Properties

Label 475.2.l.f.226.2
Level $475$
Weight $2$
Character 475.226
Analytic conductor $3.793$
Analytic rank $0$
Dimension $48$
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] = [475,2,Mod(101,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 226.2
Character \(\chi\) \(=\) 475.226
Dual form 475.2.l.f.351.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.256855 + 1.45670i) q^{2} +(1.90225 + 1.59617i) q^{3} +(-0.176607 - 0.0642796i) q^{4} +(-2.81374 + 2.36101i) q^{6} +(1.62494 + 2.81448i) q^{7} +(-1.34017 + 2.32124i) q^{8} +(0.549824 + 3.11821i) q^{9} +O(q^{10})\) \(q+(-0.256855 + 1.45670i) q^{2} +(1.90225 + 1.59617i) q^{3} +(-0.176607 - 0.0642796i) q^{4} +(-2.81374 + 2.36101i) q^{6} +(1.62494 + 2.81448i) q^{7} +(-1.34017 + 2.32124i) q^{8} +(0.549824 + 3.11821i) q^{9} +(2.09200 - 3.62344i) q^{11} +(-0.233348 - 0.404171i) q^{12} +(1.36673 - 1.14682i) q^{13} +(-4.51721 + 1.64413i) q^{14} +(-3.32506 - 2.79006i) q^{16} +(1.09959 - 6.23606i) q^{17} -4.68351 q^{18} +(-4.09399 - 1.49640i) q^{19} +(-1.40136 + 7.94751i) q^{21} +(4.74092 + 3.97810i) q^{22} +(-1.34721 - 0.490346i) q^{23} +(-6.25444 + 2.27643i) q^{24} +(1.31952 + 2.28547i) q^{26} +(-0.206494 + 0.357658i) q^{27} +(-0.106062 - 0.601506i) q^{28} +(-0.0589345 - 0.334234i) q^{29} +(1.38932 + 2.40638i) q^{31} +(0.811808 - 0.681187i) q^{32} +(9.76313 - 3.55349i) q^{33} +(8.80161 + 3.20352i) q^{34} +(0.103335 - 0.586040i) q^{36} -2.70482 q^{37} +(3.23137 - 5.57935i) q^{38} +4.43037 q^{39} +(-5.46819 - 4.58835i) q^{41} +(-11.2172 - 4.08271i) q^{42} +(-9.29755 + 3.38403i) q^{43} +(-0.602374 + 0.505452i) q^{44} +(1.06032 - 1.83654i) q^{46} +(-0.0773501 - 0.438674i) q^{47} +(-1.87167 - 10.6148i) q^{48} +(-1.78085 + 3.08452i) q^{49} +(12.0455 - 10.1074i) q^{51} +(-0.315090 + 0.114683i) q^{52} +(6.80087 + 2.47532i) q^{53} +(-0.467960 - 0.392665i) q^{54} -8.71078 q^{56} +(-5.39926 - 9.38125i) q^{57} +0.502015 q^{58} +(0.545712 - 3.09489i) q^{59} +(2.88074 + 1.04850i) q^{61} +(-3.86222 + 1.40573i) q^{62} +(-7.88269 + 6.61436i) q^{63} +(-3.55679 - 6.16055i) q^{64} +(2.66865 + 15.1347i) q^{66} +(1.48513 + 8.42261i) q^{67} +(-0.595046 + 1.03065i) q^{68} +(-1.78006 - 3.08315i) q^{69} +(-12.1153 + 4.40959i) q^{71} +(-7.97498 - 2.90266i) q^{72} +(-1.39594 - 1.17133i) q^{73} +(0.694747 - 3.94011i) q^{74} +(0.626839 + 0.527435i) q^{76} +13.5974 q^{77} +(-1.13796 + 6.45371i) q^{78} +(0.535235 + 0.449116i) q^{79} +(7.96239 - 2.89807i) q^{81} +(8.08837 - 6.78695i) q^{82} +(0.276493 + 0.478899i) q^{83} +(0.758353 - 1.31351i) q^{84} +(-2.54139 - 14.4129i) q^{86} +(0.421388 - 0.729865i) q^{87} +(5.60726 + 9.71206i) q^{88} +(5.23109 - 4.38940i) q^{89} +(5.44854 + 1.98311i) q^{91} +(0.206408 + 0.173197i) q^{92} +(-1.19816 + 6.79513i) q^{93} +0.658883 q^{94} +2.63155 q^{96} +(-2.29226 + 13.0001i) q^{97} +(-4.03579 - 3.38643i) q^{98} +(12.4489 + 4.53102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.256855 + 1.45670i −0.181624 + 1.03004i 0.748593 + 0.663030i \(0.230730\pi\)
−0.930217 + 0.367010i \(0.880381\pi\)
\(3\) 1.90225 + 1.59617i 1.09826 + 0.921552i 0.997307 0.0733394i \(-0.0233656\pi\)
0.100955 + 0.994891i \(0.467810\pi\)
\(4\) −0.176607 0.0642796i −0.0883034 0.0321398i
\(5\) 0 0
\(6\) −2.81374 + 2.36101i −1.14871 + 0.963879i
\(7\) 1.62494 + 2.81448i 0.614169 + 1.06377i 0.990530 + 0.137298i \(0.0438419\pi\)
−0.376361 + 0.926473i \(0.622825\pi\)
\(8\) −1.34017 + 2.32124i −0.473822 + 0.820684i
\(9\) 0.549824 + 3.11821i 0.183275 + 1.03940i
\(10\) 0 0
\(11\) 2.09200 3.62344i 0.630760 1.09251i −0.356636 0.934243i \(-0.616076\pi\)
0.987397 0.158265i \(-0.0505902\pi\)
\(12\) −0.233348 0.404171i −0.0673618 0.116674i
\(13\) 1.36673 1.14682i 0.379062 0.318070i −0.433272 0.901263i \(-0.642641\pi\)
0.812334 + 0.583193i \(0.198197\pi\)
\(14\) −4.51721 + 1.64413i −1.20728 + 0.439412i
\(15\) 0 0
\(16\) −3.32506 2.79006i −0.831266 0.697515i
\(17\) 1.09959 6.23606i 0.266689 1.51247i −0.497495 0.867467i \(-0.665747\pi\)
0.764183 0.644999i \(-0.223142\pi\)
\(18\) −4.68351 −1.10391
\(19\) −4.09399 1.49640i −0.939226 0.343298i
\(20\) 0 0
\(21\) −1.40136 + 7.94751i −0.305802 + 1.73429i
\(22\) 4.74092 + 3.97810i 1.01077 + 0.848134i
\(23\) −1.34721 0.490346i −0.280914 0.102244i 0.197721 0.980258i \(-0.436646\pi\)
−0.478635 + 0.878014i \(0.658868\pi\)
\(24\) −6.25444 + 2.27643i −1.27668 + 0.464675i
\(25\) 0 0
\(26\) 1.31952 + 2.28547i 0.258779 + 0.448218i
\(27\) −0.206494 + 0.357658i −0.0397398 + 0.0688313i
\(28\) −0.106062 0.601506i −0.0200438 0.113674i
\(29\) −0.0589345 0.334234i −0.0109439 0.0620657i 0.978847 0.204595i \(-0.0655877\pi\)
−0.989791 + 0.142529i \(0.954477\pi\)
\(30\) 0 0
\(31\) 1.38932 + 2.40638i 0.249530 + 0.432199i 0.963395 0.268084i \(-0.0863906\pi\)
−0.713866 + 0.700283i \(0.753057\pi\)
\(32\) 0.811808 0.681187i 0.143509 0.120418i
\(33\) 9.76313 3.55349i 1.69954 0.618583i
\(34\) 8.80161 + 3.20352i 1.50946 + 0.549400i
\(35\) 0 0
\(36\) 0.103335 0.586040i 0.0172224 0.0976733i
\(37\) −2.70482 −0.444670 −0.222335 0.974970i \(-0.571368\pi\)
−0.222335 + 0.974970i \(0.571368\pi\)
\(38\) 3.23137 5.57935i 0.524197 0.905090i
\(39\) 4.43037 0.709427
\(40\) 0 0
\(41\) −5.46819 4.58835i −0.853987 0.716581i 0.106677 0.994294i \(-0.465979\pi\)
−0.960664 + 0.277713i \(0.910423\pi\)
\(42\) −11.2172 4.08271i −1.73085 0.629977i
\(43\) −9.29755 + 3.38403i −1.41786 + 0.516060i −0.933427 0.358767i \(-0.883197\pi\)
−0.484436 + 0.874827i \(0.660975\pi\)
\(44\) −0.602374 + 0.505452i −0.0908113 + 0.0761997i
\(45\) 0 0
\(46\) 1.06032 1.83654i 0.156336 0.270782i
\(47\) −0.0773501 0.438674i −0.0112827 0.0639872i 0.978647 0.205550i \(-0.0658984\pi\)
−0.989929 + 0.141563i \(0.954787\pi\)
\(48\) −1.87167 10.6148i −0.270152 1.53211i
\(49\) −1.78085 + 3.08452i −0.254407 + 0.440645i
\(50\) 0 0
\(51\) 12.0455 10.1074i 1.68671 1.41532i
\(52\) −0.315090 + 0.114683i −0.0436952 + 0.0159037i
\(53\) 6.80087 + 2.47532i 0.934172 + 0.340011i 0.763862 0.645380i \(-0.223301\pi\)
0.170310 + 0.985391i \(0.445523\pi\)
\(54\) −0.467960 0.392665i −0.0636813 0.0534350i
\(55\) 0 0
\(56\) −8.71078 −1.16403
\(57\) −5.39926 9.38125i −0.715150 1.24258i
\(58\) 0.502015 0.0659178
\(59\) 0.545712 3.09489i 0.0710457 0.402920i −0.928459 0.371436i \(-0.878866\pi\)
0.999504 0.0314842i \(-0.0100234\pi\)
\(60\) 0 0
\(61\) 2.88074 + 1.04850i 0.368841 + 0.134247i 0.519789 0.854295i \(-0.326010\pi\)
−0.150948 + 0.988542i \(0.548233\pi\)
\(62\) −3.86222 + 1.40573i −0.490503 + 0.178528i
\(63\) −7.88269 + 6.61436i −0.993126 + 0.833331i
\(64\) −3.55679 6.16055i −0.444599 0.770068i
\(65\) 0 0
\(66\) 2.66865 + 15.1347i 0.328488 + 1.86295i
\(67\) 1.48513 + 8.42261i 0.181438 + 1.02899i 0.930447 + 0.366426i \(0.119419\pi\)
−0.749009 + 0.662559i \(0.769470\pi\)
\(68\) −0.595046 + 1.03065i −0.0721599 + 0.124985i
\(69\) −1.78006 3.08315i −0.214294 0.371167i
\(70\) 0 0
\(71\) −12.1153 + 4.40959i −1.43782 + 0.523322i −0.939161 0.343478i \(-0.888395\pi\)
−0.498656 + 0.866800i \(0.666173\pi\)
\(72\) −7.97498 2.90266i −0.939861 0.342081i
\(73\) −1.39594 1.17133i −0.163382 0.137094i 0.557431 0.830223i \(-0.311787\pi\)
−0.720813 + 0.693129i \(0.756232\pi\)
\(74\) 0.694747 3.94011i 0.0807627 0.458028i
\(75\) 0 0
\(76\) 0.626839 + 0.527435i 0.0719034 + 0.0605010i
\(77\) 13.5974 1.54957
\(78\) −1.13796 + 6.45371i −0.128849 + 0.730739i
\(79\) 0.535235 + 0.449116i 0.0602187 + 0.0505295i 0.672400 0.740188i \(-0.265263\pi\)
−0.612182 + 0.790717i \(0.709708\pi\)
\(80\) 0 0
\(81\) 7.96239 2.89807i 0.884710 0.322008i
\(82\) 8.08837 6.78695i 0.893211 0.749493i
\(83\) 0.276493 + 0.478899i 0.0303490 + 0.0525660i 0.880801 0.473487i \(-0.157005\pi\)
−0.850452 + 0.526053i \(0.823671\pi\)
\(84\) 0.758353 1.31351i 0.0827431 0.143315i
\(85\) 0 0
\(86\) −2.54139 14.4129i −0.274045 1.55419i
\(87\) 0.421388 0.729865i 0.0451775 0.0782497i
\(88\) 5.60726 + 9.71206i 0.597736 + 1.03531i
\(89\) 5.23109 4.38940i 0.554494 0.465276i −0.321965 0.946751i \(-0.604343\pi\)
0.876459 + 0.481476i \(0.159899\pi\)
\(90\) 0 0
\(91\) 5.44854 + 1.98311i 0.571162 + 0.207886i
\(92\) 0.206408 + 0.173197i 0.0215195 + 0.0180570i
\(93\) −1.19816 + 6.79513i −0.124244 + 0.704622i
\(94\) 0.658883 0.0679586
\(95\) 0 0
\(96\) 2.63155 0.268582
\(97\) −2.29226 + 13.0001i −0.232744 + 1.31996i 0.614569 + 0.788863i \(0.289330\pi\)
−0.847313 + 0.531094i \(0.821781\pi\)
\(98\) −4.03579 3.38643i −0.407676 0.342081i
\(99\) 12.4489 + 4.53102i 1.25116 + 0.455385i
\(100\) 0 0
\(101\) 13.2339 11.1046i 1.31683 1.10495i 0.329857 0.944031i \(-0.392999\pi\)
0.986968 0.160916i \(-0.0514450\pi\)
\(102\) 11.6294 + 20.1428i 1.15149 + 1.99443i
\(103\) −6.91430 + 11.9759i −0.681286 + 1.18002i 0.293302 + 0.956020i \(0.405246\pi\)
−0.974589 + 0.224003i \(0.928088\pi\)
\(104\) 0.830401 + 4.70944i 0.0814275 + 0.461798i
\(105\) 0 0
\(106\) −5.35262 + 9.27101i −0.519893 + 0.900481i
\(107\) 1.63230 + 2.82722i 0.157800 + 0.273318i 0.934075 0.357077i \(-0.116226\pi\)
−0.776275 + 0.630394i \(0.782893\pi\)
\(108\) 0.0594584 0.0498915i 0.00572138 0.00480081i
\(109\) 3.02669 1.10163i 0.289905 0.105517i −0.192974 0.981204i \(-0.561813\pi\)
0.482879 + 0.875687i \(0.339591\pi\)
\(110\) 0 0
\(111\) −5.14524 4.31737i −0.488364 0.409786i
\(112\) 2.44953 13.8920i 0.231459 1.31267i
\(113\) 4.71007 0.443086 0.221543 0.975151i \(-0.428891\pi\)
0.221543 + 0.975151i \(0.428891\pi\)
\(114\) 15.0525 5.45547i 1.40979 0.510952i
\(115\) 0 0
\(116\) −0.0110762 + 0.0628163i −0.00102840 + 0.00583234i
\(117\) 4.32748 + 3.63119i 0.400076 + 0.335704i
\(118\) 4.36815 + 1.58988i 0.402121 + 0.146360i
\(119\) 19.3380 7.03845i 1.77271 0.645214i
\(120\) 0 0
\(121\) −3.25289 5.63416i −0.295717 0.512197i
\(122\) −2.26729 + 3.92705i −0.205270 + 0.355539i
\(123\) −3.07803 17.4564i −0.277536 1.57399i
\(124\) −0.0906829 0.514288i −0.00814356 0.0461844i
\(125\) 0 0
\(126\) −7.61042 13.1816i −0.677990 1.17431i
\(127\) 0.453507 0.380538i 0.0402423 0.0337673i −0.622445 0.782664i \(-0.713860\pi\)
0.662687 + 0.748897i \(0.269416\pi\)
\(128\) 11.8793 4.32371i 1.04999 0.382165i
\(129\) −23.0877 8.40325i −2.03276 0.739865i
\(130\) 0 0
\(131\) −3.56830 + 20.2369i −0.311764 + 1.76810i 0.278053 + 0.960566i \(0.410311\pi\)
−0.589817 + 0.807537i \(0.700800\pi\)
\(132\) −1.95265 −0.169957
\(133\) −2.44090 13.9540i −0.211653 1.20997i
\(134\) −12.6507 −1.09285
\(135\) 0 0
\(136\) 13.0018 + 10.9098i 1.11489 + 0.935506i
\(137\) −8.22613 2.99407i −0.702806 0.255800i −0.0341973 0.999415i \(-0.510887\pi\)
−0.668608 + 0.743615i \(0.733110\pi\)
\(138\) 4.94843 1.80108i 0.421238 0.153318i
\(139\) 5.89041 4.94264i 0.499618 0.419229i −0.357840 0.933783i \(-0.616487\pi\)
0.857458 + 0.514553i \(0.172042\pi\)
\(140\) 0 0
\(141\) 0.553061 0.957930i 0.0465762 0.0806723i
\(142\) −3.31158 18.7809i −0.277901 1.57606i
\(143\) −1.29625 7.35139i −0.108398 0.614754i
\(144\) 6.87178 11.9023i 0.572649 0.991857i
\(145\) 0 0
\(146\) 2.06483 1.73260i 0.170887 0.143391i
\(147\) −8.31104 + 3.02497i −0.685483 + 0.249495i
\(148\) 0.477690 + 0.173865i 0.0392659 + 0.0142916i
\(149\) −11.4457 9.60412i −0.937672 0.786800i 0.0395067 0.999219i \(-0.487421\pi\)
−0.977179 + 0.212419i \(0.931866\pi\)
\(150\) 0 0
\(151\) 13.1424 1.06951 0.534757 0.845006i \(-0.320403\pi\)
0.534757 + 0.845006i \(0.320403\pi\)
\(152\) 8.96017 7.49772i 0.726765 0.608145i
\(153\) 20.0499 1.62094
\(154\) −3.49257 + 19.8074i −0.281440 + 1.59612i
\(155\) 0 0
\(156\) −0.782434 0.284783i −0.0626449 0.0228009i
\(157\) −10.1836 + 3.70654i −0.812742 + 0.295814i −0.714756 0.699374i \(-0.753462\pi\)
−0.0979861 + 0.995188i \(0.531240\pi\)
\(158\) −0.791704 + 0.664318i −0.0629846 + 0.0528503i
\(159\) 8.98590 + 15.5640i 0.712628 + 1.23431i
\(160\) 0 0
\(161\) −0.809073 4.58848i −0.0637639 0.361623i
\(162\) 2.17644 + 12.3432i 0.170997 + 0.969772i
\(163\) −4.22277 + 7.31405i −0.330753 + 0.572881i −0.982660 0.185418i \(-0.940636\pi\)
0.651907 + 0.758299i \(0.273969\pi\)
\(164\) 0.670782 + 1.16183i 0.0523792 + 0.0907235i
\(165\) 0 0
\(166\) −0.768630 + 0.279758i −0.0596573 + 0.0217135i
\(167\) 18.7011 + 6.80663i 1.44713 + 0.526713i 0.941788 0.336206i \(-0.109144\pi\)
0.505343 + 0.862919i \(0.331366\pi\)
\(168\) −16.5700 13.9039i −1.27841 1.07271i
\(169\) −1.70468 + 9.66772i −0.131129 + 0.743671i
\(170\) 0 0
\(171\) 2.41512 13.5887i 0.184689 1.03915i
\(172\) 1.85954 0.141788
\(173\) 2.03534 11.5430i 0.154744 0.877597i −0.804275 0.594257i \(-0.797446\pi\)
0.959019 0.283340i \(-0.0914426\pi\)
\(174\) 0.954956 + 0.801304i 0.0723951 + 0.0607467i
\(175\) 0 0
\(176\) −17.0656 + 6.21138i −1.28637 + 0.468200i
\(177\) 5.97806 5.01619i 0.449339 0.377040i
\(178\) 5.05040 + 8.74755i 0.378544 + 0.655657i
\(179\) −3.54189 + 6.13473i −0.264733 + 0.458532i −0.967494 0.252895i \(-0.918617\pi\)
0.702760 + 0.711427i \(0.251951\pi\)
\(180\) 0 0
\(181\) 1.61176 + 9.14076i 0.119801 + 0.679427i 0.984260 + 0.176724i \(0.0565500\pi\)
−0.864459 + 0.502703i \(0.832339\pi\)
\(182\) −4.28827 + 7.42750i −0.317868 + 0.550563i
\(183\) 3.80628 + 6.59268i 0.281369 + 0.487345i
\(184\) 2.94371 2.47007i 0.217013 0.182096i
\(185\) 0 0
\(186\) −9.59069 3.49073i −0.703224 0.255952i
\(187\) −20.2957 17.0301i −1.48417 1.24536i
\(188\) −0.0145373 + 0.0824448i −0.00106024 + 0.00601291i
\(189\) −1.34216 −0.0976277
\(190\) 0 0
\(191\) 8.12426 0.587850 0.293925 0.955828i \(-0.405038\pi\)
0.293925 + 0.955828i \(0.405038\pi\)
\(192\) 3.06741 17.3961i 0.221371 1.25546i
\(193\) 5.91649 + 4.96452i 0.425878 + 0.357354i 0.830394 0.557177i \(-0.188115\pi\)
−0.404516 + 0.914531i \(0.632560\pi\)
\(194\) −18.3484 6.67827i −1.31734 0.479472i
\(195\) 0 0
\(196\) 0.512781 0.430275i 0.0366272 0.0307339i
\(197\) −1.78381 3.08965i −0.127091 0.220129i 0.795457 0.606010i \(-0.207231\pi\)
−0.922548 + 0.385881i \(0.873897\pi\)
\(198\) −9.79788 + 16.9704i −0.696305 + 1.20604i
\(199\) −1.52279 8.63615i −0.107947 0.612201i −0.990002 0.141053i \(-0.954951\pi\)
0.882055 0.471147i \(-0.156160\pi\)
\(200\) 0 0
\(201\) −10.6189 + 18.3924i −0.748997 + 1.29730i
\(202\) 12.7768 + 22.1301i 0.898974 + 1.55707i
\(203\) 0.844928 0.708979i 0.0593023 0.0497606i
\(204\) −2.77702 + 1.01075i −0.194430 + 0.0707668i
\(205\) 0 0
\(206\) −15.6693 13.1481i −1.09173 0.916073i
\(207\) 0.788270 4.47050i 0.0547885 0.310721i
\(208\) −7.74414 −0.536960
\(209\) −13.9867 + 11.7039i −0.967483 + 0.809574i
\(210\) 0 0
\(211\) 2.05203 11.6376i 0.141267 0.801167i −0.829021 0.559217i \(-0.811102\pi\)
0.970289 0.241950i \(-0.0777870\pi\)
\(212\) −1.04197 0.874315i −0.0715627 0.0600482i
\(213\) −30.0847 10.9499i −2.06137 0.750277i
\(214\) −4.53767 + 1.65158i −0.310189 + 0.112899i
\(215\) 0 0
\(216\) −0.553474 0.958646i −0.0376592 0.0652276i
\(217\) −4.51513 + 7.82043i −0.306507 + 0.530886i
\(218\) 0.827314 + 4.69193i 0.0560328 + 0.317778i
\(219\) −0.785770 4.45633i −0.0530974 0.301131i
\(220\) 0 0
\(221\) −5.64880 9.78401i −0.379979 0.658144i
\(222\) 7.61067 6.38611i 0.510795 0.428608i
\(223\) −8.36101 + 3.04316i −0.559895 + 0.203785i −0.606437 0.795131i \(-0.707402\pi\)
0.0465426 + 0.998916i \(0.485180\pi\)
\(224\) 3.23632 + 1.17792i 0.216236 + 0.0787034i
\(225\) 0 0
\(226\) −1.20980 + 6.86114i −0.0804750 + 0.456396i
\(227\) −26.4080 −1.75276 −0.876380 0.481620i \(-0.840049\pi\)
−0.876380 + 0.481620i \(0.840049\pi\)
\(228\) 0.350523 + 2.00386i 0.0232140 + 0.132709i
\(229\) 21.7852 1.43961 0.719804 0.694177i \(-0.244232\pi\)
0.719804 + 0.694177i \(0.244232\pi\)
\(230\) 0 0
\(231\) 25.8657 + 21.7039i 1.70184 + 1.42801i
\(232\) 0.854821 + 0.311129i 0.0561217 + 0.0204266i
\(233\) −9.39780 + 3.42052i −0.615670 + 0.224086i −0.630982 0.775797i \(-0.717348\pi\)
0.0153122 + 0.999883i \(0.495126\pi\)
\(234\) −6.40108 + 5.37114i −0.418452 + 0.351123i
\(235\) 0 0
\(236\) −0.295315 + 0.511500i −0.0192234 + 0.0332958i
\(237\) 0.301282 + 1.70866i 0.0195704 + 0.110989i
\(238\) 5.28583 + 29.9774i 0.342630 + 1.94315i
\(239\) −8.91823 + 15.4468i −0.576872 + 0.999172i 0.418963 + 0.908003i \(0.362394\pi\)
−0.995835 + 0.0911689i \(0.970940\pi\)
\(240\) 0 0
\(241\) −13.1332 + 11.0201i −0.845984 + 0.709864i −0.958901 0.283740i \(-0.908425\pi\)
0.112918 + 0.993604i \(0.463980\pi\)
\(242\) 9.04279 3.29131i 0.581293 0.211573i
\(243\) 20.9365 + 7.62027i 1.34308 + 0.488840i
\(244\) −0.441361 0.370346i −0.0282552 0.0237090i
\(245\) 0 0
\(246\) 26.2192 1.67168
\(247\) −7.31147 + 2.64990i −0.465218 + 0.168609i
\(248\) −7.44772 −0.472931
\(249\) −0.238450 + 1.35232i −0.0151111 + 0.0856995i
\(250\) 0 0
\(251\) −9.11112 3.31618i −0.575089 0.209315i 0.0380697 0.999275i \(-0.487879\pi\)
−0.613159 + 0.789960i \(0.710101\pi\)
\(252\) 1.81731 0.661445i 0.114480 0.0416671i
\(253\) −4.59511 + 3.85575i −0.288892 + 0.242409i
\(254\) 0.437843 + 0.758366i 0.0274727 + 0.0475841i
\(255\) 0 0
\(256\) 0.776555 + 4.40406i 0.0485347 + 0.275254i
\(257\) −1.74528 9.89795i −0.108867 0.617417i −0.989605 0.143813i \(-0.954064\pi\)
0.880738 0.473605i \(-0.157047\pi\)
\(258\) 18.1712 31.4734i 1.13129 1.95945i
\(259\) −4.39517 7.61265i −0.273102 0.473027i
\(260\) 0 0
\(261\) 1.00981 0.367540i 0.0625055 0.0227501i
\(262\) −28.5624 10.3959i −1.76459 0.642259i
\(263\) −16.7232 14.0324i −1.03120 0.865276i −0.0402026 0.999192i \(-0.512800\pi\)
−0.990993 + 0.133916i \(0.957245\pi\)
\(264\) −4.83575 + 27.4249i −0.297620 + 1.68789i
\(265\) 0 0
\(266\) 20.9537 + 0.0285081i 1.28475 + 0.00174794i
\(267\) 16.9571 1.03776
\(268\) 0.279117 1.58295i 0.0170498 0.0966943i
\(269\) 11.8393 + 9.93433i 0.721853 + 0.605707i 0.927897 0.372836i \(-0.121615\pi\)
−0.206044 + 0.978543i \(0.566059\pi\)
\(270\) 0 0
\(271\) −4.85182 + 1.76592i −0.294727 + 0.107272i −0.485152 0.874430i \(-0.661236\pi\)
0.190425 + 0.981702i \(0.439013\pi\)
\(272\) −21.0552 + 17.6674i −1.27666 + 1.07124i
\(273\) 7.19908 + 12.4692i 0.435708 + 0.754669i
\(274\) 6.47437 11.2139i 0.391131 0.677459i
\(275\) 0 0
\(276\) 0.116186 + 0.658926i 0.00699360 + 0.0396627i
\(277\) 2.78515 4.82402i 0.167343 0.289847i −0.770142 0.637873i \(-0.779814\pi\)
0.937485 + 0.348026i \(0.113148\pi\)
\(278\) 5.68695 + 9.85009i 0.341081 + 0.590769i
\(279\) −6.73971 + 5.65529i −0.403496 + 0.338573i
\(280\) 0 0
\(281\) −25.6282 9.32789i −1.52885 0.556455i −0.565509 0.824742i \(-0.691320\pi\)
−0.963339 + 0.268287i \(0.913542\pi\)
\(282\) 1.25336 + 1.05169i 0.0746363 + 0.0626273i
\(283\) 2.61267 14.8172i 0.155307 0.880792i −0.803197 0.595714i \(-0.796869\pi\)
0.958504 0.285078i \(-0.0920196\pi\)
\(284\) 2.42308 0.143784
\(285\) 0 0
\(286\) 11.0417 0.652910
\(287\) 4.02834 22.8459i 0.237786 1.34855i
\(288\) 2.57044 + 2.15685i 0.151464 + 0.127094i
\(289\) −21.7045 7.89981i −1.27674 0.464694i
\(290\) 0 0
\(291\) −25.1108 + 21.0705i −1.47202 + 1.23517i
\(292\) 0.171240 + 0.296596i 0.0100210 + 0.0173570i
\(293\) −3.91441 + 6.77995i −0.228682 + 0.396089i −0.957418 0.288706i \(-0.906775\pi\)
0.728736 + 0.684795i \(0.240108\pi\)
\(294\) −2.27173 12.8836i −0.132490 0.751389i
\(295\) 0 0
\(296\) 3.62492 6.27855i 0.210694 0.364933i
\(297\) 0.863969 + 1.49644i 0.0501325 + 0.0868321i
\(298\) 16.9302 14.2061i 0.980740 0.822938i
\(299\) −2.40361 + 0.874843i −0.139004 + 0.0505935i
\(300\) 0 0
\(301\) −24.6322 20.6689i −1.41978 1.19133i
\(302\) −3.37569 + 19.1445i −0.194249 + 1.10164i
\(303\) 42.8990 2.46449
\(304\) 9.43773 + 16.3981i 0.541291 + 0.940496i
\(305\) 0 0
\(306\) −5.14992 + 29.2066i −0.294401 + 1.66963i
\(307\) 12.0381 + 10.1011i 0.687049 + 0.576503i 0.918057 0.396449i \(-0.129758\pi\)
−0.231008 + 0.972952i \(0.574202\pi\)
\(308\) −2.40140 0.874039i −0.136833 0.0498030i
\(309\) −32.2684 + 11.7447i −1.83568 + 0.668134i
\(310\) 0 0
\(311\) −8.99061 15.5722i −0.509810 0.883018i −0.999935 0.0113654i \(-0.996382\pi\)
0.490125 0.871652i \(-0.336951\pi\)
\(312\) −5.93746 + 10.2840i −0.336142 + 0.582216i
\(313\) −3.68143 20.8784i −0.208087 1.18012i −0.892508 0.451031i \(-0.851056\pi\)
0.684422 0.729087i \(-0.260055\pi\)
\(314\) −2.78359 15.7865i −0.157087 0.890884i
\(315\) 0 0
\(316\) −0.0656572 0.113722i −0.00369351 0.00639734i
\(317\) −2.34748 + 1.96977i −0.131848 + 0.110633i −0.706327 0.707886i \(-0.749649\pi\)
0.574479 + 0.818519i \(0.305205\pi\)
\(318\) −24.9802 + 9.09203i −1.40082 + 0.509856i
\(319\) −1.33437 0.485670i −0.0747102 0.0271923i
\(320\) 0 0
\(321\) −1.40771 + 7.98350i −0.0785706 + 0.445596i
\(322\) 6.89184 0.384067
\(323\) −13.8333 + 23.8850i −0.769708 + 1.32899i
\(324\) −1.59250 −0.0884722
\(325\) 0 0
\(326\) −9.56972 8.02995i −0.530018 0.444738i
\(327\) 7.51590 + 2.73556i 0.415630 + 0.151277i
\(328\) 17.9790 6.54382i 0.992724 0.361322i
\(329\) 1.10895 0.930518i 0.0611383 0.0513011i
\(330\) 0 0
\(331\) 12.9754 22.4741i 0.713195 1.23529i −0.250457 0.968128i \(-0.580581\pi\)
0.963652 0.267162i \(-0.0860858\pi\)
\(332\) −0.0180470 0.102350i −0.000990459 0.00561717i
\(333\) −1.48718 8.43420i −0.0814968 0.462191i
\(334\) −14.7187 + 25.4935i −0.805369 + 1.39494i
\(335\) 0 0
\(336\) 26.8336 22.5161i 1.46389 1.22835i
\(337\) 9.45093 3.43986i 0.514825 0.187381i −0.0715252 0.997439i \(-0.522787\pi\)
0.586350 + 0.810058i \(0.300564\pi\)
\(338\) −13.6451 4.96641i −0.742195 0.270137i
\(339\) 8.95971 + 7.51809i 0.486624 + 0.408326i
\(340\) 0 0
\(341\) 11.6258 0.629574
\(342\) 19.1743 + 7.00842i 1.03683 + 0.378972i
\(343\) 11.1741 0.603343
\(344\) 4.60514 26.1171i 0.248293 1.40814i
\(345\) 0 0
\(346\) 16.2918 + 5.92975i 0.875855 + 0.318785i
\(347\) 6.40683 2.33190i 0.343937 0.125183i −0.164276 0.986414i \(-0.552529\pi\)
0.508213 + 0.861232i \(0.330306\pi\)
\(348\) −0.121335 + 0.101812i −0.00650426 + 0.00545772i
\(349\) −15.7983 27.3634i −0.845663 1.46473i −0.885044 0.465507i \(-0.845872\pi\)
0.0393817 0.999224i \(-0.487461\pi\)
\(350\) 0 0
\(351\) 0.127948 + 0.725632i 0.00682938 + 0.0387314i
\(352\) −0.769945 4.36658i −0.0410382 0.232739i
\(353\) −3.15328 + 5.46165i −0.167832 + 0.290694i −0.937658 0.347561i \(-0.887010\pi\)
0.769825 + 0.638255i \(0.220343\pi\)
\(354\) 5.77157 + 9.99666i 0.306756 + 0.531316i
\(355\) 0 0
\(356\) −1.20600 + 0.438946i −0.0639176 + 0.0232641i
\(357\) 48.0202 + 17.4779i 2.54150 + 0.925030i
\(358\) −8.02670 6.73520i −0.424224 0.355966i
\(359\) 0.725269 4.11321i 0.0382782 0.217087i −0.959669 0.281134i \(-0.909290\pi\)
0.997947 + 0.0640469i \(0.0204007\pi\)
\(360\) 0 0
\(361\) 14.5216 + 12.2525i 0.764293 + 0.644870i
\(362\) −13.7293 −0.721596
\(363\) 2.80532 15.9097i 0.147241 0.835045i
\(364\) −0.834776 0.700460i −0.0437542 0.0367141i
\(365\) 0 0
\(366\) −10.5812 + 3.85124i −0.553088 + 0.201308i
\(367\) 12.6941 10.6516i 0.662627 0.556010i −0.248246 0.968697i \(-0.579854\pi\)
0.910873 + 0.412687i \(0.135410\pi\)
\(368\) 3.11148 + 5.38924i 0.162197 + 0.280933i
\(369\) 11.3009 19.5737i 0.588302 1.01897i
\(370\) 0 0
\(371\) 4.08428 + 23.1631i 0.212045 + 1.20257i
\(372\) 0.648392 1.12305i 0.0336176 0.0582274i
\(373\) −18.5002 32.0433i −0.957905 1.65914i −0.727576 0.686028i \(-0.759353\pi\)
−0.230330 0.973113i \(-0.573980\pi\)
\(374\) 30.0207 25.1904i 1.55233 1.30256i
\(375\) 0 0
\(376\) 1.12193 + 0.408350i 0.0578592 + 0.0210590i
\(377\) −0.463853 0.389219i −0.0238897 0.0200458i
\(378\) 0.344740 1.95512i 0.0177315 0.100561i
\(379\) 31.5147 1.61880 0.809400 0.587257i \(-0.199792\pi\)
0.809400 + 0.587257i \(0.199792\pi\)
\(380\) 0 0
\(381\) 1.47009 0.0753148
\(382\) −2.08676 + 11.8346i −0.106768 + 0.605510i
\(383\) 2.37331 + 1.99144i 0.121270 + 0.101758i 0.701406 0.712762i \(-0.252556\pi\)
−0.580136 + 0.814520i \(0.697000\pi\)
\(384\) 29.4987 + 10.7367i 1.50535 + 0.547903i
\(385\) 0 0
\(386\) −8.75148 + 7.34337i −0.445439 + 0.373768i
\(387\) −15.6641 27.1311i −0.796253 1.37915i
\(388\) 1.24047 2.14856i 0.0629753 0.109076i
\(389\) 4.52037 + 25.6363i 0.229192 + 1.29981i 0.854507 + 0.519439i \(0.173859\pi\)
−0.625316 + 0.780372i \(0.715030\pi\)
\(390\) 0 0
\(391\) −4.53920 + 7.86213i −0.229557 + 0.397605i
\(392\) −4.77328 8.26756i −0.241087 0.417575i
\(393\) −39.0893 + 32.7999i −1.97180 + 1.65453i
\(394\) 4.95887 1.80488i 0.249824 0.0909285i
\(395\) 0 0
\(396\) −1.90730 1.60042i −0.0958457 0.0804241i
\(397\) −2.19851 + 12.4684i −0.110340 + 0.625770i 0.878612 + 0.477536i \(0.158470\pi\)
−0.988952 + 0.148234i \(0.952641\pi\)
\(398\) 12.9714 0.650197
\(399\) 17.6298 30.4400i 0.882595 1.52391i
\(400\) 0 0
\(401\) −1.60135 + 9.08170i −0.0799675 + 0.453518i 0.918362 + 0.395741i \(0.129512\pi\)
−0.998330 + 0.0577770i \(0.981599\pi\)
\(402\) −24.0647 20.1926i −1.20024 1.00712i
\(403\) 4.65851 + 1.69556i 0.232057 + 0.0844618i
\(404\) −3.05100 + 1.11047i −0.151793 + 0.0552481i
\(405\) 0 0
\(406\) 0.815744 + 1.41291i 0.0404847 + 0.0701215i
\(407\) −5.65847 + 9.80076i −0.280480 + 0.485806i
\(408\) 7.31866 + 41.5062i 0.362328 + 2.05486i
\(409\) 5.98343 + 33.9337i 0.295861 + 1.67791i 0.663680 + 0.748016i \(0.268993\pi\)
−0.367819 + 0.929897i \(0.619895\pi\)
\(410\) 0 0
\(411\) −10.8691 18.8258i −0.536132 0.928607i
\(412\) 1.99092 1.67058i 0.0980856 0.0823036i
\(413\) 9.59724 3.49311i 0.472249 0.171885i
\(414\) 6.30969 + 2.29654i 0.310104 + 0.112869i
\(415\) 0 0
\(416\) 0.328320 1.86199i 0.0160972 0.0912917i
\(417\) 19.0943 0.935053
\(418\) −13.4564 23.3806i −0.658176 1.14358i
\(419\) −7.86047 −0.384009 −0.192005 0.981394i \(-0.561499\pi\)
−0.192005 + 0.981394i \(0.561499\pi\)
\(420\) 0 0
\(421\) 8.03752 + 6.74428i 0.391725 + 0.328696i 0.817285 0.576234i \(-0.195478\pi\)
−0.425560 + 0.904930i \(0.639923\pi\)
\(422\) 16.4254 + 5.97836i 0.799577 + 0.291022i
\(423\) 1.32535 0.482387i 0.0644406 0.0234545i
\(424\) −14.8601 + 12.4691i −0.721672 + 0.605555i
\(425\) 0 0
\(426\) 23.6781 41.0117i 1.14721 1.98702i
\(427\) 1.73004 + 9.81153i 0.0837223 + 0.474813i
\(428\) −0.106542 0.604230i −0.00514991 0.0292066i
\(429\) 9.26832 16.0532i 0.447479 0.775056i
\(430\) 0 0
\(431\) 22.8988 19.2144i 1.10300 0.925525i 0.105375 0.994433i \(-0.466396\pi\)
0.997623 + 0.0689073i \(0.0219513\pi\)
\(432\) 1.68449 0.613105i 0.0810452 0.0294980i
\(433\) 6.38969 + 2.32566i 0.307069 + 0.111764i 0.490959 0.871183i \(-0.336647\pi\)
−0.183890 + 0.982947i \(0.558869\pi\)
\(434\) −10.2323 8.58589i −0.491165 0.412136i
\(435\) 0 0
\(436\) −0.605347 −0.0289908
\(437\) 4.78173 + 4.02345i 0.228741 + 0.192468i
\(438\) 6.69335 0.319820
\(439\) 1.38329 7.84504i 0.0660209 0.374423i −0.933839 0.357693i \(-0.883563\pi\)
0.999860 0.0167300i \(-0.00532558\pi\)
\(440\) 0 0
\(441\) −10.5973 3.85711i −0.504634 0.183672i
\(442\) 15.7033 5.71552i 0.746928 0.271859i
\(443\) 16.6916 14.0059i 0.793041 0.665440i −0.153455 0.988156i \(-0.549040\pi\)
0.946496 + 0.322715i \(0.104596\pi\)
\(444\) 0.631165 + 1.09321i 0.0299538 + 0.0518815i
\(445\) 0 0
\(446\) −2.28539 12.9611i −0.108217 0.613726i
\(447\) −6.44278 36.5388i −0.304733 1.72823i
\(448\) 11.5591 20.0210i 0.546118 0.945904i
\(449\) −9.39185 16.2672i −0.443229 0.767695i 0.554698 0.832052i \(-0.312834\pi\)
−0.997927 + 0.0643569i \(0.979500\pi\)
\(450\) 0 0
\(451\) −28.0651 + 10.2148i −1.32153 + 0.480998i
\(452\) −0.831830 0.302761i −0.0391260 0.0142407i
\(453\) 25.0001 + 20.9776i 1.17461 + 0.985612i
\(454\) 6.78303 38.4685i 0.318343 1.80541i
\(455\) 0 0
\(456\) 29.0121 + 0.0394717i 1.35862 + 0.00184843i
\(457\) −28.2368 −1.32086 −0.660431 0.750887i \(-0.729627\pi\)
−0.660431 + 0.750887i \(0.729627\pi\)
\(458\) −5.59564 + 31.7345i −0.261467 + 1.48285i
\(459\) 2.00332 + 1.68098i 0.0935069 + 0.0784616i
\(460\) 0 0
\(461\) 0.184187 0.0670386i 0.00857845 0.00312230i −0.337727 0.941244i \(-0.609658\pi\)
0.346306 + 0.938122i \(0.387436\pi\)
\(462\) −38.2597 + 32.1037i −1.78000 + 1.49360i
\(463\) 6.98206 + 12.0933i 0.324484 + 0.562022i 0.981408 0.191935i \(-0.0614761\pi\)
−0.656924 + 0.753957i \(0.728143\pi\)
\(464\) −0.736571 + 1.27578i −0.0341945 + 0.0592266i
\(465\) 0 0
\(466\) −2.56879 14.5683i −0.118997 0.674865i
\(467\) −16.0512 + 27.8016i −0.742763 + 1.28650i 0.208470 + 0.978029i \(0.433152\pi\)
−0.951233 + 0.308474i \(0.900182\pi\)
\(468\) −0.530851 0.919462i −0.0245386 0.0425021i
\(469\) −21.2920 + 17.8661i −0.983172 + 0.824979i
\(470\) 0 0
\(471\) −25.2881 9.20410i −1.16521 0.424102i
\(472\) 6.45264 + 5.41441i 0.297007 + 0.249218i
\(473\) −7.18859 + 40.7685i −0.330532 + 1.87454i
\(474\) −2.56638 −0.117878
\(475\) 0 0
\(476\) −3.86765 −0.177273
\(477\) −3.97926 + 22.5675i −0.182198 + 1.03330i
\(478\) −20.2107 16.9588i −0.924414 0.775675i
\(479\) 1.86271 + 0.677972i 0.0851095 + 0.0309773i 0.384224 0.923240i \(-0.374469\pi\)
−0.299114 + 0.954217i \(0.596691\pi\)
\(480\) 0 0
\(481\) −3.69675 + 3.10194i −0.168557 + 0.141436i
\(482\) −12.6796 21.9616i −0.577538 1.00033i
\(483\) 5.78496 10.0198i 0.263225 0.455919i
\(484\) 0.212320 + 1.20413i 0.00965091 + 0.0547330i
\(485\) 0 0
\(486\) −16.4781 + 28.5409i −0.747460 + 1.29464i
\(487\) 4.29458 + 7.43843i 0.194606 + 0.337068i 0.946771 0.321907i \(-0.104324\pi\)
−0.752165 + 0.658975i \(0.770990\pi\)
\(488\) −6.29452 + 5.28173i −0.284939 + 0.239093i
\(489\) −19.7072 + 7.17285i −0.891192 + 0.324367i
\(490\) 0 0
\(491\) 19.8407 + 16.6483i 0.895398 + 0.751328i 0.969285 0.245938i \(-0.0790961\pi\)
−0.0738874 + 0.997267i \(0.523541\pi\)
\(492\) −0.578488 + 3.28077i −0.0260802 + 0.147908i
\(493\) −2.14910 −0.0967908
\(494\) −1.98211 11.3312i −0.0891794 0.509817i
\(495\) 0 0
\(496\) 2.09435 11.8777i 0.0940391 0.533322i
\(497\) −32.0972 26.9328i −1.43976 1.20810i
\(498\) −1.90867 0.694698i −0.0855294 0.0311302i
\(499\) 19.9251 7.25214i 0.891970 0.324650i 0.144939 0.989441i \(-0.453701\pi\)
0.747030 + 0.664790i \(0.231479\pi\)
\(500\) 0 0
\(501\) 24.7094 + 42.7980i 1.10394 + 1.91207i
\(502\) 7.17090 12.4204i 0.320053 0.554348i
\(503\) −4.43084 25.1285i −0.197561 1.12043i −0.908724 0.417398i \(-0.862942\pi\)
0.711162 0.703028i \(-0.248169\pi\)
\(504\) −4.78940 27.1620i −0.213337 1.20989i
\(505\) 0 0
\(506\) −4.43639 7.68405i −0.197221 0.341597i
\(507\) −18.6741 + 15.6694i −0.829346 + 0.695904i
\(508\) −0.104553 + 0.0380543i −0.00463880 + 0.00168839i
\(509\) 16.0130 + 5.82825i 0.709763 + 0.258333i 0.671574 0.740938i \(-0.265619\pi\)
0.0381894 + 0.999271i \(0.487841\pi\)
\(510\) 0 0
\(511\) 1.02837 5.83218i 0.0454924 0.258000i
\(512\) 18.6685 0.825039
\(513\) 1.38059 1.15525i 0.0609543 0.0510056i
\(514\) 14.8666 0.655738
\(515\) 0 0
\(516\) 3.53729 + 2.96814i 0.155721 + 0.130665i
\(517\) −1.75133 0.637430i −0.0770232 0.0280342i
\(518\) 12.2183 4.44708i 0.536839 0.195393i
\(519\) 22.2963 18.7088i 0.978700 0.821227i
\(520\) 0 0
\(521\) −10.8909 + 18.8635i −0.477137 + 0.826426i −0.999657 0.0262016i \(-0.991659\pi\)
0.522520 + 0.852627i \(0.324992\pi\)
\(522\) 0.276020 + 1.56539i 0.0120811 + 0.0685152i
\(523\) 3.03633 + 17.2199i 0.132769 + 0.752973i 0.976387 + 0.216028i \(0.0693104\pi\)
−0.843618 + 0.536944i \(0.819578\pi\)
\(524\) 1.93100 3.34460i 0.0843563 0.146109i
\(525\) 0 0
\(526\) 24.7364 20.7563i 1.07856 0.905018i
\(527\) 16.5340 6.01788i 0.720232 0.262143i
\(528\) −42.3775 15.4241i −1.84424 0.671249i
\(529\) −16.0445 13.4629i −0.697586 0.585344i
\(530\) 0 0
\(531\) 9.95056 0.431817
\(532\) −0.465879 + 2.62127i −0.0201984 + 0.113647i
\(533\) −12.7355 −0.551637
\(534\) −4.35551 + 24.7013i −0.188481 + 1.06893i
\(535\) 0 0
\(536\) −21.5413 7.84038i −0.930441 0.338653i
\(537\) −16.5297 + 6.01630i −0.713307 + 0.259623i
\(538\) −17.5123 + 14.6945i −0.755008 + 0.633527i
\(539\) 7.45104 + 12.9056i 0.320939 + 0.555883i
\(540\) 0 0
\(541\) 2.57157 + 14.5841i 0.110560 + 0.627018i 0.988853 + 0.148895i \(0.0475717\pi\)
−0.878293 + 0.478123i \(0.841317\pi\)
\(542\) −1.32619 7.52121i −0.0569648 0.323064i
\(543\) −11.5243 + 19.9606i −0.494554 + 0.856592i
\(544\) −3.35527 5.81150i −0.143856 0.249166i
\(545\) 0 0
\(546\) −20.0129 + 7.28411i −0.856474 + 0.311731i
\(547\) −24.9709 9.08867i −1.06768 0.388603i −0.252371 0.967631i \(-0.581210\pi\)
−0.815308 + 0.579027i \(0.803433\pi\)
\(548\) 1.26033 + 1.05754i 0.0538388 + 0.0451761i
\(549\) −1.68555 + 9.55924i −0.0719376 + 0.407979i
\(550\) 0 0
\(551\) −0.258871 + 1.45654i −0.0110283 + 0.0620507i
\(552\) 9.54231 0.406148
\(553\) −0.394301 + 2.23619i −0.0167674 + 0.0950926i
\(554\) 6.31176 + 5.29619i 0.268161 + 0.225014i
\(555\) 0 0
\(556\) −1.35800 + 0.494271i −0.0575919 + 0.0209618i
\(557\) 12.3143 10.3330i 0.521775 0.437821i −0.343475 0.939162i \(-0.611604\pi\)
0.865250 + 0.501340i \(0.167160\pi\)
\(558\) −6.50691 11.2703i −0.275460 0.477110i
\(559\) −8.82633 + 15.2877i −0.373314 + 0.646599i
\(560\) 0 0
\(561\) −11.4244 64.7908i −0.482337 2.73547i
\(562\) 20.1706 34.9365i 0.850847 1.47371i
\(563\) −1.01573 1.75929i −0.0428078 0.0741452i 0.843828 0.536614i \(-0.180297\pi\)
−0.886635 + 0.462469i \(0.846964\pi\)
\(564\) −0.159250 + 0.133626i −0.00670562 + 0.00562669i
\(565\) 0 0
\(566\) 20.9131 + 7.61175i 0.879044 + 0.319946i
\(567\) 21.0950 + 17.7008i 0.885905 + 0.743362i
\(568\) 6.00077 34.0321i 0.251787 1.42795i
\(569\) −12.8224 −0.537543 −0.268772 0.963204i \(-0.586618\pi\)
−0.268772 + 0.963204i \(0.586618\pi\)
\(570\) 0 0
\(571\) 12.9168 0.540551 0.270276 0.962783i \(-0.412885\pi\)
0.270276 + 0.962783i \(0.412885\pi\)
\(572\) −0.243618 + 1.38163i −0.0101862 + 0.0577688i
\(573\) 15.4543 + 12.9677i 0.645614 + 0.541735i
\(574\) 32.2448 + 11.7362i 1.34587 + 0.489858i
\(575\) 0 0
\(576\) 17.2543 14.4780i 0.718928 0.603252i
\(577\) −4.05680 7.02658i −0.168887 0.292520i 0.769142 0.639078i \(-0.220684\pi\)
−0.938029 + 0.346558i \(0.887351\pi\)
\(578\) 17.0825 29.5878i 0.710540 1.23069i
\(579\) 3.33037 + 18.8875i 0.138406 + 0.784937i
\(580\) 0 0
\(581\) −0.898567 + 1.55636i −0.0372788 + 0.0645689i
\(582\) −24.2435 41.9909i −1.00492 1.74058i
\(583\) 23.1966 19.4642i 0.960703 0.806126i
\(584\) 4.58975 1.67053i 0.189925 0.0691271i
\(585\) 0 0
\(586\) −8.87090 7.44357i −0.366454 0.307491i
\(587\) −5.65427 + 32.0670i −0.233377 + 1.32355i 0.612629 + 0.790371i \(0.290112\pi\)
−0.846005 + 0.533174i \(0.820999\pi\)
\(588\) 1.66223 0.0685492
\(589\) −2.08697 11.9307i −0.0859921 0.491595i
\(590\) 0 0
\(591\) 1.53837 8.72455i 0.0632802 0.358880i
\(592\) 8.99370 + 7.54661i 0.369639 + 0.310164i
\(593\) 10.7832 + 3.92476i 0.442812 + 0.161171i 0.553797 0.832652i \(-0.313178\pi\)
−0.110985 + 0.993822i \(0.535401\pi\)
\(594\) −2.40177 + 0.874173i −0.0985459 + 0.0358678i
\(595\) 0 0
\(596\) 1.40405 + 2.43188i 0.0575120 + 0.0996138i
\(597\) 10.8881 18.8587i 0.445620 0.771836i
\(598\) −0.657002 3.72604i −0.0268668 0.152369i
\(599\) 5.76684 + 32.7054i 0.235627 + 1.33631i 0.841290 + 0.540584i \(0.181797\pi\)
−0.605663 + 0.795721i \(0.707092\pi\)
\(600\) 0 0
\(601\) −13.6590 23.6581i −0.557163 0.965034i −0.997732 0.0673154i \(-0.978557\pi\)
0.440569 0.897719i \(-0.354777\pi\)
\(602\) 36.4352 30.5728i 1.48499 1.24605i
\(603\) −25.4469 + 9.26191i −1.03628 + 0.377174i
\(604\) −2.32104 0.844789i −0.0944417 0.0343740i
\(605\) 0 0
\(606\) −11.0188 + 62.4909i −0.447609 + 2.53852i
\(607\) 25.7405 1.04478 0.522388 0.852708i \(-0.325041\pi\)
0.522388 + 0.852708i \(0.325041\pi\)
\(608\) −4.34286 + 1.57399i −0.176126 + 0.0638335i
\(609\) 2.73892 0.110986
\(610\) 0 0
\(611\) −0.608796 0.510841i −0.0246293 0.0206664i
\(612\) −3.54095 1.28880i −0.143134 0.0520967i
\(613\) −38.1551 + 13.8873i −1.54107 + 0.560904i −0.966302 0.257411i \(-0.917131\pi\)
−0.574770 + 0.818315i \(0.694908\pi\)
\(614\) −17.8063 + 14.9413i −0.718606 + 0.602982i
\(615\) 0 0
\(616\) −18.2229 + 31.5630i −0.734222 + 1.27171i
\(617\) 2.46776 + 13.9954i 0.0993485 + 0.563433i 0.993328 + 0.115325i \(0.0367910\pi\)
−0.893979 + 0.448108i \(0.852098\pi\)
\(618\) −8.82021 50.0219i −0.354801 2.01218i
\(619\) 14.7818 25.6028i 0.594129 1.02906i −0.399540 0.916716i \(-0.630830\pi\)
0.993669 0.112346i \(-0.0358364\pi\)
\(620\) 0 0
\(621\) 0.453568 0.380589i 0.0182010 0.0152725i
\(622\) 24.9932 9.09680i 1.00214 0.364748i
\(623\) 20.8541 + 7.59026i 0.835500 + 0.304097i
\(624\) −14.7313 12.3610i −0.589723 0.494836i
\(625\) 0 0
\(626\) 31.3591 1.25336
\(627\) −45.2877 0.0616150i −1.80861 0.00246067i
\(628\) 2.03675 0.0812753
\(629\) −2.97418 + 16.8674i −0.118588 + 0.672548i
\(630\) 0 0
\(631\) 1.60465 + 0.584045i 0.0638801 + 0.0232505i 0.373763 0.927524i \(-0.378067\pi\)
−0.309882 + 0.950775i \(0.600290\pi\)
\(632\) −1.75981 + 0.640520i −0.0700017 + 0.0254785i
\(633\) 22.4791 18.8622i 0.893465 0.749706i
\(634\) −2.26640 3.92552i −0.0900102 0.155902i
\(635\) 0 0
\(636\) −0.586521 3.32633i −0.0232571 0.131897i
\(637\) 1.10345 + 6.25800i 0.0437204 + 0.247951i
\(638\) 1.05021 1.81902i 0.0415783 0.0720158i
\(639\) −20.4113 35.3534i −0.807459 1.39856i
\(640\) 0 0
\(641\) −2.59543 + 0.944659i −0.102513 + 0.0373118i −0.392768 0.919638i \(-0.628482\pi\)
0.290254 + 0.956950i \(0.406260\pi\)
\(642\) −11.2680 4.10121i −0.444711 0.161862i
\(643\) 16.6209 + 13.9466i 0.655465 + 0.550000i 0.908724 0.417398i \(-0.137058\pi\)
−0.253259 + 0.967398i \(0.581503\pi\)
\(644\) −0.152058 + 0.862364i −0.00599193 + 0.0339819i
\(645\) 0 0
\(646\) −31.2400 26.2860i −1.22912 1.03421i
\(647\) −28.0268 −1.10185 −0.550923 0.834556i \(-0.685724\pi\)
−0.550923 + 0.834556i \(0.685724\pi\)
\(648\) −3.94383 + 22.3666i −0.154928 + 0.878642i
\(649\) −10.0725 8.45185i −0.395381 0.331764i
\(650\) 0 0
\(651\) −21.0717 + 7.66946i −0.825864 + 0.300590i
\(652\) 1.21591 1.02027i 0.0476189 0.0399570i
\(653\) −3.79654 6.57580i −0.148570 0.257331i 0.782129 0.623116i \(-0.214134\pi\)
−0.930699 + 0.365785i \(0.880800\pi\)
\(654\) −5.91538 + 10.2457i −0.231310 + 0.400640i
\(655\) 0 0
\(656\) 5.38029 + 30.5131i 0.210065 + 1.19134i
\(657\) 2.88494 4.99686i 0.112552 0.194946i
\(658\) 1.07064 + 1.85441i 0.0417380 + 0.0722924i
\(659\) 5.50322 4.61775i 0.214375 0.179882i −0.529277 0.848449i \(-0.677537\pi\)
0.743652 + 0.668567i \(0.233092\pi\)
\(660\) 0 0
\(661\) 27.1268 + 9.87335i 1.05511 + 0.384029i 0.810589 0.585615i \(-0.199147\pi\)
0.244521 + 0.969644i \(0.421369\pi\)
\(662\) 29.4052 + 24.6739i 1.14287 + 0.958978i
\(663\) 4.87157 27.6281i 0.189196 1.07298i
\(664\) −1.48219 −0.0575201
\(665\) 0 0
\(666\) 12.6681 0.490877
\(667\) −0.0844929 + 0.479183i −0.00327158 + 0.0185540i
\(668\) −2.86521 2.40419i −0.110858 0.0930210i
\(669\) −20.7621 7.55679i −0.802710 0.292162i
\(670\) 0 0
\(671\) 9.82569 8.24473i 0.379316 0.318284i
\(672\) 4.27611 + 7.40644i 0.164954 + 0.285709i
\(673\) 11.6595 20.1949i 0.449442 0.778457i −0.548907 0.835883i \(-0.684956\pi\)
0.998350 + 0.0574263i \(0.0182894\pi\)
\(674\) 2.58331 + 14.6507i 0.0995054 + 0.564323i
\(675\) 0 0
\(676\) 0.922496 1.59781i 0.0354806 0.0614542i
\(677\) −8.75493 15.1640i −0.336479 0.582799i 0.647289 0.762245i \(-0.275903\pi\)
−0.983768 + 0.179446i \(0.942570\pi\)
\(678\) −13.2529 + 11.1205i −0.508975 + 0.427081i
\(679\) −40.3132 + 14.6728i −1.54708 + 0.563090i
\(680\) 0 0
\(681\) −50.2345 42.1518i −1.92499 1.61526i
\(682\) −2.98615 + 16.9353i −0.114346 + 0.648487i
\(683\) −22.0114 −0.842243 −0.421122 0.907004i \(-0.638363\pi\)
−0.421122 + 0.907004i \(0.638363\pi\)
\(684\) −1.30000 + 2.24461i −0.0497068 + 0.0858249i
\(685\) 0 0
\(686\) −2.87012 + 16.2772i −0.109582 + 0.621468i
\(687\) 41.4409 + 34.7730i 1.58107 + 1.32667i
\(688\) 40.3566 + 14.6886i 1.53858 + 0.559997i
\(689\) 12.1337 4.41629i 0.462256 0.168247i
\(690\) 0 0
\(691\) 1.32811 + 2.30036i 0.0505238 + 0.0875098i 0.890181 0.455607i \(-0.150578\pi\)
−0.839657 + 0.543116i \(0.817244\pi\)
\(692\) −1.10143 + 1.90774i −0.0418702 + 0.0725214i
\(693\) 7.47621 + 42.3997i 0.283998 + 1.61063i
\(694\) 1.75124 + 9.93178i 0.0664762 + 0.377005i
\(695\) 0 0
\(696\) 1.12946 + 1.95629i 0.0428122 + 0.0741529i
\(697\) −34.6260 + 29.0546i −1.31155 + 1.10052i
\(698\) 43.9181 15.9849i 1.66232 0.605037i
\(699\) −23.3367 8.49385i −0.882674 0.321267i
\(700\) 0 0
\(701\) −1.27931 + 7.25535i −0.0483190 + 0.274031i −0.999389 0.0349439i \(-0.988875\pi\)
0.951070 + 0.308975i \(0.0999859\pi\)
\(702\) −1.08989 −0.0411352
\(703\) 11.0735 + 4.04750i 0.417646 + 0.152654i
\(704\) −29.7632 −1.12174
\(705\) 0 0
\(706\) −7.14603 5.99623i −0.268944 0.225671i
\(707\) 52.7579 + 19.2023i 1.98416 + 0.722177i
\(708\) −1.37821 + 0.501626i −0.0517961 + 0.0188522i
\(709\) −4.58997 + 3.85144i −0.172380 + 0.144644i −0.724896 0.688858i \(-0.758112\pi\)
0.552516 + 0.833502i \(0.313668\pi\)
\(710\) 0 0
\(711\) −1.10615 + 1.91591i −0.0414839 + 0.0718523i
\(712\) 3.17833 + 18.0252i 0.119113 + 0.675522i
\(713\) −0.691759 3.92316i −0.0259066 0.146923i
\(714\) −37.7943 + 65.4616i −1.41441 + 2.44984i
\(715\) 0 0
\(716\) 1.01986 0.855765i 0.0381140 0.0319814i
\(717\) −41.6205 + 15.1486i −1.55435 + 0.565736i
\(718\) 5.80541 + 2.11300i 0.216656 + 0.0788563i
\(719\) 10.4040 + 8.73002i 0.388005 + 0.325575i 0.815835 0.578284i \(-0.196278\pi\)
−0.427831 + 0.903859i \(0.640722\pi\)
\(720\) 0 0
\(721\) −44.9412 −1.67370
\(722\) −21.5782 + 18.0064i −0.803056 + 0.670128i
\(723\) −42.5725 −1.58329
\(724\) 0.302916 1.71792i 0.0112578 0.0638461i
\(725\) 0 0
\(726\) 22.4551 + 8.17299i 0.833387 + 0.303328i
\(727\) 38.7574 14.1065i 1.43743 0.523183i 0.498381 0.866958i \(-0.333928\pi\)
0.939052 + 0.343776i \(0.111706\pi\)
\(728\) −11.9052 + 9.98969i −0.441238 + 0.370242i
\(729\) 14.9530 + 25.8994i 0.553816 + 0.959237i
\(730\) 0 0
\(731\) 10.8796 + 61.7011i 0.402395 + 2.28210i
\(732\) −0.248441 1.40898i −0.00918264 0.0520773i
\(733\) 0.0619240 0.107256i 0.00228722 0.00396158i −0.864880 0.501979i \(-0.832605\pi\)
0.867167 + 0.498018i \(0.165939\pi\)
\(734\) 12.2556 + 21.2274i 0.452364 + 0.783517i
\(735\) 0 0
\(736\) −1.42770 + 0.519639i −0.0526256 + 0.0191541i
\(737\) 33.6257 + 12.2388i 1.23862 + 0.450821i
\(738\) 25.6103 + 21.4896i 0.942729 + 0.791043i
\(739\) −6.34049 + 35.9587i −0.233239 + 1.32276i 0.613053 + 0.790042i \(0.289941\pi\)
−0.846291 + 0.532720i \(0.821170\pi\)
\(740\) 0 0
\(741\) −18.1379 6.62962i −0.666313 0.243545i
\(742\) −34.7907 −1.27721
\(743\) 1.57359 8.92430i 0.0577296 0.327401i −0.942242 0.334933i \(-0.891286\pi\)
0.999972 + 0.00753195i \(0.00239752\pi\)
\(744\) −14.1674 11.8879i −0.519402 0.435830i
\(745\) 0 0
\(746\) 51.4293 18.7187i 1.88296 0.685341i
\(747\) −1.34129 + 1.12547i −0.0490751 + 0.0411789i
\(748\) 2.48967 + 4.31223i 0.0910312 + 0.157671i
\(749\) −5.30476 + 9.18812i −0.193832 + 0.335727i
\(750\) 0 0
\(751\) −0.709544 4.02402i −0.0258916 0.146839i 0.969121 0.246584i \(-0.0793082\pi\)
−0.995013 + 0.0997456i \(0.968197\pi\)
\(752\) −0.966732 + 1.67443i −0.0352531 + 0.0610602i
\(753\) −12.0384 20.8511i −0.438704 0.759857i
\(754\) 0.686117 0.575721i 0.0249869 0.0209665i
\(755\) 0 0
\(756\) 0.237035 + 0.0862735i 0.00862086 + 0.00313774i
\(757\) −26.3977 22.1503i −0.959441 0.805066i 0.0214214 0.999771i \(-0.493181\pi\)
−0.980862 + 0.194704i \(0.937625\pi\)
\(758\) −8.09470 + 45.9073i −0.294013 + 1.66743i
\(759\) −14.8955 −0.540671
\(760\) 0 0
\(761\) 20.5813 0.746072 0.373036 0.927817i \(-0.378317\pi\)
0.373036 + 0.927817i \(0.378317\pi\)
\(762\) −0.377599 + 2.14147i −0.0136790 + 0.0775773i
\(763\) 8.01868 + 6.72848i 0.290296 + 0.243587i
\(764\) −1.43480 0.522224i −0.0519092 0.0188934i
\(765\) 0 0
\(766\) −3.51052 + 2.94568i −0.126840 + 0.106432i
\(767\) −2.80344 4.85570i −0.101226 0.175329i
\(768\) −5.55245 + 9.61713i −0.200357 + 0.347028i
\(769\) −5.27109 29.8939i −0.190081 1.07800i −0.919252 0.393669i \(-0.871206\pi\)
0.729172 0.684331i \(-0.239906\pi\)
\(770\) 0 0
\(771\) 12.4789 21.6141i 0.449417 0.778413i
\(772\) −0.725774 1.25708i −0.0261212 0.0452432i
\(773\) 14.9551 12.5488i 0.537898 0.451350i −0.332921 0.942955i \(-0.608034\pi\)
0.870818 + 0.491605i \(0.163590\pi\)
\(774\) 43.5452 15.8491i 1.56520 0.569686i
\(775\) 0 0
\(776\) −27.1043 22.7432i −0.972988 0.816434i
\(777\) 3.79043 21.4966i 0.135981 0.771186i
\(778\) −38.5054 −1.38048
\(779\) 15.5207 + 26.9673i 0.556087 + 0.966204i
\(780\) 0 0
\(781\) −9.36716 + 53.1238i −0.335183 + 1.90092i
\(782\) −10.2868 8.63167i −0.367856 0.308668i
\(783\) 0.131711 + 0.0479389i 0.00470697 + 0.00171320i
\(784\) 14.5274 5.28754i 0.518836 0.188841i
\(785\) 0 0
\(786\) −37.7392 65.3661i −1.34611 2.33153i
\(787\) 17.6118 30.5046i 0.627793 1.08737i −0.360200 0.932875i \(-0.617292\pi\)
0.987994 0.154495i \(-0.0493750\pi\)
\(788\) 0.116432 + 0.660316i 0.00414770 + 0.0235228i
\(789\) −9.41343 53.3862i −0.335127 1.90060i
\(790\) 0 0
\(791\) 7.65357 + 13.2564i 0.272129 + 0.471342i
\(792\) −27.2012 + 22.8245i −0.966554 + 0.811035i
\(793\) 5.13963 1.87067i 0.182514 0.0664295i
\(794\) −17.5979 6.40513i −0.624528 0.227309i
\(795\) 0 0
\(796\) −0.286194 + 1.62309i −0.0101439 + 0.0575288i
\(797\) 28.7940 1.01994 0.509969 0.860193i \(-0.329657\pi\)
0.509969 + 0.860193i \(0.329657\pi\)
\(798\) 39.8136 + 33.5000i 1.40939 + 1.18589i
\(799\) −2.82065 −0.0997874
\(800\) 0 0
\(801\) 16.5633 + 13.8982i 0.585234 + 0.491070i
\(802\) −12.8180 4.66536i −0.452618 0.164740i
\(803\) −7.16455 + 2.60768i −0.252832 + 0.0920232i
\(804\) 3.05762 2.56565i 0.107834 0.0904834i
\(805\) 0 0
\(806\) −3.66648 + 6.35052i −0.129146 + 0.223688i
\(807\) 6.66429 + 37.7951i 0.234594 + 1.33045i
\(808\) 8.04072 + 45.6012i 0.282872 + 1.60425i
\(809\) 24.0034 41.5751i 0.843915 1.46170i −0.0426458 0.999090i \(-0.513579\pi\)
0.886560 0.462613i \(-0.153088\pi\)
\(810\) 0 0
\(811\) −7.37613 + 6.18931i −0.259011 + 0.217336i −0.763041 0.646350i \(-0.776295\pi\)
0.504030 + 0.863686i \(0.331850\pi\)
\(812\) −0.194793 + 0.0708988i −0.00683589 + 0.00248806i
\(813\) −12.0481 4.38513i −0.422544 0.153793i
\(814\) −12.8233 10.7601i −0.449458 0.377140i
\(815\) 0 0
\(816\) −68.2523 −2.38931
\(817\) 43.1280 + 0.0586768i 1.50886 + 0.00205284i
\(818\) −50.9680 −1.78205
\(819\) −3.18800 + 18.0800i −0.111398 + 0.631768i
\(820\) 0 0
\(821\) 24.1743 + 8.79872i 0.843688 + 0.307077i 0.727464 0.686146i \(-0.240699\pi\)
0.116224 + 0.993223i \(0.462921\pi\)
\(822\) 30.2152 10.9974i 1.05388 0.383580i
\(823\) −10.3098 + 8.65091i −0.359376 + 0.301552i −0.804542 0.593896i \(-0.797589\pi\)
0.445166 + 0.895448i \(0.353145\pi\)
\(824\) −18.5327 32.0996i −0.645617 1.11824i
\(825\) 0 0
\(826\) 2.62330 + 14.8775i 0.0912764 + 0.517654i
\(827\) 0.0299383 + 0.169788i 0.00104106 + 0.00590412i 0.985324 0.170695i \(-0.0546014\pi\)
−0.984283 + 0.176599i \(0.943490\pi\)
\(828\) −0.426576 + 0.738851i −0.0148245 + 0.0256769i
\(829\) 21.1895 + 36.7014i 0.735943 + 1.27469i 0.954308 + 0.298824i \(0.0965942\pi\)
−0.218365 + 0.975867i \(0.570072\pi\)
\(830\) 0 0
\(831\) 12.9980 4.73089i 0.450896 0.164113i
\(832\) −11.9262 4.34078i −0.413467 0.150490i
\(833\) 17.2770 + 14.4971i 0.598614 + 0.502296i
\(834\) −4.90447 + 27.8147i −0.169828 + 0.963143i
\(835\) 0 0
\(836\) 3.22247 1.16792i 0.111452 0.0403934i
\(837\) −1.14755 −0.0396651
\(838\) 2.01900 11.4503i 0.0697452 0.395545i
\(839\) 34.5791 + 29.0153i 1.19380 + 1.00172i 0.999785 + 0.0207231i \(0.00659684\pi\)
0.194019 + 0.980998i \(0.437848\pi\)
\(840\) 0 0
\(841\) 27.1428 9.87919i 0.935960 0.340662i
\(842\) −11.8888 + 9.97593i −0.409717 + 0.343793i
\(843\) −33.8621 58.6509i −1.16627 2.02005i
\(844\) −1.11046 + 1.92338i −0.0382237 + 0.0662055i
\(845\) 0 0
\(846\) 0.362270 + 2.05453i 0.0124551 + 0.0706363i
\(847\) 10.5715 18.3103i 0.363240 0.629151i
\(848\) −15.7070 27.2054i −0.539382 0.934238i
\(849\) 28.6208 24.0157i 0.982263 0.824217i
\(850\) 0 0
\(851\) 3.64397 + 1.32630i 0.124914 + 0.0454649i
\(852\) 4.60930 + 3.86766i 0.157912 + 0.132504i
\(853\) −8.04694 + 45.6364i −0.275522 + 1.56256i 0.461778 + 0.886996i \(0.347212\pi\)
−0.737299 + 0.675566i \(0.763899\pi\)
\(854\) −14.7368 −0.504283
\(855\) 0 0
\(856\) −8.75023 −0.299077
\(857\) 3.80174 21.5607i 0.129865 0.736501i −0.848434 0.529302i \(-0.822454\pi\)
0.978299 0.207199i \(-0.0664349\pi\)
\(858\) 21.0040 + 17.6245i 0.717066 + 0.601690i
\(859\) −31.3876 11.4242i −1.07093 0.389787i −0.254406 0.967097i \(-0.581880\pi\)
−0.816525 + 0.577310i \(0.804102\pi\)
\(860\) 0 0
\(861\) 44.1289 37.0285i 1.50391 1.26193i
\(862\) 22.1079 + 38.2920i 0.752998 + 1.30423i
\(863\) 13.5627 23.4913i 0.461680 0.799653i −0.537365 0.843350i \(-0.680580\pi\)
0.999045 + 0.0436971i \(0.0139137\pi\)
\(864\) 0.0759988 + 0.431011i 0.00258553 + 0.0146633i
\(865\) 0 0
\(866\) −5.02900 + 8.71049i −0.170892 + 0.295994i
\(867\) −28.6779 49.6716i −0.973953 1.68694i
\(868\) 1.30010 1.09091i 0.0441282 0.0370279i
\(869\) 2.74705 0.999846i 0.0931875 0.0339175i
\(870\) 0 0
\(871\) 11.6890 + 9.80822i 0.396066 + 0.332339i
\(872\) −1.49914 + 8.50206i −0.0507674 + 0.287916i
\(873\) −41.7973 −1.41462
\(874\) −7.08916 + 5.93209i −0.239794 + 0.200656i
\(875\) 0 0
\(876\) −0.147679 + 0.837527i −0.00498960 + 0.0282974i
\(877\) −37.5992 31.5495i −1.26963 1.06535i −0.994586 0.103920i \(-0.966861\pi\)
−0.275049 0.961430i \(-0.588694\pi\)
\(878\) 11.0725 + 4.03008i 0.373680 + 0.136008i
\(879\) −18.2682 + 6.64906i −0.616169 + 0.224267i
\(880\) 0 0
\(881\) −18.9889 32.8898i −0.639753 1.10808i −0.985487 0.169751i \(-0.945704\pi\)
0.345734 0.938332i \(-0.387630\pi\)
\(882\) 8.34062 14.4464i 0.280843 0.486435i
\(883\) 5.76686 + 32.7055i 0.194070 + 1.10063i 0.913737 + 0.406307i \(0.133184\pi\)
−0.719666 + 0.694320i \(0.755705\pi\)
\(884\) 0.368704 + 2.09103i 0.0124009 + 0.0703288i
\(885\) 0 0
\(886\) 16.1150 + 27.9121i 0.541395 + 0.937724i
\(887\) 20.1106 16.8748i 0.675248 0.566601i −0.239365 0.970930i \(-0.576939\pi\)
0.914614 + 0.404329i \(0.132495\pi\)
\(888\) 16.9172 6.15734i 0.567703 0.206627i
\(889\) 1.80794 + 0.658035i 0.0606362 + 0.0220698i
\(890\) 0 0
\(891\) 6.15629 34.9140i 0.206243 1.16966i
\(892\) 1.67222 0.0559902
\(893\) −0.339762 + 1.91167i −0.0113697 + 0.0639718i
\(894\) 54.8808 1.83549
\(895\) 0 0
\(896\) 31.4721 + 26.4082i 1.05141 + 0.882236i
\(897\) −5.96866 2.17242i −0.199288 0.0725348i
\(898\) 26.1087 9.50278i 0.871258 0.317112i
\(899\) 0.722415 0.606178i 0.0240939 0.0202172i
\(900\) 0 0
\(901\) 22.9143 39.6888i 0.763387 1.32223i
\(902\) −7.67129 43.5060i −0.255426 1.44859i
\(903\) −13.8654 78.6346i −0.461412 2.61680i
\(904\) −6.31229 + 10.9332i −0.209944 + 0.363633i
\(905\) 0 0
\(906\) −36.9793 + 31.0294i −1.22856 + 1.03088i
\(907\) −7.44950 + 2.71140i −0.247357 + 0.0900305i −0.462723 0.886503i \(-0.653128\pi\)
0.215366 + 0.976533i \(0.430905\pi\)
\(908\) 4.66383 + 1.69750i 0.154775 + 0.0563334i
\(909\) 41.9027 + 35.1606i 1.38983 + 1.16620i
\(910\) 0 0
\(911\) −0.619746 −0.0205331 −0.0102665 0.999947i \(-0.503268\pi\)
−0.0102665 + 0.999947i \(0.503268\pi\)
\(912\) −8.22135 + 46.2575i −0.272236 + 1.53174i
\(913\) 2.31369 0.0765718
\(914\) 7.25277 41.1325i 0.239900 1.36054i
\(915\) 0 0
\(916\) −3.84742 1.40035i −0.127122 0.0462687i
\(917\) −62.7544 + 22.8407i −2.07233 + 0.754268i
\(918\) −2.96325 + 2.48646i −0.0978017 + 0.0820654i
\(919\) 17.5287 + 30.3606i 0.578219 + 1.00150i 0.995684 + 0.0928113i \(0.0295853\pi\)
−0.417465 + 0.908693i \(0.637081\pi\)
\(920\) 0 0
\(921\) 6.77620 + 38.4297i 0.223283 + 1.26630i
\(922\) 0.0503456 + 0.285524i 0.00165804 + 0.00940324i
\(923\) −11.5012 + 19.9207i −0.378568 + 0.655699i
\(924\) −3.17294 5.49569i −0.104382 0.180795i
\(925\) 0 0
\(926\) −19.4096 + 7.06452i −0.637840 + 0.232155i
\(927\) −41.1451 14.9756i −1.35138 0.491863i
\(928\) −0.275519 0.231188i −0.00904437 0.00758912i
\(929\) 2.09132 11.8605i 0.0686140 0.389129i −0.931090 0.364790i \(-0.881141\pi\)
0.999704 0.0243392i \(-0.00774816\pi\)
\(930\) 0 0
\(931\) 11.9065 9.96313i 0.390218 0.326528i
\(932\) 1.87959 0.0615679
\(933\) 7.75357 43.9727i 0.253841 1.43960i
\(934\) −36.3756 30.5228i −1.19025 0.998735i
\(935\) 0 0
\(936\) −14.2284 + 5.17873i −0.465071 + 0.169272i
\(937\) 11.4374 9.59711i 0.373643 0.313524i −0.436558 0.899676i \(-0.643802\pi\)
0.810201 + 0.586152i \(0.199358\pi\)
\(938\) −20.5565 35.6049i −0.671194 1.16254i
\(939\) 26.3226 45.5921i 0.859006 1.48784i
\(940\) 0 0
\(941\) 3.37221 + 19.1248i 0.109931 + 0.623450i 0.989136 + 0.147006i \(0.0469635\pi\)
−0.879205 + 0.476444i \(0.841925\pi\)
\(942\) 19.9029 34.4729i 0.648473 1.12319i
\(943\) 5.11694 + 8.86280i 0.166630 + 0.288612i
\(944\) −10.4494 + 8.76813i −0.340101 + 0.285378i
\(945\) 0 0
\(946\) −57.5409 20.9432i −1.87082 0.680922i
\(947\) 12.8212 + 10.7583i 0.416634 + 0.349598i 0.826881 0.562377i \(-0.190113\pi\)
−0.410247 + 0.911975i \(0.634557\pi\)
\(948\) 0.0566233 0.321127i 0.00183904 0.0104297i
\(949\) −3.25117 −0.105538
\(950\) 0 0
\(951\) −7.60959 −0.246758
\(952\) −9.57824 + 54.3209i −0.310433 + 1.76055i
\(953\) −40.7361 34.1817i −1.31957 1.10725i −0.986396 0.164389i \(-0.947435\pi\)
−0.333177 0.942864i \(-0.608121\pi\)
\(954\) −31.8520 11.5932i −1.03125 0.375343i
\(955\) 0 0
\(956\) 2.56794 2.15475i 0.0830530 0.0696897i
\(957\) −1.76308 3.05375i −0.0569923 0.0987136i
\(958\) −1.46605 + 2.53927i −0.0473658 + 0.0820400i
\(959\) −4.94022 28.0174i −0.159528 0.904729i
\(960\) 0 0
\(961\) 11.6396 20.1603i 0.375470 0.650332i
\(962\) −3.56906 6.18179i −0.115071 0.199309i
\(963\) −7.91839 + 6.64432i −0.255167 + 0.214110i
\(964\) 3.02778 1.10202i 0.0975181 0.0354937i
\(965\) 0 0
\(966\) 13.1100 + 11.0006i 0.421807 + 0.353938i
\(967\) 5.21432 29.5719i 0.167681 0.950967i −0.778576 0.627551i \(-0.784057\pi\)
0.946257 0.323416i \(-0.104831\pi\)
\(968\) 17.4377 0.560469
\(969\) −64.4390 + 23.3546i −2.07008 + 0.750259i
\(970\) 0 0
\(971\) 4.19210 23.7746i 0.134531 0.762962i −0.840654 0.541572i \(-0.817829\pi\)
0.975185 0.221390i \(-0.0710595\pi\)
\(972\) −3.20770 2.69158i −0.102887 0.0863325i
\(973\) 23.4825 + 8.54693i 0.752814 + 0.274002i
\(974\) −11.9386 + 4.34531i −0.382538 + 0.139233i
\(975\) 0 0
\(976\) −6.65325 11.5238i −0.212965 0.368867i
\(977\) 4.78840 8.29375i 0.153195 0.265341i −0.779206 0.626768i \(-0.784377\pi\)
0.932400 + 0.361428i \(0.117711\pi\)
\(978\) −5.38677 30.5499i −0.172250 0.976877i
\(979\) −4.96134 28.1372i −0.158565 0.899267i
\(980\) 0 0
\(981\) 5.09925 + 8.83216i 0.162806 + 0.281989i
\(982\) −29.3477 + 24.6257i −0.936524 + 0.785837i
\(983\) −29.2916 + 10.6613i −0.934257 + 0.340042i −0.763896 0.645340i \(-0.776716\pi\)
−0.170362 + 0.985382i \(0.554494\pi\)
\(984\) 44.6455 + 16.2497i 1.42325 + 0.518020i
\(985\) 0 0
\(986\) 0.552008 3.13060i 0.0175795 0.0996985i
\(987\) 3.59476 0.114422
\(988\) 1.46159 + 0.00198853i 0.0464994 + 6.32636e-5i
\(989\) 14.1851 0.451061
\(990\) 0 0
\(991\) −37.2791 31.2808i −1.18421 0.993669i −0.999942 0.0107922i \(-0.996565\pi\)
−0.184266 0.982876i \(-0.558991\pi\)
\(992\) 2.76706 + 1.00713i 0.0878542 + 0.0319763i
\(993\) 60.5551 22.0403i 1.92166 0.699426i
\(994\) 47.4772 39.8381i 1.50589 1.26359i
\(995\) 0 0
\(996\) 0.129038 0.223501i 0.00408873 0.00708189i
\(997\) 5.53857 + 31.4108i 0.175408 + 0.994790i 0.937672 + 0.347523i \(0.112977\pi\)
−0.762263 + 0.647267i \(0.775912\pi\)
\(998\) 5.44631 + 30.8876i 0.172400 + 0.977729i
\(999\) 0.558529 0.967401i 0.0176711 0.0306072i
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 475.2.l.f.226.2 48
5.2 odd 4 95.2.p.a.74.2 yes 48
5.3 odd 4 95.2.p.a.74.7 yes 48
5.4 even 2 inner 475.2.l.f.226.7 48
15.2 even 4 855.2.da.b.739.7 48
15.8 even 4 855.2.da.b.739.2 48
19.3 odd 18 9025.2.a.ct.1.18 24
19.9 even 9 inner 475.2.l.f.351.2 48
19.16 even 9 9025.2.a.cu.1.7 24
95.3 even 36 1805.2.b.l.1084.7 24
95.9 even 18 inner 475.2.l.f.351.7 48
95.22 even 36 1805.2.b.l.1084.18 24
95.28 odd 36 95.2.p.a.9.2 48
95.47 odd 36 95.2.p.a.9.7 yes 48
95.54 even 18 9025.2.a.cu.1.18 24
95.73 odd 36 1805.2.b.k.1084.18 24
95.79 odd 18 9025.2.a.ct.1.7 24
95.92 odd 36 1805.2.b.k.1084.7 24
285.47 even 36 855.2.da.b.199.2 48
285.218 even 36 855.2.da.b.199.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.9.2 48 95.28 odd 36
95.2.p.a.9.7 yes 48 95.47 odd 36
95.2.p.a.74.2 yes 48 5.2 odd 4
95.2.p.a.74.7 yes 48 5.3 odd 4
475.2.l.f.226.2 48 1.1 even 1 trivial
475.2.l.f.226.7 48 5.4 even 2 inner
475.2.l.f.351.2 48 19.9 even 9 inner
475.2.l.f.351.7 48 95.9 even 18 inner
855.2.da.b.199.2 48 285.47 even 36
855.2.da.b.199.7 48 285.218 even 36
855.2.da.b.739.2 48 15.8 even 4
855.2.da.b.739.7 48 15.2 even 4
1805.2.b.k.1084.7 24 95.92 odd 36
1805.2.b.k.1084.18 24 95.73 odd 36
1805.2.b.l.1084.7 24 95.3 even 36
1805.2.b.l.1084.18 24 95.22 even 36
9025.2.a.ct.1.7 24 95.79 odd 18
9025.2.a.ct.1.18 24 19.3 odd 18
9025.2.a.cu.1.7 24 19.16 even 9
9025.2.a.cu.1.18 24 95.54 even 18