Properties

Label 567.2.i.d.215.1
Level $567$
Weight $2$
Character 567.215
Analytic conductor $4.528$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(215,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.215");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 567.215
Dual form 567.2.i.d.269.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-1.22474 - 2.12132i) q^{5} +(-2.00000 + 1.73205i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q-1.41421i q^{2} +(-1.22474 - 2.12132i) q^{5} +(-2.00000 + 1.73205i) q^{7} -2.82843i q^{8} +(-3.00000 + 1.73205i) q^{10} +(1.22474 + 0.707107i) q^{11} +(-4.50000 - 2.59808i) q^{13} +(2.44949 + 2.82843i) q^{14} -4.00000 q^{16} +(-2.44949 - 4.24264i) q^{17} +(1.50000 + 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{22} +(-4.89898 + 2.82843i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-3.67423 + 6.36396i) q^{26} +(2.44949 - 1.41421i) q^{29} +1.73205i q^{31} +(-6.00000 + 3.46410i) q^{34} +(6.12372 + 2.12132i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.22474 - 2.12132i) q^{38} +(-6.00000 + 3.46410i) q^{40} +(3.67423 - 6.36396i) q^{41} +(0.500000 + 0.866025i) q^{43} +(4.00000 + 6.92820i) q^{46} -12.2474 q^{47} +(1.00000 - 6.92820i) q^{49} +(1.22474 + 0.707107i) q^{50} +(2.44949 - 1.41421i) q^{53} -3.46410i q^{55} +(4.89898 + 5.65685i) q^{56} +(-2.00000 - 3.46410i) q^{58} +4.89898 q^{59} +3.46410i q^{61} +2.44949 q^{62} -8.00000 q^{64} +12.7279i q^{65} +11.0000 q^{67} +(3.00000 - 8.66025i) q^{70} +7.07107i q^{71} +(1.50000 - 0.866025i) q^{73} +(-1.22474 - 0.707107i) q^{74} +(-3.67423 + 0.707107i) q^{77} +5.00000 q^{79} +(4.89898 + 8.48528i) q^{80} +(-9.00000 - 5.19615i) q^{82} +(-3.67423 - 6.36396i) q^{83} +(-6.00000 + 10.3923i) q^{85} +(1.22474 - 0.707107i) q^{86} +(2.00000 - 3.46410i) q^{88} +(2.44949 - 4.24264i) q^{89} +(13.5000 - 2.59808i) q^{91} +17.3205i q^{94} -4.24264i q^{95} +(9.00000 - 5.19615i) q^{97} +(-9.79796 - 1.41421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{7} - 12 q^{10} - 18 q^{13} - 16 q^{16} + 6 q^{19} + 4 q^{22} - 2 q^{25} - 24 q^{34} + 2 q^{37} - 24 q^{40} + 2 q^{43} + 16 q^{46} + 4 q^{49} - 8 q^{58} - 32 q^{64} + 44 q^{67} + 12 q^{70} + 6 q^{73} + 20 q^{79} - 36 q^{82} - 24 q^{85} + 8 q^{88} + 54 q^{91} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) −1.22474 2.12132i −0.547723 0.948683i −0.998430 0.0560116i \(-0.982162\pi\)
0.450708 0.892672i \(-0.351172\pi\)
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) −3.00000 + 1.73205i −0.948683 + 0.547723i
\(11\) 1.22474 + 0.707107i 0.369274 + 0.213201i 0.673141 0.739514i \(-0.264945\pi\)
−0.303867 + 0.952714i \(0.598278\pi\)
\(12\) 0 0
\(13\) −4.50000 2.59808i −1.24808 0.720577i −0.277350 0.960769i \(-0.589456\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 2.44949 + 2.82843i 0.654654 + 0.755929i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) −2.44949 4.24264i −0.594089 1.02899i −0.993675 0.112296i \(-0.964180\pi\)
0.399586 0.916696i \(-0.369154\pi\)
\(18\) 0 0
\(19\) 1.50000 + 0.866025i 0.344124 + 0.198680i 0.662094 0.749421i \(-0.269668\pi\)
−0.317970 + 0.948101i \(0.603001\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) −4.89898 + 2.82843i −1.02151 + 0.589768i −0.914540 0.404495i \(-0.867447\pi\)
−0.106967 + 0.994263i \(0.534114\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.67423 + 6.36396i −0.720577 + 1.24808i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.44949 1.41421i 0.454859 0.262613i −0.255021 0.966935i \(-0.582082\pi\)
0.709880 + 0.704323i \(0.248749\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −6.00000 + 3.46410i −1.02899 + 0.594089i
\(35\) 6.12372 + 2.12132i 1.03510 + 0.358569i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 1.22474 2.12132i 0.198680 0.344124i
\(39\) 0 0
\(40\) −6.00000 + 3.46410i −0.948683 + 0.547723i
\(41\) 3.67423 6.36396i 0.573819 0.993884i −0.422350 0.906433i \(-0.638795\pi\)
0.996169 0.0874508i \(-0.0278721\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000 + 6.92820i 0.589768 + 1.02151i
\(47\) −12.2474 −1.78647 −0.893237 0.449586i \(-0.851571\pi\)
−0.893237 + 0.449586i \(0.851571\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 1.22474 + 0.707107i 0.173205 + 0.100000i
\(51\) 0 0
\(52\) 0 0
\(53\) 2.44949 1.41421i 0.336463 0.194257i −0.322244 0.946657i \(-0.604437\pi\)
0.658707 + 0.752400i \(0.271104\pi\)
\(54\) 0 0
\(55\) 3.46410i 0.467099i
\(56\) 4.89898 + 5.65685i 0.654654 + 0.755929i
\(57\) 0 0
\(58\) −2.00000 3.46410i −0.262613 0.454859i
\(59\) 4.89898 0.637793 0.318896 0.947790i \(-0.396688\pi\)
0.318896 + 0.947790i \(0.396688\pi\)
\(60\) 0 0
\(61\) 3.46410i 0.443533i 0.975100 + 0.221766i \(0.0711822\pi\)
−0.975100 + 0.221766i \(0.928818\pi\)
\(62\) 2.44949 0.311086
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 12.7279i 1.57870i
\(66\) 0 0
\(67\) 11.0000 1.34386 0.671932 0.740613i \(-0.265465\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 3.00000 8.66025i 0.358569 1.03510i
\(71\) 7.07107i 0.839181i 0.907713 + 0.419591i \(0.137826\pi\)
−0.907713 + 0.419591i \(0.862174\pi\)
\(72\) 0 0
\(73\) 1.50000 0.866025i 0.175562 0.101361i −0.409644 0.912245i \(-0.634347\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) −1.22474 0.707107i −0.142374 0.0821995i
\(75\) 0 0
\(76\) 0 0
\(77\) −3.67423 + 0.707107i −0.418718 + 0.0805823i
\(78\) 0 0
\(79\) 5.00000 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) 4.89898 + 8.48528i 0.547723 + 0.948683i
\(81\) 0 0
\(82\) −9.00000 5.19615i −0.993884 0.573819i
\(83\) −3.67423 6.36396i −0.403300 0.698535i 0.590822 0.806802i \(-0.298803\pi\)
−0.994122 + 0.108266i \(0.965470\pi\)
\(84\) 0 0
\(85\) −6.00000 + 10.3923i −0.650791 + 1.12720i
\(86\) 1.22474 0.707107i 0.132068 0.0762493i
\(87\) 0 0
\(88\) 2.00000 3.46410i 0.213201 0.369274i
\(89\) 2.44949 4.24264i 0.259645 0.449719i −0.706502 0.707712i \(-0.749728\pi\)
0.966147 + 0.257993i \(0.0830610\pi\)
\(90\) 0 0
\(91\) 13.5000 2.59808i 1.41518 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) 17.3205i 1.78647i
\(95\) 4.24264i 0.435286i
\(96\) 0 0
\(97\) 9.00000 5.19615i 0.913812 0.527589i 0.0321560 0.999483i \(-0.489763\pi\)
0.881656 + 0.471894i \(0.156429\pi\)
\(98\) −9.79796 1.41421i −0.989743 0.142857i
\(99\) 0 0
\(100\) 0 0
\(101\) 8.57321 14.8492i 0.853067 1.47755i −0.0253604 0.999678i \(-0.508073\pi\)
0.878427 0.477876i \(-0.158593\pi\)
\(102\) 0 0
\(103\) 7.50000 4.33013i 0.738997 0.426660i −0.0827075 0.996574i \(-0.526357\pi\)
0.821705 + 0.569914i \(0.193023\pi\)
\(104\) −7.34847 + 12.7279i −0.720577 + 1.24808i
\(105\) 0 0
\(106\) −2.00000 3.46410i −0.194257 0.336463i
\(107\) −2.44949 1.41421i −0.236801 0.136717i 0.376905 0.926252i \(-0.376988\pi\)
−0.613706 + 0.789535i \(0.710322\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) −4.89898 −0.467099
\(111\) 0 0
\(112\) 8.00000 6.92820i 0.755929 0.654654i
\(113\) 1.22474 + 0.707107i 0.115214 + 0.0665190i 0.556500 0.830848i \(-0.312144\pi\)
−0.441285 + 0.897367i \(0.645477\pi\)
\(114\) 0 0
\(115\) 12.0000 + 6.92820i 1.11901 + 0.646058i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.92820i 0.637793i
\(119\) 12.2474 + 4.24264i 1.12272 + 0.388922i
\(120\) 0 0
\(121\) −4.50000 7.79423i −0.409091 0.708566i
\(122\) 4.89898 0.443533
\(123\) 0 0
\(124\) 0 0
\(125\) −9.79796 −0.876356
\(126\) 0 0
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 11.3137i 1.00000i
\(129\) 0 0
\(130\) 18.0000 1.57870
\(131\) −1.22474 2.12132i −0.107006 0.185341i 0.807550 0.589799i \(-0.200793\pi\)
−0.914556 + 0.404459i \(0.867460\pi\)
\(132\) 0 0
\(133\) −4.50000 + 0.866025i −0.390199 + 0.0750939i
\(134\) 15.5563i 1.34386i
\(135\) 0 0
\(136\) −12.0000 + 6.92820i −1.02899 + 0.594089i
\(137\) −9.79796 5.65685i −0.837096 0.483298i 0.0191800 0.999816i \(-0.493894\pi\)
−0.856276 + 0.516518i \(0.827228\pi\)
\(138\) 0 0
\(139\) −4.50000 2.59808i −0.381685 0.220366i 0.296866 0.954919i \(-0.404058\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 10.0000 0.839181
\(143\) −3.67423 6.36396i −0.307255 0.532181i
\(144\) 0 0
\(145\) −6.00000 3.46410i −0.498273 0.287678i
\(146\) −1.22474 2.12132i −0.101361 0.175562i
\(147\) 0 0
\(148\) 0 0
\(149\) −4.89898 + 2.82843i −0.401340 + 0.231714i −0.687062 0.726599i \(-0.741100\pi\)
0.285722 + 0.958313i \(0.407767\pi\)
\(150\) 0 0
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) 2.44949 4.24264i 0.198680 0.344124i
\(153\) 0 0
\(154\) 1.00000 + 5.19615i 0.0805823 + 0.418718i
\(155\) 3.67423 2.12132i 0.295122 0.170389i
\(156\) 0 0
\(157\) 17.3205i 1.38233i 0.722698 + 0.691164i \(0.242902\pi\)
−0.722698 + 0.691164i \(0.757098\pi\)
\(158\) 7.07107i 0.562544i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.89898 14.1421i 0.386094 1.11456i
\(162\) 0 0
\(163\) 5.00000 8.66025i 0.391630 0.678323i −0.601035 0.799223i \(-0.705245\pi\)
0.992665 + 0.120900i \(0.0385779\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −9.00000 + 5.19615i −0.698535 + 0.403300i
\(167\) 3.67423 6.36396i 0.284321 0.492458i −0.688123 0.725594i \(-0.741565\pi\)
0.972444 + 0.233136i \(0.0748986\pi\)
\(168\) 0 0
\(169\) 7.00000 + 12.1244i 0.538462 + 0.932643i
\(170\) 14.6969 + 8.48528i 1.12720 + 0.650791i
\(171\) 0 0
\(172\) 0 0
\(173\) 9.79796 0.744925 0.372463 0.928047i \(-0.378514\pi\)
0.372463 + 0.928047i \(0.378514\pi\)
\(174\) 0 0
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) −4.89898 2.82843i −0.369274 0.213201i
\(177\) 0 0
\(178\) −6.00000 3.46410i −0.449719 0.259645i
\(179\) −8.57321 + 4.94975i −0.640792 + 0.369961i −0.784920 0.619598i \(-0.787296\pi\)
0.144127 + 0.989559i \(0.453962\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i −0.815086 0.579340i \(-0.803310\pi\)
0.815086 0.579340i \(-0.196690\pi\)
\(182\) −3.67423 19.0919i −0.272352 1.41518i
\(183\) 0 0
\(184\) 8.00000 + 13.8564i 0.589768 + 1.02151i
\(185\) −2.44949 −0.180090
\(186\) 0 0
\(187\) 6.92820i 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) 1.41421i 0.102329i −0.998690 0.0511645i \(-0.983707\pi\)
0.998690 0.0511645i \(-0.0162933\pi\)
\(192\) 0 0
\(193\) 11.0000 0.791797 0.395899 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) −7.34847 12.7279i −0.527589 0.913812i
\(195\) 0 0
\(196\) 0 0
\(197\) 19.7990i 1.41062i 0.708899 + 0.705310i \(0.249192\pi\)
−0.708899 + 0.705310i \(0.750808\pi\)
\(198\) 0 0
\(199\) −12.0000 + 6.92820i −0.850657 + 0.491127i −0.860873 0.508821i \(-0.830082\pi\)
0.0102152 + 0.999948i \(0.496748\pi\)
\(200\) 2.44949 + 1.41421i 0.173205 + 0.100000i
\(201\) 0 0
\(202\) −21.0000 12.1244i −1.47755 0.853067i
\(203\) −2.44949 + 7.07107i −0.171920 + 0.496292i
\(204\) 0 0
\(205\) −18.0000 −1.25717
\(206\) −6.12372 10.6066i −0.426660 0.738997i
\(207\) 0 0
\(208\) 18.0000 + 10.3923i 1.24808 + 0.720577i
\(209\) 1.22474 + 2.12132i 0.0847174 + 0.146735i
\(210\) 0 0
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.00000 + 3.46410i −0.136717 + 0.236801i
\(215\) 1.22474 2.12132i 0.0835269 0.144673i
\(216\) 0 0
\(217\) −3.00000 3.46410i −0.203653 0.235159i
\(218\) 1.22474 0.707107i 0.0829502 0.0478913i
\(219\) 0 0
\(220\) 0 0
\(221\) 25.4558i 1.71235i
\(222\) 0 0
\(223\) −18.0000 + 10.3923i −1.20537 + 0.695920i −0.961744 0.273949i \(-0.911670\pi\)
−0.243625 + 0.969870i \(0.578337\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 1.73205i 0.0665190 0.115214i
\(227\) −13.4722 + 23.3345i −0.894181 + 1.54877i −0.0593658 + 0.998236i \(0.518908\pi\)
−0.834815 + 0.550530i \(0.814425\pi\)
\(228\) 0 0
\(229\) −19.5000 + 11.2583i −1.28860 + 0.743971i −0.978404 0.206702i \(-0.933727\pi\)
−0.310192 + 0.950674i \(0.600393\pi\)
\(230\) 9.79796 16.9706i 0.646058 1.11901i
\(231\) 0 0
\(232\) −4.00000 6.92820i −0.262613 0.454859i
\(233\) 8.57321 + 4.94975i 0.561650 + 0.324269i 0.753807 0.657095i \(-0.228215\pi\)
−0.192158 + 0.981364i \(0.561548\pi\)
\(234\) 0 0
\(235\) 15.0000 + 25.9808i 0.978492 + 1.69480i
\(236\) 0 0
\(237\) 0 0
\(238\) 6.00000 17.3205i 0.388922 1.12272i
\(239\) 23.2702 + 13.4350i 1.50522 + 0.869040i 0.999982 + 0.00606055i \(0.00192914\pi\)
0.505239 + 0.862979i \(0.331404\pi\)
\(240\) 0 0
\(241\) 12.0000 + 6.92820i 0.772988 + 0.446285i 0.833939 0.551856i \(-0.186080\pi\)
−0.0609515 + 0.998141i \(0.519414\pi\)
\(242\) −11.0227 + 6.36396i −0.708566 + 0.409091i
\(243\) 0 0
\(244\) 0 0
\(245\) −15.9217 + 6.36396i −1.01720 + 0.406579i
\(246\) 0 0
\(247\) −4.50000 7.79423i −0.286328 0.495935i
\(248\) 4.89898 0.311086
\(249\) 0 0
\(250\) 13.8564i 0.876356i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) 15.5563i 0.976092i
\(255\) 0 0
\(256\) 0 0
\(257\) −1.22474 2.12132i −0.0763975 0.132324i 0.825296 0.564701i \(-0.191008\pi\)
−0.901693 + 0.432377i \(0.857675\pi\)
\(258\) 0 0
\(259\) 0.500000 + 2.59808i 0.0310685 + 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 + 1.73205i −0.185341 + 0.107006i
\(263\) 12.2474 + 7.07107i 0.755210 + 0.436021i 0.827573 0.561358i \(-0.189721\pi\)
−0.0723633 + 0.997378i \(0.523054\pi\)
\(264\) 0 0
\(265\) −6.00000 3.46410i −0.368577 0.212798i
\(266\) 1.22474 + 6.36396i 0.0750939 + 0.390199i
\(267\) 0 0
\(268\) 0 0
\(269\) 8.57321 + 14.8492i 0.522718 + 0.905374i 0.999651 + 0.0264343i \(0.00841529\pi\)
−0.476932 + 0.878940i \(0.658251\pi\)
\(270\) 0 0
\(271\) −12.0000 6.92820i −0.728948 0.420858i 0.0890891 0.996024i \(-0.471604\pi\)
−0.818037 + 0.575165i \(0.804938\pi\)
\(272\) 9.79796 + 16.9706i 0.594089 + 1.02899i
\(273\) 0 0
\(274\) −8.00000 + 13.8564i −0.483298 + 0.837096i
\(275\) −1.22474 + 0.707107i −0.0738549 + 0.0426401i
\(276\) 0 0
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) −3.67423 + 6.36396i −0.220366 + 0.381685i
\(279\) 0 0
\(280\) 6.00000 17.3205i 0.358569 1.03510i
\(281\) −19.5959 + 11.3137i −1.16899 + 0.674919i −0.953443 0.301573i \(-0.902488\pi\)
−0.215551 + 0.976492i \(0.569155\pi\)
\(282\) 0 0
\(283\) 1.73205i 0.102960i 0.998674 + 0.0514799i \(0.0163938\pi\)
−0.998674 + 0.0514799i \(0.983606\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −9.00000 + 5.19615i −0.532181 + 0.307255i
\(287\) 3.67423 + 19.0919i 0.216883 + 1.12696i
\(288\) 0 0
\(289\) −3.50000 + 6.06218i −0.205882 + 0.356599i
\(290\) −4.89898 + 8.48528i −0.287678 + 0.498273i
\(291\) 0 0
\(292\) 0 0
\(293\) −7.34847 + 12.7279i −0.429302 + 0.743573i −0.996811 0.0797939i \(-0.974574\pi\)
0.567509 + 0.823367i \(0.307907\pi\)
\(294\) 0 0
\(295\) −6.00000 10.3923i −0.349334 0.605063i
\(296\) −2.44949 1.41421i −0.142374 0.0821995i
\(297\) 0 0
\(298\) 4.00000 + 6.92820i 0.231714 + 0.401340i
\(299\) 29.3939 1.69989
\(300\) 0 0
\(301\) −2.50000 0.866025i −0.144098 0.0499169i
\(302\) −26.9444 15.5563i −1.55048 0.895167i
\(303\) 0 0
\(304\) −6.00000 3.46410i −0.344124 0.198680i
\(305\) 7.34847 4.24264i 0.420772 0.242933i
\(306\) 0 0
\(307\) 15.5885i 0.889680i 0.895610 + 0.444840i \(0.146740\pi\)
−0.895610 + 0.444840i \(0.853260\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.00000 5.19615i −0.170389 0.295122i
\(311\) −17.1464 −0.972285 −0.486142 0.873880i \(-0.661596\pi\)
−0.486142 + 0.873880i \(0.661596\pi\)
\(312\) 0 0
\(313\) 12.1244i 0.685309i −0.939461 0.342655i \(-0.888674\pi\)
0.939461 0.342655i \(-0.111326\pi\)
\(314\) 24.4949 1.38233
\(315\) 0 0
\(316\) 0 0
\(317\) 14.1421i 0.794301i −0.917753 0.397151i \(-0.869999\pi\)
0.917753 0.397151i \(-0.130001\pi\)
\(318\) 0 0
\(319\) 4.00000 0.223957
\(320\) 9.79796 + 16.9706i 0.547723 + 0.948683i
\(321\) 0 0
\(322\) −20.0000 6.92820i −1.11456 0.386094i
\(323\) 8.48528i 0.472134i
\(324\) 0 0
\(325\) 4.50000 2.59808i 0.249615 0.144115i
\(326\) −12.2474 7.07107i −0.678323 0.391630i
\(327\) 0 0
\(328\) −18.0000 10.3923i −0.993884 0.573819i
\(329\) 24.4949 21.2132i 1.35045 1.16952i
\(330\) 0 0
\(331\) −31.0000 −1.70391 −0.851957 0.523612i \(-0.824584\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −9.00000 5.19615i −0.492458 0.284321i
\(335\) −13.4722 23.3345i −0.736065 1.27490i
\(336\) 0 0
\(337\) −11.5000 + 19.9186i −0.626445 + 1.08503i 0.361815 + 0.932250i \(0.382157\pi\)
−0.988260 + 0.152784i \(0.951176\pi\)
\(338\) 17.1464 9.89949i 0.932643 0.538462i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.22474 + 2.12132i −0.0663237 + 0.114876i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 2.44949 1.41421i 0.132068 0.0762493i
\(345\) 0 0
\(346\) 13.8564i 0.744925i
\(347\) 31.1127i 1.67022i −0.550085 0.835109i \(-0.685405\pi\)
0.550085 0.835109i \(-0.314595\pi\)
\(348\) 0 0
\(349\) 9.00000 5.19615i 0.481759 0.278144i −0.239390 0.970923i \(-0.576948\pi\)
0.721149 + 0.692780i \(0.243614\pi\)
\(350\) −3.67423 + 0.707107i −0.196396 + 0.0377964i
\(351\) 0 0
\(352\) 0 0
\(353\) 8.57321 14.8492i 0.456306 0.790345i −0.542456 0.840084i \(-0.682506\pi\)
0.998762 + 0.0497387i \(0.0158389\pi\)
\(354\) 0 0
\(355\) 15.0000 8.66025i 0.796117 0.459639i
\(356\) 0 0
\(357\) 0 0
\(358\) 7.00000 + 12.1244i 0.369961 + 0.640792i
\(359\) −24.4949 14.1421i −1.29279 0.746393i −0.313643 0.949541i \(-0.601550\pi\)
−0.979148 + 0.203148i \(0.934883\pi\)
\(360\) 0 0
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) −22.0454 −1.15868
\(363\) 0 0
\(364\) 0 0
\(365\) −3.67423 2.12132i −0.192318 0.111035i
\(366\) 0 0
\(367\) −1.50000 0.866025i −0.0782994 0.0452062i 0.460339 0.887743i \(-0.347728\pi\)
−0.538639 + 0.842537i \(0.681061\pi\)
\(368\) 19.5959 11.3137i 1.02151 0.589768i
\(369\) 0 0
\(370\) 3.46410i 0.180090i
\(371\) −2.44949 + 7.07107i −0.127171 + 0.367112i
\(372\) 0 0
\(373\) −14.5000 25.1147i −0.750782 1.30039i −0.947444 0.319921i \(-0.896344\pi\)
0.196663 0.980471i \(-0.436990\pi\)
\(374\) −9.79796 −0.506640
\(375\) 0 0
\(376\) 34.6410i 1.78647i
\(377\) −14.6969 −0.756931
\(378\) 0 0
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −2.00000 −0.102329
\(383\) 9.79796 + 16.9706i 0.500652 + 0.867155i 1.00000 0.000753393i \(0.000239813\pi\)
−0.499347 + 0.866402i \(0.666427\pi\)
\(384\) 0 0
\(385\) 6.00000 + 6.92820i 0.305788 + 0.353094i
\(386\) 15.5563i 0.791797i
\(387\) 0 0
\(388\) 0 0
\(389\) 23.2702 + 13.4350i 1.17984 + 0.681183i 0.955978 0.293437i \(-0.0947991\pi\)
0.223865 + 0.974620i \(0.428132\pi\)
\(390\) 0 0
\(391\) 24.0000 + 13.8564i 1.21373 + 0.700749i
\(392\) −19.5959 2.82843i −0.989743 0.142857i
\(393\) 0 0
\(394\) 28.0000 1.41062
\(395\) −6.12372 10.6066i −0.308118 0.533676i
\(396\) 0 0
\(397\) 1.50000 + 0.866025i 0.0752828 + 0.0434646i 0.537169 0.843475i \(-0.319494\pi\)
−0.461886 + 0.886939i \(0.652827\pi\)
\(398\) 9.79796 + 16.9706i 0.491127 + 0.850657i
\(399\) 0 0
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) 17.1464 9.89949i 0.856252 0.494357i −0.00650355 0.999979i \(-0.502070\pi\)
0.862755 + 0.505622i \(0.168737\pi\)
\(402\) 0 0
\(403\) 4.50000 7.79423i 0.224161 0.388258i
\(404\) 0 0
\(405\) 0 0
\(406\) 10.0000 + 3.46410i 0.496292 + 0.171920i
\(407\) 1.22474 0.707107i 0.0607083 0.0350500i
\(408\) 0 0
\(409\) 32.9090i 1.62724i 0.581394 + 0.813622i \(0.302507\pi\)
−0.581394 + 0.813622i \(0.697493\pi\)
\(410\) 25.4558i 1.25717i
\(411\) 0 0
\(412\) 0 0
\(413\) −9.79796 + 8.48528i −0.482126 + 0.417533i
\(414\) 0 0
\(415\) −9.00000 + 15.5885i −0.441793 + 0.765207i
\(416\) 0 0
\(417\) 0 0
\(418\) 3.00000 1.73205i 0.146735 0.0847174i
\(419\) −18.3712 + 31.8198i −0.897491 + 1.55450i −0.0667989 + 0.997766i \(0.521279\pi\)
−0.830692 + 0.556733i \(0.812055\pi\)
\(420\) 0 0
\(421\) 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i \(-0.158909\pi\)
−0.853584 + 0.520955i \(0.825576\pi\)
\(422\) −26.9444 15.5563i −1.31163 0.757271i
\(423\) 0 0
\(424\) −4.00000 6.92820i −0.194257 0.336463i
\(425\) 4.89898 0.237635
\(426\) 0 0
\(427\) −6.00000 6.92820i −0.290360 0.335279i
\(428\) 0 0
\(429\) 0 0
\(430\) −3.00000 1.73205i −0.144673 0.0835269i
\(431\) 13.4722 7.77817i 0.648933 0.374661i −0.139114 0.990276i \(-0.544426\pi\)
0.788047 + 0.615615i \(0.211092\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i −0.927200 0.374567i \(-0.877791\pi\)
0.927200 0.374567i \(-0.122209\pi\)
\(434\) −4.89898 + 4.24264i −0.235159 + 0.203653i
\(435\) 0 0
\(436\) 0 0
\(437\) −9.79796 −0.468700
\(438\) 0 0
\(439\) 27.7128i 1.32266i −0.750095 0.661330i \(-0.769992\pi\)
0.750095 0.661330i \(-0.230008\pi\)
\(440\) −9.79796 −0.467099
\(441\) 0 0
\(442\) 36.0000 1.71235
\(443\) 39.5980i 1.88136i −0.339300 0.940678i \(-0.610190\pi\)
0.339300 0.940678i \(-0.389810\pi\)
\(444\) 0 0
\(445\) −12.0000 −0.568855
\(446\) 14.6969 + 25.4558i 0.695920 + 1.20537i
\(447\) 0 0
\(448\) 16.0000 13.8564i 0.755929 0.654654i
\(449\) 7.07107i 0.333704i 0.985982 + 0.166852i \(0.0533603\pi\)
−0.985982 + 0.166852i \(0.946640\pi\)
\(450\) 0 0
\(451\) 9.00000 5.19615i 0.423793 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) 33.0000 + 19.0526i 1.54877 + 0.894181i
\(455\) −22.0454 25.4558i −1.03350 1.19339i
\(456\) 0 0
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) 15.9217 + 27.5772i 0.743971 + 1.28860i
\(459\) 0 0
\(460\) 0 0
\(461\) 7.34847 + 12.7279i 0.342252 + 0.592798i 0.984851 0.173405i \(-0.0554769\pi\)
−0.642598 + 0.766203i \(0.722144\pi\)
\(462\) 0 0
\(463\) 6.50000 11.2583i 0.302081 0.523219i −0.674526 0.738251i \(-0.735652\pi\)
0.976607 + 0.215032i \(0.0689855\pi\)
\(464\) −9.79796 + 5.65685i −0.454859 + 0.262613i
\(465\) 0 0
\(466\) 7.00000 12.1244i 0.324269 0.561650i
\(467\) 13.4722 23.3345i 0.623419 1.07979i −0.365426 0.930841i \(-0.619077\pi\)
0.988844 0.148952i \(-0.0475901\pi\)
\(468\) 0 0
\(469\) −22.0000 + 19.0526i −1.01587 + 0.879765i
\(470\) 36.7423 21.2132i 1.69480 0.978492i
\(471\) 0 0
\(472\) 13.8564i 0.637793i
\(473\) 1.41421i 0.0650256i
\(474\) 0 0
\(475\) −1.50000 + 0.866025i −0.0688247 + 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) 19.0000 32.9090i 0.869040 1.50522i
\(479\) −2.44949 + 4.24264i −0.111920 + 0.193851i −0.916544 0.399933i \(-0.869033\pi\)
0.804624 + 0.593784i \(0.202367\pi\)
\(480\) 0 0
\(481\) −4.50000 + 2.59808i −0.205182 + 0.118462i
\(482\) 9.79796 16.9706i 0.446285 0.772988i
\(483\) 0 0
\(484\) 0 0
\(485\) −22.0454 12.7279i −1.00103 0.577945i
\(486\) 0 0
\(487\) −8.50000 14.7224i −0.385172 0.667137i 0.606621 0.794991i \(-0.292524\pi\)
−0.991793 + 0.127854i \(0.959191\pi\)
\(488\) 9.79796 0.443533
\(489\) 0 0
\(490\) 9.00000 + 22.5167i 0.406579 + 1.01720i
\(491\) −9.79796 5.65685i −0.442176 0.255290i 0.262344 0.964974i \(-0.415504\pi\)
−0.704520 + 0.709684i \(0.748838\pi\)
\(492\) 0 0
\(493\) −12.0000 6.92820i −0.540453 0.312031i
\(494\) −11.0227 + 6.36396i −0.495935 + 0.286328i
\(495\) 0 0
\(496\) 6.92820i 0.311086i
\(497\) −12.2474 14.1421i −0.549373 0.634361i
\(498\) 0 0
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 22.0454 0.982956 0.491478 0.870890i \(-0.336457\pi\)
0.491478 + 0.870890i \(0.336457\pi\)
\(504\) 0 0
\(505\) −42.0000 −1.86898
\(506\) 11.3137i 0.502956i
\(507\) 0 0
\(508\) 0 0
\(509\) −1.22474 2.12132i −0.0542859 0.0940259i 0.837605 0.546276i \(-0.183955\pi\)
−0.891891 + 0.452250i \(0.850622\pi\)
\(510\) 0 0
\(511\) −1.50000 + 4.33013i −0.0663561 + 0.191554i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) −3.00000 + 1.73205i −0.132324 + 0.0763975i
\(515\) −18.3712 10.6066i −0.809531 0.467383i
\(516\) 0 0
\(517\) −15.0000 8.66025i −0.659699 0.380878i
\(518\) 3.67423 0.707107i 0.161437 0.0310685i
\(519\) 0 0
\(520\) 36.0000 1.57870
\(521\) −2.44949 4.24264i −0.107314 0.185873i 0.807367 0.590049i \(-0.200892\pi\)
−0.914681 + 0.404176i \(0.867558\pi\)
\(522\) 0 0
\(523\) 1.50000 + 0.866025i 0.0655904 + 0.0378686i 0.532437 0.846470i \(-0.321276\pi\)
−0.466846 + 0.884339i \(0.654610\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 10.0000 17.3205i 0.436021 0.755210i
\(527\) 7.34847 4.24264i 0.320104 0.184812i
\(528\) 0 0
\(529\) 4.50000 7.79423i 0.195652 0.338880i
\(530\) −4.89898 + 8.48528i −0.212798 + 0.368577i
\(531\) 0 0
\(532\) 0 0
\(533\) −33.0681 + 19.0919i −1.43234 + 0.826961i
\(534\) 0 0
\(535\) 6.92820i 0.299532i
\(536\) 31.1127i 1.34386i
\(537\) 0 0
\(538\) 21.0000 12.1244i 0.905374 0.522718i
\(539\) 6.12372 7.77817i 0.263767 0.335030i
\(540\) 0 0
\(541\) −8.50000 + 14.7224i −0.365444 + 0.632967i −0.988847 0.148933i \(-0.952416\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) −9.79796 + 16.9706i −0.420858 + 0.728948i
\(543\) 0 0
\(544\) 0 0
\(545\) 1.22474 2.12132i 0.0524623 0.0908674i
\(546\) 0 0
\(547\) 5.00000 + 8.66025i 0.213785 + 0.370286i 0.952896 0.303298i \(-0.0980876\pi\)
−0.739111 + 0.673583i \(0.764754\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.00000 + 1.73205i 0.0426401 + 0.0738549i
\(551\) 4.89898 0.208704
\(552\) 0 0
\(553\) −10.0000 + 8.66025i −0.425243 + 0.368271i
\(554\) 28.1691 + 16.2635i 1.19679 + 0.690968i
\(555\) 0 0
\(556\) 0 0
\(557\) 13.4722 7.77817i 0.570835 0.329572i −0.186648 0.982427i \(-0.559762\pi\)
0.757483 + 0.652855i \(0.226429\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) −24.4949 8.48528i −1.03510 0.358569i
\(561\) 0 0
\(562\) 16.0000 + 27.7128i 0.674919 + 1.16899i
\(563\) 26.9444 1.13557 0.567785 0.823177i \(-0.307800\pi\)
0.567785 + 0.823177i \(0.307800\pi\)
\(564\) 0 0
\(565\) 3.46410i 0.145736i
\(566\) 2.44949 0.102960
\(567\) 0 0
\(568\) 20.0000 0.839181
\(569\) 1.41421i 0.0592869i −0.999561 0.0296435i \(-0.990563\pi\)
0.999561 0.0296435i \(-0.00943719\pi\)
\(570\) 0 0
\(571\) 11.0000 0.460336 0.230168 0.973151i \(-0.426072\pi\)
0.230168 + 0.973151i \(0.426072\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 27.0000 5.19615i 1.12696 0.216883i
\(575\) 5.65685i 0.235907i
\(576\) 0 0
\(577\) 1.50000 0.866025i 0.0624458 0.0360531i −0.468452 0.883489i \(-0.655188\pi\)
0.530898 + 0.847436i \(0.321855\pi\)
\(578\) 8.57321 + 4.94975i 0.356599 + 0.205882i
\(579\) 0 0
\(580\) 0 0
\(581\) 18.3712 + 6.36396i 0.762165 + 0.264022i
\(582\) 0 0
\(583\) 4.00000 0.165663
\(584\) −2.44949 4.24264i −0.101361 0.175562i
\(585\) 0 0
\(586\) 18.0000 + 10.3923i 0.743573 + 0.429302i
\(587\) 7.34847 + 12.7279i 0.303304 + 0.525338i 0.976882 0.213778i \(-0.0685770\pi\)
−0.673578 + 0.739116i \(0.735244\pi\)
\(588\) 0 0
\(589\) −1.50000 + 2.59808i −0.0618064 + 0.107052i
\(590\) −14.6969 + 8.48528i −0.605063 + 0.349334i
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) −8.57321 + 14.8492i −0.352060 + 0.609785i −0.986610 0.163096i \(-0.947852\pi\)
0.634550 + 0.772881i \(0.281185\pi\)
\(594\) 0 0
\(595\) −6.00000 31.1769i −0.245976 1.27813i
\(596\) 0 0
\(597\) 0 0
\(598\) 41.5692i 1.69989i
\(599\) 5.65685i 0.231133i −0.993300 0.115566i \(-0.963132\pi\)
0.993300 0.115566i \(-0.0368683\pi\)
\(600\) 0 0
\(601\) 22.5000 12.9904i 0.917794 0.529889i 0.0348635 0.999392i \(-0.488900\pi\)
0.882931 + 0.469503i \(0.155567\pi\)
\(602\) −1.22474 + 3.53553i −0.0499169 + 0.144098i
\(603\) 0 0
\(604\) 0 0
\(605\) −11.0227 + 19.0919i −0.448137 + 0.776195i
\(606\) 0 0
\(607\) 34.5000 19.9186i 1.40031 0.808470i 0.405887 0.913923i \(-0.366962\pi\)
0.994424 + 0.105453i \(0.0336291\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −6.00000 10.3923i −0.242933 0.420772i
\(611\) 55.1135 + 31.8198i 2.22965 + 1.28729i
\(612\) 0 0
\(613\) −4.00000 6.92820i −0.161558 0.279827i 0.773869 0.633345i \(-0.218319\pi\)
−0.935428 + 0.353518i \(0.884985\pi\)
\(614\) 22.0454 0.889680
\(615\) 0 0
\(616\) 2.00000 + 10.3923i 0.0805823 + 0.418718i
\(617\) −20.8207 12.0208i −0.838208 0.483940i 0.0184465 0.999830i \(-0.494128\pi\)
−0.856655 + 0.515890i \(0.827461\pi\)
\(618\) 0 0
\(619\) 25.5000 + 14.7224i 1.02493 + 0.591744i 0.915529 0.402253i \(-0.131773\pi\)
0.109403 + 0.993997i \(0.465106\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.2487i 0.972285i
\(623\) 2.44949 + 12.7279i 0.0981367 + 0.509933i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −17.1464 −0.685309
\(627\) 0 0
\(628\) 0 0
\(629\) −4.89898 −0.195335
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) 14.1421i 0.562544i
\(633\) 0 0
\(634\) −20.0000 −0.794301
\(635\) −13.4722 23.3345i −0.534628 0.926002i
\(636\) 0 0
\(637\) −22.5000 + 28.5788i −0.891482 + 1.13233i
\(638\) 5.65685i 0.223957i
\(639\) 0 0
\(640\) 24.0000 13.8564i 0.948683 0.547723i
\(641\) 12.2474 + 7.07107i 0.483745 + 0.279290i 0.721976 0.691918i \(-0.243234\pi\)
−0.238231 + 0.971209i \(0.576567\pi\)
\(642\) 0 0
\(643\) 22.5000 + 12.9904i 0.887313 + 0.512291i 0.873063 0.487608i \(-0.162130\pi\)
0.0142506 + 0.999898i \(0.495464\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 8.57321 + 14.8492i 0.337048 + 0.583784i 0.983876 0.178852i \(-0.0572383\pi\)
−0.646828 + 0.762636i \(0.723905\pi\)
\(648\) 0 0
\(649\) 6.00000 + 3.46410i 0.235521 + 0.135978i
\(650\) −3.67423 6.36396i −0.144115 0.249615i
\(651\) 0 0
\(652\) 0 0
\(653\) 6.12372 3.53553i 0.239640 0.138356i −0.375371 0.926875i \(-0.622485\pi\)
0.615011 + 0.788518i \(0.289151\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) −14.6969 + 25.4558i −0.573819 + 0.993884i
\(657\) 0 0
\(658\) −30.0000 34.6410i −1.16952 1.35045i
\(659\) −19.5959 + 11.3137i −0.763349 + 0.440720i −0.830497 0.557024i \(-0.811943\pi\)
0.0671481 + 0.997743i \(0.478610\pi\)
\(660\) 0 0
\(661\) 29.4449i 1.14527i −0.819810 0.572636i \(-0.805921\pi\)
0.819810 0.572636i \(-0.194079\pi\)
\(662\) 43.8406i 1.70391i
\(663\) 0 0
\(664\) −18.0000 + 10.3923i −0.698535 + 0.403300i
\(665\) 7.34847 + 8.48528i 0.284961 + 0.329045i
\(666\) 0 0
\(667\) −8.00000 + 13.8564i −0.309761 + 0.536522i
\(668\) 0 0
\(669\) 0 0
\(670\) −33.0000 + 19.0526i −1.27490 + 0.736065i
\(671\) −2.44949 + 4.24264i −0.0945615 + 0.163785i
\(672\) 0 0
\(673\) −17.5000 30.3109i −0.674575 1.16840i −0.976593 0.215096i \(-0.930993\pi\)
0.302017 0.953302i \(-0.402340\pi\)
\(674\) 28.1691 + 16.2635i 1.08503 + 0.626445i
\(675\) 0 0
\(676\) 0 0
\(677\) 9.79796 0.376566 0.188283 0.982115i \(-0.439708\pi\)
0.188283 + 0.982115i \(0.439708\pi\)
\(678\) 0 0
\(679\) −9.00000 + 25.9808i −0.345388 + 0.997050i
\(680\) 29.3939 + 16.9706i 1.12720 + 0.650791i
\(681\) 0 0
\(682\) 3.00000 + 1.73205i 0.114876 + 0.0663237i
\(683\) −41.6413 + 24.0416i −1.59336 + 0.919927i −0.600636 + 0.799522i \(0.705086\pi\)
−0.992725 + 0.120405i \(0.961581\pi\)
\(684\) 0 0
\(685\) 27.7128i 1.05885i
\(686\) 22.0454 14.1421i 0.841698 0.539949i
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −14.6969 −0.559909
\(690\) 0 0
\(691\) 43.3013i 1.64726i −0.567129 0.823629i \(-0.691946\pi\)
0.567129 0.823629i \(-0.308054\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −44.0000 −1.67022
\(695\) 12.7279i 0.482798i
\(696\) 0 0
\(697\) −36.0000 −1.36360
\(698\) −7.34847 12.7279i −0.278144 0.481759i
\(699\) 0 0
\(700\) 0 0
\(701\) 5.65685i 0.213656i −0.994277 0.106828i \(-0.965931\pi\)
0.994277 0.106828i \(-0.0340695\pi\)
\(702\) 0 0
\(703\) 1.50000 0.866025i 0.0565736 0.0326628i
\(704\) −9.79796 5.65685i −0.369274 0.213201i
\(705\) 0 0
\(706\) −21.0000 12.1244i −0.790345 0.456306i
\(707\) 8.57321 + 44.5477i 0.322429 + 1.67539i
\(708\) 0 0
\(709\) −40.0000 −1.50223 −0.751116 0.660171i \(-0.770484\pi\)
−0.751116 + 0.660171i \(0.770484\pi\)
\(710\) −12.2474 21.2132i −0.459639 0.796117i
\(711\) 0 0
\(712\) −12.0000 6.92820i −0.449719 0.259645i
\(713\) −4.89898 8.48528i −0.183468 0.317776i
\(714\) 0 0
\(715\) −9.00000 + 15.5885i −0.336581 + 0.582975i
\(716\) 0 0
\(717\) 0 0
\(718\) −20.0000 + 34.6410i −0.746393 + 1.29279i
\(719\) 13.4722 23.3345i 0.502428 0.870231i −0.497568 0.867425i \(-0.665774\pi\)
0.999996 0.00280593i \(-0.000893157\pi\)
\(720\) 0 0
\(721\) −7.50000 + 21.6506i −0.279315 + 0.806312i
\(722\) −19.5959 + 11.3137i −0.729285 + 0.421053i
\(723\) 0 0
\(724\) 0 0
\(725\) 2.82843i 0.105045i
\(726\) 0 0
\(727\) 22.5000 12.9904i 0.834479 0.481787i −0.0209049 0.999781i \(-0.506655\pi\)
0.855384 + 0.517995i \(0.173321\pi\)
\(728\) −7.34847 38.1838i −0.272352 1.41518i
\(729\) 0 0
\(730\) −3.00000 + 5.19615i −0.111035 + 0.192318i
\(731\) 2.44949 4.24264i 0.0905977 0.156920i
\(732\) 0 0
\(733\) 34.5000 19.9186i 1.27429 0.735710i 0.298495 0.954411i \(-0.403515\pi\)
0.975792 + 0.218702i \(0.0701821\pi\)
\(734\) −1.22474 + 2.12132i −0.0452062 + 0.0782994i
\(735\) 0 0
\(736\) 0 0
\(737\) 13.4722 + 7.77817i 0.496255 + 0.286513i
\(738\) 0 0
\(739\) 0.500000 + 0.866025i 0.0183928 + 0.0318573i 0.875075 0.483987i \(-0.160812\pi\)
−0.856683 + 0.515844i \(0.827478\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 10.0000 + 3.46410i 0.367112 + 0.127171i
\(743\) −20.8207 12.0208i −0.763836 0.441001i 0.0668353 0.997764i \(-0.478710\pi\)
−0.830671 + 0.556763i \(0.812043\pi\)
\(744\) 0 0
\(745\) 12.0000 + 6.92820i 0.439646 + 0.253830i
\(746\) −35.5176 + 20.5061i −1.30039 + 0.750782i
\(747\) 0 0
\(748\) 0 0
\(749\) 7.34847 1.41421i 0.268507 0.0516742i
\(750\) 0 0
\(751\) −14.5000 25.1147i −0.529113 0.916450i −0.999424 0.0339490i \(-0.989192\pi\)
0.470311 0.882501i \(-0.344142\pi\)
\(752\) 48.9898 1.78647
\(753\) 0 0
\(754\) 20.7846i 0.756931i
\(755\) −53.8888 −1.96121
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 9.89949i 0.359566i
\(759\) 0 0
\(760\) −12.0000 −0.435286
\(761\) −12.2474 21.2132i −0.443970 0.768978i 0.554010 0.832510i \(-0.313097\pi\)
−0.997980 + 0.0635319i \(0.979764\pi\)
\(762\) 0 0
\(763\) −2.50000 0.866025i −0.0905061 0.0313522i
\(764\) 0 0
\(765\) 0 0
\(766\) 24.0000 13.8564i 0.867155 0.500652i
\(767\) −22.0454 12.7279i −0.796014 0.459579i
\(768\) 0 0
\(769\) 22.5000 + 12.9904i 0.811371 + 0.468445i 0.847432 0.530904i \(-0.178148\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 9.79796 8.48528i 0.353094 0.305788i
\(771\) 0 0
\(772\) 0 0
\(773\) −13.4722 23.3345i −0.484561 0.839284i 0.515282 0.857021i \(-0.327687\pi\)
−0.999843 + 0.0177365i \(0.994354\pi\)
\(774\) 0 0
\(775\) −1.50000 0.866025i −0.0538816 0.0311086i
\(776\) −14.6969 25.4558i −0.527589 0.913812i
\(777\) 0 0
\(778\) 19.0000 32.9090i 0.681183 1.17984i
\(779\) 11.0227 6.36396i 0.394929 0.228013i
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 19.5959 33.9411i 0.700749 1.21373i
\(783\) 0 0
\(784\) −4.00000 + 27.7128i −0.142857 + 0.989743i
\(785\) 36.7423 21.2132i 1.31139 0.757132i