Properties

Label 96.3.p.a.5.13
Level $96$
Weight $3$
Character 96.5
Analytic conductor $2.616$
Analytic rank $0$
Dimension $120$
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] = [96,3,Mod(5,96)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(96, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("96.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 96.p (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.61581053786\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(30\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 5.13
Character \(\chi\) \(=\) 96.5
Dual form 96.3.p.a.77.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.503078 + 1.93569i) q^{2} +(2.97132 - 0.413808i) q^{3} +(-3.49383 - 1.94761i) q^{4} +(2.54567 - 6.14580i) q^{5} +(-0.693801 + 5.95975i) q^{6} +(7.32134 + 7.32134i) q^{7} +(5.52764 - 5.78318i) q^{8} +(8.65753 - 2.45911i) q^{9} +O(q^{10})\) \(q+(-0.503078 + 1.93569i) q^{2} +(2.97132 - 0.413808i) q^{3} +(-3.49383 - 1.94761i) q^{4} +(2.54567 - 6.14580i) q^{5} +(-0.693801 + 5.95975i) q^{6} +(7.32134 + 7.32134i) q^{7} +(5.52764 - 5.78318i) q^{8} +(8.65753 - 2.45911i) q^{9} +(10.6157 + 8.01946i) q^{10} +(-3.73475 - 1.54698i) q^{11} +(-11.1872 - 4.34121i) q^{12} +(-20.0259 + 8.29499i) q^{13} +(-17.8551 + 10.4887i) q^{14} +(5.02084 - 19.3146i) q^{15} +(8.41363 + 13.6092i) q^{16} +11.4146 q^{17} +(0.404685 + 17.9955i) q^{18} +(-2.41656 + 1.00097i) q^{19} +(-20.8638 + 16.5144i) q^{20} +(24.7837 + 18.7244i) q^{21} +(4.87336 - 6.45108i) q^{22} +(-10.6804 - 10.6804i) q^{23} +(14.0313 - 19.4711i) q^{24} +(-13.6127 - 13.6127i) q^{25} +(-5.98199 - 42.9370i) q^{26} +(24.7067 - 10.8894i) q^{27} +(-11.3204 - 39.8386i) q^{28} +(-38.4375 + 15.9213i) q^{29} +(34.8612 + 19.4355i) q^{30} +22.9544 q^{31} +(-30.5760 + 9.43972i) q^{32} +(-11.7373 - 3.05112i) q^{33} +(-5.74243 + 22.0952i) q^{34} +(63.6332 - 26.3578i) q^{35} +(-35.0373 - 8.26977i) q^{36} +(-47.4669 - 19.6614i) q^{37} +(-0.721858 - 5.18129i) q^{38} +(-56.0708 + 32.9340i) q^{39} +(-21.4707 - 48.6939i) q^{40} +(7.45051 + 7.45051i) q^{41} +(-48.7129 + 38.5538i) q^{42} +(11.2795 - 27.2311i) q^{43} +(10.0356 + 12.6787i) q^{44} +(6.92601 - 59.4675i) q^{45} +(26.0472 - 15.3010i) q^{46} -15.6846 q^{47} +(30.6312 + 36.9558i) q^{48} +58.2041i q^{49} +(33.1983 - 19.5018i) q^{50} +(33.9165 - 4.72345i) q^{51} +(86.1223 + 10.0214i) q^{52} +(-64.5986 - 26.7576i) q^{53} +(8.64911 + 53.3028i) q^{54} +(-19.0149 + 19.0149i) q^{55} +(82.8104 - 1.87086i) q^{56} +(-6.76617 + 3.97420i) q^{57} +(-11.4818 - 82.4130i) q^{58} +(-11.4087 + 27.5431i) q^{59} +(-55.1592 + 57.7031i) q^{60} +(32.5638 + 78.6160i) q^{61} +(-11.5479 + 44.4328i) q^{62} +(81.3887 + 45.3807i) q^{63} +(-2.89031 - 63.9347i) q^{64} +144.191i q^{65} +(11.8108 - 21.1849i) q^{66} +(22.4548 + 54.2106i) q^{67} +(-39.8806 - 22.2312i) q^{68} +(-36.1547 - 27.3154i) q^{69} +(19.0081 + 136.434i) q^{70} +(3.85644 - 3.85644i) q^{71} +(33.6342 - 63.6611i) q^{72} +(-19.9311 + 19.9311i) q^{73} +(61.9381 - 81.9902i) q^{74} +(-46.0809 - 34.8148i) q^{75} +(10.3925 + 1.20930i) q^{76} +(-16.0174 - 38.6693i) q^{77} +(-35.5421 - 125.104i) q^{78} +42.0491i q^{79} +(105.058 - 17.0639i) q^{80} +(68.9055 - 42.5797i) q^{81} +(-18.1701 + 10.6737i) q^{82} +(-45.4742 - 109.785i) q^{83} +(-50.1220 - 113.689i) q^{84} +(29.0579 - 70.1519i) q^{85} +(47.0366 + 35.5330i) q^{86} +(-107.622 + 63.2132i) q^{87} +(-29.5908 + 13.0475i) q^{88} +(14.5465 - 14.5465i) q^{89} +(111.627 + 43.3234i) q^{90} +(-207.347 - 85.8858i) q^{91} +(16.5143 + 58.1169i) q^{92} +(68.2051 - 9.49873i) q^{93} +(7.89058 - 30.3606i) q^{94} +17.3998i q^{95} +(-86.9449 + 40.7011i) q^{96} +12.1654 q^{97} +(-112.665 - 29.2812i) q^{98} +(-36.1379 - 4.20887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 32 q^{10} - 4 q^{12} - 8 q^{13} - 40 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 120 q^{22} - 144 q^{24} - 8 q^{25} + 92 q^{27} - 8 q^{28} - 60 q^{30} - 16 q^{31} - 8 q^{33} - 40 q^{34} + 64 q^{36} - 8 q^{37} - 196 q^{39} - 232 q^{40} + 16 q^{42} - 8 q^{43} - 4 q^{45} - 40 q^{46} + 48 q^{48} - 40 q^{51} - 112 q^{52} + 304 q^{54} - 264 q^{55} - 4 q^{57} - 16 q^{58} + 424 q^{60} + 56 q^{61} - 8 q^{63} + 40 q^{64} + 428 q^{66} + 248 q^{67} - 4 q^{69} + 328 q^{70} + 416 q^{72} - 8 q^{73} - 104 q^{75} + 720 q^{76} + 276 q^{78} + 512 q^{82} + 232 q^{84} - 208 q^{85} - 452 q^{87} + 272 q^{88} - 304 q^{90} - 200 q^{91} - 40 q^{93} + 416 q^{94} - 616 q^{96} - 16 q^{97} + 252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(65\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.503078 + 1.93569i −0.251539 + 0.967847i
\(3\) 2.97132 0.413808i 0.990441 0.137936i
\(4\) −3.49383 1.94761i −0.873456 0.486902i
\(5\) 2.54567 6.14580i 0.509135 1.22916i −0.435248 0.900311i \(-0.643339\pi\)
0.944382 0.328849i \(-0.106661\pi\)
\(6\) −0.693801 + 5.95975i −0.115634 + 0.993292i
\(7\) 7.32134 + 7.32134i 1.04591 + 1.04591i 0.998894 + 0.0470115i \(0.0149697\pi\)
0.0470115 + 0.998894i \(0.485030\pi\)
\(8\) 5.52764 5.78318i 0.690955 0.722897i
\(9\) 8.65753 2.45911i 0.961947 0.273235i
\(10\) 10.6157 + 8.01946i 1.06157 + 0.801946i
\(11\) −3.73475 1.54698i −0.339522 0.140635i 0.206406 0.978466i \(-0.433823\pi\)
−0.545929 + 0.837832i \(0.683823\pi\)
\(12\) −11.1872 4.34121i −0.932268 0.361767i
\(13\) −20.0259 + 8.29499i −1.54045 + 0.638076i −0.981558 0.191163i \(-0.938774\pi\)
−0.558894 + 0.829239i \(0.688774\pi\)
\(14\) −17.8551 + 10.4887i −1.27536 + 0.749191i
\(15\) 5.02084 19.3146i 0.334723 1.28764i
\(16\) 8.41363 + 13.6092i 0.525852 + 0.850576i
\(17\) 11.4146 0.671447 0.335724 0.941961i \(-0.391019\pi\)
0.335724 + 0.941961i \(0.391019\pi\)
\(18\) 0.404685 + 17.9955i 0.0224825 + 0.999747i
\(19\) −2.41656 + 1.00097i −0.127187 + 0.0526828i −0.445369 0.895347i \(-0.646928\pi\)
0.318182 + 0.948030i \(0.396928\pi\)
\(20\) −20.8638 + 16.5144i −1.04319 + 0.825719i
\(21\) 24.7837 + 18.7244i 1.18018 + 0.891640i
\(22\) 4.87336 6.45108i 0.221516 0.293231i
\(23\) −10.6804 10.6804i −0.464367 0.464367i 0.435717 0.900084i \(-0.356495\pi\)
−0.900084 + 0.435717i \(0.856495\pi\)
\(24\) 14.0313 19.4711i 0.584637 0.811295i
\(25\) −13.6127 13.6127i −0.544509 0.544509i
\(26\) −5.98199 42.9370i −0.230077 1.65142i
\(27\) 24.7067 10.8894i 0.915063 0.403310i
\(28\) −11.3204 39.8386i −0.404299 1.42281i
\(29\) −38.4375 + 15.9213i −1.32543 + 0.549012i −0.929349 0.369203i \(-0.879631\pi\)
−0.396083 + 0.918215i \(0.629631\pi\)
\(30\) 34.8612 + 19.4355i 1.16204 + 0.647852i
\(31\) 22.9544 0.740466 0.370233 0.928939i \(-0.379278\pi\)
0.370233 + 0.928939i \(0.379278\pi\)
\(32\) −30.5760 + 9.43972i −0.955500 + 0.294991i
\(33\) −11.7373 3.05112i −0.355676 0.0924581i
\(34\) −5.74243 + 22.0952i −0.168895 + 0.649858i
\(35\) 63.6332 26.3578i 1.81809 0.753079i
\(36\) −35.0373 8.26977i −0.973258 0.229716i
\(37\) −47.4669 19.6614i −1.28289 0.531390i −0.366031 0.930603i \(-0.619284\pi\)
−0.916858 + 0.399212i \(0.869284\pi\)
\(38\) −0.721858 5.18129i −0.0189963 0.136350i
\(39\) −56.0708 + 32.9340i −1.43771 + 0.844461i
\(40\) −21.4707 48.6939i −0.536767 1.21735i
\(41\) 7.45051 + 7.45051i 0.181720 + 0.181720i 0.792105 0.610385i \(-0.208985\pi\)
−0.610385 + 0.792105i \(0.708985\pi\)
\(42\) −48.7129 + 38.5538i −1.15983 + 0.917948i
\(43\) 11.2795 27.2311i 0.262314 0.633281i −0.736767 0.676146i \(-0.763649\pi\)
0.999081 + 0.0428655i \(0.0136487\pi\)
\(44\) 10.0356 + 12.6787i 0.228083 + 0.288153i
\(45\) 6.92601 59.4675i 0.153911 1.32150i
\(46\) 26.0472 15.3010i 0.566243 0.332630i
\(47\) −15.6846 −0.333715 −0.166857 0.985981i \(-0.553362\pi\)
−0.166857 + 0.985981i \(0.553362\pi\)
\(48\) 30.6312 + 36.9558i 0.638150 + 0.769912i
\(49\) 58.2041i 1.18784i
\(50\) 33.1983 19.5018i 0.663967 0.390036i
\(51\) 33.9165 4.72345i 0.665029 0.0926167i
\(52\) 86.1223 + 10.0214i 1.65620 + 0.192718i
\(53\) −64.5986 26.7576i −1.21884 0.504861i −0.321801 0.946807i \(-0.604288\pi\)
−0.897041 + 0.441947i \(0.854288\pi\)
\(54\) 8.64911 + 53.3028i 0.160169 + 0.987090i
\(55\) −19.0149 + 19.0149i −0.345725 + 0.345725i
\(56\) 82.8104 1.87086i 1.47876 0.0334082i
\(57\) −6.76617 + 3.97420i −0.118705 + 0.0697229i
\(58\) −11.4818 82.4130i −0.197962 1.42091i
\(59\) −11.4087 + 27.5431i −0.193368 + 0.466832i −0.990591 0.136853i \(-0.956301\pi\)
0.797223 + 0.603685i \(0.206301\pi\)
\(60\) −55.1592 + 57.7031i −0.919320 + 0.961719i
\(61\) 32.5638 + 78.6160i 0.533833 + 1.28879i 0.928967 + 0.370163i \(0.120698\pi\)
−0.395134 + 0.918623i \(0.629302\pi\)
\(62\) −11.5479 + 44.4328i −0.186256 + 0.716658i
\(63\) 81.3887 + 45.3807i 1.29188 + 0.720328i
\(64\) −2.89031 63.9347i −0.0451611 0.998980i
\(65\) 144.191i 2.21833i
\(66\) 11.8108 21.1849i 0.178952 0.320983i
\(67\) 22.4548 + 54.2106i 0.335146 + 0.809114i 0.998167 + 0.0605135i \(0.0192738\pi\)
−0.663021 + 0.748600i \(0.730726\pi\)
\(68\) −39.8806 22.2312i −0.586480 0.326929i
\(69\) −36.1547 27.3154i −0.523981 0.395875i
\(70\) 19.0081 + 136.434i 0.271544 + 1.94906i
\(71\) 3.85644 3.85644i 0.0543160 0.0543160i −0.679427 0.733743i \(-0.737772\pi\)
0.733743 + 0.679427i \(0.237772\pi\)
\(72\) 33.6342 63.6611i 0.467142 0.884182i
\(73\) −19.9311 + 19.9311i −0.273029 + 0.273029i −0.830318 0.557289i \(-0.811841\pi\)
0.557289 + 0.830318i \(0.311841\pi\)
\(74\) 61.9381 81.9902i 0.837001 1.10798i
\(75\) −46.0809 34.8148i −0.614412 0.464197i
\(76\) 10.3925 + 1.20930i 0.136744 + 0.0159118i
\(77\) −16.0174 38.6693i −0.208018 0.502199i
\(78\) −35.5421 125.104i −0.455668 1.60390i
\(79\) 42.0491i 0.532267i 0.963936 + 0.266134i \(0.0857463\pi\)
−0.963936 + 0.266134i \(0.914254\pi\)
\(80\) 105.058 17.0639i 1.31322 0.213298i
\(81\) 68.9055 42.5797i 0.850685 0.525675i
\(82\) −18.1701 + 10.6737i −0.221587 + 0.130167i
\(83\) −45.4742 109.785i −0.547882 1.32271i −0.919051 0.394140i \(-0.871043\pi\)
0.371168 0.928566i \(-0.378957\pi\)
\(84\) −50.1220 113.689i −0.596691 1.35344i
\(85\) 29.0579 70.1519i 0.341857 0.825316i
\(86\) 47.0366 + 35.5330i 0.546937 + 0.413174i
\(87\) −107.622 + 63.2132i −1.23703 + 0.726589i
\(88\) −29.5908 + 13.0475i −0.336259 + 0.148268i
\(89\) 14.5465 14.5465i 0.163444 0.163444i −0.620646 0.784091i \(-0.713130\pi\)
0.784091 + 0.620646i \(0.213130\pi\)
\(90\) 111.627 + 43.3234i 1.24030 + 0.481371i
\(91\) −207.347 85.8858i −2.27854 0.943800i
\(92\) 16.5143 + 58.1169i 0.179503 + 0.631706i
\(93\) 68.2051 9.49873i 0.733388 0.102137i
\(94\) 7.89058 30.3606i 0.0839423 0.322985i
\(95\) 17.3998i 0.183156i
\(96\) −86.9449 + 40.7011i −0.905677 + 0.423969i
\(97\) 12.1654 0.125416 0.0627081 0.998032i \(-0.480026\pi\)
0.0627081 + 0.998032i \(0.480026\pi\)
\(98\) −112.665 29.2812i −1.14965 0.298787i
\(99\) −36.1379 4.20887i −0.365029 0.0425139i
\(100\) 21.0482 + 74.0728i 0.210482 + 0.740728i
\(101\) −4.47187 + 10.7961i −0.0442759 + 0.106892i −0.944470 0.328597i \(-0.893424\pi\)
0.900194 + 0.435488i \(0.143424\pi\)
\(102\) −7.91947 + 68.0282i −0.0776418 + 0.666943i
\(103\) 18.1126 + 18.1126i 0.175850 + 0.175850i 0.789544 0.613694i \(-0.210317\pi\)
−0.613694 + 0.789544i \(0.710317\pi\)
\(104\) −62.7245 + 161.665i −0.603120 + 1.55447i
\(105\) 178.168 104.649i 1.69684 0.996660i
\(106\) 84.2927 111.582i 0.795214 1.05266i
\(107\) 169.156 + 70.0666i 1.58089 + 0.654828i 0.988555 0.150861i \(-0.0482047\pi\)
0.592339 + 0.805689i \(0.298205\pi\)
\(108\) −107.529 10.0734i −0.995641 0.0932726i
\(109\) 187.603 77.7076i 1.72113 0.712914i 0.721332 0.692589i \(-0.243530\pi\)
0.999793 0.0203241i \(-0.00646982\pi\)
\(110\) −27.2411 46.3730i −0.247646 0.421573i
\(111\) −149.176 38.7783i −1.34392 0.349354i
\(112\) −38.0387 + 161.237i −0.339631 + 1.43961i
\(113\) 14.7282 0.130338 0.0651692 0.997874i \(-0.479241\pi\)
0.0651692 + 0.997874i \(0.479241\pi\)
\(114\) −4.28893 15.0966i −0.0376222 0.132426i
\(115\) −92.8287 + 38.4509i −0.807206 + 0.334356i
\(116\) 165.303 + 19.2349i 1.42502 + 0.165818i
\(117\) −152.976 + 121.060i −1.30749 + 1.03470i
\(118\) −47.5755 35.9401i −0.403182 0.304577i
\(119\) 83.5702 + 83.5702i 0.702271 + 0.702271i
\(120\) −83.9463 135.801i −0.699552 1.13167i
\(121\) −74.0047 74.0047i −0.611609 0.611609i
\(122\) −168.559 + 23.4836i −1.38163 + 0.192489i
\(123\) 25.2210 + 19.0548i 0.205048 + 0.154917i
\(124\) −80.1988 44.7063i −0.646765 0.360535i
\(125\) 35.3303 14.6343i 0.282642 0.117074i
\(126\) −128.788 + 134.714i −1.02213 + 1.06916i
\(127\) 106.189 0.836136 0.418068 0.908416i \(-0.362707\pi\)
0.418068 + 0.908416i \(0.362707\pi\)
\(128\) 125.212 + 26.5694i 0.978219 + 0.207573i
\(129\) 22.2466 85.5799i 0.172454 0.663410i
\(130\) −279.110 72.5395i −2.14700 0.557996i
\(131\) 76.8602 31.8365i 0.586719 0.243027i −0.0695194 0.997581i \(-0.522147\pi\)
0.656238 + 0.754554i \(0.272147\pi\)
\(132\) 35.0657 + 33.5198i 0.265649 + 0.253938i
\(133\) −25.0209 10.3640i −0.188127 0.0779249i
\(134\) −116.232 + 16.1934i −0.867401 + 0.120846i
\(135\) −4.02872 179.563i −0.0298424 1.33010i
\(136\) 63.0959 66.0127i 0.463940 0.485387i
\(137\) −85.4000 85.4000i −0.623358 0.623358i 0.323031 0.946388i \(-0.395298\pi\)
−0.946388 + 0.323031i \(0.895298\pi\)
\(138\) 71.0629 56.2427i 0.514948 0.407556i
\(139\) 65.5541 158.262i 0.471612 1.13857i −0.491838 0.870686i \(-0.663675\pi\)
0.963451 0.267886i \(-0.0863251\pi\)
\(140\) −273.658 31.8434i −1.95470 0.227453i
\(141\) −46.6040 + 6.49041i −0.330525 + 0.0460313i
\(142\) 5.52480 + 9.40498i 0.0389070 + 0.0662322i
\(143\) 87.6238 0.612754
\(144\) 106.308 + 97.1321i 0.738249 + 0.674528i
\(145\) 276.760i 1.90869i
\(146\) −28.5536 48.6074i −0.195573 0.332928i
\(147\) 24.0853 + 172.943i 0.163846 + 1.17648i
\(148\) 127.548 + 161.141i 0.861813 + 1.08879i
\(149\) 44.4674 + 18.4190i 0.298439 + 0.123617i 0.526878 0.849941i \(-0.323362\pi\)
−0.228439 + 0.973558i \(0.573362\pi\)
\(150\) 90.5730 71.6840i 0.603820 0.477893i
\(151\) −53.3283 + 53.3283i −0.353168 + 0.353168i −0.861287 0.508119i \(-0.830341\pi\)
0.508119 + 0.861287i \(0.330341\pi\)
\(152\) −7.56909 + 19.5084i −0.0497966 + 0.128345i
\(153\) 98.8222 28.0698i 0.645897 0.183463i
\(154\) 82.9100 11.5510i 0.538377 0.0750067i
\(155\) 58.4345 141.073i 0.376997 0.910151i
\(156\) 260.044 5.86143i 1.66695 0.0375733i
\(157\) −40.7468 98.3715i −0.259534 0.626570i 0.739374 0.673295i \(-0.235122\pi\)
−0.998908 + 0.0467249i \(0.985122\pi\)
\(158\) −81.3943 21.1540i −0.515154 0.133886i
\(159\) −203.016 52.7741i −1.27683 0.331913i
\(160\) −19.8219 + 211.944i −0.123887 + 1.32465i
\(161\) 156.390i 0.971368i
\(162\) 47.7564 + 154.801i 0.294793 + 0.955561i
\(163\) 79.0194 + 190.770i 0.484782 + 1.17037i 0.957313 + 0.289053i \(0.0933403\pi\)
−0.472532 + 0.881314i \(0.656660\pi\)
\(164\) −11.5201 40.5415i −0.0702445 0.247204i
\(165\) −48.6309 + 64.3679i −0.294733 + 0.390109i
\(166\) 235.386 32.7941i 1.41799 0.197555i
\(167\) −106.476 + 106.476i −0.637582 + 0.637582i −0.949958 0.312377i \(-0.898875\pi\)
0.312377 + 0.949958i \(0.398875\pi\)
\(168\) 245.282 39.8265i 1.46001 0.237063i
\(169\) 212.728 212.728i 1.25875 1.25875i
\(170\) 121.174 + 91.5390i 0.712789 + 0.538465i
\(171\) −18.4599 + 14.6085i −0.107953 + 0.0854301i
\(172\) −92.4441 + 73.1726i −0.537465 + 0.425422i
\(173\) 33.7245 + 81.4182i 0.194939 + 0.470625i 0.990880 0.134750i \(-0.0430231\pi\)
−0.795940 + 0.605375i \(0.793023\pi\)
\(174\) −68.2192 240.124i −0.392065 1.38002i
\(175\) 199.327i 1.13901i
\(176\) −10.3696 63.8427i −0.0589179 0.362743i
\(177\) −22.5015 + 86.5605i −0.127127 + 0.489042i
\(178\) 20.8396 + 35.4757i 0.117077 + 0.199302i
\(179\) 29.2463 + 70.6068i 0.163387 + 0.394451i 0.984276 0.176636i \(-0.0565216\pi\)
−0.820889 + 0.571088i \(0.806522\pi\)
\(180\) −140.018 + 194.280i −0.777877 + 1.07933i
\(181\) 54.7439 132.163i 0.302452 0.730185i −0.697456 0.716628i \(-0.745685\pi\)
0.999908 0.0135568i \(-0.00431539\pi\)
\(182\) 270.560 358.153i 1.48660 1.96787i
\(183\) 129.289 + 220.118i 0.706500 + 1.20283i
\(184\) −120.805 + 2.72922i −0.656546 + 0.0148327i
\(185\) −241.671 + 241.671i −1.30633 + 1.30633i
\(186\) −15.9258 + 136.803i −0.0856227 + 0.735499i
\(187\) −42.6307 17.6582i −0.227971 0.0944289i
\(188\) 54.7993 + 30.5475i 0.291485 + 0.162487i
\(189\) 260.611 + 101.161i 1.37889 + 0.535245i
\(190\) −33.6808 8.75348i −0.177267 0.0460709i
\(191\) 247.456i 1.29558i −0.761818 0.647791i \(-0.775693\pi\)
0.761818 0.647791i \(-0.224307\pi\)
\(192\) −35.0447 188.775i −0.182525 0.983201i
\(193\) −169.583 −0.878667 −0.439333 0.898324i \(-0.644785\pi\)
−0.439333 + 0.898324i \(0.644785\pi\)
\(194\) −6.12013 + 23.5485i −0.0315471 + 0.121384i
\(195\) 59.6675 + 428.439i 0.305987 + 2.19712i
\(196\) 113.359 203.355i 0.578361 1.03752i
\(197\) −20.0751 + 48.4655i −0.101904 + 0.246018i −0.966606 0.256267i \(-0.917507\pi\)
0.864702 + 0.502285i \(0.167507\pi\)
\(198\) 26.3273 67.8345i 0.132966 0.342598i
\(199\) 8.20250 + 8.20250i 0.0412186 + 0.0412186i 0.727416 0.686197i \(-0.240721\pi\)
−0.686197 + 0.727416i \(0.740721\pi\)
\(200\) −153.971 + 3.47853i −0.769856 + 0.0173926i
\(201\) 89.1532 + 151.785i 0.443548 + 0.755151i
\(202\) −18.6482 14.0874i −0.0923176 0.0697397i
\(203\) −397.980 164.849i −1.96049 0.812062i
\(204\) −127.698 49.5531i −0.625969 0.242908i
\(205\) 64.7559 26.8228i 0.315883 0.130843i
\(206\) −44.1725 + 25.9484i −0.214430 + 0.125963i
\(207\) −118.731 66.2018i −0.573578 0.319815i
\(208\) −281.379 202.746i −1.35278 0.974738i
\(209\) 10.5737 0.0505920
\(210\) 112.937 + 397.525i 0.537794 + 1.89298i
\(211\) 165.361 68.4947i 0.783701 0.324619i 0.0452928 0.998974i \(-0.485578\pi\)
0.738408 + 0.674354i \(0.235578\pi\)
\(212\) 173.583 + 219.299i 0.818787 + 1.03443i
\(213\) 9.86290 13.0546i 0.0463047 0.0612890i
\(214\) −220.726 + 292.185i −1.03143 + 1.36535i
\(215\) −138.643 138.643i −0.644851 0.644851i
\(216\) 73.5947 203.076i 0.340716 0.940166i
\(217\) 168.057 + 168.057i 0.774458 + 0.774458i
\(218\) 56.0394 + 402.234i 0.257061 + 1.84511i
\(219\) −50.9741 + 67.4694i −0.232758 + 0.308079i
\(220\) 103.468 29.4011i 0.470311 0.133641i
\(221\) −228.588 + 94.6840i −1.03433 + 0.428435i
\(222\) 150.110 269.250i 0.676171 1.21284i
\(223\) 336.213 1.50768 0.753841 0.657057i \(-0.228199\pi\)
0.753841 + 0.657057i \(0.228199\pi\)
\(224\) −292.969 154.746i −1.30790 0.690830i
\(225\) −151.328 84.3773i −0.672568 0.375010i
\(226\) −7.40945 + 28.5094i −0.0327852 + 0.126148i
\(227\) −179.848 + 74.4954i −0.792281 + 0.328174i −0.741860 0.670554i \(-0.766056\pi\)
−0.0504209 + 0.998728i \(0.516056\pi\)
\(228\) 31.3800 0.707310i 0.137632 0.00310224i
\(229\) −261.354 108.256i −1.14128 0.472735i −0.269682 0.962949i \(-0.586919\pi\)
−0.871602 + 0.490214i \(0.836919\pi\)
\(230\) −27.7292 199.032i −0.120562 0.865356i
\(231\) −63.5945 108.271i −0.275301 0.468706i
\(232\) −120.393 + 310.299i −0.518935 + 1.33749i
\(233\) −184.567 184.567i −0.792131 0.792131i 0.189709 0.981840i \(-0.439246\pi\)
−0.981840 + 0.189709i \(0.939246\pi\)
\(234\) −157.376 357.018i −0.672548 1.52572i
\(235\) −39.9279 + 96.3944i −0.169906 + 0.410189i
\(236\) 93.5033 74.0110i 0.396200 0.313606i
\(237\) 17.4003 + 124.942i 0.0734188 + 0.527180i
\(238\) −203.809 + 119.724i −0.856339 + 0.503042i
\(239\) 317.804 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(240\) 305.100 94.1761i 1.27125 0.392400i
\(241\) 109.362i 0.453786i −0.973920 0.226893i \(-0.927143\pi\)
0.973920 0.226893i \(-0.0728567\pi\)
\(242\) 180.481 106.020i 0.745788 0.438101i
\(243\) 187.121 155.032i 0.770044 0.637991i
\(244\) 39.3410 338.092i 0.161234 1.38562i
\(245\) 357.711 + 148.169i 1.46004 + 0.604770i
\(246\) −49.5724 + 39.2340i −0.201514 + 0.159488i
\(247\) 40.0907 40.0907i 0.162311 0.162311i
\(248\) 126.884 132.750i 0.511629 0.535281i
\(249\) −180.548 307.388i −0.725094 1.23449i
\(250\) 10.5536 + 75.7509i 0.0422145 + 0.303003i
\(251\) −177.635 + 428.849i −0.707709 + 1.70856i −0.00206260 + 0.999998i \(0.500657\pi\)
−0.705647 + 0.708564i \(0.749343\pi\)
\(252\) −195.974 317.066i −0.777675 1.25820i
\(253\) 23.3663 + 56.4112i 0.0923568 + 0.222969i
\(254\) −53.4215 + 205.550i −0.210321 + 0.809252i
\(255\) 57.3109 220.468i 0.224749 0.864581i
\(256\) −114.422 + 229.006i −0.446959 + 0.894554i
\(257\) 154.737i 0.602089i −0.953610 0.301045i \(-0.902665\pi\)
0.953610 0.301045i \(-0.0973353\pi\)
\(258\) 154.465 + 86.1159i 0.598701 + 0.333782i
\(259\) −203.573 491.470i −0.785998 1.89757i
\(260\) 280.829 503.780i 1.08011 1.93761i
\(261\) −293.621 + 232.362i −1.12499 + 0.890275i
\(262\) 22.9591 + 164.794i 0.0876303 + 0.628985i
\(263\) −7.01514 + 7.01514i −0.0266735 + 0.0266735i −0.720318 0.693644i \(-0.756004\pi\)
0.693644 + 0.720318i \(0.256004\pi\)
\(264\) −82.5248 + 51.0134i −0.312594 + 0.193233i
\(265\) −328.894 + 328.894i −1.24111 + 1.24111i
\(266\) 32.6490 43.2190i 0.122741 0.162477i
\(267\) 37.2030 49.2420i 0.139337 0.184427i
\(268\) 27.1281 233.136i 0.101224 0.869909i
\(269\) 49.5351 + 119.588i 0.184145 + 0.444566i 0.988813 0.149159i \(-0.0476566\pi\)
−0.804668 + 0.593725i \(0.797657\pi\)
\(270\) 349.606 + 82.5359i 1.29484 + 0.305689i
\(271\) 403.079i 1.48738i 0.668527 + 0.743688i \(0.266925\pi\)
−0.668527 + 0.743688i \(0.733075\pi\)
\(272\) 96.0383 + 155.344i 0.353082 + 0.571117i
\(273\) −651.635 169.393i −2.38694 0.620487i
\(274\) 208.271 122.345i 0.760114 0.446516i
\(275\) 29.7814 + 71.8988i 0.108296 + 0.261450i
\(276\) 73.1184 + 165.850i 0.264922 + 0.600907i
\(277\) −89.8284 + 216.865i −0.324290 + 0.782906i 0.674705 + 0.738088i \(0.264271\pi\)
−0.998995 + 0.0448182i \(0.985729\pi\)
\(278\) 273.367 + 206.511i 0.983335 + 0.742844i
\(279\) 198.729 56.4476i 0.712289 0.202321i
\(280\) 199.310 513.699i 0.711822 1.83464i
\(281\) 103.353 103.353i 0.367806 0.367806i −0.498871 0.866676i \(-0.666252\pi\)
0.866676 + 0.498871i \(0.166252\pi\)
\(282\) 10.8820 93.4763i 0.0385886 0.331476i
\(283\) −89.7193 37.1630i −0.317029 0.131318i 0.218494 0.975838i \(-0.429886\pi\)
−0.535523 + 0.844520i \(0.679886\pi\)
\(284\) −20.9846 + 5.96289i −0.0738893 + 0.0209961i
\(285\) 7.20020 + 51.7006i 0.0252638 + 0.181406i
\(286\) −44.0816 + 169.613i −0.154131 + 0.593052i
\(287\) 109.095i 0.380124i
\(288\) −241.499 + 156.915i −0.838539 + 0.544842i
\(289\) −158.707 −0.549159
\(290\) −535.722 139.232i −1.84732 0.480109i
\(291\) 36.1473 5.03413i 0.124217 0.0172994i
\(292\) 108.454 30.8178i 0.371417 0.105540i
\(293\) 130.388 314.784i 0.445010 1.07435i −0.529158 0.848523i \(-0.677492\pi\)
0.974168 0.225825i \(-0.0725078\pi\)
\(294\) −346.882 40.3821i −1.17987 0.137354i
\(295\) 140.231 + 140.231i 0.475361 + 0.475361i
\(296\) −376.086 + 165.828i −1.27056 + 0.560230i
\(297\) −109.119 + 2.44822i −0.367404 + 0.00824316i
\(298\) −58.0241 + 76.8091i −0.194712 + 0.257749i
\(299\) 302.479 + 125.291i 1.01164 + 0.419034i
\(300\) 93.1930 + 211.384i 0.310643 + 0.704614i
\(301\) 281.949 116.787i 0.936707 0.387997i
\(302\) −76.3990 130.056i −0.252977 0.430648i
\(303\) −8.81988 + 33.9291i −0.0291085 + 0.111977i
\(304\) −33.9545 24.4657i −0.111692 0.0804792i
\(305\) 566.055 1.85592
\(306\) 4.61932 + 205.411i 0.0150958 + 0.671278i
\(307\) −148.225 + 61.3966i −0.482816 + 0.199989i −0.610796 0.791788i \(-0.709151\pi\)
0.127980 + 0.991777i \(0.459151\pi\)
\(308\) −19.3509 + 166.300i −0.0628277 + 0.539934i
\(309\) 61.3135 + 46.3232i 0.198426 + 0.149913i
\(310\) 243.678 + 184.082i 0.786058 + 0.593814i
\(311\) −284.654 284.654i −0.915285 0.915285i 0.0813964 0.996682i \(-0.474062\pi\)
−0.996682 + 0.0813964i \(0.974062\pi\)
\(312\) −119.477 + 506.315i −0.382938 + 1.62280i
\(313\) −67.1669 67.1669i −0.214591 0.214591i 0.591624 0.806214i \(-0.298487\pi\)
−0.806214 + 0.591624i \(0.798487\pi\)
\(314\) 210.916 29.3848i 0.671707 0.0935823i
\(315\) 486.090 384.674i 1.54314 1.22119i
\(316\) 81.8953 146.912i 0.259162 0.464912i
\(317\) 34.0540 14.1056i 0.107426 0.0444973i −0.328323 0.944565i \(-0.606484\pi\)
0.435749 + 0.900068i \(0.356484\pi\)
\(318\) 204.287 366.427i 0.642413 1.15229i
\(319\) 168.184 0.527224
\(320\) −400.288 144.994i −1.25090 0.453105i
\(321\) 531.610 + 138.192i 1.65611 + 0.430506i
\(322\) 302.724 + 78.6765i 0.940136 + 0.244337i
\(323\) −27.5841 + 11.4257i −0.0853996 + 0.0353737i
\(324\) −323.672 + 14.5650i −0.998989 + 0.0449536i
\(325\) 385.524 + 159.689i 1.18623 + 0.491352i
\(326\) −409.025 + 56.9854i −1.25468 + 0.174802i
\(327\) 525.272 308.526i 1.60634 0.943504i
\(328\) 84.2714 1.90387i 0.256925 0.00580447i
\(329\) −114.832 114.832i −0.349034 0.349034i
\(330\) −100.131 126.517i −0.303429 0.383384i
\(331\) 28.5036 68.8139i 0.0861137 0.207897i −0.874956 0.484202i \(-0.839110\pi\)
0.961070 + 0.276305i \(0.0891100\pi\)
\(332\) −54.9384 + 472.134i −0.165477 + 1.42209i
\(333\) −459.296 53.4928i −1.37927 0.160639i
\(334\) −152.539 259.671i −0.456705 0.777458i
\(335\) 390.330 1.16516
\(336\) −46.3041 + 494.827i −0.137810 + 1.47270i
\(337\) 216.542i 0.642558i 0.946985 + 0.321279i \(0.104113\pi\)
−0.946985 + 0.321279i \(0.895887\pi\)
\(338\) 304.758 + 518.795i 0.901650 + 1.53490i
\(339\) 43.7624 6.09466i 0.129092 0.0179784i
\(340\) −238.152 + 188.505i −0.700446 + 0.554426i
\(341\) −85.7291 35.5101i −0.251405 0.104135i
\(342\) −18.9909 43.0820i −0.0555289 0.125971i
\(343\) −67.3861 + 67.3861i −0.196461 + 0.196461i
\(344\) −95.1332 215.755i −0.276550 0.627195i
\(345\) −259.913 + 152.663i −0.753371 + 0.442503i
\(346\) −174.567 + 24.3207i −0.504528 + 0.0702910i
\(347\) −242.438 + 585.297i −0.698668 + 1.68673i 0.0278739 + 0.999611i \(0.491126\pi\)
−0.726542 + 0.687122i \(0.758874\pi\)
\(348\) 499.127 11.2504i 1.43427 0.0323287i
\(349\) −174.726 421.826i −0.500647 1.20867i −0.949132 0.314879i \(-0.898036\pi\)
0.448484 0.893791i \(-0.351964\pi\)
\(350\) 385.836 + 100.277i 1.10239 + 0.286506i
\(351\) −404.446 + 423.011i −1.15227 + 1.20516i
\(352\) 128.797 + 12.0456i 0.365900 + 0.0342204i
\(353\) 617.057i 1.74804i 0.485893 + 0.874018i \(0.338494\pi\)
−0.485893 + 0.874018i \(0.661506\pi\)
\(354\) −156.235 87.1026i −0.441341 0.246053i
\(355\) −13.8837 33.5181i −0.0391089 0.0944173i
\(356\) −79.1541 + 22.4921i −0.222343 + 0.0631800i
\(357\) 282.896 + 213.732i 0.792426 + 0.598689i
\(358\) −151.386 + 21.0912i −0.422867 + 0.0589139i
\(359\) 243.456 243.456i 0.678151 0.678151i −0.281431 0.959582i \(-0.590809\pi\)
0.959582 + 0.281431i \(0.0908090\pi\)
\(360\) −305.627 368.770i −0.848963 1.02436i
\(361\) −250.428 + 250.428i −0.693706 + 0.693706i
\(362\) 228.288 + 172.456i 0.630629 + 0.476398i
\(363\) −250.516 189.268i −0.690126 0.521400i
\(364\) 557.161 + 703.901i 1.53066 + 1.93379i
\(365\) 71.7545 + 173.231i 0.196588 + 0.474605i
\(366\) −491.124 + 139.528i −1.34187 + 0.381225i
\(367\) 600.550i 1.63638i −0.574951 0.818188i \(-0.694979\pi\)
0.574951 0.818188i \(-0.305021\pi\)
\(368\) 55.4911 235.214i 0.150791 0.639168i
\(369\) 82.8247 + 46.1813i 0.224457 + 0.125153i
\(370\) −346.221 589.379i −0.935733 1.59292i
\(371\) −277.047 668.850i −0.746757 1.80283i
\(372\) −256.796 99.6500i −0.690313 0.267876i
\(373\) 163.825 395.509i 0.439209 1.06035i −0.537013 0.843574i \(-0.680447\pi\)
0.976222 0.216771i \(-0.0695526\pi\)
\(374\) 55.6274 73.6365i 0.148736 0.196889i
\(375\) 98.9220 58.1032i 0.263792 0.154942i
\(376\) −86.6989 + 90.7069i −0.230582 + 0.241242i
\(377\) 637.678 637.678i 1.69145 1.69145i
\(378\) −326.925 + 453.571i −0.864881 + 1.19992i
\(379\) 636.586 + 263.682i 1.67965 + 0.695732i 0.999309 0.0371673i \(-0.0118335\pi\)
0.680337 + 0.732899i \(0.261833\pi\)
\(380\) 33.8881 60.7920i 0.0891793 0.159979i
\(381\) 315.523 43.9420i 0.828144 0.115333i
\(382\) 479.000 + 124.490i 1.25393 + 0.325890i
\(383\) 211.992i 0.553504i 0.960941 + 0.276752i \(0.0892580\pi\)
−0.960941 + 0.276752i \(0.910742\pi\)
\(384\) 383.040 + 27.1324i 0.997501 + 0.0706574i
\(385\) −278.429 −0.723192
\(386\) 85.3133 328.260i 0.221019 0.850415i
\(387\) 30.6881 263.491i 0.0792973 0.680856i
\(388\) −42.5037 23.6934i −0.109546 0.0610655i
\(389\) 175.527 423.760i 0.451226 1.08936i −0.520630 0.853782i \(-0.674303\pi\)
0.971856 0.235574i \(-0.0756971\pi\)
\(390\) −859.345 100.040i −2.20345 0.256513i
\(391\) −121.913 121.913i −0.311798 0.311798i
\(392\) 336.604 + 321.731i 0.858685 + 0.820743i
\(393\) 215.202 126.402i 0.547588 0.321634i
\(394\) −83.7150 63.2411i −0.212475 0.160510i
\(395\) 258.425 + 107.043i 0.654242 + 0.270996i
\(396\) 118.062 + 85.0876i 0.298137 + 0.214868i
\(397\) −472.778 + 195.831i −1.19088 + 0.493277i −0.888040 0.459766i \(-0.847933\pi\)
−0.302835 + 0.953043i \(0.597933\pi\)
\(398\) −20.0040 + 11.7510i −0.0502614 + 0.0295252i
\(399\) −78.6340 20.4410i −0.197078 0.0512305i
\(400\) 70.7261 299.791i 0.176815 0.749478i
\(401\) −191.335 −0.477146 −0.238573 0.971125i \(-0.576680\pi\)
−0.238573 + 0.971125i \(0.576680\pi\)
\(402\) −338.661 + 96.2135i −0.842440 + 0.239337i
\(403\) −459.683 + 190.407i −1.14065 + 0.472474i
\(404\) 36.6504 29.0101i 0.0907189 0.0718071i
\(405\) −86.2754 531.873i −0.213026 1.31327i
\(406\) 519.311 687.435i 1.27909 1.69319i
\(407\) 146.861 + 146.861i 0.360838 + 0.360838i
\(408\) 160.162 222.255i 0.392553 0.544742i
\(409\) 184.985 + 184.985i 0.452285 + 0.452285i 0.896112 0.443827i \(-0.146380\pi\)
−0.443827 + 0.896112i \(0.646380\pi\)
\(410\) 19.3434 + 138.842i 0.0471791 + 0.338638i
\(411\) −289.090 218.412i −0.703383 0.531416i
\(412\) −28.0060 98.5585i −0.0679757 0.239220i
\(413\) −285.180 + 118.125i −0.690507 + 0.286017i
\(414\) 187.877 196.522i 0.453809 0.474690i
\(415\) −790.476 −1.90476
\(416\) 534.009 442.666i 1.28368 1.06410i
\(417\) 129.293 497.373i 0.310054 1.19274i
\(418\) −5.31941 + 20.4675i −0.0127259 + 0.0489653i
\(419\) 93.8787 38.8858i 0.224054 0.0928063i −0.267833 0.963465i \(-0.586307\pi\)
0.491887 + 0.870659i \(0.336307\pi\)
\(420\) −826.304 + 18.6250i −1.96739 + 0.0443452i
\(421\) 313.567 + 129.884i 0.744814 + 0.308512i 0.722624 0.691242i \(-0.242936\pi\)
0.0221902 + 0.999754i \(0.492936\pi\)
\(422\) 49.3954 + 354.546i 0.117051 + 0.840157i
\(423\) −135.790 + 38.5702i −0.321016 + 0.0911826i
\(424\) −511.822 + 225.679i −1.20713 + 0.532261i
\(425\) −155.384 155.384i −0.365609 0.365609i
\(426\) 20.3078 + 25.6590i 0.0476709 + 0.0602324i
\(427\) −337.164 + 813.985i −0.789610 + 1.90629i
\(428\) −454.538 574.250i −1.06200 1.34170i
\(429\) 260.359 36.2594i 0.606897 0.0845208i
\(430\) 338.118 198.622i 0.786322 0.461912i
\(431\) −685.354 −1.59015 −0.795074 0.606512i \(-0.792568\pi\)
−0.795074 + 0.606512i \(0.792568\pi\)
\(432\) 356.069 + 244.620i 0.824234 + 0.566249i
\(433\) 606.988i 1.40182i −0.713250 0.700910i \(-0.752778\pi\)
0.713250 0.700910i \(-0.247222\pi\)
\(434\) −409.854 + 240.762i −0.944363 + 0.554750i
\(435\) 114.525 + 822.343i 0.263277 + 1.89044i
\(436\) −806.795 93.8801i −1.85045 0.215321i
\(437\) 36.5008 + 15.1191i 0.0835257 + 0.0345975i
\(438\) −104.956 132.613i −0.239626 0.302769i
\(439\) −141.628 + 141.628i −0.322614 + 0.322614i −0.849769 0.527155i \(-0.823259\pi\)
0.527155 + 0.849769i \(0.323259\pi\)
\(440\) 4.85897 + 215.074i 0.0110431 + 0.488805i
\(441\) 143.130 + 503.903i 0.324559 + 1.14264i
\(442\) −68.2821 490.109i −0.154484 1.10884i
\(443\) 39.9642 96.4820i 0.0902125 0.217792i −0.872333 0.488912i \(-0.837394\pi\)
0.962546 + 0.271120i \(0.0873939\pi\)
\(444\) 445.669 + 426.021i 1.00376 + 0.959506i
\(445\) −52.3694 126.431i −0.117684 0.284114i
\(446\) −169.141 + 650.805i −0.379241 + 1.45920i
\(447\) 139.749 + 36.3278i 0.312637 + 0.0812703i
\(448\) 446.927 489.249i 0.997604 1.09207i
\(449\) 657.118i 1.46351i 0.681566 + 0.731757i \(0.261299\pi\)
−0.681566 + 0.731757i \(0.738701\pi\)
\(450\) 239.458 250.476i 0.532130 0.556614i
\(451\) −16.3000 39.3516i −0.0361418 0.0872541i
\(452\) −51.4579 28.6849i −0.113845 0.0634621i
\(453\) −136.388 + 180.523i −0.301077 + 0.398506i
\(454\) −53.7229 385.607i −0.118332 0.849356i
\(455\) −1055.67 + 1055.67i −2.32016 + 2.32016i
\(456\) −14.4175 + 61.0980i −0.0316172 + 0.133987i
\(457\) 290.283 290.283i 0.635192 0.635192i −0.314174 0.949365i \(-0.601727\pi\)
0.949365 + 0.314174i \(0.101727\pi\)
\(458\) 341.033 451.440i 0.744613 0.985677i
\(459\) 282.017 124.298i 0.614417 0.270802i
\(460\) 399.215 + 46.4534i 0.867858 + 0.100986i
\(461\) −98.5879 238.012i −0.213857 0.516296i 0.780153 0.625589i \(-0.215141\pi\)
−0.994010 + 0.109293i \(0.965141\pi\)
\(462\) 241.573 68.6307i 0.522884 0.148551i
\(463\) 600.670i 1.29734i 0.761068 + 0.648672i \(0.224675\pi\)
−0.761068 + 0.648672i \(0.775325\pi\)
\(464\) −540.076 389.148i −1.16396 0.838682i
\(465\) 115.251 443.355i 0.247851 0.953453i
\(466\) 450.116 264.413i 0.965914 0.567410i
\(467\) −131.441 317.326i −0.281457 0.679498i 0.718413 0.695617i \(-0.244869\pi\)
−0.999870 + 0.0161189i \(0.994869\pi\)
\(468\) 770.250 125.025i 1.64583 0.267147i
\(469\) −232.495 + 561.294i −0.495726 + 1.19679i
\(470\) −166.503 125.782i −0.354262 0.267621i
\(471\) −161.779 275.432i −0.343480 0.584782i
\(472\) 96.2233 + 218.227i 0.203863 + 0.462346i
\(473\) −84.2520 + 84.2520i −0.178123 + 0.178123i
\(474\) −250.602 29.1737i −0.528697 0.0615480i
\(475\) 46.5220 + 19.2700i 0.0979410 + 0.0405685i
\(476\) −129.218 454.742i −0.271465 0.955340i
\(477\) −625.064 72.7994i −1.31041 0.152619i
\(478\) −159.880 + 615.172i −0.334478 + 1.28697i
\(479\) 202.346i 0.422435i 0.977439 + 0.211218i \(0.0677429\pi\)
−0.977439 + 0.211218i \(0.932257\pi\)
\(480\) 28.8071 + 637.958i 0.0600148 + 1.32908i
\(481\) 1113.66 2.31530
\(482\) 211.692 + 55.0178i 0.439195 + 0.114145i
\(483\) −64.7155 464.686i −0.133987 0.962083i
\(484\) 114.427 + 402.692i 0.236420 + 0.832008i
\(485\) 30.9691 74.7660i 0.0638538 0.154157i
\(486\) 205.958 + 440.202i 0.423781 + 0.905765i
\(487\) 27.2387 + 27.2387i 0.0559316 + 0.0559316i 0.734519 0.678588i \(-0.237408\pi\)
−0.678588 + 0.734519i \(0.737408\pi\)
\(488\) 634.651 + 246.239i 1.30051 + 0.504588i
\(489\) 313.734 + 534.140i 0.641583 + 1.09231i
\(490\) −466.765 + 617.878i −0.952582 + 1.26098i
\(491\) 129.205 + 53.5185i 0.263147 + 0.108999i 0.510356 0.859963i \(-0.329514\pi\)
−0.247209 + 0.968962i \(0.579514\pi\)
\(492\) −51.0063 115.695i −0.103671 0.235152i
\(493\) −438.749 + 181.736i −0.889958 + 0.368632i
\(494\) 57.4346 + 97.7721i 0.116264 + 0.197919i
\(495\) −117.862 + 211.382i −0.238105 + 0.427034i
\(496\) 193.130 + 312.392i 0.389376 + 0.629823i
\(497\) 56.4686 0.113619
\(498\) 685.839 194.847i 1.37719 0.391258i
\(499\) 199.039 82.4448i 0.398876 0.165220i −0.174222 0.984706i \(-0.555741\pi\)
0.573099 + 0.819486i \(0.305741\pi\)
\(500\) −151.940 17.6800i −0.303880 0.0353600i
\(501\) −272.314 + 360.436i −0.543542 + 0.719432i
\(502\) −740.756 559.592i −1.47561 1.11472i
\(503\) −520.709 520.709i −1.03521 1.03521i −0.999357 0.0358487i \(-0.988587\pi\)
−0.0358487 0.999357i \(-0.511413\pi\)
\(504\) 712.332 219.837i 1.41336 0.436185i
\(505\) 54.9664 + 54.9664i 0.108844 + 0.108844i
\(506\) −120.950 + 16.8508i −0.239031 + 0.0333019i
\(507\) 544.055 720.112i 1.07309 1.42034i
\(508\) −371.007 206.815i −0.730328 0.407117i
\(509\) 46.6423 19.3199i 0.0916351 0.0379565i −0.336395 0.941721i \(-0.609208\pi\)
0.428030 + 0.903764i \(0.359208\pi\)
\(510\) 397.927 + 221.849i 0.780250 + 0.434998i
\(511\) −291.845 −0.571125
\(512\) −385.722 336.693i −0.753364 0.657604i
\(513\) −48.8053 + 51.0456i −0.0951370 + 0.0995040i
\(514\) 299.523 + 77.8447i 0.582730 + 0.151449i
\(515\) 157.425 65.2076i 0.305680 0.126617i
\(516\) −244.402 + 255.674i −0.473647 + 0.495491i
\(517\) 58.5780 + 24.2638i 0.113304 + 0.0469319i
\(518\) 1053.75 146.808i 2.03426 0.283414i
\(519\) 133.898 + 227.964i 0.257992 + 0.439238i
\(520\) 833.885 + 797.039i 1.60362 + 1.53277i
\(521\) 160.612 + 160.612i 0.308276 + 0.308276i 0.844241 0.535965i \(-0.180052\pi\)
−0.535965 + 0.844241i \(0.680052\pi\)
\(522\) −302.067 685.257i −0.578672 1.31275i
\(523\) −12.4139 + 29.9698i −0.0237360 + 0.0573037i −0.935303 0.353848i \(-0.884873\pi\)
0.911567 + 0.411151i \(0.134873\pi\)
\(524\) −330.541 38.4624i −0.630804 0.0734015i
\(525\) −82.4830 592.265i −0.157111 1.12812i
\(526\) −10.0500 17.1083i −0.0191065 0.0325253i
\(527\) 262.016 0.497184
\(528\) −57.2299 185.406i −0.108390 0.351149i
\(529\) 300.856i 0.568727i
\(530\) −471.179 802.098i −0.889017 1.51339i
\(531\) −31.0397 + 266.510i −0.0584552 + 0.501903i
\(532\) 67.2337 + 84.9410i 0.126379 + 0.159664i
\(533\) −211.005 87.4011i −0.395882 0.163980i
\(534\) 76.6014 + 96.7862i 0.143448 + 0.181248i
\(535\) 861.230 861.230i 1.60978 1.60978i
\(536\) 437.632 + 169.797i 0.816477 + 0.316786i
\(537\) 116.118 + 197.693i 0.216234 + 0.368144i
\(538\) −256.407 + 35.7226i −0.476592 + 0.0663989i
\(539\) 90.0407 217.377i 0.167051 0.403298i
\(540\) −335.644 + 635.209i −0.621562 + 1.17631i
\(541\) 387.010 + 934.325i 0.715360 + 1.72703i 0.686151 + 0.727459i \(0.259299\pi\)
0.0292095 + 0.999573i \(0.490701\pi\)
\(542\) −780.237 202.780i −1.43955 0.374133i
\(543\) 107.972 415.354i 0.198843 0.764924i
\(544\) −349.013 + 107.751i −0.641568 + 0.198071i
\(545\) 1350.79i 2.47851i
\(546\) 655.716 1176.15i 1.20094 2.15412i
\(547\) −212.847 513.858i −0.389117 0.939411i −0.990127 0.140170i \(-0.955235\pi\)
0.601011 0.799241i \(-0.294765\pi\)
\(548\) 132.047 + 464.699i 0.240961 + 0.847990i
\(549\) 475.248 + 600.542i 0.865660 + 1.09388i
\(550\) −154.156 + 21.4771i −0.280284 + 0.0390493i
\(551\) 76.9498 76.9498i 0.139655 0.139655i
\(552\) −357.820 + 58.0993i −0.648225 + 0.105252i
\(553\) −307.856 + 307.856i −0.556702 + 0.556702i
\(554\) −374.593 282.980i −0.676162 0.510795i
\(555\) −618.076 + 818.087i −1.11365 + 1.47403i
\(556\) −537.266 + 425.265i −0.966306 + 0.764864i
\(557\) 184.916 + 446.427i 0.331986 + 0.801485i 0.998434 + 0.0559338i \(0.0178136\pi\)
−0.666449 + 0.745551i \(0.732186\pi\)
\(558\) 9.28932 + 413.076i 0.0166475 + 0.740279i
\(559\) 638.890i 1.14292i
\(560\) 894.095 + 644.234i 1.59660 + 1.15042i
\(561\) −133.977 34.8273i −0.238817 0.0620808i
\(562\) 148.066 + 252.055i 0.263462 + 0.448497i
\(563\) 79.1858 + 191.171i 0.140650 + 0.339558i 0.978470 0.206387i \(-0.0661706\pi\)
−0.837821 + 0.545945i \(0.816171\pi\)
\(564\) 175.467 + 68.0901i 0.311112 + 0.120727i
\(565\) 37.4933 90.5168i 0.0663598 0.160207i
\(566\) 117.072 154.973i 0.206841 0.273804i
\(567\) 816.221 + 192.740i 1.43954 + 0.339930i
\(568\) −0.985455 43.6195i −0.00173496 0.0767949i
\(569\) −667.568 + 667.568i −1.17323 + 1.17323i −0.191794 + 0.981435i \(0.561431\pi\)
−0.981435 + 0.191794i \(0.938569\pi\)
\(570\) −103.699 12.0720i −0.181928 0.0211790i
\(571\) −817.916 338.792i −1.43243 0.593331i −0.474478 0.880267i \(-0.657363\pi\)
−0.957950 + 0.286936i \(0.907363\pi\)
\(572\) −306.142 170.657i −0.535214 0.298351i
\(573\) −102.399 735.273i −0.178708 1.28320i
\(574\) −211.176 54.8835i −0.367902 0.0956159i
\(575\) 290.780i 0.505704i
\(576\) −182.246 546.409i −0.316399 0.948626i
\(577\) 345.363 0.598549 0.299274 0.954167i \(-0.403255\pi\)
0.299274 + 0.954167i \(0.403255\pi\)
\(578\) 79.8419 307.208i 0.138135 0.531502i
\(579\) −503.885 + 70.1747i −0.870268 + 0.121200i
\(580\) 539.020 966.951i 0.929345 1.66716i
\(581\) 470.838 1136.70i 0.810392 1.95646i
\(582\) −8.44035 + 72.5026i −0.0145023 + 0.124575i
\(583\) 199.866 + 199.866i 0.342823 + 0.342823i
\(584\) 5.09309 + 225.437i 0.00872105 + 0.386023i
\(585\) 354.583 + 1248.34i 0.606125 + 2.13392i
\(586\) 543.730 + 410.752i 0.927868 + 0.700942i
\(587\) −86.0668 35.6500i −0.146621 0.0607326i 0.308166 0.951333i \(-0.400285\pi\)
−0.454787 + 0.890600i \(0.650285\pi\)
\(588\) 252.676 651.142i 0.429721 1.10738i
\(589\) −55.4708 + 22.9768i −0.0941780 + 0.0390098i
\(590\) −341.993 + 200.898i −0.579648 + 0.340505i
\(591\) −39.5941 + 152.314i −0.0669951 + 0.257722i
\(592\) −131.792 811.412i −0.222622 1.37063i
\(593\) −312.255 −0.526568 −0.263284 0.964718i \(-0.584806\pi\)
−0.263284 + 0.964718i \(0.584806\pi\)
\(594\) 50.1563 212.453i 0.0844383 0.357664i
\(595\) 726.348 300.863i 1.22075 0.505653i
\(596\) −119.488 150.958i −0.200484 0.253285i
\(597\) 27.7665 + 20.9780i 0.0465101 + 0.0351391i
\(598\) −394.696 + 522.476i −0.660026 + 0.873706i
\(599\) 804.787 + 804.787i 1.34355 + 1.34355i 0.892496 + 0.451055i \(0.148952\pi\)
0.451055 + 0.892496i \(0.351048\pi\)
\(600\) −456.059 + 74.0503i −0.760098 + 0.123417i
\(601\) −92.1209 92.1209i −0.153279 0.153279i 0.626302 0.779581i \(-0.284568\pi\)
−0.779581 + 0.626302i \(0.784568\pi\)
\(602\) 84.2218 + 604.520i 0.139903 + 1.00419i
\(603\) 327.713 + 414.111i 0.543471 + 0.686751i
\(604\) 290.183 82.4571i 0.480435 0.136518i
\(605\) −643.210 + 266.426i −1.06316 + 0.440374i
\(606\) −61.2392 34.1416i −0.101055 0.0563392i
\(607\) −683.903 −1.12669 −0.563347 0.826220i \(-0.690487\pi\)
−0.563347 + 0.826220i \(0.690487\pi\)
\(608\) 64.4399 53.4174i 0.105987 0.0878575i
\(609\) −1250.74 325.131i −2.05376 0.533877i
\(610\) −284.770 + 1095.71i −0.466835 + 1.79624i
\(611\) 314.098 130.104i 0.514072 0.212936i
\(612\) −399.937 94.3961i −0.653491 0.154242i
\(613\) −61.4439 25.4509i −0.100235 0.0415186i 0.332003 0.943278i \(-0.392276\pi\)
−0.432237 + 0.901760i \(0.642276\pi\)
\(614\) −44.2766 317.805i −0.0721117 0.517597i
\(615\) 181.311 106.496i 0.294815 0.173164i
\(616\) −312.170 121.119i −0.506770 0.196622i
\(617\) 429.320 + 429.320i 0.695819 + 0.695819i 0.963506 0.267687i \(-0.0862593\pi\)
−0.267687 + 0.963506i \(0.586259\pi\)
\(618\) −120.513 + 95.3800i −0.195005 + 0.154337i
\(619\) 310.121 748.697i 0.501003 1.20953i −0.447936 0.894066i \(-0.647841\pi\)
0.948938 0.315462i \(-0.102159\pi\)
\(620\) −478.916 + 379.078i −0.772445 + 0.611417i
\(621\) −380.182 147.575i −0.612209 0.237641i
\(622\) 694.206 407.800i 1.11609 0.655627i
\(623\) 213.000 0.341895
\(624\) −919.965 485.986i −1.47430 0.778824i
\(625\) 735.670i 1.17707i
\(626\) 163.805 96.2245i 0.261669 0.153713i
\(627\) 31.4180 4.37549i 0.0501084 0.00697846i
\(628\) −49.2271 + 423.052i −0.0783871 + 0.673649i
\(629\) −541.816 224.428i −0.861393 0.356801i
\(630\) 500.071 + 1134.44i 0.793763 + 1.80070i
\(631\) 168.809 168.809i 0.267525 0.267525i −0.560577 0.828102i \(-0.689421\pi\)
0.828102 + 0.560577i \(0.189421\pi\)
\(632\) 243.178 + 232.433i 0.384775 + 0.367773i
\(633\) 462.997 271.948i 0.731433 0.429617i
\(634\) 10.1724 + 73.0144i 0.0160448 + 0.115165i
\(635\) 270.323 652.618i 0.425706 1.02775i
\(636\) 606.519 + 579.779i 0.953646 + 0.911603i
\(637\) −482.802 1165.59i −0.757931 1.82981i
\(638\) −84.6099 + 325.554i −0.132617 + 0.510272i
\(639\) 23.9038 42.8706i 0.0374081 0.0670902i
\(640\) 482.039 701.891i 0.753186 1.09671i
\(641\) 1143.92i 1.78458i 0.451463 + 0.892290i \(0.350902\pi\)
−0.451463 + 0.892290i \(0.649098\pi\)
\(642\) −534.940 + 959.513i −0.833239 + 1.49457i
\(643\) 56.4117 + 136.190i 0.0877321 + 0.211804i 0.961656 0.274259i \(-0.0884326\pi\)
−0.873924 + 0.486063i \(0.838433\pi\)
\(644\) −304.587 + 546.400i −0.472962 + 0.848448i
\(645\) −469.324 354.581i −0.727635 0.549738i
\(646\) −8.23972 59.1424i −0.0127550 0.0915517i
\(647\) 77.9719 77.9719i 0.120513 0.120513i −0.644278 0.764791i \(-0.722842\pi\)
0.764791 + 0.644278i \(0.222842\pi\)
\(648\) 134.639 633.858i 0.207776 0.978176i
\(649\) 85.2174 85.2174i 0.131306 0.131306i
\(650\) −503.059 + 665.921i −0.773937 + 1.02449i
\(651\) 568.896 + 429.809i 0.873880 + 0.660229i
\(652\) 95.4650 820.415i 0.146419 1.25831i
\(653\) −279.659 675.157i −0.428268 1.03393i −0.979836 0.199801i \(-0.935970\pi\)
0.551568 0.834130i \(-0.314030\pi\)
\(654\) 332.959 + 1171.98i 0.509111 + 1.79202i
\(655\) 553.413i 0.844905i
\(656\) −38.7098 + 164.082i −0.0590088 + 0.250124i
\(657\) −123.541 + 221.567i −0.188038 + 0.337240i
\(658\) 280.050 164.511i 0.425608 0.250016i
\(659\) −161.133 389.010i −0.244512 0.590303i 0.753209 0.657781i \(-0.228505\pi\)
−0.997721 + 0.0674778i \(0.978505\pi\)
\(660\) 295.271 130.176i 0.447381 0.197237i
\(661\) 136.906 330.520i 0.207119 0.500030i −0.785848 0.618420i \(-0.787773\pi\)
0.992967 + 0.118390i \(0.0377733\pi\)
\(662\) 118.863 + 89.7931i 0.179551 + 0.135639i
\(663\) −640.026 + 375.928i −0.965349 + 0.567011i
\(664\) −886.269 343.864i −1.33474 0.517868i
\(665\) −127.390 + 127.390i −0.191564 + 0.191564i
\(666\) 334.607 862.145i 0.502413 1.29451i
\(667\) 580.577 + 240.483i 0.870430 + 0.360544i
\(668\) 579.383 164.635i 0.867340 0.246460i
\(669\) 998.997 139.128i 1.49327 0.207963i
\(670\) −196.366 + 755.560i −0.293084 + 1.12770i
\(671\) 343.986i 0.512647i
\(672\) −934.540 338.567i −1.39068 0.503820i
\(673\) −852.871 −1.26727 −0.633634 0.773633i \(-0.718437\pi\)
−0.633634 + 0.773633i \(0.718437\pi\)
\(674\) −419.159 108.937i −0.621898 0.161628i
\(675\) −484.560 188.092i −0.717867 0.278654i
\(676\) −1157.55 + 328.923i −1.71235 + 0.486573i
\(677\) −232.350 + 560.944i −0.343206 + 0.828573i 0.654182 + 0.756337i \(0.273013\pi\)
−0.997388 + 0.0722351i \(0.976987\pi\)
\(678\) −10.2185 + 87.7766i −0.0150715 + 0.129464i
\(679\) 89.0669 + 89.0669i 0.131174 + 0.131174i
\(680\) −245.079 555.821i −0.360411 0.817384i
\(681\) −503.559 + 295.772i −0.739441 + 0.434321i
\(682\) 111.865 148.081i 0.164025 0.217127i
\(683\) 263.384 + 109.097i 0.385629 + 0.159733i 0.567071 0.823669i \(-0.308077\pi\)
−0.181442 + 0.983402i \(0.558077\pi\)
\(684\) 92.9475 15.0870i 0.135888 0.0220569i
\(685\) −742.252 + 307.451i −1.08358 + 0.448833i
\(686\) −96.5384 164.339i −0.140727 0.239562i
\(687\) −821.365 213.514i −1.19558 0.310792i
\(688\) 465.495 75.6073i 0.676592 0.109894i
\(689\) 1515.60 2.19971
\(690\) −164.753 579.914i −0.238773 0.840454i
\(691\) 543.248 225.021i 0.786177 0.325645i 0.0467716 0.998906i \(-0.485107\pi\)
0.739405 + 0.673260i \(0.235107\pi\)
\(692\) 40.7433 350.143i 0.0588776 0.505987i
\(693\) −233.763 295.392i −0.337321 0.426252i
\(694\) −1010.99 763.735i −1.45676 1.10048i
\(695\) −805.765 805.765i −1.15937 1.15937i
\(696\) −229.322 + 971.817i −0.329486 + 1.39629i
\(697\) 85.0447 + 85.0447i 0.122015 + 0.122015i
\(698\) 904.426 126.005i 1.29574 0.180523i
\(699\) −624.782 472.032i −0.893823 0.675296i
\(700\) −388.211 + 696.413i −0.554587 + 0.994876i
\(701\) 745.399 308.754i 1.06334 0.440448i 0.218702 0.975792i \(-0.429818\pi\)
0.844634 + 0.535344i \(0.179818\pi\)
\(702\) −615.353 995.692i −0.876571 1.41836i
\(703\) 134.387 0.191163
\(704\) −88.1113 + 243.251i −0.125158 + 0.345527i
\(705\) −78.7499 + 302.942i −0.111702 + 0.429704i
\(706\) −1194.43 310.428i −1.69183 0.439699i
\(707\) −111.782 + 46.3015i −0.158107 + 0.0654901i
\(708\) 247.202 258.603i 0.349156 0.365259i
\(709\) 792.806 + 328.391i 1.11820 + 0.463175i 0.863755 0.503911i \(-0.168106\pi\)
0.254448 + 0.967086i \(0.418106\pi\)
\(710\) 71.8654 10.0123i 0.101219 0.0141018i
\(711\) 103.404 + 364.041i 0.145434 + 0.512013i
\(712\) −3.71715 164.533i −0.00522072 0.231086i
\(713\) −245.164 245.164i −0.343848 0.343848i
\(714\) −556.039 + 440.077i −0.778766 + 0.616354i
\(715\) 223.062 538.518i 0.311974 0.753173i
\(716\) 35.3331 303.648i 0.0493479 0.424090i
\(717\) 944.300 131.510i 1.31702 0.183417i
\(718\) 348.779 + 593.734i 0.485765 + 0.826928i
\(719\) 205.788 0.286214 0.143107 0.989707i \(-0.454291\pi\)
0.143107 + 0.989707i \(0.454291\pi\)
\(720\) 867.579 406.080i 1.20497 0.564000i
\(721\) 265.217i 0.367846i
\(722\) −358.767 610.736i −0.496907 0.845895i
\(723\) −45.2550 324.951i −0.0625934 0.449448i
\(724\) −448.668 + 355.136i −0.619708 + 0.490520i
\(725\) 739.973 + 306.507i 1.02065 + 0.422768i
\(726\) 492.394 389.705i 0.678229 0.536784i
\(727\) 46.0919 46.0919i 0.0634001 0.0634001i −0.674696 0.738096i \(-0.735725\pi\)
0.738096 + 0.674696i \(0.235725\pi\)
\(728\) −1642.83 + 724.377i −2.25664 + 0.995023i
\(729\) 491.843 538.081i 0.674682 0.738109i
\(730\) −371.420 + 51.7462i −0.508794 + 0.0708853i
\(731\) 128.751 310.832i 0.176130 0.425215i
\(732\) −23.0103 1020.86i −0.0314349 1.39462i
\(733\) 143.085 + 345.437i 0.195204 + 0.471265i 0.990928 0.134395i \(-0.0429092\pi\)
−0.795724 + 0.605660i \(0.792909\pi\)
\(734\) 1162.48 + 302.123i 1.58376 + 0.411612i
\(735\) 1124.19 + 292.233i 1.52951 + 0.397596i
\(736\) 427.385 + 225.745i 0.580687 + 0.306718i
\(737\) 237.200i 0.321846i
\(738\) −131.060 + 137.090i −0.177588 + 0.185759i
\(739\) 445.308 + 1075.07i 0.602581 + 1.45476i 0.870915 + 0.491434i \(0.163527\pi\)
−0.268334 + 0.963326i \(0.586473\pi\)
\(740\) 1315.03 373.675i 1.77707 0.504966i
\(741\) 102.533 135.712i 0.138371 0.183148i
\(742\) 1434.07 199.794i 1.93270 0.269265i
\(743\) 544.746 544.746i 0.733171 0.733171i −0.238076 0.971247i \(-0.576517\pi\)
0.971247 + 0.238076i \(0.0765167\pi\)
\(744\) 322.081 446.948i 0.432904 0.600736i
\(745\) 226.399 226.399i 0.303891 0.303891i
\(746\) 683.167 + 516.087i 0.915774 + 0.691806i
\(747\) −663.667 838.636i −0.888443 1.12267i
\(748\) 114.553 + 144.723i 0.153145 + 0.193479i
\(749\) 725.465 + 1751.43i 0.968578 + 2.33835i
\(750\) 62.7045 + 220.713i 0.0836061 + 0.294284i
\(751\) 9.99609i 0.0133104i −0.999978 0.00665519i \(-0.997882\pi\)
0.999978 0.00665519i \(-0.00211843\pi\)
\(752\) −131.964 213.455i −0.175485 0.283850i
\(753\) −350.350 + 1347.76i −0.465272 + 1.78985i
\(754\) 913.548 + 1555.15i 1.21160 + 2.06253i
\(755\) 191.989 + 463.502i 0.254290 + 0.613910i
\(756\) −713.507 861.009i −0.943792 1.13890i
\(757\) −200.459 + 483.951i −0.264807 + 0.639302i −0.999224 0.0393977i \(-0.987456\pi\)
0.734416 + 0.678699i \(0.237456\pi\)
\(758\) −830.661 + 1099.58i −1.09586 + 1.45064i
\(759\) 92.7722 + 157.947i 0.122229 + 0.208098i
\(760\) 100.626 + 96.1802i 0.132403 + 0.126553i
\(761\) 133.213 133.213i 0.175049 0.175049i −0.614144 0.789194i \(-0.710499\pi\)
0.789194 + 0.614144i \(0.210499\pi\)
\(762\) −73.6743 + 632.862i −0.0966854 + 0.830527i
\(763\) 1942.43 + 804.580i 2.54578 + 1.05449i
\(764\) −481.948 + 864.569i −0.630823 + 1.13164i
\(765\) 79.0576 678.798i 0.103343 0.887318i
\(766\) −410.351 106.648i −0.535707 0.139228i
\(767\) 646.210i 0.842516i
\(768\) −245.219 + 727.799i −0.319296 + 0.947655i
\(769\) 488.279 0.634953 0.317476 0.948266i \(-0.397165\pi\)
0.317476 + 0.948266i \(0.397165\pi\)
\(770\) 140.071 538.954i 0.181911 0.699940i
\(771\) −64.0314 459.773i −0.0830498 0.596334i
\(772\) 592.492 + 330.281i 0.767477 + 0.427825i
\(773\) −548.805 + 1324.93i −0.709967 + 1.71401i −0.00988404 + 0.999951i \(0.503146\pi\)
−0.700083 + 0.714061i \(0.746854\pi\)
\(774\) 494.600 + 191.959i 0.639018 + 0.248009i
\(775\) −312.473 312.473i −0.403191 0.403191i
\(776\) 67.2459 70.3546i 0.0866571 0.0906631i
\(777\) −808.256 1376.07i −1.04023 1.77101i
\(778\) 731.965 + 552.951i 0.940830 + 0.710734i
\(779\) −25.4624 10.5469i −0.0326860 0.0135390i
\(780\) 625.965 1613.10i 0.802519 2.06808i
\(781\) −20.3687 + 8.43698i −0.0260802 + 0.0108028i
\(782\) 297.318 174.655i 0.380202 0.223343i
\(783\) −776.291 + 811.925i −0.991432 + 1.03694i
\(784\) −792.112 + 489.707i −1.01035 + 0.624627i
\(785\) −708.300 −0.902292
\(786\) 136.412 + 480.156i 0.173552 + 0.610885i
\(787\) −1191.23 + 493.423i −1.51363 + 0.626967i −0.976304 0.216405i \(-0.930567\pi\)
−0.537329 + 0.843372i \(0.680567\pi\)
\(788\) 164.531 130.232i 0.208795 0.165268i
\(789\) −17.9413 + 23.7472i −0.0227393 + 0.0300978i
\(790\) −337.211 + 446.382i −0.426850 + 0.565040i
\(791\) 107.830 + 107.830i 0.136322 + 0.136322i
\(792\) −224.098 + 185.727i −0.282952 + 0.234503i
\(793\) −1304.24 1304.24i −1.64469 1.64469i
\(794\) −141.225 1013.67i −0.177865 1.27666i
\(795\) −841.152 + 1113.35i −1.05805 + 1.40044i
\(796\) −12.6828 44.6334i −0.0159332 0.0560721i
\(797\) −1162.53 + 481.538i −1.45864 + 0.604188i −0.964236 0.265045i \(-0.914613\pi\)
−0.494403 + 0.869233i \(0.664613\pi\)
\(798\) 79.1265 141.928i 0.0991560 0.177855i
\(799\) −179.034 −0.224072
\(800\) 544.723 + 287.722i 0.680904 + 0.359653i
\(801\) 90.1655 161.709i 0.112566 0.201884i
\(802\) 96.2566 370.367i 0.120021 0.461804i
\(803\) 105.271 43.6046i 0.131097 0.0543021i
\(804\) −15.8671 703.947i −0.0197351 0.875556i
\(805\) −961.143 398.119i −1.19397 0.494557i
\(806\) −137.313 985.595i −0.170364 1.22282i
\(807\) 196.671 + 334.838i 0.243707 + 0.414917i
\(808\) 37.7166 + 85.5384i 0.0466789 + 0.105864i
\(809\) −737.912 737.912i −0.912128 0.912128i 0.0843111 0.996439i \(-0.473131\pi\)
−0.996439 + 0.0843111i \(0.973131\pi\)
\(810\) 1072.95 + 100.571i 1.32463 + 0.124162i
\(811\) −59.7731 + 144.305i −0.0737030 + 0.177935i −0.956437 0.291938i \(-0.905700\pi\)
0.882734 + 0.469872i \(0.155700\pi\)
\(812\) 1069.41 + 1351.06i 1.31701 + 1.66387i
\(813\) 166.797 + 1197.68i 0.205163 + 1.47316i
\(814\) −358.161 + 210.396i −0.440001 + 0.258471i
\(815\) 1373.59 1.68539
\(816\) 349.643 + 421.835i 0.428484 + 0.516955i
\(817\) 77.0960i 0.0943647i
\(818\) −451.136 + 265.012i −0.551511 + 0.323976i
\(819\) −2006.31 233.669i −2.44971 0.285311i
\(820\) −278.486 32.4052i −0.339617 0.0395185i
\(821\) −350.123 145.026i −0.426459 0.176645i 0.159122 0.987259i \(-0.449134\pi\)
−0.585581 + 0.810614i \(0.699134\pi\)
\(822\) 568.213 449.712i 0.691257 0.547095i
\(823\) 75.3694 75.3694i 0.0915789 0.0915789i −0.659833 0.751412i \(-0.729373\pi\)
0.751412 + 0.659833i \(0.229373\pi\)
\(824\) 204.868 4.62840i 0.248627 0.00561699i
\(825\) 118.243 + 201.311i 0.143324 + 0.244013i
\(826\) −85.1868 611.447i −0.103132 0.740250i
\(827\) −586.623 + 1416.23i −0.709338 + 1.71249i −0.00769049 + 0.999970i \(0.502448\pi\)
−0.701648 + 0.712524i \(0.747552\pi\)
\(828\) 285.889 + 462.538i 0.345276 + 0.558621i
\(829\) 381.783 + 921.706i 0.460534 + 1.11183i 0.968178 + 0.250261i \(0.0805166\pi\)
−0.507644 + 0.861567i \(0.669483\pi\)
\(830\) 397.671 1530.12i 0.479122 1.84352i
\(831\) −177.169 + 681.547i −0.213199 + 0.820153i
\(832\) 588.219 + 1256.37i 0.706994 + 1.51006i
\(833\) 664.376i 0.797571i
\(834\) 897.718 + 500.488i 1.07640 + 0.600106i
\(835\) 383.327 + 925.434i 0.459075 + 1.10830i
\(836\) −36.9428 20.5935i −0.0441899 0.0246334i
\(837\) 567.129 249.960i 0.677573 0.298638i
\(838\) 28.0428 + 201.283i 0.0334639 + 0.240195i
\(839\) 455.169 455.169i 0.542514 0.542514i −0.381751 0.924265i \(-0.624679\pi\)
0.924265 + 0.381751i \(0.124679\pi\)
\(840\) 379.643 1608.84i 0.451956 1.91529i
\(841\) 629.277 629.277i 0.748249 0.748249i
\(842\) −409.163 + 541.628i −0.485942 + 0.643263i
\(843\) 264.328 349.865i 0.313556 0.415024i
\(844\) −711.143 82.7499i −0.842586 0.0980449i
\(845\) −765.848 1848.92i −0.906329 2.18807i
\(846\) −6.34732 282.252i −0.00750274 0.333631i
\(847\) 1083.63i 1.27937i
\(848\) −179.359 1104.27i −0.211508 1.30220i
\(849\) −281.963 73.2966i −0.332112 0.0863329i
\(850\) 378.946 222.606i 0.445819 0.261889i
\(851\) 296.975 + 716.960i 0.348971 + 0.842492i
\(852\) −59.8844 + 26.4012i −0.0702869 + 0.0309874i
\(853\) −178.427 + 430.761i −0.209176 + 0.504995i −0.993294 0.115617i \(-0.963116\pi\)
0.784118 + 0.620612i \(0.213116\pi\)
\(854\) −1406.01 1062.14i −1.64638 1.24373i
\(855\) 42.7882 + 150.640i 0.0500447 + 0.176187i
\(856\) 1340.24 590.954i 1.56570 0.690367i
\(857\) −320.953 + 320.953i −0.374508 + 0.374508i −0.869116 0.494608i \(-0.835312\pi\)
0.494608 + 0.869116i \(0.335312\pi\)
\(858\) −60.7935 + 522.216i −0.0708549 + 0.608644i
\(859\) −850.003 352.083i −0.989527 0.409875i −0.171580 0.985170i \(-0.554887\pi\)
−0.817946 + 0.575295i \(0.804887\pi\)
\(860\) 214.372 + 754.416i 0.249269 + 0.877228i
\(861\) 45.1446 + 324.158i 0.0524327 + 0.376490i
\(862\) 344.786 1326.64i 0.399984 1.53902i
\(863\) 541.956i 0.627991i 0.949424 + 0.313996i \(0.101668\pi\)
−0.949424 + 0.313996i \(0.898332\pi\)
\(864\) −652.640 + 566.178i −0.755370 + 0.655299i
\(865\) 586.232 0.677724
\(866\) 1174.94 + 305.362i 1.35675 + 0.352612i
\(867\) −471.569 + 65.6741i −0.543909 + 0.0757487i
\(868\) −259.853 914.473i −0.299370 1.05354i
\(869\) 65.0493 157.043i 0.0748553 0.180717i
\(870\) −1649.42 192.016i −1.89589 0.220708i
\(871\) −899.353 899.353i −1.03255 1.03255i
\(872\) 587.604 1514.48i 0.673858 1.73679i
\(873\) 105.322 29.9161i 0.120644 0.0342681i
\(874\) −47.6287 + 63.0482i −0.0544951 + 0.0721375i
\(875\) 365.808 + 151.523i 0.418066 + 0.173169i
\(876\) 309.499 136.449i 0.353309 0.155763i
\(877\) 121.619 50.3764i 0.138677 0.0574417i −0.312266 0.949995i \(-0.601088\pi\)
0.450942 + 0.892553i \(0.351088\pi\)
\(878\) −202.898 345.398i −0.231091 0.393391i
\(879\) 257.164 989.281i 0.292565 1.12546i
\(880\) −418.762 98.7935i −0.475866 0.112265i
\(881\) −954.967 −1.08396 −0.541979 0.840392i \(-0.682325\pi\)
−0.541979 + 0.840392i \(0.682325\pi\)
\(882\) −1047.41 + 23.5543i −1.18754 + 0.0267056i
\(883\) 1068.50 442.586i 1.21008 0.501230i 0.315835 0.948814i \(-0.397715\pi\)
0.894242 + 0.447584i \(0.147715\pi\)
\(884\) 983.052 + 114.390i 1.11205 + 0.129400i
\(885\) 474.702 + 358.644i 0.536386 + 0.405248i
\(886\) 166.655 + 125.896i 0.188098 + 0.142095i
\(887\) −88.0687 88.0687i −0.0992882 0.0992882i 0.655718 0.755006i \(-0.272366\pi\)
−0.755006 + 0.655718i \(0.772366\pi\)
\(888\) −1048.85 + 648.357i −1.18114 + 0.730131i
\(889\) 777.448 + 777.448i 0.874520 + 0.874520i
\(890\) 271.078 37.7666i 0.304581 0.0424343i
\(891\) −323.215 + 52.4288i −0.362755 + 0.0588426i
\(892\) −1174.67 654.812i −1.31689 0.734094i
\(893\) 37.9028 15.6999i 0.0424443 0.0175810i
\(894\) −140.624 + 252.236i −0.157298 + 0.282143i
\(895\) 508.387 0.568030
\(896\) 722.197 + 1111.24i 0.806023 + 1.24023i
\(897\) 950.610 + 247.112i 1.05977 + 0.275487i
\(898\) −1271.98 330.581i −1.41646 0.368131i
\(899\) −882.312 + 365.466i −0.981437 + 0.406525i
\(900\) 364.379 + 589.527i 0.404865 + 0.655030i
\(901\) −737.368 305.428i −0.818388 0.338987i
\(902\) 84.3728 11.7548i 0.0935397 0.0130320i
\(903\) 789.434 463.685i 0.874235 0.513494i
\(904\) 81.4124 85.1760i 0.0900580 0.0942213i
\(905\) −672.890 672.890i −0.743525 0.743525i
\(906\) −280.824 354.823i −0.309961 0.391637i
\(907\) −512.240 + 1236.66i −0.564763 + 1.36346i 0.341155 + 0.940007i \(0.389182\pi\)
−0.905918 + 0.423452i \(0.860818\pi\)
\(908\) 773.445 + 89.9995i 0.851812 + 0.0991184i
\(909\) −12.1666 + 104.464i −0.0133846 + 0.114922i
\(910\) −1512.38 2574.55i −1.66195 2.82918i
\(911\) −181.067 −0.198756 −0.0993780 0.995050i \(-0.531685\pi\)
−0.0993780 + 0.995050i \(0.531685\pi\)
\(912\) −111.014 58.6448i −0.121726 0.0643036i
\(913\) 480.365i 0.526140i
\(914\) 415.864 + 707.933i 0.454993 + 0.774544i
\(915\) 1681.93 234.238i 1.83818 0.255998i
\(916\) 702.284 + 887.245i 0.766686 + 0.968608i
\(917\) 795.806 + 329.633i 0.867836 + 0.359469i
\(918\) 98.7262 + 608.431i 0.107545 + 0.662779i
\(919\) −1075.46 + 1075.46i −1.17025 + 1.17025i −0.188095 + 0.982151i \(0.560231\pi\)
−0.982151 + 0.188095i \(0.939769\pi\)
\(920\) −290.756 + 749.388i −0.316039 + 0.814552i
\(921\) −415.017 + 243.766i −0.450615 + 0.264675i
\(922\) 510.317 71.0974i 0.553489 0.0771121i
\(923\) −45.2395 + 109.218i −0.0490135 + 0.118329i
\(924\) 11.3182 + 502.137i 0.0122492 + 0.543439i
\(925\) 378.508 + 913.800i 0.409198 + 0.987892i
\(926\) −1162.71 302.184i −1.25563 0.326332i
\(927\) 201.351 + 112.269i 0.217207 + 0.121110i
\(928\) 1024.97 849.650i 1.10450 0.915572i
\(929\) 1287.93i 1.38636i −0.720763 0.693182i \(-0.756208\pi\)
0.720763 0.693182i \(-0.243792\pi\)
\(930\) 800.221 + 446.132i 0.860452 + 0.479712i
\(931\) −58.2607 140.654i −0.0625786 0.151078i
\(932\) 285.380 + 1004.31i 0.306201 + 1.07758i
\(933\) −963.590 728.006i −1.03279 0.780286i
\(934\) 680.370 94.7893i 0.728448 0.101487i
\(935\) −217.047 + 217.047i −0.232136 + 0.232136i
\(936\) −145.486 + 1553.87i −0.155434 + 1.66011i
\(937\) −224.619 + 224.619i −0.239721 + 0.239721i −0.816735 0.577013i \(-0.804218\pi\)
0.577013 + 0.816735i \(0.304218\pi\)
\(938\) −969.530 732.414i −1.03361 0.780826i
\(939\) −227.369 171.780i −0.242139 0.182940i
\(940\) 327.240 259.021i 0.348127 0.275555i
\(941\) −51.2179 123.651i −0.0544292 0.131404i 0.894326 0.447416i \(-0.147656\pi\)
−0.948755 + 0.316013i \(0.897656\pi\)
\(942\) 614.540 174.591i 0.652378 0.185340i
\(943\) 159.149i 0.168769i
\(944\) −470.829 + 76.4736i −0.498759 + 0.0810102i
\(945\) 1285.15 1344.14i 1.35995 1.42237i
\(946\) −120.701 205.471i −0.127591 0.217200i
\(947\) −368.927 890.669i −0.389575 0.940516i −0.990030 0.140858i \(-0.955014\pi\)
0.600455 0.799658i \(-0.294986\pi\)
\(948\) 182.544 470.413i 0.192557 0.496216i
\(949\) 233.810 564.466i 0.246375 0.594801i
\(950\) −60.7050 + 80.3580i −0.0639000 + 0.0845873i
\(951\) 95.3484 56.0042i 0.100261 0.0588898i
\(952\) 945.248 21.3551i 0.992907 0.0224318i
\(953\) 624.029 624.029i 0.654804 0.654804i −0.299342 0.954146i \(-0.596767\pi\)
0.954146 + 0.299342i \(0.0967670\pi\)
\(954\) 455.373 1173.31i 0.477331 1.22988i
\(955\) −1520.82 629.943i −1.59248 0.659626i
\(956\) −1110.35 618.959i −1.16146 0.647447i
\(957\) 499.730 69.5961i 0.522184 0.0727232i
\(958\) −391.681 101.796i −0.408853 0.106259i
\(959\) 1250.49i 1.30395i
\(960\) −1249.38 265.181i −1.30144 0.276230i
\(961\) −434.093 −0.451710
\(962\) −560.257 + 2155.70i −0.582388 + 2.24085i
\(963\) 1636.77 + 190.630i 1.69966 + 0.197954i
\(964\) −212.995 + 382.093i −0.220949 + 0.396362i
\(965\) −431.702 + 1042.22i −0.447360 + 1.08002i
\(966\) 932.047 + 108.504i 0.964852 + 0.112323i
\(967\) −751.783 751.783i −0.777438 0.777438i 0.201956 0.979395i \(-0.435270\pi\)
−0.979395 + 0.201956i \(0.935270\pi\)
\(968\) −837.054 + 18.9108i −0.864726 + 0.0195359i
\(969\) −77.2332 + 45.3640i −0.0797040 + 0.0468152i
\(970\) 129.144 + 97.5598i 0.133138 + 0.100577i
\(971\) −1021.98 423.316i −1.05250 0.435959i −0.211715 0.977331i \(-0.567905\pi\)
−0.840783 + 0.541373i \(0.817905\pi\)
\(972\) −955.708 + 177.215i −0.983239 + 0.182320i
\(973\) 1638.63 678.743i 1.68410 0.697578i
\(974\) −66.4290 + 39.0226i −0.0682022 + 0.0400643i
\(975\) 1211.60 + 314.956i 1.24267 + 0.323032i
\(976\) −795.922 + 1104.61i −0.815494 + 1.13178i
\(977\) −1273.72 −1.30370 −0.651852 0.758346i \(-0.726008\pi\)
−0.651852 + 0.758346i \(0.726008\pi\)
\(978\) −1191.76 + 338.580i −1.21857 + 0.346196i
\(979\) −76.8309 + 31.8244i −0.0784790 + 0.0325071i
\(980\) −961.203 1214.36i −0.980820 1.23914i
\(981\) 1433.08 1134.09i 1.46084 1.15606i
\(982\) −168.596 + 223.178i −0.171686 + 0.227268i
\(983\) −483.972 483.972i −0.492342 0.492342i 0.416702 0.909043i \(-0.363186\pi\)
−0.909043 + 0.416702i \(0.863186\pi\)
\(984\) 249.610 40.5292i 0.253669 0.0411882i
\(985\) 246.755 + 246.755i 0.250512 + 0.250512i
\(986\) −131.060 940.711i −0.132921 0.954068i
\(987\) −388.723 293.685i −0.393842 0.297554i
\(988\) −218.151 + 61.9889i −0.220801 + 0.0627418i
\(989\) −411.310 + 170.370i −0.415884 + 0.172265i
\(990\) −349.877 334.487i −0.353411 0.337865i
\(991\) 439.266 0.443255 0.221628 0.975131i \(-0.428863\pi\)
0.221628 + 0.975131i \(0.428863\pi\)
\(992\) −701.855 + 216.684i −0.707515 + 0.218431i
\(993\) 56.2178 216.263i 0.0566141 0.217788i
\(994\) −28.4081 + 109.306i −0.0285796 + 0.109966i
\(995\) 71.2918 29.5300i 0.0716501 0.0296784i
\(996\) 32.1331 + 1425.60i 0.0322622 + 1.43132i
\(997\) 205.621 + 85.1710i 0.206240 + 0.0854272i 0.483412 0.875393i \(-0.339397\pi\)
−0.277172 + 0.960820i \(0.589397\pi\)
\(998\) 59.4556 + 426.755i 0.0595748 + 0.427611i
\(999\) −1386.85 + 31.1157i −1.38824 + 0.0311469i
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 96.3.p.a.5.13 120
3.2 odd 2 inner 96.3.p.a.5.18 yes 120
4.3 odd 2 384.3.p.a.113.2 120
12.11 even 2 384.3.p.a.113.25 120
32.13 even 8 inner 96.3.p.a.77.18 yes 120
32.19 odd 8 384.3.p.a.17.25 120
96.77 odd 8 inner 96.3.p.a.77.13 yes 120
96.83 even 8 384.3.p.a.17.2 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.3.p.a.5.13 120 1.1 even 1 trivial
96.3.p.a.5.18 yes 120 3.2 odd 2 inner
96.3.p.a.77.13 yes 120 96.77 odd 8 inner
96.3.p.a.77.18 yes 120 32.13 even 8 inner
384.3.p.a.17.2 120 96.83 even 8
384.3.p.a.17.25 120 32.19 odd 8
384.3.p.a.113.2 120 4.3 odd 2
384.3.p.a.113.25 120 12.11 even 2