Properties

Label 28.4.f.a.19.9
Level $28$
Weight $4$
Character 28.19
Analytic conductor $1.652$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [28,4,Mod(3,28)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("28.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 28.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.65205348016\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + 5376 x^{11} - 41472 x^{10} + 43008 x^{9} - 28672 x^{8} + 180224 x^{7} + \cdots + 1073741824 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.9
Root \(-2.26510 + 1.69390i\) of defining polynomial
Character \(\chi\) \(=\) 28.19
Dual form 28.4.f.a.3.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.59951 + 1.11469i) q^{2} +(1.67134 + 2.89484i) q^{3} +(5.51494 + 5.79529i) q^{4} +(-15.9583 - 9.21354i) q^{5} +(1.11782 + 9.38820i) q^{6} +(15.4841 - 10.1609i) q^{7} +(7.87623 + 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +O(q^{10})\) \(q+(2.59951 + 1.11469i) q^{2} +(1.67134 + 2.89484i) q^{3} +(5.51494 + 5.79529i) q^{4} +(-15.9583 - 9.21354i) q^{5} +(1.11782 + 9.38820i) q^{6} +(15.4841 - 10.1609i) q^{7} +(7.87623 + 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +(-31.2137 - 41.7393i) q^{10} +(-35.6274 + 20.5695i) q^{11} +(-7.55911 + 25.6508i) q^{12} -24.8455i q^{13} +(51.5773 - 9.15348i) q^{14} -61.5957i q^{15} +(-3.17079 + 63.9214i) q^{16} +(-41.3826 + 23.8923i) q^{17} +(35.8487 - 26.8086i) q^{18} +(-30.9150 + 53.5464i) q^{19} +(-34.6141 - 143.295i) q^{20} +(55.2933 + 27.8416i) q^{21} +(-115.542 + 13.7572i) q^{22} +(64.3994 + 37.1810i) q^{23} +(-48.2426 + 58.2535i) q^{24} +(107.279 + 185.812i) q^{25} +(27.6950 - 64.5862i) q^{26} +143.155 q^{27} +(144.279 + 33.6979i) q^{28} +28.8513 q^{29} +(68.6600 - 160.119i) q^{30} +(-11.5660 - 20.0328i) q^{31} +(-79.4949 + 162.630i) q^{32} +(-119.091 - 68.7571i) q^{33} +(-134.207 + 15.9796i) q^{34} +(-340.717 + 19.4877i) q^{35} +(123.072 - 29.7291i) q^{36} +(51.8900 - 89.8761i) q^{37} +(-140.052 + 104.734i) q^{38} +(71.9237 - 41.5252i) q^{39} +(69.7496 - 411.082i) q^{40} -96.1780i q^{41} +(112.701 + 134.009i) q^{42} -195.747i q^{43} +(-315.689 - 93.0315i) q^{44} +(-252.565 + 145.818i) q^{45} +(125.962 + 168.438i) q^{46} +(-89.8186 + 155.570i) q^{47} +(-190.342 + 97.6553i) q^{48} +(136.513 - 314.664i) q^{49} +(71.7499 + 602.603i) q^{50} +(-138.329 - 79.8641i) q^{51} +(143.987 - 137.021i) q^{52} +(-218.681 - 378.767i) q^{53} +(372.134 + 159.573i) q^{54} +758.071 q^{55} +(337.493 + 248.424i) q^{56} -206.678 q^{57} +(74.9993 + 32.1601i) q^{58} +(286.640 + 496.475i) q^{59} +(356.965 - 339.697i) q^{60} +(368.470 + 212.736i) q^{61} +(-7.73553 - 64.9681i) q^{62} +(-16.7374 - 292.633i) q^{63} +(-387.930 + 334.147i) q^{64} +(-228.915 + 396.492i) q^{65} +(-232.935 - 311.484i) q^{66} +(-728.093 + 420.365i) q^{67} +(-366.686 - 108.060i) q^{68} +248.568i q^{69} +(-907.422 - 329.135i) q^{70} -1179.04i q^{71} +(353.067 + 59.9061i) q^{72} +(716.185 - 413.489i) q^{73} +(235.072 - 175.793i) q^{74} +(-358.597 + 621.109i) q^{75} +(-480.812 + 116.144i) q^{76} +(-342.652 + 680.505i) q^{77} +(233.254 - 27.7728i) q^{78} +(282.007 + 162.817i) q^{79} +(639.543 - 990.864i) q^{80} +(25.6023 + 44.3445i) q^{81} +(107.208 - 250.016i) q^{82} -507.854 q^{83} +(143.589 + 473.986i) q^{84} +880.530 q^{85} +(218.197 - 508.848i) q^{86} +(48.2202 + 83.5198i) q^{87} +(-716.937 - 593.731i) q^{88} +(-176.826 - 102.090i) q^{89} +(-819.088 + 97.5260i) q^{90} +(-252.452 - 384.709i) q^{91} +(139.684 + 578.264i) q^{92} +(38.6612 - 66.9632i) q^{93} +(-406.897 + 304.288i) q^{94} +(986.704 - 569.674i) q^{95} +(-603.651 + 41.6847i) q^{96} +1116.33i q^{97} +(705.618 - 665.804i) q^{98} +651.087i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29} + 644 q^{30} - 40 q^{32} + 30 q^{33} + 208 q^{36} + 258 q^{37} - 1620 q^{38} - 1548 q^{40} - 980 q^{42} - 1248 q^{44} - 504 q^{45} + 232 q^{46} - 644 q^{49} - 864 q^{50} + 2592 q^{52} + 570 q^{53} + 4572 q^{54} + 1904 q^{56} + 1452 q^{57} + 2244 q^{58} - 736 q^{60} + 294 q^{61} + 2560 q^{64} - 124 q^{65} - 4272 q^{66} - 6084 q^{68} - 4144 q^{70} - 4672 q^{72} + 966 q^{73} + 832 q^{74} - 378 q^{77} - 4056 q^{78} + 7032 q^{80} - 1262 q^{81} + 7692 q^{82} + 6188 q^{84} - 2980 q^{85} + 5696 q^{86} - 1396 q^{88} - 3186 q^{89} + 3312 q^{92} - 306 q^{93} - 6780 q^{94} - 11784 q^{96} - 4900 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.59951 + 1.11469i 0.919067 + 0.394102i
\(3\) 1.67134 + 2.89484i 0.321649 + 0.557112i 0.980828 0.194873i \(-0.0624296\pi\)
−0.659179 + 0.751986i \(0.729096\pi\)
\(4\) 5.51494 + 5.79529i 0.689368 + 0.724411i
\(5\) −15.9583 9.21354i −1.42736 0.824084i −0.430444 0.902617i \(-0.641643\pi\)
−0.996911 + 0.0785333i \(0.974976\pi\)
\(6\) 1.11782 + 9.38820i 0.0760581 + 0.638786i
\(7\) 15.4841 10.1609i 0.836061 0.548636i
\(8\) 7.87623 + 21.2124i 0.348084 + 0.937463i
\(9\) 7.91327 13.7062i 0.293084 0.507636i
\(10\) −31.2137 41.7393i −0.987062 1.31991i
\(11\) −35.6274 + 20.5695i −0.976551 + 0.563812i −0.901227 0.433347i \(-0.857332\pi\)
−0.0753237 + 0.997159i \(0.523999\pi\)
\(12\) −7.55911 + 25.6508i −0.181844 + 0.617062i
\(13\) 24.8455i 0.530069i −0.964239 0.265035i \(-0.914617\pi\)
0.964239 0.265035i \(-0.0853834\pi\)
\(14\) 51.5773 9.15348i 0.984614 0.174741i
\(15\) 61.5957i 1.06026i
\(16\) −3.17079 + 63.9214i −0.0495436 + 0.998772i
\(17\) −41.3826 + 23.8923i −0.590398 + 0.340866i −0.765255 0.643728i \(-0.777387\pi\)
0.174857 + 0.984594i \(0.444054\pi\)
\(18\) 35.8487 26.8086i 0.469424 0.351047i
\(19\) −30.9150 + 53.5464i −0.373284 + 0.646547i −0.990069 0.140585i \(-0.955102\pi\)
0.616785 + 0.787132i \(0.288435\pi\)
\(20\) −34.6141 143.295i −0.386997 1.60209i
\(21\) 55.2933 + 27.8416i 0.574570 + 0.289312i
\(22\) −115.542 + 13.7572i −1.11971 + 0.133321i
\(23\) 64.3994 + 37.1810i 0.583835 + 0.337077i 0.762656 0.646804i \(-0.223895\pi\)
−0.178821 + 0.983882i \(0.557228\pi\)
\(24\) −48.2426 + 58.2535i −0.410312 + 0.495456i
\(25\) 107.279 + 185.812i 0.858229 + 1.48650i
\(26\) 27.6950 64.5862i 0.208901 0.487169i
\(27\) 143.155 1.02038
\(28\) 144.279 + 33.6979i 0.973792 + 0.227440i
\(29\) 28.8513 0.184743 0.0923715 0.995725i \(-0.470555\pi\)
0.0923715 + 0.995725i \(0.470555\pi\)
\(30\) 68.6600 160.119i 0.417851 0.974453i
\(31\) −11.5660 20.0328i −0.0670099 0.116065i 0.830574 0.556908i \(-0.188013\pi\)
−0.897584 + 0.440844i \(0.854679\pi\)
\(32\) −79.4949 + 162.630i −0.439151 + 0.898413i
\(33\) −119.091 68.7571i −0.628213 0.362699i
\(34\) −134.207 + 15.9796i −0.676951 + 0.0806023i
\(35\) −340.717 + 19.4877i −1.64548 + 0.0941147i
\(36\) 123.072 29.7291i 0.569780 0.137635i
\(37\) 51.8900 89.8761i 0.230558 0.399339i −0.727414 0.686199i \(-0.759278\pi\)
0.957973 + 0.286860i \(0.0926114\pi\)
\(38\) −140.052 + 104.734i −0.597878 + 0.447108i
\(39\) 71.9237 41.5252i 0.295308 0.170496i
\(40\) 69.7496 411.082i 0.275710 1.62494i
\(41\) 96.1780i 0.366353i −0.983080 0.183177i \(-0.941362\pi\)
0.983080 0.183177i \(-0.0586380\pi\)
\(42\) 112.701 + 134.009i 0.414050 + 0.492336i
\(43\) 195.747i 0.694213i −0.937826 0.347107i \(-0.887164\pi\)
0.937826 0.347107i \(-0.112836\pi\)
\(44\) −315.689 93.0315i −1.08163 0.318751i
\(45\) −252.565 + 145.818i −0.836670 + 0.483052i
\(46\) 125.962 + 168.438i 0.403741 + 0.539887i
\(47\) −89.8186 + 155.570i −0.278753 + 0.482815i −0.971075 0.238774i \(-0.923254\pi\)
0.692322 + 0.721589i \(0.256588\pi\)
\(48\) −190.342 + 97.6553i −0.572364 + 0.293653i
\(49\) 136.513 314.664i 0.397996 0.917387i
\(50\) 71.7499 + 602.603i 0.202939 + 1.70442i
\(51\) −138.329 79.8641i −0.379802 0.219279i
\(52\) 143.987 137.021i 0.383988 0.365413i
\(53\) −218.681 378.767i −0.566758 0.981654i −0.996884 0.0788851i \(-0.974864\pi\)
0.430125 0.902769i \(-0.358469\pi\)
\(54\) 372.134 + 159.573i 0.937796 + 0.402133i
\(55\) 758.071 1.85851
\(56\) 337.493 + 248.424i 0.805346 + 0.592805i
\(57\) −206.678 −0.480266
\(58\) 74.9993 + 32.1601i 0.169791 + 0.0728075i
\(59\) 286.640 + 496.475i 0.632497 + 1.09552i 0.987040 + 0.160477i \(0.0513034\pi\)
−0.354542 + 0.935040i \(0.615363\pi\)
\(60\) 356.965 339.697i 0.768067 0.730911i
\(61\) 368.470 + 212.736i 0.773405 + 0.446526i 0.834088 0.551632i \(-0.185995\pi\)
−0.0606829 + 0.998157i \(0.519328\pi\)
\(62\) −7.73553 64.9681i −0.0158454 0.133080i
\(63\) −16.7374 292.633i −0.0334717 0.585211i
\(64\) −387.930 + 334.147i −0.757675 + 0.652631i
\(65\) −228.915 + 396.492i −0.436822 + 0.756597i
\(66\) −232.935 311.484i −0.434430 0.580924i
\(67\) −728.093 + 420.365i −1.32762 + 0.766504i −0.984932 0.172944i \(-0.944672\pi\)
−0.342692 + 0.939448i \(0.611339\pi\)
\(68\) −366.686 108.060i −0.653929 0.192709i
\(69\) 248.568i 0.433682i
\(70\) −907.422 329.135i −1.54940 0.561988i
\(71\) 1179.04i 1.97079i −0.170279 0.985396i \(-0.554467\pi\)
0.170279 0.985396i \(-0.445533\pi\)
\(72\) 353.067 + 59.9061i 0.577908 + 0.0980556i
\(73\) 716.185 413.489i 1.14826 0.662949i 0.199798 0.979837i \(-0.435971\pi\)
0.948463 + 0.316888i \(0.102638\pi\)
\(74\) 235.072 175.793i 0.369279 0.276156i
\(75\) −358.597 + 621.109i −0.552097 + 0.956260i
\(76\) −480.812 + 116.144i −0.725696 + 0.175297i
\(77\) −342.652 + 680.505i −0.507128 + 1.00715i
\(78\) 233.254 27.7728i 0.338601 0.0403160i
\(79\) 282.007 + 162.817i 0.401623 + 0.231877i 0.687184 0.726483i \(-0.258847\pi\)
−0.285561 + 0.958361i \(0.592180\pi\)
\(80\) 639.543 990.864i 0.893788 1.38477i
\(81\) 25.6023 + 44.3445i 0.0351198 + 0.0608292i
\(82\) 107.208 250.016i 0.144380 0.336703i
\(83\) −507.854 −0.671617 −0.335808 0.941930i \(-0.609009\pi\)
−0.335808 + 0.941930i \(0.609009\pi\)
\(84\) 143.589 + 473.986i 0.186510 + 0.615667i
\(85\) 880.530 1.12361
\(86\) 218.197 508.848i 0.273591 0.638029i
\(87\) 48.2202 + 83.5198i 0.0594224 + 0.102923i
\(88\) −716.937 593.731i −0.868474 0.719227i
\(89\) −176.826 102.090i −0.210601 0.121590i 0.390990 0.920395i \(-0.372133\pi\)
−0.601591 + 0.798805i \(0.705466\pi\)
\(90\) −819.088 + 97.5260i −0.959327 + 0.114224i
\(91\) −252.452 384.709i −0.290815 0.443170i
\(92\) 139.684 + 578.264i 0.158295 + 0.655307i
\(93\) 38.6612 66.9632i 0.0431074 0.0746641i
\(94\) −406.897 + 304.288i −0.446471 + 0.333882i
\(95\) 986.704 569.674i 1.06562 0.615235i
\(96\) −603.651 + 41.6847i −0.641770 + 0.0443170i
\(97\) 1116.33i 1.16852i 0.811566 + 0.584261i \(0.198615\pi\)
−0.811566 + 0.584261i \(0.801385\pi\)
\(98\) 705.618 665.804i 0.727329 0.686289i
\(99\) 651.087i 0.660977i
\(100\) −485.199 + 1646.45i −0.485199 + 1.64645i
\(101\) −3.43081 + 1.98078i −0.00337999 + 0.00195144i −0.501689 0.865048i \(-0.667288\pi\)
0.498309 + 0.866999i \(0.333954\pi\)
\(102\) −270.564 361.801i −0.262645 0.351212i
\(103\) −179.406 + 310.741i −0.171626 + 0.297264i −0.938988 0.343949i \(-0.888235\pi\)
0.767363 + 0.641213i \(0.221569\pi\)
\(104\) 527.032 195.689i 0.496920 0.184508i
\(105\) −625.867 953.752i −0.581699 0.886445i
\(106\) −146.258 1228.37i −0.134017 1.12557i
\(107\) 803.472 + 463.885i 0.725931 + 0.419116i 0.816932 0.576735i \(-0.195673\pi\)
−0.0910010 + 0.995851i \(0.529007\pi\)
\(108\) 789.493 + 829.626i 0.703416 + 0.739174i
\(109\) −594.270 1029.31i −0.522209 0.904492i −0.999666 0.0258371i \(-0.991775\pi\)
0.477458 0.878655i \(-0.341558\pi\)
\(110\) 1970.62 + 845.012i 1.70810 + 0.732443i
\(111\) 346.903 0.296635
\(112\) 600.402 + 1021.98i 0.506541 + 0.862216i
\(113\) −662.367 −0.551418 −0.275709 0.961241i \(-0.588913\pi\)
−0.275709 + 0.961241i \(0.588913\pi\)
\(114\) −537.262 230.381i −0.441396 0.189273i
\(115\) −685.137 1186.69i −0.555560 0.962258i
\(116\) 159.113 + 167.201i 0.127356 + 0.133830i
\(117\) −340.537 196.609i −0.269082 0.155355i
\(118\) 191.710 + 1610.11i 0.149562 + 1.25612i
\(119\) −398.005 + 790.434i −0.306597 + 0.608899i
\(120\) 1306.59 485.142i 0.993958 0.369060i
\(121\) 180.707 312.993i 0.135768 0.235156i
\(122\) 720.708 + 963.739i 0.534835 + 0.715187i
\(123\) 278.420 160.746i 0.204100 0.117837i
\(124\) 52.3105 177.508i 0.0378840 0.128554i
\(125\) 1650.28i 1.18084i
\(126\) 282.685 779.361i 0.199870 0.551040i
\(127\) 1496.04i 1.04529i 0.852549 + 0.522647i \(0.175055\pi\)
−0.852549 + 0.522647i \(0.824945\pi\)
\(128\) −1380.90 + 436.200i −0.953558 + 0.301211i
\(129\) 566.657 327.160i 0.386755 0.223293i
\(130\) −1037.03 + 775.518i −0.699644 + 0.523211i
\(131\) 984.794 1705.71i 0.656808 1.13762i −0.324630 0.945841i \(-0.605240\pi\)
0.981437 0.191783i \(-0.0614270\pi\)
\(132\) −258.311 1069.36i −0.170327 0.705118i
\(133\) 65.3887 + 1143.24i 0.0426310 + 0.745350i
\(134\) −2361.26 + 281.148i −1.52225 + 0.181250i
\(135\) −2284.52 1318.97i −1.45644 0.840878i
\(136\) −832.751 689.643i −0.525058 0.434826i
\(137\) 896.791 + 1553.29i 0.559256 + 0.968660i 0.997559 + 0.0698322i \(0.0222464\pi\)
−0.438303 + 0.898827i \(0.644420\pi\)
\(138\) −277.076 + 646.156i −0.170915 + 0.398583i
\(139\) −306.409 −0.186973 −0.0934867 0.995621i \(-0.529801\pi\)
−0.0934867 + 0.995621i \(0.529801\pi\)
\(140\) −1991.97 1867.08i −1.20252 1.12712i
\(141\) −600.469 −0.358643
\(142\) 1314.26 3064.93i 0.776692 1.81129i
\(143\) 511.059 + 885.180i 0.298859 + 0.517639i
\(144\) 851.027 + 549.286i 0.492492 + 0.317874i
\(145\) −460.418 265.822i −0.263694 0.152244i
\(146\) 2322.64 276.549i 1.31660 0.156763i
\(147\) 1139.06 130.727i 0.639103 0.0733481i
\(148\) 807.028 194.944i 0.448225 0.108272i
\(149\) 714.928 1238.29i 0.393082 0.680838i −0.599773 0.800171i \(-0.704742\pi\)
0.992854 + 0.119333i \(0.0380756\pi\)
\(150\) −1624.52 + 1214.86i −0.884277 + 0.661285i
\(151\) −1079.16 + 623.054i −0.581595 + 0.335784i −0.761767 0.647851i \(-0.775668\pi\)
0.180172 + 0.983635i \(0.442335\pi\)
\(152\) −1379.34 234.037i −0.736048 0.124888i
\(153\) 756.264i 0.399610i
\(154\) −1649.28 + 1387.03i −0.863005 + 0.725780i
\(155\) 426.254i 0.220887i
\(156\) 637.306 + 187.810i 0.327085 + 0.0963899i
\(157\) −2201.64 + 1271.12i −1.11917 + 0.646154i −0.941189 0.337880i \(-0.890290\pi\)
−0.177982 + 0.984034i \(0.556957\pi\)
\(158\) 551.591 + 737.594i 0.277736 + 0.371391i
\(159\) 730.980 1266.10i 0.364594 0.631496i
\(160\) 2767.00 1862.87i 1.36719 0.920457i
\(161\) 1374.96 78.6420i 0.673054 0.0384960i
\(162\) 17.1233 + 143.813i 0.00830453 + 0.0697469i
\(163\) 637.434 + 368.022i 0.306305 + 0.176845i 0.645272 0.763953i \(-0.276744\pi\)
−0.338967 + 0.940798i \(0.610078\pi\)
\(164\) 557.379 530.416i 0.265390 0.252552i
\(165\) 1266.99 + 2194.49i 0.597789 + 1.03540i
\(166\) −1320.17 566.098i −0.617261 0.264685i
\(167\) −3110.82 −1.44145 −0.720726 0.693220i \(-0.756191\pi\)
−0.720726 + 0.693220i \(0.756191\pi\)
\(168\) −155.085 + 1392.19i −0.0712204 + 0.639343i
\(169\) 1579.70 0.719027
\(170\) 2288.95 + 981.515i 1.03267 + 0.442816i
\(171\) 489.278 + 847.454i 0.218807 + 0.378985i
\(172\) 1134.41 1079.54i 0.502896 0.478569i
\(173\) 2719.50 + 1570.10i 1.19514 + 0.690015i 0.959468 0.281817i \(-0.0909370\pi\)
0.235674 + 0.971832i \(0.424270\pi\)
\(174\) 32.2506 + 270.861i 0.0140512 + 0.118011i
\(175\) 3549.12 + 1787.08i 1.53308 + 0.771946i
\(176\) −1201.86 2342.57i −0.514738 1.00328i
\(177\) −958.144 + 1659.55i −0.406884 + 0.704744i
\(178\) −345.862 462.491i −0.145637 0.194748i
\(179\) 206.742 119.362i 0.0863274 0.0498411i −0.456215 0.889870i \(-0.650795\pi\)
0.542542 + 0.840028i \(0.317462\pi\)
\(180\) −2237.94 659.506i −0.926701 0.273093i
\(181\) 1947.09i 0.799591i −0.916604 0.399796i \(-0.869081\pi\)
0.916604 0.399796i \(-0.130919\pi\)
\(182\) −227.423 1281.46i −0.0926247 0.521914i
\(183\) 1422.21i 0.574498i
\(184\) −281.473 + 1658.91i −0.112774 + 0.664655i
\(185\) −1656.15 + 956.181i −0.658177 + 0.379999i
\(186\) 175.143 130.977i 0.0690438 0.0516327i
\(187\) 982.903 1702.44i 0.384369 0.665746i
\(188\) −1396.92 + 337.437i −0.541920 + 0.130905i
\(189\) 2216.62 1454.58i 0.853099 0.559817i
\(190\) 3199.96 381.008i 1.22184 0.145480i
\(191\) −393.391 227.124i −0.149030 0.0860427i 0.423631 0.905835i \(-0.360755\pi\)
−0.572661 + 0.819792i \(0.694089\pi\)
\(192\) −1615.66 564.522i −0.607295 0.212192i
\(193\) −1605.08 2780.08i −0.598634 1.03686i −0.993023 0.117921i \(-0.962377\pi\)
0.394389 0.918944i \(-0.370956\pi\)
\(194\) −1244.36 + 2901.93i −0.460516 + 1.07395i
\(195\) −1530.38 −0.562013
\(196\) 2576.43 944.223i 0.938931 0.344105i
\(197\) −4173.52 −1.50940 −0.754698 0.656073i \(-0.772216\pi\)
−0.754698 + 0.656073i \(0.772216\pi\)
\(198\) −725.758 + 1692.51i −0.260492 + 0.607482i
\(199\) −2639.30 4571.40i −0.940176 1.62843i −0.765134 0.643871i \(-0.777327\pi\)
−0.175042 0.984561i \(-0.556006\pi\)
\(200\) −3096.56 + 3739.13i −1.09480 + 1.32198i
\(201\) −2433.78 1405.14i −0.854057 0.493090i
\(202\) −11.1264 + 1.32478i −0.00387550 + 0.000461443i
\(203\) 446.735 293.155i 0.154456 0.101357i
\(204\) −300.039 1242.10i −0.102975 0.426296i
\(205\) −886.140 + 1534.84i −0.301906 + 0.522916i
\(206\) −812.748 + 607.793i −0.274888 + 0.205568i
\(207\) 1019.22 588.446i 0.342225 0.197584i
\(208\) 1588.16 + 78.7798i 0.529418 + 0.0262615i
\(209\) 2543.62i 0.841848i
\(210\) −563.815 3176.94i −0.185271 1.04395i
\(211\) 871.583i 0.284371i 0.989840 + 0.142185i \(0.0454130\pi\)
−0.989840 + 0.142185i \(0.954587\pi\)
\(212\) 989.051 3356.20i 0.320416 1.08729i
\(213\) 3413.13 1970.57i 1.09795 0.633903i
\(214\) 1571.55 + 2101.49i 0.502004 + 0.671286i
\(215\) −1803.53 + 3123.80i −0.572090 + 0.990889i
\(216\) 1127.52 + 3036.66i 0.355177 + 0.956568i
\(217\) −382.640 192.669i −0.119702 0.0602730i
\(218\) −397.459 3338.12i −0.123483 1.03709i
\(219\) 2393.97 + 1382.16i 0.738674 + 0.426474i
\(220\) 4180.72 + 4393.24i 1.28120 + 1.34633i
\(221\) 593.615 + 1028.17i 0.180683 + 0.312952i
\(222\) 901.778 + 386.688i 0.272628 + 0.116904i
\(223\) −1930.21 −0.579624 −0.289812 0.957084i \(-0.593593\pi\)
−0.289812 + 0.957084i \(0.593593\pi\)
\(224\) 421.563 + 3325.91i 0.125745 + 0.992063i
\(225\) 3395.70 1.00613
\(226\) −1721.83 738.333i −0.506790 0.217315i
\(227\) −988.231 1711.67i −0.288948 0.500473i 0.684611 0.728909i \(-0.259972\pi\)
−0.973559 + 0.228436i \(0.926639\pi\)
\(228\) −1139.82 1197.76i −0.331080 0.347910i
\(229\) −2237.66 1291.92i −0.645716 0.372804i 0.141097 0.989996i \(-0.454937\pi\)
−0.786813 + 0.617192i \(0.788270\pi\)
\(230\) −458.233 3848.54i −0.131369 1.10333i
\(231\) −2542.64 + 145.429i −0.724214 + 0.0414221i
\(232\) 227.239 + 612.004i 0.0643060 + 0.173190i
\(233\) 1724.22 2986.43i 0.484795 0.839690i −0.515052 0.857159i \(-0.672227\pi\)
0.999847 + 0.0174686i \(0.00556071\pi\)
\(234\) −666.072 890.680i −0.186079 0.248827i
\(235\) 2866.71 1655.10i 0.795759 0.459432i
\(236\) −1296.41 + 4399.19i −0.357582 + 1.21340i
\(237\) 1088.49i 0.298333i
\(238\) −1915.71 + 1611.09i −0.521751 + 0.438788i
\(239\) 3647.94i 0.987304i 0.869659 + 0.493652i \(0.164338\pi\)
−0.869659 + 0.493652i \(0.835662\pi\)
\(240\) 3937.28 + 195.307i 1.05896 + 0.0525292i
\(241\) −2194.49 + 1266.99i −0.586553 + 0.338646i −0.763733 0.645532i \(-0.776636\pi\)
0.177180 + 0.984178i \(0.443302\pi\)
\(242\) 818.639 612.198i 0.217455 0.162618i
\(243\) 1847.01 3199.12i 0.487597 0.844542i
\(244\) 799.222 + 3308.62i 0.209692 + 0.868084i
\(245\) −5077.68 + 3763.74i −1.32409 + 0.981455i
\(246\) 902.938 107.510i 0.234021 0.0278641i
\(247\) 1330.39 + 768.099i 0.342714 + 0.197866i
\(248\) 333.848 403.125i 0.0854813 0.103220i
\(249\) −848.795 1470.16i −0.216025 0.374166i
\(250\) 1839.54 4289.92i 0.465372 1.08527i
\(251\) 5658.23 1.42289 0.711443 0.702744i \(-0.248042\pi\)
0.711443 + 0.702744i \(0.248042\pi\)
\(252\) 1603.59 1710.85i 0.400859 0.427673i
\(253\) −3059.18 −0.760193
\(254\) −1667.62 + 3888.98i −0.411952 + 0.960695i
\(255\) 1471.66 + 2548.99i 0.361408 + 0.625977i
\(256\) −4075.89 405.362i −0.995091 0.0989655i
\(257\) 4328.82 + 2499.25i 1.05068 + 0.606610i 0.922840 0.385185i \(-0.125862\pi\)
0.127840 + 0.991795i \(0.459196\pi\)
\(258\) 1837.71 218.810i 0.443454 0.0528006i
\(259\) −109.753 1918.90i −0.0263310 0.460364i
\(260\) −3560.24 + 860.004i −0.849218 + 0.205135i
\(261\) 228.308 395.441i 0.0541452 0.0937822i
\(262\) 4461.32 3336.29i 1.05199 0.786704i
\(263\) −1646.99 + 950.892i −0.386152 + 0.222945i −0.680491 0.732756i \(-0.738234\pi\)
0.294340 + 0.955701i \(0.404900\pi\)
\(264\) 520.514 3067.74i 0.121346 0.715176i
\(265\) 8059.32i 1.86823i
\(266\) −1104.38 + 3044.76i −0.254563 + 0.701827i
\(267\) 682.509i 0.156438i
\(268\) −6451.53 1901.22i −1.47048 0.433342i
\(269\) 6976.20 4027.71i 1.58121 0.912913i 0.586530 0.809928i \(-0.300494\pi\)
0.994683 0.102986i \(-0.0328395\pi\)
\(270\) −4468.39 5975.19i −1.00718 1.34681i
\(271\) −2189.04 + 3791.53i −0.490682 + 0.849886i −0.999942 0.0107264i \(-0.996586\pi\)
0.509261 + 0.860612i \(0.329919\pi\)
\(272\) −1396.01 2720.99i −0.311197 0.606560i
\(273\) 691.739 1373.79i 0.153355 0.304562i
\(274\) 599.791 + 5037.44i 0.132243 + 1.11067i
\(275\) −7644.11 4413.33i −1.67621 0.967759i
\(276\) −1440.52 + 1370.84i −0.314164 + 0.298967i
\(277\) 1602.26 + 2775.19i 0.347547 + 0.601968i 0.985813 0.167847i \(-0.0536815\pi\)
−0.638266 + 0.769815i \(0.720348\pi\)
\(278\) −796.515 341.551i −0.171841 0.0736865i
\(279\) −366.098 −0.0785581
\(280\) −3096.95 7073.94i −0.660993 1.50982i
\(281\) 6258.33 1.32861 0.664307 0.747460i \(-0.268727\pi\)
0.664307 + 0.747460i \(0.268727\pi\)
\(282\) −1560.93 669.335i −0.329617 0.141342i
\(283\) 3029.37 + 5247.02i 0.636316 + 1.10213i 0.986235 + 0.165351i \(0.0528759\pi\)
−0.349919 + 0.936780i \(0.613791\pi\)
\(284\) 6832.87 6502.33i 1.42766 1.35860i
\(285\) 3298.23 + 1904.23i 0.685510 + 0.395779i
\(286\) 341.806 + 2870.71i 0.0706692 + 0.593526i
\(287\) −977.254 1489.23i −0.200995 0.306294i
\(288\) 1599.97 + 2376.51i 0.327359 + 0.486240i
\(289\) −1314.82 + 2277.33i −0.267620 + 0.463532i
\(290\) −900.554 1204.23i −0.182353 0.243844i
\(291\) −3231.61 + 1865.77i −0.650998 + 0.375854i
\(292\) 6346.01 + 1870.13i 1.27182 + 0.374798i
\(293\) 457.644i 0.0912486i −0.998959 0.0456243i \(-0.985472\pi\)
0.998959 0.0456243i \(-0.0145277\pi\)
\(294\) 3106.72 + 929.870i 0.616285 + 0.184460i
\(295\) 10563.9i 2.08492i
\(296\) 2315.18 + 392.825i 0.454619 + 0.0771367i
\(297\) −5100.24 + 2944.63i −0.996451 + 0.575301i
\(298\) 3238.77 2422.03i 0.629588 0.470821i
\(299\) 923.780 1600.03i 0.178674 0.309473i
\(300\) −5577.15 + 1347.20i −1.07332 + 0.259270i
\(301\) −1988.97 3030.96i −0.380871 0.580405i
\(302\) −3499.80 + 416.710i −0.666858 + 0.0794005i
\(303\) −11.4681 6.62110i −0.00217434 0.00125535i
\(304\) −3324.74 2145.92i −0.627259 0.404858i
\(305\) −3920.10 6789.82i −0.735949 1.27470i
\(306\) −842.997 + 1965.92i −0.157487 + 0.367268i
\(307\) −4195.62 −0.779989 −0.389995 0.920817i \(-0.627523\pi\)
−0.389995 + 0.920817i \(0.627523\pi\)
\(308\) −5833.43 + 1767.18i −1.07919 + 0.326929i
\(309\) −1199.39 −0.220813
\(310\) −475.140 + 1108.05i −0.0870520 + 0.203010i
\(311\) 3254.20 + 5636.44i 0.593341 + 1.02770i 0.993779 + 0.111372i \(0.0355246\pi\)
−0.400438 + 0.916324i \(0.631142\pi\)
\(312\) 1447.34 + 1198.61i 0.262626 + 0.217494i
\(313\) −7481.59 4319.50i −1.35107 0.780040i −0.362670 0.931918i \(-0.618135\pi\)
−0.988399 + 0.151878i \(0.951468\pi\)
\(314\) −7140.09 + 850.146i −1.28324 + 0.152792i
\(315\) −2429.09 + 4824.14i −0.434487 + 0.862888i
\(316\) 611.682 + 2532.24i 0.108892 + 0.450789i
\(317\) −463.165 + 802.226i −0.0820629 + 0.142137i −0.904136 0.427245i \(-0.859484\pi\)
0.822073 + 0.569382i \(0.192818\pi\)
\(318\) 3311.49 2476.42i 0.583960 0.436700i
\(319\) −1027.90 + 593.455i −0.180411 + 0.104160i
\(320\) 9269.39 1758.22i 1.61930 0.307149i
\(321\) 3101.23i 0.539233i
\(322\) 3661.88 + 1328.22i 0.633753 + 0.229871i
\(323\) 2954.52i 0.508960i
\(324\) −115.794 + 392.930i −0.0198549 + 0.0673749i
\(325\) 4616.59 2665.39i 0.787946 0.454921i
\(326\) 1246.79 + 1667.22i 0.211820 + 0.283248i
\(327\) 1986.45 3440.63i 0.335936 0.581858i
\(328\) 2040.16 757.520i 0.343443 0.127522i
\(329\) 189.976 + 3321.50i 0.0318351 + 0.556596i
\(330\) 847.387 + 7116.92i 0.141355 + 1.18719i
\(331\) 8260.72 + 4769.33i 1.37175 + 0.791982i 0.991149 0.132756i \(-0.0423828\pi\)
0.380604 + 0.924738i \(0.375716\pi\)
\(332\) −2800.79 2943.16i −0.462991 0.486527i
\(333\) −821.238 1422.43i −0.135146 0.234080i
\(334\) −8086.62 3467.59i −1.32479 0.568078i
\(335\) 15492.2 2.52665
\(336\) −1955.00 + 3446.14i −0.317423 + 0.559531i
\(337\) 4736.32 0.765589 0.382795 0.923833i \(-0.374962\pi\)
0.382795 + 0.923833i \(0.374962\pi\)
\(338\) 4106.46 + 1760.87i 0.660834 + 0.283370i
\(339\) −1107.04 1917.45i −0.177363 0.307202i
\(340\) 4856.07 + 5102.92i 0.774581 + 0.813956i
\(341\) 824.130 + 475.812i 0.130877 + 0.0755620i
\(342\) 327.238 + 2748.36i 0.0517398 + 0.434545i
\(343\) −1083.49 6259.36i −0.170563 0.985347i
\(344\) 4152.26 1541.75i 0.650800 0.241644i
\(345\) 2290.19 3966.73i 0.357391 0.619019i
\(346\) 5319.20 + 7112.89i 0.826479 + 1.10518i
\(347\) −1694.40 + 978.260i −0.262133 + 0.151342i −0.625307 0.780379i \(-0.715026\pi\)
0.363174 + 0.931721i \(0.381693\pi\)
\(348\) −218.090 + 740.057i −0.0335944 + 0.113998i
\(349\) 9739.50i 1.49382i −0.664924 0.746911i \(-0.731536\pi\)
0.664924 0.746911i \(-0.268464\pi\)
\(350\) 7233.96 + 8601.70i 1.10478 + 1.31366i
\(351\) 3556.76i 0.540871i
\(352\) −513.022 7429.25i −0.0776823 1.12494i
\(353\) −2590.09 + 1495.39i −0.390528 + 0.225471i −0.682389 0.730989i \(-0.739059\pi\)
0.291861 + 0.956461i \(0.405726\pi\)
\(354\) −4340.59 + 3246.00i −0.651695 + 0.487353i
\(355\) −10863.1 + 18815.5i −1.62410 + 2.81302i
\(356\) −383.540 1587.78i −0.0571000 0.236382i
\(357\) −2953.38 + 168.921i −0.437842 + 0.0250428i
\(358\) 670.480 79.8318i 0.0989831 0.0117856i
\(359\) 1144.24 + 660.628i 0.168219 + 0.0971215i 0.581746 0.813371i \(-0.302370\pi\)
−0.413527 + 0.910492i \(0.635703\pi\)
\(360\) −5082.41 4209.00i −0.744074 0.616205i
\(361\) 1518.02 + 2629.29i 0.221318 + 0.383334i
\(362\) 2170.40 5061.49i 0.315120 0.734878i
\(363\) 1208.09 0.174678
\(364\) 837.241 3584.68i 0.120559 0.516177i
\(365\) −15238.8 −2.18530
\(366\) −1585.32 + 3697.07i −0.226411 + 0.528002i
\(367\) −3367.76 5833.14i −0.479008 0.829666i 0.520703 0.853738i \(-0.325670\pi\)
−0.999710 + 0.0240726i \(0.992337\pi\)
\(368\) −2580.86 + 3998.61i −0.365589 + 0.566418i
\(369\) −1318.23 761.082i −0.185974 0.107372i
\(370\) −5371.04 + 639.511i −0.754667 + 0.0898557i
\(371\) −7234.69 3642.86i −1.01242 0.509779i
\(372\) 601.286 145.245i 0.0838044 0.0202436i
\(373\) −104.742 + 181.419i −0.0145398 + 0.0251837i −0.873204 0.487355i \(-0.837962\pi\)
0.858664 + 0.512539i \(0.171295\pi\)
\(374\) 4452.76 3329.88i 0.615632 0.460385i
\(375\) 4777.29 2758.17i 0.657862 0.379817i
\(376\) −4007.45 679.957i −0.549650 0.0932610i
\(377\) 716.824i 0.0979265i
\(378\) 7383.55 1310.37i 1.00468 0.178302i
\(379\) 1205.99i 0.163450i −0.996655 0.0817250i \(-0.973957\pi\)
0.996655 0.0817250i \(-0.0260429\pi\)
\(380\) 8743.04 + 2576.52i 1.18029 + 0.347822i
\(381\) −4330.81 + 2500.39i −0.582346 + 0.336218i
\(382\) −769.453 1028.92i −0.103059 0.137812i
\(383\) 1590.45 2754.73i 0.212188 0.367520i −0.740211 0.672375i \(-0.765274\pi\)
0.952399 + 0.304854i \(0.0986078\pi\)
\(384\) −3570.68 3268.44i −0.474519 0.434354i
\(385\) 11738.0 7702.67i 1.55383 1.01965i
\(386\) −1073.51 9016.03i −0.141555 1.18887i
\(387\) −2682.95 1549.00i −0.352408 0.203463i
\(388\) −6469.48 + 6156.52i −0.846490 + 0.805541i
\(389\) 4006.02 + 6938.63i 0.522142 + 0.904377i 0.999668 + 0.0257595i \(0.00820040\pi\)
−0.477526 + 0.878618i \(0.658466\pi\)
\(390\) −3978.23 1705.89i −0.516527 0.221490i
\(391\) −3553.36 −0.459593
\(392\) 7749.97 + 417.391i 0.998553 + 0.0537792i
\(393\) 6583.69 0.845046
\(394\) −10849.1 4652.17i −1.38724 0.594855i
\(395\) −3000.24 5196.56i −0.382173 0.661943i
\(396\) −3773.24 + 3590.71i −0.478819 + 0.455656i
\(397\) 10496.5 + 6060.15i 1.32696 + 0.766121i 0.984828 0.173531i \(-0.0555177\pi\)
0.342132 + 0.939652i \(0.388851\pi\)
\(398\) −1765.21 14825.4i −0.222317 1.86716i
\(399\) −3200.21 + 2100.03i −0.401531 + 0.263491i
\(400\) −12217.5 + 6268.23i −1.52719 + 0.783529i
\(401\) −5497.13 + 9521.31i −0.684573 + 1.18571i 0.288998 + 0.957330i \(0.406678\pi\)
−0.973571 + 0.228385i \(0.926655\pi\)
\(402\) −4760.35 6365.59i −0.590608 0.789768i
\(403\) −497.726 + 287.362i −0.0615223 + 0.0355199i
\(404\) −30.3999 8.95866i −0.00374370 0.00110324i
\(405\) 943.552i 0.115767i
\(406\) 1488.07 264.090i 0.181901 0.0322821i
\(407\) 4269.40i 0.519966i
\(408\) 604.598 3563.31i 0.0733629 0.432377i
\(409\) −1739.78 + 1004.46i −0.210333 + 0.121436i −0.601466 0.798898i \(-0.705417\pi\)
0.391133 + 0.920334i \(0.372083\pi\)
\(410\) −4014.40 + 3002.07i −0.483554 + 0.361613i
\(411\) −2997.68 + 5192.14i −0.359768 + 0.623137i
\(412\) −2790.25 + 674.007i −0.333655 + 0.0805969i
\(413\) 9482.98 + 4774.93i 1.12985 + 0.568908i
\(414\) 3305.41 393.564i 0.392396 0.0467213i
\(415\) 8104.49 + 4679.13i 0.958636 + 0.553469i
\(416\) 4040.63 + 1975.09i 0.476221 + 0.232781i
\(417\) −512.113 887.006i −0.0601398 0.104165i
\(418\) 2835.35 6612.18i 0.331773 0.773714i
\(419\) 6662.83 0.776850 0.388425 0.921480i \(-0.373019\pi\)
0.388425 + 0.921480i \(0.373019\pi\)
\(420\) 2075.65 8886.97i 0.241146 1.03248i
\(421\) 5859.67 0.678344 0.339172 0.940724i \(-0.389853\pi\)
0.339172 + 0.940724i \(0.389853\pi\)
\(422\) −971.543 + 2265.69i −0.112071 + 0.261356i
\(423\) 1421.52 + 2462.14i 0.163396 + 0.283010i
\(424\) 6312.17 7622.01i 0.722986 0.873013i
\(425\) −8878.94 5126.26i −1.01339 0.585083i
\(426\) 11069.1 1317.95i 1.25891 0.149895i
\(427\) 7867.00 449.960i 0.891594 0.0509956i
\(428\) 1742.76 + 7214.65i 0.196821 + 0.814798i
\(429\) −1708.30 + 2958.87i −0.192256 + 0.332996i
\(430\) −8170.35 + 6109.99i −0.916300 + 0.685232i
\(431\) −3178.02 + 1834.83i −0.355174 + 0.205060i −0.666962 0.745092i \(-0.732406\pi\)
0.311788 + 0.950152i \(0.399072\pi\)
\(432\) −453.915 + 9150.68i −0.0505532 + 1.01913i
\(433\) 8282.34i 0.919224i 0.888120 + 0.459612i \(0.152011\pi\)
−0.888120 + 0.459612i \(0.847989\pi\)
\(434\) −779.911 927.370i −0.0862602 0.102570i
\(435\) 1777.11i 0.195876i
\(436\) 2687.76 9120.53i 0.295230 1.00182i
\(437\) −3981.82 + 2298.90i −0.435872 + 0.251651i
\(438\) 4682.49 + 6261.47i 0.510817 + 0.683070i
\(439\) 4840.93 8384.73i 0.526298 0.911575i −0.473233 0.880938i \(-0.656913\pi\)
0.999531 0.0306374i \(-0.00975370\pi\)
\(440\) 5970.74 + 16080.5i 0.646918 + 1.74229i
\(441\) −3232.58 4361.08i −0.349053 0.470909i
\(442\) 397.021 + 3334.44i 0.0427248 + 0.358831i
\(443\) −7154.34 4130.56i −0.767298 0.443000i 0.0646117 0.997910i \(-0.479419\pi\)
−0.831910 + 0.554911i \(0.812752\pi\)
\(444\) 1913.15 + 2010.40i 0.204491 + 0.214886i
\(445\) 1881.23 + 3258.38i 0.200402 + 0.347106i
\(446\) −5017.60 2151.58i −0.532713 0.228431i
\(447\) 4779.54 0.505737
\(448\) −2611.50 + 9115.67i −0.275405 + 0.961328i
\(449\) −73.1562 −0.00768921 −0.00384461 0.999993i \(-0.501224\pi\)
−0.00384461 + 0.999993i \(0.501224\pi\)
\(450\) 8827.16 + 3785.14i 0.924703 + 0.396518i
\(451\) 1978.33 + 3426.57i 0.206554 + 0.357762i
\(452\) −3652.92 3838.61i −0.380130 0.399454i
\(453\) −3607.28 2082.67i −0.374139 0.216009i
\(454\) −660.948 5551.07i −0.0683256 0.573843i
\(455\) 484.180 + 8465.29i 0.0498873 + 0.872217i
\(456\) −1627.84 4384.13i −0.167173 0.450231i
\(457\) 6586.17 11407.6i 0.674153 1.16767i −0.302563 0.953129i \(-0.597842\pi\)
0.976716 0.214538i \(-0.0688245\pi\)
\(458\) −4376.75 5852.65i −0.446533 0.597110i
\(459\) −5924.14 + 3420.30i −0.602429 + 0.347813i
\(460\) 3098.74 10515.1i 0.314085 1.06580i
\(461\) 12655.0i 1.27853i −0.768985 0.639267i \(-0.779238\pi\)
0.768985 0.639267i \(-0.220762\pi\)
\(462\) −6771.74 2456.21i −0.681926 0.247344i
\(463\) 852.596i 0.0855799i 0.999084 + 0.0427899i \(0.0136246\pi\)
−0.999084 + 0.0427899i \(0.986375\pi\)
\(464\) −91.4813 + 1844.21i −0.00915283 + 0.184516i
\(465\) −1233.94 + 712.414i −0.123059 + 0.0710482i
\(466\) 7811.07 5841.31i 0.776483 0.580673i
\(467\) 5462.60 9461.49i 0.541282 0.937528i −0.457549 0.889185i \(-0.651272\pi\)
0.998831 0.0483436i \(-0.0153942\pi\)
\(468\) −738.635 3057.80i −0.0729560 0.302023i
\(469\) −7002.56 + 13907.0i −0.689442 + 1.36923i
\(470\) 9296.96 1106.96i 0.912419 0.108639i
\(471\) −7359.36 4248.93i −0.719961 0.415669i
\(472\) −8273.77 + 9990.67i −0.806846 + 0.974275i
\(473\) 4026.42 + 6973.96i 0.391406 + 0.677935i
\(474\) −1213.32 + 2829.54i −0.117573 + 0.274188i
\(475\) −13266.1 −1.28145
\(476\) −6775.77 + 2052.65i −0.652451 + 0.197653i
\(477\) −6921.93 −0.664431
\(478\) −4066.32 + 9482.88i −0.389098 + 0.907399i
\(479\) 5330.56 + 9232.81i 0.508475 + 0.880705i 0.999952 + 0.00981425i \(0.00312402\pi\)
−0.491477 + 0.870891i \(0.663543\pi\)
\(480\) 10017.3 + 4896.55i 0.952554 + 0.465616i
\(481\) −2233.01 1289.23i −0.211677 0.122212i
\(482\) −7116.89 + 847.384i −0.672542 + 0.0800774i
\(483\) 2525.67 + 3848.84i 0.237934 + 0.362585i
\(484\) 2810.47 678.892i 0.263944 0.0637577i
\(485\) 10285.4 17814.8i 0.962960 1.66789i
\(486\) 8367.36 6257.32i 0.780969 0.584028i
\(487\) 46.9282 27.0940i 0.00436657 0.00252104i −0.497815 0.867283i \(-0.665864\pi\)
0.502182 + 0.864762i \(0.332531\pi\)
\(488\) −1610.48 + 9491.68i −0.149392 + 0.880467i
\(489\) 2460.36i 0.227528i
\(490\) −17394.9 + 4123.87i −1.60372 + 0.380199i
\(491\) 5628.07i 0.517294i −0.965972 0.258647i \(-0.916723\pi\)
0.965972 0.258647i \(-0.0832766\pi\)
\(492\) 2467.04 + 727.020i 0.226062 + 0.0666191i
\(493\) −1193.94 + 689.322i −0.109072 + 0.0629727i
\(494\) 2602.17 + 3479.65i 0.236998 + 0.316917i
\(495\) 5998.81 10390.3i 0.544700 0.943449i
\(496\) 1317.20 675.793i 0.119242 0.0611774i
\(497\) −11980.1 18256.3i −1.08125 1.64770i
\(498\) −567.690 4767.83i −0.0510819 0.429019i
\(499\) −536.728 309.880i −0.0481508 0.0277999i 0.475731 0.879591i \(-0.342183\pi\)
−0.523882 + 0.851791i \(0.675517\pi\)
\(500\) 9563.84 9101.19i 0.855416 0.814035i
\(501\) −5199.23 9005.33i −0.463641 0.803050i
\(502\) 14708.7 + 6307.16i 1.30773 + 0.560762i
\(503\) −18680.1 −1.65587 −0.827935 0.560823i \(-0.810485\pi\)
−0.827935 + 0.560823i \(0.810485\pi\)
\(504\) 6075.62 2659.89i 0.536963 0.235081i
\(505\) 73.0000 0.00643259
\(506\) −7952.37 3410.02i −0.698668 0.299593i
\(507\) 2640.21 + 4572.98i 0.231274 + 0.400579i
\(508\) −8670.00 + 8250.59i −0.757223 + 0.720592i
\(509\) 3084.16 + 1780.64i 0.268572 + 0.155060i 0.628238 0.778021i \(-0.283776\pi\)
−0.359667 + 0.933081i \(0.617110\pi\)
\(510\) 984.275 + 8266.58i 0.0854596 + 0.717746i
\(511\) 6888.03 13679.6i 0.596298 1.18424i
\(512\) −10143.5 5597.09i −0.875553 0.483123i
\(513\) −4425.65 + 7665.44i −0.380891 + 0.659722i
\(514\) 8466.96 + 11322.1i 0.726579 + 0.971590i
\(515\) 5726.05 3305.93i 0.489941 0.282868i
\(516\) 5021.07 + 1479.68i 0.428372 + 0.126239i
\(517\) 7390.09i 0.628657i
\(518\) 1853.66 5110.54i 0.157230 0.433483i
\(519\) 10496.7i 0.887771i
\(520\) −10213.5 1732.96i −0.861333 0.146145i
\(521\) 10004.0 5775.82i 0.841235 0.485687i −0.0164486 0.999865i \(-0.505236\pi\)
0.857684 + 0.514177i \(0.171903\pi\)
\(522\) 1034.28 773.462i 0.0867228 0.0648534i
\(523\) −2135.62 + 3699.00i −0.178554 + 0.309265i −0.941386 0.337332i \(-0.890475\pi\)
0.762831 + 0.646598i \(0.223809\pi\)
\(524\) 15316.2 3699.74i 1.27689 0.308443i
\(525\) 758.474 + 13261.0i 0.0630524 + 1.10239i
\(526\) −5341.33 + 635.974i −0.442762 + 0.0527182i
\(527\) 957.260 + 552.674i 0.0791250 + 0.0456829i
\(528\) 4772.66 7394.43i 0.393377 0.609472i
\(529\) −3318.65 5748.06i −0.272758 0.472431i
\(530\) −8983.62 + 20950.3i −0.736271 + 1.71702i
\(531\) 9073.03 0.741499
\(532\) −6264.79 + 6683.85i −0.510551 + 0.544703i
\(533\) −2389.59 −0.194192
\(534\) 760.785 1774.19i 0.0616524 0.143777i
\(535\) −8548.04 14805.6i −0.690774 1.19646i
\(536\) −14651.6 12133.7i −1.18069 0.977791i
\(537\) 691.070 + 398.990i 0.0555342 + 0.0320627i
\(538\) 22624.4 2693.81i 1.81302 0.215870i
\(539\) 1608.88 + 14018.6i 0.128570 + 1.12027i
\(540\) −4955.18 20513.5i −0.394884 1.63474i
\(541\) −4878.48 + 8449.78i −0.387694 + 0.671505i −0.992139 0.125142i \(-0.960061\pi\)
0.604445 + 0.796647i \(0.293395\pi\)
\(542\) −9916.82 + 7416.04i −0.785911 + 0.587724i
\(543\) 5636.51 3254.24i 0.445462 0.257188i
\(544\) −595.896 8629.38i −0.0469647 0.680113i
\(545\) 21901.3i 1.72138i
\(546\) 3329.53 2800.11i 0.260972 0.219475i
\(547\) 19891.0i 1.55480i 0.629005 + 0.777401i \(0.283463\pi\)
−0.629005 + 0.777401i \(0.716537\pi\)
\(548\) −4056.00 + 13763.5i −0.316175 + 1.07289i
\(549\) 5831.60 3366.87i 0.453345 0.261739i
\(550\) −14951.5 19993.3i −1.15915 1.55003i
\(551\) −891.938 + 1544.88i −0.0689616 + 0.119445i
\(552\) −5272.72 + 1957.78i −0.406561 + 0.150958i
\(553\) 6020.98 344.376i 0.462998 0.0264816i
\(554\) 1071.62 + 9000.17i 0.0821819 + 0.690218i
\(555\) −5535.98 3196.20i −0.423404 0.244453i
\(556\) −1689.83 1775.73i −0.128893 0.135446i
\(557\) −3043.39 5271.30i −0.231513 0.400992i 0.726741 0.686912i \(-0.241034\pi\)
−0.958253 + 0.285920i \(0.907701\pi\)
\(558\) −951.677 408.085i −0.0722002 0.0309599i
\(559\) −4863.44 −0.367981
\(560\) −165.336 21840.9i −0.0124763 1.64812i
\(561\) 6571.05 0.494527
\(562\) 16268.6 + 6976.08i 1.22108 + 0.523609i
\(563\) −4067.94 7045.87i −0.304517 0.527439i 0.672637 0.739973i \(-0.265162\pi\)
−0.977154 + 0.212534i \(0.931828\pi\)
\(564\) −3311.55 3479.89i −0.247237 0.259805i
\(565\) 10570.3 + 6102.75i 0.787070 + 0.454415i
\(566\) 2026.10 + 17016.5i 0.150465 + 1.26371i
\(567\) 847.008 + 426.491i 0.0627354 + 0.0315890i
\(568\) 25010.2 9286.39i 1.84755 0.686000i
\(569\) −11495.9 + 19911.5i −0.846985 + 1.46702i 0.0369008 + 0.999319i \(0.488251\pi\)
−0.883886 + 0.467702i \(0.845082\pi\)
\(570\) 6451.17 + 8626.58i 0.474052 + 0.633908i
\(571\) 16493.6 9522.59i 1.20882 0.697912i 0.246318 0.969189i \(-0.420779\pi\)
0.962501 + 0.271277i \(0.0874459\pi\)
\(572\) −2311.41 + 7843.45i −0.168960 + 0.573341i
\(573\) 1518.41i 0.110702i
\(574\) −880.363 4960.60i −0.0640168 0.360717i
\(575\) 15954.9i 1.15716i
\(576\) 1510.09 + 7961.23i 0.109237 + 0.575899i
\(577\) 13902.1 8026.36i 1.00303 0.579102i 0.0938892 0.995583i \(-0.470070\pi\)
0.909144 + 0.416481i \(0.136737\pi\)
\(578\) −5956.40 + 4454.35i −0.428640 + 0.320547i
\(579\) 5365.27 9292.92i 0.385100 0.667013i
\(580\) −998.660 4134.25i −0.0714950 0.295975i
\(581\) −7863.64 + 5160.25i −0.561513 + 0.368473i
\(582\) −10480.4 + 1247.86i −0.746435 + 0.0888755i
\(583\) 15582.1 + 8996.32i 1.10694 + 0.639090i
\(584\) 14411.9 + 11935.2i 1.02118 + 0.845691i
\(585\) 3622.93 + 6275.10i 0.256051 + 0.443493i
\(586\) 510.130 1189.65i 0.0359612 0.0838635i
\(587\) −21155.6 −1.48754 −0.743770 0.668436i \(-0.766964\pi\)
−0.743770 + 0.668436i \(0.766964\pi\)
\(588\) 7039.45 + 5880.23i 0.493711 + 0.412409i
\(589\) 1430.25 0.100055
\(590\) 11775.4 27460.9i 0.821672 1.91618i
\(591\) −6975.36 12081.7i −0.485495 0.840903i
\(592\) 5580.47 + 3601.86i 0.387426 + 0.250060i
\(593\) −1240.18 716.018i −0.0858821 0.0495840i 0.456444 0.889752i \(-0.349123\pi\)
−0.542326 + 0.840168i \(0.682456\pi\)
\(594\) −16540.5 + 1969.42i −1.14253 + 0.136038i
\(595\) 13634.2 8946.96i 0.939406 0.616453i
\(596\) 11119.0 2685.89i 0.764184 0.184595i
\(597\) 8822.32 15280.7i 0.604813 1.04757i
\(598\) 4184.92 3129.59i 0.286177 0.214010i
\(599\) −4611.09 + 2662.21i −0.314531 + 0.181595i −0.648952 0.760829i \(-0.724793\pi\)
0.334421 + 0.942424i \(0.391459\pi\)
\(600\) −15999.6 2714.70i −1.08863 0.184712i
\(601\) 8711.39i 0.591256i 0.955303 + 0.295628i \(0.0955289\pi\)
−0.955303 + 0.295628i \(0.904471\pi\)
\(602\) −1791.77 10096.1i −0.121307 0.683533i
\(603\) 13305.8i 0.898599i
\(604\) −9562.29 2817.94i −0.644179 0.189835i
\(605\) −5767.55 + 3329.90i −0.387577 + 0.223768i
\(606\) −22.4310 29.9950i −0.00150363 0.00201067i
\(607\) −12379.6 + 21442.1i −0.827796 + 1.43378i 0.0719681 + 0.997407i \(0.477072\pi\)
−0.899764 + 0.436377i \(0.856261\pi\)
\(608\) −6250.67 9284.38i −0.416938 0.619295i
\(609\) 1595.28 + 803.266i 0.106148 + 0.0534483i
\(610\) −2621.84 22019.9i −0.174025 1.46157i
\(611\) 3865.22 + 2231.59i 0.255925 + 0.147758i
\(612\) −4382.77 + 4170.75i −0.289482 + 0.275478i
\(613\) −3167.74 5486.69i −0.208717 0.361509i 0.742593 0.669743i \(-0.233596\pi\)
−0.951311 + 0.308233i \(0.900262\pi\)
\(614\) −10906.6 4676.81i −0.716862 0.307395i
\(615\) −5924.15 −0.388431
\(616\) −17133.9 1908.66i −1.12069 0.124841i
\(617\) 12720.7 0.830013 0.415006 0.909819i \(-0.363779\pi\)
0.415006 + 0.909819i \(0.363779\pi\)
\(618\) −3117.84 1336.95i −0.202942 0.0870226i
\(619\) −11135.8 19287.7i −0.723077 1.25241i −0.959761 0.280820i \(-0.909394\pi\)
0.236683 0.971587i \(-0.423940\pi\)
\(620\) −2470.26 + 2350.77i −0.160013 + 0.152273i
\(621\) 9219.10 + 5322.65i 0.595733 + 0.343946i
\(622\) 2176.47 + 18279.4i 0.140303 + 1.17836i
\(623\) −3775.31 + 215.932i −0.242784 + 0.0138863i
\(624\) 2426.29 + 4729.13i 0.155656 + 0.303392i
\(625\) −1795.08 + 3109.16i −0.114885 + 0.198987i
\(626\) −14633.6 19568.2i −0.934308 1.24937i
\(627\) 7363.39 4251.25i 0.469004 0.270779i
\(628\) −19508.4 5749.00i −1.23960 0.365303i
\(629\) 4959.08i 0.314358i
\(630\) −11691.9 + 9832.76i −0.739388 + 0.621820i
\(631\) 7895.30i 0.498110i −0.968489 0.249055i \(-0.919880\pi\)
0.968489 0.249055i \(-0.0801199\pi\)
\(632\) −1232.58 + 7264.42i −0.0775780 + 0.457220i
\(633\) −2523.10 + 1456.71i −0.158427 + 0.0914676i
\(634\) −2098.23 + 1569.11i −0.131438 + 0.0982924i
\(635\) 13783.8 23874.3i 0.861410 1.49201i
\(636\) 11368.7 2746.20i 0.708803 0.171217i
\(637\) −7817.98 3391.72i −0.486279 0.210965i
\(638\) −3333.54 + 396.914i −0.206859 + 0.0246301i
\(639\) −16160.1 9330.05i −1.00045 0.577607i
\(640\) 26055.8 + 5761.95i 1.60929 + 0.355876i
\(641\) −4213.92 7298.73i −0.259657 0.449739i 0.706493 0.707720i \(-0.250276\pi\)
−0.966150 + 0.257981i \(0.916943\pi\)
\(642\) −3456.90 + 8061.69i −0.212513 + 0.495591i
\(643\) 12838.8 0.787424 0.393712 0.919234i \(-0.371191\pi\)
0.393712 + 0.919234i \(0.371191\pi\)
\(644\) 8038.56 + 7534.57i 0.491869 + 0.461030i
\(645\) −12057.2 −0.736049
\(646\) 3293.37 7680.32i 0.200582 0.467768i
\(647\) 11376.3 + 19704.4i 0.691267 + 1.19731i 0.971423 + 0.237355i \(0.0762805\pi\)
−0.280156 + 0.959955i \(0.590386\pi\)
\(648\) −739.003 + 892.354i −0.0448006 + 0.0540972i
\(649\) −20424.5 11792.1i −1.23533 0.713219i
\(650\) 14972.0 1782.66i 0.903460 0.107572i
\(651\) −81.7728 1429.70i −0.00492309 0.0860740i
\(652\) 1382.61 + 5723.74i 0.0830480 + 0.343802i
\(653\) −430.103 + 744.961i −0.0257753 + 0.0446441i −0.878625 0.477512i \(-0.841539\pi\)
0.852850 + 0.522156i \(0.174872\pi\)
\(654\) 8999.04 6729.70i 0.538058 0.402373i
\(655\) −31431.3 + 18146.9i −1.87500 + 1.08253i
\(656\) 6147.83 + 304.960i 0.365903 + 0.0181504i
\(657\) 13088.2i 0.777199i
\(658\) −3208.59 + 8846.05i −0.190097 + 0.524096i
\(659\) 19262.8i 1.13865i −0.822111 0.569327i \(-0.807204\pi\)
0.822111 0.569327i \(-0.192796\pi\)
\(660\) −5730.34 + 19445.1i −0.337959 + 1.14682i
\(661\) 3499.64 2020.52i 0.205931 0.118894i −0.393488 0.919330i \(-0.628732\pi\)
0.599419 + 0.800436i \(0.295398\pi\)
\(662\) 16157.5 + 21606.1i 0.948611 + 1.26849i
\(663\) −1984.26 + 3436.84i −0.116233 + 0.201321i
\(664\) −3999.98 10772.8i −0.233779 0.629616i
\(665\) 9489.80 18846.7i 0.553381 1.09901i
\(666\) −549.259 4613.04i −0.0319570 0.268396i
\(667\) 1858.00 + 1072.72i 0.107859 + 0.0622727i
\(668\) −17156.0 18028.1i −0.993691 1.04420i
\(669\) −3226.03 5587.64i −0.186435 0.322916i
\(670\) 40272.2 + 17269.0i 2.32216 + 0.995758i
\(671\) −17503.5 −1.00703
\(672\) −8923.42 + 6779.08i −0.512245 + 0.389150i
\(673\) −30094.8 −1.72373 −0.861863 0.507141i \(-0.830702\pi\)
−0.861863 + 0.507141i \(0.830702\pi\)
\(674\) 12312.1 + 5279.51i 0.703628 + 0.301720i
\(675\) 15357.5 + 26599.9i 0.875718 + 1.51679i
\(676\) 8711.97 + 9154.83i 0.495674 + 0.520871i
\(677\) 16898.8 + 9756.55i 0.959343 + 0.553877i 0.895971 0.444113i \(-0.146481\pi\)
0.0633724 + 0.997990i \(0.479814\pi\)
\(678\) −740.408 6218.43i −0.0419398 0.352238i
\(679\) 11342.9 + 17285.4i 0.641093 + 0.976955i
\(680\) 6935.26 + 18678.1i 0.391110 + 1.05334i
\(681\) 3303.34 5721.55i 0.185880 0.321953i
\(682\) 1611.96 + 2155.53i 0.0905058 + 0.121025i
\(683\) 19594.6 11312.9i 1.09775 0.633788i 0.162123 0.986771i \(-0.448166\pi\)
0.935630 + 0.352982i \(0.114832\pi\)
\(684\) −2212.90 + 7509.17i −0.123702 + 0.419766i
\(685\) 33050.5i 1.84350i
\(686\) 4160.68 17479.1i 0.231568 0.972819i
\(687\) 8636.90i 0.479648i
\(688\) 12512.4 + 620.673i 0.693361 + 0.0343938i
\(689\) −9410.66 + 5433.24i −0.520345 + 0.300421i
\(690\) 10375.0 7758.71i 0.572422 0.428071i
\(691\) 102.478 177.498i 0.00564177 0.00977182i −0.863191 0.504878i \(-0.831537\pi\)
0.868833 + 0.495106i \(0.164871\pi\)
\(692\) 5898.67 + 24419.3i 0.324037 + 1.34145i
\(693\) 6615.62 + 10081.5i 0.362636 + 0.552617i
\(694\) −5495.06 + 654.279i −0.300562 + 0.0357869i
\(695\) 4889.78 + 2823.11i 0.266877 + 0.154082i
\(696\) −1391.86 + 1680.69i −0.0758022 + 0.0915320i
\(697\) 2297.91 + 3980.10i 0.124877 + 0.216294i
\(698\) 10856.5 25318.0i 0.588717 1.37292i
\(699\) 11527.0 0.623736
\(700\) 9216.58 + 30423.9i 0.497649 + 1.64273i
\(701\) 9946.71 0.535923 0.267962 0.963430i \(-0.413650\pi\)
0.267962 + 0.963430i \(0.413650\pi\)
\(702\) 3964.67 9245.84i 0.213158 0.497097i
\(703\) 3208.36 + 5557.04i 0.172127 + 0.298133i
\(704\) 6947.69 19884.3i 0.371947 1.06451i
\(705\) 9582.47 + 5532.44i 0.511910 + 0.295552i
\(706\) −8399.85 + 1000.14i −0.447780 + 0.0533157i
\(707\) −32.9964 + 65.5307i −0.00175525 + 0.00348590i
\(708\) −14901.7 + 3599.62i −0.791018 + 0.191076i
\(709\) −14432.4 + 24997.6i −0.764484 + 1.32412i 0.176035 + 0.984384i \(0.443673\pi\)
−0.940519 + 0.339741i \(0.889661\pi\)
\(710\) −49212.2 + 36802.1i −2.60127 + 1.94529i
\(711\) 4463.19 2576.82i 0.235419 0.135919i
\(712\) 772.858 4554.98i 0.0406799 0.239754i
\(713\) 1720.14i 0.0903501i
\(714\) −7865.65 2852.98i −0.412275 0.149538i
\(715\) 18834.6i 0.985141i
\(716\) 1831.91 + 539.852i 0.0956168 + 0.0281777i
\(717\) −10560.2 + 6096.94i −0.550039 + 0.317565i
\(718\) 2238.08 + 2992.78i 0.116329 + 0.155557i
\(719\) 3063.07 5305.39i 0.158878 0.275185i −0.775586 0.631241i \(-0.782546\pi\)
0.934464 + 0.356057i \(0.115879\pi\)
\(720\) −8520.09 16606.7i −0.441007 0.859574i
\(721\) 379.464 + 6634.46i 0.0196005 + 0.342691i
\(722\) 1015.28 + 8527.00i 0.0523336 + 0.439532i
\(723\) −7335.45 4235.12i −0.377328 0.217851i
\(724\) 11283.9 10738.1i 0.579233 0.551213i
\(725\) 3095.12 + 5360.91i 0.158552 + 0.274620i
\(726\) 3140.44 + 1346.64i 0.160541 + 0.0688409i
\(727\) 20742.9 1.05820 0.529101 0.848559i \(-0.322529\pi\)
0.529101 + 0.848559i \(0.322529\pi\)
\(728\) 6172.22 8385.17i 0.314228 0.426889i
\(729\) 13730.5 0.697579
\(730\) −39613.5 16986.5i −2.00844 0.861231i
\(731\) 4676.85 + 8100.54i 0.236634 + 0.409862i
\(732\) −8242.15 + 7843.43i −0.416173 + 0.396040i
\(733\) −15694.9 9061.44i −0.790864 0.456606i 0.0494026 0.998779i \(-0.484268\pi\)
−0.840267 + 0.542173i \(0.817602\pi\)
\(734\) −2252.42 18917.3i −0.113268 0.951296i
\(735\) −19381.9 8408.59i −0.972672 0.421980i
\(736\) −11166.2 + 7517.58i −0.559227 + 0.376497i
\(737\) 17293.4 29953.0i 0.864328 1.49706i
\(738\) −2578.40 3447.86i −0.128607 0.171975i
\(739\) −32754.4 + 18910.8i −1.63043 + 0.941332i −0.646476 + 0.762934i \(0.723758\pi\)
−0.983958 + 0.178398i \(0.942909\pi\)
\(740\) −14674.9 4324.61i −0.729002 0.214832i
\(741\) 5135.01i 0.254574i
\(742\) −14746.0 17534.1i −0.729573 0.867515i
\(743\) 4974.35i 0.245614i 0.992431 + 0.122807i \(0.0391896\pi\)
−0.992431 + 0.122807i \(0.960810\pi\)
\(744\) 1724.95 + 292.679i 0.0849999 + 0.0144222i
\(745\) −22818.1 + 13174.0i −1.12213 + 0.647865i
\(746\) −474.504 + 354.846i −0.0232880 + 0.0174153i
\(747\) −4018.78 + 6960.73i −0.196840 + 0.340937i
\(748\) 15286.8 3692.64i 0.747246 0.180503i
\(749\) 17154.5 981.168i 0.836865 0.0478653i
\(750\) 15493.1 1844.72i 0.754306 0.0898127i
\(751\) −19034.7 10989.7i −0.924884 0.533982i −0.0396939 0.999212i \(-0.512638\pi\)
−0.885190 + 0.465230i \(0.845972\pi\)
\(752\) −9659.49 6234.61i −0.468411 0.302331i
\(753\) 9456.81 + 16379.7i 0.457670 + 0.792707i
\(754\) 799.035 1863.39i 0.0385930 0.0900011i
\(755\) 22962.1 1.10686
\(756\) 20654.3 + 4824.03i 0.993637 + 0.232075i
\(757\) −10241.5 −0.491722 −0.245861 0.969305i \(-0.579071\pi\)
−0.245861 + 0.969305i \(0.579071\pi\)
\(758\) 1344.30 3134.99i 0.0644159 0.150221i
\(759\) −5112.91 8855.83i −0.244515 0.423513i
\(760\) 19855.6 + 16443.4i 0.947684 + 0.784824i
\(761\) −18578.2 10726.2i −0.884968 0.510937i −0.0126751 0.999920i \(-0.504035\pi\)
−0.872293 + 0.488983i \(0.837368\pi\)
\(762\) −14045.1 + 1672.31i −0.667719 + 0.0795031i
\(763\) −19660.4 9899.53i −0.932836 0.469708i
\(764\) −853.278 3532.39i −0.0404064 0.167274i
\(765\) 6967.86 12068.7i 0.329312 0.570385i
\(766\) 7205.05 5388.12i 0.339855 0.254152i
\(767\) 12335.2 7121.71i 0.580700 0.335267i
\(768\) −5638.73 12476.6i −0.264935 0.586210i
\(769\) 26466.5i 1.24110i 0.784166 + 0.620551i \(0.213091\pi\)
−0.784166 + 0.620551i \(0.786909\pi\)
\(770\) 39099.2 6938.98i 1.82992 0.324758i
\(771\) 16708.3i 0.780462i
\(772\) 7259.46 24633.9i 0.338437 1.14844i
\(773\) 9692.09 5595.73i 0.450971 0.260368i −0.257269 0.966340i \(-0.582823\pi\)
0.708240 + 0.705972i \(0.249489\pi\)
\(774\) −5247.71 7017.29i −0.243701 0.325880i
\(775\) 2481.56 4298.19i 0.115020 0.199220i
\(776\) −23680.1 + 8792.51i −1.09545 + 0.406743i
\(777\) 5371.46 3524.84i 0.248005 0.162745i
\(778\) 2679.30 + 22502.5i 0.123467 + 1.03696i
\(779\) 5149.99 + 2973.35i 0.236864 + 0.136754i
\(780\) −8439.94 8868.97i −0.387434 0.407128i
\(781\) 24252.2 + 42006.1i 1.11116 + 1.92458i
\(782\) −9237.00 3960.88i −0.422397 0.181126i
\(783\) 4130.21 0.188508
\(784\) 19680.9 + 9723.81i 0.896542 + 0.442958i
\(785\) 46845.9 2.12994
\(786\) 17114.4 + 7338.75i 0.776654 + 0.333034i
\(787\) −15026.0 26025.7i −0.680582 1.17880i −0.974804 0.223065i \(-0.928394\pi\)
0.294222 0.955737i \(-0.404939\pi\)
\(788\) −23016.7 24186.8i −1.04053 1.09342i
\(789\) −5505.36 3178.52i −0.248411 0.143420i
\(790\) −2006.61 16852.9i −0.0903698 0.758985i
\(791\) −10256.1 + 6730.24i −0.461019 + 0.302528i
\(792\) −13811.1 + 5128.11i −0.619641 + 0.230075i
\(793\) 5285.53 9154.81i 0.236689 0.409958i
\(794\) 20530.6 + 27453.7i 0.917636 + 1.22707i
\(795\) −23330.4 + 13469.8i −1.04081 + 0.600913i
\(796\) 11937.0 40506.5i 0.531528 1.80366i
\(797\) 26567.8i 1.18078i 0.807119 + 0.590389i \(0.201026\pi\)
−0.807119 + 0.590389i \(0.798974\pi\)
\(798\) −10659.9 + 1891.82i −0.472876 + 0.0839219i
\(799\) 8583.89i 0.380070i
\(800\) −38746.7 + 2675.63i −1.71238 + 0.118247i
\(801\) −2798.54 + 1615.74i −0.123447 + 0.0712724i
\(802\) −24903.2 + 18623.2i −1.09646 + 0.819960i
\(803\) −17010.5 + 29463.1i −0.747557 + 1.29481i
\(804\) −5278.94 21853.7i −0.231560 0.958609i
\(805\) −22666.6 11413.2i −0.992412 0.499706i
\(806\) −1614.16 + 192.193i −0.0705415 + 0.00839914i
\(807\) 23319.1 + 13463.3i 1.01719 + 0.587275i
\(808\) −69.0390 57.1746i −0.00300592 0.00248935i
\(809\) 980.413 + 1698.13i 0.0426075 + 0.0737984i 0.886543 0.462647i \(-0.153100\pi\)
−0.843935 + 0.536445i \(0.819767\pi\)
\(810\) 1051.77 2452.78i 0.0456238 0.106397i
\(811\) −2633.82 −0.114040 −0.0570198 0.998373i \(-0.518160\pi\)
−0.0570198 + 0.998373i \(0.518160\pi\)
\(812\) 4162.63 + 972.228i 0.179901 + 0.0420179i
\(813\) −14634.5 −0.631309
\(814\) −4759.04 + 11098.4i −0.204919 + 0.477884i
\(815\) −6781.58 11746.0i −0.291470 0.504841i
\(816\) 5543.63 8588.93i 0.237826 0.368471i
\(817\) 10481.6 + 6051.53i 0.448841 + 0.259139i
\(818\) −5642.23 + 671.801i −0.241169 + 0.0287151i
\(819\) −7270.61 + 415.850i −0.310202 + 0.0177423i
\(820\) −13781.8 + 3329.11i −0.586931 + 0.141778i
\(821\) −5333.16 + 9237.30i −0.226710 + 0.392672i −0.956831 0.290645i \(-0.906130\pi\)
0.730121 + 0.683317i \(0.239463\pi\)
\(822\) −13580.1 + 10155.6i −0.576230 + 0.430919i
\(823\) 32943.1 19019.7i 1.39529 0.805571i 0.401395 0.915905i \(-0.368525\pi\)
0.993895 + 0.110334i \(0.0351922\pi\)
\(824\) −8004.60 1358.17i −0.338414 0.0574199i
\(825\) 29504.6i 1.24512i
\(826\) 19328.6 + 22983.1i 0.814198 + 0.968139i
\(827\) 22277.0i 0.936697i −0.883544 0.468349i \(-0.844849\pi\)
0.883544 0.468349i \(-0.155151\pi\)
\(828\) 9031.15 + 2661.42i 0.379051 + 0.111704i
\(829\) 18752.2 10826.6i 0.785633 0.453585i −0.0527901 0.998606i \(-0.516811\pi\)
0.838423 + 0.545020i \(0.183478\pi\)
\(830\) 15852.0 + 21197.4i 0.662928 + 0.886475i
\(831\) −5355.83 + 9276.57i −0.223576 + 0.387245i
\(832\) 8302.05 + 9638.31i 0.345940 + 0.401620i
\(833\) 1868.78 + 16283.2i 0.0777304 + 0.677287i
\(834\) −342.511 2876.63i −0.0142208 0.119436i
\(835\) 49643.4 + 28661.7i 2.05746 + 1.18788i
\(836\) 14741.0 14027.9i 0.609844 0.580343i
\(837\) −1655.73 2867.80i −0.0683755 0.118430i
\(838\) 17320.1 + 7426.97i 0.713977 + 0.306158i
\(839\) 47337.4 1.94788 0.973939 0.226811i \(-0.0728299\pi\)
0.973939 + 0.226811i \(0.0728299\pi\)
\(840\) 15301.9 20788.1i 0.628529 0.853878i
\(841\) −23556.6 −0.965870
\(842\) 15232.3 + 6531.70i 0.623443 + 0.267336i
\(843\) 10459.8 + 18116.9i 0.427347 + 0.740187i
\(844\) −5051.08 + 4806.73i −0.206002 + 0.196036i
\(845\) −25209.4 14554.6i −1.02631 0.592538i
\(846\) 950.737 + 7984.92i 0.0386371 + 0.324500i
\(847\) −382.215 6682.55i −0.0155054 0.271092i
\(848\) 24904.7 12777.4i 1.00853 0.517428i
\(849\) −10126.2 + 17539.1i −0.409341 + 0.708999i
\(850\) −17366.8 23223.0i −0.700794 0.937110i
\(851\) 6683.37 3858.64i 0.269216 0.155432i
\(852\) 30243.3 + 8912.49i 1.21610 + 0.358377i
\(853\) 16562.9i 0.664833i −0.943133 0.332417i \(-0.892136\pi\)
0.943133 0.332417i \(-0.107864\pi\)
\(854\) 20951.9 + 7599.56i 0.839532 + 0.304510i
\(855\) 18031.9i 0.721261i
\(856\) −3511.76 + 20697.2i −0.140222 + 0.826421i
\(857\) −28076.8 + 16210.2i −1.11912 + 0.646124i −0.941176 0.337917i \(-0.890278\pi\)
−0.177944 + 0.984041i \(0.556944\pi\)
\(858\) −7738.97 + 5787.39i −0.307930 + 0.230278i
\(859\) −16065.2 + 27825.8i −0.638112 + 1.10524i 0.347735 + 0.937593i \(0.386951\pi\)
−0.985847 + 0.167649i \(0.946382\pi\)
\(860\) −28049.7 + 6775.61i −1.11219 + 0.268659i
\(861\) 2677.75 5317.99i 0.105990 0.210496i
\(862\) −10306.6 + 1227.17i −0.407243 + 0.0484891i
\(863\) −33292.7 19221.5i −1.31320 0.758179i −0.330579 0.943778i \(-0.607244\pi\)
−0.982625 + 0.185600i \(0.940577\pi\)
\(864\) −11380.1 + 23281.3i −0.448101 + 0.916721i
\(865\) −28932.4 50112.4i −1.13726 1.96979i
\(866\) −9232.22 + 21530.1i −0.362267 + 0.844828i
\(867\) −8790.02 −0.344319
\(868\) −993.661 3280.07i −0.0388561 0.128264i
\(869\) −13396.2 −0.522941
\(870\) 1980.93 4619.63i 0.0771951 0.180023i
\(871\) 10444.2 + 18089.8i 0.406300 + 0.703732i
\(872\) 17153.4 20712.9i 0.666156 0.804390i
\(873\) 15300.7 + 8833.85i 0.593184 + 0.342475i
\(874\) −12913.4 + 1537.55i −0.499772 + 0.0595062i
\(875\) −16768.3 25553.0i −0.647854 0.987257i
\(876\) 5192.60 + 21496.3i 0.200276 + 0.829101i
\(877\) 10742.3 18606.2i 0.413616 0.716404i −0.581666 0.813428i \(-0.697599\pi\)
0.995282 + 0.0970237i \(0.0309323\pi\)
\(878\) 21930.4 16400.1i 0.842956 0.630383i
\(879\) 1324.81 764.877i 0.0508357 0.0293500i
\(880\) −2403.68 + 48456.9i −0.0920774 + 1.85623i
\(881\) 17193.8i 0.657517i −0.944414 0.328759i \(-0.893370\pi\)
0.944414 0.328759i \(-0.106630\pi\)
\(882\) −3541.88 14940.0i −0.135217 0.570359i
\(883\) 16514.2i 0.629384i −0.949194 0.314692i \(-0.898099\pi\)
0.949194 0.314692i \(-0.101901\pi\)
\(884\) −2684.80 + 9110.48i −0.102149 + 0.346627i
\(885\) 30580.7 17655.8i 1.16154 0.670614i
\(886\) −13993.5 18712.3i −0.530612 0.709540i
\(887\) −10239.6 + 17735.5i −0.387612 + 0.671364i −0.992128 0.125229i \(-0.960033\pi\)
0.604516 + 0.796593i \(0.293367\pi\)
\(888\) 2732.29 + 7358.63i 0.103254 + 0.278085i
\(889\) 15201.1 + 23164.8i 0.573486 + 0.873929i
\(890\) 1258.20 + 10567.2i 0.0473876 + 0.397992i
\(891\) −1824.29 1053.25i −0.0685925 0.0396019i
\(892\) −10645.0 11186.1i −0.399574 0.419886i
\(893\) −5553.49 9618.93i −0.208108 0.360454i
\(894\) 12424.5 + 5327.70i 0.464806 + 0.199312i
\(895\) −4399.00 −0.164293
\(896\) −16949.7 + 20785.3i −0.631977 + 0.774987i
\(897\) 6175.79 0.229882
\(898\) −190.171 81.5463i −0.00706690 0.00303033i
\(899\) −333.693 577.973i −0.0123796 0.0214421i
\(900\) 18727.1 + 19679.0i 0.693595 + 0.728854i
\(901\) 18099.2 + 10449.6i 0.669226 + 0.386378i
\(902\) 1323.14 + 11112.6i 0.0488424 + 0.410211i
\(903\) 5449.92 10823.5i 0.200844 0.398874i
\(904\) −5216.96 14050.4i −0.191940 0.516935i
\(905\) −17939.6 + 31072.3i −0.658930 + 1.14130i
\(906\) −7055.66 9434.91i −0.258729 0.345976i
\(907\) −26983.7 + 15579.0i −0.987848 + 0.570334i −0.904630 0.426197i \(-0.859853\pi\)
−0.0832177 + 0.996531i \(0.526520\pi\)
\(908\) 4469.57 15166.8i 0.163357 0.554327i
\(909\) 62.6978i 0.00228774i
\(910\) −8177.52 + 22545.4i −0.297892 + 0.821287i
\(911\) 412.348i 0.0149964i 0.999972 + 0.00749818i \(0.00238677\pi\)
−0.999972 + 0.00749818i \(0.997613\pi\)
\(912\) 655.331 13211.1i 0.0237941 0.479676i
\(913\) 18093.5 10446.3i 0.655868 0.378666i
\(914\) 29836.7 22312.6i 1.07977 0.807480i
\(915\) 13103.6 22696.2i 0.473435 0.820013i
\(916\) −4853.56 20092.7i −0.175072 0.724763i
\(917\) −2082.95 36417.7i −0.0750109 1.31147i
\(918\) −19212.4 + 2287.56i −0.690746 + 0.0822448i
\(919\) 8444.08 + 4875.19i 0.303095 + 0.174992i 0.643832 0.765166i \(-0.277343\pi\)
−0.340737 + 0.940159i \(0.610677\pi\)
\(920\) 19776.3 23880.1i 0.708700 0.855763i
\(921\) −7012.30 12145.7i −0.250883 0.434542i
\(922\) 14106.4 32897.0i 0.503872 1.17506i
\(923\) −29293.8 −1.04466
\(924\) −14865.3 13933.3i −0.529257 0.496074i
\(925\) 22266.7 0.791487
\(926\) −950.378 + 2216.33i −0.0337272 + 0.0786536i
\(927\) 2839.38 + 4917.95i 0.100601 + 0.174247i
\(928\) −2293.53 + 4692.09i −0.0811301 + 0.165976i
\(929\) −19036.4 10990.7i −0.672297 0.388151i 0.124650 0.992201i \(-0.460219\pi\)
−0.796946 + 0.604050i \(0.793553\pi\)
\(930\) −4001.75 + 476.475i −0.141100 + 0.0168003i
\(931\) 12628.8 + 17037.6i 0.444568 + 0.599769i
\(932\) 26816.2 6477.67i 0.942484 0.227664i
\(933\) −10877.7 + 18840.8i −0.381695 + 0.661115i
\(934\) 24746.7 18506.2i 0.866956 0.648331i
\(935\) −31371.0 + 18112.0i −1.09726 + 0.633505i
\(936\) 1488.40 8772.13i 0.0519762 0.306331i
\(937\) 19723.5i 0.687662i 0.939032 + 0.343831i \(0.111725\pi\)
−0.939032 + 0.343831i \(0.888275\pi\)
\(938\) −33705.3 + 28345.9i −1.17326 + 0.986700i
\(939\) 28877.4i 1.00360i
\(940\) 25401.5 + 7485.65i 0.881389 + 0.259739i
\(941\) −9773.15 + 5642.53i −0.338571 + 0.195474i −0.659640 0.751582i \(-0.729291\pi\)
0.321069 + 0.947056i \(0.395958\pi\)
\(942\) −14394.5 19248.5i −0.497876 0.665766i
\(943\) 3575.99 6193.80i 0.123489 0.213890i
\(944\) −32644.2 + 16748.2i −1.12551 + 0.577445i
\(945\) −48775.4 + 2789.76i −1.67901 + 0.0960327i
\(946\) 2692.94 + 22617.1i 0.0925530 + 0.777321i
\(947\) −26386.0 15234.0i −0.905417 0.522743i −0.0264635 0.999650i \(-0.508425\pi\)
−0.878954 + 0.476907i \(0.841758\pi\)
\(948\) −6308.10 + 6002.94i −0.216115 + 0.205661i
\(949\) −10273.3 17794.0i −0.351409 0.608658i
\(950\) −34485.4 14787.5i −1.17774 0.505022i
\(951\) −3096.42 −0.105582
\(952\) −19901.8 2216.98i −0.677542 0.0754756i
\(953\) 11791.2 0.400791 0.200395 0.979715i \(-0.435777\pi\)
0.200395 + 0.979715i \(0.435777\pi\)
\(954\) −17993.7 7715.79i −0.610657 0.261853i
\(955\) 4185.24 + 7249.05i 0.141813 + 0.245627i
\(956\) −21140.9 + 20118.2i −0.715215 + 0.680616i
\(957\) −3435.92 1983.73i −0.116058 0.0670061i
\(958\) 3565.18 + 29942.7i 0.120236 + 1.00982i
\(959\) 29668.8 + 14939.0i 0.999014 + 0.503030i
\(960\) 20582.0 + 23894.8i 0.691961 + 0.803335i
\(961\) 14628.0 25336.4i 0.491019 0.850470i
\(962\) −4367.66 5840.49i −0.146382 0.195743i
\(963\) 12716.2 7341.69i 0.425517 0.245672i
\(964\) −19445.0 5730.32i −0.649670 0.191454i
\(965\) 59154.0i 1.97330i
\(966\) 2275.26 + 12820.5i 0.0757819 + 0.427010i
\(967\) 40914.1i 1.36061i −0.732929 0.680305i \(-0.761847\pi\)
0.732929 0.680305i \(-0.238153\pi\)
\(968\) 8062.61 + 1368.01i 0.267709 + 0.0454230i
\(969\) 8552.87 4938.00i 0.283548 0.163706i
\(970\) 46595.0 34844.9i 1.54234 1.15340i
\(971\) 9276.00 16066.5i 0.306572 0.530997i −0.671038 0.741423i \(-0.734151\pi\)
0.977610 + 0.210425i \(0.0674848\pi\)
\(972\) 28726.0 6939.00i 0.947930 0.228980i
\(973\) −4744.46 + 3113.39i −0.156321 + 0.102580i
\(974\) 152.192 18.1210i 0.00500671 0.000596133i
\(975\) 15431.8 + 8909.53i 0.506884 + 0.292650i
\(976\) −14766.7 + 22878.6i −0.484294 + 0.750333i
\(977\) 1455.74 + 2521.42i 0.0476697 + 0.0825664i 0.888876 0.458148i \(-0.151487\pi\)
−0.841206 + 0.540715i \(0.818154\pi\)
\(978\) −2742.53 + 6395.74i −0.0896692 + 0.209114i
\(979\) 8399.78 0.274217
\(980\) −49815.1 8669.81i −1.62376 0.282599i
\(981\) −18810.5 −0.612204
\(982\) 6273.54 14630.3i 0.203866 0.475428i
\(983\) 18251.1 + 31611.8i 0.592186 + 1.02570i 0.993937 + 0.109947i \(0.0350682\pi\)
−0.401752 + 0.915749i \(0.631598\pi\)
\(984\) 5602.70 + 4639.88i 0.181512 + 0.150319i
\(985\) 66602.3 + 38452.9i 2.15444 + 1.24387i
\(986\) −3872.05 + 461.032i −0.125062 + 0.0148907i
\(987\) −9297.70 + 6101.30i −0.299847 + 0.196764i
\(988\) 2885.65 + 11946.0i 0.0929198 + 0.384669i
\(989\) 7278.08 12606.0i 0.234004 0.405306i
\(990\) 27175.9 20322.8i 0.872431 0.652425i
\(991\) 31879.7 18405.7i 1.02189 0.589987i 0.107238 0.994233i \(-0.465799\pi\)
0.914650 + 0.404246i \(0.132466\pi\)
\(992\) 4177.38 288.466i 0.133701 0.00923266i
\(993\) 31884.6i 1.01896i
\(994\) −10792.3 60811.6i −0.344378 1.94047i
\(995\) 97269.2i 3.09914i
\(996\) 3838.92 13026.8i 0.122129 0.414429i
\(997\) −10060.1 + 5808.18i −0.319564 + 0.184500i −0.651198 0.758908i \(-0.725733\pi\)
0.331634 + 0.943408i \(0.392400\pi\)
\(998\) −1049.81 1403.82i −0.0332978 0.0445262i
\(999\) 7428.32 12866.2i 0.235257 0.407477i
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 28.4.f.a.19.9 yes 20
4.3 odd 2 inner 28.4.f.a.19.2 yes 20
7.2 even 3 196.4.d.b.195.9 20
7.3 odd 6 inner 28.4.f.a.3.2 20
7.4 even 3 196.4.f.d.31.2 20
7.5 odd 6 196.4.d.b.195.10 20
7.6 odd 2 196.4.f.d.19.9 20
8.3 odd 2 448.4.p.h.383.7 20
8.5 even 2 448.4.p.h.383.4 20
28.3 even 6 inner 28.4.f.a.3.9 yes 20
28.11 odd 6 196.4.f.d.31.9 20
28.19 even 6 196.4.d.b.195.11 20
28.23 odd 6 196.4.d.b.195.12 20
28.27 even 2 196.4.f.d.19.2 20
56.3 even 6 448.4.p.h.255.4 20
56.45 odd 6 448.4.p.h.255.7 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.f.a.3.2 20 7.3 odd 6 inner
28.4.f.a.3.9 yes 20 28.3 even 6 inner
28.4.f.a.19.2 yes 20 4.3 odd 2 inner
28.4.f.a.19.9 yes 20 1.1 even 1 trivial
196.4.d.b.195.9 20 7.2 even 3
196.4.d.b.195.10 20 7.5 odd 6
196.4.d.b.195.11 20 28.19 even 6
196.4.d.b.195.12 20 28.23 odd 6
196.4.f.d.19.2 20 28.27 even 2
196.4.f.d.19.9 20 7.6 odd 2
196.4.f.d.31.2 20 7.4 even 3
196.4.f.d.31.9 20 28.11 odd 6
448.4.p.h.255.4 20 56.3 even 6
448.4.p.h.255.7 20 56.45 odd 6
448.4.p.h.383.4 20 8.5 even 2
448.4.p.h.383.7 20 8.3 odd 2