Properties

Label 560.2.bd.a.141.2
Level $560$
Weight $2$
Character 560.141
Analytic conductor $4.472$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [560,2,Mod(141,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.141");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bd (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: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 141.2
Character \(\chi\) \(=\) 560.141
Dual form 560.2.bd.a.421.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40016 - 0.198865i) q^{2} +(1.92081 + 1.92081i) q^{3} +(1.92091 + 0.556887i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.30746 - 3.07142i) q^{6} -1.00000i q^{7} +(-2.57883 - 1.16173i) q^{8} +4.37899i q^{9} +O(q^{10})\) \(q+(-1.40016 - 0.198865i) q^{2} +(1.92081 + 1.92081i) q^{3} +(1.92091 + 0.556887i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.30746 - 3.07142i) q^{6} -1.00000i q^{7} +(-2.57883 - 1.16173i) q^{8} +4.37899i q^{9} +(-1.13068 + 0.849445i) q^{10} +(2.40494 - 2.40494i) q^{11} +(2.62001 + 4.75936i) q^{12} +(-0.230047 - 0.230047i) q^{13} +(-0.198865 + 1.40016i) q^{14} +2.71643 q^{15} +(3.37975 + 2.13945i) q^{16} +3.07426 q^{17} +(0.870827 - 6.13129i) q^{18} +(4.98381 + 4.98381i) q^{19} +(1.75206 - 0.964507i) q^{20} +(1.92081 - 1.92081i) q^{21} +(-3.84556 + 2.88904i) q^{22} -2.85562i q^{23} +(-2.72197 - 7.18490i) q^{24} -1.00000i q^{25} +(0.276355 + 0.367851i) q^{26} +(-2.64876 + 2.64876i) q^{27} +(0.556887 - 1.92091i) q^{28} +(3.04810 + 3.04810i) q^{29} +(-3.80344 - 0.540203i) q^{30} -5.50995 q^{31} +(-4.30674 - 3.66769i) q^{32} +9.23884 q^{33} +(-4.30446 - 0.611363i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(-2.43860 + 8.41162i) q^{36} +(-5.74684 + 5.74684i) q^{37} +(-5.98703 - 7.96925i) q^{38} -0.883751i q^{39} +(-2.64498 + 1.00204i) q^{40} +2.73725i q^{41} +(-3.07142 + 2.30746i) q^{42} +(-1.65787 + 1.65787i) q^{43} +(5.95894 - 3.28038i) q^{44} +(3.09641 + 3.09641i) q^{45} +(-0.567883 + 3.99833i) q^{46} -12.0114 q^{47} +(2.38238 + 10.6013i) q^{48} -1.00000 q^{49} +(-0.198865 + 1.40016i) q^{50} +(5.90505 + 5.90505i) q^{51} +(-0.313789 - 0.570009i) q^{52} +(9.26864 - 9.26864i) q^{53} +(4.23544 - 3.18195i) q^{54} -3.40110i q^{55} +(-1.16173 + 2.57883i) q^{56} +19.1459i q^{57} +(-3.66167 - 4.87400i) q^{58} +(-1.23554 + 1.23554i) q^{59} +(5.21800 + 1.51274i) q^{60} +(0.354752 + 0.354752i) q^{61} +(7.71482 + 1.09574i) q^{62} +4.37899 q^{63} +(5.30076 + 5.99183i) q^{64} -0.325336 q^{65} +(-12.9359 - 1.83728i) q^{66} +(-10.8475 - 10.8475i) q^{67} +(5.90536 + 1.71201i) q^{68} +(5.48509 - 5.48509i) q^{69} +(0.849445 + 1.13068i) q^{70} -1.43189i q^{71} +(5.08721 - 11.2927i) q^{72} +11.5526i q^{73} +(9.18934 - 6.90365i) q^{74} +(1.92081 - 1.92081i) q^{75} +(6.79801 + 12.3488i) q^{76} +(-2.40494 - 2.40494i) q^{77} +(-0.175747 + 1.23739i) q^{78} +8.10993 q^{79} +(3.90267 - 0.877026i) q^{80} +2.96144 q^{81} +(0.544344 - 3.83260i) q^{82} +(-0.0148642 - 0.0148642i) q^{83} +(4.75936 - 2.62001i) q^{84} +(2.17383 - 2.17383i) q^{85} +(2.65097 - 1.99159i) q^{86} +11.7096i q^{87} +(-8.99583 + 3.40804i) q^{88} -11.4609i q^{89} +(-3.71971 - 4.95124i) q^{90} +(-0.230047 + 0.230047i) q^{91} +(1.59026 - 5.48537i) q^{92} +(-10.5835 - 10.5835i) q^{93} +(16.8179 + 2.38864i) q^{94} +7.04817 q^{95} +(-1.22748 - 15.3173i) q^{96} +7.61510 q^{97} +(1.40016 + 0.198865i) q^{98} +(10.5312 + 10.5312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40016 0.198865i −0.990064 0.140619i
\(3\) 1.92081 + 1.92081i 1.10898 + 1.10898i 0.993285 + 0.115692i \(0.0369087\pi\)
0.115692 + 0.993285i \(0.463091\pi\)
\(4\) 1.92091 + 0.556887i 0.960453 + 0.278443i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −2.30746 3.07142i −0.942015 1.25390i
\(7\) 1.00000i 0.377964i
\(8\) −2.57883 1.16173i −0.911755 0.410734i
\(9\) 4.37899i 1.45966i
\(10\) −1.13068 + 0.849445i −0.357553 + 0.268618i
\(11\) 2.40494 2.40494i 0.725116 0.725116i −0.244526 0.969643i \(-0.578632\pi\)
0.969643 + 0.244526i \(0.0786325\pi\)
\(12\) 2.62001 + 4.75936i 0.756333 + 1.37391i
\(13\) −0.230047 0.230047i −0.0638036 0.0638036i 0.674485 0.738289i \(-0.264366\pi\)
−0.738289 + 0.674485i \(0.764366\pi\)
\(14\) −0.198865 + 1.40016i −0.0531489 + 0.374209i
\(15\) 2.71643 0.701379
\(16\) 3.37975 + 2.13945i 0.844939 + 0.534863i
\(17\) 3.07426 0.745617 0.372809 0.927908i \(-0.378395\pi\)
0.372809 + 0.927908i \(0.378395\pi\)
\(18\) 0.870827 6.13129i 0.205256 1.44516i
\(19\) 4.98381 + 4.98381i 1.14336 + 1.14336i 0.987831 + 0.155534i \(0.0497098\pi\)
0.155534 + 0.987831i \(0.450290\pi\)
\(20\) 1.75206 0.964507i 0.391773 0.215670i
\(21\) 1.92081 1.92081i 0.419154 0.419154i
\(22\) −3.84556 + 2.88904i −0.819876 + 0.615946i
\(23\) 2.85562i 0.595438i −0.954654 0.297719i \(-0.903774\pi\)
0.954654 0.297719i \(-0.0962258\pi\)
\(24\) −2.72197 7.18490i −0.555621 1.46661i
\(25\) 1.00000i 0.200000i
\(26\) 0.276355 + 0.367851i 0.0541976 + 0.0721416i
\(27\) −2.64876 + 2.64876i −0.509755 + 0.509755i
\(28\) 0.556887 1.92091i 0.105242 0.363017i
\(29\) 3.04810 + 3.04810i 0.566018 + 0.566018i 0.931011 0.364992i \(-0.118928\pi\)
−0.364992 + 0.931011i \(0.618928\pi\)
\(30\) −3.80344 0.540203i −0.694410 0.0986271i
\(31\) −5.50995 −0.989616 −0.494808 0.869002i \(-0.664762\pi\)
−0.494808 + 0.869002i \(0.664762\pi\)
\(32\) −4.30674 3.66769i −0.761331 0.648363i
\(33\) 9.23884 1.60828
\(34\) −4.30446 0.611363i −0.738209 0.104848i
\(35\) −0.707107 0.707107i −0.119523 0.119523i
\(36\) −2.43860 + 8.41162i −0.406433 + 1.40194i
\(37\) −5.74684 + 5.74684i −0.944774 + 0.944774i −0.998553 0.0537789i \(-0.982873\pi\)
0.0537789 + 0.998553i \(0.482873\pi\)
\(38\) −5.98703 7.96925i −0.971225 1.29278i
\(39\) 0.883751i 0.141513i
\(40\) −2.64498 + 1.00204i −0.418208 + 0.158437i
\(41\) 2.73725i 0.427487i 0.976890 + 0.213744i \(0.0685657\pi\)
−0.976890 + 0.213744i \(0.931434\pi\)
\(42\) −3.07142 + 2.30746i −0.473930 + 0.356048i
\(43\) −1.65787 + 1.65787i −0.252822 + 0.252822i −0.822127 0.569304i \(-0.807213\pi\)
0.569304 + 0.822127i \(0.307213\pi\)
\(44\) 5.95894 3.28038i 0.898344 0.494536i
\(45\) 3.09641 + 3.09641i 0.461586 + 0.461586i
\(46\) −0.567883 + 3.99833i −0.0837298 + 0.589521i
\(47\) −12.0114 −1.75204 −0.876019 0.482276i \(-0.839810\pi\)
−0.876019 + 0.482276i \(0.839810\pi\)
\(48\) 2.38238 + 10.6013i 0.343867 + 1.53017i
\(49\) −1.00000 −0.142857
\(50\) −0.198865 + 1.40016i −0.0281238 + 0.198013i
\(51\) 5.90505 + 5.90505i 0.826873 + 0.826873i
\(52\) −0.313789 0.570009i −0.0435146 0.0790460i
\(53\) 9.26864 9.26864i 1.27315 1.27315i 0.328717 0.944428i \(-0.393384\pi\)
0.944428 0.328717i \(-0.106616\pi\)
\(54\) 4.23544 3.18195i 0.576371 0.433008i
\(55\) 3.40110i 0.458604i
\(56\) −1.16173 + 2.57883i −0.155243 + 0.344611i
\(57\) 19.1459i 2.53593i
\(58\) −3.66167 4.87400i −0.480801 0.639987i
\(59\) −1.23554 + 1.23554i −0.160854 + 0.160854i −0.782945 0.622091i \(-0.786283\pi\)
0.622091 + 0.782945i \(0.286283\pi\)
\(60\) 5.21800 + 1.51274i 0.673641 + 0.195294i
\(61\) 0.354752 + 0.354752i 0.0454213 + 0.0454213i 0.729453 0.684031i \(-0.239775\pi\)
−0.684031 + 0.729453i \(0.739775\pi\)
\(62\) 7.71482 + 1.09574i 0.979783 + 0.139159i
\(63\) 4.37899 0.551700
\(64\) 5.30076 + 5.99183i 0.662595 + 0.748978i
\(65\) −0.325336 −0.0403529
\(66\) −12.9359 1.83728i −1.59230 0.226154i
\(67\) −10.8475 10.8475i −1.32524 1.32524i −0.909474 0.415761i \(-0.863515\pi\)
−0.415761 0.909474i \(-0.636485\pi\)
\(68\) 5.90536 + 1.71201i 0.716130 + 0.207612i
\(69\) 5.48509 5.48509i 0.660327 0.660327i
\(70\) 0.849445 + 1.13068i 0.101528 + 0.135142i
\(71\) 1.43189i 0.169934i −0.996384 0.0849671i \(-0.972921\pi\)
0.996384 0.0849671i \(-0.0270785\pi\)
\(72\) 5.08721 11.2927i 0.599533 1.33085i
\(73\) 11.5526i 1.35213i 0.736844 + 0.676063i \(0.236315\pi\)
−0.736844 + 0.676063i \(0.763685\pi\)
\(74\) 9.18934 6.90365i 1.06824 0.802534i
\(75\) 1.92081 1.92081i 0.221795 0.221795i
\(76\) 6.79801 + 12.3488i 0.779785 + 1.41651i
\(77\) −2.40494 2.40494i −0.274068 0.274068i
\(78\) −0.175747 + 1.23739i −0.0198995 + 0.140107i
\(79\) 8.10993 0.912439 0.456219 0.889867i \(-0.349203\pi\)
0.456219 + 0.889867i \(0.349203\pi\)
\(80\) 3.90267 0.877026i 0.436332 0.0980545i
\(81\) 2.96144 0.329049
\(82\) 0.544344 3.83260i 0.0601127 0.423239i
\(83\) −0.0148642 0.0148642i −0.00163155 0.00163155i 0.706291 0.707922i \(-0.250367\pi\)
−0.707922 + 0.706291i \(0.750367\pi\)
\(84\) 4.75936 2.62001i 0.519288 0.285867i
\(85\) 2.17383 2.17383i 0.235785 0.235785i
\(86\) 2.65097 1.99159i 0.285862 0.214759i
\(87\) 11.7096i 1.25540i
\(88\) −8.99583 + 3.40804i −0.958959 + 0.363298i
\(89\) 11.4609i 1.21486i −0.794375 0.607428i \(-0.792201\pi\)
0.794375 0.607428i \(-0.207799\pi\)
\(90\) −3.71971 4.95124i −0.392092 0.521907i
\(91\) −0.230047 + 0.230047i −0.0241155 + 0.0241155i
\(92\) 1.59026 5.48537i 0.165796 0.571890i
\(93\) −10.5835 10.5835i −1.09746 1.09746i
\(94\) 16.8179 + 2.38864i 1.73463 + 0.246370i
\(95\) 7.04817 0.723127
\(96\) −1.22748 15.3173i −0.125279 1.56332i
\(97\) 7.61510 0.773197 0.386598 0.922248i \(-0.373650\pi\)
0.386598 + 0.922248i \(0.373650\pi\)
\(98\) 1.40016 + 0.198865i 0.141438 + 0.0200884i
\(99\) 10.5312 + 10.5312i 1.05842 + 1.05842i
\(100\) 0.556887 1.92091i 0.0556887 0.192091i
\(101\) 6.10829 6.10829i 0.607797 0.607797i −0.334573 0.942370i \(-0.608592\pi\)
0.942370 + 0.334573i \(0.108592\pi\)
\(102\) −7.09372 9.44234i −0.702383 0.934931i
\(103\) 9.38744i 0.924972i 0.886627 + 0.462486i \(0.153042\pi\)
−0.886627 + 0.462486i \(0.846958\pi\)
\(104\) 0.326000 + 0.860506i 0.0319669 + 0.0843796i
\(105\) 2.71643i 0.265096i
\(106\) −14.8208 + 11.1344i −1.43952 + 1.08147i
\(107\) −4.06190 + 4.06190i −0.392679 + 0.392679i −0.875641 0.482962i \(-0.839561\pi\)
0.482962 + 0.875641i \(0.339561\pi\)
\(108\) −6.56308 + 3.61296i −0.631533 + 0.347657i
\(109\) −11.6383 11.6383i −1.11475 1.11475i −0.992499 0.122252i \(-0.960988\pi\)
−0.122252 0.992499i \(-0.539012\pi\)
\(110\) −0.676359 + 4.76209i −0.0644883 + 0.454047i
\(111\) −22.0771 −2.09547
\(112\) 2.13945 3.37975i 0.202159 0.319357i
\(113\) −14.3735 −1.35215 −0.676074 0.736833i \(-0.736320\pi\)
−0.676074 + 0.736833i \(0.736320\pi\)
\(114\) 3.80744 26.8073i 0.356600 2.51073i
\(115\) −2.01923 2.01923i −0.188294 0.188294i
\(116\) 4.15767 + 7.55256i 0.386030 + 0.701238i
\(117\) 1.00737 1.00737i 0.0931316 0.0931316i
\(118\) 1.97567 1.48426i 0.181875 0.136637i
\(119\) 3.07426i 0.281817i
\(120\) −7.00522 3.15576i −0.639486 0.288080i
\(121\) 0.567460i 0.0515873i
\(122\) −0.426162 0.567258i −0.0385829 0.0513571i
\(123\) −5.25773 + 5.25773i −0.474074 + 0.474074i
\(124\) −10.5841 3.06842i −0.950479 0.275552i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) −6.13129 0.870827i −0.546219 0.0775795i
\(127\) −16.3150 −1.44772 −0.723860 0.689947i \(-0.757634\pi\)
−0.723860 + 0.689947i \(0.757634\pi\)
\(128\) −6.23035 9.44366i −0.550690 0.834710i
\(129\) −6.36888 −0.560748
\(130\) 0.455523 + 0.0646979i 0.0399520 + 0.00567438i
\(131\) 1.51297 + 1.51297i 0.132189 + 0.132189i 0.770105 0.637917i \(-0.220204\pi\)
−0.637917 + 0.770105i \(0.720204\pi\)
\(132\) 17.7469 + 5.14498i 1.54467 + 0.447813i
\(133\) 4.98381 4.98381i 0.432151 0.432151i
\(134\) 13.0311 + 17.3455i 1.12571 + 1.49842i
\(135\) 3.74592i 0.322397i
\(136\) −7.92800 3.57147i −0.679820 0.306251i
\(137\) 5.04227i 0.430790i −0.976527 0.215395i \(-0.930896\pi\)
0.976527 0.215395i \(-0.0691040\pi\)
\(138\) −8.77080 + 6.58922i −0.746620 + 0.560912i
\(139\) −13.0200 + 13.0200i −1.10434 + 1.10434i −0.110465 + 0.993880i \(0.535234\pi\)
−0.993880 + 0.110465i \(0.964766\pi\)
\(140\) −0.964507 1.75206i −0.0815157 0.148076i
\(141\) −23.0715 23.0715i −1.94297 1.94297i
\(142\) −0.284753 + 2.00488i −0.0238959 + 0.168246i
\(143\) −1.10650 −0.0925300
\(144\) −9.36863 + 14.7999i −0.780719 + 1.23332i
\(145\) 4.31067 0.357981
\(146\) 2.29740 16.1755i 0.190134 1.33869i
\(147\) −1.92081 1.92081i −0.158425 0.158425i
\(148\) −14.2395 + 7.83879i −1.17048 + 0.644345i
\(149\) 2.92851 2.92851i 0.239913 0.239913i −0.576901 0.816814i \(-0.695738\pi\)
0.816814 + 0.576901i \(0.195738\pi\)
\(150\) −3.07142 + 2.30746i −0.250780 + 0.188403i
\(151\) 10.4902i 0.853682i 0.904327 + 0.426841i \(0.140374\pi\)
−0.904327 + 0.426841i \(0.859626\pi\)
\(152\) −7.06256 18.6423i −0.572849 1.51209i
\(153\) 13.4621i 1.08835i
\(154\) 2.88904 + 3.84556i 0.232806 + 0.309884i
\(155\) −3.89612 + 3.89612i −0.312944 + 0.312944i
\(156\) 0.492149 1.69760i 0.0394035 0.135917i
\(157\) 11.3888 + 11.3888i 0.908924 + 0.908924i 0.996185 0.0872612i \(-0.0278115\pi\)
−0.0872612 + 0.996185i \(0.527811\pi\)
\(158\) −11.3552 1.61278i −0.903373 0.128306i
\(159\) 35.6065 2.82378
\(160\) −5.63878 + 0.451874i −0.445784 + 0.0357238i
\(161\) −2.85562 −0.225054
\(162\) −4.14650 0.588927i −0.325780 0.0462705i
\(163\) −6.58819 6.58819i −0.516027 0.516027i 0.400340 0.916367i \(-0.368892\pi\)
−0.916367 + 0.400340i \(0.868892\pi\)
\(164\) −1.52434 + 5.25800i −0.119031 + 0.410581i
\(165\) 6.53284 6.53284i 0.508581 0.508581i
\(166\) 0.0178563 + 0.0237682i 0.00138591 + 0.00184477i
\(167\) 16.1238i 1.24770i −0.781544 0.623850i \(-0.785568\pi\)
0.781544 0.623850i \(-0.214432\pi\)
\(168\) −7.18490 + 2.72197i −0.554327 + 0.210005i
\(169\) 12.8942i 0.991858i
\(170\) −3.47601 + 2.61141i −0.266598 + 0.200286i
\(171\) −21.8240 + 21.8240i −1.66893 + 1.66893i
\(172\) −4.10785 + 2.26136i −0.313221 + 0.172427i
\(173\) −9.13304 9.13304i −0.694372 0.694372i 0.268818 0.963191i \(-0.413367\pi\)
−0.963191 + 0.268818i \(0.913367\pi\)
\(174\) 2.32863 16.3954i 0.176533 1.24293i
\(175\) −1.00000 −0.0755929
\(176\) 13.2734 2.98285i 1.00052 0.224841i
\(177\) −4.74648 −0.356767
\(178\) −2.27918 + 16.0471i −0.170832 + 1.20278i
\(179\) −10.1552 10.1552i −0.759035 0.759035i 0.217112 0.976147i \(-0.430336\pi\)
−0.976147 + 0.217112i \(0.930336\pi\)
\(180\) 4.22356 + 7.67226i 0.314806 + 0.571857i
\(181\) 9.05901 9.05901i 0.673351 0.673351i −0.285136 0.958487i \(-0.592039\pi\)
0.958487 + 0.285136i \(0.0920388\pi\)
\(182\) 0.367851 0.276355i 0.0272670 0.0204848i
\(183\) 1.36282i 0.100742i
\(184\) −3.31746 + 7.36417i −0.244567 + 0.542893i
\(185\) 8.12725i 0.597528i
\(186\) 12.7140 + 16.9234i 0.932233 + 1.24088i
\(187\) 7.39340 7.39340i 0.540659 0.540659i
\(188\) −23.0727 6.68897i −1.68275 0.487843i
\(189\) 2.64876 + 2.64876i 0.192669 + 0.192669i
\(190\) −9.86858 1.40164i −0.715942 0.101685i
\(191\) 22.0651 1.59657 0.798286 0.602279i \(-0.205741\pi\)
0.798286 + 0.602279i \(0.205741\pi\)
\(192\) −1.32741 + 21.6909i −0.0957975 + 1.56540i
\(193\) 23.6088 1.69940 0.849700 0.527267i \(-0.176783\pi\)
0.849700 + 0.527267i \(0.176783\pi\)
\(194\) −10.6624 1.51438i −0.765514 0.108726i
\(195\) −0.624906 0.624906i −0.0447505 0.0447505i
\(196\) −1.92091 0.556887i −0.137208 0.0397776i
\(197\) −1.33955 + 1.33955i −0.0954387 + 0.0954387i −0.753214 0.657775i \(-0.771498\pi\)
0.657775 + 0.753214i \(0.271498\pi\)
\(198\) −12.6511 16.8397i −0.899073 1.19674i
\(199\) 17.9500i 1.27244i −0.771508 0.636220i \(-0.780497\pi\)
0.771508 0.636220i \(-0.219503\pi\)
\(200\) −1.16173 + 2.57883i −0.0821469 + 0.182351i
\(201\) 41.6719i 2.93931i
\(202\) −9.76731 + 7.33786i −0.687226 + 0.516290i
\(203\) 3.04810 3.04810i 0.213935 0.213935i
\(204\) 8.05460 + 14.6315i 0.563935 + 1.02441i
\(205\) 1.93553 + 1.93553i 0.135183 + 0.135183i
\(206\) 1.86683 13.1439i 0.130068 0.915781i
\(207\) 12.5047 0.869138
\(208\) −0.285328 1.26968i −0.0197839 0.0880363i
\(209\) 23.9715 1.65814
\(210\) −0.540203 + 3.80344i −0.0372775 + 0.262462i
\(211\) −10.8590 10.8590i −0.747567 0.747567i 0.226455 0.974022i \(-0.427286\pi\)
−0.974022 + 0.226455i \(0.927286\pi\)
\(212\) 22.9658 12.6426i 1.57729 0.868297i
\(213\) 2.75038 2.75038i 0.188453 0.188453i
\(214\) 6.49509 4.87955i 0.443995 0.333559i
\(215\) 2.34458i 0.159899i
\(216\) 9.90787 3.75356i 0.674145 0.255398i
\(217\) 5.50995i 0.374040i
\(218\) 13.9811 + 18.6100i 0.946920 + 1.26043i
\(219\) −22.1902 + 22.1902i −1.49948 + 1.49948i
\(220\) 1.89402 6.53319i 0.127695 0.440467i
\(221\) −0.707224 0.707224i −0.0475731 0.0475731i
\(222\) 30.9115 + 4.39037i 2.07465 + 0.294662i
\(223\) −1.51828 −0.101671 −0.0508357 0.998707i \(-0.516188\pi\)
−0.0508357 + 0.998707i \(0.516188\pi\)
\(224\) −3.66769 + 4.30674i −0.245058 + 0.287756i
\(225\) 4.37899 0.291932
\(226\) 20.1253 + 2.85839i 1.33871 + 0.190138i
\(227\) −6.58491 6.58491i −0.437056 0.437056i 0.453964 0.891020i \(-0.350009\pi\)
−0.891020 + 0.453964i \(0.850009\pi\)
\(228\) −10.6621 + 36.7774i −0.706113 + 2.43564i
\(229\) −6.51956 + 6.51956i −0.430825 + 0.430825i −0.888909 0.458084i \(-0.848536\pi\)
0.458084 + 0.888909i \(0.348536\pi\)
\(230\) 2.42569 + 3.22880i 0.159945 + 0.212901i
\(231\) 9.23884i 0.607871i
\(232\) −4.31947 11.4016i −0.283587 0.748553i
\(233\) 18.0402i 1.18185i 0.806725 + 0.590927i \(0.201238\pi\)
−0.806725 + 0.590927i \(0.798762\pi\)
\(234\) −1.61082 + 1.21015i −0.105302 + 0.0791102i
\(235\) −8.49332 + 8.49332i −0.554043 + 0.554043i
\(236\) −3.06142 + 1.68531i −0.199282 + 0.109704i
\(237\) 15.5776 + 15.5776i 1.01187 + 1.01187i
\(238\) −0.611363 + 4.30446i −0.0396288 + 0.279017i
\(239\) −14.0959 −0.911785 −0.455892 0.890035i \(-0.650680\pi\)
−0.455892 + 0.890035i \(0.650680\pi\)
\(240\) 9.18086 + 5.81167i 0.592622 + 0.375142i
\(241\) 11.0900 0.714370 0.357185 0.934034i \(-0.383737\pi\)
0.357185 + 0.934034i \(0.383737\pi\)
\(242\) −0.112848 + 0.794536i −0.00725414 + 0.0510747i
\(243\) 13.6346 + 13.6346i 0.874663 + 0.874663i
\(244\) 0.483888 + 0.879001i 0.0309778 + 0.0562723i
\(245\) −0.707107 + 0.707107i −0.0451754 + 0.0451754i
\(246\) 8.40725 6.31609i 0.536027 0.402699i
\(247\) 2.29302i 0.145901i
\(248\) 14.2092 + 6.40108i 0.902287 + 0.406469i
\(249\) 0.0571023i 0.00361871i
\(250\) 0.849445 + 1.13068i 0.0537236 + 0.0715106i
\(251\) −6.24897 + 6.24897i −0.394432 + 0.394432i −0.876264 0.481832i \(-0.839972\pi\)
0.481832 + 0.876264i \(0.339972\pi\)
\(252\) 8.41162 + 2.43860i 0.529882 + 0.153617i
\(253\) −6.86759 6.86759i −0.431762 0.431762i
\(254\) 22.8436 + 3.24448i 1.43334 + 0.203577i
\(255\) 8.35101 0.522960
\(256\) 6.84549 + 14.4617i 0.427843 + 0.903853i
\(257\) −16.6585 −1.03913 −0.519564 0.854431i \(-0.673906\pi\)
−0.519564 + 0.854431i \(0.673906\pi\)
\(258\) 8.91746 + 1.26655i 0.555177 + 0.0788518i
\(259\) 5.74684 + 5.74684i 0.357091 + 0.357091i
\(260\) −0.624939 0.181175i −0.0387571 0.0112360i
\(261\) −13.3476 + 13.3476i −0.826195 + 0.826195i
\(262\) −1.81752 2.41928i −0.112287 0.149463i
\(263\) 14.5446i 0.896860i 0.893818 + 0.448430i \(0.148017\pi\)
−0.893818 + 0.448430i \(0.851983\pi\)
\(264\) −23.8254 10.7331i −1.46635 0.660574i
\(265\) 13.1078i 0.805208i
\(266\) −7.96925 + 5.98703i −0.488626 + 0.367089i
\(267\) 22.0142 22.0142i 1.34725 1.34725i
\(268\) −14.7962 26.8779i −0.903823 1.64183i
\(269\) −2.07516 2.07516i −0.126525 0.126525i 0.641009 0.767534i \(-0.278516\pi\)
−0.767534 + 0.641009i \(0.778516\pi\)
\(270\) 0.744932 5.24489i 0.0453351 0.319194i
\(271\) −7.78531 −0.472924 −0.236462 0.971641i \(-0.575988\pi\)
−0.236462 + 0.971641i \(0.575988\pi\)
\(272\) 10.3902 + 6.57723i 0.630001 + 0.398803i
\(273\) −0.883751 −0.0534871
\(274\) −1.00273 + 7.06000i −0.0605772 + 0.426510i
\(275\) −2.40494 2.40494i −0.145023 0.145023i
\(276\) 13.5909 7.48176i 0.818077 0.450349i
\(277\) −4.89400 + 4.89400i −0.294052 + 0.294052i −0.838679 0.544626i \(-0.816671\pi\)
0.544626 + 0.838679i \(0.316671\pi\)
\(278\) 20.8194 15.6409i 1.24866 0.938080i
\(279\) 24.1280i 1.44450i
\(280\) 1.00204 + 2.64498i 0.0598834 + 0.158068i
\(281\) 8.10490i 0.483498i 0.970339 + 0.241749i \(0.0777210\pi\)
−0.970339 + 0.241749i \(0.922279\pi\)
\(282\) 27.7157 + 36.8920i 1.65045 + 2.19688i
\(283\) 14.8117 14.8117i 0.880467 0.880467i −0.113115 0.993582i \(-0.536083\pi\)
0.993582 + 0.113115i \(0.0360828\pi\)
\(284\) 0.797401 2.75053i 0.0473170 0.163214i
\(285\) 13.5382 + 13.5382i 0.801932 + 0.801932i
\(286\) 1.54928 + 0.220044i 0.0916106 + 0.0130115i
\(287\) 2.73725 0.161575
\(288\) 16.0608 18.8592i 0.946391 1.11129i
\(289\) −7.54893 −0.444055
\(290\) −6.03563 0.857241i −0.354424 0.0503389i
\(291\) 14.6271 + 14.6271i 0.857458 + 0.857458i
\(292\) −6.43347 + 22.1914i −0.376490 + 1.29865i
\(293\) −5.07959 + 5.07959i −0.296753 + 0.296753i −0.839741 0.542988i \(-0.817293\pi\)
0.542988 + 0.839741i \(0.317293\pi\)
\(294\) 2.30746 + 3.07142i 0.134574 + 0.179129i
\(295\) 1.74732i 0.101733i
\(296\) 21.4964 8.14384i 1.24945 0.473351i
\(297\) 12.7402i 0.739263i
\(298\) −4.68277 + 3.51801i −0.271266 + 0.203793i
\(299\) −0.656927 + 0.656927i −0.0379911 + 0.0379911i
\(300\) 4.75936 2.62001i 0.274782 0.151267i
\(301\) 1.65787 + 1.65787i 0.0955578 + 0.0955578i
\(302\) 2.08614 14.6880i 0.120044 0.845200i
\(303\) 23.4657 1.34807
\(304\) 6.18143 + 27.5067i 0.354529 + 1.57762i
\(305\) 0.501695 0.0287270
\(306\) 2.67715 18.8492i 0.153042 1.07754i
\(307\) −24.6662 24.6662i −1.40778 1.40778i −0.771275 0.636502i \(-0.780381\pi\)
−0.636502 0.771275i \(-0.719619\pi\)
\(308\) −3.28038 5.95894i −0.186917 0.339542i
\(309\) −18.0314 + 18.0314i −1.02577 + 1.02577i
\(310\) 6.23000 4.68040i 0.353840 0.265829i
\(311\) 18.5460i 1.05165i 0.850594 + 0.525823i \(0.176243\pi\)
−0.850594 + 0.525823i \(0.823757\pi\)
\(312\) −1.02668 + 2.27905i −0.0581244 + 0.129026i
\(313\) 10.3997i 0.587825i −0.955832 0.293913i \(-0.905043\pi\)
0.955832 0.293913i \(-0.0949575\pi\)
\(314\) −13.6813 18.2110i −0.772081 1.02770i
\(315\) 3.09641 3.09641i 0.174463 0.174463i
\(316\) 15.5784 + 4.51631i 0.876354 + 0.254062i
\(317\) −12.3716 12.3716i −0.694857 0.694857i 0.268439 0.963297i \(-0.413492\pi\)
−0.963297 + 0.268439i \(0.913492\pi\)
\(318\) −49.8549 7.08089i −2.79572 0.397077i
\(319\) 14.6610 0.820858
\(320\) 7.98506 + 0.488660i 0.446379 + 0.0273169i
\(321\) −15.6042 −0.870944
\(322\) 3.99833 + 0.567883i 0.222818 + 0.0316469i
\(323\) 15.3215 + 15.3215i 0.852512 + 0.852512i
\(324\) 5.68865 + 1.64919i 0.316036 + 0.0916215i
\(325\) −0.230047 + 0.230047i −0.0127607 + 0.0127607i
\(326\) 7.91437 + 10.5347i 0.438336 + 0.583462i
\(327\) 44.7100i 2.47247i
\(328\) 3.17995 7.05892i 0.175584 0.389763i
\(329\) 12.0114i 0.662208i
\(330\) −10.4462 + 7.84788i −0.575044 + 0.432012i
\(331\) −17.6765 + 17.6765i −0.971590 + 0.971590i −0.999607 0.0280173i \(-0.991081\pi\)
0.0280173 + 0.999607i \(0.491081\pi\)
\(332\) −0.0202750 0.0368303i −0.00111273 0.00202132i
\(333\) −25.1653 25.1653i −1.37905 1.37905i
\(334\) −3.20647 + 22.5760i −0.175450 + 1.23530i
\(335\) −15.3407 −0.838152
\(336\) 10.6013 2.38238i 0.578350 0.129969i
\(337\) 18.6279 1.01473 0.507364 0.861732i \(-0.330620\pi\)
0.507364 + 0.861732i \(0.330620\pi\)
\(338\) −2.56420 + 18.0539i −0.139474 + 0.982003i
\(339\) −27.6088 27.6088i −1.49950 1.49950i
\(340\) 5.38630 2.96514i 0.292113 0.160808i
\(341\) −13.2511 + 13.2511i −0.717587 + 0.717587i
\(342\) 34.8972 26.2171i 1.88703 1.41766i
\(343\) 1.00000i 0.0539949i
\(344\) 6.20136 2.34936i 0.334355 0.126669i
\(345\) 7.75709i 0.417628i
\(346\) 10.9715 + 14.6040i 0.589831 + 0.785115i
\(347\) 7.00942 7.00942i 0.376286 0.376286i −0.493475 0.869760i \(-0.664273\pi\)
0.869760 + 0.493475i \(0.164273\pi\)
\(348\) −6.52093 + 22.4931i −0.349559 + 1.20576i
\(349\) 21.6394 + 21.6394i 1.15833 + 1.15833i 0.984835 + 0.173495i \(0.0555061\pi\)
0.173495 + 0.984835i \(0.444494\pi\)
\(350\) 1.40016 + 0.198865i 0.0748418 + 0.0106298i
\(351\) 1.21868 0.0650483
\(352\) −19.1780 + 1.53687i −1.02219 + 0.0819153i
\(353\) 29.6199 1.57651 0.788253 0.615351i \(-0.210986\pi\)
0.788253 + 0.615351i \(0.210986\pi\)
\(354\) 6.64584 + 0.943910i 0.353223 + 0.0501682i
\(355\) −1.01250 1.01250i −0.0537379 0.0537379i
\(356\) 6.38243 22.0153i 0.338268 1.16681i
\(357\) 5.90505 5.90505i 0.312529 0.312529i
\(358\) 12.1994 + 16.2384i 0.644758 + 0.858227i
\(359\) 25.4894i 1.34528i 0.739971 + 0.672638i \(0.234839\pi\)
−0.739971 + 0.672638i \(0.765161\pi\)
\(360\) −4.38793 11.5823i −0.231264 0.610442i
\(361\) 30.6767i 1.61456i
\(362\) −14.4856 + 10.8826i −0.761346 + 0.571975i
\(363\) 1.08998 1.08998i 0.0572091 0.0572091i
\(364\) −0.570009 + 0.313789i −0.0298766 + 0.0164470i
\(365\) 8.16890 + 8.16890i 0.427580 + 0.427580i
\(366\) 0.271017 1.90817i 0.0141663 0.0997414i
\(367\) 25.4780 1.32994 0.664970 0.746870i \(-0.268444\pi\)
0.664970 + 0.746870i \(0.268444\pi\)
\(368\) 6.10946 9.65129i 0.318478 0.503108i
\(369\) −11.9864 −0.623987
\(370\) 1.61623 11.3795i 0.0840236 0.591590i
\(371\) −9.26864 9.26864i −0.481204 0.481204i
\(372\) −14.4361 26.2238i −0.748479 1.35964i
\(373\) −9.10570 + 9.10570i −0.471475 + 0.471475i −0.902392 0.430917i \(-0.858190\pi\)
0.430917 + 0.902392i \(0.358190\pi\)
\(374\) −11.8223 + 8.88167i −0.611314 + 0.459260i
\(375\) 2.71643i 0.140276i
\(376\) 30.9753 + 13.9540i 1.59743 + 0.719622i
\(377\) 1.40241i 0.0722280i
\(378\) −3.18195 4.23544i −0.163662 0.217848i
\(379\) −9.54063 + 9.54063i −0.490069 + 0.490069i −0.908328 0.418259i \(-0.862641\pi\)
0.418259 + 0.908328i \(0.362641\pi\)
\(380\) 13.5389 + 3.92503i 0.694529 + 0.201350i
\(381\) −31.3379 31.3379i −1.60549 1.60549i
\(382\) −30.8946 4.38797i −1.58071 0.224508i
\(383\) −2.95979 −0.151238 −0.0756191 0.997137i \(-0.524093\pi\)
−0.0756191 + 0.997137i \(0.524093\pi\)
\(384\) 6.17214 30.1067i 0.314971 1.53638i
\(385\) −3.40110 −0.173336
\(386\) −33.0562 4.69497i −1.68251 0.238968i
\(387\) −7.25977 7.25977i −0.369035 0.369035i
\(388\) 14.6279 + 4.24075i 0.742619 + 0.215291i
\(389\) −17.7128 + 17.7128i −0.898077 + 0.898077i −0.995266 0.0971889i \(-0.969015\pi\)
0.0971889 + 0.995266i \(0.469015\pi\)
\(390\) 0.750698 + 0.999242i 0.0380131 + 0.0505986i
\(391\) 8.77891i 0.443969i
\(392\) 2.57883 + 1.16173i 0.130251 + 0.0586763i
\(393\) 5.81224i 0.293189i
\(394\) 2.14197 1.60919i 0.107911 0.0810699i
\(395\) 5.73459 5.73459i 0.288538 0.288538i
\(396\) 14.3647 + 26.0941i 0.721856 + 1.31128i
\(397\) −3.14511 3.14511i −0.157849 0.157849i 0.623764 0.781613i \(-0.285603\pi\)
−0.781613 + 0.623764i \(0.785603\pi\)
\(398\) −3.56962 + 25.1329i −0.178929 + 1.25980i
\(399\) 19.1459 0.958492
\(400\) 2.13945 3.37975i 0.106973 0.168988i
\(401\) −23.9530 −1.19616 −0.598078 0.801438i \(-0.704069\pi\)
−0.598078 + 0.801438i \(0.704069\pi\)
\(402\) −8.28709 + 58.3474i −0.413323 + 2.91011i
\(403\) 1.26755 + 1.26755i 0.0631410 + 0.0631410i
\(404\) 15.1351 8.33182i 0.752997 0.414523i
\(405\) 2.09406 2.09406i 0.104054 0.104054i
\(406\) −4.87400 + 3.66167i −0.241892 + 0.181726i
\(407\) 27.6416i 1.37014i
\(408\) −8.36805 22.0882i −0.414280 1.09353i
\(409\) 5.26405i 0.260291i −0.991495 0.130145i \(-0.958456\pi\)
0.991495 0.130145i \(-0.0415444\pi\)
\(410\) −2.32515 3.09496i −0.114831 0.152849i
\(411\) 9.68522 9.68522i 0.477737 0.477737i
\(412\) −5.22774 + 18.0324i −0.257552 + 0.888392i
\(413\) 1.23554 + 1.23554i 0.0607972 + 0.0607972i
\(414\) −17.5086 2.48675i −0.860502 0.122217i
\(415\) −0.0210211 −0.00103188
\(416\) 0.147011 + 1.83450i 0.00720779 + 0.0899435i
\(417\) −50.0179 −2.44939
\(418\) −33.5640 4.76710i −1.64167 0.233166i
\(419\) −5.40200 5.40200i −0.263905 0.263905i 0.562733 0.826638i \(-0.309750\pi\)
−0.826638 + 0.562733i \(0.809750\pi\)
\(420\) 1.51274 5.21800i 0.0738143 0.254612i
\(421\) −14.2595 + 14.2595i −0.694963 + 0.694963i −0.963320 0.268357i \(-0.913519\pi\)
0.268357 + 0.963320i \(0.413519\pi\)
\(422\) 13.0449 + 17.3639i 0.635017 + 0.845261i
\(423\) 52.5976i 2.55738i
\(424\) −34.6699 + 13.1346i −1.68372 + 0.637872i
\(425\) 3.07426i 0.149123i
\(426\) −4.39794 + 3.30403i −0.213081 + 0.160081i
\(427\) 0.354752 0.354752i 0.0171676 0.0171676i
\(428\) −10.0645 + 5.54051i −0.486488 + 0.267811i
\(429\) −2.12537 2.12537i −0.102614 0.102614i
\(430\) 0.466255 3.28279i 0.0224848 0.158310i
\(431\) −5.88265 −0.283357 −0.141679 0.989913i \(-0.545250\pi\)
−0.141679 + 0.989913i \(0.545250\pi\)
\(432\) −14.6191 + 3.28527i −0.703360 + 0.158062i
\(433\) 34.1231 1.63985 0.819925 0.572471i \(-0.194015\pi\)
0.819925 + 0.572471i \(0.194015\pi\)
\(434\) 1.09574 7.71482i 0.0525970 0.370323i
\(435\) 8.27995 + 8.27995i 0.396993 + 0.396993i
\(436\) −15.8749 28.8374i −0.760271 1.38106i
\(437\) 14.2319 14.2319i 0.680802 0.680802i
\(438\) 35.4828 26.6571i 1.69543 1.27372i
\(439\) 30.0006i 1.43185i −0.698176 0.715926i \(-0.746005\pi\)
0.698176 0.715926i \(-0.253995\pi\)
\(440\) −3.95116 + 8.77086i −0.188364 + 0.418134i
\(441\) 4.37899i 0.208523i
\(442\) 0.849586 + 1.13087i 0.0404107 + 0.0537900i
\(443\) 21.0503 21.0503i 1.00013 1.00013i 0.000131473 1.00000i \(-0.499958\pi\)
1.00000 0.000131473i \(-4.18492e-5\pi\)
\(444\) −42.4080 12.2944i −2.01260 0.583468i
\(445\) −8.10410 8.10410i −0.384171 0.384171i
\(446\) 2.12583 + 0.301932i 0.100661 + 0.0142969i
\(447\) 11.2502 0.532116
\(448\) 5.99183 5.30076i 0.283087 0.250437i
\(449\) −13.0169 −0.614305 −0.307153 0.951660i \(-0.599376\pi\)
−0.307153 + 0.951660i \(0.599376\pi\)
\(450\) −6.13129 0.870827i −0.289032 0.0410512i
\(451\) 6.58293 + 6.58293i 0.309978 + 0.309978i
\(452\) −27.6102 8.00443i −1.29867 0.376497i
\(453\) −20.1497 + 20.1497i −0.946715 + 0.946715i
\(454\) 7.91042 + 10.5294i 0.371255 + 0.494171i
\(455\) 0.325336i 0.0152520i
\(456\) 22.2424 49.3740i 1.04159 2.31215i
\(457\) 27.5356i 1.28806i 0.764999 + 0.644031i \(0.222739\pi\)
−0.764999 + 0.644031i \(0.777261\pi\)
\(458\) 10.4250 7.83193i 0.487126 0.365962i
\(459\) −8.14298 + 8.14298i −0.380082 + 0.380082i
\(460\) −2.75426 5.00323i −0.128418 0.233277i
\(461\) −3.02388 3.02388i −0.140836 0.140836i 0.633174 0.774010i \(-0.281752\pi\)
−0.774010 + 0.633174i \(0.781752\pi\)
\(462\) −1.83728 + 12.9359i −0.0854781 + 0.601831i
\(463\) −29.8214 −1.38592 −0.692958 0.720978i \(-0.743693\pi\)
−0.692958 + 0.720978i \(0.743693\pi\)
\(464\) 3.78057 + 16.8231i 0.175508 + 0.780993i
\(465\) −14.9674 −0.694096
\(466\) 3.58757 25.2592i 0.166191 1.17011i
\(467\) −20.0298 20.0298i −0.926870 0.926870i 0.0706323 0.997502i \(-0.477498\pi\)
−0.997502 + 0.0706323i \(0.977498\pi\)
\(468\) 2.49606 1.37408i 0.115380 0.0635167i
\(469\) −10.8475 + 10.8475i −0.500892 + 0.500892i
\(470\) 13.5811 10.2030i 0.626447 0.470629i
\(471\) 43.7513i 2.01595i
\(472\) 4.62164 1.75089i 0.212728 0.0805913i
\(473\) 7.97414i 0.366651i
\(474\) −18.7133 24.9090i −0.859531 1.14411i
\(475\) 4.98381 4.98381i 0.228673 0.228673i
\(476\) 1.71201 5.90536i 0.0784700 0.270672i
\(477\) 40.5872 + 40.5872i 1.85836 + 1.85836i
\(478\) 19.7365 + 2.80317i 0.902725 + 0.128214i
\(479\) 27.6154 1.26178 0.630889 0.775873i \(-0.282690\pi\)
0.630889 + 0.775873i \(0.282690\pi\)
\(480\) −11.6990 9.96303i −0.533982 0.454748i
\(481\) 2.64409 0.120560
\(482\) −15.5278 2.20541i −0.707272 0.100454i
\(483\) −5.48509 5.48509i −0.249580 0.249580i
\(484\) 0.316011 1.09004i 0.0143641 0.0495471i
\(485\) 5.38469 5.38469i 0.244506 0.244506i
\(486\) −16.3792 21.8022i −0.742978 0.988966i
\(487\) 26.5614i 1.20361i 0.798642 + 0.601807i \(0.205552\pi\)
−0.798642 + 0.601807i \(0.794448\pi\)
\(488\) −0.502719 1.32697i −0.0227570 0.0600692i
\(489\) 25.3092i 1.14452i
\(490\) 1.13068 0.849445i 0.0510790 0.0383740i
\(491\) −1.69651 + 1.69651i −0.0765626 + 0.0765626i −0.744351 0.667789i \(-0.767241\pi\)
0.667789 + 0.744351i \(0.267241\pi\)
\(492\) −13.0276 + 7.17164i −0.587328 + 0.323323i
\(493\) 9.37066 + 9.37066i 0.422033 + 0.422033i
\(494\) −0.456002 + 3.21060i −0.0205165 + 0.144452i
\(495\) 14.8934 0.669406
\(496\) −18.6223 11.7883i −0.836165 0.529309i
\(497\) −1.43189 −0.0642291
\(498\) −0.0113557 + 0.0799524i −0.000508859 + 0.00358275i
\(499\) −18.0448 18.0448i −0.807795 0.807795i 0.176505 0.984300i \(-0.443521\pi\)
−0.984300 + 0.176505i \(0.943521\pi\)
\(500\) −0.964507 1.75206i −0.0431341 0.0783547i
\(501\) 30.9707 30.9707i 1.38367 1.38367i
\(502\) 9.99227 7.50687i 0.445977 0.335048i
\(503\) 28.8592i 1.28677i 0.765544 + 0.643383i \(0.222470\pi\)
−0.765544 + 0.643383i \(0.777530\pi\)
\(504\) −11.2927 5.08721i −0.503016 0.226602i
\(505\) 8.63842i 0.384405i
\(506\) 8.25001 + 10.9815i 0.366758 + 0.488185i
\(507\) 24.7672 24.7672i 1.09995 1.09995i
\(508\) −31.3395 9.08559i −1.39047 0.403108i
\(509\) 12.7993 + 12.7993i 0.567318 + 0.567318i 0.931376 0.364058i \(-0.118609\pi\)
−0.364058 + 0.931376i \(0.618609\pi\)
\(510\) −11.6928 1.66072i −0.517764 0.0735381i
\(511\) 11.5526 0.511056
\(512\) −6.70887 21.6100i −0.296493 0.955035i
\(513\) −26.4019 −1.16567
\(514\) 23.3246 + 3.31279i 1.02880 + 0.146121i
\(515\) 6.63792 + 6.63792i 0.292502 + 0.292502i
\(516\) −12.2340 3.54674i −0.538572 0.156137i
\(517\) −28.8866 + 28.8866i −1.27043 + 1.27043i
\(518\) −6.90365 9.18934i −0.303329 0.403757i
\(519\) 35.0856i 1.54009i
\(520\) 0.838986 + 0.377953i 0.0367920 + 0.0165743i
\(521\) 35.5497i 1.55746i 0.627358 + 0.778731i \(0.284136\pi\)
−0.627358 + 0.778731i \(0.715864\pi\)
\(522\) 21.3432 16.0344i 0.934165 0.701807i
\(523\) 2.94875 2.94875i 0.128940 0.128940i −0.639692 0.768632i \(-0.720938\pi\)
0.768632 + 0.639692i \(0.220938\pi\)
\(524\) 2.06372 + 3.74882i 0.0901539 + 0.163768i
\(525\) −1.92081 1.92081i −0.0838308 0.0838308i
\(526\) 2.89242 20.3648i 0.126115 0.887949i
\(527\) −16.9390 −0.737875
\(528\) 31.2250 + 19.7661i 1.35889 + 0.860207i
\(529\) 14.8454 0.645454
\(530\) −2.60669 + 18.3531i −0.113227 + 0.797207i
\(531\) −5.41043 5.41043i −0.234793 0.234793i
\(532\) 12.3488 6.79801i 0.535390 0.294731i
\(533\) 0.629697 0.629697i 0.0272752 0.0272752i
\(534\) −35.2013 + 26.4456i −1.52331 + 1.14441i
\(535\) 5.74439i 0.248352i
\(536\) 15.3720 + 40.5758i 0.663970 + 1.75261i
\(537\) 39.0123i 1.68350i
\(538\) 2.49288 + 3.31824i 0.107476 + 0.143059i
\(539\) −2.40494 + 2.40494i −0.103588 + 0.103588i
\(540\) −2.08605 + 7.19555i −0.0897693 + 0.309647i
\(541\) −0.870655 0.870655i −0.0374324 0.0374324i 0.688143 0.725575i \(-0.258426\pi\)
−0.725575 + 0.688143i \(0.758426\pi\)
\(542\) 10.9007 + 1.54823i 0.468225 + 0.0665021i
\(543\) 34.8012 1.49346
\(544\) −13.2400 11.2754i −0.567662 0.483431i
\(545\) −16.4591 −0.705030
\(546\) 1.23739 + 0.175747i 0.0529556 + 0.00752129i
\(547\) 27.4186 + 27.4186i 1.17233 + 1.17233i 0.981652 + 0.190681i \(0.0610695\pi\)
0.190681 + 0.981652i \(0.438930\pi\)
\(548\) 2.80797 9.68573i 0.119951 0.413754i
\(549\) −1.55345 + 1.55345i −0.0662998 + 0.0662998i
\(550\) 2.88904 + 3.84556i 0.123189 + 0.163975i
\(551\) 30.3823i 1.29433i
\(552\) −20.5173 + 7.77292i −0.873276 + 0.330838i
\(553\) 8.10993i 0.344869i
\(554\) 7.82564 5.87915i 0.332480 0.249781i
\(555\) −15.6109 + 15.6109i −0.662645 + 0.662645i
\(556\) −32.2609 + 17.7596i −1.36817 + 0.753174i
\(557\) 9.50051 + 9.50051i 0.402550 + 0.402550i 0.879131 0.476581i \(-0.158124\pi\)
−0.476581 + 0.879131i \(0.658124\pi\)
\(558\) −4.79821 + 33.7831i −0.203125 + 1.43015i
\(559\) 0.762775 0.0322619
\(560\) −0.877026 3.90267i −0.0370611 0.164918i
\(561\) 28.4026 1.19916
\(562\) 1.61178 11.3482i 0.0679889 0.478694i
\(563\) −23.3659 23.3659i −0.984754 0.984754i 0.0151319 0.999886i \(-0.495183\pi\)
−0.999886 + 0.0151319i \(0.995183\pi\)
\(564\) −31.4700 57.1664i −1.32512 2.40714i
\(565\) −10.1636 + 10.1636i −0.427587 + 0.427587i
\(566\) −23.6844 + 17.7933i −0.995529 + 0.747908i
\(567\) 2.96144i 0.124369i
\(568\) −1.66347 + 3.69261i −0.0697978 + 0.154938i
\(569\) 3.93387i 0.164917i 0.996595 + 0.0824583i \(0.0262771\pi\)
−0.996595 + 0.0824583i \(0.973723\pi\)
\(570\) −16.2634 21.6479i −0.681197 0.906730i
\(571\) 13.0268 13.0268i 0.545157 0.545157i −0.379879 0.925036i \(-0.624035\pi\)
0.925036 + 0.379879i \(0.124035\pi\)
\(572\) −2.12548 0.616194i −0.0888707 0.0257644i
\(573\) 42.3827 + 42.3827i 1.77056 + 1.77056i
\(574\) −3.83260 0.544344i −0.159969 0.0227205i
\(575\) −2.85562 −0.119088
\(576\) −26.2381 + 23.2119i −1.09325 + 0.967164i
\(577\) 18.7292 0.779709 0.389854 0.920877i \(-0.372525\pi\)
0.389854 + 0.920877i \(0.372525\pi\)
\(578\) 10.5697 + 1.50122i 0.439643 + 0.0624425i
\(579\) 45.3479 + 45.3479i 1.88460 + 1.88460i
\(580\) 8.28038 + 2.40055i 0.343824 + 0.0996775i
\(581\) −0.0148642 + 0.0148642i −0.000616669 + 0.000616669i
\(582\) −17.5715 23.3892i −0.728363 0.969513i
\(583\) 44.5810i 1.84636i
\(584\) 13.4210 29.7921i 0.555365 1.23281i
\(585\) 1.42464i 0.0589016i
\(586\) 8.12240 6.10209i 0.335533 0.252075i
\(587\) −2.58925 + 2.58925i −0.106870 + 0.106870i −0.758520 0.651650i \(-0.774077\pi\)
0.651650 + 0.758520i \(0.274077\pi\)
\(588\) −2.62001 4.75936i −0.108048 0.196273i
\(589\) −27.4605 27.4605i −1.13149 1.13149i
\(590\) 0.347482 2.44654i 0.0143056 0.100722i
\(591\) −5.14601 −0.211679
\(592\) −31.7180 + 7.12781i −1.30360 + 0.292951i
\(593\) 35.5707 1.46072 0.730358 0.683065i \(-0.239353\pi\)
0.730358 + 0.683065i \(0.239353\pi\)
\(594\) 2.53359 17.8384i 0.103954 0.731917i
\(595\) −2.17383 2.17383i −0.0891183 0.0891183i
\(596\) 7.25624 3.99455i 0.297227 0.163623i
\(597\) 34.4784 34.4784i 1.41111 1.41111i
\(598\) 1.05044 0.789164i 0.0429558 0.0322713i
\(599\) 16.7637i 0.684945i −0.939528 0.342473i \(-0.888736\pi\)
0.939528 0.342473i \(-0.111264\pi\)
\(600\) −7.18490 + 2.72197i −0.293322 + 0.111124i
\(601\) 31.5684i 1.28770i 0.765151 + 0.643850i \(0.222664\pi\)
−0.765151 + 0.643850i \(0.777336\pi\)
\(602\) −1.99159 2.65097i −0.0811711 0.108046i
\(603\) 47.5011 47.5011i 1.93440 1.93440i
\(604\) −5.84187 + 20.1507i −0.237702 + 0.819922i
\(605\) −0.401255 0.401255i −0.0163133 0.0163133i
\(606\) −32.8557 4.66650i −1.33467 0.189564i
\(607\) −5.46877 −0.221970 −0.110985 0.993822i \(-0.535401\pi\)
−0.110985 + 0.993822i \(0.535401\pi\)
\(608\) −3.18488 39.7431i −0.129164 1.61179i
\(609\) 11.7096 0.474498
\(610\) −0.702454 0.0997696i −0.0284415 0.00403955i
\(611\) 2.76318 + 2.76318i 0.111786 + 0.111786i
\(612\) −7.49688 + 25.8595i −0.303044 + 1.04531i
\(613\) 26.1963 26.1963i 1.05806 1.05806i 0.0598509 0.998207i \(-0.480937\pi\)
0.998207 0.0598509i \(-0.0190625\pi\)
\(614\) 29.6315 + 39.4420i 1.19583 + 1.59175i
\(615\) 7.43555i 0.299830i
\(616\) 3.40804 + 8.99583i 0.137314 + 0.362452i
\(617\) 26.9821i 1.08626i 0.839649 + 0.543129i \(0.182761\pi\)
−0.839649 + 0.543129i \(0.817239\pi\)
\(618\) 28.8328 21.6611i 1.15982 0.871338i
\(619\) 27.0870 27.0870i 1.08872 1.08872i 0.0930566 0.995661i \(-0.470336\pi\)
0.995661 0.0930566i \(-0.0296637\pi\)
\(620\) −9.65378 + 5.31438i −0.387705 + 0.213431i
\(621\) 7.56386 + 7.56386i 0.303527 + 0.303527i
\(622\) 3.68815 25.9674i 0.147881 1.04120i
\(623\) −11.4609 −0.459172
\(624\) 1.89074 2.98686i 0.0756903 0.119570i
\(625\) −1.00000 −0.0400000
\(626\) −2.06814 + 14.5612i −0.0826593 + 0.581985i
\(627\) 46.0446 + 46.0446i 1.83884 + 1.83884i
\(628\) 15.5345 + 28.2190i 0.619895 + 1.12606i
\(629\) −17.6673 + 17.6673i −0.704440 + 0.704440i
\(630\) −4.95124 + 3.71971i −0.197262 + 0.148197i
\(631\) 30.8360i 1.22756i −0.789476 0.613781i \(-0.789648\pi\)
0.789476 0.613781i \(-0.210352\pi\)
\(632\) −20.9142 9.42157i −0.831921 0.374770i
\(633\) 41.7162i 1.65807i
\(634\) 14.8619 + 19.7825i 0.590243 + 0.785663i
\(635\) −11.5364 + 11.5364i −0.457809 + 0.457809i
\(636\) 68.3967 + 19.8288i 2.71211 + 0.786262i
\(637\) 0.230047 + 0.230047i 0.00911480 + 0.00911480i
\(638\) −20.5278 2.91556i −0.812702 0.115428i
\(639\) 6.27023 0.248046
\(640\) −11.0832 2.27215i −0.438102 0.0898147i
\(641\) −21.0782 −0.832540 −0.416270 0.909241i \(-0.636663\pi\)
−0.416270 + 0.909241i \(0.636663\pi\)
\(642\) 21.8485 + 3.10314i 0.862290 + 0.122471i
\(643\) 25.6837 + 25.6837i 1.01286 + 1.01286i 0.999916 + 0.0129487i \(0.00412181\pi\)
0.0129487 + 0.999916i \(0.495878\pi\)
\(644\) −5.48537 1.59026i −0.216154 0.0626649i
\(645\) −4.50348 + 4.50348i −0.177324 + 0.177324i
\(646\) −18.4057 24.4995i −0.724162 0.963921i
\(647\) 4.30694i 0.169323i −0.996410 0.0846616i \(-0.973019\pi\)
0.996410 0.0846616i \(-0.0269809\pi\)
\(648\) −7.63706 3.44040i −0.300012 0.135152i
\(649\) 5.94282i 0.233276i
\(650\) 0.367851 0.276355i 0.0144283 0.0108395i
\(651\) −10.5835 + 10.5835i −0.414802 + 0.414802i
\(652\) −8.98641 16.3242i −0.351935 0.639303i
\(653\) 7.40886 + 7.40886i 0.289931 + 0.289931i 0.837053 0.547122i \(-0.184277\pi\)
−0.547122 + 0.837053i \(0.684277\pi\)
\(654\) −8.89125 + 62.6012i −0.347675 + 2.44790i
\(655\) 2.13966 0.0836035
\(656\) −5.85622 + 9.25124i −0.228647 + 0.361200i
\(657\) −50.5885 −1.97365
\(658\) 2.38864 16.8179i 0.0931190 0.655629i
\(659\) 5.83069 + 5.83069i 0.227132 + 0.227132i 0.811493 0.584362i \(-0.198655\pi\)
−0.584362 + 0.811493i \(0.698655\pi\)
\(660\) 16.1870 8.91092i 0.630079 0.346857i
\(661\) 21.9055 21.9055i 0.852026 0.852026i −0.138357 0.990382i \(-0.544182\pi\)
0.990382 + 0.138357i \(0.0441821\pi\)
\(662\) 28.2652 21.2348i 1.09856 0.825312i
\(663\) 2.71688i 0.105515i
\(664\) 0.0210640 + 0.0556003i 0.000817442 + 0.00215771i
\(665\) 7.04817i 0.273316i
\(666\) 30.2310 + 40.2400i 1.17143 + 1.55927i
\(667\) 8.70422 8.70422i 0.337029 0.337029i
\(668\) 8.97914 30.9723i 0.347413 1.19836i
\(669\) −2.91631 2.91631i −0.112751 0.112751i
\(670\) 21.4795 + 3.05073i 0.829824 + 0.117860i
\(671\) 1.70631 0.0658715
\(672\) −15.3173 + 1.22748i −0.590879 + 0.0473512i
\(673\) 22.3632 0.862038 0.431019 0.902343i \(-0.358154\pi\)
0.431019 + 0.902343i \(0.358154\pi\)
\(674\) −26.0821 3.70445i −1.00465 0.142690i
\(675\) 2.64876 + 2.64876i 0.101951 + 0.101951i
\(676\) 7.18058 24.7685i 0.276176 0.952633i
\(677\) 8.00808 8.00808i 0.307775 0.307775i −0.536271 0.844046i \(-0.680167\pi\)
0.844046 + 0.536271i \(0.180167\pi\)
\(678\) 33.1663 + 44.1472i 1.27374 + 1.69546i
\(679\) 7.61510i 0.292241i
\(680\) −8.13135 + 3.08054i −0.311823 + 0.118133i
\(681\) 25.2966i 0.969369i
\(682\) 21.1888 15.9185i 0.811363 0.609550i
\(683\) −31.7140 + 31.7140i −1.21350 + 1.21350i −0.243636 + 0.969867i \(0.578340\pi\)
−0.969867 + 0.243636i \(0.921660\pi\)
\(684\) −54.0754 + 29.7684i −2.06763 + 1.13822i
\(685\) −3.56542 3.56542i −0.136228 0.136228i
\(686\) 0.198865 1.40016i 0.00759270 0.0534584i
\(687\) −25.0456 −0.955550
\(688\) −9.15011 + 2.05626i −0.348845 + 0.0783940i
\(689\) −4.26445 −0.162462
\(690\) −1.54261 + 10.8612i −0.0587263 + 0.413478i
\(691\) 33.6095 + 33.6095i 1.27857 + 1.27857i 0.941471 + 0.337095i \(0.109444\pi\)
0.337095 + 0.941471i \(0.390556\pi\)
\(692\) −12.4576 22.6298i −0.473569 0.860255i
\(693\) 10.5312 10.5312i 0.400047 0.400047i
\(694\) −11.2083 + 8.42040i −0.425460 + 0.319634i
\(695\) 18.4131i 0.698449i
\(696\) 13.6034 30.1972i 0.515637 1.14462i
\(697\) 8.41502i 0.318742i
\(698\) −25.9953 34.6020i −0.983938 1.30970i
\(699\) −34.6518 + 34.6518i −1.31065 + 1.31065i
\(700\) −1.92091 0.556887i −0.0726034 0.0210483i
\(701\) −12.7954 12.7954i −0.483277 0.483277i 0.422900 0.906176i \(-0.361012\pi\)
−0.906176 + 0.422900i \(0.861012\pi\)
\(702\) −1.70635 0.242353i −0.0644020 0.00914702i
\(703\) −57.2823 −2.16044
\(704\) 27.1580 + 1.66198i 1.02355 + 0.0626382i
\(705\) −32.6280 −1.22884
\(706\) −41.4726 5.89036i −1.56084 0.221687i
\(707\) −6.10829 6.10829i −0.229726 0.229726i
\(708\) −9.11754 2.64325i −0.342658 0.0993395i
\(709\) 16.8053 16.8053i 0.631135 0.631135i −0.317218 0.948353i \(-0.602749\pi\)
0.948353 + 0.317218i \(0.102749\pi\)
\(710\) 1.21631 + 1.61901i 0.0456474 + 0.0607605i
\(711\) 35.5133i 1.33185i
\(712\) −13.3145 + 29.5558i −0.498983 + 1.10765i
\(713\) 15.7343i 0.589255i
\(714\) −9.44234 + 7.09372i −0.353371 + 0.265476i
\(715\) −0.782412 + 0.782412i −0.0292606 + 0.0292606i
\(716\) −13.8519 25.1625i −0.517669 0.940365i
\(717\) −27.0754 27.0754i −1.01115 1.01115i
\(718\) 5.06894 35.6892i 0.189171 1.33191i
\(719\) −33.0315 −1.23187 −0.615934 0.787798i \(-0.711221\pi\)
−0.615934 + 0.787798i \(0.711221\pi\)
\(720\) 3.84048 + 17.0897i 0.143126 + 0.636897i
\(721\) 9.38744 0.349606
\(722\) 6.10053 42.9524i 0.227038 1.59852i
\(723\) 21.3017 + 21.3017i 0.792220 + 0.792220i
\(724\) 22.4463 12.3567i 0.834212 0.459232i
\(725\) 3.04810 3.04810i 0.113204 0.113204i
\(726\) −1.74291 + 1.30939i −0.0646854 + 0.0485960i
\(727\) 41.3991i 1.53541i 0.640805 + 0.767704i \(0.278601\pi\)
−0.640805 + 0.767704i \(0.721399\pi\)
\(728\) 0.860506 0.326000i 0.0318925 0.0120824i
\(729\) 43.4947i 1.61091i
\(730\) −9.81327 13.0623i −0.363206 0.483457i
\(731\) −5.09671 + 5.09671i −0.188509 + 0.188509i
\(732\) −0.758935 + 2.61785i −0.0280511 + 0.0967583i
\(733\) 19.7963 + 19.7963i 0.731195 + 0.731195i 0.970856 0.239662i \(-0.0770366\pi\)
−0.239662 + 0.970856i \(0.577037\pi\)
\(734\) −35.6733 5.06669i −1.31673 0.187015i
\(735\) −2.71643 −0.100197
\(736\) −10.4735 + 12.2984i −0.386060 + 0.453326i
\(737\) −52.1752 −1.92190
\(738\) 16.7829 + 2.38367i 0.617787 + 0.0877443i
\(739\) 0.304171 + 0.304171i 0.0111891 + 0.0111891i 0.712679 0.701490i \(-0.247482\pi\)
−0.701490 + 0.712679i \(0.747482\pi\)
\(740\) −4.52596 + 15.6117i −0.166378 + 0.573897i
\(741\) 4.40445 4.40445i 0.161801 0.161801i
\(742\) 11.1344 + 14.8208i 0.408756 + 0.544089i
\(743\) 47.0701i 1.72684i 0.504490 + 0.863418i \(0.331681\pi\)
−0.504490 + 0.863418i \(0.668319\pi\)
\(744\) 14.9979 + 39.5884i 0.549851 + 1.45138i
\(745\) 4.14154i 0.151734i
\(746\) 14.5603 10.9386i 0.533089 0.400492i
\(747\) 0.0650899 0.0650899i 0.00238152 0.00238152i
\(748\) 18.3193 10.0847i 0.669821 0.368735i
\(749\) 4.06190 + 4.06190i 0.148419 + 0.148419i
\(750\) −0.540203 + 3.80344i −0.0197254 + 0.138882i
\(751\) −17.5637 −0.640910 −0.320455 0.947264i \(-0.603836\pi\)
−0.320455 + 0.947264i \(0.603836\pi\)
\(752\) −40.5955 25.6978i −1.48037 0.937101i
\(753\) −24.0061 −0.874831
\(754\) −0.278891 + 1.96361i −0.0101566 + 0.0715103i
\(755\) 7.41771 + 7.41771i 0.269958 + 0.269958i
\(756\) 3.61296 + 6.56308i 0.131402 + 0.238697i
\(757\) −7.56441 + 7.56441i −0.274933 + 0.274933i −0.831082 0.556149i \(-0.812278\pi\)
0.556149 + 0.831082i \(0.312278\pi\)
\(758\) 15.2557 11.4611i 0.554113 0.416287i
\(759\) 26.3826i 0.957628i
\(760\) −18.1761 8.18809i −0.659315 0.297013i
\(761\) 48.4501i 1.75631i −0.478372 0.878157i \(-0.658773\pi\)
0.478372 0.878157i \(-0.341227\pi\)
\(762\) 37.6461 + 50.1101i 1.36377 + 1.81530i
\(763\) −11.6383 + 11.6383i −0.421336 + 0.421336i
\(764\) 42.3849 + 12.2877i 1.53343 + 0.444554i
\(765\) 9.51917 + 9.51917i 0.344166 + 0.344166i
\(766\) 4.14419 + 0.588599i 0.149736 + 0.0212669i
\(767\) 0.568467 0.0205262
\(768\) −14.6292 + 40.9269i −0.527885 + 1.47682i
\(769\) 1.55437 0.0560519 0.0280259 0.999607i \(-0.491078\pi\)
0.0280259 + 0.999607i \(0.491078\pi\)
\(770\) 4.76209 + 0.676359i 0.171614 + 0.0243743i
\(771\) −31.9977 31.9977i −1.15237 1.15237i
\(772\) 45.3503 + 13.1474i 1.63219 + 0.473186i
\(773\) −8.53373 + 8.53373i −0.306937 + 0.306937i −0.843720 0.536783i \(-0.819639\pi\)
0.536783 + 0.843720i \(0.319639\pi\)
\(774\) 8.72114 + 11.6086i 0.313475 + 0.417262i
\(775\) 5.50995i 0.197923i
\(776\) −19.6381 8.84671i −0.704966 0.317578i
\(777\) 22.0771i 0.792012i
\(778\) 28.3233 21.2784i 1.01544 0.762867i
\(779\) −13.6419 + 13.6419i −0.488774 + 0.488774i
\(780\) −0.852384 1.54839i −0.0305203 0.0554412i
\(781\) −3.44361 3.44361i −0.123222 0.123222i
\(782\) −1.74582 + 12.2919i −0.0624304 + 0.439557i
\(783\) −16.1474 −0.577061
\(784\) −3.37975 2.13945i −0.120706 0.0764090i
\(785\) 16.1062 0.574854
\(786\) 1.15585 8.13807i 0.0412278 0.290275i
\(787\) 0.786007 + 0.786007i 0.0280181 + 0.0280181i 0.720977 0.692959i \(-0.243693\pi\)
−0.692959 + 0.720977i \(0.743693\pi\)
\(788\) −3.31911 + 1.82717i −0.118239 + 0.0650901i
\(789\) −27.9374 + 27.9374i −0.994598 + 0.994598i
\(790\) −9.16976 + 6.88894i −0.326245 + 0.245098i
\(791\) 14.3735i 0.511064i
\(792\) −14.9238 39.3926i −0.530293 1.39976i
\(793\) 0.163219i 0.00579609i
\(794\) 3.77821 + 5.02912i 0.134084 + 0.178477i
\(795\) 25.1776 25.1776i 0.892957 0.892957i
\(796\) 9.99610 34.4802i 0.354302 1.22212i
\(797\) −22.3948 22.3948i −0.793264 0.793264i 0.188759 0.982023i \(-0.439554\pi\)
−0.982023 + 0.188759i \(0.939554\pi\)
\(798\) −26.8073 3.80744i −0.948968 0.134782i
\(799\) −36.9261 −1.30635
\(800\) −3.66769 + 4.30674i −0.129673 + 0.152266i
\(801\) 50.1872 1.77328
\(802\) 33.5381 + 4.76342i 1.18427 + 0.168202i
\(803\) 27.7832 + 27.7832i 0.980449 + 0.980449i
\(804\) 23.2065 80.0478i 0.818432 2.82307i
\(805\) −2.01923 + 2.01923i −0.0711684 + 0.0711684i
\(806\) −1.52270 2.02684i −0.0536348 0.0713925i
\(807\) 7.97196i 0.280626i
\(808\) −22.8484 + 8.65606i −0.803805 + 0.304519i
\(809\) 4.46309i 0.156914i 0.996918 + 0.0784569i \(0.0249993\pi\)
−0.996918 + 0.0784569i \(0.975001\pi\)
\(810\) −3.34845 + 2.51558i −0.117653 + 0.0883885i
\(811\) 38.5046 38.5046i 1.35208 1.35208i 0.468750 0.883331i \(-0.344704\pi\)
0.883331 0.468750i \(-0.155296\pi\)
\(812\) 7.55256 4.15767i 0.265043 0.145906i
\(813\) −14.9541 14.9541i −0.524462 0.524462i
\(814\) 5.49694 38.7027i 0.192668 1.35653i
\(815\) −9.31710 −0.326364
\(816\) 7.32405 + 32.5912i 0.256393 + 1.14092i
\(817\) −16.5250 −0.578136
\(818\) −1.04684 + 7.37052i −0.0366018 + 0.257704i
\(819\) −1.00737 1.00737i −0.0352005 0.0352005i
\(820\) 2.64010 + 4.79584i 0.0921963 + 0.167478i
\(821\) −9.18132 + 9.18132i −0.320430 + 0.320430i −0.848932 0.528502i \(-0.822754\pi\)
0.528502 + 0.848932i \(0.322754\pi\)
\(822\) −15.4869 + 11.6348i −0.540169 + 0.405811i
\(823\) 42.0956i 1.46736i −0.679495 0.733680i \(-0.737801\pi\)
0.679495 0.733680i \(-0.262199\pi\)
\(824\) 10.9057 24.2086i 0.379918 0.843348i
\(825\) 9.23884i 0.321655i
\(826\) −1.48426 1.97567i −0.0516439 0.0687423i
\(827\) 34.6267 34.6267i 1.20409 1.20409i 0.231178 0.972912i \(-0.425742\pi\)
0.972912 0.231178i \(-0.0742578\pi\)
\(828\) 24.0204 + 6.96371i 0.834766 + 0.242006i
\(829\) −4.45262 4.45262i −0.154646 0.154646i 0.625543 0.780189i \(-0.284877\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(830\) 0.0294329 + 0.00418036i 0.00102163 + 0.000145102i
\(831\) −18.8009 −0.652195
\(832\) 0.158978 2.59783i 0.00551158 0.0900634i
\(833\) −3.07426 −0.106517
\(834\) 70.0331 + 9.94681i 2.42505 + 0.344430i
\(835\) −11.4013 11.4013i −0.394557 0.394557i
\(836\) 46.0470 + 13.3494i 1.59257 + 0.461699i
\(837\) 14.5945 14.5945i 0.504461 0.504461i
\(838\) 6.48941 + 8.63795i 0.224173 + 0.298393i
\(839\) 7.15578i 0.247045i −0.992342 0.123523i \(-0.960581\pi\)
0.992342 0.123523i \(-0.0394191\pi\)
\(840\) −3.15576 + 7.00522i −0.108884 + 0.241703i
\(841\) 10.4181i 0.359247i
\(842\) 22.8012 17.1298i 0.785783 0.590333i
\(843\) −15.5679 + 15.5679i −0.536188 + 0.536188i
\(844\) −14.8119 26.9064i −0.509848 0.926157i
\(845\) −9.11755 9.11755i −0.313653 0.313653i
\(846\) −10.4598 + 73.6452i −0.359616 + 2.53197i
\(847\) −0.567460 −0.0194982
\(848\) 51.1555 11.4959i 1.75669 0.394771i
\(849\) 56.9010 1.95284
\(850\) −0.611363 + 4.30446i −0.0209696 + 0.147642i
\(851\) 16.4108 + 16.4108i 0.562554 + 0.562554i
\(852\) 6.81488 3.75157i 0.233474 0.128527i
\(853\) −17.4128 + 17.4128i −0.596205 + 0.596205i −0.939300 0.343096i \(-0.888524\pi\)
0.343096 + 0.939300i \(0.388524\pi\)
\(854\) −0.567258 + 0.426162i −0.0194112 + 0.0145830i
\(855\) 30.8638i 1.05552i
\(856\) 15.1938 5.75612i 0.519313 0.196740i
\(857\) 33.3568i 1.13945i −0.821837 0.569723i \(-0.807050\pi\)
0.821837 0.569723i \(-0.192950\pi\)
\(858\) 2.55320 + 3.39852i 0.0871647 + 0.116024i
\(859\) 2.96984 2.96984i 0.101330 0.101330i −0.654624 0.755954i \(-0.727173\pi\)
0.755954 + 0.654624i \(0.227173\pi\)
\(860\) −1.30566 + 4.50371i −0.0445228 + 0.153575i
\(861\) 5.25773 + 5.25773i 0.179183 + 0.179183i
\(862\) 8.23666 + 1.16985i 0.280542 + 0.0398453i
\(863\) 30.1859 1.02754 0.513770 0.857928i \(-0.328249\pi\)
0.513770 + 0.857928i \(0.328249\pi\)
\(864\) 21.1224 1.69268i 0.718598 0.0575862i
\(865\) −12.9161 −0.439160
\(866\) −47.7778 6.78589i −1.62356 0.230594i
\(867\) −14.5000 14.5000i −0.492447 0.492447i
\(868\) −3.06842 + 10.5841i −0.104149 + 0.359247i
\(869\) 19.5039 19.5039i 0.661624 0.661624i
\(870\) −9.94668 13.2399i −0.337224 0.448873i
\(871\) 4.99088i 0.169109i
\(872\) 16.4927 + 43.5340i 0.558513 + 1.47425i
\(873\) 33.3464i 1.12861i
\(874\) −22.7571 + 17.0967i −0.769772 + 0.578304i
\(875\) −0.707107 + 0.707107i −0.0239046 + 0.0239046i
\(876\) −54.9828 + 30.2679i −1.85770 + 1.02266i
\(877\) 17.5002 + 17.5002i 0.590941 + 0.590941i 0.937886 0.346945i \(-0.112781\pi\)
−0.346945 + 0.937886i \(0.612781\pi\)
\(878\) −5.96608 + 42.0057i −0.201345 + 1.41762i
\(879\) −19.5138 −0.658184
\(880\) 7.27649 11.4949i 0.245290 0.387492i
\(881\) 27.1194 0.913677 0.456839 0.889550i \(-0.348982\pi\)
0.456839 + 0.889550i \(0.348982\pi\)
\(882\) −0.870827 + 6.13129i −0.0293223 + 0.206451i
\(883\) −26.3544 26.3544i −0.886897 0.886897i 0.107326 0.994224i \(-0.465771\pi\)
−0.994224 + 0.107326i \(0.965771\pi\)
\(884\) −0.964667 1.75235i −0.0324453 0.0589381i
\(885\) −3.35627 + 3.35627i −0.112820 + 0.112820i
\(886\) −33.6600 + 25.2877i −1.13083 + 0.849557i
\(887\) 34.8464i 1.17003i 0.811024 + 0.585013i \(0.198911\pi\)
−0.811024 + 0.585013i \(0.801089\pi\)
\(888\) 56.9332 + 25.6477i 1.91055 + 0.860680i
\(889\) 16.3150i 0.547187i
\(890\) 9.73542 + 12.9587i 0.326332 + 0.434375i
\(891\) 7.12209 7.12209i 0.238599 0.238599i
\(892\) −2.91647 0.845508i −0.0976505 0.0283097i
\(893\) −59.8624 59.8624i −2.00322 2.00322i
\(894\) −15.7521 2.23727i −0.526829 0.0748256i
\(895\) −14.3616 −0.480056
\(896\) −9.44366 + 6.23035i −0.315491 + 0.208141i
\(897\) −2.52366 −0.0842625
\(898\) 18.2258 + 2.58861i 0.608202 + 0.0863829i
\(899\) −16.7949 16.7949i −0.560141 0.560141i
\(900\) 8.41162 + 2.43860i 0.280387 + 0.0812866i
\(901\) 28.4942 28.4942i 0.949279 0.949279i
\(902\) −7.90805 10.5263i −0.263309 0.350487i
\(903\) 6.36888i 0.211943i
\(904\) 37.0669 + 16.6982i 1.23283 + 0.555374i
\(905\) 12.8114i 0.425865i
\(906\) 32.2199 24.2057i 1.07043 0.804182i
\(907\) 5.34624 5.34624i 0.177519 0.177519i −0.612754 0.790273i \(-0.709938\pi\)
0.790273 + 0.612754i \(0.209938\pi\)
\(908\) −8.98193 16.3160i −0.298076 0.541466i
\(909\) 26.7481 + 26.7481i 0.887178 + 0.887178i
\(910\) 0.0646979 0.455523i 0.00214471 0.0151004i
\(911\) 14.0817 0.466546 0.233273 0.972411i \(-0.425056\pi\)
0.233273 + 0.972411i \(0.425056\pi\)
\(912\) −40.9617 + 64.7083i −1.35638 + 2.14271i
\(913\) −0.0714948 −0.00236613
\(914\) 5.47588 38.5543i 0.181126 1.27526i
\(915\) 0.963658 + 0.963658i 0.0318576 + 0.0318576i
\(916\) −16.1541 + 8.89281i −0.533747 + 0.293827i
\(917\) 1.51297 1.51297i 0.0499626 0.0499626i
\(918\) 13.0208 9.78214i 0.429752 0.322859i
\(919\) 12.1569i 0.401020i 0.979692 + 0.200510i \(0.0642599\pi\)
−0.979692 + 0.200510i \(0.935740\pi\)
\(920\) 2.86145 + 7.55305i 0.0943392 + 0.249017i
\(921\) 94.7581i 3.12239i
\(922\) 3.63258 + 4.83527i 0.119633 + 0.159241i
\(923\) −0.329402 + 0.329402i −0.0108424 + 0.0108424i
\(924\) 5.14498 17.7469i 0.169258 0.583831i
\(925\) 5.74684 + 5.74684i 0.188955 + 0.188955i
\(926\) 41.7547 + 5.93043i 1.37215 + 0.194886i
\(927\) −41.1075 −1.35015
\(928\) −1.94788 24.3069i −0.0639422 0.797913i
\(929\) −38.5694 −1.26542 −0.632711 0.774388i \(-0.718058\pi\)
−0.632711 + 0.774388i \(0.718058\pi\)
\(930\) 20.9568 + 2.97649i 0.687199 + 0.0976029i
\(931\) −4.98381 4.98381i −0.163338 0.163338i
\(932\) −10.0464 + 34.6536i −0.329080 + 1.13512i
\(933\) −35.6232 + 35.6232i −1.16625 + 1.16625i
\(934\) 24.0618 + 32.0282i 0.787325 + 1.04800i
\(935\) 10.4559i 0.341943i
\(936\) −3.76814 + 1.42755i −0.123166 + 0.0466609i
\(937\) 0.399807i 0.0130611i −0.999979 0.00653056i \(-0.997921\pi\)
0.999979 0.00653056i \(-0.00207876\pi\)
\(938\) 17.3455 13.0311i 0.566350 0.425480i
\(939\) 19.9758 19.9758i 0.651885 0.651885i
\(940\) −21.0447 + 11.5851i −0.686402 + 0.377863i
\(941\) 35.2038 + 35.2038i 1.14761 + 1.14761i 0.987021 + 0.160589i \(0.0513394\pi\)
0.160589 + 0.987021i \(0.448661\pi\)
\(942\) 8.70060 61.2589i 0.283481 1.99592i
\(943\) 7.81655 0.254542
\(944\) −6.81923 + 1.53245i −0.221947 + 0.0498770i
\(945\) 3.74592 0.121855
\(946\) 1.58578 11.1651i 0.0515581 0.363008i
\(947\) −16.0232 16.0232i −0.520685 0.520685i 0.397093 0.917778i \(-0.370019\pi\)
−0.917778 + 0.397093i \(0.870019\pi\)
\(948\) 21.2481 + 38.5981i 0.690108 + 1.25361i
\(949\) 2.65764 2.65764i 0.0862705 0.0862705i
\(950\) −7.96925 + 5.98703i −0.258556 + 0.194245i
\(951\) 47.5268i 1.54116i
\(952\) −3.57147 + 7.92800i −0.115752 + 0.256948i
\(953\) 29.2213i 0.946572i 0.880909 + 0.473286i \(0.156932\pi\)
−0.880909 + 0.473286i \(0.843068\pi\)
\(954\) −48.7573 64.9001i −1.57858 2.10122i
\(955\) 15.6023 15.6023i 0.504880 0.504880i
\(956\) −27.0768 7.84979i −0.875726 0.253880i
\(957\) 28.1609 + 28.1609i 0.910313 + 0.910313i
\(958\) −38.6660 5.49173i −1.24924 0.177430i
\(959\) −5.04227 −0.162823
\(960\) 14.3991 + 16.2764i 0.464730 + 0.525318i
\(961\) −0.640466 −0.0206602
\(962\) −3.70215 0.525816i −0.119362 0.0169530i
\(963\) −17.7870 17.7870i −0.573178 0.573178i
\(964\) 21.3028 + 6.17587i 0.686119 + 0.198911i
\(965\) 16.6940 16.6940i 0.537397 0.537397i
\(966\) 6.58922 + 8.77080i 0.212005 + 0.282196i
\(967\) 10.4230i 0.335183i 0.985857 + 0.167591i \(0.0535989\pi\)
−0.985857 + 0.167591i \(0.946401\pi\)
\(968\) −0.659236 + 1.46338i −0.0211887 + 0.0470350i
\(969\) 58.8593i 1.89083i
\(970\) −8.61027 + 6.46861i −0.276459 + 0.207695i
\(971\) −2.97442 + 2.97442i −0.0954537 + 0.0954537i −0.753221 0.657767i \(-0.771501\pi\)
0.657767 + 0.753221i \(0.271501\pi\)
\(972\) 18.5979 + 33.7838i 0.596528 + 1.08362i
\(973\) 13.0200 + 13.0200i 0.417403 + 0.417403i
\(974\) 5.28214 37.1903i 0.169251 1.19165i
\(975\) −0.883751 −0.0283027
\(976\) 0.440000 + 1.95795i 0.0140840 + 0.0626724i
\(977\) −12.4194 −0.397331 −0.198666 0.980067i \(-0.563661\pi\)
−0.198666 + 0.980067i \(0.563661\pi\)
\(978\) −5.03313 + 35.4370i −0.160942 + 1.13315i
\(979\) −27.5628 27.5628i −0.880911 0.880911i
\(980\) −1.75206 + 0.964507i −0.0559676 + 0.0308100i
\(981\) 50.9641 50.9641i 1.62716 1.62716i
\(982\) 2.71277 2.03802i 0.0865680 0.0650357i
\(983\) 44.7477i 1.42723i 0.700538 + 0.713615i \(0.252943\pi\)
−0.700538 + 0.713615i \(0.747057\pi\)
\(984\) 19.6669 7.45073i 0.626957 0.237521i
\(985\) 1.89440i 0.0603607i
\(986\) −11.2569 14.9839i −0.358494 0.477185i
\(987\) −23.0715 + 23.0715i −0.734374 + 0.734374i
\(988\) 1.27695 4.40468i 0.0406253 0.140131i
\(989\) 4.73424 + 4.73424i 0.150540 + 0.150540i
\(990\) −20.8531 2.96177i −0.662755 0.0941312i
\(991\) −16.8014 −0.533714 −0.266857 0.963736i \(-0.585985\pi\)
−0.266857 + 0.963736i \(0.585985\pi\)
\(992\) 23.7299 + 20.2088i 0.753426 + 0.641630i
\(993\) −67.9064 −2.15494
\(994\) 2.00488 + 0.284753i 0.0635909 + 0.00903182i
\(995\) −12.6925 12.6925i −0.402381 0.402381i
\(996\) 0.0317995 0.109688i 0.00100761 0.00347560i
\(997\) −8.71750 + 8.71750i −0.276086 + 0.276086i −0.831544 0.555458i \(-0.812543\pi\)
0.555458 + 0.831544i \(0.312543\pi\)
\(998\) 21.6771 + 28.8541i 0.686177 + 0.913360i
\(999\) 30.4440i 0.963206i
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 560.2.bd.a.141.2 44
4.3 odd 2 2240.2.bd.a.1681.3 44
16.5 even 4 inner 560.2.bd.a.421.2 yes 44
16.11 odd 4 2240.2.bd.a.561.3 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
560.2.bd.a.141.2 44 1.1 even 1 trivial
560.2.bd.a.421.2 yes 44 16.5 even 4 inner
2240.2.bd.a.561.3 44 16.11 odd 4
2240.2.bd.a.1681.3 44 4.3 odd 2