1580i 1.00689 + 0.640780i
\(804\) 15.8768 14.6274i 0.559933 0.515870i
\(805\) 27.0390 + 1.27460i 0.952999 + 0.0449236i
\(806\) 55.7797 + 18.1239i 1.96476 + 0.638388i
\(807\) 2.45241 + 3.68357i 0.0863290 + 0.129668i
\(808\) 6.52954 12.8149i 0.229708 0.450828i
\(809\) −13.9841 + 10.1600i −0.491653 + 0.357207i −0.805820 0.592161i \(-0.798275\pi\)
0.314166 + 0.949368i \(0.398275\pi\)
\(810\) 18.2852 47.4347i 0.642475 1.66668i
\(811\) −9.26839 + 6.73388i −0.325457 + 0.236459i −0.738501 0.674253i \(-0.764466\pi\)
0.413043 + 0.910711i \(0.364466\pi\)
\(812\) −30.4946 + 59.8490i −1.07015 + 2.10029i
\(813\) 22.6774 + 34.0618i 0.795331 + 1.19460i
\(814\) −17.0695 28.9466i −0.598287 1.01458i
\(815\) −21.7365 12.3977i −0.761396 0.434273i
\(816\) 22.7563 + 49.5793i 0.796630 + 1.73562i
\(817\) 6.26792 + 12.3015i 0.219287 + 0.430375i
\(818\) 29.5734 + 58.0411i 1.03401 + 2.02936i
\(819\) −13.2717 + 8.07223i −0.463752 + 0.282067i
\(820\) −71.9451 + 19.6835i −2.51243 + 0.687377i
\(821\) 28.1857 9.15809i 0.983688 0.319620i 0.227359 0.973811i \(-0.426991\pi\)
0.756329 + 0.654191i \(0.226991\pi\)
\(822\) −11.0527 39.4412i −0.385506 1.37567i
\(823\) 3.41608 + 21.5683i 0.119077 + 0.751823i 0.972894 + 0.231250i \(0.0742816\pi\)
−0.853817 + 0.520573i \(0.825718\pi\)
\(824\) −47.5974 −1.65813
\(825\) −26.4816 + 11.1232i −0.921970 + 0.387261i
\(826\) −9.57928 −0.333306
\(827\) −5.65712 35.7177i −0.196717 1.24202i −0.866390 0.499368i \(-0.833565\pi\)
0.669672 0.742657i \(-0.266435\pi\)
\(828\) 67.5969 27.7361i 2.34916 0.963894i
\(829\) −29.8342 + 9.69371i −1.03618 + 0.336676i −0.777232 0.629214i \(-0.783377\pi\)
−0.258951 + 0.965890i \(0.583377\pi\)
\(830\) −27.7577 10.4881i −0.963484 0.364049i
\(831\) −40.1402 + 18.4238i −1.39245 + 0.639116i
\(832\) 2.38277 + 4.67645i 0.0826077 + 0.162127i
\(833\) −5.01880 9.84994i −0.173891 0.341280i
\(834\) −56.1469 + 25.7708i −1.94421 + 0.892368i
\(835\) −32.8404 + 29.8836i −1.13649 + 1.03417i
\(836\) −16.4456 + 3.65417i −0.568785 + 0.126382i
\(837\) −34.6266 + 37.0853i −1.19687 + 1.28186i
\(838\) −31.8647 + 62.5380i −1.10075 + 2.16034i
\(839\) 40.0073 29.0670i 1.38120 1.00350i 0.384438 0.923151i \(-0.374395\pi\)
0.996766 0.0803532i \(-0.0256048\pi\)
\(840\) 46.6841 + 19.8589i 1.61076 + 0.685196i
\(841\) −16.6383 + 12.0884i −0.573734 + 0.416842i
\(842\) −12.7564 + 25.0359i −0.439616 + 0.862795i
\(843\) −5.43331 + 3.61734i −0.187133 + 0.124588i
\(844\) 43.9746 + 14.2882i 1.51367 + 0.491820i
\(845\) −13.7294 + 9.01890i −0.472305 + 0.310260i
\(846\) 57.6283 67.0206i 1.98130 2.30421i
\(847\) 18.8903 + 14.7296i 0.649077 + 0.506115i
\(848\) 41.4400 + 21.1147i 1.42306 + 0.725083i
\(849\) 3.92962 3.62038i 0.134864 0.124251i
\(850\) 56.7569 + 24.5583i 1.94675 + 0.842342i
\(851\) 21.2059 + 6.89022i 0.726929 + 0.236194i
\(852\) −0.978541 1.46979i −0.0335243 0.0503540i
\(853\) −24.1729 24.1729i −0.827664 0.827664i 0.159529 0.987193i \(-0.449002\pi\)
−0.987193 + 0.159529i \(0.949002\pi\)
\(854\) −7.78877 23.9714i −0.266526 0.820284i
\(855\) −1.43201 7.64435i −0.0489738 0.261431i
\(856\) −4.17895 −0.142834
\(857\) 13.6178 + 13.6178i 0.465176 + 0.465176i 0.900348 0.435171i \(-0.143312\pi\)
−0.435171 + 0.900348i \(0.643312\pi\)
\(858\) 33.9612 6.09955i 1.15942 0.208235i
\(859\) −2.37775 0.772578i −0.0811278 0.0263600i 0.268172 0.963371i \(-0.413580\pi\)
−0.349300 + 0.937011i \(0.613580\pi\)
\(860\) −57.7997 + 101.338i −1.97095 + 3.45560i
\(861\) −21.1203 + 19.4582i −0.719777 + 0.663135i
\(862\) 41.6437 6.59572i 1.41839 0.224651i
\(863\) 7.14691 45.1238i 0.243284 1.53603i −0.499389 0.866378i \(-0.666442\pi\)
0.742673 0.669655i \(-0.233558\pi\)
\(864\) 21.9104 0.751205i 0.745405 0.0255565i
\(865\) −35.0584 7.25954i −1.19202 0.246832i
\(866\) 59.5813i 2.02465i
\(867\) 9.47251 + 7.49314i 0.321703 + 0.254480i
\(868\) −65.8747 65.8747i −2.23593 2.23593i
\(869\) 23.0533 + 2.20865i 0.782028 + 0.0749232i
\(870\) 44.2340 + 52.7990i 1.49967 + 1.79005i
\(871\) −2.09028 + 6.43323i −0.0708265 + 0.217982i
\(872\) 3.52398 + 22.2495i 0.119337 + 0.753464i
\(873\) −40.5677 25.0462i −1.37301 0.847686i
\(874\) 9.56959 13.1714i 0.323696 0.445530i
\(875\) 23.0338 7.88774i 0.778684 0.266654i
\(876\) −75.8692 15.2228i −2.56338 0.514329i
\(877\) −3.22470 + 20.3600i −0.108890 + 0.687507i 0.871493 + 0.490408i \(0.163152\pi\)
−0.980384 + 0.197099i \(0.936848\pi\)
\(878\) 23.0582 + 45.2542i 0.778176 + 1.52726i
\(879\) −15.1977 16.4959i −0.512607 0.556392i
\(880\) −34.2174 33.2418i −1.15347 1.12058i
\(881\) 9.77534 13.4546i 0.329339 0.453297i −0.611950 0.790896i \(-0.709615\pi\)
0.941290 + 0.337599i \(0.109615\pi\)
\(882\) −17.0621 + 1.28563i −0.574512 + 0.0432895i
\(883\) 27.2171 13.8678i 0.915927 0.466688i 0.0685308 0.997649i \(-0.478169\pi\)
0.847396 + 0.530961i \(0.178169\pi\)
\(884\) −41.2652 29.9809i −1.38790 1.00837i
\(885\) −2.64002 + 6.20613i −0.0887432 + 0.208617i
\(886\) −29.3532 + 90.3398i −0.986140 + 3.03503i
\(887\) −7.32389 46.2412i −0.245912 1.55263i −0.733583 0.679600i \(-0.762153\pi\)
0.487670 0.873028i \(-0.337847\pi\)
\(888\) 32.7746 + 25.9261i 1.09984 + 0.870022i
\(889\) 22.8264 31.4178i 0.765572 1.05372i
\(890\) −0.325194 0.720188i −0.0109005 0.0241408i
\(891\) −7.65236 + 28.8521i −0.256364 + 0.966580i
\(892\) −56.2215 + 8.90462i −1.88244 + 0.298149i
\(893\) 2.11537 13.3559i 0.0707881 0.446939i
\(894\) 0.473721 2.36099i 0.0158436 0.0789635i
\(895\) 18.4797 23.0673i 0.617707 0.771056i
\(896\) 30.5181i 1.01954i
\(897\) −14.2037 + 17.9557i −0.474247 + 0.599522i
\(898\) 5.43153 + 5.43153i 0.181253 + 0.181253i
\(899\) −21.2434 65.3805i −0.708507 2.18056i
\(900\) 47.3444 45.5786i 1.57815 1.51929i
\(901\) 35.4007 1.17937
\(902\) 59.3389 23.4070i 1.97577 0.779369i
\(903\) −1.83817 + 44.8785i −0.0611704 + 1.49346i
\(904\) −6.91478 2.24675i −0.229982 0.0747257i
\(905\) 11.8903 3.25306i 0.395246 0.108135i
\(906\) 8.93168 8.22881i 0.296735 0.273384i
\(907\) −51.0772 + 8.08984i −1.69599 + 0.268619i −0.928200 0.372082i \(-0.878644\pi\)
−0.767791 + 0.640700i \(0.778644\pi\)
\(908\) 43.3391 + 22.0824i 1.43826 + 0.732829i
\(909\) −6.61788 2.76709i −0.219501 0.0917784i
\(910\) −29.0712 + 3.21006i −0.963700 + 0.106413i
\(911\) 21.4190 29.4807i 0.709643 0.976739i −0.290162 0.956978i \(-0.593709\pi\)
0.999805 0.0197618i \(-0.00629079\pi\)
\(912\) 10.7524 7.15861i 0.356046 0.237045i
\(913\) 16.8701 + 4.35429i 0.558318 + 0.144106i
\(914\) −9.60458 29.5599i −0.317691 0.977754i
\(915\) −17.6769 1.56031i −0.584381 0.0515823i
\(916\) 24.6250 0.813633
\(917\) 6.87282 + 1.08855i 0.226961 + 0.0359470i
\(918\) 56.2300 31.1222i 1.85587 1.02719i
\(919\) −38.0829 + 12.3739i −1.25624 + 0.408177i −0.860153 0.510036i \(-0.829632\pi\)
−0.396087 + 0.918213i \(0.629632\pi\)
\(920\) 74.6884 + 3.52075i 2.46240 + 0.116076i
\(921\) −17.5952 + 31.2962i −0.579783 + 1.03124i
\(922\) 31.5426 + 61.9059i 1.03880 + 2.03876i
\(923\) 0.492968 + 0.251180i 0.0162262 + 0.00826768i
\(924\) −52.4634 15.8577i −1.72592 0.521679i
\(925\) 20.0153 1.26004i 0.658100 0.0414300i
\(926\) 53.1651 + 73.1755i 1.74711 + 2.40470i
\(927\) 1.78364 + 23.6714i 0.0585823 + 0.777470i
\(928\) −13.4853 + 26.4664i −0.442678 + 0.868804i
\(929\) 1.60841 0.0527701 0.0263851 0.999652i \(-0.491600\pi\)
0.0263851 + 0.999652i \(0.491600\pi\)
\(930\) −88.6030 + 35.7182i −2.90541 + 1.17125i
\(931\) −2.11774 + 1.53862i −0.0694060 + 0.0504264i
\(932\) −22.9126 + 44.9686i −0.750528 + 1.47299i
\(933\) −26.5604 21.0104i −0.869548 0.687849i
\(934\) 0.226689 + 0.0736558i 0.00741750 + 0.00241009i
\(935\) −34.6929 10.7203i −1.13458 0.350592i
\(936\) −36.6598 + 22.2975i −1.19826 + 0.728816i
\(937\) −4.70200 2.39579i −0.153608 0.0782670i 0.375497 0.926824i \(-0.377472\pi\)
−0.529105 + 0.848557i \(0.677472\pi\)
\(938\) 11.0657 11.0657i 0.361309 0.361309i
\(939\) −18.1788 + 2.12090i −0.593244 + 0.0692131i
\(940\) 104.140 47.0233i 3.39666 1.53373i
\(941\) −12.1185 16.6797i −0.395053 0.543743i 0.564441 0.825473i \(-0.309092\pi\)
−0.959494 + 0.281730i \(0.909092\pi\)
\(942\) 4.12741 100.770i 0.134478 3.28326i
\(943\) −19.2150 + 37.7116i −0.625727 + 1.22806i
\(944\) −11.2017 −0.364583
\(945\) 8.12691 23.9614i 0.264368 0.779463i
\(946\) 39.7395 91.5143i 1.29204 2.97539i
\(947\) −25.0775 3.97188i −0.814908 0.129069i −0.264951 0.964262i \(-0.585356\pi\)
−0.549957 + 0.835193i \(0.685356\pi\)
\(948\) −51.0223 + 14.2980i −1.65713 + 0.464379i
\(949\) 23.0598 7.49258i 0.748552 0.243219i
\(950\) 3.64114 14.1836i 0.118134 0.460178i
\(951\) −29.8516 16.7831i −0.968005 0.544229i
\(952\) 29.1172 + 57.1457i 0.943694 + 1.85210i
\(953\) −17.5393 8.93671i −0.568153 0.289488i 0.146222 0.989252i \(-0.453289\pi\)
−0.714375 + 0.699763i \(0.753289\pi\)
\(954\) 21.1368 50.5516i 0.684329 1.63667i
\(955\) 17.3738 + 13.9185i 0.562204 + 0.450392i
\(956\) 33.5405 46.1646i 1.08478 1.49307i
\(957\) −29.1817 28.0019i −0.943311 0.905173i
\(958\) −9.12096 57.5875i −0.294685 1.86057i
\(959\) −6.29977 19.3887i −0.203430 0.626094i
\(960\) −7.86676 3.34643i −0.253898 0.108005i
\(961\) 64.3453 2.07565
\(962\) −23.7954 3.76881i −0.767193 0.121511i
\(963\) 0.156600 + 2.07830i 0.00504635 + 0.0669722i
\(964\) 24.6608i 0.794269i
\(965\) −24.2643 + 2.67929i −0.781096 + 0.0862492i
\(966\) 48.1379 22.0947i 1.54881 0.710886i
\(967\) −33.2067 + 5.25942i −1.06785 + 0.169131i −0.665534 0.746368i \(-0.731796\pi\)
−0.402320 + 0.915499i \(0.631796\pi\)
\(968\) 52.1796 + 40.6868i 1.67712 + 1.30772i
\(969\) 4.81847 8.57048i 0.154792 0.275323i
\(970\) −49.2860 75.0275i −1.58248 2.40899i
\(971\) 1.14100 1.57045i 0.0366164 0.0503981i −0.790316 0.612699i \(-0.790084\pi\)
0.826933 + 0.562301i \(0.190084\pi\)
\(972\) −7.46216 67.8876i −0.239349 2.17749i
\(973\) −27.3966 + 13.9592i −0.878294 + 0.447513i
\(974\) 72.0031 + 52.3133i 2.30713 + 1.67623i
\(975\) −5.93221 + 19.7190i −0.189983 + 0.631515i
\(976\) −9.10790 28.0312i −0.291537 0.897258i
\(977\) −5.95651 37.6079i −0.190566 1.20318i −0.878619 0.477524i \(-0.841534\pi\)
0.688053 0.725661i \(-0.258466\pi\)
\(978\) −48.9229 2.00382i −1.56438 0.0640752i
\(979\) 0.235679 + 0.399666i 0.00753232 + 0.0127734i
\(980\) −20.6915 7.81819i −0.660964 0.249743i
\(981\) 10.9332 2.58633i 0.349070 0.0825751i
\(982\) 7.11217 + 3.62383i 0.226958 + 0.115641i
\(983\) −1.93745 + 12.2326i −0.0617949 + 0.390158i 0.937334 + 0.348432i \(0.113286\pi\)
−0.999129 + 0.0417261i \(0.986714\pi\)
\(984\) −58.3394 + 53.7484i −1.85979 + 1.71344i
\(985\) 1.92196 9.28170i 0.0612387 0.295739i
\(986\) 87.0777i 2.77312i
\(987\) 27.2930 34.5027i 0.868747 1.09823i
\(988\) −5.48320 + 10.7614i −0.174444 + 0.342366i
\(989\) 20.4566 + 62.9590i 0.650483 + 2.00198i
\(990\) −36.0227 + 43.1401i −1.14488 + 1.37108i
\(991\) −1.72999 + 5.32436i −0.0549550 + 0.169134i −0.974767 0.223226i \(-0.928341\pi\)
0.919812 + 0.392360i \(0.128341\pi\)
\(992\) −29.1311 29.1311i −0.924914 0.924914i
\(993\) 8.01585 + 2.97239i 0.254375 + 0.0943258i
\(994\) −0.752365 1.03554i −0.0238636 0.0328454i
\(995\) 7.51124 + 0.354074i 0.238122 + 0.0112249i
\(996\) −39.5955 + 4.61956i −1.25463 + 0.146376i
\(997\) 41.3707 + 21.0794i 1.31022 + 0.667592i 0.962825 0.270125i \(-0.0870652\pi\)
0.347398 + 0.937718i \(0.387065\pi\)
\(998\) 16.7127 105.520i 0.529030 3.34016i
\(999\) 11.6655 17.2712i 0.369080 0.546436i
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 825.2.cv.a.608.8 yes 928
3.2 odd 2 inner 825.2.cv.a.608.109 yes 928
11.4 even 5 825.2.df.a.158.109 yes 928
25.22 odd 20 825.2.df.a.47.8 yes 928
33.26 odd 10 825.2.df.a.158.8 yes 928
75.47 even 20 825.2.df.a.47.109 yes 928
275.147 odd 20 inner 825.2.cv.a.422.109 yes 928
825.422 even 20 inner 825.2.cv.a.422.8 928
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
825.2.cv.a.422.8 928 825.422 even 20 inner
825.2.cv.a.422.109 yes 928 275.147 odd 20 inner
825.2.cv.a.608.8 yes 928 1.1 even 1 trivial
825.2.cv.a.608.109 yes 928 3.2 odd 2 inner
825.2.df.a.47.8 yes 928 25.22 odd 20
825.2.df.a.47.109 yes 928 75.47 even 20
825.2.df.a.158.8 yes 928 33.26 odd 10
825.2.df.a.158.109 yes 928 11.4 even 5