Properties

Label 189.2.i.b.143.3
Level $189$
Weight $2$
Character 189.143
Analytic conductor $1.509$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(143,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 143.3
Root \(-0.539982 + 0.935277i\) of defining polynomial
Character \(\chi\) \(=\) 189.143
Dual form 189.2.i.b.152.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.293869i q^{2} +1.91364 q^{4} +(-1.53014 + 2.65027i) q^{5} +(-1.41763 + 2.23391i) q^{7} +1.15010i q^{8} +O(q^{10})\) \(q+0.293869i q^{2} +1.91364 q^{4} +(-1.53014 + 2.65027i) q^{5} +(-1.41763 + 2.23391i) q^{7} +1.15010i q^{8} +(-0.778834 - 0.449660i) q^{10} +(3.37445 - 1.94824i) q^{11} +(-2.02935 + 1.17164i) q^{13} +(-0.656477 - 0.416597i) q^{14} +3.48930 q^{16} +(1.68263 - 2.91440i) q^{17} +(2.20696 - 1.27419i) q^{19} +(-2.92813 + 5.07167i) q^{20} +(0.572527 + 0.991647i) q^{22} +(-2.58141 - 1.49038i) q^{23} +(-2.18263 - 3.78042i) q^{25} +(-0.344311 - 0.596363i) q^{26} +(-2.71283 + 4.27489i) q^{28} +(3.67241 + 2.12027i) q^{29} -0.472735i q^{31} +3.32560i q^{32} +(0.856452 + 0.494473i) q^{34} +(-3.75130 - 7.17527i) q^{35} +(-3.89395 - 6.74451i) q^{37} +(0.374446 + 0.648559i) q^{38} +(-3.04808 - 1.75981i) q^{40} +(-3.12737 - 5.41676i) q^{41} +(2.06191 - 3.57133i) q^{43} +(6.45748 - 3.72823i) q^{44} +(0.437976 - 0.758597i) q^{46} +4.05388 q^{47} +(-2.98068 - 6.33369i) q^{49} +(1.11095 - 0.641408i) q^{50} +(-3.88344 + 2.24211i) q^{52} +(-4.99439 - 2.88351i) q^{53} +11.9243i q^{55} +(-2.56921 - 1.63041i) q^{56} +(-0.623082 + 1.07921i) q^{58} +4.68705 q^{59} +1.60018i q^{61} +0.138922 q^{62} +6.00131 q^{64} -7.17110i q^{65} +1.57566 q^{67} +(3.21994 - 5.57711i) q^{68} +(2.10859 - 1.10239i) q^{70} +13.6132i q^{71} +(-0.856452 - 0.494473i) q^{73} +(1.98201 - 1.14431i) q^{74} +(4.22333 - 2.43834i) q^{76} +(-0.431520 + 10.3001i) q^{77} -9.27815 q^{79} +(-5.33910 + 9.24760i) q^{80} +(1.59182 - 0.919038i) q^{82} +(-5.49361 + 9.51520i) q^{83} +(5.14930 + 8.91884i) q^{85} +(1.04950 + 0.605932i) q^{86} +(2.24067 + 3.88095i) q^{88} +(2.15849 + 3.73861i) q^{89} +(0.259511 - 6.19433i) q^{91} +(-4.93989 - 2.85205i) q^{92} +1.19131i q^{94} +7.79874i q^{95} +(4.98797 + 2.87980i) q^{97} +(1.86128 - 0.875930i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 8 q^{4} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 8 q^{4} - 6 q^{7} - 15 q^{10} + 12 q^{11} - 6 q^{13} - 12 q^{14} + 12 q^{16} - 12 q^{17} + 3 q^{19} - 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 15 q^{29} - 3 q^{34} - 15 q^{35} + 6 q^{37} - 18 q^{38} + 15 q^{40} - 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} - 30 q^{47} + 4 q^{49} - 3 q^{50} - 12 q^{52} - 9 q^{53} + 30 q^{56} + 8 q^{58} + 36 q^{59} + 12 q^{62} + 6 q^{64} + 20 q^{67} + 27 q^{68} + 6 q^{70} + 3 q^{73} + 30 q^{74} - 9 q^{76} - 39 q^{77} - 40 q^{79} - 30 q^{80} + 9 q^{82} - 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} - 39 q^{92} - 6 q^{97} + 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.293869i 0.207797i 0.994588 + 0.103899i \(0.0331317\pi\)
−0.994588 + 0.103899i \(0.966868\pi\)
\(3\) 0 0
\(4\) 1.91364 0.956820
\(5\) −1.53014 + 2.65027i −0.684297 + 1.18524i 0.289360 + 0.957220i \(0.406558\pi\)
−0.973657 + 0.228017i \(0.926776\pi\)
\(6\) 0 0
\(7\) −1.41763 + 2.23391i −0.535812 + 0.844337i
\(8\) 1.15010i 0.406622i
\(9\) 0 0
\(10\) −0.778834 0.449660i −0.246289 0.142195i
\(11\) 3.37445 1.94824i 1.01743 0.587416i 0.104074 0.994570i \(-0.466812\pi\)
0.913360 + 0.407154i \(0.133479\pi\)
\(12\) 0 0
\(13\) −2.02935 + 1.17164i −0.562840 + 0.324956i −0.754285 0.656548i \(-0.772016\pi\)
0.191445 + 0.981503i \(0.438683\pi\)
\(14\) −0.656477 0.416597i −0.175451 0.111340i
\(15\) 0 0
\(16\) 3.48930 0.872326
\(17\) 1.68263 2.91440i 0.408097 0.706845i −0.586579 0.809892i \(-0.699526\pi\)
0.994677 + 0.103047i \(0.0328591\pi\)
\(18\) 0 0
\(19\) 2.20696 1.27419i 0.506312 0.292319i −0.225004 0.974358i \(-0.572240\pi\)
0.731316 + 0.682038i \(0.238906\pi\)
\(20\) −2.92813 + 5.07167i −0.654750 + 1.13406i
\(21\) 0 0
\(22\) 0.572527 + 0.991647i 0.122063 + 0.211420i
\(23\) −2.58141 1.49038i −0.538261 0.310765i 0.206113 0.978528i \(-0.433919\pi\)
−0.744374 + 0.667763i \(0.767252\pi\)
\(24\) 0 0
\(25\) −2.18263 3.78042i −0.436525 0.756084i
\(26\) −0.344311 0.596363i −0.0675249 0.116956i
\(27\) 0 0
\(28\) −2.71283 + 4.27489i −0.512676 + 0.807879i
\(29\) 3.67241 + 2.12027i 0.681949 + 0.393724i 0.800589 0.599214i \(-0.204520\pi\)
−0.118640 + 0.992937i \(0.537853\pi\)
\(30\) 0 0
\(31\) 0.472735i 0.0849057i −0.999098 0.0424528i \(-0.986483\pi\)
0.999098 0.0424528i \(-0.0135172\pi\)
\(32\) 3.32560i 0.587888i
\(33\) 0 0
\(34\) 0.856452 + 0.494473i 0.146880 + 0.0848014i
\(35\) −3.75130 7.17527i −0.634086 1.21284i
\(36\) 0 0
\(37\) −3.89395 6.74451i −0.640161 1.10879i −0.985397 0.170275i \(-0.945534\pi\)
0.345236 0.938516i \(-0.387799\pi\)
\(38\) 0.374446 + 0.648559i 0.0607431 + 0.105210i
\(39\) 0 0
\(40\) −3.04808 1.75981i −0.481943 0.278250i
\(41\) −3.12737 5.41676i −0.488413 0.845956i 0.511498 0.859284i \(-0.329091\pi\)
−0.999911 + 0.0133282i \(0.995757\pi\)
\(42\) 0 0
\(43\) 2.06191 3.57133i 0.314438 0.544623i −0.664880 0.746950i \(-0.731517\pi\)
0.979318 + 0.202328i \(0.0648506\pi\)
\(44\) 6.45748 3.72823i 0.973501 0.562051i
\(45\) 0 0
\(46\) 0.437976 0.758597i 0.0645761 0.111849i
\(47\) 4.05388 0.591319 0.295659 0.955293i \(-0.404461\pi\)
0.295659 + 0.955293i \(0.404461\pi\)
\(48\) 0 0
\(49\) −2.98068 6.33369i −0.425811 0.904812i
\(50\) 1.11095 0.641408i 0.157112 0.0907087i
\(51\) 0 0
\(52\) −3.88344 + 2.24211i −0.538537 + 0.310924i
\(53\) −4.99439 2.88351i −0.686033 0.396081i 0.116091 0.993239i \(-0.462963\pi\)
−0.802124 + 0.597157i \(0.796297\pi\)
\(54\) 0 0
\(55\) 11.9243i 1.60787i
\(56\) −2.56921 1.63041i −0.343326 0.217873i
\(57\) 0 0
\(58\) −0.623082 + 1.07921i −0.0818146 + 0.141707i
\(59\) 4.68705 0.610201 0.305101 0.952320i \(-0.401310\pi\)
0.305101 + 0.952320i \(0.401310\pi\)
\(60\) 0 0
\(61\) 1.60018i 0.204883i 0.994739 + 0.102441i \(0.0326654\pi\)
−0.994739 + 0.102441i \(0.967335\pi\)
\(62\) 0.138922 0.0176432
\(63\) 0 0
\(64\) 6.00131 0.750164
\(65\) 7.17110i 0.889465i
\(66\) 0 0
\(67\) 1.57566 0.192498 0.0962489 0.995357i \(-0.469316\pi\)
0.0962489 + 0.995357i \(0.469316\pi\)
\(68\) 3.21994 5.57711i 0.390476 0.676324i
\(69\) 0 0
\(70\) 2.10859 1.10239i 0.252025 0.131761i
\(71\) 13.6132i 1.61559i 0.589462 + 0.807796i \(0.299340\pi\)
−0.589462 + 0.807796i \(0.700660\pi\)
\(72\) 0 0
\(73\) −0.856452 0.494473i −0.100240 0.0578737i 0.449042 0.893511i \(-0.351765\pi\)
−0.549282 + 0.835637i \(0.685099\pi\)
\(74\) 1.98201 1.14431i 0.230404 0.133024i
\(75\) 0 0
\(76\) 4.22333 2.43834i 0.484450 0.279697i
\(77\) −0.431520 + 10.3001i −0.0491763 + 1.17380i
\(78\) 0 0
\(79\) −9.27815 −1.04387 −0.521937 0.852984i \(-0.674790\pi\)
−0.521937 + 0.852984i \(0.674790\pi\)
\(80\) −5.33910 + 9.24760i −0.596930 + 1.03391i
\(81\) 0 0
\(82\) 1.59182 0.919038i 0.175787 0.101491i
\(83\) −5.49361 + 9.51520i −0.603002 + 1.04443i 0.389362 + 0.921085i \(0.372695\pi\)
−0.992364 + 0.123345i \(0.960638\pi\)
\(84\) 0 0
\(85\) 5.14930 + 8.91884i 0.558519 + 0.967384i
\(86\) 1.04950 + 0.605932i 0.113171 + 0.0653393i
\(87\) 0 0
\(88\) 2.24067 + 3.88095i 0.238856 + 0.413710i
\(89\) 2.15849 + 3.73861i 0.228799 + 0.396292i 0.957452 0.288591i \(-0.0931868\pi\)
−0.728653 + 0.684883i \(0.759853\pi\)
\(90\) 0 0
\(91\) 0.259511 6.19433i 0.0272041 0.649342i
\(92\) −4.93989 2.85205i −0.515019 0.297346i
\(93\) 0 0
\(94\) 1.19131i 0.122874i
\(95\) 7.79874i 0.800133i
\(96\) 0 0
\(97\) 4.98797 + 2.87980i 0.506451 + 0.292400i 0.731374 0.681977i \(-0.238880\pi\)
−0.224923 + 0.974377i \(0.572213\pi\)
\(98\) 1.86128 0.875930i 0.188017 0.0884823i
\(99\) 0 0
\(100\) −4.17676 7.23437i −0.417676 0.723437i
\(101\) −8.57900 14.8593i −0.853642 1.47855i −0.877899 0.478846i \(-0.841055\pi\)
0.0242566 0.999706i \(-0.492278\pi\)
\(102\) 0 0
\(103\) 8.50422 + 4.90992i 0.837946 + 0.483788i 0.856566 0.516038i \(-0.172594\pi\)
−0.0186195 + 0.999827i \(0.505927\pi\)
\(104\) −1.34751 2.33395i −0.132134 0.228863i
\(105\) 0 0
\(106\) 0.847377 1.46770i 0.0823045 0.142556i
\(107\) 3.00501 1.73494i 0.290505 0.167723i −0.347664 0.937619i \(-0.613025\pi\)
0.638170 + 0.769896i \(0.279692\pi\)
\(108\) 0 0
\(109\) 0.611066 1.05840i 0.0585295 0.101376i −0.835276 0.549831i \(-0.814692\pi\)
0.893806 + 0.448455i \(0.148025\pi\)
\(110\) −3.50418 −0.334110
\(111\) 0 0
\(112\) −4.94652 + 7.79478i −0.467403 + 0.736537i
\(113\) 1.87681 1.08358i 0.176555 0.101934i −0.409118 0.912482i \(-0.634164\pi\)
0.585673 + 0.810547i \(0.300830\pi\)
\(114\) 0 0
\(115\) 7.89981 4.56096i 0.736661 0.425311i
\(116\) 7.02767 + 4.05743i 0.652503 + 0.376723i
\(117\) 0 0
\(118\) 1.37738i 0.126798i
\(119\) 4.12515 + 7.89035i 0.378152 + 0.723308i
\(120\) 0 0
\(121\) 2.09126 3.62216i 0.190114 0.329287i
\(122\) −0.470245 −0.0425740
\(123\) 0 0
\(124\) 0.904645i 0.0812395i
\(125\) −1.94249 −0.173742
\(126\) 0 0
\(127\) 2.74889 0.243925 0.121962 0.992535i \(-0.461081\pi\)
0.121962 + 0.992535i \(0.461081\pi\)
\(128\) 8.41480i 0.743770i
\(129\) 0 0
\(130\) 2.10737 0.184828
\(131\) 3.73911 6.47632i 0.326687 0.565839i −0.655165 0.755486i \(-0.727401\pi\)
0.981852 + 0.189647i \(0.0607343\pi\)
\(132\) 0 0
\(133\) −0.282224 + 6.73647i −0.0244719 + 0.584126i
\(134\) 0.463039i 0.0400005i
\(135\) 0 0
\(136\) 3.35185 + 1.93519i 0.287418 + 0.165941i
\(137\) 10.5731 6.10439i 0.903321 0.521533i 0.0250451 0.999686i \(-0.492027\pi\)
0.878276 + 0.478153i \(0.158694\pi\)
\(138\) 0 0
\(139\) −11.5501 + 6.66842i −0.979663 + 0.565608i −0.902168 0.431384i \(-0.858025\pi\)
−0.0774943 + 0.996993i \(0.524692\pi\)
\(140\) −7.17864 13.7309i −0.606706 1.16047i
\(141\) 0 0
\(142\) −4.00051 −0.335715
\(143\) −4.56528 + 7.90730i −0.381768 + 0.661242i
\(144\) 0 0
\(145\) −11.2386 + 6.48859i −0.933312 + 0.538848i
\(146\) 0.145310 0.251685i 0.0120260 0.0208296i
\(147\) 0 0
\(148\) −7.45161 12.9066i −0.612519 1.06091i
\(149\) 7.33827 + 4.23675i 0.601174 + 0.347088i 0.769503 0.638643i \(-0.220504\pi\)
−0.168329 + 0.985731i \(0.553837\pi\)
\(150\) 0 0
\(151\) 1.67827 + 2.90685i 0.136576 + 0.236556i 0.926198 0.377037i \(-0.123057\pi\)
−0.789623 + 0.613593i \(0.789724\pi\)
\(152\) 1.46545 + 2.53823i 0.118863 + 0.205877i
\(153\) 0 0
\(154\) −3.02688 0.126811i −0.243913 0.0102187i
\(155\) 1.25288 + 0.723348i 0.100633 + 0.0581007i
\(156\) 0 0
\(157\) 16.7085i 1.33349i −0.745288 0.666743i \(-0.767688\pi\)
0.745288 0.666743i \(-0.232312\pi\)
\(158\) 2.72657i 0.216914i
\(159\) 0 0
\(160\) −8.81374 5.08862i −0.696787 0.402290i
\(161\) 6.98883 3.65383i 0.550797 0.287962i
\(162\) 0 0
\(163\) 12.6662 + 21.9385i 0.992094 + 1.71836i 0.604731 + 0.796430i \(0.293281\pi\)
0.387363 + 0.921927i \(0.373386\pi\)
\(164\) −5.98466 10.3657i −0.467324 0.809428i
\(165\) 0 0
\(166\) −2.79623 1.61440i −0.217029 0.125302i
\(167\) −0.875828 1.51698i −0.0677736 0.117387i 0.830147 0.557544i \(-0.188256\pi\)
−0.897921 + 0.440157i \(0.854923\pi\)
\(168\) 0 0
\(169\) −3.75450 + 6.50298i −0.288808 + 0.500229i
\(170\) −2.62097 + 1.51322i −0.201020 + 0.116059i
\(171\) 0 0
\(172\) 3.94575 6.83424i 0.300861 0.521106i
\(173\) −23.9266 −1.81910 −0.909551 0.415592i \(-0.863574\pi\)
−0.909551 + 0.415592i \(0.863574\pi\)
\(174\) 0 0
\(175\) 11.5393 + 0.483436i 0.872286 + 0.0365443i
\(176\) 11.7745 6.79799i 0.887533 0.512418i
\(177\) 0 0
\(178\) −1.09866 + 0.634313i −0.0823482 + 0.0475438i
\(179\) −21.9857 12.6935i −1.64329 0.948755i −0.979652 0.200702i \(-0.935678\pi\)
−0.663639 0.748053i \(-0.730989\pi\)
\(180\) 0 0
\(181\) 22.4032i 1.66522i −0.553859 0.832610i \(-0.686845\pi\)
0.553859 0.832610i \(-0.313155\pi\)
\(182\) 1.82032 + 0.0762622i 0.134931 + 0.00565293i
\(183\) 0 0
\(184\) 1.71408 2.96888i 0.126364 0.218869i
\(185\) 23.8331 1.75224
\(186\) 0 0
\(187\) 13.1126i 0.958890i
\(188\) 7.75766 0.565786
\(189\) 0 0
\(190\) −2.29181 −0.166265
\(191\) 4.28895i 0.310337i 0.987888 + 0.155169i \(0.0495921\pi\)
−0.987888 + 0.155169i \(0.950408\pi\)
\(192\) 0 0
\(193\) −23.3449 −1.68041 −0.840203 0.542272i \(-0.817564\pi\)
−0.840203 + 0.542272i \(0.817564\pi\)
\(194\) −0.846286 + 1.46581i −0.0607598 + 0.105239i
\(195\) 0 0
\(196\) −5.70394 12.1204i −0.407425 0.865743i
\(197\) 18.7811i 1.33809i −0.743220 0.669047i \(-0.766702\pi\)
0.743220 0.669047i \(-0.233298\pi\)
\(198\) 0 0
\(199\) −3.92927 2.26856i −0.278539 0.160814i 0.354223 0.935161i \(-0.384745\pi\)
−0.632762 + 0.774347i \(0.718079\pi\)
\(200\) 4.34786 2.51024i 0.307440 0.177501i
\(201\) 0 0
\(202\) 4.36668 2.52111i 0.307239 0.177384i
\(203\) −9.94258 + 5.19808i −0.697832 + 0.364833i
\(204\) 0 0
\(205\) 19.1412 1.33688
\(206\) −1.44287 + 2.49913i −0.100530 + 0.174123i
\(207\) 0 0
\(208\) −7.08101 + 4.08822i −0.490980 + 0.283467i
\(209\) 4.96485 8.59937i 0.343426 0.594831i
\(210\) 0 0
\(211\) −3.44148 5.96082i −0.236921 0.410360i 0.722908 0.690944i \(-0.242805\pi\)
−0.959829 + 0.280584i \(0.909472\pi\)
\(212\) −9.55747 5.51801i −0.656410 0.378978i
\(213\) 0 0
\(214\) 0.509847 + 0.883081i 0.0348524 + 0.0603662i
\(215\) 6.31000 + 10.9292i 0.430338 + 0.745368i
\(216\) 0 0
\(217\) 1.05605 + 0.670161i 0.0716890 + 0.0454935i
\(218\) 0.311031 + 0.179574i 0.0210657 + 0.0121623i
\(219\) 0 0
\(220\) 22.8188i 1.53844i
\(221\) 7.88576i 0.530454i
\(222\) 0 0
\(223\) 5.57176 + 3.21686i 0.373113 + 0.215417i 0.674818 0.737985i \(-0.264222\pi\)
−0.301705 + 0.953401i \(0.597556\pi\)
\(224\) −7.42908 4.71445i −0.496376 0.314998i
\(225\) 0 0
\(226\) 0.318430 + 0.551537i 0.0211816 + 0.0366877i
\(227\) 9.86983 + 17.0951i 0.655084 + 1.13464i 0.981873 + 0.189541i \(0.0607000\pi\)
−0.326789 + 0.945097i \(0.605967\pi\)
\(228\) 0 0
\(229\) 9.44564 + 5.45344i 0.624185 + 0.360373i 0.778497 0.627649i \(-0.215983\pi\)
−0.154311 + 0.988022i \(0.549316\pi\)
\(230\) 1.34033 + 2.32151i 0.0883785 + 0.153076i
\(231\) 0 0
\(232\) −2.43852 + 4.22364i −0.160097 + 0.277295i
\(233\) −17.9944 + 10.3891i −1.17885 + 0.680611i −0.955749 0.294184i \(-0.904952\pi\)
−0.223104 + 0.974795i \(0.571619\pi\)
\(234\) 0 0
\(235\) −6.20298 + 10.7439i −0.404638 + 0.700853i
\(236\) 8.96932 0.583853
\(237\) 0 0
\(238\) −2.31873 + 1.21226i −0.150301 + 0.0785789i
\(239\) −23.6739 + 13.6681i −1.53134 + 0.884119i −0.532039 + 0.846720i \(0.678574\pi\)
−0.999300 + 0.0373991i \(0.988093\pi\)
\(240\) 0 0
\(241\) −18.4688 + 10.6630i −1.18968 + 0.686861i −0.958234 0.285987i \(-0.907679\pi\)
−0.231445 + 0.972848i \(0.574345\pi\)
\(242\) 1.06444 + 0.614556i 0.0684250 + 0.0395052i
\(243\) 0 0
\(244\) 3.06218i 0.196036i
\(245\) 21.3468 + 1.79179i 1.36380 + 0.114473i
\(246\) 0 0
\(247\) −2.98580 + 5.17155i −0.189982 + 0.329058i
\(248\) 0.543692 0.0345245
\(249\) 0 0
\(250\) 0.570839i 0.0361030i
\(251\) 26.7381 1.68769 0.843847 0.536584i \(-0.180286\pi\)
0.843847 + 0.536584i \(0.180286\pi\)
\(252\) 0 0
\(253\) −11.6144 −0.730193
\(254\) 0.807815i 0.0506868i
\(255\) 0 0
\(256\) 9.52977 0.595611
\(257\) 1.52640 2.64380i 0.0952140 0.164916i −0.814484 0.580186i \(-0.802980\pi\)
0.909698 + 0.415271i \(0.136313\pi\)
\(258\) 0 0
\(259\) 20.5868 + 0.862480i 1.27920 + 0.0535919i
\(260\) 13.7229i 0.851058i
\(261\) 0 0
\(262\) 1.90319 + 1.09881i 0.117580 + 0.0678847i
\(263\) −14.0447 + 8.10868i −0.866030 + 0.500003i −0.866027 0.499997i \(-0.833334\pi\)
−3.24009e−6 1.00000i \(0.500001\pi\)
\(264\) 0 0
\(265\) 15.2842 8.82433i 0.938901 0.542074i
\(266\) −1.97964 0.0829370i −0.121380 0.00508519i
\(267\) 0 0
\(268\) 3.01525 0.184186
\(269\) −0.303255 + 0.525254i −0.0184898 + 0.0320253i −0.875122 0.483902i \(-0.839219\pi\)
0.856632 + 0.515927i \(0.172552\pi\)
\(270\) 0 0
\(271\) 19.8948 11.4863i 1.20852 0.697742i 0.246088 0.969248i \(-0.420855\pi\)
0.962437 + 0.271505i \(0.0875215\pi\)
\(272\) 5.87120 10.1692i 0.355994 0.616599i
\(273\) 0 0
\(274\) 1.79389 + 3.10711i 0.108373 + 0.187708i
\(275\) −14.7303 8.50455i −0.888271 0.512844i
\(276\) 0 0
\(277\) −6.64173 11.5038i −0.399063 0.691197i 0.594548 0.804060i \(-0.297331\pi\)
−0.993611 + 0.112863i \(0.963998\pi\)
\(278\) −1.95965 3.39421i −0.117532 0.203571i
\(279\) 0 0
\(280\) 8.25228 4.31437i 0.493168 0.257833i
\(281\) −5.68377 3.28153i −0.339065 0.195759i 0.320793 0.947149i \(-0.396050\pi\)
−0.659859 + 0.751390i \(0.729384\pi\)
\(282\) 0 0
\(283\) 2.97234i 0.176687i 0.996090 + 0.0883437i \(0.0281574\pi\)
−0.996090 + 0.0883437i \(0.971843\pi\)
\(284\) 26.0508i 1.54583i
\(285\) 0 0
\(286\) −2.32371 1.34160i −0.137404 0.0793303i
\(287\) 16.5340 + 0.692689i 0.975970 + 0.0408882i
\(288\) 0 0
\(289\) 2.83753 + 4.91475i 0.166914 + 0.289103i
\(290\) −1.90680 3.30267i −0.111971 0.193940i
\(291\) 0 0
\(292\) −1.63894 0.946243i −0.0959118 0.0553747i
\(293\) −3.03087 5.24962i −0.177065 0.306686i 0.763809 0.645443i \(-0.223327\pi\)
−0.940874 + 0.338756i \(0.889994\pi\)
\(294\) 0 0
\(295\) −7.17181 + 12.4219i −0.417559 + 0.723234i
\(296\) 7.75686 4.47843i 0.450858 0.260303i
\(297\) 0 0
\(298\) −1.24505 + 2.15649i −0.0721239 + 0.124922i
\(299\) 6.98477 0.403940
\(300\) 0 0
\(301\) 5.05500 + 9.66892i 0.291366 + 0.557307i
\(302\) −0.854235 + 0.493193i −0.0491557 + 0.0283801i
\(303\) 0 0
\(304\) 7.70076 4.44604i 0.441669 0.254998i
\(305\) −4.24092 2.44850i −0.242834 0.140201i
\(306\) 0 0
\(307\) 21.6030i 1.23295i −0.787375 0.616474i \(-0.788561\pi\)
0.787375 0.616474i \(-0.211439\pi\)
\(308\) −0.825775 + 19.7106i −0.0470529 + 1.12312i
\(309\) 0 0
\(310\) −0.212570 + 0.368182i −0.0120732 + 0.0209113i
\(311\) −11.0234 −0.625081 −0.312540 0.949905i \(-0.601180\pi\)
−0.312540 + 0.949905i \(0.601180\pi\)
\(312\) 0 0
\(313\) 13.5542i 0.766129i 0.923722 + 0.383064i \(0.125131\pi\)
−0.923722 + 0.383064i \(0.874869\pi\)
\(314\) 4.91012 0.277094
\(315\) 0 0
\(316\) −17.7551 −0.998800
\(317\) 11.1541i 0.626479i 0.949674 + 0.313240i \(0.101414\pi\)
−0.949674 + 0.313240i \(0.898586\pi\)
\(318\) 0 0
\(319\) 16.5231 0.925118
\(320\) −9.18282 + 15.9051i −0.513335 + 0.889123i
\(321\) 0 0
\(322\) 1.07375 + 2.05380i 0.0598377 + 0.114454i
\(323\) 8.57595i 0.477179i
\(324\) 0 0
\(325\) 8.85862 + 5.11453i 0.491388 + 0.283703i
\(326\) −6.44706 + 3.72221i −0.357070 + 0.206154i
\(327\) 0 0
\(328\) 6.22982 3.59679i 0.343984 0.198599i
\(329\) −5.74688 + 9.05598i −0.316836 + 0.499272i
\(330\) 0 0
\(331\) −19.0202 −1.04544 −0.522722 0.852503i \(-0.675083\pi\)
−0.522722 + 0.852503i \(0.675083\pi\)
\(332\) −10.5128 + 18.2087i −0.576964 + 0.999331i
\(333\) 0 0
\(334\) 0.445794 0.257379i 0.0243927 0.0140832i
\(335\) −2.41098 + 4.17593i −0.131726 + 0.228156i
\(336\) 0 0
\(337\) 3.32635 + 5.76140i 0.181198 + 0.313843i 0.942289 0.334802i \(-0.108669\pi\)
−0.761091 + 0.648645i \(0.775336\pi\)
\(338\) −1.91103 1.10333i −0.103946 0.0600134i
\(339\) 0 0
\(340\) 9.85390 + 17.0675i 0.534403 + 0.925613i
\(341\) −0.921000 1.59522i −0.0498749 0.0863859i
\(342\) 0 0
\(343\) 18.3743 + 2.32024i 0.992121 + 0.125281i
\(344\) 4.10738 + 2.37140i 0.221455 + 0.127857i
\(345\) 0 0
\(346\) 7.03128i 0.378004i
\(347\) 26.6501i 1.43065i −0.698792 0.715325i \(-0.746279\pi\)
0.698792 0.715325i \(-0.253721\pi\)
\(348\) 0 0
\(349\) −20.5135 11.8435i −1.09806 0.633966i −0.162350 0.986733i \(-0.551907\pi\)
−0.935711 + 0.352768i \(0.885241\pi\)
\(350\) −0.142067 + 3.39104i −0.00759380 + 0.181258i
\(351\) 0 0
\(352\) 6.47905 + 11.2221i 0.345335 + 0.598137i
\(353\) −2.29422 3.97371i −0.122109 0.211499i 0.798490 0.602008i \(-0.205632\pi\)
−0.920599 + 0.390509i \(0.872299\pi\)
\(354\) 0 0
\(355\) −36.0788 20.8301i −1.91486 1.10555i
\(356\) 4.13057 + 7.15435i 0.218920 + 0.379180i
\(357\) 0 0
\(358\) 3.73022 6.46094i 0.197148 0.341471i
\(359\) 5.30942 3.06540i 0.280221 0.161785i −0.353303 0.935509i \(-0.614941\pi\)
0.633523 + 0.773724i \(0.281608\pi\)
\(360\) 0 0
\(361\) −6.25288 + 10.8303i −0.329099 + 0.570016i
\(362\) 6.58363 0.346028
\(363\) 0 0
\(364\) 0.496610 11.8537i 0.0260294 0.621303i
\(365\) 2.62097 1.51322i 0.137188 0.0792056i
\(366\) 0 0
\(367\) 22.8860 13.2132i 1.19464 0.689725i 0.235283 0.971927i \(-0.424398\pi\)
0.959355 + 0.282202i \(0.0910650\pi\)
\(368\) −9.00732 5.20038i −0.469539 0.271088i
\(369\) 0 0
\(370\) 7.00381i 0.364111i
\(371\) 13.5217 7.06926i 0.702011 0.367018i
\(372\) 0 0
\(373\) −10.0581 + 17.4211i −0.520789 + 0.902033i 0.478919 + 0.877859i \(0.341029\pi\)
−0.999708 + 0.0241735i \(0.992305\pi\)
\(374\) 3.85340 0.199255
\(375\) 0 0
\(376\) 4.66236i 0.240443i
\(377\) −9.93679 −0.511771
\(378\) 0 0
\(379\) −17.4561 −0.896660 −0.448330 0.893868i \(-0.647981\pi\)
−0.448330 + 0.893868i \(0.647981\pi\)
\(380\) 14.9240i 0.765584i
\(381\) 0 0
\(382\) −1.26039 −0.0644872
\(383\) 14.0317 24.3036i 0.716985 1.24185i −0.245204 0.969471i \(-0.578855\pi\)
0.962189 0.272383i \(-0.0878117\pi\)
\(384\) 0 0
\(385\) −26.6377 16.9041i −1.35758 0.861515i
\(386\) 6.86037i 0.349183i
\(387\) 0 0
\(388\) 9.54517 + 5.51091i 0.484583 + 0.279774i
\(389\) 29.6520 17.1196i 1.50342 0.867999i 0.503426 0.864038i \(-0.332072\pi\)
0.999992 0.00396103i \(-0.00126084\pi\)
\(390\) 0 0
\(391\) −8.68710 + 5.01550i −0.439325 + 0.253645i
\(392\) 7.28437 3.42807i 0.367916 0.173144i
\(393\) 0 0
\(394\) 5.51918 0.278052
\(395\) 14.1968 24.5896i 0.714320 1.23724i
\(396\) 0 0
\(397\) −11.2926 + 6.51981i −0.566762 + 0.327220i −0.755855 0.654739i \(-0.772778\pi\)
0.189093 + 0.981959i \(0.439445\pi\)
\(398\) 0.666662 1.15469i 0.0334167 0.0578795i
\(399\) 0 0
\(400\) −7.61585 13.1910i −0.380792 0.659552i
\(401\) 15.8943 + 9.17659i 0.793725 + 0.458257i 0.841272 0.540612i \(-0.181807\pi\)
−0.0475475 + 0.998869i \(0.515141\pi\)
\(402\) 0 0
\(403\) 0.553877 + 0.959344i 0.0275906 + 0.0477883i
\(404\) −16.4171 28.4353i −0.816782 1.41471i
\(405\) 0 0
\(406\) −1.52756 2.92182i −0.0758113 0.145007i
\(407\) −26.2798 15.1727i −1.30264 0.752081i
\(408\) 0 0
\(409\) 6.46786i 0.319815i −0.987132 0.159907i \(-0.948880\pi\)
0.987132 0.159907i \(-0.0511196\pi\)
\(410\) 5.62501i 0.277800i
\(411\) 0 0
\(412\) 16.2740 + 9.39581i 0.801764 + 0.462899i
\(413\) −6.64448 + 10.4704i −0.326953 + 0.515216i
\(414\) 0 0
\(415\) −16.8119 29.1191i −0.825265 1.42940i
\(416\) −3.89642 6.74880i −0.191038 0.330887i
\(417\) 0 0
\(418\) 2.52709 + 1.45902i 0.123604 + 0.0713629i
\(419\) −7.11542 12.3243i −0.347611 0.602080i 0.638214 0.769859i \(-0.279674\pi\)
−0.985825 + 0.167779i \(0.946340\pi\)
\(420\) 0 0
\(421\) 15.1718 26.2784i 0.739429 1.28073i −0.213324 0.976982i \(-0.568429\pi\)
0.952753 0.303747i \(-0.0982378\pi\)
\(422\) 1.75170 1.01135i 0.0852716 0.0492316i
\(423\) 0 0
\(424\) 3.31633 5.74405i 0.161055 0.278956i
\(425\) −14.6902 −0.712579
\(426\) 0 0
\(427\) −3.57466 2.26846i −0.172990 0.109779i
\(428\) 5.75051 3.32006i 0.277962 0.160481i
\(429\) 0 0
\(430\) −3.21177 + 1.85432i −0.154885 + 0.0894230i
\(431\) 2.12663 + 1.22781i 0.102436 + 0.0591415i 0.550343 0.834939i \(-0.314497\pi\)
−0.447907 + 0.894080i \(0.647830\pi\)
\(432\) 0 0
\(433\) 12.4545i 0.598525i 0.954171 + 0.299262i \(0.0967406\pi\)
−0.954171 + 0.299262i \(0.903259\pi\)
\(434\) −0.196940 + 0.310340i −0.00945342 + 0.0148968i
\(435\) 0 0
\(436\) 1.16936 2.02539i 0.0560022 0.0969987i
\(437\) −7.59610 −0.363371
\(438\) 0 0
\(439\) 17.5300i 0.836663i 0.908294 + 0.418331i \(0.137385\pi\)
−0.908294 + 0.418331i \(0.862615\pi\)
\(440\) −13.7141 −0.653794
\(441\) 0 0
\(442\) −2.31739 −0.110227
\(443\) 9.00464i 0.427824i −0.976853 0.213912i \(-0.931379\pi\)
0.976853 0.213912i \(-0.0686205\pi\)
\(444\) 0 0
\(445\) −13.2111 −0.626266
\(446\) −0.945337 + 1.63737i −0.0447630 + 0.0775318i
\(447\) 0 0
\(448\) −8.50761 + 13.4064i −0.401947 + 0.633392i
\(449\) 30.8120i 1.45411i 0.686581 + 0.727054i \(0.259111\pi\)
−0.686581 + 0.727054i \(0.740889\pi\)
\(450\) 0 0
\(451\) −21.1063 12.1857i −0.993856 0.573803i
\(452\) 3.59154 2.07357i 0.168932 0.0975327i
\(453\) 0 0
\(454\) −5.02371 + 2.90044i −0.235775 + 0.136125i
\(455\) 16.0196 + 10.1659i 0.751009 + 0.476586i
\(456\) 0 0
\(457\) 13.8286 0.646874 0.323437 0.946250i \(-0.395162\pi\)
0.323437 + 0.946250i \(0.395162\pi\)
\(458\) −1.60260 + 2.77578i −0.0748846 + 0.129704i
\(459\) 0 0
\(460\) 15.1174 8.72803i 0.704852 0.406947i
\(461\) −6.16989 + 10.6866i −0.287360 + 0.497723i −0.973179 0.230050i \(-0.926111\pi\)
0.685818 + 0.727773i \(0.259444\pi\)
\(462\) 0 0
\(463\) 6.37802 + 11.0471i 0.296412 + 0.513401i 0.975312 0.220830i \(-0.0708765\pi\)
−0.678900 + 0.734230i \(0.737543\pi\)
\(464\) 12.8141 + 7.39825i 0.594882 + 0.343455i
\(465\) 0 0
\(466\) −3.05303 5.28801i −0.141429 0.244962i
\(467\) 5.48999 + 9.50894i 0.254046 + 0.440021i 0.964636 0.263585i \(-0.0849051\pi\)
−0.710590 + 0.703607i \(0.751572\pi\)
\(468\) 0 0
\(469\) −2.23370 + 3.51988i −0.103143 + 0.162533i
\(470\) −3.15730 1.82287i −0.145635 0.0840825i
\(471\) 0 0
\(472\) 5.39057i 0.248121i
\(473\) 16.0683i 0.738823i
\(474\) 0 0
\(475\) −9.63396 5.56217i −0.442036 0.255210i
\(476\) 7.89406 + 15.0993i 0.361824 + 0.692075i
\(477\) 0 0
\(478\) −4.01665 6.95704i −0.183717 0.318208i
\(479\) 5.59729 + 9.69478i 0.255747 + 0.442966i 0.965098 0.261889i \(-0.0843454\pi\)
−0.709351 + 0.704855i \(0.751012\pi\)
\(480\) 0 0
\(481\) 15.8043 + 9.12464i 0.720616 + 0.416048i
\(482\) −3.13352 5.42741i −0.142728 0.247212i
\(483\) 0 0
\(484\) 4.00191 6.93152i 0.181905 0.315069i
\(485\) −15.2645 + 8.81298i −0.693126 + 0.400177i
\(486\) 0 0
\(487\) −1.48332 + 2.56919i −0.0672158 + 0.116421i −0.897675 0.440659i \(-0.854745\pi\)
0.830459 + 0.557080i \(0.188078\pi\)
\(488\) −1.84037 −0.0833097
\(489\) 0 0
\(490\) −0.526553 + 6.27318i −0.0237872 + 0.283393i
\(491\) 20.1795 11.6507i 0.910690 0.525787i 0.0300367 0.999549i \(-0.490438\pi\)
0.880653 + 0.473762i \(0.157104\pi\)
\(492\) 0 0
\(493\) 12.3586 7.13524i 0.556603 0.321355i
\(494\) −1.51976 0.877435i −0.0683773 0.0394776i
\(495\) 0 0
\(496\) 1.64952i 0.0740654i
\(497\) −30.4107 19.2985i −1.36411 0.865654i
\(498\) 0 0
\(499\) 2.29296 3.97152i 0.102647 0.177790i −0.810127 0.586254i \(-0.800602\pi\)
0.912774 + 0.408464i \(0.133935\pi\)
\(500\) −3.71723 −0.166240
\(501\) 0 0
\(502\) 7.85751i 0.350698i
\(503\) 23.1383 1.03169 0.515844 0.856683i \(-0.327479\pi\)
0.515844 + 0.856683i \(0.327479\pi\)
\(504\) 0 0
\(505\) 52.5081 2.33658
\(506\) 3.41313i 0.151732i
\(507\) 0 0
\(508\) 5.26039 0.233392
\(509\) −4.82853 + 8.36326i −0.214021 + 0.370695i −0.952969 0.303067i \(-0.901989\pi\)
0.738948 + 0.673762i \(0.235323\pi\)
\(510\) 0 0
\(511\) 2.31873 1.21226i 0.102575 0.0536271i
\(512\) 19.6301i 0.867536i
\(513\) 0 0
\(514\) 0.776931 + 0.448561i 0.0342690 + 0.0197852i
\(515\) −26.0252 + 15.0257i −1.14681 + 0.662110i
\(516\) 0 0
\(517\) 13.6796 7.89791i 0.601627 0.347350i
\(518\) −0.253457 + 6.04982i −0.0111362 + 0.265814i
\(519\) 0 0
\(520\) 8.24748 0.361676
\(521\) −5.00035 + 8.66086i −0.219069 + 0.379439i −0.954524 0.298135i \(-0.903635\pi\)
0.735454 + 0.677574i \(0.236969\pi\)
\(522\) 0 0
\(523\) −10.7796 + 6.22361i −0.471359 + 0.272139i −0.716809 0.697270i \(-0.754398\pi\)
0.245449 + 0.969409i \(0.421065\pi\)
\(524\) 7.15531 12.3934i 0.312581 0.541406i
\(525\) 0 0
\(526\) −2.38289 4.12729i −0.103899 0.179959i
\(527\) −1.37774 0.795437i −0.0600152 0.0346498i
\(528\) 0 0
\(529\) −7.05755 12.2240i −0.306850 0.531480i
\(530\) 2.59320 + 4.49156i 0.112641 + 0.195101i
\(531\) 0 0
\(532\) −0.540075 + 12.8912i −0.0234152 + 0.558904i
\(533\) 12.6930 + 7.32833i 0.549797 + 0.317425i
\(534\) 0 0
\(535\) 10.6188i 0.459091i
\(536\) 1.81217i 0.0782737i
\(537\) 0 0
\(538\) −0.154356 0.0891175i −0.00665476 0.00384213i
\(539\) −22.3977 15.5656i −0.964735 0.670458i
\(540\) 0 0
\(541\) 6.96514 + 12.0640i 0.299455 + 0.518671i 0.976011 0.217720i \(-0.0698619\pi\)
−0.676557 + 0.736391i \(0.736529\pi\)
\(542\) 3.37547 + 5.84648i 0.144989 + 0.251128i
\(543\) 0 0
\(544\) 9.69211 + 5.59574i 0.415546 + 0.239916i
\(545\) 1.87003 + 3.23898i 0.0801032 + 0.138743i
\(546\) 0 0
\(547\) −21.6768 + 37.5454i −0.926834 + 1.60532i −0.138250 + 0.990397i \(0.544148\pi\)
−0.788584 + 0.614926i \(0.789186\pi\)
\(548\) 20.2331 11.6816i 0.864316 0.499013i
\(549\) 0 0
\(550\) 2.49923 4.32879i 0.106567 0.184580i
\(551\) 10.8065 0.460372
\(552\) 0 0
\(553\) 13.1529 20.7265i 0.559320 0.881382i
\(554\) 3.38062 1.95180i 0.143629 0.0829241i
\(555\) 0 0
\(556\) −22.1026 + 12.7610i −0.937361 + 0.541186i
\(557\) 31.1339 + 17.9752i 1.31919 + 0.761632i 0.983598 0.180377i \(-0.0577317\pi\)
0.335588 + 0.942009i \(0.391065\pi\)
\(558\) 0 0
\(559\) 9.66329i 0.408714i
\(560\) −13.0894 25.0367i −0.553129 1.05799i
\(561\) 0 0
\(562\) 0.964340 1.67029i 0.0406782 0.0704568i
\(563\) −6.11108 −0.257551 −0.128776 0.991674i \(-0.541105\pi\)
−0.128776 + 0.991674i \(0.541105\pi\)
\(564\) 0 0
\(565\) 6.63207i 0.279013i
\(566\) −0.873481 −0.0367151
\(567\) 0 0
\(568\) −15.6566 −0.656935
\(569\) 19.3045i 0.809285i −0.914475 0.404642i \(-0.867396\pi\)
0.914475 0.404642i \(-0.132604\pi\)
\(570\) 0 0
\(571\) 12.7224 0.532415 0.266207 0.963916i \(-0.414229\pi\)
0.266207 + 0.963916i \(0.414229\pi\)
\(572\) −8.73631 + 15.1317i −0.365284 + 0.632690i
\(573\) 0 0
\(574\) −0.203560 + 4.85883i −0.00849644 + 0.202804i
\(575\) 13.0118i 0.542628i
\(576\) 0 0
\(577\) 7.05520 + 4.07332i 0.293712 + 0.169575i 0.639615 0.768696i \(-0.279094\pi\)
−0.345903 + 0.938270i \(0.612427\pi\)
\(578\) −1.44429 + 0.833863i −0.0600747 + 0.0346841i
\(579\) 0 0
\(580\) −21.5066 + 12.4168i −0.893012 + 0.515581i
\(581\) −13.4682 25.7612i −0.558755 1.06875i
\(582\) 0 0
\(583\) −22.4711 −0.930657
\(584\) 0.568693 0.985005i 0.0235327 0.0407598i
\(585\) 0 0
\(586\) 1.54270 0.890680i 0.0637285 0.0367937i
\(587\) −12.3041 + 21.3113i −0.507843 + 0.879610i 0.492116 + 0.870530i \(0.336224\pi\)
−0.999959 + 0.00908019i \(0.997110\pi\)
\(588\) 0 0
\(589\) −0.602354 1.04331i −0.0248196 0.0429888i
\(590\) −3.65043 2.10758i −0.150286 0.0867676i
\(591\) 0 0
\(592\) −13.5872 23.5336i −0.558429 0.967227i
\(593\) 18.9321 + 32.7913i 0.777447 + 1.34658i 0.933409 + 0.358814i \(0.116819\pi\)
−0.155962 + 0.987763i \(0.549848\pi\)
\(594\) 0 0
\(595\) −27.2236 1.14053i −1.11606 0.0467572i
\(596\) 14.0428 + 8.10762i 0.575216 + 0.332101i
\(597\) 0 0
\(598\) 2.05261i 0.0839375i
\(599\) 10.6529i 0.435268i 0.976030 + 0.217634i \(0.0698339\pi\)
−0.976030 + 0.217634i \(0.930166\pi\)
\(600\) 0 0
\(601\) 39.8636 + 23.0153i 1.62607 + 0.938812i 0.985250 + 0.171122i \(0.0547391\pi\)
0.640821 + 0.767691i \(0.278594\pi\)
\(602\) −2.84140 + 1.48551i −0.115807 + 0.0605449i
\(603\) 0 0
\(604\) 3.21161 + 5.56267i 0.130679 + 0.226342i
\(605\) 6.39981 + 11.0848i 0.260189 + 0.450661i
\(606\) 0 0
\(607\) 3.74063 + 2.15965i 0.151827 + 0.0876576i 0.573989 0.818863i \(-0.305395\pi\)
−0.422162 + 0.906521i \(0.638729\pi\)
\(608\) 4.23745 + 7.33947i 0.171851 + 0.297655i
\(609\) 0 0
\(610\) 0.719539 1.24628i 0.0291333 0.0504603i
\(611\) −8.22672 + 4.74970i −0.332818 + 0.192152i
\(612\) 0 0
\(613\) 14.3838 24.9135i 0.580956 1.00624i −0.414411 0.910090i \(-0.636012\pi\)
0.995366 0.0961549i \(-0.0306544\pi\)
\(614\) 6.34846 0.256203
\(615\) 0 0
\(616\) −11.8461 0.496291i −0.477293 0.0199961i
\(617\) −0.935498 + 0.540110i −0.0376617 + 0.0217440i −0.518713 0.854949i \(-0.673589\pi\)
0.481051 + 0.876693i \(0.340255\pi\)
\(618\) 0 0
\(619\) −6.57128 + 3.79393i −0.264122 + 0.152491i −0.626214 0.779652i \(-0.715396\pi\)
0.362091 + 0.932143i \(0.382063\pi\)
\(620\) 2.39755 + 1.38423i 0.0962881 + 0.0555920i
\(621\) 0 0
\(622\) 3.23944i 0.129890i
\(623\) −11.4116 0.478089i −0.457197 0.0191542i
\(624\) 0 0
\(625\) 13.8854 24.0502i 0.555416 0.962010i
\(626\) −3.98316 −0.159199
\(627\) 0 0
\(628\) 31.9741i 1.27591i
\(629\) −26.2082 −1.04499
\(630\) 0 0
\(631\) 35.0387 1.39487 0.697435 0.716648i \(-0.254325\pi\)
0.697435 + 0.716648i \(0.254325\pi\)
\(632\) 10.6708i 0.424462i
\(633\) 0 0
\(634\) −3.27786 −0.130181
\(635\) −4.20618 + 7.28531i −0.166917 + 0.289109i
\(636\) 0 0
\(637\) 13.4697 + 9.36096i 0.533687 + 0.370895i
\(638\) 4.85564i 0.192237i
\(639\) 0 0
\(640\) −22.3015 12.8758i −0.881544 0.508960i
\(641\) −26.9229 + 15.5439i −1.06339 + 0.613949i −0.926368 0.376619i \(-0.877087\pi\)
−0.137023 + 0.990568i \(0.543753\pi\)
\(642\) 0 0
\(643\) 0.977928 0.564607i 0.0385657 0.0222659i −0.480593 0.876944i \(-0.659579\pi\)
0.519159 + 0.854678i \(0.326245\pi\)
\(644\) 13.3741 6.99212i 0.527014 0.275528i
\(645\) 0 0
\(646\) 2.52021 0.0991564
\(647\) 13.5992 23.5545i 0.534640 0.926023i −0.464541 0.885552i \(-0.653781\pi\)
0.999181 0.0404713i \(-0.0128859\pi\)
\(648\) 0 0
\(649\) 15.8162 9.13148i 0.620839 0.358442i
\(650\) −1.50300 + 2.60328i −0.0589526 + 0.102109i
\(651\) 0 0
\(652\) 24.2386 + 41.9824i 0.949256 + 1.64416i
\(653\) 19.3030 + 11.1446i 0.755384 + 0.436121i 0.827636 0.561265i \(-0.189685\pi\)
−0.0722517 + 0.997386i \(0.523019\pi\)
\(654\) 0 0
\(655\) 11.4427 + 19.8193i 0.447102 + 0.774404i
\(656\) −10.9123 18.9007i −0.426055 0.737949i
\(657\) 0 0
\(658\) −2.66128 1.68883i −0.103747 0.0658375i
\(659\) 7.69208 + 4.44103i 0.299641 + 0.172998i 0.642282 0.766469i \(-0.277988\pi\)
−0.342641 + 0.939467i \(0.611321\pi\)
\(660\) 0 0
\(661\) 19.3670i 0.753291i 0.926358 + 0.376645i \(0.122922\pi\)
−0.926358 + 0.376645i \(0.877078\pi\)
\(662\) 5.58945i 0.217240i
\(663\) 0 0
\(664\) −10.9434 6.31819i −0.424687 0.245193i
\(665\) −17.4216 11.0557i −0.675583 0.428721i
\(666\) 0 0
\(667\) −6.31999 10.9465i −0.244711 0.423852i
\(668\) −1.67602 2.90295i −0.0648472 0.112319i
\(669\) 0 0
\(670\) −1.22718 0.708512i −0.0474101 0.0273722i
\(671\) 3.11754 + 5.39973i 0.120351 + 0.208454i
\(672\) 0 0
\(673\) 11.5828 20.0620i 0.446484 0.773333i −0.551670 0.834062i \(-0.686009\pi\)
0.998154 + 0.0607292i \(0.0193426\pi\)
\(674\) −1.69310 + 0.977511i −0.0652157 + 0.0376523i
\(675\) 0 0
\(676\) −7.18476 + 12.4444i −0.276337 + 0.478630i
\(677\) −3.12693 −0.120177 −0.0600887 0.998193i \(-0.519138\pi\)
−0.0600887 + 0.998193i \(0.519138\pi\)
\(678\) 0 0
\(679\) −13.5043 + 7.06017i −0.518247 + 0.270944i
\(680\) −10.2576 + 5.92220i −0.393359 + 0.227106i
\(681\) 0 0
\(682\) 0.468786 0.270654i 0.0179507 0.0103639i
\(683\) 27.1966 + 15.7020i 1.04065 + 0.600819i 0.920017 0.391878i \(-0.128175\pi\)
0.120632 + 0.992697i \(0.461508\pi\)
\(684\) 0 0
\(685\) 37.3621i 1.42753i
\(686\) −0.681848 + 5.39966i −0.0260331 + 0.206160i
\(687\) 0 0
\(688\) 7.19462 12.4614i 0.274292 0.475088i
\(689\) 13.5138 0.514835
\(690\) 0 0
\(691\) 44.1739i 1.68045i −0.542235 0.840227i \(-0.682422\pi\)
0.542235 0.840227i \(-0.317578\pi\)
\(692\) −45.7868 −1.74055
\(693\) 0 0
\(694\) 7.83164 0.297285
\(695\) 40.8144i 1.54818i
\(696\) 0 0
\(697\) −21.0488 −0.797280
\(698\) 3.48043 6.02828i 0.131736 0.228174i
\(699\) 0 0
\(700\) 22.0820 + 0.925123i 0.834621 + 0.0349664i
\(701\) 9.69906i 0.366328i −0.983082 0.183164i \(-0.941366\pi\)
0.983082 0.183164i \(-0.0586340\pi\)
\(702\) 0 0
\(703\) −17.1876 9.92326i −0.648242 0.374263i
\(704\) 20.2511 11.6920i 0.763242 0.440658i
\(705\) 0 0
\(706\) 1.16775 0.674202i 0.0439490 0.0253739i
\(707\) 45.3560 + 1.90019i 1.70579 + 0.0714638i
\(708\) 0 0
\(709\) −1.09786 −0.0412311 −0.0206156 0.999787i \(-0.506563\pi\)
−0.0206156 + 0.999787i \(0.506563\pi\)
\(710\) 6.12132 10.6024i 0.229729 0.397903i
\(711\) 0 0
\(712\) −4.29977 + 2.48247i −0.161141 + 0.0930346i
\(713\) −0.704553 + 1.22032i −0.0263857 + 0.0457014i
\(714\) 0 0
\(715\) −13.9710 24.1985i −0.522486 0.904972i
\(716\) −42.0728 24.2908i −1.57233 0.907788i
\(717\) 0 0
\(718\) 0.900826 + 1.56028i 0.0336185 + 0.0582290i
\(719\) −11.3648 19.6844i −0.423835 0.734103i 0.572476 0.819921i \(-0.305983\pi\)
−0.996311 + 0.0858183i \(0.972650\pi\)
\(720\) 0 0
\(721\) −23.0241 + 12.0372i −0.857462 + 0.448289i
\(722\) −3.18269 1.83753i −0.118448 0.0683858i
\(723\) 0 0
\(724\) 42.8718i 1.59332i
\(725\) 18.5110i 0.687482i
\(726\) 0 0
\(727\) −3.47919 2.00871i −0.129036 0.0744990i 0.434093 0.900868i \(-0.357069\pi\)
−0.563129 + 0.826369i \(0.690402\pi\)
\(728\) 7.12409 + 0.298463i 0.264036 + 0.0110618i
\(729\) 0 0
\(730\) 0.444689 + 0.770224i 0.0164587 + 0.0285073i
\(731\) −6.93885 12.0184i −0.256643 0.444518i
\(732\) 0 0
\(733\) −7.20188 4.15801i −0.266008 0.153580i 0.361064 0.932541i \(-0.382413\pi\)
−0.627072 + 0.778961i \(0.715747\pi\)
\(734\) 3.88296 + 6.72549i 0.143323 + 0.248242i
\(735\) 0 0
\(736\) 4.95640 8.58473i 0.182695 0.316437i
\(737\) 5.31698 3.06976i 0.195854 0.113076i
\(738\) 0 0
\(739\) −2.28507 + 3.95785i −0.0840576 + 0.145592i −0.904989 0.425434i \(-0.860121\pi\)
0.820932 + 0.571026i \(0.193455\pi\)
\(740\) 45.6079 1.67658
\(741\) 0 0
\(742\) 2.07744 + 3.97361i 0.0762653 + 0.145876i
\(743\) −1.51258 + 0.873286i −0.0554910 + 0.0320378i −0.527489 0.849562i \(-0.676866\pi\)
0.471998 + 0.881600i \(0.343533\pi\)
\(744\) 0 0
\(745\) −22.4571 + 12.9656i −0.822764 + 0.475023i
\(746\) −5.11954 2.95577i −0.187440 0.108218i
\(747\) 0 0
\(748\) 25.0929i 0.917486i
\(749\) −0.384277 + 9.17242i −0.0140412 + 0.335153i
\(750\) 0 0
\(751\) −2.91647 + 5.05147i −0.106423 + 0.184331i −0.914319 0.404995i \(-0.867273\pi\)
0.807895 + 0.589326i \(0.200607\pi\)
\(752\) 14.1452 0.515822
\(753\) 0 0
\(754\) 2.92012i 0.106345i
\(755\) −10.2719 −0.373834
\(756\) 0 0
\(757\) −42.0967 −1.53003 −0.765015 0.644013i \(-0.777268\pi\)
−0.765015 + 0.644013i \(0.777268\pi\)
\(758\) 5.12982i 0.186323i
\(759\) 0 0
\(760\) −8.96932 −0.325352
\(761\) −0.293431 + 0.508238i −0.0106369 + 0.0184236i −0.871295 0.490760i \(-0.836719\pi\)
0.860658 + 0.509184i \(0.170053\pi\)
\(762\) 0 0
\(763\) 1.49810 + 2.86547i 0.0542348 + 0.103737i
\(764\) 8.20750i 0.296937i
\(765\) 0 0
\(766\) 7.14208 + 4.12348i 0.258054 + 0.148987i
\(767\) −9.51165 + 5.49155i −0.343446 + 0.198288i
\(768\) 0 0
\(769\) −45.1905 + 26.0907i −1.62961 + 0.940856i −0.645403 + 0.763843i \(0.723310\pi\)
−0.984208 + 0.177014i \(0.943356\pi\)
\(770\) 4.96761 7.82800i 0.179020 0.282102i
\(771\) 0 0
\(772\) −44.6738 −1.60785
\(773\) 16.3906 28.3894i 0.589530 1.02110i −0.404764 0.914421i \(-0.632646\pi\)
0.994294 0.106674i \(-0.0340202\pi\)
\(774\) 0 0
\(775\) −1.78714 + 1.03180i −0.0641959 + 0.0370635i
\(776\) −3.31206 + 5.73666i −0.118896 + 0.205934i
\(777\) 0 0
\(778\) 5.03093 + 8.71383i 0.180368 + 0.312406i
\(779\) −13.8040 7.96973i −0.494579 0.285545i
\(780\) 0 0
\(781\) 26.5218 + 45.9371i 0.949024 + 1.64376i
\(782\) −1.47390 2.55287i −0.0527066 0.0912906i
\(783\) 0 0
\(784\) −10.4005 22.1001i −0.371446 0.789291i
\(785\) 44.2821 + 25.5663i 1.58050 + 0.912500i
\(786\) 0 0
\(787\) 40.9934i 1.46126i −0.682775 0.730628i \(-0.739227\pi\)
0.682775 0.730628i \(-0.260773\pi\)
\(788\) 35.9402i 1.28032i
\(789\) 0 0
\(790\) 7.22614 + 4.17201i 0.257095 + 0.148434i
\(791\) −0.240004 + 5.72872i −0.00853356 + 0.203690i
\(792\) 0 0
\(793\) −1.87485 3.24733i −0.0665778 0.115316i
\(794\) −1.91597 3.31856i −0.0679954 0.117771i
\(795\) 0 0
\(796\) −7.51921 4.34122i −0.266511 0.153870i
\(797\) 17.0441 + 29.5213i 0.603734 + 1.04570i 0.992250 + 0.124256i \(0.0396544\pi\)
−0.388516 + 0.921442i \(0.627012\pi\)
\(798\) 0 0
\(799\) 6.82116 11.8146i 0.241315 0.417971i
\(800\) 12.5722 7.25854i 0.444493 0.256628i
\(801\) 0 0
\(802\) −2.69672 + 4.67086i −0.0952245 + 0.164934i
\(803\) −3.85340 −0.135984
\(804\) 0 0
\(805\) −1.01022 + 24.1132i −0.0356055 + 0.849877i
\(806\) −0.281922 + 0.162768i −0.00993027 + 0.00573324i
\(807\) 0 0
\(808\) 17.0896 9.86670i 0.601211 0.347109i
\(809\) 6.01547 + 3.47304i 0.211493 + 0.122105i 0.602005 0.798492i \(-0.294369\pi\)
−0.390512 + 0.920598i \(0.627702\pi\)
\(810\) 0 0
\(811\) 39.8573i 1.39958i 0.714350 + 0.699789i \(0.246723\pi\)
−0.714350 + 0.699789i \(0.753277\pi\)
\(812\) −19.0265 + 9.94725i −0.667700 + 0.349080i
\(813\) 0 0
\(814\) 4.45878 7.72284i 0.156280 0.270685i
\(815\) −77.5240 −2.71555
\(816\) 0 0
\(817\) 10.5091i 0.367665i
\(818\) 1.90071 0.0664566
\(819\) 0 0
\(820\) 36.6294 1.27915
\(821\) 42.1017i 1.46936i 0.678414 + 0.734680i \(0.262668\pi\)
−0.678414 + 0.734680i \(0.737332\pi\)
\(822\) 0 0
\(823\) 32.6821 1.13923 0.569614 0.821913i \(-0.307093\pi\)
0.569614 + 0.821913i \(0.307093\pi\)
\(824\) −5.64689 + 9.78070i −0.196719 + 0.340727i
\(825\) 0 0
\(826\) −3.07694 1.95261i −0.107060 0.0679399i
\(827\) 31.4399i 1.09327i −0.837370 0.546637i \(-0.815908\pi\)
0.837370 0.546637i \(-0.184092\pi\)
\(828\) 0 0
\(829\) 35.7122 + 20.6185i 1.24034 + 0.716109i 0.969163 0.246421i \(-0.0792547\pi\)
0.271174 + 0.962530i \(0.412588\pi\)
\(830\) 8.55721 4.94051i 0.297025 0.171488i
\(831\) 0 0
\(832\) −12.1788 + 7.03141i −0.422222 + 0.243770i
\(833\) −23.4742 1.97036i −0.813334 0.0682689i
\(834\) 0 0
\(835\) 5.36054 0.185509
\(836\) 9.50094 16.4561i 0.328597 0.569147i
\(837\) 0 0
\(838\) 3.62173 2.09100i 0.125110 0.0722326i
\(839\) 4.04385 7.00416i 0.139609 0.241810i −0.787740 0.616009i \(-0.788749\pi\)
0.927349 + 0.374198i \(0.122082\pi\)
\(840\) 0 0
\(841\) −5.50894 9.54177i −0.189963 0.329026i
\(842\) 7.72241 + 4.45853i 0.266132 + 0.153651i
\(843\) 0 0
\(844\) −6.58576 11.4069i −0.226691 0.392641i
\(845\) −11.4898 19.9009i −0.395260 0.684611i
\(846\) 0 0
\(847\) 5.12695 + 9.80654i 0.176164 + 0.336957i
\(848\) −17.4269 10.0615i −0.598444 0.345512i
\(849\) 0 0
\(850\) 4.31700i 0.148072i
\(851\) 23.2138i 0.795759i
\(852\) 0 0
\(853\) −24.5887 14.1963i −0.841900 0.486071i 0.0160098 0.999872i \(-0.494904\pi\)
−0.857910 + 0.513801i \(0.828237\pi\)
\(854\) 0.666631 1.05048i 0.0228117 0.0359468i
\(855\) 0 0
\(856\) 1.99536 + 3.45606i 0.0682000 + 0.118126i
\(857\) 25.6587 + 44.4422i 0.876485 + 1.51812i 0.855172 + 0.518344i \(0.173451\pi\)
0.0213132 + 0.999773i \(0.493215\pi\)
\(858\) 0 0
\(859\) 14.5234 + 8.38509i 0.495532 + 0.286096i 0.726867 0.686779i \(-0.240976\pi\)
−0.231334 + 0.972874i \(0.574309\pi\)
\(860\) 12.0751 + 20.9146i 0.411756 + 0.713183i
\(861\) 0 0
\(862\) −0.360816 + 0.624951i −0.0122894 + 0.0212859i
\(863\) 14.2380 8.22033i 0.484668 0.279823i −0.237692 0.971341i \(-0.576391\pi\)
0.722360 + 0.691517i \(0.243057\pi\)
\(864\) 0 0
\(865\) 36.6109 63.4119i 1.24481 2.15607i
\(866\) −3.66000 −0.124372
\(867\) 0 0
\(868\) 2.02089 + 1.28245i 0.0685935 + 0.0435291i
\(869\) −31.3086 + 18.0760i −1.06207 + 0.613188i
\(870\) 0 0
\(871\) −3.19757 + 1.84612i −0.108345 + 0.0625532i
\(872\) 1.21726 + 0.702787i 0.0412217 + 0.0237994i
\(873\) 0 0
\(874\) 2.23226i 0.0755074i
\(875\) 2.75373 4.33934i 0.0930929 0.146697i
\(876\) 0 0
\(877\) −3.06175 + 5.30311i −0.103388 + 0.179073i −0.913078 0.407784i \(-0.866302\pi\)
0.809690 + 0.586857i \(0.199635\pi\)
\(878\) −5.15154 −0.173856
\(879\) 0 0
\(880\) 41.6074i 1.40258i
\(881\) −41.3283 −1.39238 −0.696192 0.717855i \(-0.745124\pi\)
−0.696192 + 0.717855i \(0.745124\pi\)
\(882\) 0 0
\(883\) 24.2918 0.817483 0.408741 0.912650i \(-0.365968\pi\)
0.408741 + 0.912650i \(0.365968\pi\)
\(884\) 15.0905i 0.507549i
\(885\) 0 0
\(886\) 2.64619 0.0889005
\(887\) −3.35036 + 5.80299i −0.112494 + 0.194845i −0.916775 0.399404i \(-0.869217\pi\)
0.804281 + 0.594249i \(0.202551\pi\)
\(888\) 0 0
\(889\) −3.89690 + 6.14077i −0.130698 + 0.205955i
\(890\) 3.88234i 0.130136i
\(891\) 0 0
\(892\) 10.6624 + 6.15591i 0.357002 + 0.206115i
\(893\) 8.94675 5.16541i 0.299392 0.172854i
\(894\) 0 0
\(895\) 67.2823 38.8455i 2.24900 1.29846i
\(896\) −18.7979 11.9290i −0.627993 0.398521i
\(897\) 0 0
\(898\) −9.05470 −0.302159
\(899\) 1.00232 1.73608i 0.0334294 0.0579014i
\(900\) 0 0
\(901\) −16.8074 + 9.70376i −0.559936 + 0.323279i
\(902\) 3.58101 6.20249i 0.119235 0.206520i
\(903\) 0 0
\(904\) 1.24622 + 2.15852i 0.0414487 + 0.0717912i
\(905\) 59.3747 + 34.2800i 1.97368 + 1.13951i
\(906\) 0 0
\(907\) −10.1494 17.5793i −0.337005 0.583710i 0.646863 0.762606i \(-0.276081\pi\)
−0.983868 + 0.178897i \(0.942747\pi\)
\(908\) 18.8873 + 32.7138i 0.626798 + 1.08565i
\(909\) 0 0
\(910\) −2.98746 + 4.70766i −0.0990332 + 0.156057i
\(911\) 30.3982 + 17.5504i 1.00714 + 0.581472i 0.910353 0.413833i \(-0.135810\pi\)
0.0967861 + 0.995305i \(0.469144\pi\)
\(912\) 0 0
\(913\) 42.8114i 1.41685i
\(914\) 4.06380i 0.134419i
\(915\) 0 0
\(916\) 18.0756 + 10.4359i 0.597233 + 0.344813i
\(917\) 9.16685 + 17.5338i 0.302716 + 0.579018i
\(918\) 0 0
\(919\) −16.9132 29.2946i −0.557916 0.966339i −0.997670 0.0682206i \(-0.978268\pi\)
0.439754 0.898118i \(-0.355066\pi\)
\(920\) 5.24555 + 9.08557i 0.172941 + 0.299542i
\(921\) 0 0
\(922\) −3.14046 1.81314i −0.103425 0.0597127i
\(923\) −15.9499 27.6260i −0.524996 0.909320i
\(924\) 0 0
\(925\) −16.9981 + 29.4415i −0.558893 + 0.968031i
\(926\) −3.24639 + 1.87431i −0.106683 + 0.0615935i
\(927\) 0 0
\(928\) −7.05115 + 12.2130i −0.231465 + 0.400910i
\(929\) −32.1171 −1.05373 −0.526864 0.849950i \(-0.676632\pi\)
−0.526864 + 0.849950i \(0.676632\pi\)
\(930\) 0 0
\(931\) −14.6486 10.1803i −0.480087 0.333644i
\(932\) −34.4348 + 19.8810i −1.12795 + 0.651222i
\(933\) 0 0
\(934\) −2.79439 + 1.61334i −0.0914351 + 0.0527901i
\(935\) 34.7520 + 20.0641i 1.13651 + 0.656166i
\(936\) 0 0
\(937\) 13.9224i 0.454824i −0.973799 0.227412i \(-0.926974\pi\)
0.973799 0.227412i \(-0.0730263\pi\)
\(938\) −1.03439 0.656416i −0.0337739 0.0214327i
\(939\) 0 0
\(940\) −11.8703 + 20.5599i −0.387166 + 0.670590i
\(941\) −57.2094 −1.86497 −0.932487 0.361203i \(-0.882366\pi\)
−0.932487 + 0.361203i \(0.882366\pi\)
\(942\) 0 0
\(943\) 18.6438i 0.607127i
\(944\) 16.3545 0.532294
\(945\) 0 0
\(946\) 4.72200 0.153525
\(947\) 34.4861i 1.12065i −0.828274 0.560324i \(-0.810677\pi\)
0.828274 0.560324i \(-0.189323\pi\)
\(948\) 0 0
\(949\) 2.31739 0.0752255
\(950\) 1.63455 2.83113i 0.0530318 0.0918538i
\(951\) 0 0
\(952\) −9.07469 + 4.74434i −0.294112 + 0.153765i
\(953\) 2.58761i 0.0838209i 0.999121 + 0.0419104i \(0.0133444\pi\)
−0.999121 + 0.0419104i \(0.986656\pi\)
\(954\) 0 0
\(955\) −11.3669 6.56267i −0.367824 0.212363i
\(956\) −45.3034 + 26.1559i −1.46522 + 0.845943i
\(957\) 0 0
\(958\) −2.84900 + 1.64487i −0.0920470 + 0.0531434i
\(959\) −1.35208 + 32.2731i −0.0436608 + 1.04215i
\(960\) 0 0
\(961\) 30.7765 0.992791
\(962\) −2.68145 + 4.64441i −0.0864535 + 0.149742i
\(963\) 0 0
\(964\) −35.3426 + 20.4051i −1.13831 + 0.657203i
\(965\) 35.7209 61.8704i 1.14990 1.99168i
\(966\) 0 0
\(967\) 2.79472 + 4.84059i 0.0898721 + 0.155663i 0.907457 0.420145i \(-0.138021\pi\)
−0.817585 + 0.575808i \(0.804688\pi\)
\(968\) 4.16585 + 2.40515i 0.133895 + 0.0773045i
\(969\) 0 0
\(970\) −2.58986 4.48578i −0.0831555 0.144030i
\(971\) −8.01661 13.8852i −0.257265 0.445597i 0.708243 0.705969i \(-0.249488\pi\)
−0.965508 + 0.260372i \(0.916155\pi\)
\(972\) 0 0
\(973\) 1.47701 35.2551i 0.0473507 1.13023i
\(974\) −0.755007 0.435904i −0.0241920 0.0139673i
\(975\) 0 0
\(976\) 5.58353i 0.178724i
\(977\) 43.9026i 1.40457i −0.711896 0.702285i \(-0.752163\pi\)
0.711896 0.702285i \(-0.247837\pi\)
\(978\) 0 0
\(979\) 14.5674 + 8.41048i 0.465576 + 0.268800i
\(980\) 40.8502 + 3.42884i 1.30491 + 0.109530i
\(981\) 0 0
\(982\) 3.42377 + 5.93015i 0.109257 + 0.189239i
\(983\) 9.08808 + 15.7410i 0.289865 + 0.502061i 0.973777 0.227503i \(-0.0730563\pi\)
−0.683912 + 0.729564i \(0.739723\pi\)
\(984\) 0 0
\(985\) 49.7749 + 28.7376i 1.58596 + 0.915655i
\(986\) 2.09683 + 3.63181i 0.0667766 + 0.115660i
\(987\) 0 0
\(988\) −5.71374 + 9.89649i −0.181778 + 0.314849i
\(989\) −10.6453 + 6.14604i −0.338499 + 0.195433i
\(990\) 0 0
\(991\) −23.8146 + 41.2481i −0.756496 + 1.31029i 0.188131 + 0.982144i \(0.439757\pi\)
−0.944627 + 0.328145i \(0.893576\pi\)
\(992\) 1.57213 0.0499151
\(993\) 0 0
\(994\) 5.67123 8.93677i 0.179880 0.283457i
\(995\) 12.0246 6.94242i 0.381206 0.220090i
\(996\) 0 0
\(997\) 28.4838 16.4451i 0.902090 0.520822i 0.0242120 0.999707i \(-0.492292\pi\)
0.877878 + 0.478885i \(0.158959\pi\)
\(998\) 1.16711 + 0.673830i 0.0369442 + 0.0213297i
\(999\) 0 0
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 189.2.i.b.143.3 10
3.2 odd 2 63.2.i.b.38.3 yes 10
4.3 odd 2 3024.2.ca.b.2033.1 10
7.2 even 3 1323.2.s.b.656.3 10
7.3 odd 6 1323.2.o.d.440.3 10
7.4 even 3 1323.2.o.c.440.3 10
7.5 odd 6 189.2.s.b.89.3 10
7.6 odd 2 1323.2.i.b.521.3 10
9.2 odd 6 567.2.p.d.80.3 10
9.4 even 3 63.2.s.b.59.3 yes 10
9.5 odd 6 189.2.s.b.17.3 10
9.7 even 3 567.2.p.c.80.3 10
12.11 even 2 1008.2.ca.b.353.4 10
21.2 odd 6 441.2.s.b.362.3 10
21.5 even 6 63.2.s.b.47.3 yes 10
21.11 odd 6 441.2.o.d.146.3 10
21.17 even 6 441.2.o.c.146.3 10
21.20 even 2 441.2.i.b.227.3 10
28.19 even 6 3024.2.df.b.1601.1 10
36.23 even 6 3024.2.df.b.17.1 10
36.31 odd 6 1008.2.df.b.689.5 10
63.4 even 3 441.2.o.c.293.3 10
63.5 even 6 inner 189.2.i.b.152.3 10
63.13 odd 6 441.2.s.b.374.3 10
63.23 odd 6 1323.2.i.b.1097.3 10
63.31 odd 6 441.2.o.d.293.3 10
63.32 odd 6 1323.2.o.d.881.3 10
63.40 odd 6 63.2.i.b.5.3 10
63.41 even 6 1323.2.s.b.962.3 10
63.47 even 6 567.2.p.c.404.3 10
63.58 even 3 441.2.i.b.68.3 10
63.59 even 6 1323.2.o.c.881.3 10
63.61 odd 6 567.2.p.d.404.3 10
84.47 odd 6 1008.2.df.b.929.5 10
252.103 even 6 1008.2.ca.b.257.4 10
252.131 odd 6 3024.2.ca.b.2609.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.3 10 63.40 odd 6
63.2.i.b.38.3 yes 10 3.2 odd 2
63.2.s.b.47.3 yes 10 21.5 even 6
63.2.s.b.59.3 yes 10 9.4 even 3
189.2.i.b.143.3 10 1.1 even 1 trivial
189.2.i.b.152.3 10 63.5 even 6 inner
189.2.s.b.17.3 10 9.5 odd 6
189.2.s.b.89.3 10 7.5 odd 6
441.2.i.b.68.3 10 63.58 even 3
441.2.i.b.227.3 10 21.20 even 2
441.2.o.c.146.3 10 21.17 even 6
441.2.o.c.293.3 10 63.4 even 3
441.2.o.d.146.3 10 21.11 odd 6
441.2.o.d.293.3 10 63.31 odd 6
441.2.s.b.362.3 10 21.2 odd 6
441.2.s.b.374.3 10 63.13 odd 6
567.2.p.c.80.3 10 9.7 even 3
567.2.p.c.404.3 10 63.47 even 6
567.2.p.d.80.3 10 9.2 odd 6
567.2.p.d.404.3 10 63.61 odd 6
1008.2.ca.b.257.4 10 252.103 even 6
1008.2.ca.b.353.4 10 12.11 even 2
1008.2.df.b.689.5 10 36.31 odd 6
1008.2.df.b.929.5 10 84.47 odd 6
1323.2.i.b.521.3 10 7.6 odd 2
1323.2.i.b.1097.3 10 63.23 odd 6
1323.2.o.c.440.3 10 7.4 even 3
1323.2.o.c.881.3 10 63.59 even 6
1323.2.o.d.440.3 10 7.3 odd 6
1323.2.o.d.881.3 10 63.32 odd 6
1323.2.s.b.656.3 10 7.2 even 3
1323.2.s.b.962.3 10 63.41 even 6
3024.2.ca.b.2033.1 10 4.3 odd 2
3024.2.ca.b.2609.1 10 252.131 odd 6
3024.2.df.b.17.1 10 36.23 even 6
3024.2.df.b.1601.1 10 28.19 even 6