Properties

Label 675.2.u.a.124.2
Level $675$
Weight $2$
Character 675.124
Analytic conductor $5.390$
Analytic rank $0$
Dimension $12$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(49,675)]
 
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, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.u (of order \(18\), degree \(6\), not 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 \(\Q(\zeta_{18})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 124.2
Root \(-0.342020 - 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 675.124
Dual form 675.2.u.a.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62760 - 1.93969i) q^{2} +(1.32683 - 1.11334i) q^{3} +(-0.766044 - 4.34445i) q^{4} -4.38571i q^{6} +(3.01763 + 0.532089i) q^{7} +(-5.28801 - 3.05303i) q^{8} +(0.520945 - 2.95442i) q^{9} +O(q^{10})\) \(q+(1.62760 - 1.93969i) q^{2} +(1.32683 - 1.11334i) q^{3} +(-0.766044 - 4.34445i) q^{4} -4.38571i q^{6} +(3.01763 + 0.532089i) q^{7} +(-5.28801 - 3.05303i) q^{8} +(0.520945 - 2.95442i) q^{9} +(-5.29813 + 1.92836i) q^{11} +(-5.85327 - 4.91147i) q^{12} +(2.71686 + 3.23783i) q^{13} +(5.94356 - 4.98724i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(1.43128 - 0.826352i) q^{17} +(-4.88279 - 5.81908i) q^{18} +(0.120615 - 0.208911i) q^{19} +(4.59627 - 2.65366i) q^{21} +(-4.88279 + 13.4153i) q^{22} +(-7.34013 + 1.29426i) q^{23} +(-10.4153 + 1.83651i) q^{24} +10.7023 q^{26} +(-2.59808 - 4.50000i) q^{27} -13.5175i q^{28} +(5.90033 + 4.95096i) q^{29} +(0.858441 + 4.86846i) q^{31} +(-1.57202 + 4.31908i) q^{32} +(-4.88279 + 8.45723i) q^{33} +(0.726682 - 4.12122i) q^{34} -13.2344 q^{36} +(2.15658 - 1.24510i) q^{37} +(-0.208911 - 0.573978i) q^{38} +(7.20961 + 1.27125i) q^{39} +(-0.109470 + 0.0918566i) q^{41} +(2.33359 - 13.2344i) q^{42} +(0.256867 + 0.705737i) q^{43} +(12.4363 + 21.5403i) q^{44} +(-9.43629 + 16.3441i) q^{46} +(-4.58202 - 0.807934i) q^{47} +(-5.74881 + 9.95723i) q^{48} +(2.24510 + 0.817150i) q^{49} +(0.979055 - 2.68993i) q^{51} +(11.9854 - 14.2836i) q^{52} +12.1061i q^{53} +(-12.9572 - 2.28471i) q^{54} +(-14.3327 - 12.0266i) q^{56} +(-0.0725540 - 0.411474i) q^{57} +(19.2067 - 3.38666i) q^{58} +(-4.45336 - 1.62089i) q^{59} +(2.41488 - 13.6955i) q^{61} +(10.8405 + 6.25877i) q^{62} +(3.14403 - 8.63816i) q^{63} +(-0.819078 - 1.41868i) q^{64} +(8.45723 + 23.2361i) q^{66} +(-4.73708 - 5.64543i) q^{67} +(-4.68647 - 5.58512i) q^{68} +(-8.29813 + 9.88933i) q^{69} +(2.45084 + 4.24497i) q^{71} +(-11.7747 + 14.0326i) q^{72} +(0.196312 + 0.113341i) q^{73} +(1.09492 - 6.20961i) q^{74} +(-1.00000 - 0.363970i) q^{76} +(-17.0138 + 3.00000i) q^{77} +(14.2002 - 11.9153i) q^{78} +(7.53596 + 6.32342i) q^{79} +(-8.45723 - 3.07818i) q^{81} +0.361844i q^{82} +(5.69323 - 6.78493i) q^{83} +(-15.0496 - 17.9355i) q^{84} +(1.78699 + 0.650411i) q^{86} +13.3408 q^{87} +(33.9039 + 5.97818i) q^{88} +(3.33022 - 5.76811i) q^{89} +(6.47565 + 11.2162i) q^{91} +(11.2457 + 30.8974i) q^{92} +(6.55926 + 5.50387i) q^{93} +(-9.02481 + 7.57272i) q^{94} +(2.72281 + 7.48086i) q^{96} +(-3.26017 - 8.95723i) q^{97} +(5.23913 - 3.02481i) q^{98} +(2.93717 + 16.6575i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 36 q^{11} + 12 q^{14} - 36 q^{16} + 24 q^{19} - 36 q^{24} + 24 q^{26} + 42 q^{29} - 6 q^{31} - 18 q^{34} - 36 q^{36} + 18 q^{39} - 36 q^{41} + 54 q^{44} - 18 q^{46} + 24 q^{49} + 18 q^{51} - 54 q^{54} - 96 q^{56} + 72 q^{61} + 24 q^{64} - 72 q^{69} + 6 q^{71} - 24 q^{74} - 12 q^{76} + 24 q^{79} - 72 q^{84} + 6 q^{86} - 6 q^{89} - 54 q^{94} + 54 q^{96} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62760 1.93969i 1.15088 1.37157i 0.234087 0.972216i \(-0.424790\pi\)
0.916797 0.399354i \(-0.130766\pi\)
\(3\) 1.32683 1.11334i 0.766044 0.642788i
\(4\) −0.766044 4.34445i −0.383022 2.17223i
\(5\) 0 0
\(6\) 4.38571i 1.79046i
\(7\) 3.01763 + 0.532089i 1.14056 + 0.201111i 0.711849 0.702333i \(-0.247858\pi\)
0.428707 + 0.903444i \(0.358969\pi\)
\(8\) −5.28801 3.05303i −1.86959 1.07941i
\(9\) 0.520945 2.95442i 0.173648 0.984808i
\(10\) 0 0
\(11\) −5.29813 + 1.92836i −1.59745 + 0.581423i −0.978903 0.204326i \(-0.934500\pi\)
−0.618545 + 0.785750i \(0.712277\pi\)
\(12\) −5.85327 4.91147i −1.68969 1.41782i
\(13\) 2.71686 + 3.23783i 0.753521 + 0.898011i 0.997420 0.0717893i \(-0.0228709\pi\)
−0.243899 + 0.969801i \(0.578426\pi\)
\(14\) 5.94356 4.98724i 1.58848 1.33290i
\(15\) 0 0
\(16\) −6.23783 + 2.27038i −1.55946 + 0.567596i
\(17\) 1.43128 0.826352i 0.347137 0.200420i −0.316286 0.948664i \(-0.602436\pi\)
0.663424 + 0.748244i \(0.269103\pi\)
\(18\) −4.88279 5.81908i −1.15088 1.37157i
\(19\) 0.120615 0.208911i 0.0276709 0.0479274i −0.851858 0.523772i \(-0.824524\pi\)
0.879529 + 0.475845i \(0.157858\pi\)
\(20\) 0 0
\(21\) 4.59627 2.65366i 1.00299 0.579075i
\(22\) −4.88279 + 13.4153i −1.04101 + 2.86016i
\(23\) −7.34013 + 1.29426i −1.53052 + 0.269872i −0.874559 0.484920i \(-0.838849\pi\)
−0.655964 + 0.754792i \(0.727738\pi\)
\(24\) −10.4153 + 1.83651i −2.12602 + 0.374875i
\(25\) 0 0
\(26\) 10.7023 2.09890
\(27\) −2.59808 4.50000i −0.500000 0.866025i
\(28\) 13.5175i 2.55458i
\(29\) 5.90033 + 4.95096i 1.09566 + 0.919371i 0.997126 0.0757623i \(-0.0241390\pi\)
0.0985378 + 0.995133i \(0.468583\pi\)
\(30\) 0 0
\(31\) 0.858441 + 4.86846i 0.154181 + 0.874401i 0.959531 + 0.281602i \(0.0908659\pi\)
−0.805351 + 0.592799i \(0.798023\pi\)
\(32\) −1.57202 + 4.31908i −0.277896 + 0.763512i
\(33\) −4.88279 + 8.45723i −0.849984 + 1.47222i
\(34\) 0.726682 4.12122i 0.124625 0.706783i
\(35\) 0 0
\(36\) −13.2344 −2.20574
\(37\) 2.15658 1.24510i 0.354539 0.204693i −0.312144 0.950035i \(-0.601047\pi\)
0.666683 + 0.745342i \(0.267714\pi\)
\(38\) −0.208911 0.573978i −0.0338898 0.0931115i
\(39\) 7.20961 + 1.27125i 1.15446 + 0.203563i
\(40\) 0 0
\(41\) −0.109470 + 0.0918566i −0.0170964 + 0.0143456i −0.651296 0.758824i \(-0.725774\pi\)
0.634199 + 0.773170i \(0.281330\pi\)
\(42\) 2.33359 13.2344i 0.360080 2.04212i
\(43\) 0.256867 + 0.705737i 0.0391719 + 0.107624i 0.957737 0.287647i \(-0.0928730\pi\)
−0.918565 + 0.395271i \(0.870651\pi\)
\(44\) 12.4363 + 21.5403i 1.87484 + 3.24732i
\(45\) 0 0
\(46\) −9.43629 + 16.3441i −1.39130 + 2.40981i
\(47\) −4.58202 0.807934i −0.668356 0.117849i −0.170833 0.985300i \(-0.554646\pi\)
−0.497523 + 0.867451i \(0.665757\pi\)
\(48\) −5.74881 + 9.95723i −0.829769 + 1.43720i
\(49\) 2.24510 + 0.817150i 0.320729 + 0.116736i
\(50\) 0 0
\(51\) 0.979055 2.68993i 0.137095 0.376666i
\(52\) 11.9854 14.2836i 1.66207 1.98078i
\(53\) 12.1061i 1.66290i 0.555602 + 0.831448i \(0.312488\pi\)
−0.555602 + 0.831448i \(0.687512\pi\)
\(54\) −12.9572 2.28471i −1.76326 0.310910i
\(55\) 0 0
\(56\) −14.3327 12.0266i −1.91529 1.60712i
\(57\) −0.0725540 0.411474i −0.00961001 0.0545011i
\(58\) 19.2067 3.38666i 2.52196 0.444690i
\(59\) −4.45336 1.62089i −0.579779 0.211022i 0.0354493 0.999371i \(-0.488714\pi\)
−0.615228 + 0.788349i \(0.710936\pi\)
\(60\) 0 0
\(61\) 2.41488 13.6955i 0.309193 1.75352i −0.293885 0.955841i \(-0.594948\pi\)
0.603078 0.797682i \(-0.293941\pi\)
\(62\) 10.8405 + 6.25877i 1.37675 + 0.794865i
\(63\) 3.14403 8.63816i 0.396111 1.08831i
\(64\) −0.819078 1.41868i −0.102385 0.177336i
\(65\) 0 0
\(66\) 8.45723 + 23.2361i 1.04101 + 2.86016i
\(67\) −4.73708 5.64543i −0.578726 0.689699i 0.394671 0.918822i \(-0.370859\pi\)
−0.973397 + 0.229123i \(0.926414\pi\)
\(68\) −4.68647 5.58512i −0.568318 0.677296i
\(69\) −8.29813 + 9.88933i −0.998978 + 1.19054i
\(70\) 0 0
\(71\) 2.45084 + 4.24497i 0.290861 + 0.503786i 0.974014 0.226490i \(-0.0727250\pi\)
−0.683153 + 0.730276i \(0.739392\pi\)
\(72\) −11.7747 + 14.0326i −1.38766 + 1.65375i
\(73\) 0.196312 + 0.113341i 0.0229766 + 0.0132655i 0.511444 0.859316i \(-0.329111\pi\)
−0.488468 + 0.872582i \(0.662444\pi\)
\(74\) 1.09492 6.20961i 0.127282 0.721853i
\(75\) 0 0
\(76\) −1.00000 0.363970i −0.114708 0.0417502i
\(77\) −17.0138 + 3.00000i −1.93891 + 0.341882i
\(78\) 14.2002 11.9153i 1.60785 1.34915i
\(79\) 7.53596 + 6.32342i 0.847862 + 0.711440i 0.959318 0.282329i \(-0.0911070\pi\)
−0.111456 + 0.993769i \(0.535551\pi\)
\(80\) 0 0
\(81\) −8.45723 3.07818i −0.939693 0.342020i
\(82\) 0.361844i 0.0399590i
\(83\) 5.69323 6.78493i 0.624913 0.744743i −0.356994 0.934107i \(-0.616198\pi\)
0.981907 + 0.189364i \(0.0606426\pi\)
\(84\) −15.0496 17.9355i −1.64205 1.95692i
\(85\) 0 0
\(86\) 1.78699 + 0.650411i 0.192696 + 0.0701356i
\(87\) 13.3408 1.43029
\(88\) 33.9039 + 5.97818i 3.61417 + 0.637276i
\(89\) 3.33022 5.76811i 0.353003 0.611419i −0.633771 0.773521i \(-0.718494\pi\)
0.986774 + 0.162102i \(0.0518273\pi\)
\(90\) 0 0
\(91\) 6.47565 + 11.2162i 0.678833 + 1.17577i
\(92\) 11.2457 + 30.8974i 1.17245 + 3.22128i
\(93\) 6.55926 + 5.50387i 0.680163 + 0.570725i
\(94\) −9.02481 + 7.57272i −0.930839 + 0.781066i
\(95\) 0 0
\(96\) 2.72281 + 7.48086i 0.277896 + 0.763512i
\(97\) −3.26017 8.95723i −0.331020 0.909469i −0.987847 0.155428i \(-0.950324\pi\)
0.656827 0.754041i \(-0.271898\pi\)
\(98\) 5.23913 3.02481i 0.529232 0.305552i
\(99\) 2.93717 + 16.6575i 0.295196 + 1.67414i
\(100\) 0 0
\(101\) −0.405078 + 2.29731i −0.0403067 + 0.228591i −0.998306 0.0581793i \(-0.981470\pi\)
0.957999 + 0.286770i \(0.0925816\pi\)
\(102\) −3.62414 6.27719i −0.358843 0.621534i
\(103\) −6.37462 + 17.5141i −0.628110 + 1.72572i 0.0580946 + 0.998311i \(0.481497\pi\)
−0.686205 + 0.727408i \(0.740725\pi\)
\(104\) −4.48158 25.4163i −0.439455 2.49227i
\(105\) 0 0
\(106\) 23.4820 + 19.7038i 2.28078 + 1.91380i
\(107\) 10.4037i 1.00577i −0.864354 0.502883i \(-0.832272\pi\)
0.864354 0.502883i \(-0.167728\pi\)
\(108\) −17.5598 + 14.7344i −1.68969 + 1.41782i
\(109\) −0.147956 −0.0141716 −0.00708580 0.999975i \(-0.502255\pi\)
−0.00708580 + 0.999975i \(0.502255\pi\)
\(110\) 0 0
\(111\) 1.47519 4.05304i 0.140018 0.384697i
\(112\) −20.0315 + 3.53209i −1.89280 + 0.333751i
\(113\) 2.42107 6.65183i 0.227755 0.625751i −0.772199 0.635381i \(-0.780843\pi\)
0.999954 + 0.00962978i \(0.00306530\pi\)
\(114\) −0.916222 0.528981i −0.0858120 0.0495436i
\(115\) 0 0
\(116\) 16.9893 29.4264i 1.57742 2.73217i
\(117\) 10.9812 6.34002i 1.01522 0.586135i
\(118\) −10.3923 + 6.00000i −0.956689 + 0.552345i
\(119\) 4.75877 1.73205i 0.436236 0.158777i
\(120\) 0 0
\(121\) 15.9251 13.3628i 1.44774 1.21480i
\(122\) −22.6345 26.9748i −2.04923 2.44218i
\(123\) −0.0429807 + 0.243756i −0.00387544 + 0.0219787i
\(124\) 20.4932 7.45891i 1.84034 0.669830i
\(125\) 0 0
\(126\) −11.6382 20.1579i −1.03681 1.79581i
\(127\) −0.211239 0.121959i −0.0187444 0.0108221i 0.490599 0.871386i \(-0.336778\pi\)
−0.509343 + 0.860564i \(0.670112\pi\)
\(128\) −13.1378 2.31655i −1.16123 0.204756i
\(129\) 1.12654 + 0.650411i 0.0991867 + 0.0572655i
\(130\) 0 0
\(131\) 1.57263 + 8.91885i 0.137402 + 0.779243i 0.973157 + 0.230142i \(0.0739190\pi\)
−0.835755 + 0.549102i \(0.814970\pi\)
\(132\) 40.4825 + 14.7344i 3.52355 + 1.28247i
\(133\) 0.475129 0.566237i 0.0411989 0.0490990i
\(134\) −18.6604 −1.61202
\(135\) 0 0
\(136\) −10.0915 −0.865341
\(137\) −7.97357 + 9.50253i −0.681228 + 0.811856i −0.990265 0.139194i \(-0.955549\pi\)
0.309037 + 0.951050i \(0.399993\pi\)
\(138\) 5.67626 + 32.1917i 0.483195 + 2.74034i
\(139\) −3.21823 18.2515i −0.272966 1.54807i −0.745348 0.666675i \(-0.767717\pi\)
0.472382 0.881394i \(-0.343394\pi\)
\(140\) 0 0
\(141\) −6.97906 + 4.02936i −0.587742 + 0.339333i
\(142\) 12.2229 + 2.15523i 1.02572 + 0.180863i
\(143\) −20.6380 11.9153i −1.72583 0.996411i
\(144\) 3.45811 + 19.6119i 0.288176 + 1.63433i
\(145\) 0 0
\(146\) 0.539363 0.196312i 0.0446380 0.0162469i
\(147\) 3.88863 1.41534i 0.320729 0.116736i
\(148\) −7.06131 8.41534i −0.580436 0.691737i
\(149\) 3.66044 3.07148i 0.299875 0.251625i −0.480417 0.877040i \(-0.659515\pi\)
0.780292 + 0.625415i \(0.215070\pi\)
\(150\) 0 0
\(151\) 5.25877 1.91404i 0.427953 0.155762i −0.119059 0.992887i \(-0.537988\pi\)
0.547011 + 0.837125i \(0.315765\pi\)
\(152\) −1.27562 + 0.736482i −0.103467 + 0.0597366i
\(153\) −1.69577 4.65910i −0.137095 0.376666i
\(154\) −21.8726 + 37.8844i −1.76254 + 3.05281i
\(155\) 0 0
\(156\) 32.2956i 2.58572i
\(157\) −6.84478 + 18.8059i −0.546273 + 1.50087i 0.292432 + 0.956286i \(0.405535\pi\)
−0.838705 + 0.544586i \(0.816687\pi\)
\(158\) 24.5310 4.32547i 1.95158 0.344116i
\(159\) 13.4782 + 16.0627i 1.06889 + 1.27385i
\(160\) 0 0
\(161\) −22.8384 −1.79992
\(162\) −19.7357 + 11.3944i −1.55058 + 0.895229i
\(163\) 9.95811i 0.779979i 0.920819 + 0.389990i \(0.127521\pi\)
−0.920819 + 0.389990i \(0.872479\pi\)
\(164\) 0.482926 + 0.405223i 0.0377102 + 0.0316426i
\(165\) 0 0
\(166\) −3.89440 22.0862i −0.302264 1.71422i
\(167\) −1.08164 + 2.97178i −0.0836998 + 0.229963i −0.974481 0.224468i \(-0.927935\pi\)
0.890782 + 0.454432i \(0.150158\pi\)
\(168\) −32.4068 −2.50024
\(169\) −0.844770 + 4.79093i −0.0649823 + 0.368533i
\(170\) 0 0
\(171\) −0.554378 0.465178i −0.0423943 0.0355731i
\(172\) 2.86927 1.65657i 0.218780 0.126313i
\(173\) −6.75557 18.5608i −0.513616 1.41115i −0.877442 0.479682i \(-0.840752\pi\)
0.363826 0.931467i \(-0.381470\pi\)
\(174\) 21.7135 25.8771i 1.64609 1.96174i
\(175\) 0 0
\(176\) 28.6707 24.0576i 2.16114 1.81341i
\(177\) −7.71345 + 2.80747i −0.579779 + 0.211022i
\(178\) −5.76811 15.8478i −0.432338 1.18784i
\(179\) −4.05051 7.01568i −0.302749 0.524377i 0.674009 0.738724i \(-0.264571\pi\)
−0.976758 + 0.214347i \(0.931238\pi\)
\(180\) 0 0
\(181\) 4.45723 7.72016i 0.331304 0.573835i −0.651464 0.758679i \(-0.725845\pi\)
0.982768 + 0.184845i \(0.0591782\pi\)
\(182\) 32.2956 + 5.69459i 2.39391 + 0.422111i
\(183\) −12.0436 20.8601i −0.890287 1.54202i
\(184\) 42.7661 + 15.5656i 3.15276 + 1.14751i
\(185\) 0 0
\(186\) 21.3516 3.76487i 1.56558 0.276054i
\(187\) −5.98962 + 7.13816i −0.438005 + 0.521994i
\(188\) 20.5253i 1.49696i
\(189\) −5.44562 14.9617i −0.396111 1.08831i
\(190\) 0 0
\(191\) −4.27584 3.58786i −0.309389 0.259608i 0.474850 0.880067i \(-0.342502\pi\)
−0.784240 + 0.620458i \(0.786947\pi\)
\(192\) −2.66625 0.970437i −0.192420 0.0700353i
\(193\) −24.9412 + 4.39780i −1.79531 + 0.316561i −0.969074 0.246770i \(-0.920631\pi\)
−0.826232 + 0.563331i \(0.809520\pi\)
\(194\) −22.6805 8.25503i −1.62837 0.592677i
\(195\) 0 0
\(196\) 1.83022 10.3797i 0.130730 0.741408i
\(197\) 4.22800 + 2.44104i 0.301233 + 0.173917i 0.642996 0.765869i \(-0.277691\pi\)
−0.341764 + 0.939786i \(0.611024\pi\)
\(198\) 37.0909 + 21.4145i 2.63594 + 1.52186i
\(199\) 8.68092 + 15.0358i 0.615374 + 1.06586i 0.990319 + 0.138812i \(0.0443284\pi\)
−0.374944 + 0.927047i \(0.622338\pi\)
\(200\) 0 0
\(201\) −12.5706 2.21653i −0.886660 0.156342i
\(202\) 3.79677 + 4.52481i 0.267140 + 0.318365i
\(203\) 15.1706 + 18.0797i 1.06477 + 1.26894i
\(204\) −12.4363 2.19285i −0.870714 0.153530i
\(205\) 0 0
\(206\) 23.5967 + 40.8707i 1.64406 + 2.84760i
\(207\) 22.3601i 1.55413i
\(208\) −24.2984 14.0287i −1.68479 0.972714i
\(209\) −0.236177 + 1.33943i −0.0163367 + 0.0926501i
\(210\) 0 0
\(211\) −10.7699 3.91993i −0.741432 0.269859i −0.0564359 0.998406i \(-0.517974\pi\)
−0.684996 + 0.728547i \(0.740196\pi\)
\(212\) 52.5942 9.27379i 3.61219 0.636926i
\(213\) 7.97794 + 2.90373i 0.546640 + 0.198961i
\(214\) −20.1800 16.9331i −1.37948 1.15752i
\(215\) 0 0
\(216\) 31.7281i 2.15882i
\(217\) 15.1480i 1.02831i
\(218\) −0.240812 + 0.286989i −0.0163099 + 0.0194373i
\(219\) 0.386659 0.0681784i 0.0261280 0.00460707i
\(220\) 0 0
\(221\) 6.56418 + 2.38917i 0.441554 + 0.160713i
\(222\) −5.46064 9.45811i −0.366494 0.634787i
\(223\) 0.433877 + 0.0765042i 0.0290545 + 0.00512310i 0.188157 0.982139i \(-0.439749\pi\)
−0.159102 + 0.987262i \(0.550860\pi\)
\(224\) −7.04189 + 12.1969i −0.470506 + 0.814940i
\(225\) 0 0
\(226\) −8.96198 15.5226i −0.596142 1.03255i
\(227\) 1.81720 + 4.99273i 0.120612 + 0.331379i 0.985276 0.170972i \(-0.0546908\pi\)
−0.864664 + 0.502351i \(0.832469\pi\)
\(228\) −1.73205 + 0.630415i −0.114708 + 0.0417502i
\(229\) −0.0603074 + 0.0506039i −0.00398522 + 0.00334400i −0.644778 0.764370i \(-0.723050\pi\)
0.640793 + 0.767714i \(0.278606\pi\)
\(230\) 0 0
\(231\) −19.2344 + 22.9227i −1.26553 + 1.50820i
\(232\) −16.0855 44.1946i −1.05607 2.90152i
\(233\) −0.324446 + 0.187319i −0.0212551 + 0.0122717i −0.510590 0.859824i \(-0.670573\pi\)
0.489335 + 0.872096i \(0.337240\pi\)
\(234\) 5.57532 31.6192i 0.364470 2.06701i
\(235\) 0 0
\(236\) −3.63041 + 20.5891i −0.236320 + 1.34024i
\(237\) 17.0390 1.10680
\(238\) 4.38571 12.0496i 0.284283 0.781061i
\(239\) 1.88666 + 10.6998i 0.122038 + 0.692111i 0.983023 + 0.183481i \(0.0587367\pi\)
−0.860985 + 0.508630i \(0.830152\pi\)
\(240\) 0 0
\(241\) 20.4893 + 17.1926i 1.31983 + 1.10747i 0.986341 + 0.164719i \(0.0526717\pi\)
0.333493 + 0.942753i \(0.391773\pi\)
\(242\) 52.6391i 3.38377i
\(243\) −14.6484 + 5.33157i −0.939693 + 0.342020i
\(244\) −61.3492 −3.92748
\(245\) 0 0
\(246\) 0.402856 + 0.480105i 0.0256852 + 0.0306104i
\(247\) 1.00411 0.177052i 0.0638900 0.0112655i
\(248\) 10.3241 28.3653i 0.655583 1.80120i
\(249\) 15.3409i 0.972193i
\(250\) 0 0
\(251\) 2.99660 5.19026i 0.189143 0.327606i −0.755821 0.654778i \(-0.772762\pi\)
0.944965 + 0.327172i \(0.106096\pi\)
\(252\) −39.9365 7.04189i −2.51577 0.443597i
\(253\) 36.3932 21.0116i 2.28802 1.32099i
\(254\) −0.580375 + 0.211239i −0.0364159 + 0.0132543i
\(255\) 0 0
\(256\) −23.3666 + 19.6069i −1.46042 + 1.22543i
\(257\) 4.06564 + 4.84524i 0.253607 + 0.302238i 0.877795 0.479037i \(-0.159014\pi\)
−0.624187 + 0.781275i \(0.714570\pi\)
\(258\) 3.09516 1.12654i 0.192696 0.0701356i
\(259\) 7.17024 2.60976i 0.445537 0.162162i
\(260\) 0 0
\(261\) 17.7010 14.8529i 1.09566 0.919371i
\(262\) 19.8594 + 11.4659i 1.22692 + 0.708363i
\(263\) −0.460802 0.0812519i −0.0284143 0.00501021i 0.159423 0.987210i \(-0.449037\pi\)
−0.187837 + 0.982200i \(0.560148\pi\)
\(264\) 51.6404 29.8146i 3.17825 1.83496i
\(265\) 0 0
\(266\) −0.325008 1.84321i −0.0199275 0.113014i
\(267\) −2.00324 11.3610i −0.122597 0.695280i
\(268\) −20.8975 + 24.9047i −1.27652 + 1.52129i
\(269\) −1.84524 −0.112506 −0.0562530 0.998417i \(-0.517915\pi\)
−0.0562530 + 0.998417i \(0.517915\pi\)
\(270\) 0 0
\(271\) −4.12567 −0.250616 −0.125308 0.992118i \(-0.539992\pi\)
−0.125308 + 0.992118i \(0.539992\pi\)
\(272\) −7.05196 + 8.40420i −0.427588 + 0.509579i
\(273\) 21.0795 + 7.67230i 1.27579 + 0.464349i
\(274\) 5.45424 + 30.9325i 0.329503 + 1.86870i
\(275\) 0 0
\(276\) 49.3205 + 28.4752i 2.96874 + 1.71401i
\(277\) −0.0605553 0.0106775i −0.00363841 0.000641550i 0.171829 0.985127i \(-0.445032\pi\)
−0.175467 + 0.984485i \(0.556144\pi\)
\(278\) −40.6402 23.4636i −2.43744 1.40726i
\(279\) 14.8307 0.887890
\(280\) 0 0
\(281\) 5.68479 2.06910i 0.339126 0.123432i −0.166843 0.985984i \(-0.553357\pi\)
0.505969 + 0.862552i \(0.331135\pi\)
\(282\) −3.54336 + 20.0954i −0.211004 + 1.19666i
\(283\) 5.37051 + 6.40033i 0.319244 + 0.380460i 0.901671 0.432423i \(-0.142341\pi\)
−0.582427 + 0.812883i \(0.697897\pi\)
\(284\) 16.5646 13.8994i 0.982931 0.824777i
\(285\) 0 0
\(286\) −56.7024 + 20.6380i −3.35288 + 1.22035i
\(287\) −0.379217 + 0.218941i −0.0223844 + 0.0129237i
\(288\) 11.9415 + 6.89440i 0.703657 + 0.406256i
\(289\) −7.13429 + 12.3569i −0.419664 + 0.726879i
\(290\) 0 0
\(291\) −14.2981 8.25503i −0.838171 0.483918i
\(292\) 0.342020 0.939693i 0.0200152 0.0549914i
\(293\) 11.8303 2.08600i 0.691133 0.121865i 0.182960 0.983120i \(-0.441432\pi\)
0.508173 + 0.861255i \(0.330321\pi\)
\(294\) 3.58378 9.84635i 0.209010 0.574251i
\(295\) 0 0
\(296\) −15.2053 −0.883792
\(297\) 22.4426 + 18.8316i 1.30225 + 1.09272i
\(298\) 12.0993i 0.700891i
\(299\) −24.1327 20.2497i −1.39563 1.17107i
\(300\) 0 0
\(301\) 0.399615 + 2.26633i 0.0230334 + 0.130629i
\(302\) 4.84651 13.3157i 0.278885 0.766231i
\(303\) 2.02022 + 3.49912i 0.116059 + 0.201019i
\(304\) −0.278066 + 1.57699i −0.0159482 + 0.0904467i
\(305\) 0 0
\(306\) −11.7973 4.29385i −0.674404 0.245463i
\(307\) −9.33667 + 5.39053i −0.532872 + 0.307654i −0.742185 0.670195i \(-0.766211\pi\)
0.209313 + 0.977849i \(0.432877\pi\)
\(308\) 26.0667 + 71.6177i 1.48529 + 4.08080i
\(309\) 11.0412 + 30.3354i 0.628110 + 1.72572i
\(310\) 0 0
\(311\) −11.8341 + 9.92998i −0.671050 + 0.563078i −0.913376 0.407117i \(-0.866534\pi\)
0.242326 + 0.970195i \(0.422090\pi\)
\(312\) −34.2433 28.7335i −1.93865 1.62672i
\(313\) 1.58370 + 4.35117i 0.0895157 + 0.245942i 0.976370 0.216108i \(-0.0693362\pi\)
−0.886854 + 0.462050i \(0.847114\pi\)
\(314\) 25.3371 + 43.8851i 1.42985 + 2.47658i
\(315\) 0 0
\(316\) 21.6989 37.5836i 1.22066 2.11425i
\(317\) −7.65787 1.35029i −0.430109 0.0758398i −0.0455972 0.998960i \(-0.514519\pi\)
−0.384512 + 0.923120i \(0.625630\pi\)
\(318\) 53.0937 2.97734
\(319\) −40.8080 14.8529i −2.28481 0.831602i
\(320\) 0 0
\(321\) −11.5829 13.8040i −0.646494 0.770462i
\(322\) −37.1717 + 44.2995i −2.07150 + 2.46872i
\(323\) 0.398681i 0.0221832i
\(324\) −6.89440 + 39.1001i −0.383022 + 2.17223i
\(325\) 0 0
\(326\) 19.3157 + 16.2078i 1.06980 + 0.897666i
\(327\) −0.196312 + 0.164725i −0.0108561 + 0.00910933i
\(328\) 0.859322 0.151522i 0.0474481 0.00836638i
\(329\) −13.3969 4.87608i −0.738596 0.268827i
\(330\) 0 0
\(331\) 1.31655 7.46654i 0.0723642 0.410398i −0.927010 0.375036i \(-0.877630\pi\)
0.999375 0.0353621i \(-0.0112585\pi\)
\(332\) −33.8381 19.5364i −1.85711 1.07220i
\(333\) −2.55510 7.02007i −0.140018 0.384697i
\(334\) 4.00387 + 6.93491i 0.219082 + 0.379461i
\(335\) 0 0
\(336\) −22.6459 + 26.9883i −1.23543 + 1.47233i
\(337\) −10.6348 12.6741i −0.579317 0.690403i 0.394198 0.919025i \(-0.371022\pi\)
−0.973515 + 0.228622i \(0.926578\pi\)
\(338\) 7.91799 + 9.43629i 0.430682 + 0.513266i
\(339\) −4.19341 11.5213i −0.227755 0.625751i
\(340\) 0 0
\(341\) −13.9363 24.1384i −0.754692 1.30717i
\(342\) −1.80460 + 0.318201i −0.0975819 + 0.0172063i
\(343\) −12.2355 7.06418i −0.660656 0.381430i
\(344\) 0.796322 4.51617i 0.0429348 0.243495i
\(345\) 0 0
\(346\) −46.9975 17.1057i −2.52660 0.919608i
\(347\) −14.9550 + 2.63697i −0.802828 + 0.141560i −0.559982 0.828505i \(-0.689192\pi\)
−0.242846 + 0.970065i \(0.578081\pi\)
\(348\) −10.2197 57.9586i −0.547832 3.10691i
\(349\) −10.8191 9.07828i −0.579132 0.485949i 0.305530 0.952182i \(-0.401166\pi\)
−0.884662 + 0.466233i \(0.845611\pi\)
\(350\) 0 0
\(351\) 7.51161 20.6380i 0.400940 1.10157i
\(352\) 25.9145i 1.38125i
\(353\) −2.67733 + 3.19072i −0.142500 + 0.169825i −0.832574 0.553914i \(-0.813134\pi\)
0.690074 + 0.723739i \(0.257578\pi\)
\(354\) −7.10876 + 19.5311i −0.377826 + 1.03807i
\(355\) 0 0
\(356\) −27.6104 10.0494i −1.46335 0.532615i
\(357\) 4.38571 7.59627i 0.232116 0.402037i
\(358\) −20.2009 3.56196i −1.06765 0.188255i
\(359\) −3.29679 + 5.71021i −0.173998 + 0.301373i −0.939814 0.341686i \(-0.889002\pi\)
0.765816 + 0.643060i \(0.222335\pi\)
\(360\) 0 0
\(361\) 9.47090 + 16.4041i 0.498469 + 0.863373i
\(362\) −7.72016 21.2110i −0.405762 1.11482i
\(363\) 6.25259 35.4602i 0.328176 1.86118i
\(364\) 43.7674 36.7252i 2.29404 1.92493i
\(365\) 0 0
\(366\) −60.0642 10.5909i −3.13961 0.553598i
\(367\) 4.34008 + 11.9243i 0.226550 + 0.622442i 0.999934 0.0114966i \(-0.00365955\pi\)
−0.773384 + 0.633938i \(0.781437\pi\)
\(368\) 42.8480 24.7383i 2.23361 1.28957i
\(369\) 0.214355 + 0.371274i 0.0111589 + 0.0193278i
\(370\) 0 0
\(371\) −6.44150 + 36.5316i −0.334426 + 1.89663i
\(372\) 18.8866 32.7126i 0.979226 1.69607i
\(373\) 2.61159 7.17530i 0.135223 0.371523i −0.853537 0.521032i \(-0.825547\pi\)
0.988760 + 0.149509i \(0.0477694\pi\)
\(374\) 4.09714 + 23.2361i 0.211858 + 1.20151i
\(375\) 0 0
\(376\) 21.7631 + 18.2614i 1.12235 + 0.941761i
\(377\) 32.5553i 1.67668i
\(378\) −37.8844 13.7888i −1.94856 0.709219i
\(379\) 27.0838 1.39120 0.695600 0.718429i \(-0.255139\pi\)
0.695600 + 0.718429i \(0.255139\pi\)
\(380\) 0 0
\(381\) −0.416060 + 0.0733626i −0.0213154 + 0.00375848i
\(382\) −13.9187 + 2.45424i −0.712142 + 0.125570i
\(383\) −3.52201 + 9.67664i −0.179966 + 0.494453i −0.996571 0.0827443i \(-0.973632\pi\)
0.816605 + 0.577198i \(0.195854\pi\)
\(384\) −20.0107 + 11.5532i −1.02117 + 0.589572i
\(385\) 0 0
\(386\) −32.0638 + 55.5361i −1.63200 + 2.82671i
\(387\) 2.21886 0.391245i 0.112791 0.0198881i
\(388\) −36.4169 + 21.0253i −1.84879 + 1.06740i
\(389\) 3.89780 1.41868i 0.197626 0.0719302i −0.241311 0.970448i \(-0.577577\pi\)
0.438937 + 0.898518i \(0.355355\pi\)
\(390\) 0 0
\(391\) −9.43629 + 7.91799i −0.477214 + 0.400430i
\(392\) −9.37732 11.1755i −0.473626 0.564446i
\(393\) 12.0163 + 10.0829i 0.606144 + 0.508615i
\(394\) 11.6163 4.22800i 0.585222 0.213004i
\(395\) 0 0
\(396\) 70.1177 25.5208i 3.52355 1.28247i
\(397\) −19.1444 11.0530i −0.960831 0.554736i −0.0644021 0.997924i \(-0.520514\pi\)
−0.896429 + 0.443188i \(0.853847\pi\)
\(398\) 43.2939 + 7.63387i 2.17012 + 0.382652i
\(399\) 1.28028i 0.0640942i
\(400\) 0 0
\(401\) −2.92855 16.6086i −0.146245 0.829395i −0.966359 0.257196i \(-0.917201\pi\)
0.820115 0.572199i \(-0.193910\pi\)
\(402\) −24.7592 + 20.7754i −1.23488 + 1.03618i
\(403\) −13.4310 + 16.0064i −0.669044 + 0.797335i
\(404\) 10.2909 0.511989
\(405\) 0 0
\(406\) 59.7606 2.96587
\(407\) −9.02482 + 10.7554i −0.447344 + 0.533124i
\(408\) −13.3897 + 11.2353i −0.662889 + 0.556230i
\(409\) 6.09199 + 34.5494i 0.301229 + 1.70836i 0.640743 + 0.767755i \(0.278626\pi\)
−0.339514 + 0.940601i \(0.610263\pi\)
\(410\) 0 0
\(411\) 21.4855i 1.05980i
\(412\) 80.9726 + 14.2777i 3.98923 + 0.703410i
\(413\) −12.5761 7.26083i −0.618831 0.357282i
\(414\) 43.3717 + 36.3932i 2.13160 + 1.78863i
\(415\) 0 0
\(416\) −18.2554 + 6.64441i −0.895043 + 0.325769i
\(417\) −24.5901 20.6336i −1.20418 1.01043i
\(418\) 2.21368 + 2.63816i 0.108274 + 0.129036i
\(419\) −12.7665 + 10.7124i −0.623685 + 0.523334i −0.898959 0.438032i \(-0.855676\pi\)
0.275275 + 0.961366i \(0.411231\pi\)
\(420\) 0 0
\(421\) 25.7841 9.38463i 1.25664 0.457379i 0.373998 0.927429i \(-0.377987\pi\)
0.882639 + 0.470051i \(0.155764\pi\)
\(422\) −25.1325 + 14.5103i −1.22343 + 0.706349i
\(423\) −4.77396 + 13.1163i −0.232118 + 0.637738i
\(424\) 36.9602 64.0170i 1.79495 3.10894i
\(425\) 0 0
\(426\) 18.6172 10.7487i 0.902007 0.520774i
\(427\) 14.5744 40.0428i 0.705304 1.93781i
\(428\) −45.1985 + 7.96972i −2.18475 + 0.385231i
\(429\) −40.6489 + 7.16750i −1.96255 + 0.346050i
\(430\) 0 0
\(431\) −14.9436 −0.719806 −0.359903 0.932990i \(-0.617190\pi\)
−0.359903 + 0.932990i \(0.617190\pi\)
\(432\) 26.4231 + 22.1716i 1.27128 + 1.06673i
\(433\) 23.3919i 1.12414i 0.827089 + 0.562071i \(0.189995\pi\)
−0.827089 + 0.562071i \(0.810005\pi\)
\(434\) 29.3824 + 24.6547i 1.41040 + 1.18347i
\(435\) 0 0
\(436\) 0.113341 + 0.642788i 0.00542804 + 0.0307839i
\(437\) −0.614942 + 1.68954i −0.0294167 + 0.0808217i
\(438\) 0.497079 0.860967i 0.0237514 0.0411386i
\(439\) 4.55959 25.8587i 0.217617 1.23417i −0.658689 0.752415i \(-0.728889\pi\)
0.876306 0.481754i \(-0.160000\pi\)
\(440\) 0 0
\(441\) 3.58378 6.20729i 0.170656 0.295585i
\(442\) 15.3181 8.84389i 0.728606 0.420661i
\(443\) −10.8554 29.8251i −0.515757 1.41703i −0.875153 0.483846i \(-0.839239\pi\)
0.359396 0.933185i \(-0.382983\pi\)
\(444\) −18.7383 3.30407i −0.889280 0.156804i
\(445\) 0 0
\(446\) 0.854570 0.717070i 0.0404651 0.0339542i
\(447\) 1.43718 8.15064i 0.0679762 0.385512i
\(448\) −1.71680 4.71688i −0.0811114 0.222852i
\(449\) −9.23695 15.9989i −0.435919 0.755033i 0.561452 0.827510i \(-0.310243\pi\)
−0.997370 + 0.0724765i \(0.976910\pi\)
\(450\) 0 0
\(451\) 0.402856 0.697767i 0.0189697 0.0328566i
\(452\) −30.7532 5.42262i −1.44651 0.255059i
\(453\) 4.84651 8.39440i 0.227709 0.394403i
\(454\) 12.6420 + 4.60132i 0.593320 + 0.215951i
\(455\) 0 0
\(456\) −0.872578 + 2.39739i −0.0408622 + 0.112268i
\(457\) 6.86998 8.18732i 0.321364 0.382987i −0.581042 0.813874i \(-0.697355\pi\)
0.902406 + 0.430887i \(0.141799\pi\)
\(458\) 0.199340i 0.00931457i
\(459\) −7.43717 4.29385i −0.347137 0.200420i
\(460\) 0 0
\(461\) 21.1689 + 17.7628i 0.985934 + 0.827297i 0.984974 0.172703i \(-0.0552500\pi\)
0.000959987 1.00000i \(0.499694\pi\)
\(462\) 13.1571 + 74.6177i 0.612125 + 3.47153i
\(463\) 4.54077 0.800660i 0.211027 0.0372098i −0.0671350 0.997744i \(-0.521386\pi\)
0.278162 + 0.960534i \(0.410275\pi\)
\(464\) −48.0458 17.4872i −2.23047 0.811825i
\(465\) 0 0
\(466\) −0.164725 + 0.934204i −0.00763075 + 0.0432762i
\(467\) −16.9310 9.77513i −0.783474 0.452339i 0.0541859 0.998531i \(-0.482744\pi\)
−0.837660 + 0.546192i \(0.816077\pi\)
\(468\) −35.9561 42.8508i −1.66207 1.98078i
\(469\) −11.2909 19.5563i −0.521363 0.903028i
\(470\) 0 0
\(471\) 11.8555 + 32.5727i 0.546273 + 1.50087i
\(472\) 18.6008 + 22.1676i 0.856171 + 1.02034i
\(473\) −2.72183 3.24376i −0.125150 0.149148i
\(474\) 27.7327 33.0505i 1.27380 1.51806i
\(475\) 0 0
\(476\) −11.1702 19.3474i −0.511987 0.886788i
\(477\) 35.7664 + 6.30659i 1.63763 + 0.288759i
\(478\) 23.8250 + 13.7554i 1.08973 + 0.629156i
\(479\) 0.449493 2.54920i 0.0205379 0.116476i −0.972815 0.231582i \(-0.925610\pi\)
0.993353 + 0.115106i \(0.0367209\pi\)
\(480\) 0 0
\(481\) 9.89053 + 3.59986i 0.450969 + 0.164139i
\(482\) 66.6967 11.7604i 3.03795 0.535672i
\(483\) −30.3027 + 25.4270i −1.37882 + 1.15697i
\(484\) −70.2534 58.9496i −3.19333 2.67953i
\(485\) 0 0
\(486\) −13.5000 + 37.0909i −0.612372 + 1.68248i
\(487\) 40.7870i 1.84824i −0.382105 0.924119i \(-0.624801\pi\)
0.382105 0.924119i \(-0.375199\pi\)
\(488\) −54.5826 + 65.0490i −2.47084 + 2.94463i
\(489\) 11.0868 + 13.2127i 0.501361 + 0.597499i
\(490\) 0 0
\(491\) −37.9761 13.8222i −1.71384 0.623786i −0.716561 0.697525i \(-0.754285\pi\)
−0.997278 + 0.0737387i \(0.976507\pi\)
\(492\) 1.09191 0.0492271
\(493\) 12.5363 + 2.21048i 0.564606 + 0.0995552i
\(494\) 1.29086 2.23583i 0.0580785 0.100595i
\(495\) 0 0
\(496\) −16.4081 28.4196i −0.736744 1.27608i
\(497\) 5.13701 + 14.1138i 0.230426 + 0.633091i
\(498\) −29.7567 24.9688i −1.33343 1.11888i
\(499\) 10.2226 8.57775i 0.457625 0.383993i −0.384631 0.923070i \(-0.625671\pi\)
0.842256 + 0.539077i \(0.181227\pi\)
\(500\) 0 0
\(501\) 1.87346 + 5.14728i 0.0836998 + 0.229963i
\(502\) −5.19026 14.2601i −0.231653 0.636460i
\(503\) 15.6373 9.02822i 0.697234 0.402548i −0.109082 0.994033i \(-0.534791\pi\)
0.806316 + 0.591484i \(0.201458\pi\)
\(504\) −42.9982 + 36.0798i −1.91529 + 1.60712i
\(505\) 0 0
\(506\) 18.4773 104.790i 0.821416 4.65848i
\(507\) 4.21307 + 7.29726i 0.187109 + 0.324083i
\(508\) −0.368026 + 1.01114i −0.0163285 + 0.0448623i
\(509\) −4.18779 23.7501i −0.185620 1.05271i −0.925156 0.379588i \(-0.876066\pi\)
0.739535 0.673118i \(-0.235045\pi\)
\(510\) 0 0
\(511\) 0.532089 + 0.446476i 0.0235382 + 0.0197509i
\(512\) 50.5553i 2.23425i
\(513\) −1.25347 −0.0553418
\(514\) 16.0155 0.706413
\(515\) 0 0
\(516\) 1.96270 5.39246i 0.0864029 0.237390i
\(517\) 25.8341 4.55525i 1.13618 0.200340i
\(518\) 6.60813 18.1557i 0.290345 0.797716i
\(519\) −29.6279 17.1057i −1.30052 0.750857i
\(520\) 0 0
\(521\) 20.6682 35.7983i 0.905490 1.56835i 0.0852310 0.996361i \(-0.472837\pi\)
0.820259 0.571993i \(-0.193829\pi\)
\(522\) 58.5090i 2.56087i
\(523\) 5.66955 3.27332i 0.247912 0.143132i −0.370896 0.928675i \(-0.620949\pi\)
0.618808 + 0.785542i \(0.287616\pi\)
\(524\) 37.5428 13.6645i 1.64007 0.596935i
\(525\) 0 0
\(526\) −0.907604 + 0.761570i −0.0395734 + 0.0332060i
\(527\) 5.25173 + 6.25877i 0.228769 + 0.272636i
\(528\) 11.2568 63.8405i 0.489890 2.77830i
\(529\) 30.5895 11.1337i 1.32998 0.484072i
\(530\) 0 0
\(531\) −7.10876 + 12.3127i −0.308494 + 0.534327i
\(532\) −2.82396 1.63041i −0.122434 0.0706875i
\(533\) −0.594831 0.104885i −0.0257650 0.00454306i
\(534\) −25.2973 14.6054i −1.09472 0.632037i
\(535\) 0 0
\(536\) 7.81403 + 44.3155i 0.337514 + 1.91414i
\(537\) −13.1852 4.79901i −0.568982 0.207093i
\(538\) −3.00330 + 3.57919i −0.129481 + 0.154310i
\(539\) −13.4706 −0.580220
\(540\) 0 0
\(541\) −30.3560 −1.30511 −0.652553 0.757743i \(-0.726302\pi\)
−0.652553 + 0.757743i \(0.726302\pi\)
\(542\) −6.71492 + 8.00253i −0.288430 + 0.343738i
\(543\) −2.68118 15.2057i −0.115061 0.652541i
\(544\) 1.31908 + 7.48086i 0.0565550 + 0.320739i
\(545\) 0 0
\(546\) 49.1908 28.4003i 2.10517 1.21542i
\(547\) 38.0907 + 6.71641i 1.62864 + 0.287173i 0.911975 0.410245i \(-0.134557\pi\)
0.716664 + 0.697418i \(0.245668\pi\)
\(548\) 47.3914 + 27.3614i 2.02446 + 1.16882i
\(549\) −39.2041 14.2691i −1.67319 0.608992i
\(550\) 0 0
\(551\) 1.74598 0.635484i 0.0743811 0.0270725i
\(552\) 74.0731 26.9604i 3.15276 1.14751i
\(553\) 19.3761 + 23.0915i 0.823955 + 0.981951i
\(554\) −0.119271 + 0.100080i −0.00506732 + 0.00425199i
\(555\) 0 0
\(556\) −76.8273 + 27.9629i −3.25821 + 1.18589i
\(557\) 12.8808 7.43676i 0.545779 0.315105i −0.201639 0.979460i \(-0.564627\pi\)
0.747418 + 0.664354i \(0.231293\pi\)
\(558\) 24.1384 28.7670i 1.02186 1.21780i
\(559\) −1.58718 + 2.74908i −0.0671306 + 0.116274i
\(560\) 0 0
\(561\) 16.1396i 0.681414i
\(562\) 5.23913 14.3944i 0.220999 0.607191i
\(563\) 28.8485 5.08677i 1.21582 0.214382i 0.471294 0.881976i \(-0.343787\pi\)
0.744525 + 0.667594i \(0.232676\pi\)
\(564\) 22.8516 + 27.2335i 0.962227 + 1.14674i
\(565\) 0 0
\(566\) 21.1557 0.889240
\(567\) −23.8829 13.7888i −1.00299 0.579075i
\(568\) 29.9299i 1.25583i
\(569\) 24.4127 + 20.4847i 1.02343 + 0.858761i 0.990055 0.140682i \(-0.0449294\pi\)
0.0333769 + 0.999443i \(0.489374\pi\)
\(570\) 0 0
\(571\) −2.78817 15.8125i −0.116681 0.661733i −0.985904 0.167312i \(-0.946491\pi\)
0.869223 0.494421i \(-0.164620\pi\)
\(572\) −35.9561 + 98.7884i −1.50340 + 4.13055i
\(573\) −9.66782 −0.403879
\(574\) −0.192533 + 1.09191i −0.00803619 + 0.0455755i
\(575\) 0 0
\(576\) −4.61809 + 1.68085i −0.192420 + 0.0700353i
\(577\) −1.96464 + 1.13429i −0.0817890 + 0.0472209i −0.540337 0.841449i \(-0.681703\pi\)
0.458548 + 0.888670i \(0.348370\pi\)
\(578\) 12.3569 + 33.9504i 0.513981 + 1.41215i
\(579\) −28.1964 + 33.6032i −1.17180 + 1.39650i
\(580\) 0 0
\(581\) 20.7902 17.4451i 0.862524 0.723744i
\(582\) −39.2838 + 14.2981i −1.62837 + 0.592677i
\(583\) −23.3449 64.1396i −0.966847 2.65639i
\(584\) −0.692066 1.19869i −0.0286379 0.0496023i
\(585\) 0 0
\(586\) 15.2087 26.3423i 0.628267 1.08819i
\(587\) −32.8120 5.78564i −1.35430 0.238799i −0.551064 0.834463i \(-0.685778\pi\)
−0.803234 + 0.595664i \(0.796889\pi\)
\(588\) −9.12776 15.8097i −0.376422 0.651983i
\(589\) 1.12061 + 0.407870i 0.0461741 + 0.0168060i
\(590\) 0 0
\(591\) 8.32753 1.46837i 0.342549 0.0604006i
\(592\) −10.6255 + 12.6630i −0.436705 + 0.520445i
\(593\) 24.7793i 1.01756i 0.860895 + 0.508782i \(0.169904\pi\)
−0.860895 + 0.508782i \(0.830096\pi\)
\(594\) 73.0549 12.8816i 2.99748 0.528536i
\(595\) 0 0
\(596\) −16.1480 13.5497i −0.661446 0.555019i
\(597\) 28.2581 + 10.2851i 1.15653 + 0.420941i
\(598\) −78.5565 + 13.8516i −3.21241 + 0.566435i
\(599\) 35.9368 + 13.0799i 1.46834 + 0.534431i 0.947648 0.319316i \(-0.103453\pi\)
0.520688 + 0.853747i \(0.325676\pi\)
\(600\) 0 0
\(601\) 7.80747 44.2783i 0.318473 1.80615i −0.233575 0.972339i \(-0.575042\pi\)
0.552048 0.833812i \(-0.313847\pi\)
\(602\) 5.04639 + 2.91353i 0.205675 + 0.118747i
\(603\) −19.1467 + 11.0544i −0.779716 + 0.450169i
\(604\) −12.3439 21.3802i −0.502266 0.869950i
\(605\) 0 0
\(606\) 10.0753 + 1.77655i 0.409282 + 0.0721675i
\(607\) 10.1845 + 12.1374i 0.413377 + 0.492644i 0.932050 0.362329i \(-0.118018\pi\)
−0.518673 + 0.854973i \(0.673574\pi\)
\(608\) 0.712694 + 0.849356i 0.0289036 + 0.0344459i
\(609\) 40.2576 + 7.09851i 1.63132 + 0.287646i
\(610\) 0 0
\(611\) −9.83275 17.0308i −0.397790 0.688993i
\(612\) −18.9422 + 10.9363i −0.765693 + 0.442073i
\(613\) 18.0265 + 10.4076i 0.728083 + 0.420359i 0.817721 0.575615i \(-0.195237\pi\)
−0.0896372 + 0.995974i \(0.528571\pi\)
\(614\) −4.74035 + 26.8839i −0.191305 + 1.08494i
\(615\) 0 0
\(616\) 99.1285 + 36.0798i 3.99400 + 1.45370i
\(617\) 29.4752 5.19728i 1.18663 0.209235i 0.454718 0.890635i \(-0.349740\pi\)
0.731911 + 0.681401i \(0.238629\pi\)
\(618\) 76.8119 + 27.9572i 3.08983 + 1.12460i
\(619\) 2.69775 + 2.26368i 0.108432 + 0.0909850i 0.695392 0.718631i \(-0.255231\pi\)
−0.586960 + 0.809616i \(0.699675\pi\)
\(620\) 0 0
\(621\) 24.8944 + 29.6680i 0.998978 + 1.19054i
\(622\) 39.1165i 1.56843i
\(623\) 13.1185 15.6340i 0.525582 0.626364i
\(624\) −47.8585 + 8.43874i −1.91587 + 0.337820i
\(625\) 0 0
\(626\) 11.0175 + 4.01006i 0.440349 + 0.160274i
\(627\) 1.17787 + 2.04013i 0.0470397 + 0.0814751i
\(628\) 86.9447 + 15.3307i 3.46947 + 0.611761i
\(629\) 2.05778 3.56418i 0.0820491 0.142113i
\(630\) 0 0
\(631\) −9.53730 16.5191i −0.379674 0.657615i 0.611341 0.791368i \(-0.290631\pi\)
−0.991015 + 0.133753i \(0.957297\pi\)
\(632\) −20.5446 56.4458i −0.817221 2.24529i
\(633\) −18.6540 + 6.78952i −0.741432 + 0.269859i
\(634\) −15.0831 + 12.6562i −0.599025 + 0.502642i
\(635\) 0 0
\(636\) 59.4586 70.8600i 2.35769 2.80978i
\(637\) 3.45383 + 9.48932i 0.136846 + 0.375981i
\(638\) −95.2289 + 54.9805i −3.77015 + 2.17670i
\(639\) 13.8182 5.02941i 0.546640 0.198961i
\(640\) 0 0
\(641\) 1.60711 9.11435i 0.0634769 0.359995i −0.936480 0.350721i \(-0.885937\pi\)
0.999957 0.00927459i \(-0.00295224\pi\)
\(642\) −45.6277 −1.80078
\(643\) −9.77411 + 26.8542i −0.385453 + 1.05902i 0.583571 + 0.812062i \(0.301655\pi\)
−0.969025 + 0.246963i \(0.920567\pi\)
\(644\) 17.4953 + 99.2205i 0.689410 + 3.90984i
\(645\) 0 0
\(646\) −0.773318 0.648891i −0.0304258 0.0255303i
\(647\) 21.6928i 0.852833i −0.904527 0.426417i \(-0.859776\pi\)
0.904527 0.426417i \(-0.140224\pi\)
\(648\) 35.3241 + 42.0977i 1.38766 + 1.65375i
\(649\) 26.7202 1.04886
\(650\) 0 0
\(651\) 16.8648 + 20.0987i 0.660985 + 0.787731i
\(652\) 43.2626 7.62836i 1.69429 0.298749i
\(653\) −10.5760 + 29.0574i −0.413872 + 1.13710i 0.541243 + 0.840866i \(0.317954\pi\)
−0.955115 + 0.296237i \(0.904268\pi\)
\(654\) 0.648891i 0.0253737i
\(655\) 0 0
\(656\) 0.474308 0.821525i 0.0185186 0.0320752i
\(657\) 0.437124 0.520945i 0.0170538 0.0203240i
\(658\) −31.2629 + 18.0496i −1.21875 + 0.703648i
\(659\) 35.7581 13.0149i 1.39294 0.506987i 0.466862 0.884330i \(-0.345384\pi\)
0.926074 + 0.377343i \(0.123162\pi\)
\(660\) 0 0
\(661\) −20.7271 + 17.3921i −0.806193 + 0.676476i −0.949696 0.313174i \(-0.898608\pi\)
0.143503 + 0.989650i \(0.454163\pi\)
\(662\) −12.3400 14.7062i −0.479607 0.571573i
\(663\) 11.3695 4.13816i 0.441554 0.160713i
\(664\) −50.8205 + 18.4971i −1.97222 + 0.717828i
\(665\) 0 0
\(666\) −17.7754 6.46973i −0.688784 0.250697i
\(667\) −49.7170 28.7041i −1.92505 1.11143i
\(668\) 13.7394 + 2.42262i 0.531591 + 0.0937339i
\(669\) 0.660855 0.381545i 0.0255501 0.0147514i
\(670\) 0 0
\(671\) 13.6155 + 77.2171i 0.525619 + 2.98093i
\(672\) 4.23594 + 24.0232i 0.163405 + 0.926716i
\(673\) 19.8109 23.6097i 0.763653 0.910087i −0.234420 0.972135i \(-0.575319\pi\)
0.998073 + 0.0620488i \(0.0197635\pi\)
\(674\) −41.8931 −1.61366
\(675\) 0 0
\(676\) 21.4611 0.825427
\(677\) 29.9708 35.7178i 1.15187 1.37275i 0.235766 0.971810i \(-0.424240\pi\)
0.916105 0.400937i \(-0.131315\pi\)
\(678\) −29.1730 10.6181i −1.12038 0.407785i
\(679\) −5.07192 28.7643i −0.194642 1.10387i
\(680\) 0 0
\(681\) 7.96972 + 4.60132i 0.305400 + 0.176323i
\(682\) −69.5036 12.2554i −2.66143 0.469282i
\(683\) 35.8923 + 20.7224i 1.37338 + 0.792921i 0.991352 0.131231i \(-0.0418928\pi\)
0.382027 + 0.924151i \(0.375226\pi\)
\(684\) −1.59627 + 2.76481i −0.0610348 + 0.105715i
\(685\) 0 0
\(686\) −33.6168 + 12.2355i −1.28350 + 0.467154i
\(687\) −0.0236781 + 0.134285i −0.000903377 + 0.00512330i
\(688\) −3.20459 3.81908i −0.122174 0.145601i
\(689\) −39.1973 + 32.8905i −1.49330 + 1.25303i
\(690\) 0 0
\(691\) −4.99185 + 1.81688i −0.189899 + 0.0691175i −0.435219 0.900325i \(-0.643329\pi\)
0.245320 + 0.969442i \(0.421107\pi\)
\(692\) −75.4614 + 43.5676i −2.86861 + 1.65619i
\(693\) 51.8289i 1.96882i
\(694\) −19.2258 + 33.3001i −0.729802 + 1.26405i
\(695\) 0 0
\(696\) −70.5464 40.7300i −2.67406 1.54387i
\(697\) −0.0807773 + 0.221934i −0.00305966 + 0.00840634i
\(698\) −35.2182 + 6.20991i −1.33303 + 0.235049i
\(699\) −0.221934 + 0.609758i −0.00839431 + 0.0230632i
\(700\) 0 0
\(701\) 9.66962 0.365216 0.182608 0.983186i \(-0.441546\pi\)
0.182608 + 0.983186i \(0.441546\pi\)
\(702\) −27.8055 48.1605i −1.04945 1.81770i
\(703\) 0.600710i 0.0226562i
\(704\) 7.07532 + 5.93690i 0.266661 + 0.223755i
\(705\) 0 0
\(706\) 1.83140 + 10.3864i 0.0689258 + 0.390898i
\(707\) −2.44474 + 6.71688i −0.0919441 + 0.252614i
\(708\) 18.1058 + 31.3601i 0.680456 + 1.17858i
\(709\) −4.07057 + 23.0854i −0.152874 + 0.866989i 0.807830 + 0.589415i \(0.200642\pi\)
−0.960704 + 0.277575i \(0.910469\pi\)
\(710\) 0 0
\(711\) 22.6079 18.9703i 0.847862 0.711440i
\(712\) −35.2205 + 20.3346i −1.31994 + 0.762070i
\(713\) −12.6021 34.6241i −0.471954 1.29668i
\(714\) −7.59627 20.8706i −0.284283 0.781061i
\(715\) 0 0
\(716\) −27.3764 + 22.9716i −1.02311 + 0.858488i
\(717\) 14.4158 + 12.0963i 0.538367 + 0.451743i
\(718\) 5.71021 + 15.6887i 0.213103 + 0.585496i
\(719\) −13.1133 22.7130i −0.489045 0.847051i 0.510875 0.859655i \(-0.329321\pi\)
−0.999921 + 0.0126038i \(0.995988\pi\)
\(720\) 0 0
\(721\) −28.5553 + 49.4592i −1.06346 + 1.84196i
\(722\) 47.2337 + 8.32857i 1.75786 + 0.309957i
\(723\) 46.3270 1.72292
\(724\) −36.9543 13.4503i −1.37340 0.499875i
\(725\) 0 0
\(726\) −58.6052 69.8430i −2.17504 2.59212i
\(727\) −12.2559 + 14.6061i −0.454548 + 0.541709i −0.943836 0.330413i \(-0.892812\pi\)
0.489289 + 0.872122i \(0.337256\pi\)
\(728\) 79.0815i 2.93096i
\(729\) −13.5000 + 23.3827i −0.500000 + 0.866025i
\(730\) 0 0
\(731\) 0.950837 + 0.797847i 0.0351680 + 0.0295094i
\(732\) −81.3998 + 68.3025i −3.00862 + 2.52453i
\(733\) −6.64268 + 1.17128i −0.245353 + 0.0432624i −0.294972 0.955506i \(-0.595310\pi\)
0.0496191 + 0.998768i \(0.484199\pi\)
\(734\) 30.1933 + 10.9895i 1.11446 + 0.405629i
\(735\) 0 0
\(736\) 5.94878 33.7372i 0.219275 1.24357i
\(737\) 35.9841 + 20.7754i 1.32549 + 0.765273i
\(738\) 1.06904 + 0.188501i 0.0393519 + 0.00693881i
\(739\) −18.0069 31.1888i −0.662393 1.14730i −0.979985 0.199071i \(-0.936208\pi\)
0.317592 0.948228i \(-0.397126\pi\)
\(740\) 0 0
\(741\) 1.13516 1.35283i 0.0417012 0.0496976i
\(742\) 60.3759 + 71.9532i 2.21647 + 2.64148i
\(743\) 23.0508 + 27.4709i 0.845653 + 1.00781i 0.999805 + 0.0197626i \(0.00629103\pi\)
−0.154152 + 0.988047i \(0.549265\pi\)
\(744\) −17.8819 49.1301i −0.655583 1.80120i
\(745\) 0 0
\(746\) −9.66725 16.7442i −0.353943 0.613048i
\(747\) −17.0797 20.3548i −0.624913 0.744743i
\(748\) 35.5997 + 20.5535i 1.30165 + 0.751510i
\(749\) 5.53571 31.3946i 0.202270 1.14713i
\(750\) 0 0
\(751\) 45.0899 + 16.4114i 1.64535 + 0.598860i 0.987963 0.154689i \(-0.0494376\pi\)
0.657392 + 0.753549i \(0.271660\pi\)
\(752\) 30.4162 5.36319i 1.10916 0.195575i
\(753\) −1.80256 10.2228i −0.0656888 0.372540i
\(754\) 63.1473 + 52.9869i 2.29969 + 1.92967i
\(755\) 0 0
\(756\) −60.8289 + 35.1196i −2.21233 + 1.27729i
\(757\) 24.2172i 0.880189i −0.897952 0.440094i \(-0.854945\pi\)
0.897952 0.440094i \(-0.145055\pi\)
\(758\) 44.0814 52.5342i 1.60111 1.90813i
\(759\) 24.8944 68.3968i 0.903609 2.48265i
\(760\) 0 0
\(761\) 42.1391 + 15.3374i 1.52754 + 0.555979i 0.963018 0.269438i \(-0.0868379\pi\)
0.564523 + 0.825417i \(0.309060\pi\)
\(762\) −0.534876 + 0.926433i −0.0193765 + 0.0335611i
\(763\) −0.446476 0.0787257i −0.0161635 0.00285006i
\(764\) −12.3118 + 21.3247i −0.445425 + 0.771499i
\(765\) 0 0
\(766\) 13.0373 + 22.5813i 0.471057 + 0.815895i
\(767\) −6.85099 18.8229i −0.247375 0.679657i
\(768\) −9.17431 + 52.0301i −0.331049 + 1.87747i
\(769\) −0.682733 + 0.572881i −0.0246200 + 0.0206586i −0.655015 0.755616i \(-0.727338\pi\)
0.630395 + 0.776275i \(0.282893\pi\)
\(770\) 0 0
\(771\) 10.7888 + 1.90236i 0.388549 + 0.0685117i
\(772\) 38.2121 + 104.987i 1.37528 + 3.77856i
\(773\) −26.6217 + 15.3701i −0.957516 + 0.552822i −0.895408 0.445247i \(-0.853116\pi\)
−0.0621086 + 0.998069i </