Properties

Label 1575.2.bk.c.26.2
Level $1575$
Weight $2$
Character 1575.26
Analytic conductor $12.576$
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] = [1575,2,Mod(26,1575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1575, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1575.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.bk (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(12.5764383184\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1575.26
Dual form 1575.2.bk.c.1151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +(1.22474 - 0.707107i) q^{11} -5.19615i q^{13} +(-1.22474 + 3.53553i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.44949 - 4.24264i) q^{17} +(1.50000 + 0.866025i) q^{19} +2.00000 q^{22} +(4.89898 + 2.82843i) q^{23} +(3.67423 - 6.36396i) q^{26} -2.82843i q^{29} +(1.50000 - 0.866025i) q^{31} -6.92820i q^{34} +(-0.500000 + 0.866025i) q^{37} +(1.22474 + 2.12132i) q^{38} +7.34847 q^{41} +1.00000 q^{43} +(4.00000 + 6.92820i) q^{46} +(6.12372 - 10.6066i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(2.44949 - 1.41421i) q^{53} +(7.34847 - 1.41421i) q^{56} +(2.00000 - 3.46410i) q^{58} +(2.44949 + 4.24264i) q^{59} +(-3.00000 - 1.73205i) q^{61} +2.44949 q^{62} -8.00000 q^{64} +(5.50000 + 9.52628i) q^{67} -7.07107i q^{71} +(-1.50000 + 0.866025i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(2.44949 + 2.82843i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(9.00000 + 5.19615i) q^{82} +7.34847 q^{83} +(1.22474 + 0.707107i) q^{86} +(-2.00000 - 3.46410i) q^{88} +(-2.44949 + 4.24264i) q^{89} +(13.5000 - 2.59808i) q^{91} +(15.0000 - 8.66025i) q^{94} -10.3923i q^{97} +(-9.79796 - 1.41421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{7} + 8 q^{16} + 6 q^{19} + 8 q^{22} + 6 q^{31} - 2 q^{37} + 4 q^{43} + 16 q^{46} - 26 q^{49} + 8 q^{58} - 12 q^{61} - 32 q^{64} + 22 q^{67} - 6 q^{73} - 10 q^{79} + 36 q^{82} - 8 q^{88} + 54 q^{91} + 60 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(1226\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.22474 0.707107i 0.369274 0.213201i −0.303867 0.952714i \(-0.598278\pi\)
0.673141 + 0.739514i \(0.264945\pi\)
\(12\) 0 0
\(13\) 5.19615i 1.44115i −0.693375 0.720577i \(-0.743877\pi\)
0.693375 0.720577i \(-0.256123\pi\)
\(14\) −1.22474 + 3.53553i −0.327327 + 0.944911i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −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
\(22\) 2.00000 0.426401
\(23\) 4.89898 + 2.82843i 1.02151 + 0.589768i 0.914540 0.404495i \(-0.132553\pi\)
0.106967 + 0.994263i \(0.465886\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.67423 6.36396i 0.720577 1.24808i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.82843i 0.525226i −0.964901 0.262613i \(-0.915416\pi\)
0.964901 0.262613i \(-0.0845842\pi\)
\(30\) 0 0
\(31\) 1.50000 0.866025i 0.269408 0.155543i −0.359211 0.933257i \(-0.616954\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 6.92820i 1.18818i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.500000 + 0.866025i −0.0821995 + 0.142374i −0.904194 0.427121i \(-0.859528\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 1.22474 + 2.12132i 0.198680 + 0.344124i
\(39\) 0 0
\(40\) 0 0
\(41\) 7.34847 1.14764 0.573819 0.818982i \(-0.305461\pi\)
0.573819 + 0.818982i \(0.305461\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000 + 6.92820i 0.589768 + 1.02151i
\(47\) 6.12372 10.6066i 0.893237 1.54713i 0.0572655 0.998359i \(-0.481762\pi\)
0.835971 0.548773i \(-0.184905\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) 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
\(55\) 0 0
\(56\) 7.34847 1.41421i 0.981981 0.188982i
\(57\) 0 0
\(58\) 2.00000 3.46410i 0.262613 0.454859i
\(59\) 2.44949 + 4.24264i 0.318896 + 0.552345i 0.980258 0.197722i \(-0.0633545\pi\)
−0.661362 + 0.750067i \(0.730021\pi\)
\(60\) 0 0
\(61\) −3.00000 1.73205i −0.384111 0.221766i 0.295495 0.955344i \(-0.404516\pi\)
−0.679605 + 0.733578i \(0.737849\pi\)
\(62\) 2.44949 0.311086
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 5.50000 + 9.52628i 0.671932 + 1.16382i 0.977356 + 0.211604i \(0.0678686\pi\)
−0.305424 + 0.952217i \(0.598798\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.07107i 0.839181i −0.907713 0.419591i \(-0.862174\pi\)
0.907713 0.419591i \(-0.137826\pi\)
\(72\) 0 0
\(73\) −1.50000 + 0.866025i −0.175562 + 0.101361i −0.585206 0.810885i \(-0.698986\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) −1.22474 + 0.707107i −0.142374 + 0.0821995i
\(75\) 0 0
\(76\) 0 0
\(77\) 2.44949 + 2.82843i 0.279145 + 0.322329i
\(78\) 0 0
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 9.00000 + 5.19615i 0.993884 + 0.573819i
\(83\) 7.34847 0.806599 0.403300 0.915068i \(-0.367863\pi\)
0.403300 + 0.915068i \(0.367863\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 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 −0.966147 0.257993i \(-0.916939\pi\)
0.706502 + 0.707712i \(0.250272\pi\)
\(90\) 0 0
\(91\) 13.5000 2.59808i 1.41518 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) 15.0000 8.66025i 1.54713 0.893237i
\(95\) 0 0
\(96\) 0 0
\(97\) 10.3923i 1.05518i −0.849500 0.527589i \(-0.823096\pi\)
0.849500 0.527589i \(-0.176904\pi\)
\(98\) −9.79796 1.41421i −0.989743 0.142857i
\(99\) 0 0
\(100\) 0 0
\(101\) −8.57321 14.8492i −0.853067 1.47755i −0.878427 0.477876i \(-0.841407\pi\)
0.0253604 0.999678i \(-0.491927\pi\)
\(102\) 0 0
\(103\) 7.50000 + 4.33013i 0.738997 + 0.426660i 0.821705 0.569914i \(-0.193023\pi\)
−0.0827075 + 0.996574i \(0.526357\pi\)
\(104\) −14.6969 −1.44115
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) −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 \(0.818083\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 10.0000 + 3.46410i 0.944911 + 0.327327i
\(113\) 1.41421i 0.133038i −0.997785 0.0665190i \(-0.978811\pi\)
0.997785 0.0665190i \(-0.0211893\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 6.92820i 0.637793i
\(119\) 9.79796 8.48528i 0.898177 0.777844i
\(120\) 0 0
\(121\) −4.50000 + 7.79423i −0.409091 + 0.708566i
\(122\) −2.44949 4.24264i −0.221766 0.384111i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) −9.79796 5.65685i −0.866025 0.500000i
\(129\) 0 0
\(130\) 0 0
\(131\) 1.22474 2.12132i 0.107006 0.185341i −0.807550 0.589799i \(-0.799207\pi\)
0.914556 + 0.404459i \(0.132540\pi\)
\(132\) 0 0
\(133\) −1.50000 + 4.33013i −0.130066 + 0.375470i
\(134\) 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 \(-0.506106\pi\)
0.856276 + 0.516518i \(0.172772\pi\)
\(138\) 0 0
\(139\) 5.19615i 0.440732i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.00000 8.66025i 0.419591 0.726752i
\(143\) −3.67423 6.36396i −0.307255 0.532181i
\(144\) 0 0
\(145\) 0 0
\(146\) −2.44949 −0.202721
\(147\) 0 0
\(148\) 0 0
\(149\) −4.89898 2.82843i −0.401340 0.231714i 0.285722 0.958313i \(-0.407767\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(150\) 0 0
\(151\) 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i \(0.186277\pi\)
0.0615699 + 0.998103i \(0.480389\pi\)
\(152\) 2.44949 4.24264i 0.198680 0.344124i
\(153\) 0 0
\(154\) 1.00000 + 5.19615i 0.0805823 + 0.418718i
\(155\) 0 0
\(156\) 0 0
\(157\) −15.0000 + 8.66025i −1.19713 + 0.691164i −0.959914 0.280293i \(-0.909568\pi\)
−0.237216 + 0.971457i \(0.576235\pi\)
\(158\) −6.12372 + 3.53553i −0.487177 + 0.281272i
\(159\) 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 −0.992665 0.120900i \(-0.961422\pi\)
0.601035 + 0.799223i \(0.294755\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 9.00000 + 5.19615i 0.698535 + 0.403300i
\(167\) −7.34847 −0.568642 −0.284321 0.958729i \(-0.591768\pi\)
−0.284321 + 0.958729i \(0.591768\pi\)
\(168\) 0 0
\(169\) −14.0000 −1.07692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4.89898 + 8.48528i −0.372463 + 0.645124i −0.989944 0.141462i \(-0.954820\pi\)
0.617481 + 0.786586i \(0.288153\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.65685i 0.426401i
\(177\) 0 0
\(178\) −6.00000 + 3.46410i −0.449719 + 0.259645i
\(179\) 8.57321 4.94975i 0.640792 0.369961i −0.144127 0.989559i \(-0.546038\pi\)
0.784920 + 0.619598i \(0.212704\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i −0.815086 0.579340i \(-0.803310\pi\)
0.815086 0.579340i \(-0.196690\pi\)
\(182\) 18.3712 + 6.36396i 1.36176 + 0.471728i
\(183\) 0 0
\(184\) 8.00000 13.8564i 0.589768 1.02151i
\(185\) 0 0
\(186\) 0 0
\(187\) −6.00000 3.46410i −0.438763 0.253320i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.22474 0.707107i −0.0886194 0.0511645i 0.455035 0.890473i \(-0.349627\pi\)
−0.543655 + 0.839309i \(0.682960\pi\)
\(192\) 0 0
\(193\) 5.50000 + 9.52628i 0.395899 + 0.685717i 0.993215 0.116289i \(-0.0370998\pi\)
−0.597317 + 0.802005i \(0.703766\pi\)
\(194\) 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 \(0.496748\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 24.2487i 1.70613i
\(203\) 7.34847 1.41421i 0.515761 0.0992583i
\(204\) 0 0
\(205\) 0 0
\(206\) 6.12372 + 10.6066i 0.426660 + 0.738997i
\(207\) 0 0
\(208\) −18.0000 10.3923i −1.24808 0.720577i
\(209\) 2.44949 0.169435
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.00000 3.46410i −0.136717 0.236801i
\(215\) 0 0
\(216\) 0 0
\(217\) 3.00000 + 3.46410i 0.203653 + 0.235159i
\(218\) 1.41421i 0.0957826i
\(219\) 0 0
\(220\) 0 0
\(221\) −22.0454 + 12.7279i −1.48293 + 0.856173i
\(222\) 0 0
\(223\) 20.7846i 1.39184i 0.718119 + 0.695920i \(0.245003\pi\)
−0.718119 + 0.695920i \(0.754997\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 1.73205i 0.0665190 0.115214i
\(227\) −13.4722 23.3345i −0.894181 1.54877i −0.834815 0.550530i \(-0.814425\pi\)
−0.0593658 0.998236i \(-0.518908\pi\)
\(228\) 0 0
\(229\) 19.5000 + 11.2583i 1.28860 + 0.743971i 0.978404 0.206702i \(-0.0662732\pi\)
0.310192 + 0.950674i \(0.399607\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) 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
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 18.0000 3.46410i 1.16677 0.224544i
\(239\) 26.8701i 1.73808i 0.494742 + 0.869040i \(0.335262\pi\)
−0.494742 + 0.869040i \(0.664738\pi\)
\(240\) 0 0
\(241\) −12.0000 + 6.92820i −0.772988 + 0.446285i −0.833939 0.551856i \(-0.813920\pi\)
0.0609515 + 0.998141i \(0.480586\pi\)
\(242\) −11.0227 + 6.36396i −0.708566 + 0.409091i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.50000 7.79423i 0.286328 0.495935i
\(248\) −2.44949 4.24264i −0.155543 0.269408i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −13.4722 7.77817i −0.845321 0.488046i
\(255\) 0 0
\(256\) 0 0
\(257\) −1.22474 + 2.12132i −0.0763975 + 0.132324i −0.901693 0.432377i \(-0.857675\pi\)
0.825296 + 0.564701i \(0.191008\pi\)
\(258\) 0 0
\(259\) −2.50000 0.866025i −0.155342 0.0538122i
\(260\) 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 \(-0.810279\pi\)
0.0723633 + 0.997378i \(0.476946\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.89898 + 4.24264i −0.300376 + 0.260133i
\(267\) 0 0
\(268\) 0 0
\(269\) −8.57321 14.8492i −0.522718 0.905374i −0.999651 0.0264343i \(-0.991585\pi\)
0.476932 0.878940i \(-0.341749\pi\)
\(270\) 0 0
\(271\) −12.0000 6.92820i −0.728948 0.420858i 0.0890891 0.996024i \(-0.471604\pi\)
−0.818037 + 0.575165i \(0.804938\pi\)
\(272\) −19.5959 −1.18818
\(273\) 0 0
\(274\) 16.0000 0.966595
\(275\) 0 0
\(276\) 0 0
\(277\) 11.5000 + 19.9186i 0.690968 + 1.19679i 0.971521 + 0.236953i \(0.0761488\pi\)
−0.280553 + 0.959839i \(0.590518\pi\)
\(278\) −3.67423 + 6.36396i −0.220366 + 0.381685i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.6274i 1.34984i 0.737892 + 0.674919i \(0.235822\pi\)
−0.737892 + 0.674919i \(0.764178\pi\)
\(282\) 0 0
\(283\) −1.50000 + 0.866025i −0.0891657 + 0.0514799i −0.543920 0.839137i \(-0.683060\pi\)
0.454754 + 0.890617i \(0.349727\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 10.3923i 0.614510i
\(287\) 3.67423 + 19.0919i 0.216883 + 1.12696i
\(288\) 0 0
\(289\) −3.50000 + 6.06218i −0.205882 + 0.356599i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.6969 0.858604 0.429302 0.903161i \(-0.358760\pi\)
0.429302 + 0.903161i \(0.358760\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2.44949 + 1.41421i 0.142374 + 0.0821995i
\(297\) 0 0
\(298\) −4.00000 6.92820i −0.231714 0.401340i
\(299\) 14.6969 25.4558i 0.849946 1.47215i
\(300\) 0 0
\(301\) 0.500000 + 2.59808i 0.0288195 + 0.149751i
\(302\) 31.1127i 1.79033i
\(303\) 0 0
\(304\) 6.00000 3.46410i 0.344124 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 15.5885i 0.889680i −0.895610 0.444840i \(-0.853260\pi\)
0.895610 0.444840i \(-0.146740\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8.57321 14.8492i −0.486142 0.842023i 0.513731 0.857951i \(-0.328263\pi\)
−0.999873 + 0.0159282i \(0.994930\pi\)
\(312\) 0 0
\(313\) −10.5000 6.06218i −0.593495 0.342655i 0.172983 0.984925i \(-0.444659\pi\)
−0.766478 + 0.642270i \(0.777993\pi\)
\(314\) −24.4949 −1.38233
\(315\) 0 0
\(316\) 0 0
\(317\) 12.2474 + 7.07107i 0.687885 + 0.397151i 0.802819 0.596222i \(-0.203332\pi\)
−0.114934 + 0.993373i \(0.536666\pi\)
\(318\) 0 0
\(319\) −2.00000 3.46410i −0.111979 0.193952i
\(320\) 0 0
\(321\) 0 0
\(322\) −16.0000 + 13.8564i −0.891645 + 0.772187i
\(323\) 8.48528i 0.472134i
\(324\) 0 0
\(325\) 0 0
\(326\) −12.2474 + 7.07107i −0.678323 + 0.391630i
\(327\) 0 0
\(328\) 20.7846i 1.14764i
\(329\) 30.6186 + 10.6066i 1.68806 + 0.584761i
\(330\) 0 0
\(331\) 15.5000 26.8468i 0.851957 1.47563i −0.0274825 0.999622i \(-0.508749\pi\)
0.879440 0.476011i \(-0.157918\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −9.00000 5.19615i −0.492458 0.284321i
\(335\) 0 0
\(336\) 0 0
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) −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
\(344\) 2.82843i 0.152499i
\(345\) 0 0
\(346\) −12.0000 + 6.92820i −0.645124 + 0.372463i
\(347\) −26.9444 + 15.5563i −1.44645 + 0.835109i −0.998268 0.0588334i \(-0.981262\pi\)
−0.448183 + 0.893942i \(0.647929\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.57321 + 14.8492i 0.456306 + 0.790345i 0.998762 0.0497387i \(-0.0158389\pi\)
−0.542456 + 0.840084i \(0.682506\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 14.0000 0.739923
\(359\) 24.4949 + 14.1421i 1.29279 + 0.746393i 0.979148 0.203148i \(-0.0651171\pi\)
0.313643 + 0.949541i \(0.398450\pi\)
\(360\) 0 0
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) 11.0227 19.0919i 0.579340 1.00345i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.50000 + 0.866025i −0.0782994 + 0.0452062i −0.538639 0.842537i \(-0.681061\pi\)
0.460339 + 0.887743i \(0.347728\pi\)
\(368\) 19.5959 11.3137i 1.02151 0.589768i
\(369\) 0 0
\(370\) 0 0
\(371\) 4.89898 + 5.65685i 0.254342 + 0.293689i
\(372\) 0 0
\(373\) 14.5000 25.1147i 0.750782 1.30039i −0.196663 0.980471i \(-0.563010\pi\)
0.947444 0.319921i \(-0.103656\pi\)
\(374\) −4.89898 8.48528i −0.253320 0.438763i
\(375\) 0 0
\(376\) −30.0000 17.3205i −1.54713 0.893237i
\(377\) −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
\(382\) −1.00000 1.73205i −0.0511645 0.0886194i
\(383\) 9.79796 16.9706i 0.500652 0.867155i −0.499347 0.866402i \(-0.666427\pi\)
1.00000 0.000753393i \(-0.000239813\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.5563i 0.791797i
\(387\) 0 0
\(388\) 0 0
\(389\) 23.2702 13.4350i 1.17984 0.681183i 0.223865 0.974620i \(-0.428132\pi\)
0.955978 + 0.293437i \(0.0947991\pi\)
\(390\) 0 0
\(391\) 27.7128i 1.40150i
\(392\) 7.34847 + 18.3848i 0.371154 + 0.928571i
\(393\) 0 0
\(394\) −14.0000 + 24.2487i −0.705310 + 1.22163i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.50000 0.866025i −0.0752828 0.0434646i 0.461886 0.886939i \(-0.347173\pi\)
−0.537169 + 0.843475i \(0.680506\pi\)
\(398\) −19.5959 −0.982255
\(399\) 0 0
\(400\) 0 0
\(401\) 17.1464 + 9.89949i 0.856252 + 0.494357i 0.862755 0.505622i \(-0.168737\pi\)
−0.00650355 + 0.999979i \(0.502070\pi\)
\(402\) 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
\(407\) 1.41421i 0.0701000i
\(408\) 0 0
\(409\) 28.5000 16.4545i 1.40923 0.813622i 0.413920 0.910313i \(-0.364159\pi\)
0.995314 + 0.0966915i \(0.0308260\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −9.79796 + 8.48528i −0.482126 + 0.417533i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 3.00000 + 1.73205i 0.146735 + 0.0847174i
\(419\) −36.7423 −1.79498 −0.897491 0.441034i \(-0.854612\pi\)
−0.897491 + 0.441034i \(0.854612\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) −26.9444 15.5563i −1.31163 0.757271i
\(423\) 0 0
\(424\) −4.00000 6.92820i −0.194257 0.336463i
\(425\) 0 0
\(426\) 0 0
\(427\) 3.00000 8.66025i 0.145180 0.419099i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.4722 + 7.77817i −0.648933 + 0.374661i −0.788047 0.615615i \(-0.788908\pi\)
0.139114 + 0.990276i \(0.455574\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i 0.927200 + 0.374567i \(0.122209\pi\)
−0.927200 + 0.374567i \(0.877791\pi\)
\(434\) 1.22474 + 6.36396i 0.0587896 + 0.305480i
\(435\) 0 0
\(436\) 0 0
\(437\) 4.89898 + 8.48528i 0.234350 + 0.405906i
\(438\) 0 0
\(439\) 24.0000 + 13.8564i 1.14546 + 0.661330i 0.947776 0.318936i \(-0.103326\pi\)
0.197681 + 0.980266i \(0.436659\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −36.0000 −1.71235
\(443\) 34.2929 + 19.7990i 1.62930 + 0.940678i 0.984301 + 0.176497i \(0.0564767\pi\)
0.645002 + 0.764181i \(0.276857\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −14.6969 + 25.4558i −0.695920 + 1.20537i
\(447\) 0 0
\(448\) −4.00000 20.7846i −0.188982 0.981981i
\(449\) 7.07107i 0.333704i −0.985982 0.166852i \(-0.946640\pi\)
0.985982 0.166852i \(-0.0533603\pi\)
\(450\) 0 0
\(451\) 9.00000 5.19615i 0.423793 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) 38.1051i 1.78836i
\(455\) 0 0
\(456\) 0 0
\(457\) 2.50000 4.33013i 0.116945 0.202555i −0.801611 0.597847i \(-0.796023\pi\)
0.918556 + 0.395292i \(0.129357\pi\)
\(458\) 15.9217 + 27.5772i 0.743971 + 1.28860i
\(459\) 0 0
\(460\) 0 0
\(461\) 14.6969 0.684505 0.342252 0.939608i \(-0.388810\pi\)
0.342252 + 0.939608i \(0.388810\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) −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
\(470\) 0 0
\(471\) 0 0
\(472\) 12.0000 6.92820i 0.552345 0.318896i
\(473\) 1.22474 0.707107i 0.0563138 0.0325128i
\(474\) 0 0
\(475\) 0 0
\(476\) 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 \(-0.130967\pi\)
−0.804624 + 0.593784i \(0.797633\pi\)
\(480\) 0 0
\(481\) 4.50000 + 2.59808i 0.205182 + 0.118462i
\(482\) −19.5959 −0.892570
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.50000 + 14.7224i 0.385172 + 0.667137i 0.991793 0.127854i \(-0.0408089\pi\)
−0.606621 + 0.794991i \(0.707476\pi\)
\(488\) −4.89898 + 8.48528i −0.221766 + 0.384111i
\(489\) 0 0
\(490\) 0 0
\(491\) 11.3137i 0.510581i −0.966864 0.255290i \(-0.917829\pi\)
0.966864 0.255290i \(-0.0821710\pi\)
\(492\) 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
\(497\) 18.3712 3.53553i 0.824060 0.158590i
\(498\) 0 0
\(499\) 12.5000 21.6506i 0.559577 0.969216i −0.437955 0.898997i \(-0.644297\pi\)
0.997532 0.0702185i \(-0.0223697\pi\)
\(500\) 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
\(505\) 0 0
\(506\) 9.79796 + 5.65685i 0.435572 + 0.251478i
\(507\) 0 0
\(508\) 0 0
\(509\) 1.22474 2.12132i 0.0542859 0.0940259i −0.837605 0.546276i \(-0.816045\pi\)
0.891891 + 0.452250i \(0.149378\pi\)
\(510\) 0 0
\(511\) −3.00000 3.46410i −0.132712 0.153243i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) −3.00000 + 1.73205i −0.132324 + 0.0763975i
\(515\) 0 0
\(516\) 0 0
\(517\) 17.3205i 0.761755i
\(518\) −2.44949 2.82843i −0.107624 0.124274i
\(519\) 0 0
\(520\) 0 0
\(521\) 2.44949 + 4.24264i 0.107314 + 0.185873i 0.914681 0.404176i \(-0.132442\pi\)
−0.807367 + 0.590049i \(0.799108\pi\)
\(522\) 0 0
\(523\) −1.50000 0.866025i −0.0655904 0.0378686i 0.466846 0.884339i \(-0.345390\pi\)
−0.532437 + 0.846470i \(0.678724\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −20.0000 −0.872041
\(527\) −7.34847 4.24264i −0.320104 0.184812i
\(528\) 0 0
\(529\) 4.50000 + 7.79423i 0.195652 + 0.338880i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 38.1838i 1.65392i
\(534\) 0 0
\(535\) 0 0
\(536\) 26.9444 15.5563i 1.16382 0.671932i
\(537\) 0 0
\(538\) 24.2487i 1.04544i
\(539\) −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
\(545\) 0 0
\(546\) 0 0
\(547\) 10.0000 0.427569 0.213785 0.976881i \(-0.431421\pi\)
0.213785 + 0.976881i \(0.431421\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.44949 4.24264i 0.104352 0.180743i
\(552\) 0 0
\(553\) −12.5000 4.33013i −0.531554 0.184136i
\(554\) 32.5269i 1.38194i
\(555\) 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
\(560\) 0 0
\(561\) 0 0
\(562\) −16.0000 + 27.7128i −0.674919 + 1.16899i
\(563\) −13.4722 23.3345i −0.567785 0.983433i −0.996785 0.0801281i \(-0.974467\pi\)
0.428999 0.903305i \(-0.358866\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.44949 −0.102960
\(567\) 0 0
\(568\) −20.0000 −0.839181
\(569\) −1.22474 0.707107i −0.0513440 0.0296435i 0.474108 0.880467i \(-0.342771\pi\)
−0.525452 + 0.850823i \(0.676104\pi\)
\(570\) 0 0
\(571\) −5.50000 9.52628i −0.230168 0.398662i 0.727690 0.685907i \(-0.240594\pi\)
−0.957857 + 0.287244i \(0.907261\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −9.00000 + 25.9808i −0.375653 + 1.08442i
\(575\) 0 0
\(576\) 0 0
\(577\) −1.50000 + 0.866025i −0.0624458 + 0.0360531i −0.530898 0.847436i \(-0.678145\pi\)
0.468452 + 0.883489i \(0.344812\pi\)
\(578\) −8.57321 + 4.94975i −0.356599 + 0.205882i
\(579\) 0 0
\(580\) 0 0
\(581\) 3.67423 + 19.0919i 0.152433 + 0.792065i
\(582\) 0 0
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) 2.44949 + 4.24264i 0.101361 + 0.175562i
\(585\) 0 0
\(586\) 18.0000 + 10.3923i 0.743573 + 0.429302i
\(587\) −14.6969 −0.606608 −0.303304 0.952894i \(-0.598090\pi\)
−0.303304 + 0.952894i \(0.598090\pi\)
\(588\) 0 0
\(589\) 3.00000 0.123613
\(590\) 0 0
\(591\) 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
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 36.0000 20.7846i 1.47215 0.849946i
\(599\) 4.89898 2.82843i 0.200167 0.115566i −0.396566 0.918006i \(-0.629798\pi\)
0.596733 + 0.802440i \(0.296465\pi\)
\(600\) 0 0
\(601\) 25.9808i 1.05978i 0.848067 + 0.529889i \(0.177766\pi\)
−0.848067 + 0.529889i \(0.822234\pi\)
\(602\) −1.22474 + 3.53553i −0.0499169 + 0.144098i
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 34.5000 + 19.9186i 1.40031 + 0.808470i 0.994424 0.105453i \(-0.0336291\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −55.1135 31.8198i −2.22965 1.28729i
\(612\) 0 0
\(613\) 4.00000 + 6.92820i 0.161558 + 0.279827i 0.935428 0.353518i \(-0.115015\pi\)
−0.773869 + 0.633345i \(0.781681\pi\)
\(614\) 11.0227 19.0919i 0.444840 0.770486i
\(615\) 0 0
\(616\) 8.00000 6.92820i 0.322329 0.279145i
\(617\) 24.0416i 0.967880i 0.875101 + 0.483940i \(0.160795\pi\)
−0.875101 + 0.483940i \(0.839205\pi\)
\(618\) 0 0
\(619\) −25.5000 + 14.7224i −1.02493 + 0.591744i −0.915529 0.402253i \(-0.868227\pi\)
−0.109403 + 0.993997i \(0.534894\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.2487i 0.972285i
\(623\) −12.2474 4.24264i −0.490684 0.169978i
\(624\) 0 0
\(625\) 0 0
\(626\) −8.57321 14.8492i −0.342655 0.593495i
\(627\) 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 \(0.226967\pi\)
\(632\) 12.2474 + 7.07107i 0.487177 + 0.281272i
\(633\) 0 0
\(634\) 10.0000 + 17.3205i 0.397151 + 0.687885i
\(635\) 0 0
\(636\) 0 0
\(637\) 13.5000 + 33.7750i 0.534889 + 1.33821i
\(638\) 5.65685i 0.223957i
\(639\) 0 0
\(640\) 0 0
\(641\) 12.2474 7.07107i 0.483745 0.279290i −0.238231 0.971209i \(-0.576567\pi\)
0.721976 + 0.691918i \(0.243234\pi\)
\(642\) 0 0
\(643\) 25.9808i 1.02458i 0.858812 + 0.512291i \(0.171203\pi\)
−0.858812 + 0.512291i \(0.828797\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) 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
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.12372 3.53553i −0.239640 0.138356i 0.375371 0.926875i \(-0.377515\pi\)
−0.615011 + 0.788518i \(0.710849\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 14.6969 25.4558i 0.573819 0.993884i
\(657\) 0 0
\(658\) 30.0000 + 34.6410i 1.16952 + 1.35045i
\(659\) 22.6274i 0.881439i 0.897645 + 0.440720i \(0.145277\pi\)
−0.897645 + 0.440720i \(0.854723\pi\)
\(660\) 0 0
\(661\) −25.5000 + 14.7224i −0.991835 + 0.572636i −0.905822 0.423658i \(-0.860746\pi\)
−0.0860127 + 0.996294i \(0.527413\pi\)
\(662\) 37.9671 21.9203i 1.47563 0.851957i
\(663\) 0 0
\(664\) 20.7846i 0.806599i
\(665\) 0 0
\(666\) 0 0
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.89898 −0.189123
\(672\) 0 0
\(673\) −35.0000 −1.34915 −0.674575 0.738206i \(-0.735673\pi\)
−0.674575 + 0.738206i \(0.735673\pi\)
\(674\) −28.1691 16.2635i −1.08503 0.626445i
\(675\) 0 0
\(676\) 0 0
\(677\) −4.89898 + 8.48528i −0.188283 + 0.326116i −0.944678 0.327999i \(-0.893626\pi\)
0.756395 + 0.654115i \(0.226959\pi\)
\(678\) 0 0
\(679\) 27.0000 5.19615i 1.03616 0.199410i
\(680\) 0 0
\(681\) 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
\(685\) 0 0
\(686\) −1.22474 26.1630i −0.0467610 0.998906i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −7.34847 12.7279i −0.279954 0.484895i
\(690\) 0 0
\(691\) 37.5000 + 21.6506i 1.42657 + 0.823629i 0.996848 0.0793336i \(-0.0252792\pi\)
0.429719 + 0.902963i \(0.358613\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −44.0000 −1.67022
\(695\) 0 0
\(696\) 0 0
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) −7.34847 + 12.7279i −0.278144 + 0.481759i
\(699\) 0 0
\(700\) 0 0
\(701\) 5.65685i 0.213656i 0.994277 + 0.106828i \(0.0340695\pi\)
−0.994277 + 0.106828i \(0.965931\pi\)
\(702\) 0 0
\(703\) −1.50000 + 0.866025i −0.0565736 + 0.0326628i
\(704\) −9.79796 + 5.65685i −0.369274 + 0.213201i
\(705\) 0 0
\(706\) 24.2487i 0.912612i
\(707\) 34.2929 29.6985i 1.28972 1.11693i
\(708\) 0 0
\(709\) 20.0000 34.6410i 0.751116 1.30097i −0.196167 0.980571i \(-0.562849\pi\)
0.947282 0.320400i \(-0.103817\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 12.0000 + 6.92820i 0.449719 + 0.259645i
\(713\) 9.79796 0.366936
\(714\) 0 0
\(715\) 0 0
\(716\) 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 \(0.334226\pi\)
−0.999996 + 0.00280593i \(0.999107\pi\)
\(720\) 0 0
\(721\) −7.50000 + 21.6506i −0.279315 + 0.806312i
\(722\) 22.6274i 0.842105i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 25.9808i 0.963573i −0.876289 0.481787i \(-0.839988\pi\)
0.876289 0.481787i \(-0.160012\pi\)
\(728\) −7.34847 38.1838i −0.272352 1.41518i
\(729\) 0 0
\(730\) 0 0
\(731\) −2.44949 4.24264i −0.0905977 0.156920i
\(732\) 0 0
\(733\) 34.5000 + 19.9186i 1.27429 + 0.735710i 0.975792 0.218702i \(-0.0701821\pi\)
0.298495 + 0.954411i \(0.403515\pi\)
\(734\) −2.44949 −0.0904123
\(735\) 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
\(742\) 2.00000 + 10.3923i 0.0734223 + 0.381514i
\(743\) 24.0416i 0.882002i 0.897507 + 0.441001i \(0.145376\pi\)
−0.897507 + 0.441001i \(0.854624\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 35.5176 20.5061i 1.30039 0.750782i
\(747\) 0 0
\(748\) 0 0
\(749\) 2.44949 7.07107i 0.0895024 0.258371i
\(750\) 0 0
\(751\) −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i \(0.344142\pi\)
−0.999424 + 0.0339490i \(0.989192\pi\)
\(752\) −24.4949 42.4264i −0.893237 1.54713i
\(753\) 0 0
\(754\) −18.0000 10.3923i −0.655521 0.378465i
\(755\) 0 0
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −8.57321 4.94975i −0.311393 0.179783i
\(759\) 0 0
\(760\) 0 0
\(761\) 12.2474 21.2132i 0.443970 0.768978i −0.554010 0.832510i \(-0.686903\pi\)
0.997980 + 0.0635319i \(0.0202365\pi\)
\(762\) 0 0
\(763\) −2.00000 + 1.73205i −0.0724049 + 0.0627044i
\(764\) 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
\(769\) 25.9808i 0.936890i −0.883493 0.468445i \(-0.844814\pi\)
0.883493 0.468445i \(-0.155186\pi\)
\(770\) 0 0
\(771\) 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
\(775\) 0 0
\(776\) −29.3939 −1.05518
\(777\) 0 0
\(778\) 38.0000 1.36237
\(779\) 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
\(785\) 0 0
\(786\) 0 0
\(787\) 39.0000 22.5167i 1.39020 0.802632i 0.396863 0.917878i \(-0.370099\pi\)
0.993337 + 0.115246i \(0.0367655\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.67423 0.707107i 0.130641 0.0251418i
\(792\) 0