Properties

Label 370.2.g.d.327.3
Level $370$
Weight $2$
Character 370.327
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
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] = [370,2,Mod(43,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 3x^{8} - 8x^{7} - 26x^{6} + 12x^{5} + 24x^{4} + 166x^{3} + 113x^{2} - 152x + 160 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 327.3
Root \(-0.551861 + 1.73844i\) of defining polynomial
Character \(\chi\) \(=\) 370.327
Dual form 370.2.g.d.43.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.215231 + 0.215231i) q^{3} -1.00000 q^{4} +(0.336630 - 2.21058i) q^{5} +(-0.215231 + 0.215231i) q^{6} +(-0.673260 - 0.673260i) q^{7} -1.00000i q^{8} -2.90735i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.215231 + 0.215231i) q^{3} -1.00000 q^{4} +(0.336630 - 2.21058i) q^{5} +(-0.215231 + 0.215231i) q^{6} +(-0.673260 - 0.673260i) q^{7} -1.00000i q^{8} -2.90735i q^{9} +(2.21058 + 0.336630i) q^{10} -1.69991i q^{11} +(-0.215231 - 0.215231i) q^{12} -2.06054i q^{13} +(0.673260 - 0.673260i) q^{14} +(0.548239 - 0.403333i) q^{15} +1.00000 q^{16} +2.58061 q^{17} +2.90735 q^{18} +(-0.312630 - 0.312630i) q^{19} +(-0.336630 + 2.21058i) q^{20} -0.289813i q^{21} +1.69991 q^{22} +3.40706i q^{23} +(0.215231 - 0.215231i) q^{24} +(-4.77336 - 1.48830i) q^{25} +2.06054 q^{26} +(1.27145 - 1.27145i) q^{27} +(0.673260 + 0.673260i) q^{28} +(2.85460 - 2.85460i) q^{29} +(0.403333 + 0.548239i) q^{30} +(-0.382954 - 0.382954i) q^{31} +1.00000i q^{32} +(0.365873 - 0.365873i) q^{33} +2.58061i q^{34} +(-1.71494 + 1.26166i) q^{35} +2.90735i q^{36} +(5.90735 + 1.45024i) q^{37} +(0.312630 - 0.312630i) q^{38} +(0.443492 - 0.443492i) q^{39} +(-2.21058 - 0.336630i) q^{40} +3.11626i q^{41} +0.289813 q^{42} +7.38424i q^{43} +1.69991i q^{44} +(-6.42694 - 0.978702i) q^{45} -3.40706 q^{46} +(1.26620 + 1.26620i) q^{47} +(0.215231 + 0.215231i) q^{48} -6.09344i q^{49} +(1.48830 - 4.77336i) q^{50} +(0.555428 + 0.555428i) q^{51} +2.06054i q^{52} +(-2.69991 + 2.69991i) q^{53} +(1.27145 + 1.27145i) q^{54} +(-3.75779 - 0.572240i) q^{55} +(-0.673260 + 0.673260i) q^{56} -0.134575i q^{57} +(2.85460 + 2.85460i) q^{58} +(3.61030 + 3.61030i) q^{59} +(-0.548239 + 0.403333i) q^{60} +(-4.54721 - 4.54721i) q^{61} +(0.382954 - 0.382954i) q^{62} +(-1.95740 + 1.95740i) q^{63} -1.00000 q^{64} +(-4.55499 - 0.693639i) q^{65} +(0.365873 + 0.365873i) q^{66} +(8.19766 - 8.19766i) q^{67} -2.58061 q^{68} +(-0.733305 + 0.733305i) q^{69} +(-1.26166 - 1.71494i) q^{70} -8.12107 q^{71} -2.90735 q^{72} +(3.81038 + 3.81038i) q^{73} +(-1.45024 + 5.90735i) q^{74} +(-0.707048 - 1.34770i) q^{75} +(0.312630 + 0.312630i) q^{76} +(-1.14448 + 1.14448i) q^{77} +(0.443492 + 0.443492i) q^{78} +(-3.33149 - 3.33149i) q^{79} +(0.336630 - 2.21058i) q^{80} -8.17474 q^{81} -3.11626 q^{82} +(-6.48170 + 6.48170i) q^{83} +0.289813i q^{84} +(0.868711 - 5.70466i) q^{85} -7.38424 q^{86} +1.22880 q^{87} -1.69991 q^{88} +(-0.486184 + 0.486184i) q^{89} +(0.978702 - 6.42694i) q^{90} +(-1.38728 + 1.38728i) q^{91} -3.40706i q^{92} -0.164847i q^{93} +(-1.26620 + 1.26620i) q^{94} +(-0.796335 + 0.585854i) q^{95} +(-0.215231 + 0.215231i) q^{96} +0.430462 q^{97} +6.09344 q^{98} -4.94223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{3} - 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{3} - 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 2 q^{10} + 2 q^{12} + 4 q^{14} - 6 q^{15} + 10 q^{16} - 24 q^{17} - 18 q^{18} - 8 q^{19} - 2 q^{20} - 8 q^{22} - 2 q^{24} - 28 q^{25} - 12 q^{26} + 28 q^{27} + 4 q^{28} + 32 q^{29} + 14 q^{30} - 26 q^{31} - 24 q^{33} - 22 q^{35} + 12 q^{37} + 8 q^{38} - 6 q^{39} - 2 q^{40} - 40 q^{42} + 4 q^{45} + 4 q^{46} + 48 q^{47} - 2 q^{48} + 16 q^{51} - 2 q^{53} + 28 q^{54} + 18 q^{55} - 4 q^{56} + 32 q^{58} + 20 q^{59} + 6 q^{60} - 24 q^{61} + 26 q^{62} + 20 q^{63} - 10 q^{64} - 28 q^{65} - 24 q^{66} + 10 q^{67} + 24 q^{68} + 46 q^{69} + 22 q^{70} - 16 q^{71} + 18 q^{72} - 4 q^{73} + 2 q^{74} - 48 q^{75} + 8 q^{76} + 24 q^{77} - 6 q^{78} + 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} + 10 q^{85} + 12 q^{86} + 8 q^{88} + 2 q^{89} - 10 q^{90} + 16 q^{91} - 48 q^{94} + 28 q^{95} + 2 q^{96} - 4 q^{97} - 18 q^{98} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.215231 + 0.215231i 0.124264 + 0.124264i 0.766504 0.642240i \(-0.221995\pi\)
−0.642240 + 0.766504i \(0.721995\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0.336630 2.21058i 0.150546 0.988603i
\(6\) −0.215231 + 0.215231i −0.0878677 + 0.0878677i
\(7\) −0.673260 0.673260i −0.254468 0.254468i 0.568331 0.822800i \(-0.307589\pi\)
−0.822800 + 0.568331i \(0.807589\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.90735i 0.969117i
\(10\) 2.21058 + 0.336630i 0.699048 + 0.106452i
\(11\) 1.69991i 0.512541i −0.966605 0.256271i \(-0.917506\pi\)
0.966605 0.256271i \(-0.0824938\pi\)
\(12\) −0.215231 0.215231i −0.0621319 0.0621319i
\(13\) 2.06054i 0.571490i −0.958306 0.285745i \(-0.907759\pi\)
0.958306 0.285745i \(-0.0922411\pi\)
\(14\) 0.673260 0.673260i 0.179936 0.179936i
\(15\) 0.548239 0.403333i 0.141555 0.104140i
\(16\) 1.00000 0.250000
\(17\) 2.58061 0.625890 0.312945 0.949771i \(-0.398684\pi\)
0.312945 + 0.949771i \(0.398684\pi\)
\(18\) 2.90735 0.685269
\(19\) −0.312630 0.312630i −0.0717222 0.0717222i 0.670336 0.742058i \(-0.266150\pi\)
−0.742058 + 0.670336i \(0.766150\pi\)
\(20\) −0.336630 + 2.21058i −0.0752728 + 0.494302i
\(21\) 0.289813i 0.0632424i
\(22\) 1.69991 0.362421
\(23\) 3.40706i 0.710421i 0.934786 + 0.355210i \(0.115591\pi\)
−0.934786 + 0.355210i \(0.884409\pi\)
\(24\) 0.215231 0.215231i 0.0439339 0.0439339i
\(25\) −4.77336 1.48830i −0.954672 0.297660i
\(26\) 2.06054 0.404105
\(27\) 1.27145 1.27145i 0.244690 0.244690i
\(28\) 0.673260 + 0.673260i 0.127234 + 0.127234i
\(29\) 2.85460 2.85460i 0.530086 0.530086i −0.390512 0.920598i \(-0.627702\pi\)
0.920598 + 0.390512i \(0.127702\pi\)
\(30\) 0.403333 + 0.548239i 0.0736382 + 0.100094i
\(31\) −0.382954 0.382954i −0.0687806 0.0687806i 0.671880 0.740660i \(-0.265487\pi\)
−0.740660 + 0.671880i \(0.765487\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.365873 0.365873i 0.0636903 0.0636903i
\(34\) 2.58061i 0.442571i
\(35\) −1.71494 + 1.26166i −0.289877 + 0.213259i
\(36\) 2.90735i 0.484559i
\(37\) 5.90735 + 1.45024i 0.971163 + 0.238418i
\(38\) 0.312630 0.312630i 0.0507152 0.0507152i
\(39\) 0.443492 0.443492i 0.0710155 0.0710155i
\(40\) −2.21058 0.336630i −0.349524 0.0532259i
\(41\) 3.11626i 0.486678i 0.969941 + 0.243339i \(0.0782427\pi\)
−0.969941 + 0.243339i \(0.921757\pi\)
\(42\) 0.289813 0.0447191
\(43\) 7.38424i 1.12609i 0.826428 + 0.563043i \(0.190369\pi\)
−0.826428 + 0.563043i \(0.809631\pi\)
\(44\) 1.69991i 0.256271i
\(45\) −6.42694 0.978702i −0.958072 0.145896i
\(46\) −3.40706 −0.502343
\(47\) 1.26620 + 1.26620i 0.184695 + 0.184695i 0.793398 0.608703i \(-0.208310\pi\)
−0.608703 + 0.793398i \(0.708310\pi\)
\(48\) 0.215231 + 0.215231i 0.0310659 + 0.0310659i
\(49\) 6.09344i 0.870492i
\(50\) 1.48830 4.77336i 0.210477 0.675055i
\(51\) 0.555428 + 0.555428i 0.0777754 + 0.0777754i
\(52\) 2.06054i 0.285745i
\(53\) −2.69991 + 2.69991i −0.370861 + 0.370861i −0.867791 0.496930i \(-0.834461\pi\)
0.496930 + 0.867791i \(0.334461\pi\)
\(54\) 1.27145 + 1.27145i 0.173022 + 0.173022i
\(55\) −3.75779 0.572240i −0.506700 0.0771608i
\(56\) −0.673260 + 0.673260i −0.0899681 + 0.0899681i
\(57\) 0.134575i 0.0178249i
\(58\) 2.85460 + 2.85460i 0.374827 + 0.374827i
\(59\) 3.61030 + 3.61030i 0.470020 + 0.470020i 0.901921 0.431901i \(-0.142157\pi\)
−0.431901 + 0.901921i \(0.642157\pi\)
\(60\) −0.548239 + 0.403333i −0.0707774 + 0.0520701i
\(61\) −4.54721 4.54721i −0.582211 0.582211i 0.353299 0.935510i \(-0.385060\pi\)
−0.935510 + 0.353299i \(0.885060\pi\)
\(62\) 0.382954 0.382954i 0.0486353 0.0486353i
\(63\) −1.95740 + 1.95740i −0.246610 + 0.246610i
\(64\) −1.00000 −0.125000
\(65\) −4.55499 0.693639i −0.564977 0.0860353i
\(66\) 0.365873 + 0.365873i 0.0450358 + 0.0450358i
\(67\) 8.19766 8.19766i 1.00150 1.00150i 0.00150430 0.999999i \(-0.499521\pi\)
0.999999 0.00150430i \(-0.000478835\pi\)
\(68\) −2.58061 −0.312945
\(69\) −0.733305 + 0.733305i −0.0882795 + 0.0882795i
\(70\) −1.26166 1.71494i −0.150797 0.204974i
\(71\) −8.12107 −0.963794 −0.481897 0.876228i \(-0.660052\pi\)
−0.481897 + 0.876228i \(0.660052\pi\)
\(72\) −2.90735 −0.342635
\(73\) 3.81038 + 3.81038i 0.445971 + 0.445971i 0.894013 0.448042i \(-0.147878\pi\)
−0.448042 + 0.894013i \(0.647878\pi\)
\(74\) −1.45024 + 5.90735i −0.168587 + 0.686716i
\(75\) −0.707048 1.34770i −0.0816428 0.155619i
\(76\) 0.312630 + 0.312630i 0.0358611 + 0.0358611i
\(77\) −1.14448 + 1.14448i −0.130426 + 0.130426i
\(78\) 0.443492 + 0.443492i 0.0502155 + 0.0502155i
\(79\) −3.33149 3.33149i −0.374822 0.374822i 0.494408 0.869230i \(-0.335385\pi\)
−0.869230 + 0.494408i \(0.835385\pi\)
\(80\) 0.336630 2.21058i 0.0376364 0.247151i
\(81\) −8.17474 −0.908305
\(82\) −3.11626 −0.344133
\(83\) −6.48170 + 6.48170i −0.711460 + 0.711460i −0.966840 0.255381i \(-0.917799\pi\)
0.255381 + 0.966840i \(0.417799\pi\)
\(84\) 0.289813i 0.0316212i
\(85\) 0.868711 5.70466i 0.0942249 0.618757i
\(86\) −7.38424 −0.796263
\(87\) 1.22880 0.131741
\(88\) −1.69991 −0.181211
\(89\) −0.486184 + 0.486184i −0.0515354 + 0.0515354i −0.732405 0.680869i \(-0.761602\pi\)
0.680869 + 0.732405i \(0.261602\pi\)
\(90\) 0.978702 6.42694i 0.103164 0.677459i
\(91\) −1.38728 + 1.38728i −0.145426 + 0.145426i
\(92\) 3.40706i 0.355210i
\(93\) 0.164847i 0.0170939i
\(94\) −1.26620 + 1.26620i −0.130599 + 0.130599i
\(95\) −0.796335 + 0.585854i −0.0817022 + 0.0601073i
\(96\) −0.215231 + 0.215231i −0.0219669 + 0.0219669i
\(97\) 0.430462 0.0437068 0.0218534 0.999761i \(-0.493043\pi\)
0.0218534 + 0.999761i \(0.493043\pi\)
\(98\) 6.09344 0.615531
\(99\) −4.94223 −0.496712
\(100\) 4.77336 + 1.48830i 0.477336 + 0.148830i
\(101\) 2.72028i 0.270677i 0.990799 + 0.135339i \(0.0432123\pi\)
−0.990799 + 0.135339i \(0.956788\pi\)
\(102\) −0.555428 + 0.555428i −0.0549955 + 0.0549955i
\(103\) 13.5156 1.33173 0.665866 0.746072i \(-0.268062\pi\)
0.665866 + 0.746072i \(0.268062\pi\)
\(104\) −2.06054 −0.202052
\(105\) −0.640656 0.0975597i −0.0625216 0.00952085i
\(106\) −2.69991 2.69991i −0.262238 0.262238i
\(107\) 12.0332 + 12.0332i 1.16329 + 1.16329i 0.983751 + 0.179540i \(0.0574611\pi\)
0.179540 + 0.983751i \(0.442539\pi\)
\(108\) −1.27145 + 1.27145i −0.122345 + 0.122345i
\(109\) −12.8690 12.8690i −1.23262 1.23262i −0.962952 0.269673i \(-0.913084\pi\)
−0.269673 0.962952i \(-0.586916\pi\)
\(110\) 0.572240 3.75779i 0.0545609 0.358291i
\(111\) 0.959308 + 1.58358i 0.0910535 + 0.150307i
\(112\) −0.673260 0.673260i −0.0636171 0.0636171i
\(113\) −4.08335 −0.384130 −0.192065 0.981382i \(-0.561518\pi\)
−0.192065 + 0.981382i \(0.561518\pi\)
\(114\) 0.134575 0.0126041
\(115\) 7.53158 + 1.14692i 0.702324 + 0.106951i
\(116\) −2.85460 + 2.85460i −0.265043 + 0.265043i
\(117\) −5.99071 −0.553841
\(118\) −3.61030 + 3.61030i −0.332355 + 0.332355i
\(119\) −1.73742 1.73742i −0.159269 0.159269i
\(120\) −0.403333 0.548239i −0.0368191 0.0500472i
\(121\) 8.11032 0.737301
\(122\) 4.54721 4.54721i 0.411685 0.411685i
\(123\) −0.670716 + 0.670716i −0.0604764 + 0.0604764i
\(124\) 0.382954 + 0.382954i 0.0343903 + 0.0343903i
\(125\) −4.89686 + 10.0509i −0.437989 + 0.898980i
\(126\) −1.95740 1.95740i −0.174379 0.174379i
\(127\) −2.18226 2.18226i −0.193644 0.193644i 0.603624 0.797269i \(-0.293723\pi\)
−0.797269 + 0.603624i \(0.793723\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.58932 + 1.58932i −0.139932 + 0.139932i
\(130\) 0.693639 4.55499i 0.0608361 0.399499i
\(131\) 13.2125 + 13.2125i 1.15438 + 1.15438i 0.985665 + 0.168713i \(0.0539612\pi\)
0.168713 + 0.985665i \(0.446039\pi\)
\(132\) −0.365873 + 0.365873i −0.0318451 + 0.0318451i
\(133\) 0.420962i 0.0365021i
\(134\) 8.19766 + 8.19766i 0.708170 + 0.708170i
\(135\) −2.38263 3.23864i −0.205064 0.278738i
\(136\) 2.58061i 0.221286i
\(137\) 8.89131 + 8.89131i 0.759636 + 0.759636i 0.976256 0.216620i \(-0.0695034\pi\)
−0.216620 + 0.976256i \(0.569503\pi\)
\(138\) −0.733305 0.733305i −0.0624230 0.0624230i
\(139\) −5.78423 −0.490612 −0.245306 0.969446i \(-0.578888\pi\)
−0.245306 + 0.969446i \(0.578888\pi\)
\(140\) 1.71494 1.26166i 0.144939 0.106630i
\(141\) 0.545052i 0.0459017i
\(142\) 8.12107i 0.681505i
\(143\) −3.50272 −0.292912
\(144\) 2.90735i 0.242279i
\(145\) −5.34939 7.27128i −0.444243 0.603847i
\(146\) −3.81038 + 3.81038i −0.315349 + 0.315349i
\(147\) 1.31150 1.31150i 0.108171 0.108171i
\(148\) −5.90735 1.45024i −0.485581 0.119209i
\(149\) 8.17437i 0.669670i 0.942277 + 0.334835i \(0.108681\pi\)
−0.942277 + 0.334835i \(0.891319\pi\)
\(150\) 1.34770 0.707048i 0.110040 0.0577302i
\(151\) 11.8313i 0.962814i 0.876497 + 0.481407i \(0.159874\pi\)
−0.876497 + 0.481407i \(0.840126\pi\)
\(152\) −0.312630 + 0.312630i −0.0253576 + 0.0253576i
\(153\) 7.50274i 0.606561i
\(154\) −1.14448 1.14448i −0.0922248 0.0922248i
\(155\) −0.975467 + 0.717639i −0.0783514 + 0.0576421i
\(156\) −0.443492 + 0.443492i −0.0355077 + 0.0355077i
\(157\) −2.88552 2.88552i −0.230290 0.230290i 0.582524 0.812814i \(-0.302065\pi\)
−0.812814 + 0.582524i \(0.802065\pi\)
\(158\) 3.33149 3.33149i 0.265039 0.265039i
\(159\) −1.16221 −0.0921691
\(160\) 2.21058 + 0.336630i 0.174762 + 0.0266129i
\(161\) 2.29384 2.29384i 0.180780 0.180780i
\(162\) 8.17474i 0.642269i
\(163\) 11.0884 0.868507 0.434253 0.900791i \(-0.357012\pi\)
0.434253 + 0.900791i \(0.357012\pi\)
\(164\) 3.11626i 0.243339i
\(165\) −0.685629 0.931956i −0.0533761 0.0725527i
\(166\) −6.48170 6.48170i −0.503078 0.503078i
\(167\) 7.75419 0.600037 0.300018 0.953933i \(-0.403007\pi\)
0.300018 + 0.953933i \(0.403007\pi\)
\(168\) −0.289813 −0.0223596
\(169\) 8.75419 0.673399
\(170\) 5.70466 + 0.868711i 0.437527 + 0.0666271i
\(171\) −0.908925 + 0.908925i −0.0695072 + 0.0695072i
\(172\) 7.38424i 0.563043i
\(173\) 1.45954 + 1.45954i 0.110967 + 0.110967i 0.760410 0.649443i \(-0.224998\pi\)
−0.649443 + 0.760410i \(0.724998\pi\)
\(174\) 1.22880i 0.0931549i
\(175\) 2.21170 + 4.21572i 0.167189 + 0.318679i
\(176\) 1.69991i 0.128135i
\(177\) 1.55410i 0.116813i
\(178\) −0.486184 0.486184i −0.0364410 0.0364410i
\(179\) 4.31587 4.31587i 0.322583 0.322583i −0.527174 0.849757i \(-0.676748\pi\)
0.849757 + 0.527174i \(0.176748\pi\)
\(180\) 6.42694 + 0.978702i 0.479036 + 0.0729481i
\(181\) 11.8012 0.877176 0.438588 0.898688i \(-0.355479\pi\)
0.438588 + 0.898688i \(0.355479\pi\)
\(182\) −1.38728 1.38728i −0.102832 0.102832i
\(183\) 1.95740i 0.144695i
\(184\) 3.40706 0.251172
\(185\) 5.19447 12.5705i 0.381905 0.924201i
\(186\) 0.164847 0.0120872
\(187\) 4.38680i 0.320795i
\(188\) −1.26620 1.26620i −0.0923473 0.0923473i
\(189\) −1.71203 −0.124532
\(190\) −0.585854 0.796335i −0.0425023 0.0577722i
\(191\) −0.707267 + 0.707267i −0.0511760 + 0.0511760i −0.732232 0.681056i \(-0.761521\pi\)
0.681056 + 0.732232i \(0.261521\pi\)
\(192\) −0.215231 0.215231i −0.0155330 0.0155330i
\(193\) 8.39923i 0.604590i −0.953214 0.302295i \(-0.902247\pi\)
0.953214 0.302295i \(-0.0977527\pi\)
\(194\) 0.430462i 0.0309054i
\(195\) −0.831083 1.12967i −0.0595151 0.0808972i
\(196\) 6.09344i 0.435246i
\(197\) 15.0419 + 15.0419i 1.07169 + 1.07169i 0.997223 + 0.0744696i \(0.0237264\pi\)
0.0744696 + 0.997223i \(0.476274\pi\)
\(198\) 4.94223i 0.351229i
\(199\) −1.52878 + 1.52878i −0.108372 + 0.108372i −0.759214 0.650841i \(-0.774416\pi\)
0.650841 + 0.759214i \(0.274416\pi\)
\(200\) −1.48830 + 4.77336i −0.105239 + 0.337528i
\(201\) 3.52878 0.248901
\(202\) −2.72028 −0.191398
\(203\) −3.84378 −0.269780
\(204\) −0.555428 0.555428i −0.0388877 0.0388877i
\(205\) 6.88875 + 1.04903i 0.481131 + 0.0732672i
\(206\) 13.5156i 0.941676i
\(207\) 9.90551 0.688481
\(208\) 2.06054i 0.142873i
\(209\) −0.531442 + 0.531442i −0.0367606 + 0.0367606i
\(210\) 0.0975597 0.640656i 0.00673226 0.0442094i
\(211\) 24.1444 1.66217 0.831085 0.556146i \(-0.187720\pi\)
0.831085 + 0.556146i \(0.187720\pi\)
\(212\) 2.69991 2.69991i 0.185430 0.185430i
\(213\) −1.74791 1.74791i −0.119765 0.119765i
\(214\) −12.0332 + 12.0332i −0.822571 + 0.822571i
\(215\) 16.3235 + 2.48576i 1.11325 + 0.169527i
\(216\) −1.27145 1.27145i −0.0865109 0.0865109i
\(217\) 0.515656i 0.0350050i
\(218\) 12.8690 12.8690i 0.871597 0.871597i
\(219\) 1.64022i 0.110836i
\(220\) 3.75779 + 0.572240i 0.253350 + 0.0385804i
\(221\) 5.31745i 0.357690i
\(222\) −1.58358 + 0.959308i −0.106283 + 0.0643846i
\(223\) −10.0159 + 10.0159i −0.670714 + 0.670714i −0.957881 0.287167i \(-0.907287\pi\)
0.287167 + 0.957881i \(0.407287\pi\)
\(224\) 0.673260 0.673260i 0.0449841 0.0449841i
\(225\) −4.32700 + 13.8778i −0.288467 + 0.925189i
\(226\) 4.08335i 0.271621i
\(227\) −3.05788 −0.202959 −0.101479 0.994838i \(-0.532358\pi\)
−0.101479 + 0.994838i \(0.532358\pi\)
\(228\) 0.134575i 0.00891247i
\(229\) 26.8791i 1.77622i −0.459632 0.888109i \(-0.652019\pi\)
0.459632 0.888109i \(-0.347981\pi\)
\(230\) −1.14692 + 7.53158i −0.0756255 + 0.496618i
\(231\) −0.492655 −0.0324143
\(232\) −2.85460 2.85460i −0.187414 0.187414i
\(233\) −0.315711 0.315711i −0.0206829 0.0206829i 0.696690 0.717373i \(-0.254655\pi\)
−0.717373 + 0.696690i \(0.754655\pi\)
\(234\) 5.99071i 0.391625i
\(235\) 3.22529 2.37281i 0.210395 0.154785i
\(236\) −3.61030 3.61030i −0.235010 0.235010i
\(237\) 1.43408i 0.0931535i
\(238\) 1.73742 1.73742i 0.112620 0.112620i
\(239\) 7.59846 + 7.59846i 0.491503 + 0.491503i 0.908780 0.417276i \(-0.137015\pi\)
−0.417276 + 0.908780i \(0.637015\pi\)
\(240\) 0.548239 0.403333i 0.0353887 0.0260350i
\(241\) 3.57132 3.57132i 0.230049 0.230049i −0.582664 0.812713i \(-0.697990\pi\)
0.812713 + 0.582664i \(0.197990\pi\)
\(242\) 8.11032i 0.521351i
\(243\) −5.57380 5.57380i −0.357559 0.357559i
\(244\) 4.54721 + 4.54721i 0.291106 + 0.291106i
\(245\) −13.4701 2.05124i −0.860571 0.131049i
\(246\) −0.670716 0.670716i −0.0427633 0.0427633i
\(247\) −0.644185 + 0.644185i −0.0409885 + 0.0409885i
\(248\) −0.382954 + 0.382954i −0.0243176 + 0.0243176i
\(249\) −2.79013 −0.176817
\(250\) −10.0509 4.89686i −0.635675 0.309705i
\(251\) 19.0270 + 19.0270i 1.20097 + 1.20097i 0.973872 + 0.227100i \(0.0729243\pi\)
0.227100 + 0.973872i \(0.427076\pi\)
\(252\) 1.95740 1.95740i 0.123305 0.123305i
\(253\) 5.79168 0.364120
\(254\) 2.18226 2.18226i 0.136927 0.136927i
\(255\) 1.41479 1.04085i 0.0885978 0.0651803i
\(256\) 1.00000 0.0625000
\(257\) −24.5612 −1.53208 −0.766042 0.642791i \(-0.777776\pi\)
−0.766042 + 0.642791i \(0.777776\pi\)
\(258\) −1.58932 1.58932i −0.0989466 0.0989466i
\(259\) −3.00079 4.95357i −0.186460 0.307800i
\(260\) 4.55499 + 0.693639i 0.282488 + 0.0430176i
\(261\) −8.29933 8.29933i −0.513715 0.513715i
\(262\) −13.2125 + 13.2125i −0.816269 + 0.816269i
\(263\) −15.9933 15.9933i −0.986188 0.986188i 0.0137182 0.999906i \(-0.495633\pi\)
−0.999906 + 0.0137182i \(0.995633\pi\)
\(264\) −0.365873 0.365873i −0.0225179 0.0225179i
\(265\) 5.05950 + 6.87724i 0.310803 + 0.422466i
\(266\) −0.420962 −0.0258109
\(267\) −0.209284 −0.0128080
\(268\) −8.19766 + 8.19766i −0.500752 + 0.500752i
\(269\) 8.06679i 0.491841i −0.969290 0.245921i \(-0.920910\pi\)
0.969290 0.245921i \(-0.0790902\pi\)
\(270\) 3.23864 2.38263i 0.197098 0.145002i
\(271\) −24.2256 −1.47160 −0.735800 0.677199i \(-0.763194\pi\)
−0.735800 + 0.677199i \(0.763194\pi\)
\(272\) 2.58061 0.156473
\(273\) −0.597170 −0.0361424
\(274\) −8.89131 + 8.89131i −0.537143 + 0.537143i
\(275\) −2.52997 + 8.11427i −0.152563 + 0.489309i
\(276\) 0.733305 0.733305i 0.0441397 0.0441397i
\(277\) 18.8030i 1.12976i −0.825173 0.564881i \(-0.808922\pi\)
0.825173 0.564881i \(-0.191078\pi\)
\(278\) 5.78423i 0.346915i
\(279\) −1.11338 + 1.11338i −0.0666565 + 0.0666565i
\(280\) 1.26166 + 1.71494i 0.0753985 + 0.102487i
\(281\) 14.2311 14.2311i 0.848954 0.848954i −0.141049 0.990003i \(-0.545048\pi\)
0.990003 + 0.141049i \(0.0450475\pi\)
\(282\) −0.545052 −0.0324574
\(283\) −0.905573 −0.0538307 −0.0269154 0.999638i \(-0.508568\pi\)
−0.0269154 + 0.999638i \(0.508568\pi\)
\(284\) 8.12107 0.481897
\(285\) −0.297490 0.0453021i −0.0176218 0.00268346i
\(286\) 3.50272i 0.207120i
\(287\) 2.09805 2.09805i 0.123844 0.123844i
\(288\) 2.90735 0.171317
\(289\) −10.3404 −0.608262
\(290\) 7.27128 5.34939i 0.426984 0.314127i
\(291\) 0.0926488 + 0.0926488i 0.00543117 + 0.00543117i
\(292\) −3.81038 3.81038i −0.222986 0.222986i
\(293\) −14.1364 + 14.1364i −0.825855 + 0.825855i −0.986940 0.161086i \(-0.948500\pi\)
0.161086 + 0.986940i \(0.448500\pi\)
\(294\) 1.31150 + 1.31150i 0.0764881 + 0.0764881i
\(295\) 9.19619 6.76553i 0.535423 0.393904i
\(296\) 1.45024 5.90735i 0.0842936 0.343358i
\(297\) −2.16134 2.16134i −0.125414 0.125414i
\(298\) −8.17437 −0.473528
\(299\) 7.02037 0.405998
\(300\) 0.707048 + 1.34770i 0.0408214 + 0.0778097i
\(301\) 4.97151 4.97151i 0.286553 0.286553i
\(302\) −11.8313 −0.680813
\(303\) −0.585488 + 0.585488i −0.0336354 + 0.0336354i
\(304\) −0.312630 0.312630i −0.0179305 0.0179305i
\(305\) −11.5827 + 8.52127i −0.663225 + 0.487926i
\(306\) 7.50274 0.428903
\(307\) −22.5470 + 22.5470i −1.28682 + 1.28682i −0.350120 + 0.936705i \(0.613859\pi\)
−0.936705 + 0.350120i \(0.886141\pi\)
\(308\) 1.14448 1.14448i 0.0652128 0.0652128i
\(309\) 2.90898 + 2.90898i 0.165486 + 0.165486i
\(310\) −0.717639 0.975467i −0.0407591 0.0554028i
\(311\) −18.8440 18.8440i −1.06855 1.06855i −0.997471 0.0710771i \(-0.977356\pi\)
−0.0710771 0.997471i \(-0.522644\pi\)
\(312\) −0.443492 0.443492i −0.0251078 0.0251078i
\(313\) 13.8468i 0.782669i 0.920248 + 0.391335i \(0.127987\pi\)
−0.920248 + 0.391335i \(0.872013\pi\)
\(314\) 2.88552 2.88552i 0.162839 0.162839i
\(315\) 3.66808 + 4.98592i 0.206673 + 0.280925i
\(316\) 3.33149 + 3.33149i 0.187411 + 0.187411i
\(317\) −9.84958 + 9.84958i −0.553207 + 0.553207i −0.927365 0.374158i \(-0.877932\pi\)
0.374158 + 0.927365i \(0.377932\pi\)
\(318\) 1.16221i 0.0651734i
\(319\) −4.85256 4.85256i −0.271691 0.271691i
\(320\) −0.336630 + 2.21058i −0.0188182 + 0.123575i
\(321\) 5.17983i 0.289110i
\(322\) 2.29384 + 2.29384i 0.127830 + 0.127830i
\(323\) −0.806776 0.806776i −0.0448902 0.0448902i
\(324\) 8.17474 0.454152
\(325\) −3.06669 + 9.83569i −0.170109 + 0.545586i
\(326\) 11.0884i 0.614127i
\(327\) 5.53961i 0.306341i
\(328\) 3.11626 0.172067
\(329\) 1.70497i 0.0939979i
\(330\) 0.931956 0.685629i 0.0513025 0.0377426i
\(331\) −11.7035 + 11.7035i −0.643281 + 0.643281i −0.951360 0.308080i \(-0.900314\pi\)
0.308080 + 0.951360i \(0.400314\pi\)
\(332\) 6.48170 6.48170i 0.355730 0.355730i
\(333\) 4.21636 17.1747i 0.231055 0.941170i
\(334\) 7.75419i 0.424290i
\(335\) −15.3620 20.8812i −0.839317 1.14086i
\(336\) 0.289813i 0.0158106i
\(337\) −2.42851 + 2.42851i −0.132289 + 0.132289i −0.770151 0.637862i \(-0.779819\pi\)
0.637862 + 0.770151i \(0.279819\pi\)
\(338\) 8.75419i 0.476165i
\(339\) −0.878865 0.878865i −0.0477334 0.0477334i
\(340\) −0.868711 + 5.70466i −0.0471125 + 0.309378i
\(341\) −0.650987 + 0.650987i −0.0352529 + 0.0352529i
\(342\) −0.908925 0.908925i −0.0491490 0.0491490i
\(343\) −8.81529 + 8.81529i −0.475981 + 0.475981i
\(344\) 7.38424 0.398132
\(345\) 1.37418 + 1.86788i 0.0739833 + 0.100563i
\(346\) −1.45954 + 1.45954i −0.0784652 + 0.0784652i
\(347\) 6.68904i 0.359086i −0.983750 0.179543i \(-0.942538\pi\)
0.983750 0.179543i \(-0.0574620\pi\)
\(348\) −1.22880 −0.0658705
\(349\) 18.6205i 0.996732i 0.866967 + 0.498366i \(0.166066\pi\)
−0.866967 + 0.498366i \(0.833934\pi\)
\(350\) −4.21572 + 2.21170i −0.225340 + 0.118220i
\(351\) −2.61986 2.61986i −0.139838 0.139838i
\(352\) 1.69991 0.0906053
\(353\) 4.81726 0.256397 0.128198 0.991749i \(-0.459081\pi\)
0.128198 + 0.991749i \(0.459081\pi\)
\(354\) −1.55410 −0.0825992
\(355\) −2.73380 + 17.9523i −0.145095 + 0.952810i
\(356\) 0.486184 0.486184i 0.0257677 0.0257677i
\(357\) 0.747894i 0.0395828i
\(358\) 4.31587 + 4.31587i 0.228101 + 0.228101i
\(359\) 9.55311i 0.504194i 0.967702 + 0.252097i \(0.0811202\pi\)
−0.967702 + 0.252097i \(0.918880\pi\)
\(360\) −0.978702 + 6.42694i −0.0515821 + 0.338730i
\(361\) 18.8045i 0.989712i
\(362\) 11.8012i 0.620257i
\(363\) 1.74559 + 1.74559i 0.0916198 + 0.0916198i
\(364\) 1.38728 1.38728i 0.0727131 0.0727131i
\(365\) 9.70585 7.14047i 0.508027 0.373750i
\(366\) 1.95740 0.102315
\(367\) −22.7113 22.7113i −1.18552 1.18552i −0.978293 0.207229i \(-0.933556\pi\)
−0.207229 0.978293i \(-0.566444\pi\)
\(368\) 3.40706i 0.177605i
\(369\) 9.06006 0.471648
\(370\) 12.5705 + 5.19447i 0.653509 + 0.270048i
\(371\) 3.63548 0.188745
\(372\) 0.164847i 0.00854694i
\(373\) 22.7358 + 22.7358i 1.17721 + 1.17721i 0.980451 + 0.196763i \(0.0630430\pi\)
0.196763 + 0.980451i \(0.436957\pi\)
\(374\) 4.38680 0.226836
\(375\) −3.21722 + 1.10931i −0.166137 + 0.0572845i
\(376\) 1.26620 1.26620i 0.0652994 0.0652994i
\(377\) −5.88201 5.88201i −0.302939 0.302939i
\(378\) 1.71203i 0.0880571i
\(379\) 3.70695i 0.190413i −0.995458 0.0952065i \(-0.969649\pi\)
0.995458 0.0952065i \(-0.0303511\pi\)
\(380\) 0.796335 0.585854i 0.0408511 0.0300537i
\(381\) 0.939381i 0.0481259i
\(382\) −0.707267 0.707267i −0.0361869 0.0361869i
\(383\) 23.3542i 1.19334i −0.802486 0.596671i \(-0.796490\pi\)
0.802486 0.596671i \(-0.203510\pi\)
\(384\) 0.215231 0.215231i 0.0109835 0.0109835i
\(385\) 2.14470 + 2.91523i 0.109304 + 0.148574i
\(386\) 8.39923 0.427509
\(387\) 21.4686 1.09131
\(388\) −0.430462 −0.0218534
\(389\) 16.1783 + 16.1783i 0.820273 + 0.820273i 0.986147 0.165874i \(-0.0530446\pi\)
−0.165874 + 0.986147i \(0.553045\pi\)
\(390\) 1.12967 0.831083i 0.0572030 0.0420835i
\(391\) 8.79229i 0.444645i
\(392\) −6.09344 −0.307765
\(393\) 5.68747i 0.286895i
\(394\) −15.0419 + 15.0419i −0.757801 + 0.757801i
\(395\) −8.48602 + 6.24306i −0.426978 + 0.314122i
\(396\) 4.94223 0.248356
\(397\) −14.6564 + 14.6564i −0.735586 + 0.735586i −0.971720 0.236134i \(-0.924119\pi\)
0.236134 + 0.971720i \(0.424119\pi\)
\(398\) −1.52878 1.52878i −0.0766308 0.0766308i
\(399\) −0.0906042 + 0.0906042i −0.00453588 + 0.00453588i
\(400\) −4.77336 1.48830i −0.238668 0.0744149i
\(401\) −14.9949 14.9949i −0.748810 0.748810i 0.225446 0.974256i \(-0.427616\pi\)
−0.974256 + 0.225446i \(0.927616\pi\)
\(402\) 3.52878i 0.176000i
\(403\) −0.789092 + 0.789092i −0.0393075 + 0.0393075i
\(404\) 2.72028i 0.135339i
\(405\) −2.75186 + 18.0710i −0.136741 + 0.897953i
\(406\) 3.84378i 0.190763i
\(407\) 2.46528 10.0419i 0.122199 0.497761i
\(408\) 0.555428 0.555428i 0.0274978 0.0274978i
\(409\) 10.9013 10.9013i 0.539035 0.539035i −0.384211 0.923245i \(-0.625526\pi\)
0.923245 + 0.384211i \(0.125526\pi\)
\(410\) −1.04903 + 6.88875i −0.0518077 + 0.340211i
\(411\) 3.82737i 0.188790i
\(412\) −13.5156 −0.665866
\(413\) 4.86133i 0.239211i
\(414\) 9.90551i 0.486829i
\(415\) 12.1464 + 16.5103i 0.596244 + 0.810458i
\(416\) 2.06054 0.101026
\(417\) −1.24494 1.24494i −0.0609652 0.0609652i
\(418\) −0.531442 0.531442i −0.0259937 0.0259937i
\(419\) 13.2565i 0.647621i 0.946122 + 0.323810i \(0.104964\pi\)
−0.946122 + 0.323810i \(0.895036\pi\)
\(420\) 0.640656 + 0.0975597i 0.0312608 + 0.00476043i
\(421\) −23.9484 23.9484i −1.16717 1.16717i −0.982870 0.184302i \(-0.940998\pi\)
−0.184302 0.982870i \(-0.559002\pi\)
\(422\) 24.1444i 1.17533i
\(423\) 3.68130 3.68130i 0.178991 0.178991i
\(424\) 2.69991 + 2.69991i 0.131119 + 0.131119i
\(425\) −12.3182 3.84072i −0.597520 0.186302i
\(426\) 1.74791 1.74791i 0.0846864 0.0846864i
\(427\) 6.12291i 0.296309i
\(428\) −12.0332 12.0332i −0.581645 0.581645i
\(429\) −0.753894 0.753894i −0.0363984 0.0363984i
\(430\) −2.48576 + 16.3235i −0.119874 + 0.787188i
\(431\) −10.5581 10.5581i −0.508567 0.508567i 0.405519 0.914087i \(-0.367091\pi\)
−0.914087 + 0.405519i \(0.867091\pi\)
\(432\) 1.27145 1.27145i 0.0611724 0.0611724i
\(433\) 4.00718 4.00718i 0.192573 0.192573i −0.604234 0.796807i \(-0.706521\pi\)
0.796807 + 0.604234i \(0.206521\pi\)
\(434\) −0.515656 −0.0247523
\(435\) 0.413650 2.71636i 0.0198330 0.130239i
\(436\) 12.8690 + 12.8690i 0.616312 + 0.616312i
\(437\) 1.06515 1.06515i 0.0509529 0.0509529i
\(438\) −1.64022 −0.0783729
\(439\) 16.2656 16.2656i 0.776315 0.776315i −0.202887 0.979202i \(-0.565033\pi\)
0.979202 + 0.202887i \(0.0650326\pi\)
\(440\) −0.572240 + 3.75779i −0.0272805 + 0.179145i
\(441\) −17.7158 −0.843608
\(442\) 5.31745 0.252925
\(443\) −8.83849 8.83849i −0.419929 0.419929i 0.465250 0.885179i \(-0.345964\pi\)
−0.885179 + 0.465250i \(0.845964\pi\)
\(444\) −0.959308 1.58358i −0.0455268 0.0751535i
\(445\) 0.911086 + 1.23841i 0.0431896 + 0.0587065i
\(446\) −10.0159 10.0159i −0.474266 0.474266i
\(447\) −1.75938 + 1.75938i −0.0832157 + 0.0832157i
\(448\) 0.673260 + 0.673260i 0.0318085 + 0.0318085i
\(449\) 23.1025 + 23.1025i 1.09027 + 1.09027i 0.995499 + 0.0947738i \(0.0302128\pi\)
0.0947738 + 0.995499i \(0.469787\pi\)
\(450\) −13.8778 4.32700i −0.654207 0.203977i
\(451\) 5.29735 0.249442
\(452\) 4.08335 0.192065
\(453\) −2.54645 + 2.54645i −0.119643 + 0.119643i
\(454\) 3.05788i 0.143514i
\(455\) 2.59969 + 3.53369i 0.121876 + 0.165662i
\(456\) −0.134575 −0.00630206
\(457\) 7.81169 0.365415 0.182708 0.983167i \(-0.441514\pi\)
0.182708 + 0.983167i \(0.441514\pi\)
\(458\) 26.8791 1.25598
\(459\) 3.28111 3.28111i 0.153149 0.153149i
\(460\) −7.53158 1.14692i −0.351162 0.0534753i
\(461\) 5.55252 5.55252i 0.258607 0.258607i −0.565881 0.824487i \(-0.691464\pi\)
0.824487 + 0.565881i \(0.191464\pi\)
\(462\) 0.492655i 0.0229204i
\(463\) 27.6492i 1.28497i −0.766299 0.642484i \(-0.777904\pi\)
0.766299 0.642484i \(-0.222096\pi\)
\(464\) 2.85460 2.85460i 0.132522 0.132522i
\(465\) −0.364409 0.0554926i −0.0168991 0.00257341i
\(466\) 0.315711 0.315711i 0.0146250 0.0146250i
\(467\) −36.0724 −1.66923 −0.834616 0.550832i \(-0.814311\pi\)
−0.834616 + 0.550832i \(0.814311\pi\)
\(468\) 5.99071 0.276920
\(469\) −11.0383 −0.509702
\(470\) 2.37281 + 3.22529i 0.109449 + 0.148771i
\(471\) 1.24211i 0.0572333i
\(472\) 3.61030 3.61030i 0.166177 0.166177i
\(473\) 12.5525 0.577166
\(474\) 1.43408 0.0658695
\(475\) 1.02701 + 1.95758i 0.0471224 + 0.0898200i
\(476\) 1.73742 + 1.73742i 0.0796346 + 0.0796346i
\(477\) 7.84958 + 7.84958i 0.359407 + 0.359407i
\(478\) −7.59846 + 7.59846i −0.347545 + 0.347545i
\(479\) −15.5362 15.5362i −0.709869 0.709869i 0.256639 0.966507i \(-0.417385\pi\)
−0.966507 + 0.256639i \(0.917385\pi\)
\(480\) 0.403333 + 0.548239i 0.0184095 + 0.0250236i
\(481\) 2.98828 12.1723i 0.136254 0.555010i
\(482\) 3.57132 + 3.57132i 0.162669 + 0.162669i
\(483\) 0.987409 0.0449287
\(484\) −8.11032 −0.368651
\(485\) 0.144906 0.951573i 0.00657986 0.0432087i
\(486\) 5.57380 5.57380i 0.252832 0.252832i
\(487\) −28.9759 −1.31302 −0.656512 0.754315i \(-0.727969\pi\)
−0.656512 + 0.754315i \(0.727969\pi\)
\(488\) −4.54721 + 4.54721i −0.205843 + 0.205843i
\(489\) 2.38656 + 2.38656i 0.107924 + 0.107924i
\(490\) 2.05124 13.4701i 0.0926654 0.608515i
\(491\) 42.0592 1.89810 0.949052 0.315118i \(-0.102044\pi\)
0.949052 + 0.315118i \(0.102044\pi\)
\(492\) 0.670716 0.670716i 0.0302382 0.0302382i
\(493\) 7.36661 7.36661i 0.331776 0.331776i
\(494\) −0.644185 0.644185i −0.0289833 0.0289833i
\(495\) −1.66370 + 10.9252i −0.0747778 + 0.491051i
\(496\) −0.382954 0.382954i −0.0171952 0.0171952i
\(497\) 5.46759 + 5.46759i 0.245255 + 0.245255i
\(498\) 2.79013i 0.125029i
\(499\) −9.34143 + 9.34143i −0.418180 + 0.418180i −0.884576 0.466396i \(-0.845552\pi\)
0.466396 + 0.884576i \(0.345552\pi\)
\(500\) 4.89686 10.0509i 0.218994 0.449490i
\(501\) 1.66894 + 1.66894i 0.0745628 + 0.0745628i
\(502\) −19.0270 + 19.0270i −0.849215 + 0.849215i
\(503\) 17.7689i 0.792274i −0.918191 0.396137i \(-0.870350\pi\)
0.918191 0.396137i \(-0.129650\pi\)
\(504\) 1.95740 + 1.95740i 0.0871897 + 0.0871897i
\(505\) 6.01340 + 0.915726i 0.267593 + 0.0407493i
\(506\) 5.79168i 0.257472i
\(507\) 1.88417 + 1.88417i 0.0836791 + 0.0836791i
\(508\) 2.18226 + 2.18226i 0.0968222 + 0.0968222i
\(509\) 18.7841 0.832592 0.416296 0.909229i \(-0.363328\pi\)
0.416296 + 0.909229i \(0.363328\pi\)
\(510\) 1.04085 + 1.41479i 0.0460894 + 0.0626481i
\(511\) 5.13075i 0.226971i
\(512\) 1.00000i 0.0441942i
\(513\) −0.794983 −0.0350994
\(514\) 24.5612i 1.08335i
\(515\) 4.54975 29.8774i 0.200486 1.31655i
\(516\) 1.58932 1.58932i 0.0699658 0.0699658i
\(517\) 2.15243 2.15243i 0.0946636 0.0946636i
\(518\) 4.95357 3.00079i 0.217648 0.131847i
\(519\) 0.628275i 0.0275782i
\(520\) −0.693639 + 4.55499i −0.0304181 + 0.199750i
\(521\) 16.1307i 0.706699i 0.935491 + 0.353350i \(0.114957\pi\)
−0.935491 + 0.353350i \(0.885043\pi\)
\(522\) 8.29933 8.29933i 0.363252 0.363252i
\(523\) 5.32902i 0.233022i −0.993189 0.116511i \(-0.962829\pi\)
0.993189 0.116511i \(-0.0371710\pi\)
\(524\) −13.2125 13.2125i −0.577189 0.577189i
\(525\) −0.431328 + 1.38338i −0.0188247 + 0.0603757i
\(526\) 15.9933 15.9933i 0.697340 0.697340i
\(527\) −0.988256 0.988256i −0.0430491 0.0430491i
\(528\) 0.365873 0.365873i 0.0159226 0.0159226i
\(529\) 11.3920 0.495303
\(530\) −6.87724 + 5.05950i −0.298728 + 0.219771i
\(531\) 10.4964 10.4964i 0.455505 0.455505i
\(532\) 0.420962i 0.0182510i
\(533\) 6.42117 0.278132
\(534\) 0.209284i 0.00905659i
\(535\) 30.6511 22.5496i 1.32516 0.974905i
\(536\) −8.19766 8.19766i −0.354085 0.354085i
\(537\) 1.85782 0.0801708
\(538\) 8.06679 0.347784
\(539\) −10.3583 −0.446163
\(540\) 2.38263 + 3.23864i 0.102532 + 0.139369i
\(541\) 15.5936 15.5936i 0.670423 0.670423i −0.287391 0.957813i \(-0.592788\pi\)
0.957813 + 0.287391i \(0.0927877\pi\)
\(542\) 24.2256i 1.04058i
\(543\) 2.53999 + 2.53999i 0.109001 + 0.109001i
\(544\) 2.58061i 0.110643i
\(545\) −32.7800 + 24.1159i −1.40414 + 1.03301i
\(546\) 0.597170i 0.0255565i
\(547\) 45.2269i 1.93376i 0.255230 + 0.966880i \(0.417849\pi\)
−0.255230 + 0.966880i \(0.582151\pi\)
\(548\) −8.89131 8.89131i −0.379818 0.379818i
\(549\) −13.2203 + 13.2203i −0.564231 + 0.564231i
\(550\) −8.11427 2.52997i −0.345994 0.107878i
\(551\) −1.78487 −0.0760379
\(552\) 0.733305 + 0.733305i 0.0312115 + 0.0312115i
\(553\) 4.48592i 0.190761i
\(554\) 18.8030 0.798862
\(555\) 3.82357 1.58755i 0.162302 0.0673877i
\(556\) 5.78423 0.245306
\(557\) 11.9401i 0.505919i −0.967477 0.252959i \(-0.918596\pi\)
0.967477 0.252959i \(-0.0814039\pi\)
\(558\) −1.11338 1.11338i −0.0471333 0.0471333i
\(559\) 15.2155 0.643547
\(560\) −1.71494 + 1.26166i −0.0724693 + 0.0533148i
\(561\) 0.944175 0.944175i 0.0398631 0.0398631i
\(562\) 14.2311 + 14.2311i 0.600301 + 0.600301i
\(563\) 5.67895i 0.239339i −0.992814 0.119670i \(-0.961816\pi\)
0.992814 0.119670i \(-0.0381835\pi\)
\(564\) 0.545052i 0.0229508i
\(565\) −1.37458 + 9.02660i −0.0578290 + 0.379752i
\(566\) 0.905573i 0.0380641i
\(567\) 5.50373 + 5.50373i 0.231135 + 0.231135i
\(568\) 8.12107i 0.340753i
\(569\) 5.85876 5.85876i 0.245612 0.245612i −0.573555 0.819167i \(-0.694436\pi\)
0.819167 + 0.573555i \(0.194436\pi\)
\(570\) 0.0453021 0.297490i 0.00189750 0.0124605i
\(571\) 35.6191 1.49061 0.745307 0.666721i \(-0.232303\pi\)
0.745307 + 0.666721i \(0.232303\pi\)
\(572\) 3.50272 0.146456
\(573\) −0.304452 −0.0127186
\(574\) 2.09805 + 2.09805i 0.0875710 + 0.0875710i
\(575\) 5.07071 16.2631i 0.211463 0.678219i
\(576\) 2.90735i 0.121140i
\(577\) −10.6524 −0.443464 −0.221732 0.975108i \(-0.571171\pi\)
−0.221732 + 0.975108i \(0.571171\pi\)
\(578\) 10.3404i 0.430106i
\(579\) 1.80777 1.80777i 0.0751285 0.0751285i
\(580\) 5.34939 + 7.27128i 0.222121 + 0.301923i
\(581\) 8.72774 0.362088
\(582\) −0.0926488 + 0.0926488i −0.00384042 + 0.00384042i
\(583\) 4.58959 + 4.58959i 0.190081 + 0.190081i
\(584\) 3.81038 3.81038i 0.157675 0.157675i
\(585\) −2.01665 + 13.2430i −0.0833783 + 0.547529i
\(586\) −14.1364 14.1364i −0.583967 0.583967i
\(587\) 4.99347i 0.206103i −0.994676 0.103051i \(-0.967139\pi\)
0.994676 0.103051i \(-0.0328606\pi\)
\(588\) −1.31150 + 1.31150i −0.0540853 + 0.0540853i
\(589\) 0.239446i 0.00986620i
\(590\) 6.76553 + 9.19619i 0.278532 + 0.378601i
\(591\) 6.47498i 0.266345i
\(592\) 5.90735 + 1.45024i 0.242791 + 0.0596046i
\(593\) 7.45193 7.45193i 0.306014 0.306014i −0.537347 0.843361i \(-0.680573\pi\)
0.843361 + 0.537347i \(0.180573\pi\)
\(594\) 2.16134 2.16134i 0.0886808 0.0886808i
\(595\) −4.42559 + 3.25585i −0.181431 + 0.133477i
\(596\) 8.17437i 0.334835i
\(597\) −0.658082 −0.0269335
\(598\) 7.02037i 0.287084i
\(599\) 9.88045i 0.403704i −0.979416 0.201852i \(-0.935304\pi\)
0.979416 0.201852i \(-0.0646961\pi\)
\(600\) −1.34770 + 0.707048i −0.0550198 + 0.0288651i
\(601\) 1.44426 0.0589125 0.0294562 0.999566i \(-0.490622\pi\)
0.0294562 + 0.999566i \(0.490622\pi\)
\(602\) 4.97151 + 4.97151i 0.202624 + 0.202624i
\(603\) −23.8335 23.8335i −0.970574 0.970574i
\(604\) 11.8313i 0.481407i
\(605\) 2.73018 17.9285i 0.110997 0.728899i
\(606\) −0.585488 0.585488i −0.0237838 0.0237838i
\(607\) 28.7523i 1.16702i −0.812106 0.583510i \(-0.801679\pi\)
0.812106 0.583510i \(-0.198321\pi\)
\(608\) 0.312630 0.312630i 0.0126788 0.0126788i
\(609\) −0.827300 0.827300i −0.0335239 0.0335239i
\(610\) −8.52127 11.5827i −0.345016 0.468971i
\(611\) 2.60906 2.60906i 0.105551 0.105551i
\(612\) 7.50274i 0.303280i
\(613\) 33.5232 + 33.5232i 1.35399 + 1.35399i 0.881148 + 0.472841i \(0.156772\pi\)
0.472841 + 0.881148i \(0.343228\pi\)
\(614\) −22.5470 22.5470i −0.909923 0.909923i
\(615\) 1.25689 + 1.70846i 0.0506827 + 0.0688916i
\(616\) 1.14448 + 1.14448i 0.0461124 + 0.0461124i
\(617\) −9.02064 + 9.02064i −0.363157 + 0.363157i −0.864974 0.501817i \(-0.832665\pi\)
0.501817 + 0.864974i \(0.332665\pi\)
\(618\) −2.90898 + 2.90898i −0.117016 + 0.117016i
\(619\) −41.8727 −1.68301 −0.841504 0.540251i \(-0.818329\pi\)
−0.841504 + 0.540251i \(0.818329\pi\)
\(620\) 0.975467 0.717639i 0.0391757 0.0288211i
\(621\) 4.33189 + 4.33189i 0.173833 + 0.173833i
\(622\) 18.8440 18.8440i 0.755577 0.755577i
\(623\) 0.654656 0.0262282
\(624\) 0.443492 0.443492i 0.0177539 0.0177539i
\(625\) 20.5699 + 14.2084i 0.822798 + 0.568334i
\(626\) −13.8468 −0.553431
\(627\) −0.228765 −0.00913601
\(628\) 2.88552 + 2.88552i 0.115145 + 0.115145i
\(629\) 15.2446 + 3.74251i 0.607841 + 0.149224i
\(630\) −4.98592 + 3.66808i −0.198644 + 0.146140i
\(631\) −4.63219 4.63219i −0.184405 0.184405i 0.608867 0.793272i \(-0.291624\pi\)
−0.793272 + 0.608867i \(0.791624\pi\)
\(632\) −3.33149 + 3.33149i −0.132520 + 0.132520i
\(633\) 5.19663 + 5.19663i 0.206547 + 0.206547i
\(634\) −9.84958 9.84958i −0.391177 0.391177i
\(635\) −5.55868 + 4.08946i −0.220590 + 0.162285i
\(636\) 1.16221 0.0460845
\(637\) −12.5558 −0.497477
\(638\) 4.85256 4.85256i 0.192115 0.192115i
\(639\) 23.6108i 0.934029i
\(640\) −2.21058 0.336630i −0.0873810 0.0133065i
\(641\) 1.32847 0.0524714 0.0262357 0.999656i \(-0.491648\pi\)
0.0262357 + 0.999656i \(0.491648\pi\)
\(642\) −5.17983 −0.204431
\(643\) −3.72617 −0.146946 −0.0734729 0.997297i \(-0.523408\pi\)
−0.0734729 + 0.997297i \(0.523408\pi\)
\(644\) −2.29384 + 2.29384i −0.0903898 + 0.0903898i
\(645\) 2.97831 + 4.04833i 0.117271 + 0.159403i
\(646\) 0.806776 0.806776i 0.0317422 0.0317422i
\(647\) 31.4105i 1.23487i −0.786621 0.617437i \(-0.788171\pi\)
0.786621 0.617437i \(-0.211829\pi\)
\(648\) 8.17474i 0.321134i
\(649\) 6.13717 6.13717i 0.240905 0.240905i
\(650\) −9.83569 3.06669i −0.385787 0.120286i
\(651\) −0.110985 + 0.110985i −0.00434985 + 0.00434985i
\(652\) −11.0884 −0.434253
\(653\) 3.85917 0.151021 0.0755104 0.997145i \(-0.475941\pi\)
0.0755104 + 0.997145i \(0.475941\pi\)
\(654\) 5.53961 0.216616
\(655\) 33.6550 24.7595i 1.31501 0.967436i
\(656\) 3.11626i 0.121669i
\(657\) 11.0781 11.0781i 0.432198 0.432198i
\(658\) 1.70497 0.0664665
\(659\) −20.7025 −0.806457 −0.403228 0.915099i \(-0.632112\pi\)
−0.403228 + 0.915099i \(0.632112\pi\)
\(660\) 0.685629 + 0.931956i 0.0266881 + 0.0362763i
\(661\) −18.0647 18.0647i −0.702635 0.702635i 0.262340 0.964975i \(-0.415506\pi\)
−0.964975 + 0.262340i \(0.915506\pi\)
\(662\) −11.7035 11.7035i −0.454868 0.454868i
\(663\) 1.14448 1.14448i 0.0444479 0.0444479i
\(664\) 6.48170 + 6.48170i 0.251539 + 0.251539i
\(665\) 0.930572 + 0.141709i 0.0360860 + 0.00549522i
\(666\) 17.1747 + 4.21636i 0.665508 + 0.163381i
\(667\) 9.72579 + 9.72579i 0.376584 + 0.376584i
\(668\) −7.75419 −0.300018
\(669\) −4.31146 −0.166691
\(670\) 20.8812 15.3620i 0.806710 0.593487i
\(671\) −7.72984 + 7.72984i −0.298407 + 0.298407i
\(672\) 0.289813 0.0111798
\(673\) −18.6183 + 18.6183i −0.717681 + 0.717681i −0.968130 0.250449i \(-0.919422\pi\)
0.250449 + 0.968130i \(0.419422\pi\)
\(674\) −2.42851 2.42851i −0.0935426 0.0935426i
\(675\) −7.96136 + 4.17678i −0.306433 + 0.160764i
\(676\) −8.75419 −0.336699
\(677\) −22.0917 + 22.0917i −0.849054 + 0.849054i −0.990015 0.140961i \(-0.954981\pi\)
0.140961 + 0.990015i \(0.454981\pi\)
\(678\) 0.878865 0.878865i 0.0337526 0.0337526i
\(679\) −0.289813 0.289813i −0.0111220 0.0111220i
\(680\) −5.70466 0.868711i −0.218764 0.0333136i
\(681\) −0.658151 0.658151i −0.0252204 0.0252204i
\(682\) −0.650987 0.650987i −0.0249276 0.0249276i
\(683\) 4.05946i 0.155331i 0.996979 + 0.0776654i \(0.0247466\pi\)
−0.996979 + 0.0776654i \(0.975253\pi\)
\(684\) 0.908925 0.908925i 0.0347536 0.0347536i
\(685\) 22.6481 16.6619i 0.865338 0.636618i
\(686\) −8.81529 8.81529i −0.336569 0.336569i
\(687\) 5.78521 5.78521i 0.220720 0.220720i
\(688\) 7.38424i 0.281522i
\(689\) 5.56326 + 5.56326i 0.211943 + 0.211943i
\(690\) −1.86788 + 1.37418i −0.0711091 + 0.0523141i
\(691\) 19.1786i 0.729590i 0.931088 + 0.364795i \(0.118861\pi\)
−0.931088 + 0.364795i \(0.881139\pi\)
\(692\) −1.45954 1.45954i −0.0554833 0.0554833i
\(693\) 3.32740 + 3.32740i 0.126398 + 0.126398i
\(694\) 6.68904 0.253912
\(695\) −1.94714 + 12.7865i −0.0738594 + 0.485020i
\(696\) 1.22880i 0.0465774i
\(697\) 8.04185i 0.304607i
\(698\) −18.6205 −0.704796
\(699\) 0.135902i 0.00514027i
\(700\) −2.21170 4.21572i −0.0835945 0.159339i
\(701\) −24.6018 + 24.6018i −0.929198 + 0.929198i −0.997654 0.0684559i \(-0.978193\pi\)
0.0684559 + 0.997654i \(0.478193\pi\)
\(702\) 2.61986 2.61986i 0.0988803 0.0988803i
\(703\) −1.39343 2.30020i −0.0525540 0.0867538i
\(704\) 1.69991i 0.0640677i
\(705\) 1.20488 + 0.183481i 0.0453785 + 0.00691029i
\(706\) 4.81726i 0.181300i
\(707\) 1.83145 1.83145i 0.0688789 0.0688789i
\(708\) 1.55410i 0.0584065i
\(709\) 33.2828 + 33.2828i 1.24996 + 1.24996i 0.955736 + 0.294227i \(0.0950622\pi\)
0.294227 + 0.955736i \(0.404938\pi\)
\(710\) −17.9523 2.73380i −0.673738 0.102598i
\(711\) −9.68581 + 9.68581i −0.363246 + 0.363246i
\(712\) 0.486184 + 0.486184i 0.0182205 + 0.0182205i
\(713\) 1.30475 1.30475i 0.0488632 0.0488632i
\(714\) 0.747894 0.0279892
\(715\) −1.17912 + 7.74306i −0.0440966 + 0.289574i
\(716\) −4.31587 + 4.31587i −0.161292 + 0.161292i
\(717\) 3.27085i 0.122152i
\(718\) −9.55311 −0.356519
\(719\) 30.9253i 1.15332i 0.816984 + 0.576660i \(0.195644\pi\)
−0.816984 + 0.576660i \(0.804356\pi\)
\(720\) −6.42694 0.978702i −0.239518 0.0364741i
\(721\) −9.09951 9.09951i −0.338883 0.338883i
\(722\) 18.8045 0.699832
\(723\) 1.53732 0.0571734
\(724\) −11.8012 −0.438588
\(725\) −17.8745 + 9.37754i −0.663844 + 0.348273i
\(726\) −1.74559 + 1.74559i −0.0647850 + 0.0647850i
\(727\) 44.0653i 1.63429i −0.576431 0.817146i \(-0.695555\pi\)
0.576431 0.817146i \(-0.304445\pi\)
\(728\) 1.38728 + 1.38728i 0.0514159 + 0.0514159i
\(729\) 22.1249i 0.819442i
\(730\) 7.14047 + 9.70585i 0.264281 + 0.359230i
\(731\) 19.0559i 0.704806i
\(732\) 1.95740i 0.0723477i
\(733\) −4.94476 4.94476i −0.182639 0.182639i 0.609866 0.792505i \(-0.291223\pi\)
−0.792505 + 0.609866i \(0.791223\pi\)
\(734\) 22.7113 22.7113i 0.838290 0.838290i
\(735\) −2.45769 3.34067i −0.0906531 0.123222i
\(736\) −3.40706 −0.125586
\(737\) −13.9353 13.9353i −0.513312 0.513312i
\(738\) 9.06006i 0.333505i
\(739\) −19.8515 −0.730251 −0.365125 0.930958i \(-0.618974\pi\)
−0.365125 + 0.930958i \(0.618974\pi\)
\(740\) −5.19447 + 12.5705i −0.190953 + 0.462101i
\(741\) −0.277297 −0.0101868
\(742\) 3.63548i 0.133463i
\(743\) −10.5608 10.5608i −0.387439 0.387439i 0.486334 0.873773i \(-0.338334\pi\)
−0.873773 + 0.486334i \(0.838334\pi\)
\(744\) −0.164847 −0.00604360
\(745\) 18.0701 + 2.75174i 0.662038 + 0.100816i
\(746\) −22.7358 + 22.7358i −0.832416 + 0.832416i
\(747\) 18.8446 + 18.8446i 0.689488 + 0.689488i
\(748\) 4.38680i 0.160397i
\(749\) 16.2029i 0.592041i
\(750\) −1.10931 3.21722i −0.0405063 0.117476i
\(751\) 30.0307i 1.09583i 0.836533 + 0.547917i \(0.184579\pi\)
−0.836533 + 0.547917i \(0.815421\pi\)
\(752\) 1.26620 + 1.26620i 0.0461737 + 0.0461737i
\(753\) 8.19039i 0.298474i
\(754\) 5.88201 5.88201i 0.214210 0.214210i
\(755\) 26.1540 + 3.98276i 0.951841 + 0.144947i
\(756\) 1.71203 0.0622658
\(757\) 45.2685 1.64531 0.822655 0.568541i \(-0.192492\pi\)
0.822655 + 0.568541i \(0.192492\pi\)
\(758\) 3.70695 0.134642
\(759\) 1.24655 + 1.24655i 0.0452469 + 0.0452469i
\(760\) 0.585854 + 0.796335i 0.0212511 + 0.0288861i
\(761\) 48.5501i 1.75994i 0.475029 + 0.879970i \(0.342437\pi\)
−0.475029 + 0.879970i \(0.657563\pi\)
\(762\) 0.939381 0.0340302
\(763\) 17.3283i 0.627328i
\(764\) 0.707267 0.707267i 0.0255880 0.0255880i
\(765\) −16.5854 2.52565i −0.599648 0.0913150i
\(766\) 23.3542 0.843821
\(767\) 7.43915 7.43915i 0.268612 0.268612i
\(768\) 0.215231 + 0.215231i 0.00776648 + 0.00776648i
\(769\) −20.0854 + 20.0854i −0.724300 + 0.724300i −0.969478 0.245178i \(-0.921154\pi\)
0.245178 + 0.969478i \(0.421154\pi\)
\(770\) −2.91523 + 2.14470i −0.105058 + 0.0772897i
\(771\) −5.28633 5.28633i −0.190382 0.190382i
\(772\) 8.39923i 0.302295i
\(773\) −22.9236 + 22.9236i −0.824504 + 0.824504i −0.986750 0.162247i \(-0.948126\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(774\) 21.4686i 0.771672i
\(775\) 1.25803 + 2.39793i 0.0451897 + 0.0861362i
\(776\) 0.430462i 0.0154527i
\(777\) 0.420299 1.71203i 0.0150781 0.0614186i
\(778\) −16.1783 + 16.1783i −0.580020 + 0.580020i
\(779\) 0.974235 0.974235i 0.0349056 0.0349056i
\(780\) 0.831083 + 1.12967i 0.0297575 + 0.0404486i
\(781\) 13.8051i 0.493984i
\(782\) −8.79229 −0.314412
\(783\) 7.25894i 0.259413i
\(784\) 6.09344i 0.217623i
\(785\) −7.35004 + 5.40733i −0.262334 + 0.192996i
\(786\) −5.68747 −0.202865
\(787\) 22.0858 + 22.0858i 0.787274 + 0.787274i 0.981047 0.193772i \(-0.0620723\pi\)
−0.193772 + 0.981047i \(0.562072\pi\)
\(788\) −15.0419 15.0419i −0.535846 0.535846i
\(789\) 6.88450i 0.245095i
\(790\) −6.24306 8.48602i −0.222118 0.301919i
\(791\) 2.74916 + 2.74916i 0.0977488 + 0.0977488i
\(792\) 4.94223i 0.175614i
\(793\) −9.36970 + 9.36970i −0.332728 + 0.332728i
\(794\) −14.6564 14.6564i −0.520138 0.520138i
\(795\) −0.391234 + 2.56916i −0.0138756 + 0.0911186i
\(796\) 1.52878 1.52878i 0.0541862 0.0541862i
\(797\) 3.09119i 0.109495i −0.998500 0.0547477i \(-0.982565\pi\)
0.998500 0.0547477i \(-0.0174355\pi\)
\(798\) −0.0906042 0.0906042i −0.00320735 0.00320735i
\(799\) 3.26758 + 3.26758i 0.115599 + 0.115599i
\(800\) 1.48830 4.77336i 0.0526193 0.168764i
\(801\) 1.41351 + 1.41351i 0.0499438 + 0.0499438i
\(802\) 14.9949 14.9949i 0.529489 0.529489i
\(803\) 6.47729 6.47729i 0.228579 0.228579i
\(804\) −3.52878 −0.124450
\(805\) −4.29854 5.84289i −0.151504 0.205935i
\(806\) −0.789092 0.789092i −0.0277946 0.0277946i
\(807\) 1.73622 1.73622i 0.0611180 0.0611180i
\(808\) 2.72028 0.0956989
\(809\) 32.0623 32.0623i 1.12725 1.12725i 0.136629 0.990622i \(-0.456373\pi\)
0.990622 0.136629i \(-0.0436267\pi\)
\(810\) −18.0710 2.75186i −0.634949 0.0966906i
\(811\) −48.8130 −1.71406 −0.857029 0.515269i \(-0.827692\pi\)
−0.857029 + 0.515269i \(0.827692\pi\)
\(812\) 3.84378 0.134890
\(813\) −5.21410 5.21410i −0.182866 0.182866i
\(814\) 10.0419 + 2.46528i 0.351970 + 0.0864079i
\(815\) 3.73267 24.5117i 0.130750 0.858609i
\(816\) 0.555428 + 0.555428i 0.0194439 + 0.0194439i
\(817\) 2.30853 2.30853i 0.0807654 0.0807654i
\(818\) 10.9013 + 10.9013i 0.381155 + 0.381155i
\(819\) 4.03330 + 4.03330i 0.140935 + 0.140935i
\(820\) −6.88875 1.04903i −0.240566 0.0366336i
\(821\) −28.2934 −0.987445 −0.493723 0.869619i \(-0.664364\pi\)
−0.493723 + 0.869619i \(0.664364\pi\)
\(822\) −3.82737 −0.133495
\(823\) 15.4120 15.4120i 0.537229 0.537229i −0.385485 0.922714i \(-0.625966\pi\)
0.922714 + 0.385485i \(0.125966\pi\)
\(824\) 13.5156i 0.470838i
\(825\) −2.29097 + 1.20192i −0.0797613 + 0.0418453i
\(826\) 4.86133 0.169147
\(827\) 9.92069 0.344976 0.172488 0.985012i \(-0.444819\pi\)
0.172488 + 0.985012i \(0.444819\pi\)
\(828\) −9.90551 −0.344240
\(829\) 6.35906 6.35906i 0.220859 0.220859i −0.588001 0.808860i \(-0.700085\pi\)
0.808860 + 0.588001i \(0.200085\pi\)
\(830\) −16.5103 + 12.1464i −0.573080 + 0.421608i
\(831\) 4.04699 4.04699i 0.140388 0.140388i
\(832\) 2.06054i 0.0714363i
\(833\) 15.7248i 0.544832i
\(834\) 1.24494 1.24494i 0.0431089 0.0431089i
\(835\) 2.61029 17.1413i 0.0903329 0.593198i
\(836\) 0.531442 0.531442i 0.0183803 0.0183803i
\(837\) −0.973811 −0.0336598
\(838\) −13.2565 −0.457937
\(839\) −12.9249 −0.446218 −0.223109 0.974793i \(-0.571621\pi\)
−0.223109 + 0.974793i \(0.571621\pi\)
\(840\) −0.0975597 + 0.640656i −0.00336613 + 0.0221047i
\(841\) 12.7025i 0.438018i
\(842\) 23.9484 23.9484i 0.825315 0.825315i
\(843\) 6.12593 0.210988
\(844\) −24.1444 −0.831085
\(845\) 2.94692 19.3519i 0.101377 0.665724i
\(846\) 3.68130 + 3.68130i 0.126566 + 0.126566i
\(847\) −5.46035 5.46035i −0.187620 0.187620i
\(848\) −2.69991 + 2.69991i −0.0927152 + 0.0927152i
\(849\) −0.194907 0.194907i −0.00668920 0.00668920i
\(850\) 3.84072 12.3182i 0.131736 0.422510i
\(851\) −4.94106 + 20.1267i −0.169377 + 0.689934i
\(852\) 1.74791 + 1.74791i 0.0598823 + 0.0598823i
\(853\) 14.2055 0.486387 0.243193 0.969978i \(-0.421805\pi\)
0.243193 + 0.969978i \(0.421805\pi\)
\(854\) −6.12291 −0.209522
\(855\) 1.70328 + 2.31523i 0.0582510 + 0.0791790i
\(856\) 12.0332 12.0332i 0.411285 0.411285i
\(857\) −25.8639 −0.883494 −0.441747 0.897140i \(-0.645641\pi\)
−0.441747 + 0.897140i \(0.645641\pi\)
\(858\) 0.753894 0.753894i 0.0257375 0.0257375i
\(859\) −30.1371 30.1371i −1.02827 1.02827i −0.999589 0.0286775i \(-0.990870\pi\)
−0.0286775 0.999589i \(-0.509130\pi\)
\(860\) −16.3235 2.48576i −0.556626 0.0847636i
\(861\) 0.903132 0.0307787
\(862\) 10.5581 10.5581i 0.359611 0.359611i
\(863\) −23.5513 + 23.5513i −0.801695 + 0.801695i −0.983360 0.181665i \(-0.941851\pi\)
0.181665 + 0.983360i \(0.441851\pi\)
\(864\) 1.27145 + 1.27145i 0.0432555 + 0.0432555i
\(865\) 3.71775 2.73510i 0.126407 0.0929963i
\(866\) 4.00718 + 4.00718i 0.136169 + 0.136169i
\(867\) −2.22559 2.22559i −0.0755848 0.0755848i
\(868\) 0.515656i 0.0175025i
\(869\) −5.66322 + 5.66322i −0.192112 + 0.192112i
\(870\) 2.71636 + 0.413650i 0.0920932 + 0.0140241i
\(871\) −16.8916 16.8916i −0.572349 0.572349i
\(872\) −12.8690 + 12.8690i −0.435799 + 0.435799i
\(873\) 1.25150i 0.0423570i
\(874\) 1.06515 + 1.06515i 0.0360292 + 0.0360292i
\(875\) 10.0637 3.47001i 0.340216 0.117308i
\(876\) 1.64022i 0.0554180i
\(877\) 23.0266 + 23.0266i 0.777553 + 0.777553i 0.979414 0.201862i \(-0.0646991\pi\)
−0.201862 + 0.979414i \(0.564699\pi\)
\(878\) 16.2656 + 16.2656i 0.548937 + 0.548937i
\(879\) −6.08516 −0.205248
\(880\) −3.75779 0.572240i −0.126675 0.0192902i
\(881\) 27.1213i 0.913741i −0.889533 0.456870i \(-0.848970\pi\)
0.889533 0.456870i \(-0.151030\pi\)
\(882\) 17.7158i 0.596521i
\(883\) −49.1920 −1.65544 −0.827722 0.561139i \(-0.810363\pi\)
−0.827722 + 0.561139i \(0.810363\pi\)
\(884\) 5.31745i 0.178845i
\(885\) 3.43546 + 0.523155i 0.115482 + 0.0175857i
\(886\) 8.83849 8.83849i 0.296935 0.296935i
\(887\) −5.87709 + 5.87709i −0.197333 + 0.197333i −0.798856 0.601523i \(-0.794561\pi\)
0.601523 + 0.798856i \(0.294561\pi\)
\(888\) 1.58358 0.959308i 0.0531416 0.0321923i
\(889\) 2.93846i 0.0985527i
\(890\) −1.23841 + 0.911086i −0.0415117 + 0.0305397i
\(891\) 13.8963i 0.465544i
\(892\) 10.0159 10.0159i 0.335357 0.335357i
\(893\) 0.791705i 0.0264934i
\(894\) −1.75938 1.75938i −0.0588424 0.0588424i
\(895\) −8.08774 10.9934i −0.270343 0.367470i
\(896\) −0.673260 + 0.673260i −0.0224920 + 0.0224920i
\(897\) 1.51100 + 1.51100i 0.0504509 + 0.0504509i
\(898\) −23.1025 + 23.1025i −0.770939 + 0.770939i
\(899\) −2.18636 −0.0729193
\(900\) 4.32700 13.8778i 0.144233 0.462595i
\(901\) −6.96741 + 6.96741i −0.232118 + 0.232118i
\(902\) 5.29735i 0.176382i
\(903\) 2.14005 0.0712163
\(904\) 4.08335i 0.135810i
\(905\) 3.97264 26.0875i 0.132055 0.867179i
\(906\) −2.54645 2.54645i −0.0846003 0.0846003i
\(907\) −1.31786 −0.0437587 −0.0218793 0.999761i \(-0.506965\pi\)
−0.0218793 + 0.999761i \(0.506965\pi\)
\(908\) 3.05788 0.101479
\(909\) 7.90879 0.262318
\(910\) −3.53369 + 2.59969i −0.117141 + 0.0861790i
\(911\) −14.9006 + 14.9006i −0.493679 + 0.493679i −0.909463 0.415784i \(-0.863507\pi\)
0.415784 + 0.909463i \(0.363507\pi\)
\(912\) 0.134575i 0.00445623i
\(913\) 11.0183 + 11.0183i 0.364652 + 0.364652i
\(914\) 7.81169i 0.258388i
\(915\) −4.32700 0.658921i −0.143046 0.0217832i
\(916\) 26.8791i 0.888109i
\(917\) 17.7908i 0.587506i
\(918\) 3.28111 + 3.28111i 0.108293 + 0.108293i
\(919\) −34.2859 + 34.2859i −1.13099 + 1.13099i −0.140975 + 0.990013i \(0.545024\pi\)
−0.990013 + 0.140975i \(0.954976\pi\)
\(920\) 1.14692 7.53158i 0.0378128 0.248309i
\(921\) −9.70563 −0.319811
\(922\) 5.55252 + 5.55252i 0.182863 + 0.182863i
\(923\) 16.7338i 0.550799i
\(924\) 0.492655 0.0162072
\(925\) −26.0395 15.7144i −0.856174 0.516687i
\(926\) 27.6492 0.908609
\(927\) 39.2946i 1.29060i
\(928\) 2.85460 + 2.85460i 0.0937069 + 0.0937069i
\(929\) −36.4095 −1.19456 −0.597278 0.802034i \(-0.703751\pi\)
−0.597278 + 0.802034i \(0.703751\pi\)
\(930\) 0.0554926 0.364409i 0.00181967 0.0119494i
\(931\) −1.90499 + 1.90499i −0.0624336 + 0.0624336i
\(932\) 0.315711 + 0.315711i 0.0103415 + 0.0103415i
\(933\) 8.11165i 0.265563i
\(934\) 36.0724i 1.18033i
\(935\) −9.69739 1.47673i −0.317138 0.0482942i
\(936\) 5.99071i 0.195812i
\(937\) 35.9882 + 35.9882i 1.17568 + 1.17568i 0.980833 + 0.194848i \(0.0624214\pi\)
0.194848 + 0.980833i \(0.437579\pi\)
\(938\) 11.0383i 0.360414i
\(939\) −2.98027 + 2.98027i −0.0972574 + 0.0972574i
\(940\) −3.22529 + 2.37281i −0.105197 + 0.0773924i
\(941\) 31.5238 1.02765 0.513823 0.857896i \(-0.328229\pi\)
0.513823 + 0.857896i \(0.328229\pi\)
\(942\) 1.24211 0.0404700
\(943\) −10.6173 −0.345746
\(944\) 3.61030 + 3.61030i 0.117505 + 0.117505i
\(945\) −0.576320 + 3.78458i −0.0187477 + 0.123112i
\(946\) 12.5525i 0.408118i
\(947\) 48.9752 1.59148 0.795741 0.605637i \(-0.207082\pi\)
0.795741 + 0.605637i \(0.207082\pi\)
\(948\) 1.43408i 0.0465768i
\(949\) 7.85143 7.85143i 0.254868 0.254868i
\(950\) −1.95758 + 1.02701i −0.0635123 + 0.0333206i
\(951\) −4.23987 −0.137487
\(952\) −1.73742 + 1.73742i −0.0563102 + 0.0563102i
\(953\) 9.58879 + 9.58879i 0.310611 + 0.310611i 0.845146 0.534535i \(-0.179513\pi\)
−0.534535 + 0.845146i \(0.679513\pi\)
\(954\) −7.84958 + 7.84958i −0.254139 + 0.254139i
\(955\) 1.32539 + 1.80156i 0.0428885 + 0.0582971i
\(956\) −7.59846 7.59846i −0.245752 0.245752i
\(957\) 2.08884i 0.0675227i
\(958\) 15.5362 15.5362i 0.501953 0.501953i
\(959\) 11.9723i 0.386606i
\(960\) −0.548239 + 0.403333i −0.0176944 + 0.0130175i
\(961\) 30.7067i 0.990538i
\(962\) 12.1723 + 2.98828i 0.392451 + 0.0963459i
\(963\) 34.9847 34.9847i 1.12737 1.12737i
\(964\) −3.57132 + 3.57132i −0.115024 + 0.115024i
\(965\) −18.5672 2.82743i −0.597699 0.0910182i
\(966\) 0.987409i 0.0317694i
\(967\) −29.6562 −0.953681 −0.476840 0.878990i \(-0.658218\pi\)
−0.476840 + 0.878990i \(0.658218\pi\)
\(968\) 8.11032i 0.260675i
\(969\) 0.347286i 0.0111564i
\(970\) 0.951573 + 0.144906i 0.0305532 + 0.00465267i
\(971\) −23.8296 −0.764729 −0.382365 0.924012i \(-0.624890\pi\)
−0.382365 + 0.924012i \(0.624890\pi\)
\(972\) 5.57380 + 5.57380i 0.178780 + 0.178780i
\(973\) 3.89429 + 3.89429i 0.124845 + 0.124845i
\(974\) 28.9759i 0.928449i
\(975\) −2.77699 + 1.45690i −0.0889349 + 0.0466581i
\(976\) −4.54721 4.54721i −0.145553 0.145553i
\(977\) 29.1322i 0.932023i −0.884779 0.466011i \(-0.845691\pi\)
0.884779 0.466011i \(-0.154309\pi\)
\(978\) −2.38656 + 2.38656i −0.0763137 + 0.0763137i
\(979\) 0.826467 + 0.826467i 0.0264140 + 0.0264140i
\(980\) 13.4701 + 2.05124i 0.430285 + 0.0655243i
\(981\) −37.4146 + 37.4146i −1.19456 + 1.19456i
\(982\) 42.0592i 1.34216i
\(983\) −7.65743 7.65743i −0.244234 0.244234i 0.574365 0.818599i \(-0.305249\pi\)
−0.818599 + 0.574365i \(0.805249\pi\)
\(984\) 0.670716 + 0.670716i 0.0213816 + 0.0213816i
\(985\) 38.3150 28.1879i 1.22082 0.898140i
\(986\) 7.36661 + 7.36661i 0.234601 + 0.234601i
\(987\) 0.366962 0.366962i 0.0116805 0.0116805i
\(988\) 0.644185 0.644185i 0.0204943 0.0204943i
\(989\) −25.1585 −0.799995
\(990\) −10.9252 1.66370i −0.347226 0.0528759i
\(991\) 23.2373 + 23.2373i 0.738158 + 0.738158i 0.972221 0.234063i \(-0.0752023\pi\)
−0.234063 + 0.972221i \(0.575202\pi\)
\(992\) 0.382954 0.382954i 0.0121588 0.0121588i
\(993\) −5.03790 −0.159873
\(994\) −5.46759 + 5.46759i −0.173422 + 0.173422i
\(995\) 2.86486 + 3.89413i 0.0908223 + 0.123452i
\(996\) 2.79013 0.0884086
\(997\) −4.12715 −0.130708 −0.0653540 0.997862i \(-0.520818\pi\)
−0.0653540 + 0.997862i \(0.520818\pi\)
\(998\) −9.34143 9.34143i −0.295698 0.295698i
\(999\) 9.35478 5.66697i 0.295972 0.179295i
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 370.2.g.d.327.3 yes 10
5.3 odd 4 370.2.h.d.253.3 yes 10
37.6 odd 4 370.2.h.d.117.3 yes 10
185.43 even 4 inner 370.2.g.d.43.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.g.d.43.3 10 185.43 even 4 inner
370.2.g.d.327.3 yes 10 1.1 even 1 trivial
370.2.h.d.117.3 yes 10 37.6 odd 4
370.2.h.d.253.3 yes 10 5.3 odd 4