Properties

Label 675.2.l.c.526.1
Level $675$
Weight $2$
Character 675.526
Analytic conductor $5.390$
Analytic rank $0$
Dimension $12$
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] = [675,2,Mod(76,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\), degree \(6\), 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 526.1
Root \(0.500000 + 1.00210i\) of defining polynomial
Character \(\chi\) \(=\) 675.526
Dual form 675.2.l.c.376.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.183082 - 1.03831i) q^{2} +(1.72962 + 0.0916693i) q^{3} +(0.834822 - 0.303850i) q^{4} +(-0.221481 - 1.81266i) q^{6} +(2.31094 + 0.841112i) q^{7} +(-1.52266 - 2.63732i) q^{8} +(2.98319 + 0.317107i) q^{9} +O(q^{10})\) \(q+(-0.183082 - 1.03831i) q^{2} +(1.72962 + 0.0916693i) q^{3} +(0.834822 - 0.303850i) q^{4} +(-0.221481 - 1.81266i) q^{6} +(2.31094 + 0.841112i) q^{7} +(-1.52266 - 2.63732i) q^{8} +(2.98319 + 0.317107i) q^{9} +(-0.960783 + 0.806193i) q^{11} +(1.47178 - 0.449019i) q^{12} +(0.789931 - 4.47992i) q^{13} +(0.450243 - 2.55345i) q^{14} +(-1.09847 + 0.921724i) q^{16} +(-3.32358 + 5.75662i) q^{17} +(-0.216914 - 3.15553i) q^{18} +(-0.124578 - 0.215776i) q^{19} +(3.91994 + 1.66665i) q^{21} +(1.01298 + 0.849989i) q^{22} +(0.791222 - 0.287981i) q^{23} +(-2.39186 - 4.70115i) q^{24} -4.79615 q^{26} +(5.13073 + 0.821942i) q^{27} +2.18479 q^{28} +(-0.0889744 - 0.504599i) q^{29} +(0.770551 - 0.280458i) q^{31} +(-3.50754 - 2.94318i) q^{32} +(-1.73570 + 1.30634i) q^{33} +(6.58563 + 2.39697i) q^{34} +(2.58679 - 0.641717i) q^{36} +(1.30403 - 2.25865i) q^{37} +(-0.201233 + 0.168855i) q^{38} +(1.77695 - 7.67616i) q^{39} +(-1.41572 + 8.02895i) q^{41} +(1.01282 - 4.37524i) q^{42} +(-3.31478 + 2.78143i) q^{43} +(-0.557121 + 0.964962i) q^{44} +(-0.443871 - 0.768808i) q^{46} +(-4.98256 - 1.81351i) q^{47} +(-1.98443 + 1.49354i) q^{48} +(-0.729356 - 0.612002i) q^{49} +(-6.27625 + 9.65211i) q^{51} +(-0.701774 - 3.97996i) q^{52} +10.4841 q^{53} +(-0.0859140 - 5.47776i) q^{54} +(-1.30048 - 7.37539i) q^{56} +(-0.195693 - 0.384630i) q^{57} +(-0.507639 + 0.184765i) q^{58} +(-2.30289 - 1.93235i) q^{59} +(-2.70930 - 0.986103i) q^{61} +(-0.432275 - 0.748722i) q^{62} +(6.62725 + 3.24201i) q^{63} +(-3.84771 + 6.66442i) q^{64} +(1.67415 + 1.56302i) q^{66} +(-1.75146 + 9.93303i) q^{67} +(-1.02545 + 5.81562i) q^{68} +(1.39492 - 0.425568i) q^{69} +(-0.0447378 + 0.0774882i) q^{71} +(-3.70607 - 8.35047i) q^{72} +(-2.66057 - 4.60824i) q^{73} +(-2.58391 - 0.940468i) q^{74} +(-0.169564 - 0.142281i) q^{76} +(-2.89841 + 1.05493i) q^{77} +(-8.29554 - 0.439660i) q^{78} +(0.829503 + 4.70435i) q^{79} +(8.79889 + 1.89198i) q^{81} +8.59571 q^{82} +(-1.39625 - 7.91851i) q^{83} +(3.77887 + 0.200278i) q^{84} +(3.49486 + 2.93254i) q^{86} +(-0.107636 - 0.880922i) q^{87} +(3.58913 + 1.30634i) q^{88} +(-3.35189 - 5.80564i) q^{89} +(5.59359 - 9.68839i) q^{91} +(0.573026 - 0.480826i) q^{92} +(1.35847 - 0.414450i) q^{93} +(-0.970760 + 5.50545i) q^{94} +(-5.79693 - 5.41213i) q^{96} +(-4.20603 + 3.52928i) q^{97} +(-0.501915 + 0.869342i) q^{98} +(-3.12185 + 2.10036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.183082 1.03831i −0.129458 0.734194i −0.978560 0.205964i \(-0.933967\pi\)
0.849101 0.528230i \(-0.177144\pi\)
\(3\) 1.72962 + 0.0916693i 0.998598 + 0.0529253i
\(4\) 0.834822 0.303850i 0.417411 0.151925i
\(5\) 0 0
\(6\) −0.221481 1.81266i −0.0904194 0.740017i
\(7\) 2.31094 + 0.841112i 0.873452 + 0.317910i 0.739564 0.673086i \(-0.235032\pi\)
0.133888 + 0.990997i \(0.457254\pi\)
\(8\) −1.52266 2.63732i −0.538340 0.932432i
\(9\) 2.98319 + 0.317107i 0.994398 + 0.105702i
\(10\) 0 0
\(11\) −0.960783 + 0.806193i −0.289687 + 0.243076i −0.776036 0.630688i \(-0.782773\pi\)
0.486349 + 0.873764i \(0.338328\pi\)
\(12\) 1.47178 0.449019i 0.424867 0.129621i
\(13\) 0.789931 4.47992i 0.219087 1.24251i −0.654584 0.755989i \(-0.727156\pi\)
0.873671 0.486517i \(-0.161733\pi\)
\(14\) 0.450243 2.55345i 0.120332 0.682439i
\(15\) 0 0
\(16\) −1.09847 + 0.921724i −0.274617 + 0.230431i
\(17\) −3.32358 + 5.75662i −0.806088 + 1.39618i 0.109467 + 0.993990i \(0.465086\pi\)
−0.915554 + 0.402194i \(0.868248\pi\)
\(18\) −0.216914 3.15553i −0.0511270 0.743765i
\(19\) −0.124578 0.215776i −0.0285802 0.0495023i 0.851382 0.524547i \(-0.175765\pi\)
−0.879962 + 0.475045i \(0.842432\pi\)
\(20\) 0 0
\(21\) 3.91994 + 1.66665i 0.855402 + 0.363693i
\(22\) 1.01298 + 0.849989i 0.215967 + 0.181218i
\(23\) 0.791222 0.287981i 0.164981 0.0600483i −0.258209 0.966089i \(-0.583132\pi\)
0.423190 + 0.906041i \(0.360910\pi\)
\(24\) −2.39186 4.70115i −0.488236 0.959617i
\(25\) 0 0
\(26\) −4.79615 −0.940603
\(27\) 5.13073 + 0.821942i 0.987410 + 0.158183i
\(28\) 2.18479 0.412887
\(29\) −0.0889744 0.504599i −0.0165221 0.0937016i 0.975432 0.220302i \(-0.0707044\pi\)
−0.991954 + 0.126601i \(0.959593\pi\)
\(30\) 0 0
\(31\) 0.770551 0.280458i 0.138395 0.0503717i −0.271894 0.962327i \(-0.587650\pi\)
0.410289 + 0.911956i \(0.365428\pi\)
\(32\) −3.50754 2.94318i −0.620052 0.520286i
\(33\) −1.73570 + 1.30634i −0.302146 + 0.227404i
\(34\) 6.58563 + 2.39697i 1.12943 + 0.411077i
\(35\) 0 0
\(36\) 2.58679 0.641717i 0.431131 0.106953i
\(37\) 1.30403 2.25865i 0.214381 0.371319i −0.738700 0.674035i \(-0.764560\pi\)
0.953081 + 0.302715i \(0.0978931\pi\)
\(38\) −0.201233 + 0.168855i −0.0326444 + 0.0273919i
\(39\) 1.77695 7.67616i 0.284540 1.22917i
\(40\) 0 0
\(41\) −1.41572 + 8.02895i −0.221099 + 1.25391i 0.648906 + 0.760869i \(0.275227\pi\)
−0.870005 + 0.493044i \(0.835884\pi\)
\(42\) 1.01282 4.37524i 0.156282 0.675114i
\(43\) −3.31478 + 2.78143i −0.505500 + 0.424165i −0.859542 0.511065i \(-0.829251\pi\)
0.354042 + 0.935229i \(0.384807\pi\)
\(44\) −0.557121 + 0.964962i −0.0839891 + 0.145473i
\(45\) 0 0
\(46\) −0.443871 0.768808i −0.0654452 0.113354i
\(47\) −4.98256 1.81351i −0.726782 0.264527i −0.0479798 0.998848i \(-0.515278\pi\)
−0.678802 + 0.734321i \(0.737501\pi\)
\(48\) −1.98443 + 1.49354i −0.286428 + 0.215574i
\(49\) −0.729356 0.612002i −0.104194 0.0874289i
\(50\) 0 0
\(51\) −6.27625 + 9.65211i −0.878851 + 1.35157i
\(52\) −0.701774 3.97996i −0.0973185 0.551921i
\(53\) 10.4841 1.44010 0.720052 0.693920i \(-0.244118\pi\)
0.720052 + 0.693920i \(0.244118\pi\)
\(54\) −0.0859140 5.47776i −0.0116914 0.745429i
\(55\) 0 0
\(56\) −1.30048 7.37539i −0.173784 0.985578i
\(57\) −0.195693 0.384630i −0.0259202 0.0509456i
\(58\) −0.507639 + 0.184765i −0.0666563 + 0.0242609i
\(59\) −2.30289 1.93235i −0.299810 0.251571i 0.480455 0.877019i \(-0.340471\pi\)
−0.780265 + 0.625449i \(0.784916\pi\)
\(60\) 0 0
\(61\) −2.70930 0.986103i −0.346890 0.126258i 0.162699 0.986676i \(-0.447980\pi\)
−0.509589 + 0.860418i \(0.670202\pi\)
\(62\) −0.432275 0.748722i −0.0548990 0.0950878i
\(63\) 6.62725 + 3.24201i 0.834955 + 0.408455i
\(64\) −3.84771 + 6.66442i −0.480963 + 0.833053i
\(65\) 0 0
\(66\) 1.67415 + 1.56302i 0.206074 + 0.192394i
\(67\) −1.75146 + 9.93303i −0.213975 + 1.21351i 0.668701 + 0.743531i \(0.266851\pi\)
−0.882676 + 0.469982i \(0.844261\pi\)
\(68\) −1.02545 + 5.81562i −0.124354 + 0.705248i
\(69\) 1.39492 0.425568i 0.167928 0.0512324i
\(70\) 0 0
\(71\) −0.0447378 + 0.0774882i −0.00530940 + 0.00919615i −0.868668 0.495395i \(-0.835023\pi\)
0.863358 + 0.504591i \(0.168357\pi\)
\(72\) −3.70607 8.35047i −0.436764 0.984112i
\(73\) −2.66057 4.60824i −0.311396 0.539354i 0.667269 0.744817i \(-0.267463\pi\)
−0.978665 + 0.205463i \(0.934130\pi\)
\(74\) −2.58391 0.940468i −0.300374 0.109327i
\(75\) 0 0
\(76\) −0.169564 0.142281i −0.0194503 0.0163208i
\(77\) −2.89841 + 1.05493i −0.330304 + 0.120221i
\(78\) −8.29554 0.439660i −0.939285 0.0497817i
\(79\) 0.829503 + 4.70435i 0.0933264 + 0.529280i 0.995247 + 0.0973792i \(0.0310460\pi\)
−0.901921 + 0.431901i \(0.857843\pi\)
\(80\) 0 0
\(81\) 8.79889 + 1.89198i 0.977654 + 0.210220i
\(82\) 8.59571 0.949238
\(83\) −1.39625 7.91851i −0.153258 0.869169i −0.960361 0.278759i \(-0.910077\pi\)
0.807103 0.590410i \(-0.201034\pi\)
\(84\) 3.77887 + 0.200278i 0.412308 + 0.0218522i
\(85\) 0 0
\(86\) 3.49486 + 2.93254i 0.376860 + 0.316223i
\(87\) −0.107636 0.880922i −0.0115398 0.0944448i
\(88\) 3.58913 + 1.30634i 0.382602 + 0.139256i
\(89\) −3.35189 5.80564i −0.355299 0.615396i 0.631870 0.775074i \(-0.282288\pi\)
−0.987169 + 0.159678i \(0.948954\pi\)
\(90\) 0 0
\(91\) 5.59359 9.68839i 0.586368 1.01562i
\(92\) 0.573026 0.480826i 0.0597421 0.0501296i
\(93\) 1.35847 0.414450i 0.140867 0.0429765i
\(94\) −0.970760 + 5.50545i −0.100126 + 0.567844i
\(95\) 0 0
\(96\) −5.79693 5.41213i −0.591647 0.552373i
\(97\) −4.20603 + 3.52928i −0.427057 + 0.358344i −0.830840 0.556511i \(-0.812140\pi\)
0.403783 + 0.914855i \(0.367695\pi\)
\(98\) −0.501915 + 0.869342i −0.0507010 + 0.0878168i
\(99\) −3.12185 + 2.10036i −0.313758 + 0.211094i
\(100\) 0 0
\(101\) −4.70360 1.71197i −0.468025 0.170347i 0.0972322 0.995262i \(-0.469001\pi\)
−0.565258 + 0.824914i \(0.691223\pi\)
\(102\) 11.1709 + 4.74956i 1.10609 + 0.470276i
\(103\) −8.90079 7.46865i −0.877021 0.735908i 0.0885431 0.996072i \(-0.471779\pi\)
−0.965564 + 0.260164i \(0.916223\pi\)
\(104\) −13.0178 + 4.73808i −1.27650 + 0.464607i
\(105\) 0 0
\(106\) −1.91945 10.8857i −0.186433 1.05732i
\(107\) −19.4581 −1.88109 −0.940544 0.339673i \(-0.889684\pi\)
−0.940544 + 0.339673i \(0.889684\pi\)
\(108\) 4.53300 0.872799i 0.436188 0.0839852i
\(109\) 6.31515 0.604881 0.302441 0.953168i \(-0.402199\pi\)
0.302441 + 0.953168i \(0.402199\pi\)
\(110\) 0 0
\(111\) 2.46253 3.78707i 0.233733 0.359453i
\(112\) −3.31376 + 1.20611i −0.313121 + 0.113967i
\(113\) 5.29775 + 4.44534i 0.498371 + 0.418183i 0.857015 0.515292i \(-0.172316\pi\)
−0.358644 + 0.933474i \(0.616761\pi\)
\(114\) −0.363537 + 0.273608i −0.0340483 + 0.0256258i
\(115\) 0 0
\(116\) −0.227600 0.394215i −0.0211322 0.0366020i
\(117\) 3.77713 13.1140i 0.349196 1.21239i
\(118\) −1.58476 + 2.74488i −0.145889 + 0.252687i
\(119\) −12.5226 + 10.5077i −1.14794 + 0.963236i
\(120\) 0 0
\(121\) −1.63697 + 9.28373i −0.148816 + 0.843976i
\(122\) −0.527856 + 2.99362i −0.0477898 + 0.271030i
\(123\) −3.18467 + 13.7573i −0.287152 + 1.24045i
\(124\) 0.558056 0.468265i 0.0501149 0.0420514i
\(125\) 0 0
\(126\) 2.15288 7.47467i 0.191794 0.665897i
\(127\) 6.01162 + 10.4124i 0.533445 + 0.923954i 0.999237 + 0.0390598i \(0.0124363\pi\)
−0.465792 + 0.884894i \(0.654230\pi\)
\(128\) −0.981117 0.357098i −0.0867194 0.0315633i
\(129\) −5.98830 + 4.50697i −0.527240 + 0.396817i
\(130\) 0 0
\(131\) 13.2354 4.81728i 1.15638 0.420888i 0.308577 0.951199i \(-0.400147\pi\)
0.847803 + 0.530311i \(0.177925\pi\)
\(132\) −1.05207 + 1.61795i −0.0915706 + 0.140824i
\(133\) −0.106401 0.603428i −0.00922610 0.0523238i
\(134\) 10.6342 0.918655
\(135\) 0 0
\(136\) 20.2427 1.73580
\(137\) −0.392122 2.22383i −0.0335012 0.189995i 0.963465 0.267836i \(-0.0863085\pi\)
−0.996966 + 0.0778409i \(0.975197\pi\)
\(138\) −0.697254 1.37044i −0.0593542 0.116659i
\(139\) 7.49414 2.72764i 0.635644 0.231356i −0.00404179 0.999992i \(-0.501287\pi\)
0.639686 + 0.768636i \(0.279064\pi\)
\(140\) 0 0
\(141\) −8.45172 3.59343i −0.711763 0.302621i
\(142\) 0.0886472 + 0.0322649i 0.00743911 + 0.00270761i
\(143\) 2.85273 + 4.94107i 0.238557 + 0.413193i
\(144\) −3.56923 + 2.40135i −0.297436 + 0.200113i
\(145\) 0 0
\(146\) −4.29767 + 3.60617i −0.355678 + 0.298449i
\(147\) −1.20541 1.12539i −0.0994204 0.0928208i
\(148\) 0.402343 2.28180i 0.0330724 0.187563i
\(149\) −0.0185697 + 0.105314i −0.00152129 + 0.00862764i −0.985559 0.169333i \(-0.945839\pi\)
0.984038 + 0.177960i \(0.0569499\pi\)
\(150\) 0 0
\(151\) −15.5196 + 13.0225i −1.26297 + 1.05976i −0.267609 + 0.963528i \(0.586233\pi\)
−0.995359 + 0.0962282i \(0.969322\pi\)
\(152\) −0.379379 + 0.657104i −0.0307717 + 0.0532982i
\(153\) −11.7404 + 16.1192i −0.949152 + 1.30316i
\(154\) 1.62599 + 2.81630i 0.131026 + 0.226944i
\(155\) 0 0
\(156\) −0.848964 6.94816i −0.0679716 0.556298i
\(157\) 15.8953 + 13.3377i 1.26858 + 1.06447i 0.994712 + 0.102701i \(0.0327485\pi\)
0.273871 + 0.961767i \(0.411696\pi\)
\(158\) 4.73269 1.72256i 0.376513 0.137039i
\(159\) 18.1336 + 0.961071i 1.43809 + 0.0762179i
\(160\) 0 0
\(161\) 2.07069 0.163193
\(162\) 0.353543 9.48234i 0.0277770 0.745003i
\(163\) 20.1346 1.57706 0.788531 0.614995i \(-0.210842\pi\)
0.788531 + 0.614995i \(0.210842\pi\)
\(164\) 1.25773 + 7.13292i 0.0982119 + 0.556987i
\(165\) 0 0
\(166\) −7.96622 + 2.89947i −0.618298 + 0.225042i
\(167\) 15.2156 + 12.7674i 1.17742 + 0.987974i 0.999993 + 0.00383999i \(0.00122231\pi\)
0.177429 + 0.984134i \(0.443222\pi\)
\(168\) −1.57325 12.8759i −0.121378 0.993395i
\(169\) −7.22968 2.63139i −0.556130 0.202415i
\(170\) 0 0
\(171\) −0.303217 0.683205i −0.0231876 0.0522460i
\(172\) −1.92212 + 3.32920i −0.146560 + 0.253849i
\(173\) −14.4975 + 12.1648i −1.10222 + 0.924875i −0.997573 0.0696342i \(-0.977817\pi\)
−0.104650 + 0.994509i \(0.533372\pi\)
\(174\) −0.894962 + 0.273040i −0.0678469 + 0.0206991i
\(175\) 0 0
\(176\) 0.312302 1.77115i 0.0235407 0.133506i
\(177\) −3.80599 3.55334i −0.286075 0.267085i
\(178\) −5.41436 + 4.54319i −0.405824 + 0.340527i
\(179\) −5.45683 + 9.45151i −0.407863 + 0.706439i −0.994650 0.103302i \(-0.967059\pi\)
0.586787 + 0.809741i \(0.300392\pi\)
\(180\) 0 0
\(181\) 8.97393 + 15.5433i 0.667027 + 1.15532i 0.978731 + 0.205146i \(0.0657668\pi\)
−0.311704 + 0.950179i \(0.600900\pi\)
\(182\) −11.0836 4.03410i −0.821572 0.299028i
\(183\) −4.59567 1.95395i −0.339721 0.144440i
\(184\) −1.96426 1.64821i −0.144807 0.121507i
\(185\) 0 0
\(186\) −0.679038 1.33463i −0.0497895 0.0978601i
\(187\) −1.44770 8.21031i −0.105866 0.600397i
\(188\) −4.71059 −0.343555
\(189\) 11.1654 + 6.21498i 0.812167 + 0.452073i
\(190\) 0 0
\(191\) −4.68261 26.5564i −0.338822 1.92155i −0.385641 0.922649i \(-0.626020\pi\)
0.0468192 0.998903i \(-0.485092\pi\)
\(192\) −7.26601 + 11.1742i −0.524379 + 0.806430i
\(193\) −16.1202 + 5.86729i −1.16036 + 0.422337i −0.849226 0.528029i \(-0.822931\pi\)
−0.311135 + 0.950366i \(0.600709\pi\)
\(194\) 4.43452 + 3.72100i 0.318380 + 0.267152i
\(195\) 0 0
\(196\) −0.794839 0.289298i −0.0567742 0.0206641i
\(197\) 1.25612 + 2.17567i 0.0894951 + 0.155010i 0.907298 0.420489i \(-0.138141\pi\)
−0.817803 + 0.575499i \(0.804808\pi\)
\(198\) 2.75237 + 2.85690i 0.195602 + 0.203031i
\(199\) −9.26942 + 16.0551i −0.657092 + 1.13812i 0.324273 + 0.945964i \(0.394880\pi\)
−0.981365 + 0.192153i \(0.938453\pi\)
\(200\) 0 0
\(201\) −3.93992 + 17.0198i −0.277901 + 1.20049i
\(202\) −0.916408 + 5.19721i −0.0644783 + 0.365674i
\(203\) 0.218810 1.24093i 0.0153574 0.0870964i
\(204\) −2.30676 + 9.96484i −0.161505 + 0.697678i
\(205\) 0 0
\(206\) −6.12519 + 10.6091i −0.426762 + 0.739173i
\(207\) 2.45169 0.608202i 0.170404 0.0422730i
\(208\) 3.26154 + 5.64915i 0.226147 + 0.391698i
\(209\) 0.293649 + 0.106880i 0.0203121 + 0.00739301i
\(210\) 0 0
\(211\) −2.82761 2.37264i −0.194661 0.163340i 0.540248 0.841506i \(-0.318330\pi\)
−0.734908 + 0.678166i \(0.762775\pi\)
\(212\) 8.75237 3.18560i 0.601115 0.218788i
\(213\) −0.0844829 + 0.129924i −0.00578867 + 0.00890226i
\(214\) 3.56242 + 20.2035i 0.243522 + 1.38108i
\(215\) 0 0
\(216\) −5.64462 14.7829i −0.384067 1.00585i
\(217\) 2.01659 0.136895
\(218\) −1.15619 6.55706i −0.0783069 0.444100i
\(219\) −4.17935 8.21441i −0.282414 0.555079i
\(220\) 0 0
\(221\) 23.1638 + 19.4367i 1.55816 + 1.30746i
\(222\) −4.38299 1.86352i −0.294167 0.125071i
\(223\) −19.9601 7.26487i −1.33662 0.486491i −0.427876 0.903837i \(-0.640738\pi\)
−0.908748 + 0.417346i \(0.862960\pi\)
\(224\) −5.63017 9.75174i −0.376181 0.651565i
\(225\) 0 0
\(226\) 3.64571 6.31456i 0.242509 0.420038i
\(227\) 10.9851 9.21761i 0.729108 0.611794i −0.200781 0.979636i \(-0.564348\pi\)
0.929888 + 0.367842i \(0.119903\pi\)
\(228\) −0.280239 0.261637i −0.0185593 0.0173273i
\(229\) 2.93219 16.6293i 0.193765 1.09889i −0.720403 0.693556i \(-0.756043\pi\)
0.914167 0.405337i \(-0.132846\pi\)
\(230\) 0 0
\(231\) −5.10985 + 1.55894i −0.336204 + 0.102571i
\(232\) −1.19531 + 1.00298i −0.0784759 + 0.0658491i
\(233\) 2.79972 4.84926i 0.183416 0.317686i −0.759626 0.650361i \(-0.774618\pi\)
0.943042 + 0.332675i \(0.107951\pi\)
\(234\) −14.3079 1.52089i −0.935334 0.0994238i
\(235\) 0 0
\(236\) −2.50964 0.913436i −0.163364 0.0594596i
\(237\) 1.00348 + 8.21279i 0.0651833 + 0.533478i
\(238\) 13.2028 + 11.0785i 0.855813 + 0.718112i
\(239\) 4.95620 1.80391i 0.320590 0.116685i −0.176712 0.984263i \(-0.556546\pi\)
0.497302 + 0.867577i \(0.334324\pi\)
\(240\) 0 0
\(241\) −1.54590 8.76723i −0.0995801 0.564747i −0.993247 0.116017i \(-0.962987\pi\)
0.893667 0.448730i \(-0.148124\pi\)
\(242\) 9.93907 0.638907
\(243\) 15.0453 + 4.07900i 0.965158 + 0.261668i
\(244\) −2.56141 −0.163977
\(245\) 0 0
\(246\) 14.8673 + 0.787963i 0.947908 + 0.0502387i
\(247\) −1.06507 + 0.387652i −0.0677685 + 0.0246657i
\(248\) −1.91294 1.60515i −0.121472 0.101927i
\(249\) −1.68910 13.8240i −0.107042 0.876062i
\(250\) 0 0
\(251\) 3.89010 + 6.73786i 0.245541 + 0.425290i 0.962284 0.272048i \(-0.0877010\pi\)
−0.716742 + 0.697338i \(0.754368\pi\)
\(252\) 6.51766 + 0.692812i 0.410574 + 0.0436431i
\(253\) −0.528024 + 0.914565i −0.0331966 + 0.0574982i
\(254\) 9.71069 8.14824i 0.609303 0.511266i
\(255\) 0 0
\(256\) −2.86374 + 16.2411i −0.178984 + 1.01507i
\(257\) 3.54877 20.1261i 0.221366 1.25543i −0.648145 0.761517i \(-0.724455\pi\)
0.869511 0.493913i \(-0.164434\pi\)
\(258\) 5.77597 + 5.39255i 0.359596 + 0.335726i
\(259\) 4.91331 4.12275i 0.305298 0.256175i
\(260\) 0 0
\(261\) −0.105416 1.53353i −0.00652510 0.0949231i
\(262\) −7.42498 12.8604i −0.458717 0.794520i
\(263\) 10.5996 + 3.85792i 0.653596 + 0.237890i 0.647469 0.762092i \(-0.275827\pi\)
0.00612723 + 0.999981i \(0.498050\pi\)
\(264\) 6.08809 + 2.58848i 0.374696 + 0.159310i
\(265\) 0 0
\(266\) −0.607063 + 0.220953i −0.0372214 + 0.0135475i
\(267\) −5.26530 10.3488i −0.322231 0.633338i
\(268\) 1.55600 + 8.82450i 0.0950476 + 0.539042i
\(269\) −0.307761 −0.0187645 −0.00938226 0.999956i \(-0.502987\pi\)
−0.00938226 + 0.999956i \(0.502987\pi\)
\(270\) 0 0
\(271\) −2.22251 −0.135008 −0.0675040 0.997719i \(-0.521504\pi\)
−0.0675040 + 0.997719i \(0.521504\pi\)
\(272\) −1.65516 9.38689i −0.100359 0.569164i
\(273\) 10.5629 16.2445i 0.639298 0.983162i
\(274\) −2.23723 + 0.814286i −0.135156 + 0.0491928i
\(275\) 0 0
\(276\) 1.03520 0.779119i 0.0623115 0.0468975i
\(277\) −21.9228 7.97924i −1.31721 0.479426i −0.414648 0.909982i \(-0.636095\pi\)
−0.902564 + 0.430556i \(0.858317\pi\)
\(278\) −4.20417 7.28184i −0.252149 0.436735i
\(279\) 2.38764 0.592313i 0.142944 0.0354608i
\(280\) 0 0
\(281\) 5.53502 4.64443i 0.330192 0.277064i −0.462586 0.886574i \(-0.653078\pi\)
0.792778 + 0.609511i \(0.208634\pi\)
\(282\) −2.18373 + 9.43337i −0.130039 + 0.561749i
\(283\) −1.23643 + 7.01212i −0.0734979 + 0.416827i 0.925753 + 0.378129i \(0.123432\pi\)
−0.999251 + 0.0386985i \(0.987679\pi\)
\(284\) −0.0138033 + 0.0782824i −0.000819076 + 0.00464521i
\(285\) 0 0
\(286\) 4.60806 3.86662i 0.272480 0.228638i
\(287\) −10.0249 + 17.3636i −0.591751 + 1.02494i
\(288\) −9.53038 9.89234i −0.561583 0.582912i
\(289\) −13.5924 23.5428i −0.799555 1.38487i
\(290\) 0 0
\(291\) −7.59837 + 5.71875i −0.445424 + 0.335239i
\(292\) −3.62132 3.03865i −0.211922 0.177823i
\(293\) 0.519166 0.188961i 0.0303300 0.0110392i −0.326811 0.945090i \(-0.605974\pi\)
0.357141 + 0.934051i \(0.383752\pi\)
\(294\) −0.947815 + 1.45762i −0.0552777 + 0.0850103i
\(295\) 0 0
\(296\) −7.94236 −0.461640
\(297\) −5.59216 + 3.34665i −0.324490 + 0.194192i
\(298\) 0.112748 0.00653131
\(299\) −0.665122 3.77210i −0.0384650 0.218146i
\(300\) 0 0
\(301\) −9.99975 + 3.63961i −0.576376 + 0.209784i
\(302\) 16.3627 + 13.7299i 0.941568 + 0.790069i
\(303\) −7.97852 3.39224i −0.458354 0.194879i
\(304\) 0.335731 + 0.122196i 0.0192555 + 0.00700842i
\(305\) 0 0
\(306\) 18.8861 + 9.23898i 1.07965 + 0.528157i
\(307\) 3.36438 5.82728i 0.192015 0.332580i −0.753903 0.656986i \(-0.771831\pi\)
0.945918 + 0.324406i \(0.105164\pi\)
\(308\) −2.09911 + 1.76136i −0.119608 + 0.100363i
\(309\) −14.7104 13.7339i −0.836844 0.781293i
\(310\) 0 0
\(311\) 2.67825 15.1891i 0.151870 0.861297i −0.809722 0.586814i \(-0.800382\pi\)
0.961592 0.274483i \(-0.0885068\pi\)
\(312\) −22.9502 + 7.00176i −1.29930 + 0.396397i
\(313\) 18.0487 15.1446i 1.02017 0.856025i 0.0305223 0.999534i \(-0.490283\pi\)
0.989649 + 0.143509i \(0.0458385\pi\)
\(314\) 10.9385 18.9461i 0.617297 1.06919i
\(315\) 0 0
\(316\) 2.12191 + 3.67525i 0.119367 + 0.206749i
\(317\) 6.81469 + 2.48034i 0.382751 + 0.139310i 0.526228 0.850344i \(-0.323606\pi\)
−0.143477 + 0.989654i \(0.545828\pi\)
\(318\) −2.32204 19.0042i −0.130213 1.06570i
\(319\) 0.492289 + 0.413079i 0.0275629 + 0.0231280i
\(320\) 0 0
\(321\) −33.6552 1.78371i −1.87845 0.0995571i
\(322\) −0.379105 2.15001i −0.0211267 0.119815i
\(323\) 1.65618 0.0921525
\(324\) 7.92038 1.09408i 0.440021 0.0607821i
\(325\) 0 0
\(326\) −3.68627 20.9059i −0.204164 1.15787i
\(327\) 10.9228 + 0.578905i 0.604034 + 0.0320135i
\(328\) 23.3306 8.49163i 1.28821 0.468872i
\(329\) −9.98903 8.38179i −0.550713 0.462103i
\(330\) 0 0
\(331\) −27.2835 9.93037i −1.49964 0.545823i −0.543669 0.839300i \(-0.682965\pi\)
−0.955966 + 0.293477i \(0.905188\pi\)
\(332\) −3.57166 6.18629i −0.196020 0.339517i
\(333\) 4.60641 6.32447i 0.252430 0.346579i
\(334\) 10.4708 18.1360i 0.572938 0.992357i
\(335\) 0 0
\(336\) −5.84213 + 1.78235i −0.318714 + 0.0972351i
\(337\) 0.201275 1.14149i 0.0109641 0.0621807i −0.978835 0.204652i \(-0.934394\pi\)
0.989799 + 0.142471i \(0.0455049\pi\)
\(338\) −1.40857 + 7.98839i −0.0766161 + 0.434511i
\(339\) 8.75561 + 8.17441i 0.475540 + 0.443973i
\(340\) 0 0
\(341\) −0.514230 + 0.890672i −0.0278471 + 0.0482326i
\(342\) −0.653863 + 0.439914i −0.0353569 + 0.0237878i
\(343\) −9.77810 16.9362i −0.527968 0.914467i
\(344\) 12.3828 + 4.50697i 0.667636 + 0.243000i
\(345\) 0 0
\(346\) 15.2851 + 12.8257i 0.821730 + 0.689513i
\(347\) 5.53452 2.01440i 0.297108 0.108139i −0.189165 0.981945i \(-0.560578\pi\)
0.486273 + 0.873807i \(0.338356\pi\)
\(348\) −0.357525 0.702708i −0.0191654 0.0376691i
\(349\) −5.31237 30.1279i −0.284364 1.61271i −0.707547 0.706666i \(-0.750198\pi\)
0.423183 0.906044i \(-0.360913\pi\)
\(350\) 0 0
\(351\) 7.73516 22.3360i 0.412872 1.19221i
\(352\) 5.74276 0.306090
\(353\) −6.41826 36.3997i −0.341609 1.93736i −0.348294 0.937385i \(-0.613239\pi\)
0.00668455 0.999978i \(-0.497872\pi\)
\(354\) −2.99265 + 4.60233i −0.159058 + 0.244611i
\(355\) 0 0
\(356\) −4.56227 3.82820i −0.241800 0.202894i
\(357\) −22.6225 + 17.0264i −1.19731 + 0.901131i
\(358\) 10.8126 + 3.93547i 0.571464 + 0.207996i
\(359\) 13.1880 + 22.8423i 0.696037 + 1.20557i 0.969830 + 0.243783i \(0.0783886\pi\)
−0.273792 + 0.961789i \(0.588278\pi\)
\(360\) 0 0
\(361\) 9.46896 16.4007i 0.498366 0.863196i
\(362\) 14.4958 12.1634i 0.761881 0.639294i
\(363\) −3.68238 + 15.9073i −0.193275 + 0.834917i
\(364\) 1.72583 9.78769i 0.0904583 0.513015i
\(365\) 0 0
\(366\) −1.18741 + 5.12944i −0.0620671 + 0.268120i
\(367\) 8.66636 7.27194i 0.452380 0.379592i −0.387938 0.921685i \(-0.626813\pi\)
0.840318 + 0.542093i \(0.182368\pi\)
\(368\) −0.603693 + 1.04563i −0.0314697 + 0.0545071i
\(369\) −6.76941 + 23.5030i −0.352401 + 1.22352i
\(370\) 0 0
\(371\) 24.2281 + 8.81831i 1.25786 + 0.457824i
\(372\) 1.00815 0.758765i 0.0522703 0.0393401i
\(373\) −4.47682 3.75650i −0.231801 0.194504i 0.519487 0.854478i \(-0.326123\pi\)
−0.751289 + 0.659974i \(0.770567\pi\)
\(374\) −8.25978 + 3.00631i −0.427103 + 0.155453i
\(375\) 0 0
\(376\) 2.80394 + 15.9019i 0.144602 + 0.820080i
\(377\) −2.33085 −0.120045
\(378\) 4.40887 12.7310i 0.226768 0.654813i
\(379\) 24.3265 1.24957 0.624783 0.780798i \(-0.285187\pi\)
0.624783 + 0.780798i \(0.285187\pi\)
\(380\) 0 0
\(381\) 9.44334 + 18.5607i 0.483797 + 0.950892i
\(382\) −26.7164 + 9.72397i −1.36693 + 0.497522i
\(383\) 2.92326 + 2.45291i 0.149372 + 0.125338i 0.714411 0.699726i \(-0.246695\pi\)
−0.565039 + 0.825064i \(0.691139\pi\)
\(384\) −1.66423 0.707583i −0.0849273 0.0361087i
\(385\) 0 0
\(386\) 9.04337 + 15.6636i 0.460295 + 0.797255i
\(387\) −10.7707 + 7.24642i −0.547503 + 0.368356i
\(388\) −2.43891 + 4.22432i −0.123817 + 0.214457i
\(389\) 8.30534 6.96901i 0.421097 0.353343i −0.407483 0.913213i \(-0.633593\pi\)
0.828580 + 0.559870i \(0.189149\pi\)
\(390\) 0 0
\(391\) −0.971896 + 5.51189i −0.0491509 + 0.278748i
\(392\) −0.503486 + 2.85541i −0.0254299 + 0.144220i
\(393\) 23.3338 7.11881i 1.17704 0.359096i
\(394\) 2.02904 1.70257i 0.102222 0.0857741i
\(395\) 0 0
\(396\) −1.96799 + 2.70200i −0.0988955 + 0.135781i
\(397\) −5.25461 9.10124i −0.263721 0.456778i 0.703507 0.710689i \(-0.251617\pi\)
−0.967228 + 0.253910i \(0.918283\pi\)
\(398\) 18.3672 + 6.68511i 0.920665 + 0.335094i
\(399\) −0.128717 1.05346i −0.00644392 0.0527388i
\(400\) 0 0
\(401\) −13.4992 + 4.91332i −0.674119 + 0.245359i −0.656320 0.754482i \(-0.727888\pi\)
−0.0177987 + 0.999842i \(0.505666\pi\)
\(402\) 18.3932 + 0.974829i 0.917367 + 0.0486201i
\(403\) −0.647746 3.67355i −0.0322665 0.182993i
\(404\) −4.44685 −0.221239
\(405\) 0 0
\(406\) −1.32853 −0.0659338
\(407\) 0.568014 + 3.22137i 0.0281554 + 0.159677i
\(408\) 35.0122 + 1.85563i 1.73336 + 0.0918675i
\(409\) −16.6159 + 6.04769i −0.821603 + 0.299039i −0.718408 0.695622i \(-0.755129\pi\)
−0.103195 + 0.994661i \(0.532907\pi\)
\(410\) 0 0
\(411\) −0.474366 3.88234i −0.0233988 0.191502i
\(412\) −9.69993 3.53049i −0.477881 0.173935i
\(413\) −3.69650 6.40252i −0.181893 0.315047i
\(414\) −1.08036 2.43426i −0.0530968 0.119637i
\(415\) 0 0
\(416\) −15.9559 + 13.3886i −0.782303 + 0.656431i
\(417\) 13.2121 4.03081i 0.646998 0.197390i
\(418\) 0.0572121 0.324466i 0.00279833 0.0158701i
\(419\) 1.58606 8.99500i 0.0774842 0.439435i −0.921243 0.388988i \(-0.872825\pi\)
0.998727 0.0504461i \(-0.0160643\pi\)
\(420\) 0 0
\(421\) 18.5344 15.5522i 0.903310 0.757967i −0.0675243 0.997718i \(-0.521510\pi\)
0.970835 + 0.239750i \(0.0770656\pi\)
\(422\) −1.94585 + 3.37031i −0.0947226 + 0.164064i
\(423\) −14.2889 6.99004i −0.694749 0.339867i
\(424\) −15.9637 27.6499i −0.775265 1.34280i
\(425\) 0 0
\(426\) 0.150369 + 0.0639324i 0.00728538 + 0.00309754i
\(427\) −5.43159 4.55764i −0.262853 0.220560i
\(428\) −16.2441 + 5.91236i −0.785187 + 0.285785i
\(429\) 4.48120 + 8.80769i 0.216354 + 0.425239i
\(430\) 0 0
\(431\) −29.5332 −1.42256 −0.711282 0.702907i \(-0.751885\pi\)
−0.711282 + 0.702907i \(0.751885\pi\)
\(432\) −6.39355 + 3.82624i −0.307610 + 0.184090i
\(433\) −0.669754 −0.0321863 −0.0160932 0.999870i \(-0.505123\pi\)
−0.0160932 + 0.999870i \(0.505123\pi\)
\(434\) −0.369201 2.09384i −0.0177222 0.100508i
\(435\) 0 0
\(436\) 5.27203 1.91886i 0.252484 0.0918967i
\(437\) −0.160708 0.134850i −0.00768772 0.00645076i
\(438\) −7.76392 + 5.84336i −0.370975 + 0.279206i
\(439\) 5.96599 + 2.17144i 0.284741 + 0.103637i 0.480442 0.877026i \(-0.340476\pi\)
−0.195701 + 0.980664i \(0.562698\pi\)
\(440\) 0 0
\(441\) −1.98174 2.05700i −0.0943685 0.0979526i
\(442\) 15.9404 27.6096i 0.758209 1.31326i
\(443\) −11.7618 + 9.86931i −0.558819 + 0.468905i −0.877914 0.478818i \(-0.841066\pi\)
0.319095 + 0.947723i \(0.396621\pi\)
\(444\) 0.905072 3.90977i 0.0429528 0.185550i
\(445\) 0 0
\(446\) −3.88884 + 22.0547i −0.184142 + 1.04432i
\(447\) −0.0417726 + 0.180451i −0.00197577 + 0.00853503i
\(448\) −14.4973 + 12.1647i −0.684934 + 0.574728i
\(449\) 16.0199 27.7473i 0.756027 1.30948i −0.188836 0.982009i \(-0.560471\pi\)
0.944862 0.327468i \(-0.106195\pi\)
\(450\) 0 0
\(451\) −5.11268 8.85543i −0.240747 0.416986i
\(452\) 5.77340 + 2.10135i 0.271558 + 0.0988390i
\(453\) −28.0368 + 21.1013i −1.31729 + 0.991428i
\(454\) −11.5819 9.71835i −0.543565 0.456105i
\(455\) 0 0
\(456\) −0.716419 + 1.10176i −0.0335494 + 0.0515949i
\(457\) −3.32849 18.8768i −0.155700 0.883021i −0.958143 0.286291i \(-0.907578\pi\)
0.802442 0.596730i \(-0.203534\pi\)
\(458\) −17.8031 −0.831886
\(459\) −21.7840 + 26.8039i −1.01679 + 1.25110i
\(460\) 0 0
\(461\) −0.906494 5.14098i −0.0422196 0.239440i 0.956394 0.292080i \(-0.0943474\pi\)
−0.998614 + 0.0526405i \(0.983236\pi\)
\(462\) 2.55418 + 5.02019i 0.118831 + 0.233560i
\(463\) 1.59502 0.580541i 0.0741271 0.0269800i −0.304690 0.952451i \(-0.598553\pi\)
0.378818 + 0.925471i \(0.376331\pi\)
\(464\) 0.562837 + 0.472276i 0.0261290 + 0.0219249i
\(465\) 0 0
\(466\) −5.54760 2.01916i −0.256988 0.0935359i
\(467\) 9.84136 + 17.0457i 0.455404 + 0.788783i 0.998711 0.0507511i \(-0.0161615\pi\)
−0.543307 + 0.839534i \(0.682828\pi\)
\(468\) −0.831456 12.0955i −0.0384341 0.559115i
\(469\) −12.4023 + 21.4814i −0.572685 + 0.991920i
\(470\) 0 0
\(471\) 26.2702 + 24.5264i 1.21047 + 1.13012i
\(472\) −1.58972 + 9.01574i −0.0731727 + 0.414983i
\(473\) 0.942416 5.34471i 0.0433324 0.245750i
\(474\) 8.34368 2.54554i 0.383238 0.116920i
\(475\) 0 0
\(476\) −7.26134 + 12.5770i −0.332823 + 0.576467i
\(477\) 31.2761 + 3.32458i 1.43204 + 0.152222i
\(478\) −2.78040 4.81579i −0.127173 0.220269i
\(479\) 27.4892 + 10.0053i 1.25601 + 0.457152i 0.882430 0.470444i \(-0.155906\pi\)
0.373585 + 0.927596i \(0.378128\pi\)
\(480\) 0 0
\(481\) −9.08847 7.62613i −0.414398 0.347722i
\(482\) −8.82005 + 3.21024i −0.401742 + 0.146222i
\(483\) 3.58151 + 0.189818i 0.162964 + 0.00863704i
\(484\) 1.45429 + 8.24766i 0.0661039 + 0.374894i
\(485\) 0 0
\(486\) 1.48074 16.3685i 0.0671675 0.742488i
\(487\) 20.5056 0.929199 0.464600 0.885521i \(-0.346198\pi\)
0.464600 + 0.885521i \(0.346198\pi\)
\(488\) 1.52466 + 8.64677i 0.0690180 + 0.391421i
\(489\) 34.8252 + 1.84572i 1.57485 + 0.0834664i
\(490\) 0 0
\(491\) 13.4265 + 11.2661i 0.605927 + 0.508433i 0.893345 0.449372i \(-0.148352\pi\)
−0.287417 + 0.957805i \(0.592797\pi\)
\(492\) 1.52152 + 12.4526i 0.0685955 + 0.561404i
\(493\) 3.20050 + 1.16489i 0.144143 + 0.0524638i
\(494\) 0.597496 + 1.03489i 0.0268826 + 0.0465620i
\(495\) 0 0
\(496\) −0.587922 + 1.01831i −0.0263985 + 0.0457235i
\(497\) −0.168562 + 0.141441i −0.00756106 + 0.00634448i
\(498\) −14.0443 + 4.28473i −0.629342 + 0.192003i
\(499\) −3.31772 + 18.8157i −0.148522 + 0.842307i 0.815950 + 0.578122i \(0.196214\pi\)
−0.964472 + 0.264185i \(0.914897\pi\)
\(500\) 0 0
\(501\) 25.1469 + 23.4777i 1.12348 + 1.04890i
\(502\) 6.28376 5.27270i 0.280458 0.235332i
\(503\) −5.48381 + 9.49824i −0.244511 + 0.423506i −0.961994 0.273070i \(-0.911961\pi\)
0.717483 + 0.696576i \(0.245294\pi\)
\(504\) −1.54080 22.4146i −0.0686327 0.998426i
\(505\) 0 0
\(506\) 1.04627 + 0.380811i 0.0465124 + 0.0169291i
\(507\) −12.2634 5.21405i −0.544637 0.231564i
\(508\) 8.18246 + 6.86590i 0.363038 + 0.304625i
\(509\) 18.6993 6.80598i 0.828831 0.301670i 0.107452 0.994210i \(-0.465731\pi\)
0.721379 + 0.692540i \(0.243509\pi\)
\(510\) 0 0
\(511\) −2.27236 12.8872i −0.100523 0.570096i
\(512\) 15.2994 0.676143
\(513\) −0.461822 1.20948i −0.0203899 0.0534000i
\(514\) −21.5468 −0.950387
\(515\) 0 0
\(516\) −3.62972 + 5.58207i −0.159790 + 0.245737i
\(517\) 6.24920 2.27452i 0.274839 0.100033i
\(518\) −5.18022 4.34672i −0.227606 0.190984i
\(519\) −26.1903 + 19.7116i −1.14963 + 0.865243i
\(520\) 0 0
\(521\) −17.5583 30.4119i −0.769244 1.33237i −0.937973 0.346708i \(-0.887300\pi\)
0.168729 0.985662i \(-0.446034\pi\)
\(522\) −1.57298 + 0.390216i −0.0688473 + 0.0170793i
\(523\) −7.12269 + 12.3369i −0.311453 + 0.539453i −0.978677 0.205404i \(-0.934149\pi\)
0.667224 + 0.744857i \(0.267482\pi\)
\(524\) 9.58545 8.04315i 0.418742 0.351367i
\(525\) 0 0
\(526\) 2.06513 11.7119i 0.0900437 0.510663i
\(527\) −0.946505 + 5.36789i −0.0412304 + 0.233829i
\(528\) 0.702526 3.03480i 0.0305735 0.132073i
\(529\) −17.0759 + 14.3284i −0.742431 + 0.622974i
\(530\) 0 0
\(531\) −6.25719 6.49483i −0.271539 0.281852i
\(532\) −0.272177 0.471425i −0.0118004 0.0204389i
\(533\) 34.8507 + 12.6846i 1.50955 + 0.549433i
\(534\) −9.78128 + 7.36168i −0.423277 + 0.318571i
\(535\) 0 0
\(536\) 28.8634 10.5054i 1.24671 0.453765i
\(537\) −10.3047 + 15.8473i −0.444679 + 0.683862i
\(538\) 0.0563454 + 0.319550i 0.00242922 + 0.0137768i
\(539\) 1.19414 0.0514354
\(540\) 0 0
\(541\) −13.2368 −0.569094 −0.284547 0.958662i \(-0.591843\pi\)
−0.284547 + 0.958662i \(0.591843\pi\)
\(542\) 0.406901 + 2.30765i 0.0174779 + 0.0991222i
\(543\) 14.0967 + 27.7067i 0.604946 + 1.18901i
\(544\) 28.6004 10.4097i 1.22623 0.446312i
\(545\) 0 0
\(546\) −18.8007 7.99350i −0.804594 0.342090i
\(547\) −15.3216 5.57661i −0.655105 0.238439i −0.00698326 0.999976i \(-0.502223\pi\)
−0.648121 + 0.761537i \(0.724445\pi\)
\(548\) −1.00306 1.73736i −0.0428488 0.0742163i
\(549\) −7.76965 3.80087i −0.331601 0.162217i
\(550\) 0 0
\(551\) −0.0977958 + 0.0820605i −0.00416624 + 0.00349589i
\(552\) −3.24633 3.03084i −0.138173 0.129001i
\(553\) −2.03995 + 11.5692i −0.0867476 + 0.491970i
\(554\) −4.27124 + 24.2234i −0.181468 + 1.02915i
\(555\) 0 0
\(556\) 5.42748 4.55419i 0.230176 0.193141i
\(557\) 15.4486 26.7577i 0.654577 1.13376i −0.327422 0.944878i \(-0.606180\pi\)
0.982000 0.188883i \(-0.0604867\pi\)
\(558\) −1.05214 2.37066i −0.0445404 0.100358i
\(559\) 9.84215 + 17.0471i 0.416279 + 0.721016i
\(560\) 0 0
\(561\) −1.75134 14.3335i −0.0739417 0.605159i
\(562\) −5.83571 4.89674i −0.246165 0.206557i
\(563\) 25.1612 9.15791i 1.06042 0.385960i 0.247832 0.968803i \(-0.420282\pi\)
0.812585 + 0.582843i \(0.198060\pi\)
\(564\) −8.14755 0.431816i −0.343074 0.0181827i
\(565\) 0 0
\(566\) 7.50710 0.315547
\(567\) 18.7423 + 11.7731i 0.787102 + 0.494423i
\(568\) 0.272481 0.0114331
\(569\) 3.30985 + 18.7711i 0.138756 + 0.786924i 0.972170 + 0.234275i \(0.0752717\pi\)
−0.833414 + 0.552649i \(0.813617\pi\)
\(570\) 0 0
\(571\) 17.6420 6.42116i 0.738294 0.268717i 0.0546227 0.998507i \(-0.482604\pi\)
0.683671 + 0.729790i \(0.260382\pi\)
\(572\) 3.88286 + 3.25811i 0.162351 + 0.136228i
\(573\) −5.66474 46.3618i −0.236648 1.93679i
\(574\) 19.8641 + 7.22996i 0.829113 + 0.301773i
\(575\) 0 0
\(576\) −13.5918 + 18.6611i −0.566324 + 0.777547i
\(577\) −2.42981 + 4.20856i −0.101154 + 0.175204i −0.912161 0.409833i \(-0.865587\pi\)
0.811006 + 0.585038i \(0.198920\pi\)
\(578\) −21.9561 + 18.4234i −0.913254 + 0.766311i
\(579\) −28.4198 + 8.67047i −1.18109 + 0.360332i
\(580\) 0 0
\(581\) 3.43371 19.4736i 0.142454 0.807899i
\(582\) 7.32894 + 6.84244i 0.303795 + 0.283628i
\(583\) −10.0730 + 8.45221i −0.417179 + 0.350055i
\(584\) −8.10226 + 14.0335i −0.335274 + 0.580712i
\(585\) 0 0
\(586\) −0.291249 0.504459i −0.0120314 0.0208390i
\(587\) −30.8194 11.2174i −1.27205 0.462990i −0.384257 0.923226i \(-0.625542\pi\)
−0.887796 + 0.460236i \(0.847765\pi\)
\(588\) −1.34825 0.573239i −0.0556010 0.0236400i
\(589\) −0.156510 0.131327i −0.00644887 0.00541125i
\(590\) 0 0
\(591\) 1.97318 + 3.87824i 0.0811657 + 0.159529i
\(592\) 0.649414 + 3.68301i 0.0266908 + 0.151371i
\(593\) −17.3446 −0.712258 −0.356129 0.934437i \(-0.615904\pi\)
−0.356129 + 0.934437i \(0.615904\pi\)
\(594\) 4.49867 + 5.19367i 0.184583 + 0.213099i
\(595\) 0 0
\(596\) 0.0164973 + 0.0935607i 0.000675754 + 0.00383239i
\(597\) −17.5044 + 26.9196i −0.716406 + 1.10174i
\(598\) −3.79482 + 1.38120i −0.155182 + 0.0564816i
\(599\) 18.6975 + 15.6891i 0.763961 + 0.641039i 0.939155 0.343495i \(-0.111611\pi\)
−0.175194 + 0.984534i \(0.556055\pi\)
\(600\) 0 0
\(601\) −7.39563 2.69179i −0.301674 0.109800i 0.186748 0.982408i \(-0.440205\pi\)
−0.488422 + 0.872607i \(0.662427\pi\)
\(602\) 5.60981 + 9.71647i 0.228639 + 0.396014i
\(603\) −8.37478 + 29.0768i −0.341047 + 1.18410i
\(604\) −8.99922 + 15.5871i −0.366173 + 0.634230i
\(605\) 0 0
\(606\) −2.06147 + 8.90521i −0.0837413 + 0.361749i
\(607\) 1.77772 10.0819i 0.0721553 0.409213i −0.927241 0.374466i \(-0.877826\pi\)
0.999396 0.0347476i \(-0.0110627\pi\)
\(608\) −0.198103 + 1.12350i −0.00803414 + 0.0455639i
\(609\) 0.492214 2.12629i 0.0199455 0.0861615i
\(610\) 0 0
\(611\) −12.0602 + 20.8889i −0.487905 + 0.845076i
\(612\) −4.90329 + 17.0240i −0.198204 + 0.688153i
\(613\) 1.11753 + 1.93563i 0.0451368 + 0.0781792i 0.887711 0.460401i \(-0.152294\pi\)
−0.842574 + 0.538580i \(0.818961\pi\)
\(614\) −6.66646 2.42639i −0.269036 0.0979213i
\(615\) 0 0
\(616\) 7.19547 + 6.03771i 0.289914 + 0.243266i
\(617\) 31.9267 11.6204i 1.28532 0.467818i 0.393132 0.919482i \(-0.371391\pi\)
0.892188 + 0.451664i \(0.149169\pi\)
\(618\) −11.5668 + 17.7883i −0.465285 + 0.715551i
\(619\) −5.01079 28.4176i −0.201401 1.14220i −0.903004 0.429632i \(-0.858643\pi\)
0.701604 0.712567i \(-0.252468\pi\)
\(620\) 0 0
\(621\) 4.29625 0.827216i 0.172403 0.0331950i
\(622\) −16.2613 −0.652020
\(623\) −2.86280 16.2358i −0.114696 0.650472i
\(624\) 5.12338 + 10.0699i 0.205099 + 0.403118i
\(625\) 0 0
\(626\) −19.0292 15.9674i −0.760558 0.638184i
\(627\) 0.498105 + 0.211780i 0.0198924 + 0.00845768i
\(628\) 17.3224 + 6.30485i 0.691240 + 0.251591i
\(629\) 8.66811 + 15.0136i 0.345620 + 0.598632i
\(630\) 0 0
\(631\) 1.57039 2.71999i 0.0625162 0.108281i −0.833073 0.553163i \(-0.813421\pi\)
0.895590 + 0.444881i \(0.146754\pi\)
\(632\) 11.1438 9.35076i 0.443277 0.371953i
\(633\) −4.67320 4.36299i −0.185743 0.173413i
\(634\) 1.32772 7.52985i 0.0527303 0.299049i
\(635\) 0 0
\(636\) 15.4303 4.70757i 0.611852 0.186667i
\(637\) −3.31786 + 2.78402i −0.131458 + 0.110307i
\(638\) 0.338774 0.586774i 0.0134122 0.0232306i
\(639\) −0.158034 + 0.216976i −0.00625171 + 0.00858342i
\(640\) 0 0
\(641\) 29.9034 + 10.8839i 1.18111 + 0.429890i 0.856595 0.515989i \(-0.172576\pi\)
0.324518 + 0.945879i \(0.394798\pi\)
\(642\) 4.30961 + 35.2710i 0.170087 + 1.39204i
\(643\) 9.84142 + 8.25794i 0.388108 + 0.325661i 0.815876 0.578228i \(-0.196255\pi\)
−0.427768 + 0.903889i \(0.640700\pi\)
\(644\) 1.72866 0.629179i 0.0681186 0.0247931i
\(645\) 0 0
\(646\) −0.303217 1.71963i −0.0119299 0.0676578i
\(647\) −28.2444 −1.11040 −0.555200 0.831717i \(-0.687358\pi\)
−0.555200 + 0.831717i \(0.687358\pi\)
\(648\) −8.40792 26.0863i −0.330294 1.02477i
\(649\) 3.77042 0.148002
\(650\) 0 0
\(651\) 3.48794 + 0.184859i 0.136703 + 0.00724521i
\(652\) 16.8088 6.11790i 0.658283 0.239595i
\(653\) −19.9099 16.7064i −0.779134 0.653771i 0.163897 0.986477i \(-0.447594\pi\)
−0.943030 + 0.332707i \(0.892038\pi\)
\(654\) −1.39869 11.4472i −0.0546930 0.447622i
\(655\) 0 0
\(656\) −5.84536 10.1245i −0.228223 0.395294i
\(657\) −6.47569 14.5910i −0.252641 0.569248i
\(658\) −6.87407 + 11.9062i −0.267979 + 0.464153i
\(659\) −36.4774 + 30.6081i −1.42096 + 1.19232i −0.470131 + 0.882597i \(0.655793\pi\)
−0.950826 + 0.309727i \(0.899762\pi\)
\(660\) 0 0
\(661\) −0.152204 + 0.863192i −0.00592005 + 0.0335743i −0.987625 0.156836i \(-0.949871\pi\)
0.981705 + 0.190410i \(0.0609818\pi\)
\(662\) −5.31568 + 30.1467i −0.206600 + 1.17168i
\(663\) 38.2829 + 35.7416i 1.48678 + 1.38809i
\(664\) −18.7576 + 15.7395i −0.727936 + 0.610811i
\(665\) 0 0
\(666\) −7.41009 3.62497i −0.287135 0.140465i
\(667\) −0.215714 0.373627i −0.00835246 0.0144669i
\(668\) 16.5817 + 6.03526i 0.641567 + 0.233511i
\(669\) −33.8574 14.3952i −1.30900 0.556551i
\(670\) 0 0
\(671\) 3.39803 1.23678i 0.131180 0.0477455i
\(672\) −8.84413 17.3829i −0.341170 0.670562i
\(673\) −6.48393 36.7722i −0.249937 1.41746i −0.808742 0.588164i \(-0.799851\pi\)
0.558805 0.829299i \(-0.311260\pi\)
\(674\) −1.22206 −0.0470721
\(675\) 0 0
\(676\) −6.83505 −0.262886
\(677\) 2.38231 + 13.5107i 0.0915596 + 0.519260i 0.995747 + 0.0921251i \(0.0293660\pi\)
−0.904188 + 0.427135i \(0.859523\pi\)
\(678\) 6.88456 10.5876i 0.264400 0.406614i
\(679\) −12.6884 + 4.61819i −0.486935 + 0.177230i
\(680\) 0 0
\(681\) 19.8451 14.9360i 0.760465 0.572348i
\(682\) 1.01894 + 0.370863i 0.0390171 + 0.0142011i
\(683\) 24.9943 + 43.2914i 0.956381 + 1.65650i 0.731175 + 0.682190i \(0.238972\pi\)
0.225206 + 0.974311i \(0.427694\pi\)
\(684\) −0.460724 0.478222i −0.0176162 0.0182853i
\(685\) 0 0
\(686\) −15.7947 + 13.2534i −0.603046 + 0.506016i
\(687\) 6.59598 28.4936i 0.251652 1.08710i
\(688\) 1.07747 6.11064i 0.0410782 0.232966i
\(689\) 8.28172 46.9680i 0.315509 1.78934i
\(690\) 0 0
\(691\) 18.2434 15.3080i 0.694011 0.582345i −0.226052 0.974115i \(-0.572582\pi\)
0.920063 + 0.391771i \(0.128137\pi\)
\(692\) −8.40653 + 14.5605i −0.319568 + 0.553508i
\(693\) −8.98103 + 2.22797i −0.341161 + 0.0846335i
\(694\) −3.10483 5.37773i −0.117858 0.204136i
\(695\) 0 0
\(696\) −2.15938 + 1.62521i −0.0818510 + 0.0616035i
\(697\) −41.5144 34.8347i −1.57247 1.31946i
\(698\) −30.3094 + 11.0317i −1.14723 + 0.417557i
\(699\) 5.28700 8.13075i 0.199973 0.307533i
\(700\) 0 0
\(701\) 34.4493 1.30113 0.650565 0.759450i \(-0.274532\pi\)
0.650565 + 0.759450i \(0.274532\pi\)
\(702\) −24.6078 3.94216i −0.928761 0.148787i
\(703\) −0.649815 −0.0245082
\(704\) −1.67600 9.50506i −0.0631665 0.358235i
\(705\) 0 0
\(706\) −36.6191 + 13.3282i −1.37818 + 0.501615i
\(707\) −9.42975 7.91250i −0.354642 0.297580i
\(708\) −4.25701 1.80996i −0.159988 0.0680224i
\(709\) −14.5871 5.30927i −0.547830 0.199394i 0.0532520 0.998581i \(-0.483041\pi\)
−0.601082 + 0.799187i \(0.705264\pi\)
\(710\) 0 0
\(711\) 0.982789 + 14.2970i 0.0368575 + 0.536180i
\(712\) −10.2075 + 17.6800i −0.382543 + 0.662585i
\(713\) 0.528911 0.443809i 0.0198079 0.0166208i
\(714\) 21.8204 + 20.3719i 0.816607 + 0.762400i
\(715\) 0 0
\(716\) −1.68364 + 9.54839i −0.0629205 + 0.356840i
\(717\) 8.73772 2.66575i 0.326316 0.0995543i
\(718\) 21.3029 17.8752i 0.795016 0.667098i
\(719\) −6.02686 + 10.4388i −0.224764 + 0.389303i −0.956249 0.292555i \(-0.905494\pi\)
0.731485 + 0.681858i \(0.238828\pi\)
\(720\) 0 0
\(721\) −14.2872 24.7461i −0.532083 0.921594i
\(722\) −18.7626 6.82902i −0.698271 0.254150i
\(723\) −1.87014 15.3057i −0.0695512 0.569226i
\(724\) 12.2145 + 10.2492i 0.453947 + 0.380907i
\(725\) 0 0
\(726\) 17.1908 + 0.911107i 0.638012 + 0.0338144i
\(727\) 5.49253 + 31.1497i 0.203707 + 1.15528i 0.899462 + 0.437000i \(0.143959\pi\)
−0.695755 + 0.718279i \(0.744930\pi\)
\(728\) −34.0685 −1.26266
\(729\) 25.6488 + 8.43433i 0.949956 + 0.312383i
\(730\) 0 0
\(731\) −4.99469 28.3263i −0.184735 1.04769i
\(732\) −4.43027 0.234802i −0.163748 0.00867855i
\(733\) −17.8831 + 6.50891i −0.660527 + 0.240412i −0.650464 0.759537i \(-0.725425\pi\)
−0.0100630 + 0.999949i \(0.503203\pi\)
\(734\) −9.13716 7.66699i −0.337259 0.282994i
\(735\) 0 0
\(736\) −3.62283 1.31860i −0.133539 0.0486043i
\(737\) −6.32516 10.9555i −0.232990 0.403551i
\(738\) 25.6427 + 2.72576i 0.943920 + 0.100337i
\(739\) −8.30036 + 14.3767i −0.305334 + 0.528854i −0.977336 0.211696i \(-0.932101\pi\)
0.672002 + 0.740550i \(0.265435\pi\)
\(740\) 0 0
\(741\) −1.87770 + 0.572858i −0.0689789 + 0.0210445i
\(742\) 4.72040 26.7707i 0.173291 0.982783i
\(743\) 5.78310 32.7976i 0.212161 1.20323i −0.673604 0.739093i \(-0.735255\pi\)
0.885765 0.464134i \(-0.153634\pi\)
\(744\) −3.16152 2.95166i −0.115907 0.108213i
\(745\) 0 0
\(746\) −3.08078 + 5.33606i −0.112795 + 0.195367i
\(747\) −1.65426 24.0652i −0.0605263 0.880499i
\(748\) −3.70328 6.41426i −0.135405 0.234529i
\(749\) −44.9665 16.3665i −1.64304 0.598017i
\(750\) 0 0
\(751\) 21.2819 + 17.8577i 0.776589 + 0.651636i 0.942387 0.334524i \(-0.108576\pi\)
−0.165798 + 0.986160i \(0.553020\pi\)
\(752\) 7.14474 2.60047i 0.260542 0.0948295i
\(753\) 6.11076 + 12.0106i 0.222688 + 0.437689i
\(754\) 0.426735 + 2.42013i 0.0155408 + 0.0881361i
\(755\) 0 0
\(756\) 11.2096 + 1.79577i 0.407689 + 0.0653116i
\(757\) 3.12036 0.113411 0.0567057 0.998391i \(-0.481940\pi\)
0.0567057 + 0.998391i \(0.481940\pi\)
\(758\) −4.45373 25.2583i −0.161767 0.917424i
\(759\) −0.997121 + 1.53345i −0.0361932 + 0.0556607i
\(760\) 0 0
\(761\) −33.6747 28.2564i −1.22071 1.02429i −0.998787 0.0492297i \(-0.984323\pi\)
−0.221919 0.975065i \(-0.571232\pi\)
\(762\) 17.5428 13.2032i 0.635508 0.478302i
\(763\) 14.5939 + 5.31175i 0.528335 + 0.192298i
\(764\) −11.9783 20.7470i −0.433360 0.750602i
\(765\) 0 0
\(766\) 2.01168 3.48433i 0.0726849 0.125894i
\(767\) −10.4759 + 8.79032i −0.378263 + 0.317400i
\(768\) −6.44200 + 27.8284i −0.232456 + 1.00417i
\(769\) 0.644731 3.65645i 0.0232496 0.131855i −0.970974 0.239186i \(-0.923119\pi\)
0.994223 + 0.107331i \(0.0342305\pi\)
\(770\) 0 0
\(771\) 7.98298 34.4852i 0.287500 1.24195i
\(772\) −11.6748 + 9.79629i −0.420184 + 0.352576i
\(773\) −4.48452 + 7.76741i −0.161297 + 0.279374i −0.935334 0.353766i \(-0.884901\pi\)
0.774037 + 0.633140i \(0.218234\pi\)
\(774\) 9.49592 + 9.85656i 0.341324 + 0.354287i
\(775\) 0 0
\(776\) 15.7121 + 5.71875i 0.564033 + 0.205291i
\(777\) 8.87610 6.68041i 0.318428 0.239658i
\(778\) −8.75652 7.34760i −0.313937 0.263424i
\(779\) 1.90882 0.694754i 0.0683906 0.0248921i
\(780\) 0 0
\(781\) −0.0194871 0.110517i −0.000697302 0.00395459i
\(782\) 5.90098 0.211018
\(783\) −0.0417527 2.66209i −0.00149212 0.0951354i
\(784\) 1.36527 0.0487597
\(785\) 0 0
\(786\) −11.6635 22.9243i −0.416023 0.817684i
\(787\) 41.2069 14.9981i 1.46887 0.534624i 0.521074 0.853512i \(-0.325532\pi\)
0.947792 + 0.318888i \(0.103309\pi\)
\(788\) 1.70972 + 1.43462i 0.0609062 + 0.0511063i
\(789\) 17.9796 + 7.64441i 0.640090 + 0.272148i
\(790\) 0 0
\(791\) 8.50374 + 14.7289i 0.302358 + 0.523699i
\(792\) 10.2928 + 5.03519i 0.365739 + 0.178918i
\(793\) −6.55782 + 11.3585i −0.232875 + 0.403351i
\(794\) −8.48787 + 7.12217i −0.301223 + 0.252756i
\(795\) 0 0
\(796\) −2.85997 + 16.2197i −0.101369 + 0.574891i
\(797\) −2.08656 + 11.8335i −0.0739097 + 0.419163i 0.925294 + 0.379252i \(0.123819\pi\)
−0.999203 + 0.0399111i \(0.987293\pi\)
\(798\) −1.07025 + 0.326516i −0.0378863 + 0.0115586i
\(799\) 26.9996 22.6554i 0.955178 0.801490i
\(800\) 0 0
\(801\) −8.15832 18.3822i −0.288260 0.649504i
\(802\) 7.57299 + 13.1168i 0.267412 + 0.463171i
\(803\) 6.27136 + 2.28259i 0.221311 + 0.0805508i
\(804\) 1.88235 + 15.4057i 0.0663855 + 0.543317i
\(805\) 0 0
\(806\) −3.69568 + 1.34512i −0.130175 + 0.0473798i
\(807\) −0.532311 0.0282122i −0.0187382 0.000993117i
\(808\) 2.64695 + 15.0116i 0.0931195 + 0.528107i
\(809\) −8.02937 −0.282298 −0.141149 0.989988i \(-0.545080\pi\)
−0.141149 + 0.989988i \(0.545080\pi\)
\(810\) 0 0
\(811\) −12.8345 −0.450681 −0.225341 0.974280i \(-0.572349\pi\)
−0.225341 + 0.974280i \(0.572349\pi\)
\(812\) −0.194391 1.10244i −0.00682177 0.0386882i
\(813\) −3.84411 0.203736i −0.134819 0.00714534i
\(814\) 3.24078 1.17955i 0.113589 0.0413431i
\(815\) 0 0
\(816\) −2.00232 16.3875i −0.0700951 0.573678i
\(817\) 1.01312 + 0.368744i 0.0354444 + 0.0129007i
\(818\) 9.32142 + 16.1452i 0.325916 + 0.564503i
\(819\) 19.7590 27.1286i 0.690436 0.947949i
\(820\) 0 0
\(821\) −22.7250 + 19.0685i −0.793108 + 0.665497i −0.946513 0.322667i \(-0.895421\pi\)
0.153404 + 0.988163i \(0.450976\pi\)
\(822\) −3.94422 + 1.20332i −0.137570 + 0.0419707i
\(823\) −8.60266 + 48.7881i −0.299870 + 1.70065i 0.346852 + 0.937920i \(0.387251\pi\)
−0.646722 + 0.762726i \(0.723861\pi\)
\(824\) −6.14436 + 34.8464i −0.214049 + 1.21393i
\(825\) 0 0
\(826\) −5.97102 + 5.01028i −0.207758 + 0.174330i
\(827\) 20.4215 35.3711i 0.710126 1.22997i −0.254683 0.967025i \(-0.581971\pi\)
0.964809 0.262950i \(-0.0846955\pi\)
\(828\) 1.86192 1.25269i 0.0647063 0.0435339i
\(829\) 4.72638 + 8.18633i 0.164154 + 0.284323i 0.936355 0.351056i \(-0.114177\pi\)
−0.772201 + 0.635379i \(0.780844\pi\)
\(830\) 0 0
\(831\) −37.1867 15.8107i −1.28999 0.548468i
\(832\) 26.8167 + 22.5018i 0.929700 + 0.780111i
\(833\) 5.94714 2.16458i 0.206056 0.0749983i
\(834\) −6.60411 12.9802i −0.228682 0.449468i
\(835\) 0 0
\(836\) 0.277620 0.00960170
\(837\) 4.18401 0.805605i 0.144621 0.0278458i
\(838\) −9.62995 −0.332661
\(839\) −2.13360 12.1002i −0.0736599 0.417746i −0.999232 0.0391756i \(-0.987527\pi\)
0.925572 0.378571i \(-0.123584\pi\)
\(840\) 0 0
\(841\) 27.0044 9.82879i 0.931186 0.338924i
\(842\) −19.5413 16.3971i −0.673436 0.565080i
\(843\) 9.99925 7.52573i 0.344392 0.259200i
\(844\) −3.08148 1.12157i −0.106069 0.0386059i
\(845\) 0 0
\(846\) −4.64178 + 16.1160i −0.159588 + 0.554079i
\(847\) −11.5916 + 20.0772i −0.398292 + 0.689862i
\(848\) −11.5165 + 9.66346i −0.395477 + 0.331845i
\(849\) −2.78135 + 12.0150i −0.0954556 + 0.412353i
\(850\) 0 0
\(851\) 0.381330 2.16263i 0.0130718 0.0741339i
\(852\) −0.0310506 + 0.134134i −0.00106378 + 0.00459535i
\(853\) 23.6446 19.8402i 0.809576 0.679315i −0.140930 0.990020i \(-0.545009\pi\)
0.950507 + 0.310704i \(0.100565\pi\)
\(854\) −3.73781 + 6.47408i −0.127905 + 0.221538i
\(855\) 0 0
\(856\) 29.6280 + 51.3172i 1.01266 + 1.75399i
\(857\) 10.4738 + 3.81217i 0.357780 + 0.130221i 0.514655 0.857397i \(-0.327920\pi\)
−0.156876 + 0.987618i \(0.550142\pi\)
\(858\) 8.32466 6.26539i 0.284199 0.213897i
\(859\) 3.17807 + 2.66672i 0.108434 + 0.0909872i 0.695393 0.718630i \(-0.255230\pi\)
−0.586958 + 0.809617i \(0.699675\pi\)
\(860\) 0 0
\(861\) −18.9310 + 29.1135i −0.645167 + 0.992187i
\(862\) 5.40698 + 30.6645i 0.184163 + 1.04444i
\(863\) 47.2534 1.60852 0.804262 0.594275i \(-0.202561\pi\)
0.804262 + 0.594275i \(0.202561\pi\)
\(864\) −15.5771 17.9837i −0.529945 0.611817i
\(865\) 0 0
\(866\) 0.122620 + 0.695411i 0.00416678 + 0.0236310i
\(867\) −21.3516 41.9662i −0.725140 1.42525i
\(868\) 1.68349 0.612742i 0.0571415 0.0207978i
\(869\) −4.58958 3.85112i −0.155691 0.130640i
\(870\) 0 0
\(871\) 43.1156 + 15.6928i 1.46092 + 0.531731i
\(872\) −9.61579 16.6550i −0.325632 0.564011i
\(873\) −13.6665 + 9.19475i −0.462543 + 0.311195i
\(874\) −0.110593 + 0.191553i −0.00374087 + 0.00647938i
\(875\) 0 0
\(876\) −5.98497 5.58768i −0.202213 0.188790i
\(877\) −6.10381 + 34.6164i −0.206111 + 1.16891i 0.689571 + 0.724218i \(0.257799\pi\)
−0.895682 + 0.444695i \(0.853312\pi\)
\(878\) 1.16236 6.59208i 0.0392278 0.222472i
\(879\) 0.915284 0.279240i 0.0308718 0.00941852i
\(880\) 0 0
\(881\) 9.67981 16.7659i 0.326121 0.564858i −0.655618 0.755093i \(-0.727592\pi\)
0.981739 + 0.190235i \(0.0609250\pi\)
\(882\) −1.77298 + 2.43425i −0.0596994 + 0.0819656i
\(883\) −6.89302 11.9391i −0.231969 0.401781i 0.726419 0.687252i \(-0.241183\pi\)
−0.958387 + 0.285471i \(0.907850\pi\)
\(884\) 25.2435 + 9.18788i 0.849031 + 0.309022i
\(885\) 0 0
\(886\) 12.4007 + 10.4055i 0.416611 + 0.349578i
\(887\) −28.0192 + 10.1982i −0.940794 + 0.342421i −0.766479 0.642269i \(-0.777993\pi\)
−0.174315 + 0.984690i \(0.555771\pi\)
\(888\) −13.7373 0.728070i −0.460993 0.0244324i
\(889\) 5.13445 + 29.1189i 0.172204 + 0.976617i
\(890\) 0 0
\(891\) −9.97912 + 5.27581i −0.334313 + 0.176746i
\(892\) −18.8705 −0.631832
\(893\) 0.229408 + 1.30104i 0.00767685 + 0.0435376i
\(894\) 0.195011 + 0.0103355i 0.00652215 + 0.000345671i
\(895\) 0 0
\(896\) −1.96694 1.65046i −0.0657109 0.0551380i
\(897\) −0.804626 6.58528i −0.0268657 0.219876i
\(898\) −31.7432 11.5536i −1.05928 0.385548i
\(899\) −0.210078 0.363866i −0.00700649 0.0121356i
\(900\) 0 0
\(901\) −34.8448 + 60.3530i −1.16085 + 2.01065i
\(902\) −8.25862 + 6.92980i −0.274982 + 0.230737i
\(903\) −17.6294 + 5.37849i −0.586671 + 0.178985i
\(904\) 3.65712 20.7406i 0.121634 0.689821i
\(905\) 0 0
\(906\) 27.0427 + 25.2476i 0.898434 + 0.838795i
\(907\) 4.77366 4.00558i 0.158507 0.133003i −0.560085 0.828435i \(-0.689231\pi\)
0.718592 + 0.695432i \(0.244787\pi\)
\(908\) 6.36984 11.0329i 0.211391 0.366139i
\(909\) −13.4889 6.59868i −0.447397 0.218864i
\(910\) 0 0
\(911\) 29.7314 + 10.8213i 0.985044 + 0.358527i 0.783799 0.621014i \(-0.213279\pi\)
0.201245 + 0.979541i \(0.435501\pi\)
\(912\) 0.569486 + 0.242129i 0.0188576 + 0.00801770i
\(913\) 7.72533 + 6.48232i 0.255671 + 0.214534i
\(914\) −18.9906 + 6.91200i −0.628152 + 0.228629i
\(915\) 0 0
\(916\) −2.60496 14.7734i −0.0860701 0.488128i
\(917\) 34.6380 1.14385
\(918\) 31.8189 + 17.7112i 1.05018 + 0.584557i
\(919\) 36.0031 1.18763 0.593816 0.804601i \(-0.297621\pi\)
0.593816 + 0.804601i \(0.297621\pi\)
\(920\) 0 0
\(921\) 6.35329 9.77058i 0.209348 0.321952i
\(922\) −5.17196 + 1.88244i −0.170329 + 0.0619948i
\(923\) 0.311801 + 0.261632i 0.0102631 + 0.00861173i
\(924\) −3.79213 + 2.85407i −0.124752 + 0.0938921i
\(925\) 0 0
\(926\) −0.894800 1.54984i −0.0294049 0.0509309i
\(927\) −24.1844 25.1029i −0.794321 0.824489i
\(928\) −1.17304 + 2.03177i −0.0385070 + 0.0666961i
\(929\) 19.4941 16.3575i 0.639580 0.536672i −0.264309 0.964438i \(-0.585144\pi\)
0.903889 + 0.427767i \(0.140699\pi\)
\(930\) 0 0
\(931\) −0.0411934 + 0.233619i −0.00135006 + 0.00765656i
\(932\) 0.863820 4.89897i 0.0282954 0.160471i
\(933\) 6.02475 26.0260i 0.197241 0.852052i
\(934\) 15.8969 13.3391i 0.520164 0.436469i
\(935\) 0 0
\(936\) −40.3370 + 10.0066i −1.31846 + 0.327075i
\(937\) 14.1524 + 24.5127i 0.462338 + 0.800794i 0.999077 0.0429549i \(-0.0136772\pi\)
−0.536739 + 0.843749i \(0.680344\pi\)
\(938\) 24.5750 + 8.94455i 0.802401 + 0.292050i
\(939\) 32.6057 24.5400i 1.06405 0.800833i
\(940\) 0 0
\(941\) −7.79422 + 2.83687i −0.254084 + 0.0924792i −0.465922 0.884826i \(-0.654277\pi\)
0.211838 + 0.977305i \(0.432055\pi\)
\(942\) 20.6563 31.7669i 0.673019 1.03502i
\(943\) 1.19204 + 6.76039i 0.0388181 + 0.220149i
\(944\) 4.31074 0.140303
\(945\) 0 0
\(946\) −5.72199 −0.186038
\(947\) 7.71877 + 43.7753i 0.250826 + 1.42251i 0.806563 + 0.591148i \(0.201325\pi\)
−0.555737 + 0.831358i \(0.687564\pi\)
\(948\) 3.33319 + 6.55131i 0.108257 + 0.212777i
\(949\) −22.7462 + 8.27895i −0.738373 + 0.268746i
\(950\) 0 0
\(951\) 11.5595 + 4.91476i 0.374842 + 0.159372i
\(952\) 46.7796 + 17.0264i 1.51613 + 0.551828i
\(953\) −4.83574 8.37576i −0.156645 0.271317i 0.777012 0.629486i \(-0.216735\pi\)
−0.933657 + 0.358169i \(0.883401\pi\)
\(954\) −2.27415 33.0829i −0.0736283 1.07110i
\(955\) 0 0
\(956\) 3.58942 3.01188i 0.116090 0.0974113i
\(957\) 0.813608 + 0.759599i 0.0263002 + 0.0245544i
\(958\) 5.35576 30.3740i 0.173037 0.981341i
\(959\) 0.964325 5.46896i 0.0311397 0.176602i
\(960\) 0 0
\(961\) −23.2323 + 19.4942i −0.749429 + 0.628845i
\(962\) −6.25433 + 10.8328i −0.201648 + 0.349264i
\(963\) −58.0473 6.17030i −1.87055 0.198835i
\(964\) −3.95448 6.84936i −0.127365 0.220603i
\(965\) 0 0
\(966\) −0.458619 3.75346i −0.0147558 0.120766i
\(967\) 25.3676 + 21.2860i 0.815768 + 0.684510i 0.951977 0.306170i \(-0.0990475\pi\)
−0.136209 + 0.990680i \(0.543492\pi\)
\(968\) 26.9767 9.81871i 0.867064 0.315585i
\(969\) 2.86457 + 0.151821i 0.0920234 + 0.00487720i
\(970\) 0 0
\(971\) −27.4309 −0.880298 −0.440149 0.897925i \(-0.645074\pi\)
−0.440149 + 0.897925i \(0.645074\pi\)
\(972\) 13.7996 1.16629i 0.442622 0.0374087i
\(973\) 19.6127 0.628755
\(974\) −3.75420 21.2912i −0.120292 0.682213i
\(975\) 0 0
\(976\) 3.88499 1.41402i 0.124356 0.0452617i
\(977\) −27.8668 23.3831i −0.891539 0.748090i 0.0769792 0.997033i \(-0.475473\pi\)
−0.968518 + 0.248943i \(0.919917\pi\)
\(978\) −4.45943 36.4972i −0.142597 1.16705i
\(979\) 7.90089 + 2.87569i 0.252514 + 0.0919075i
\(980\) 0 0
\(981\) 18.8393 + 2.00258i 0.601493 + 0.0639373i
\(982\) 9.23957 16.0034i 0.294847 0.510689i
\(983\) −32.2790 + 27.0853i −1.02954 + 0.863886i −0.990796 0.135363i \(-0.956780\pi\)
−0.0387434 + 0.999249i \(0.512335\pi\)
\(984\) 41.1315 12.5486i 1.31122 0.400035i
\(985\) 0 0
\(986\) 0.623557 3.53637i 0.0198581 0.112621i
\(987\) −16.5089 15.4130i −0.525484 0.490602i
\(988\) −0.771352 + 0.647241i −0.0245400 + 0.0205915i
\(989\) −1.82173 + 3.15533i −0.0579276 + 0.100334i
\(990\) 0 0
\(991\) −12.7705 22.1191i −0.405667 0.702635i 0.588732 0.808328i \(-0.299627\pi\)
−0.994399 + 0.105693i \(0.966294\pi\)
\(992\) −3.52818 1.28415i −0.112020 0.0407719i
\(993\) −46.2798 19.6769i −1.46865 0.624426i
\(994\) 0.177720 + 0.149124i 0.00563692 + 0.00472994i
\(995\) 0 0
\(996\) −5.61053 11.0274i −0.177776 0.349416i
\(997\) −4.08644 23.1754i −0.129419 0.733971i −0.978585 0.205845i \(-0.934006\pi\)
0.849166 0.528126i \(-0.177105\pi\)
\(998\) 20.1439 0.637644
\(999\) 8.54711 10.5167i 0.270419 0.332733i
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 675.2.l.c.526.1 12
5.2 odd 4 675.2.u.b.499.3 24
5.3 odd 4 675.2.u.b.499.2 24
5.4 even 2 27.2.e.a.13.2 12
15.14 odd 2 81.2.e.a.10.1 12
20.19 odd 2 432.2.u.c.337.2 12
27.25 even 9 inner 675.2.l.c.376.1 12
45.4 even 6 243.2.e.d.190.1 12
45.14 odd 6 243.2.e.a.190.2 12
45.29 odd 6 243.2.e.b.109.1 12
45.34 even 6 243.2.e.c.109.2 12
135.4 even 18 729.2.c.e.487.2 12
135.14 odd 18 729.2.c.b.244.5 12
135.29 odd 18 81.2.e.a.73.1 12
135.34 even 18 243.2.e.c.136.2 12
135.49 even 18 729.2.a.a.1.5 6
135.52 odd 36 675.2.u.b.349.2 24
135.59 odd 18 729.2.a.d.1.2 6
135.74 odd 18 243.2.e.b.136.1 12
135.79 even 18 27.2.e.a.25.2 yes 12
135.94 even 18 729.2.c.e.244.2 12
135.104 odd 18 729.2.c.b.487.5 12
135.119 odd 18 243.2.e.a.55.2 12
135.124 even 18 243.2.e.d.55.1 12
135.133 odd 36 675.2.u.b.349.3 24
540.79 odd 18 432.2.u.c.241.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.13.2 12 5.4 even 2
27.2.e.a.25.2 yes 12 135.79 even 18
81.2.e.a.10.1 12 15.14 odd 2
81.2.e.a.73.1 12 135.29 odd 18
243.2.e.a.55.2 12 135.119 odd 18
243.2.e.a.190.2 12 45.14 odd 6
243.2.e.b.109.1 12 45.29 odd 6
243.2.e.b.136.1 12 135.74 odd 18
243.2.e.c.109.2 12 45.34 even 6
243.2.e.c.136.2 12 135.34 even 18
243.2.e.d.55.1 12 135.124 even 18
243.2.e.d.190.1 12 45.4 even 6
432.2.u.c.241.2 12 540.79 odd 18
432.2.u.c.337.2 12 20.19 odd 2
675.2.l.c.376.1 12 27.25 even 9 inner
675.2.l.c.526.1 12 1.1 even 1 trivial
675.2.u.b.349.2 24 135.52 odd 36
675.2.u.b.349.3 24 135.133 odd 36
675.2.u.b.499.2 24 5.3 odd 4
675.2.u.b.499.3 24 5.2 odd 4
729.2.a.a.1.5 6 135.49 even 18
729.2.a.d.1.2 6 135.59 odd 18
729.2.c.b.244.5 12 135.14 odd 18
729.2.c.b.487.5 12 135.104 odd 18
729.2.c.e.244.2 12 135.94 even 18
729.2.c.e.487.2 12 135.4 even 18