Properties

Label 416.2.k.d.255.1
Level $416$
Weight $2$
Character 416.255
Analytic conductor $3.322$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(31,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.k (of order \(4\), 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: \(3.32177672409\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 255.1
Root \(-1.58114 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 416.255
Dual form 416.2.k.d.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{3} +(-1.58114 - 1.58114i) q^{5} +(-1.58114 - 1.58114i) q^{7} +2.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{3} +(-1.58114 - 1.58114i) q^{5} +(-1.58114 - 1.58114i) q^{7} +2.00000 q^{9} +(4.16228 + 4.16228i) q^{11} +(3.58114 - 0.418861i) q^{13} +(1.58114 - 1.58114i) q^{15} -7.32456i q^{17} +(1.16228 - 1.16228i) q^{19} +(1.58114 - 1.58114i) q^{21} +7.16228 q^{23} +5.00000i q^{27} -1.16228 q^{29} +(-1.16228 + 1.16228i) q^{31} +(-4.16228 + 4.16228i) q^{33} +5.00000i q^{35} +(-3.58114 + 3.58114i) q^{37} +(0.418861 + 3.58114i) q^{39} +(5.16228 + 5.16228i) q^{41} -5.00000 q^{43} +(-3.16228 - 3.16228i) q^{45} +(-6.74342 - 6.74342i) q^{47} -2.00000i q^{49} +7.32456 q^{51} +9.48683 q^{53} -13.1623i q^{55} +(1.16228 + 1.16228i) q^{57} +(-4.00000 - 4.00000i) q^{59} +2.00000 q^{61} +(-3.16228 - 3.16228i) q^{63} +(-6.32456 - 5.00000i) q^{65} +(-7.32456 + 7.32456i) q^{67} +7.16228i q^{69} +(-1.58114 + 1.58114i) q^{71} +(-6.00000 + 6.00000i) q^{73} -13.1623i q^{77} +3.48683i q^{79} +1.00000 q^{81} +(5.83772 - 5.83772i) q^{83} +(-11.5811 + 11.5811i) q^{85} -1.16228i q^{87} +(-2.83772 + 2.83772i) q^{89} +(-6.32456 - 5.00000i) q^{91} +(-1.16228 - 1.16228i) q^{93} -3.67544 q^{95} +(-3.83772 - 3.83772i) q^{97} +(8.32456 + 8.32456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{9} + 4 q^{11} + 8 q^{13} - 8 q^{19} + 16 q^{23} + 8 q^{29} + 8 q^{31} - 4 q^{33} - 8 q^{37} + 8 q^{39} + 8 q^{41} - 20 q^{43} - 8 q^{47} + 4 q^{51} - 8 q^{57} - 16 q^{59} + 8 q^{61} - 4 q^{67} - 24 q^{73} + 4 q^{81} + 36 q^{83} - 40 q^{85} - 24 q^{89} + 8 q^{93} - 40 q^{95} - 28 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(287\) \(353\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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 0
\(3\) 1.00000i 0.577350i 0.957427 + 0.288675i \(0.0932147\pi\)
−0.957427 + 0.288675i \(0.906785\pi\)
\(4\) 0 0
\(5\) −1.58114 1.58114i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(6\) 0 0
\(7\) −1.58114 1.58114i −0.597614 0.597614i 0.342063 0.939677i \(-0.388874\pi\)
−0.939677 + 0.342063i \(0.888874\pi\)
\(8\) 0 0
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) 4.16228 + 4.16228i 1.25497 + 1.25497i 0.953463 + 0.301511i \(0.0974911\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 3.58114 0.418861i 0.993229 0.116171i
\(14\) 0 0
\(15\) 1.58114 1.58114i 0.408248 0.408248i
\(16\) 0 0
\(17\) 7.32456i 1.77647i −0.459394 0.888233i \(-0.651933\pi\)
0.459394 0.888233i \(-0.348067\pi\)
\(18\) 0 0
\(19\) 1.16228 1.16228i 0.266645 0.266645i −0.561102 0.827747i \(-0.689622\pi\)
0.827747 + 0.561102i \(0.189622\pi\)
\(20\) 0 0
\(21\) 1.58114 1.58114i 0.345033 0.345033i
\(22\) 0 0
\(23\) 7.16228 1.49344 0.746719 0.665140i \(-0.231628\pi\)
0.746719 + 0.665140i \(0.231628\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) −1.16228 −0.215830 −0.107915 0.994160i \(-0.534417\pi\)
−0.107915 + 0.994160i \(0.534417\pi\)
\(30\) 0 0
\(31\) −1.16228 + 1.16228i −0.208751 + 0.208751i −0.803737 0.594985i \(-0.797158\pi\)
0.594985 + 0.803737i \(0.297158\pi\)
\(32\) 0 0
\(33\) −4.16228 + 4.16228i −0.724560 + 0.724560i
\(34\) 0 0
\(35\) 5.00000i 0.845154i
\(36\) 0 0
\(37\) −3.58114 + 3.58114i −0.588736 + 0.588736i −0.937289 0.348553i \(-0.886673\pi\)
0.348553 + 0.937289i \(0.386673\pi\)
\(38\) 0 0
\(39\) 0.418861 + 3.58114i 0.0670715 + 0.573441i
\(40\) 0 0
\(41\) 5.16228 + 5.16228i 0.806212 + 0.806212i 0.984058 0.177846i \(-0.0569129\pi\)
−0.177846 + 0.984058i \(0.556913\pi\)
\(42\) 0 0
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) −3.16228 3.16228i −0.471405 0.471405i
\(46\) 0 0
\(47\) −6.74342 6.74342i −0.983628 0.983628i 0.0162397 0.999868i \(-0.494831\pi\)
−0.999868 + 0.0162397i \(0.994831\pi\)
\(48\) 0 0
\(49\) 2.00000i 0.285714i
\(50\) 0 0
\(51\) 7.32456 1.02564
\(52\) 0 0
\(53\) 9.48683 1.30312 0.651558 0.758599i \(-0.274116\pi\)
0.651558 + 0.758599i \(0.274116\pi\)
\(54\) 0 0
\(55\) 13.1623i 1.77480i
\(56\) 0 0
\(57\) 1.16228 + 1.16228i 0.153947 + 0.153947i
\(58\) 0 0
\(59\) −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) −3.16228 3.16228i −0.398410 0.398410i
\(64\) 0 0
\(65\) −6.32456 5.00000i −0.784465 0.620174i
\(66\) 0 0
\(67\) −7.32456 + 7.32456i −0.894837 + 0.894837i −0.994974 0.100137i \(-0.968072\pi\)
0.100137 + 0.994974i \(0.468072\pi\)
\(68\) 0 0
\(69\) 7.16228i 0.862237i
\(70\) 0 0
\(71\) −1.58114 + 1.58114i −0.187647 + 0.187647i −0.794678 0.607031i \(-0.792360\pi\)
0.607031 + 0.794678i \(0.292360\pi\)
\(72\) 0 0
\(73\) −6.00000 + 6.00000i −0.702247 + 0.702247i −0.964892 0.262646i \(-0.915405\pi\)
0.262646 + 0.964892i \(0.415405\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13.1623i 1.49998i
\(78\) 0 0
\(79\) 3.48683i 0.392299i 0.980574 + 0.196150i \(0.0628438\pi\)
−0.980574 + 0.196150i \(0.937156\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 5.83772 5.83772i 0.640773 0.640773i −0.309972 0.950746i \(-0.600320\pi\)
0.950746 + 0.309972i \(0.100320\pi\)
\(84\) 0 0
\(85\) −11.5811 + 11.5811i −1.25615 + 1.25615i
\(86\) 0 0
\(87\) 1.16228i 0.124609i
\(88\) 0 0
\(89\) −2.83772 + 2.83772i −0.300798 + 0.300798i −0.841326 0.540528i \(-0.818224\pi\)
0.540528 + 0.841326i \(0.318224\pi\)
\(90\) 0 0
\(91\) −6.32456 5.00000i −0.662994 0.524142i
\(92\) 0 0
\(93\) −1.16228 1.16228i −0.120523 0.120523i
\(94\) 0 0
\(95\) −3.67544 −0.377093
\(96\) 0 0
\(97\) −3.83772 3.83772i −0.389662 0.389662i 0.484905 0.874567i \(-0.338854\pi\)
−0.874567 + 0.484905i \(0.838854\pi\)
\(98\) 0 0
\(99\) 8.32456 + 8.32456i 0.836649 + 0.836649i
\(100\) 0 0
\(101\) 10.3246i 1.02733i 0.857990 + 0.513666i \(0.171713\pi\)
−0.857990 + 0.513666i \(0.828287\pi\)
\(102\) 0 0
\(103\) −7.48683 −0.737700 −0.368850 0.929489i \(-0.620248\pi\)
−0.368850 + 0.929489i \(0.620248\pi\)
\(104\) 0 0
\(105\) −5.00000 −0.487950
\(106\) 0 0
\(107\) 12.3246i 1.19146i −0.803185 0.595730i \(-0.796863\pi\)
0.803185 0.595730i \(-0.203137\pi\)
\(108\) 0 0
\(109\) −1.25658 1.25658i −0.120359 0.120359i 0.644362 0.764721i \(-0.277123\pi\)
−0.764721 + 0.644362i \(0.777123\pi\)
\(110\) 0 0
\(111\) −3.58114 3.58114i −0.339907 0.339907i
\(112\) 0 0
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 0 0
\(115\) −11.3246 11.3246i −1.05602 1.05602i
\(116\) 0 0
\(117\) 7.16228 0.837722i 0.662153 0.0774475i
\(118\) 0 0
\(119\) −11.5811 + 11.5811i −1.06164 + 1.06164i
\(120\) 0 0
\(121\) 23.6491i 2.14992i
\(122\) 0 0
\(123\) −5.16228 + 5.16228i −0.465467 + 0.465467i
\(124\) 0 0
\(125\) −7.90569 + 7.90569i −0.707107 + 0.707107i
\(126\) 0 0
\(127\) 8.83772 0.784221 0.392111 0.919918i \(-0.371745\pi\)
0.392111 + 0.919918i \(0.371745\pi\)
\(128\) 0 0
\(129\) 5.00000i 0.440225i
\(130\) 0 0
\(131\) 11.6491i 1.01779i −0.860829 0.508894i \(-0.830055\pi\)
0.860829 0.508894i \(-0.169945\pi\)
\(132\) 0 0
\(133\) −3.67544 −0.318701
\(134\) 0 0
\(135\) 7.90569 7.90569i 0.680414 0.680414i
\(136\) 0 0
\(137\) −3.00000 + 3.00000i −0.256307 + 0.256307i −0.823550 0.567243i \(-0.808010\pi\)
0.567243 + 0.823550i \(0.308010\pi\)
\(138\) 0 0
\(139\) 15.3246i 1.29981i 0.760015 + 0.649906i \(0.225192\pi\)
−0.760015 + 0.649906i \(0.774808\pi\)
\(140\) 0 0
\(141\) 6.74342 6.74342i 0.567898 0.567898i
\(142\) 0 0
\(143\) 16.6491 + 13.1623i 1.39227 + 1.10068i
\(144\) 0 0
\(145\) 1.83772 + 1.83772i 0.152615 + 0.152615i
\(146\) 0 0
\(147\) 2.00000 0.164957
\(148\) 0 0
\(149\) 2.00000 + 2.00000i 0.163846 + 0.163846i 0.784268 0.620422i \(-0.213039\pi\)
−0.620422 + 0.784268i \(0.713039\pi\)
\(150\) 0 0
\(151\) −1.25658 1.25658i −0.102259 0.102259i 0.654126 0.756385i \(-0.273037\pi\)
−0.756385 + 0.654126i \(0.773037\pi\)
\(152\) 0 0
\(153\) 14.6491i 1.18431i
\(154\) 0 0
\(155\) 3.67544 0.295219
\(156\) 0 0
\(157\) −22.9737 −1.83350 −0.916749 0.399464i \(-0.869196\pi\)
−0.916749 + 0.399464i \(0.869196\pi\)
\(158\) 0 0
\(159\) 9.48683i 0.752355i
\(160\) 0 0
\(161\) −11.3246 11.3246i −0.892500 0.892500i
\(162\) 0 0
\(163\) −9.00000 9.00000i −0.704934 0.704934i 0.260531 0.965465i \(-0.416102\pi\)
−0.965465 + 0.260531i \(0.916102\pi\)
\(164\) 0 0
\(165\) 13.1623 1.02468
\(166\) 0 0
\(167\) 17.4868 + 17.4868i 1.35317 + 1.35317i 0.882089 + 0.471083i \(0.156137\pi\)
0.471083 + 0.882089i \(0.343863\pi\)
\(168\) 0 0
\(169\) 12.6491 3.00000i 0.973009 0.230769i
\(170\) 0 0
\(171\) 2.32456 2.32456i 0.177763 0.177763i
\(172\) 0 0
\(173\) 3.48683i 0.265099i −0.991176 0.132550i \(-0.957684\pi\)
0.991176 0.132550i \(-0.0423164\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000 4.00000i 0.300658 0.300658i
\(178\) 0 0
\(179\) −15.6491 −1.16967 −0.584835 0.811152i \(-0.698841\pi\)
−0.584835 + 0.811152i \(0.698841\pi\)
\(180\) 0 0
\(181\) 2.83772i 0.210926i −0.994423 0.105463i \(-0.966368\pi\)
0.994423 0.105463i \(-0.0336325\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 0 0
\(185\) 11.3246 0.832598
\(186\) 0 0
\(187\) 30.4868 30.4868i 2.22942 2.22942i
\(188\) 0 0
\(189\) 7.90569 7.90569i 0.575055 0.575055i
\(190\) 0 0
\(191\) 18.8377i 1.36305i 0.731795 + 0.681525i \(0.238683\pi\)
−0.731795 + 0.681525i \(0.761317\pi\)
\(192\) 0 0
\(193\) −2.16228 + 2.16228i −0.155644 + 0.155644i −0.780633 0.624989i \(-0.785103\pi\)
0.624989 + 0.780633i \(0.285103\pi\)
\(194\) 0 0
\(195\) 5.00000 6.32456i 0.358057 0.452911i
\(196\) 0 0
\(197\) 7.58114 + 7.58114i 0.540134 + 0.540134i 0.923568 0.383434i \(-0.125259\pi\)
−0.383434 + 0.923568i \(0.625259\pi\)
\(198\) 0 0
\(199\) −27.1623 −1.92548 −0.962741 0.270424i \(-0.912836\pi\)
−0.962741 + 0.270424i \(0.912836\pi\)
\(200\) 0 0
\(201\) −7.32456 7.32456i −0.516634 0.516634i
\(202\) 0 0
\(203\) 1.83772 + 1.83772i 0.128983 + 0.128983i
\(204\) 0 0
\(205\) 16.3246i 1.14016i
\(206\) 0 0
\(207\) 14.3246 0.995625
\(208\) 0 0
\(209\) 9.67544 0.669265
\(210\) 0 0
\(211\) 9.64911i 0.664272i 0.943231 + 0.332136i \(0.107769\pi\)
−0.943231 + 0.332136i \(0.892231\pi\)
\(212\) 0 0
\(213\) −1.58114 1.58114i −0.108338 0.108338i
\(214\) 0 0
\(215\) 7.90569 + 7.90569i 0.539164 + 0.539164i
\(216\) 0 0
\(217\) 3.67544 0.249505
\(218\) 0 0
\(219\) −6.00000 6.00000i −0.405442 0.405442i
\(220\) 0 0
\(221\) −3.06797 26.2302i −0.206374 1.76444i
\(222\) 0 0
\(223\) 9.06797 9.06797i 0.607236 0.607236i −0.334987 0.942223i \(-0.608732\pi\)
0.942223 + 0.334987i \(0.108732\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.16228 3.16228i 0.209888 0.209888i −0.594332 0.804220i \(-0.702583\pi\)
0.804220 + 0.594332i \(0.202583\pi\)
\(228\) 0 0
\(229\) 5.90569 5.90569i 0.390259 0.390259i −0.484521 0.874780i \(-0.661006\pi\)
0.874780 + 0.484521i \(0.161006\pi\)
\(230\) 0 0
\(231\) 13.1623 0.866014
\(232\) 0 0
\(233\) 7.32456i 0.479848i 0.970792 + 0.239924i \(0.0771225\pi\)
−0.970792 + 0.239924i \(0.922878\pi\)
\(234\) 0 0
\(235\) 21.3246i 1.39106i
\(236\) 0 0
\(237\) −3.48683 −0.226494
\(238\) 0 0
\(239\) −12.4189 + 12.4189i −0.803309 + 0.803309i −0.983611 0.180302i \(-0.942293\pi\)
0.180302 + 0.983611i \(0.442293\pi\)
\(240\) 0 0
\(241\) 3.48683 3.48683i 0.224607 0.224607i −0.585828 0.810435i \(-0.699231\pi\)
0.810435 + 0.585828i \(0.199231\pi\)
\(242\) 0 0
\(243\) 16.0000i 1.02640i
\(244\) 0 0
\(245\) −3.16228 + 3.16228i −0.202031 + 0.202031i
\(246\) 0 0
\(247\) 3.67544 4.64911i 0.233863 0.295816i
\(248\) 0 0
\(249\) 5.83772 + 5.83772i 0.369951 + 0.369951i
\(250\) 0 0
\(251\) −6.64911 −0.419688 −0.209844 0.977735i \(-0.567296\pi\)
−0.209844 + 0.977735i \(0.567296\pi\)
\(252\) 0 0
\(253\) 29.8114 + 29.8114i 1.87423 + 1.87423i
\(254\) 0 0
\(255\) −11.5811 11.5811i −0.725239 0.725239i
\(256\) 0 0
\(257\) 4.35089i 0.271401i −0.990750 0.135701i \(-0.956672\pi\)
0.990750 0.135701i \(-0.0433285\pi\)
\(258\) 0 0
\(259\) 11.3246 0.703674
\(260\) 0 0
\(261\) −2.32456 −0.143886
\(262\) 0 0
\(263\) 6.00000i 0.369976i 0.982741 + 0.184988i \(0.0592246\pi\)
−0.982741 + 0.184988i \(0.940775\pi\)
\(264\) 0 0
\(265\) −15.0000 15.0000i −0.921443 0.921443i
\(266\) 0 0
\(267\) −2.83772 2.83772i −0.173666 0.173666i
\(268\) 0 0
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) −9.06797 9.06797i −0.550840 0.550840i 0.375843 0.926683i \(-0.377353\pi\)
−0.926683 + 0.375843i \(0.877353\pi\)
\(272\) 0 0
\(273\) 5.00000 6.32456i 0.302614 0.382780i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12.3246i 0.740511i 0.928930 + 0.370255i \(0.120730\pi\)
−0.928930 + 0.370255i \(0.879270\pi\)
\(278\) 0 0
\(279\) −2.32456 + 2.32456i −0.139167 + 0.139167i
\(280\) 0 0
\(281\) 1.48683 1.48683i 0.0886970 0.0886970i −0.661366 0.750063i \(-0.730023\pi\)
0.750063 + 0.661366i \(0.230023\pi\)
\(282\) 0 0
\(283\) 0.649111 0.0385856 0.0192928 0.999814i \(-0.493859\pi\)
0.0192928 + 0.999814i \(0.493859\pi\)
\(284\) 0 0
\(285\) 3.67544i 0.217715i
\(286\) 0 0
\(287\) 16.3246i 0.963608i
\(288\) 0 0
\(289\) −36.6491 −2.15583
\(290\) 0 0
\(291\) 3.83772 3.83772i 0.224971 0.224971i
\(292\) 0 0
\(293\) −7.25658 + 7.25658i −0.423934 + 0.423934i −0.886556 0.462622i \(-0.846909\pi\)
0.462622 + 0.886556i \(0.346909\pi\)
\(294\) 0 0
\(295\) 12.6491i 0.736460i
\(296\) 0 0
\(297\) −20.8114 + 20.8114i −1.20760 + 1.20760i
\(298\) 0 0
\(299\) 25.6491 3.00000i 1.48333 0.173494i
\(300\) 0 0
\(301\) 7.90569 + 7.90569i 0.455677 + 0.455677i
\(302\) 0 0
\(303\) −10.3246 −0.593130
\(304\) 0 0
\(305\) −3.16228 3.16228i −0.181071 0.181071i
\(306\) 0 0
\(307\) −0.324555 0.324555i −0.0185234 0.0185234i 0.697784 0.716308i \(-0.254169\pi\)
−0.716308 + 0.697784i \(0.754169\pi\)
\(308\) 0 0
\(309\) 7.48683i 0.425911i
\(310\) 0 0
\(311\) 24.9737 1.41613 0.708063 0.706149i \(-0.249569\pi\)
0.708063 + 0.706149i \(0.249569\pi\)
\(312\) 0 0
\(313\) 15.6491 0.884540 0.442270 0.896882i \(-0.354173\pi\)
0.442270 + 0.896882i \(0.354173\pi\)
\(314\) 0 0
\(315\) 10.0000i 0.563436i
\(316\) 0 0
\(317\) −20.3246 20.3246i −1.14154 1.14154i −0.988168 0.153372i \(-0.950987\pi\)
−0.153372 0.988168i \(-0.549013\pi\)
\(318\) 0 0
\(319\) −4.83772 4.83772i −0.270860 0.270860i
\(320\) 0 0
\(321\) 12.3246 0.687890
\(322\) 0 0
\(323\) −8.51317 8.51317i −0.473685 0.473685i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.25658 1.25658i 0.0694892 0.0694892i
\(328\) 0 0
\(329\) 21.3246i 1.17566i
\(330\) 0 0
\(331\) −14.4868 + 14.4868i −0.796268 + 0.796268i −0.982505 0.186237i \(-0.940371\pi\)
0.186237 + 0.982505i \(0.440371\pi\)
\(332\) 0 0
\(333\) −7.16228 + 7.16228i −0.392490 + 0.392490i
\(334\) 0 0
\(335\) 23.1623 1.26549
\(336\) 0 0
\(337\) 9.64911i 0.525621i −0.964848 0.262810i \(-0.915351\pi\)
0.964848 0.262810i \(-0.0846493\pi\)
\(338\) 0 0
\(339\) 16.0000i 0.869001i
\(340\) 0 0
\(341\) −9.67544 −0.523955
\(342\) 0 0
\(343\) −14.2302 + 14.2302i −0.768361 + 0.768361i
\(344\) 0 0
\(345\) 11.3246 11.3246i 0.609694 0.609694i
\(346\) 0 0
\(347\) 24.2982i 1.30440i −0.758048 0.652198i \(-0.773847\pi\)
0.758048 0.652198i \(-0.226153\pi\)
\(348\) 0 0
\(349\) −2.41886 + 2.41886i −0.129479 + 0.129479i −0.768876 0.639398i \(-0.779184\pi\)
0.639398 + 0.768876i \(0.279184\pi\)
\(350\) 0 0
\(351\) 2.09431 + 17.9057i 0.111786 + 0.955735i
\(352\) 0 0
\(353\) 0.162278 + 0.162278i 0.00863717 + 0.00863717i 0.711412 0.702775i \(-0.248056\pi\)
−0.702775 + 0.711412i \(0.748056\pi\)
\(354\) 0 0
\(355\) 5.00000 0.265372
\(356\) 0 0
\(357\) −11.5811 11.5811i −0.612939 0.612939i
\(358\) 0 0
\(359\) −14.8377 14.8377i −0.783105 0.783105i 0.197248 0.980354i \(-0.436799\pi\)
−0.980354 + 0.197248i \(0.936799\pi\)
\(360\) 0 0
\(361\) 16.2982i 0.857801i
\(362\) 0 0
\(363\) −23.6491 −1.24126
\(364\) 0 0
\(365\) 18.9737 0.993127
\(366\) 0 0
\(367\) 23.1623i 1.20906i −0.796582 0.604531i \(-0.793361\pi\)
0.796582 0.604531i \(-0.206639\pi\)
\(368\) 0 0
\(369\) 10.3246 + 10.3246i 0.537475 + 0.537475i
\(370\) 0 0
\(371\) −15.0000 15.0000i −0.778761 0.778761i
\(372\) 0 0
\(373\) −12.6491 −0.654946 −0.327473 0.944861i \(-0.606197\pi\)
−0.327473 + 0.944861i \(0.606197\pi\)
\(374\) 0 0
\(375\) −7.90569 7.90569i −0.408248 0.408248i
\(376\) 0 0
\(377\) −4.16228 + 0.486833i −0.214368 + 0.0250732i
\(378\) 0 0
\(379\) −13.0000 + 13.0000i −0.667765 + 0.667765i −0.957198 0.289433i \(-0.906533\pi\)
0.289433 + 0.957198i \(0.406533\pi\)
\(380\) 0 0
\(381\) 8.83772i 0.452770i
\(382\) 0 0
\(383\) 16.7434 16.7434i 0.855549 0.855549i −0.135261 0.990810i \(-0.543187\pi\)
0.990810 + 0.135261i \(0.0431874\pi\)
\(384\) 0 0
\(385\) −20.8114 + 20.8114i −1.06065 + 1.06065i
\(386\) 0 0
\(387\) −10.0000 −0.508329
\(388\) 0 0
\(389\) 4.00000i 0.202808i 0.994845 + 0.101404i \(0.0323335\pi\)
−0.994845 + 0.101404i \(0.967667\pi\)
\(390\) 0 0
\(391\) 52.4605i 2.65304i
\(392\) 0 0
\(393\) 11.6491 0.587620
\(394\) 0 0
\(395\) 5.51317 5.51317i 0.277398 0.277398i
\(396\) 0 0
\(397\) −23.2982 + 23.2982i −1.16930 + 1.16930i −0.186931 + 0.982373i \(0.559854\pi\)
−0.982373 + 0.186931i \(0.940146\pi\)
\(398\) 0 0
\(399\) 3.67544i 0.184002i
\(400\) 0 0
\(401\) 23.9737 23.9737i 1.19719 1.19719i 0.222183 0.975005i \(-0.428682\pi\)
0.975005 0.222183i \(-0.0713181\pi\)
\(402\) 0 0
\(403\) −3.67544 + 4.64911i −0.183087 + 0.231589i
\(404\) 0 0
\(405\) −1.58114 1.58114i −0.0785674 0.0785674i
\(406\) 0 0
\(407\) −29.8114 −1.47770
\(408\) 0 0
\(409\) 23.3246 + 23.3246i 1.15333 + 1.15333i 0.985882 + 0.167443i \(0.0535511\pi\)
0.167443 + 0.985882i \(0.446449\pi\)
\(410\) 0 0
\(411\) −3.00000 3.00000i −0.147979 0.147979i
\(412\) 0 0
\(413\) 12.6491i 0.622422i
\(414\) 0 0
\(415\) −18.4605 −0.906190
\(416\) 0 0
\(417\) −15.3246 −0.750447
\(418\) 0 0
\(419\) 4.67544i 0.228410i 0.993457 + 0.114205i \(0.0364321\pi\)
−0.993457 + 0.114205i \(0.963568\pi\)
\(420\) 0 0
\(421\) −2.41886 2.41886i −0.117888 0.117888i 0.645702 0.763590i \(-0.276565\pi\)
−0.763590 + 0.645702i \(0.776565\pi\)
\(422\) 0 0
\(423\) −13.4868 13.4868i −0.655752 0.655752i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.16228 3.16228i −0.153033 0.153033i
\(428\) 0 0
\(429\) −13.1623 + 16.6491i −0.635481 + 0.803827i
\(430\) 0 0
\(431\) −23.3925 + 23.3925i −1.12678 + 1.12678i −0.136081 + 0.990698i \(0.543451\pi\)
−0.990698 + 0.136081i \(0.956549\pi\)
\(432\) 0 0
\(433\) 9.97367i 0.479304i −0.970859 0.239652i \(-0.922967\pi\)
0.970859 0.239652i \(-0.0770333\pi\)
\(434\) 0 0
\(435\) −1.83772 + 1.83772i −0.0881120 + 0.0881120i
\(436\) 0 0
\(437\) 8.32456 8.32456i 0.398217 0.398217i
\(438\) 0 0
\(439\) −0.649111 −0.0309804 −0.0154902 0.999880i \(-0.504931\pi\)
−0.0154902 + 0.999880i \(0.504931\pi\)
\(440\) 0 0
\(441\) 4.00000i 0.190476i
\(442\) 0 0
\(443\) 30.2982i 1.43951i 0.694227 + 0.719756i \(0.255746\pi\)
−0.694227 + 0.719756i \(0.744254\pi\)
\(444\) 0 0
\(445\) 8.97367 0.425393
\(446\) 0 0
\(447\) −2.00000 + 2.00000i −0.0945968 + 0.0945968i
\(448\) 0 0
\(449\) −26.4868 + 26.4868i −1.24999 + 1.24999i −0.294268 + 0.955723i \(0.595076\pi\)
−0.955723 + 0.294268i \(0.904924\pi\)
\(450\) 0 0
\(451\) 42.9737i 2.02355i
\(452\) 0 0
\(453\) 1.25658 1.25658i 0.0590394 0.0590394i
\(454\) 0 0
\(455\) 2.09431 + 17.9057i 0.0981826 + 0.839432i
\(456\) 0 0
\(457\) −25.8114 25.8114i −1.20741 1.20741i −0.971864 0.235542i \(-0.924314\pi\)
−0.235542 0.971864i \(-0.575686\pi\)
\(458\) 0 0
\(459\) 36.6228 1.70940
\(460\) 0 0
\(461\) −11.0680 11.0680i −0.515487 0.515487i 0.400716 0.916202i \(-0.368762\pi\)
−0.916202 + 0.400716i \(0.868762\pi\)
\(462\) 0 0
\(463\) −0.837722 0.837722i −0.0389323 0.0389323i 0.687373 0.726305i \(-0.258764\pi\)
−0.726305 + 0.687373i \(0.758764\pi\)
\(464\) 0 0
\(465\) 3.67544i 0.170445i
\(466\) 0 0
\(467\) 9.35089 0.432708 0.216354 0.976315i \(-0.430584\pi\)
0.216354 + 0.976315i \(0.430584\pi\)
\(468\) 0 0
\(469\) 23.1623 1.06953
\(470\) 0 0
\(471\) 22.9737i 1.05857i
\(472\) 0 0
\(473\) −20.8114 20.8114i −0.956909 0.956909i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 18.9737 0.868744
\(478\) 0 0
\(479\) 5.39253 + 5.39253i 0.246391 + 0.246391i 0.819488 0.573097i \(-0.194258\pi\)
−0.573097 + 0.819488i \(0.694258\pi\)
\(480\) 0 0
\(481\) −11.3246 + 14.3246i −0.516355 + 0.653144i
\(482\) 0 0
\(483\) 11.3246 11.3246i 0.515285 0.515285i
\(484\) 0 0
\(485\) 12.1359i 0.551065i
\(486\) 0 0
\(487\) 27.8114 27.8114i 1.26025 1.26025i 0.309285 0.950969i \(-0.399910\pi\)
0.950969 0.309285i \(-0.100090\pi\)
\(488\) 0 0
\(489\) 9.00000 9.00000i 0.406994 0.406994i
\(490\) 0 0
\(491\) −28.6754 −1.29410 −0.647052 0.762446i \(-0.723998\pi\)
−0.647052 + 0.762446i \(0.723998\pi\)
\(492\) 0 0
\(493\) 8.51317i 0.383414i
\(494\) 0 0
\(495\) 26.3246i 1.18320i
\(496\) 0 0
\(497\) 5.00000 0.224281
\(498\) 0 0
\(499\) 15.4868 15.4868i 0.693286 0.693286i −0.269668 0.962953i \(-0.586914\pi\)
0.962953 + 0.269668i \(0.0869138\pi\)
\(500\) 0 0
\(501\) −17.4868 + 17.4868i −0.781254 + 0.781254i
\(502\) 0 0
\(503\) 14.6491i 0.653172i −0.945168 0.326586i \(-0.894102\pi\)
0.945168 0.326586i \(-0.105898\pi\)
\(504\) 0 0
\(505\) 16.3246 16.3246i 0.726433 0.726433i
\(506\) 0 0
\(507\) 3.00000 + 12.6491i 0.133235 + 0.561767i
\(508\) 0 0
\(509\) 2.00000 + 2.00000i 0.0886484 + 0.0886484i 0.750040 0.661392i \(-0.230034\pi\)
−0.661392 + 0.750040i \(0.730034\pi\)
\(510\) 0 0
\(511\) 18.9737 0.839346
\(512\) 0 0
\(513\) 5.81139 + 5.81139i 0.256579 + 0.256579i
\(514\) 0 0
\(515\) 11.8377 + 11.8377i 0.521632 + 0.521632i
\(516\) 0 0
\(517\) 56.1359i 2.46886i
\(518\) 0 0
\(519\) 3.48683 0.153055
\(520\) 0 0
\(521\) −10.6754 −0.467700 −0.233850 0.972273i \(-0.575132\pi\)
−0.233850 + 0.972273i \(0.575132\pi\)
\(522\) 0 0
\(523\) 0.324555i 0.0141918i −0.999975 0.00709591i \(-0.997741\pi\)
0.999975 0.00709591i \(-0.00225872\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.51317 + 8.51317i 0.370839 + 0.370839i
\(528\) 0 0
\(529\) 28.2982 1.23036
\(530\) 0 0
\(531\) −8.00000 8.00000i −0.347170 0.347170i
\(532\) 0 0
\(533\) 20.6491 + 16.3246i 0.894412 + 0.707095i
\(534\) 0 0
\(535\) −19.4868 + 19.4868i −0.842489 + 0.842489i
\(536\) 0 0
\(537\) 15.6491i 0.675309i
\(538\) 0 0
\(539\) 8.32456 8.32456i 0.358564 0.358564i
\(540\) 0 0
\(541\) 15.0680 15.0680i 0.647823 0.647823i −0.304644 0.952466i \(-0.598537\pi\)
0.952466 + 0.304644i \(0.0985374\pi\)
\(542\) 0 0
\(543\) 2.83772 0.121778
\(544\) 0 0
\(545\) 3.97367i 0.170213i
\(546\) 0 0
\(547\) 23.3246i 0.997286i 0.866807 + 0.498643i \(0.166168\pi\)
−0.866807 + 0.498643i \(0.833832\pi\)
\(548\) 0 0
\(549\) 4.00000 0.170716
\(550\) 0 0
\(551\) −1.35089 + 1.35089i −0.0575498 + 0.0575498i
\(552\) 0 0
\(553\) 5.51317 5.51317i 0.234444 0.234444i
\(554\) 0 0
\(555\) 11.3246i 0.480701i
\(556\) 0 0
\(557\) −9.58114 + 9.58114i −0.405966 + 0.405966i −0.880329 0.474363i \(-0.842678\pi\)
0.474363 + 0.880329i \(0.342678\pi\)
\(558\) 0 0
\(559\) −17.9057 + 2.09431i −0.757330 + 0.0885797i
\(560\) 0 0
\(561\) 30.4868 + 30.4868i 1.28716 + 1.28716i
\(562\) 0 0
\(563\) 13.3246 0.561563 0.280782 0.959772i \(-0.409406\pi\)
0.280782 + 0.959772i \(0.409406\pi\)
\(564\) 0 0
\(565\) −25.2982 25.2982i −1.06430 1.06430i
\(566\) 0 0
\(567\) −1.58114 1.58114i −0.0664016 0.0664016i
\(568\) 0 0
\(569\) 3.97367i 0.166585i −0.996525 0.0832924i \(-0.973456\pi\)
0.996525 0.0832924i \(-0.0265435\pi\)
\(570\) 0 0
\(571\) 13.9737 0.584780 0.292390 0.956299i \(-0.405550\pi\)
0.292390 + 0.956299i \(0.405550\pi\)
\(572\) 0 0
\(573\) −18.8377 −0.786957
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 20.9737 + 20.9737i 0.873145 + 0.873145i 0.992814 0.119669i \(-0.0381832\pi\)
−0.119669 + 0.992814i \(0.538183\pi\)
\(578\) 0 0
\(579\) −2.16228 2.16228i −0.0898612 0.0898612i
\(580\) 0 0
\(581\) −18.4605 −0.765871
\(582\) 0 0
\(583\) 39.4868 + 39.4868i 1.63538 + 1.63538i
\(584\) 0 0
\(585\) −12.6491 10.0000i −0.522976 0.413449i
\(586\) 0 0
\(587\) 7.00000 7.00000i 0.288921 0.288921i −0.547733 0.836653i \(-0.684509\pi\)
0.836653 + 0.547733i \(0.184509\pi\)
\(588\) 0 0
\(589\) 2.70178i 0.111325i
\(590\) 0 0
\(591\) −7.58114 + 7.58114i −0.311846 + 0.311846i
\(592\) 0 0
\(593\) −12.4868 + 12.4868i −0.512773 + 0.512773i −0.915375 0.402602i \(-0.868106\pi\)
0.402602 + 0.915375i \(0.368106\pi\)
\(594\) 0 0
\(595\) 36.6228 1.50139
\(596\) 0 0
\(597\) 27.1623i 1.11168i
\(598\) 0 0
\(599\) 27.6228i 1.12864i 0.825557 + 0.564318i \(0.190861\pi\)
−0.825557 + 0.564318i \(0.809139\pi\)
\(600\) 0 0
\(601\) −30.9473 −1.26237 −0.631184 0.775633i \(-0.717431\pi\)
−0.631184 + 0.775633i \(0.717431\pi\)
\(602\) 0 0
\(603\) −14.6491 + 14.6491i −0.596558 + 0.596558i
\(604\) 0 0
\(605\) 37.3925 37.3925i 1.52022 1.52022i
\(606\) 0 0
\(607\) 18.9737i 0.770117i −0.922892 0.385059i \(-0.874181\pi\)
0.922892 0.385059i \(-0.125819\pi\)
\(608\) 0 0
\(609\) −1.83772 + 1.83772i −0.0744683 + 0.0744683i
\(610\) 0 0
\(611\) −26.9737 21.3246i −1.09124 0.862699i
\(612\) 0 0
\(613\) 2.51317 + 2.51317i 0.101506 + 0.101506i 0.756036 0.654530i \(-0.227133\pi\)
−0.654530 + 0.756036i \(0.727133\pi\)
\(614\) 0 0
\(615\) 16.3246 0.658270
\(616\) 0 0
\(617\) −14.9737 14.9737i −0.602817 0.602817i 0.338242 0.941059i \(-0.390168\pi\)
−0.941059 + 0.338242i \(0.890168\pi\)
\(618\) 0 0
\(619\) 8.51317 + 8.51317i 0.342173 + 0.342173i 0.857184 0.515011i \(-0.172212\pi\)
−0.515011 + 0.857184i \(0.672212\pi\)
\(620\) 0 0
\(621\) 35.8114i 1.43706i
\(622\) 0 0
\(623\) 8.97367 0.359522
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 9.67544i 0.386400i
\(628\) 0 0
\(629\) 26.2302 + 26.2302i 1.04587 + 1.04587i
\(630\) 0 0
\(631\) 28.2302 + 28.2302i 1.12383 + 1.12383i 0.991161 + 0.132668i \(0.0423544\pi\)
0.132668 + 0.991161i \(0.457646\pi\)
\(632\) 0 0
\(633\) −9.64911 −0.383518
\(634\) 0 0
\(635\) −13.9737 13.9737i −0.554528 0.554528i
\(636\) 0 0
\(637\) −0.837722 7.16228i −0.0331918 0.283780i
\(638\) 0 0
\(639\) −3.16228 + 3.16228i −0.125098 + 0.125098i
\(640\) 0 0
\(641\) 21.6754i 0.856129i −0.903748 0.428064i \(-0.859196\pi\)
0.903748 0.428064i \(-0.140804\pi\)
\(642\) 0 0
\(643\) −19.3246 + 19.3246i −0.762086 + 0.762086i −0.976699 0.214613i \(-0.931151\pi\)
0.214613 + 0.976699i \(0.431151\pi\)
\(644\) 0 0
\(645\) −7.90569 + 7.90569i −0.311286 + 0.311286i
\(646\) 0 0
\(647\) −22.9737 −0.903188 −0.451594 0.892224i \(-0.649144\pi\)
−0.451594 + 0.892224i \(0.649144\pi\)
\(648\) 0 0
\(649\) 33.2982i 1.30707i
\(650\) 0 0
\(651\) 3.67544i 0.144052i
\(652\) 0 0
\(653\) 5.02633 0.196696 0.0983478 0.995152i \(-0.468644\pi\)
0.0983478 + 0.995152i \(0.468644\pi\)
\(654\) 0 0
\(655\) −18.4189 + 18.4189i −0.719684 + 0.719684i
\(656\) 0 0
\(657\) −12.0000 + 12.0000i −0.468165 + 0.468165i
\(658\) 0 0
\(659\) 28.9737i 1.12865i −0.825551 0.564327i \(-0.809136\pi\)
0.825551 0.564327i \(-0.190864\pi\)
\(660\) 0 0
\(661\) 23.1623 23.1623i 0.900908 0.900908i −0.0946066 0.995515i \(-0.530159\pi\)
0.995515 + 0.0946066i \(0.0301593\pi\)
\(662\) 0 0
\(663\) 26.2302 3.06797i 1.01870 0.119150i
\(664\) 0 0
\(665\) 5.81139 + 5.81139i 0.225356 + 0.225356i
\(666\) 0 0
\(667\) −8.32456 −0.322328
\(668\) 0 0
\(669\) 9.06797 + 9.06797i 0.350588 + 0.350588i
\(670\) 0 0
\(671\) 8.32456 + 8.32456i 0.321366 + 0.321366i
\(672\) 0 0
\(673\) 17.9737i 0.692834i −0.938081 0.346417i \(-0.887398\pi\)
0.938081 0.346417i \(-0.112602\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17.1623 0.659600 0.329800 0.944051i \(-0.393019\pi\)
0.329800 + 0.944051i \(0.393019\pi\)
\(678\) 0 0
\(679\) 12.1359i 0.465735i
\(680\) 0 0
\(681\) 3.16228 + 3.16228i 0.121179 + 0.121179i
\(682\) 0 0
\(683\) −30.8114 30.8114i −1.17897 1.17897i −0.980008 0.198957i \(-0.936245\pi\)
−0.198957 0.980008i \(-0.563755\pi\)
\(684\) 0 0
\(685\) 9.48683 0.362473
\(686\) 0 0
\(687\) 5.90569 + 5.90569i 0.225316 + 0.225316i
\(688\) 0 0
\(689\) 33.9737 3.97367i 1.29429 0.151385i
\(690\) 0 0
\(691\) 22.6491 22.6491i 0.861613 0.861613i −0.129913 0.991525i \(-0.541470\pi\)
0.991525 + 0.129913i \(0.0414697\pi\)
\(692\) 0 0
\(693\) 26.3246i 0.999987i
\(694\) 0 0
\(695\) 24.2302 24.2302i 0.919106 0.919106i
\(696\) 0 0
\(697\) 37.8114 37.8114i 1.43221 1.43221i
\(698\) 0 0
\(699\) −7.32456 −0.277040
\(700\) 0 0
\(701\) 24.8377i 0.938108i 0.883170 + 0.469054i \(0.155405\pi\)
−0.883170 + 0.469054i \(0.844595\pi\)
\(702\) 0 0
\(703\) 8.32456i 0.313967i
\(704\) 0 0
\(705\) −21.3246 −0.803129
\(706\) 0 0
\(707\) 16.3246 16.3246i 0.613948 0.613948i
\(708\) 0 0
\(709\) 34.6491 34.6491i 1.30127 1.30127i 0.373742 0.927533i \(-0.378075\pi\)
0.927533 0.373742i \(-0.121925\pi\)
\(710\) 0 0
\(711\) 6.97367i 0.261533i
\(712\) 0 0
\(713\) −8.32456 + 8.32456i −0.311757 + 0.311757i
\(714\) 0 0
\(715\) −5.51317 47.1359i −0.206181 1.76278i
\(716\) 0 0
\(717\) −12.4189 12.4189i −0.463791 0.463791i
\(718\) 0 0
\(719\) −31.8114 −1.18636 −0.593182 0.805068i \(-0.702129\pi\)
−0.593182 + 0.805068i \(0.702129\pi\)
\(720\) 0 0
\(721\) 11.8377 + 11.8377i 0.440860 + 0.440860i
\(722\) 0 0
\(723\) 3.48683 + 3.48683i 0.129677 + 0.129677i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 22.4605 0.833014 0.416507 0.909133i \(-0.363254\pi\)
0.416507 + 0.909133i \(0.363254\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 36.6228i 1.35454i
\(732\) 0 0
\(733\) −5.58114 5.58114i −0.206144 0.206144i 0.596482 0.802626i \(-0.296565\pi\)
−0.802626 + 0.596482i \(0.796565\pi\)
\(734\) 0 0
\(735\) −3.16228 3.16228i −0.116642 0.116642i
\(736\) 0 0
\(737\) −60.9737 −2.24599
\(738\) 0 0
\(739\) 9.16228 + 9.16228i 0.337040 + 0.337040i 0.855252 0.518212i \(-0.173402\pi\)
−0.518212 + 0.855252i \(0.673402\pi\)
\(740\) 0 0
\(741\) 4.64911 + 3.67544i 0.170789 + 0.135021i
\(742\) 0 0
\(743\) 0.230249 0.230249i 0.00844703 0.00844703i −0.702871 0.711318i \(-0.748099\pi\)
0.711318 + 0.702871i \(0.248099\pi\)
\(744\) 0 0
\(745\) 6.32456i 0.231714i
\(746\) 0 0
\(747\) 11.6754 11.6754i 0.427182 0.427182i
\(748\) 0 0
\(749\) −19.4868 + 19.4868i −0.712033 + 0.712033i
\(750\) 0 0
\(751\) 48.9737 1.78707 0.893537 0.448989i \(-0.148216\pi\)
0.893537 + 0.448989i \(0.148216\pi\)
\(752\) 0 0
\(753\) 6.64911i 0.242307i
\(754\) 0 0
\(755\) 3.97367i 0.144617i
\(756\) 0 0
\(757\) −28.4605 −1.03441 −0.517207 0.855860i \(-0.673028\pi\)
−0.517207 + 0.855860i \(0.673028\pi\)
\(758\) 0 0
\(759\) −29.8114 + 29.8114i −1.08208 + 1.08208i
\(760\) 0 0
\(761\) 5.67544 5.67544i 0.205735 0.205735i −0.596717 0.802452i \(-0.703529\pi\)
0.802452 + 0.596717i \(0.203529\pi\)
\(762\) 0 0
\(763\) 3.97367i 0.143856i
\(764\) 0 0
\(765\) −23.1623 + 23.1623i −0.837434 + 0.837434i
\(766\) 0 0
\(767\) −16.0000 12.6491i −0.577727 0.456733i
\(768\) 0 0
\(769\) 0.649111 + 0.649111i 0.0234075 + 0.0234075i 0.718714 0.695306i \(-0.244731\pi\)
−0.695306 + 0.718714i \(0.744731\pi\)
\(770\) 0 0
\(771\) 4.35089 0.156693
\(772\) 0 0
\(773\) −21.2566 21.2566i −0.764546 0.764546i 0.212594 0.977141i \(-0.431809\pi\)
−0.977141 + 0.212594i \(0.931809\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 11.3246i 0.406266i
\(778\) 0 0
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) −13.1623 −0.470983
\(782\) 0 0
\(783\) 5.81139i 0.207682i
\(784\) 0 0
\(785\) 36.3246 + 36.3246i 1.29648 + 1.29648i
\(786\) 0 0
\(787\) 8.51317 + 8.51317i 0.303462 + 0.303462i 0.842367 0.538905i \(-0.181162\pi\)
−0.538905 + 0.842367i \(0.681162\pi\)
\(788\) 0 0
\(789\) −6.00000 −0.213606
\(790\) 0 0
\(791\) −25.2982 25.2982i −0.899501 0.899501i
\(792\)