Properties

Label 725.2.j.a.418.1
Level $725$
Weight $2$
Character 725.418
Analytic conductor $5.789$
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] = [725,2,Mod(307,725)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(725, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("725.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 725.j (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: \(5.78915414654\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 3x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 418.1
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 725.418
Dual form 725.2.j.a.307.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.23607 q^{2} +3.00000 q^{4} +(2.23607 - 2.23607i) q^{7} -2.23607 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-2.23607 q^{2} +3.00000 q^{4} +(2.23607 - 2.23607i) q^{7} -2.23607 q^{8} +3.00000 q^{9} +(4.00000 + 4.00000i) q^{11} +(-4.47214 + 4.47214i) q^{13} +(-5.00000 + 5.00000i) q^{14} -1.00000 q^{16} +4.47214 q^{17} -6.70820 q^{18} +(2.00000 - 2.00000i) q^{19} +(-8.94427 - 8.94427i) q^{22} +(-2.23607 - 2.23607i) q^{23} +(10.0000 - 10.0000i) q^{26} +(6.70820 - 6.70820i) q^{28} +(-2.00000 + 5.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} +6.70820 q^{32} -10.0000 q^{34} +9.00000 q^{36} +4.47214i q^{37} +(-4.47214 + 4.47214i) q^{38} +(1.00000 - 1.00000i) q^{41} +4.47214i q^{43} +(12.0000 + 12.0000i) q^{44} +(5.00000 + 5.00000i) q^{46} -4.47214i q^{47} -3.00000i q^{49} +(-13.4164 + 13.4164i) q^{52} +(8.94427 + 8.94427i) q^{53} +(-5.00000 + 5.00000i) q^{56} +(4.47214 - 11.1803i) q^{58} +(-9.00000 - 9.00000i) q^{61} +(8.94427 + 8.94427i) q^{62} +(6.70820 - 6.70820i) q^{63} -13.0000 q^{64} +(2.23607 + 2.23607i) q^{67} +13.4164 q^{68} +12.0000i q^{71} -6.70820 q^{72} +4.47214 q^{73} -10.0000i q^{74} +(6.00000 - 6.00000i) q^{76} +17.8885 q^{77} +(2.00000 - 2.00000i) q^{79} +9.00000 q^{81} +(-2.23607 + 2.23607i) q^{82} +(6.70820 + 6.70820i) q^{83} -10.0000i q^{86} +(-8.94427 - 8.94427i) q^{88} +(7.00000 - 7.00000i) q^{89} +20.0000i q^{91} +(-6.70820 - 6.70820i) q^{92} +10.0000i q^{94} -4.47214i q^{97} +6.70820i q^{98} +(12.0000 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{4} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{4} + 12 q^{9} + 16 q^{11} - 20 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 8 q^{29} - 16 q^{31} - 40 q^{34} + 36 q^{36} + 4 q^{41} + 48 q^{44} + 20 q^{46} - 20 q^{56} - 36 q^{61} - 52 q^{64} + 24 q^{76} + 8 q^{79} + 36 q^{81} + 28 q^{89} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/725\mathbb{Z}\right)^\times\).

\(n\) \(176\) \(552\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23607 −1.58114 −0.790569 0.612372i \(-0.790215\pi\)
−0.790569 + 0.612372i \(0.790215\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 3.00000 1.50000
\(5\) 0 0
\(6\) 0 0
\(7\) 2.23607 2.23607i 0.845154 0.845154i −0.144370 0.989524i \(-0.546115\pi\)
0.989524 + 0.144370i \(0.0461154\pi\)
\(8\) −2.23607 −0.790569
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 4.00000 + 4.00000i 1.20605 + 1.20605i 0.972297 + 0.233748i \(0.0750991\pi\)
0.233748 + 0.972297i \(0.424901\pi\)
\(12\) 0 0
\(13\) −4.47214 + 4.47214i −1.24035 + 1.24035i −0.280491 + 0.959857i \(0.590497\pi\)
−0.959857 + 0.280491i \(0.909503\pi\)
\(14\) −5.00000 + 5.00000i −1.33631 + 1.33631i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 4.47214 1.08465 0.542326 0.840168i \(-0.317544\pi\)
0.542326 + 0.840168i \(0.317544\pi\)
\(18\) −6.70820 −1.58114
\(19\) 2.00000 2.00000i 0.458831 0.458831i −0.439440 0.898272i \(-0.644823\pi\)
0.898272 + 0.439440i \(0.144823\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −8.94427 8.94427i −1.90693 1.90693i
\(23\) −2.23607 2.23607i −0.466252 0.466252i 0.434446 0.900698i \(-0.356944\pi\)
−0.900698 + 0.434446i \(0.856944\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 10.0000 10.0000i 1.96116 1.96116i
\(27\) 0 0
\(28\) 6.70820 6.70820i 1.26773 1.26773i
\(29\) −2.00000 + 5.00000i −0.371391 + 0.928477i
\(30\) 0 0
\(31\) −4.00000 4.00000i −0.718421 0.718421i 0.249861 0.968282i \(-0.419615\pi\)
−0.968282 + 0.249861i \(0.919615\pi\)
\(32\) 6.70820 1.18585
\(33\) 0 0
\(34\) −10.0000 −1.71499
\(35\) 0 0
\(36\) 9.00000 1.50000
\(37\) 4.47214i 0.735215i 0.929981 + 0.367607i \(0.119823\pi\)
−0.929981 + 0.367607i \(0.880177\pi\)
\(38\) −4.47214 + 4.47214i −0.725476 + 0.725476i
\(39\) 0 0
\(40\) 0 0
\(41\) 1.00000 1.00000i 0.156174 0.156174i −0.624695 0.780869i \(-0.714777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 4.47214i 0.681994i 0.940064 + 0.340997i \(0.110765\pi\)
−0.940064 + 0.340997i \(0.889235\pi\)
\(44\) 12.0000 + 12.0000i 1.80907 + 1.80907i
\(45\) 0 0
\(46\) 5.00000 + 5.00000i 0.737210 + 0.737210i
\(47\) 4.47214i 0.652328i −0.945313 0.326164i \(-0.894244\pi\)
0.945313 0.326164i \(-0.105756\pi\)
\(48\) 0 0
\(49\) 3.00000i 0.428571i
\(50\) 0 0
\(51\) 0 0
\(52\) −13.4164 + 13.4164i −1.86052 + 1.86052i
\(53\) 8.94427 + 8.94427i 1.22859 + 1.22859i 0.964497 + 0.264093i \(0.0850726\pi\)
0.264093 + 0.964497i \(0.414927\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −5.00000 + 5.00000i −0.668153 + 0.668153i
\(57\) 0 0
\(58\) 4.47214 11.1803i 0.587220 1.46805i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −9.00000 9.00000i −1.15233 1.15233i −0.986084 0.166248i \(-0.946835\pi\)
−0.166248 0.986084i \(-0.553165\pi\)
\(62\) 8.94427 + 8.94427i 1.13592 + 1.13592i
\(63\) 6.70820 6.70820i 0.845154 0.845154i
\(64\) −13.0000 −1.62500
\(65\) 0 0
\(66\) 0 0
\(67\) 2.23607 + 2.23607i 0.273179 + 0.273179i 0.830379 0.557199i \(-0.188124\pi\)
−0.557199 + 0.830379i \(0.688124\pi\)
\(68\) 13.4164 1.62698
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) −6.70820 −0.790569
\(73\) 4.47214 0.523424 0.261712 0.965146i \(-0.415713\pi\)
0.261712 + 0.965146i \(0.415713\pi\)
\(74\) 10.0000i 1.16248i
\(75\) 0 0
\(76\) 6.00000 6.00000i 0.688247 0.688247i
\(77\) 17.8885 2.03859
\(78\) 0 0
\(79\) 2.00000 2.00000i 0.225018 0.225018i −0.585590 0.810607i \(-0.699137\pi\)
0.810607 + 0.585590i \(0.199137\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) −2.23607 + 2.23607i −0.246932 + 0.246932i
\(83\) 6.70820 + 6.70820i 0.736321 + 0.736321i 0.971864 0.235543i \(-0.0756868\pi\)
−0.235543 + 0.971864i \(0.575687\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 10.0000i 1.07833i
\(87\) 0 0
\(88\) −8.94427 8.94427i −0.953463 0.953463i
\(89\) 7.00000 7.00000i 0.741999 0.741999i −0.230964 0.972962i \(-0.574188\pi\)
0.972962 + 0.230964i \(0.0741879\pi\)
\(90\) 0 0
\(91\) 20.0000i 2.09657i
\(92\) −6.70820 6.70820i −0.699379 0.699379i
\(93\) 0 0
\(94\) 10.0000i 1.03142i
\(95\) 0 0
\(96\) 0 0
\(97\) 4.47214i 0.454077i −0.973886 0.227038i \(-0.927096\pi\)
0.973886 0.227038i \(-0.0729043\pi\)
\(98\) 6.70820i 0.677631i
\(99\) 12.0000 + 12.0000i 1.20605 + 1.20605i
\(100\) 0 0
\(101\) −1.00000 1.00000i −0.0995037 0.0995037i 0.655602 0.755106i \(-0.272415\pi\)
−0.755106 + 0.655602i \(0.772415\pi\)
\(102\) 0 0
\(103\) −6.70820 6.70820i −0.660979 0.660979i 0.294632 0.955611i \(-0.404803\pi\)
−0.955611 + 0.294632i \(0.904803\pi\)
\(104\) 10.0000 10.0000i 0.980581 0.980581i
\(105\) 0 0
\(106\) −20.0000 20.0000i −1.94257 1.94257i
\(107\) 6.70820 6.70820i 0.648507 0.648507i −0.304125 0.952632i \(-0.598364\pi\)
0.952632 + 0.304125i \(0.0983642\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.23607 + 2.23607i −0.211289 + 0.211289i
\(113\) 4.47214 0.420703 0.210352 0.977626i \(-0.432539\pi\)
0.210352 + 0.977626i \(0.432539\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 + 15.0000i −0.557086 + 1.39272i
\(117\) −13.4164 + 13.4164i −1.24035 + 1.24035i
\(118\) 0 0
\(119\) 10.0000 10.0000i 0.916698 0.916698i
\(120\) 0 0
\(121\) 21.0000i 1.90909i
\(122\) 20.1246 + 20.1246i 1.82200 + 1.82200i
\(123\) 0 0
\(124\) −12.0000 12.0000i −1.07763 1.07763i
\(125\) 0 0
\(126\) −15.0000 + 15.0000i −1.33631 + 1.33631i
\(127\) 4.47214 0.396838 0.198419 0.980117i \(-0.436419\pi\)
0.198419 + 0.980117i \(0.436419\pi\)
\(128\) 15.6525 1.38350
\(129\) 0 0
\(130\) 0 0
\(131\) 14.0000 14.0000i 1.22319 1.22319i 0.256693 0.966493i \(-0.417367\pi\)
0.966493 0.256693i \(-0.0826328\pi\)
\(132\) 0 0
\(133\) 8.94427i 0.775567i
\(134\) −5.00000 5.00000i −0.431934 0.431934i
\(135\) 0 0
\(136\) −10.0000 −0.857493
\(137\) −13.4164 −1.14624 −0.573121 0.819471i \(-0.694267\pi\)
−0.573121 + 0.819471i \(0.694267\pi\)
\(138\) 0 0
\(139\) 4.00000i 0.339276i 0.985506 + 0.169638i \(0.0542598\pi\)
−0.985506 + 0.169638i \(0.945740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 26.8328i 2.25176i
\(143\) −35.7771 −2.99183
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) 13.4164i 1.10282i
\(149\) −20.0000 −1.63846 −0.819232 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) −4.47214 + 4.47214i −0.362738 + 0.362738i
\(153\) 13.4164 1.08465
\(154\) −40.0000 −3.22329
\(155\) 0 0
\(156\) 0 0
\(157\) 13.4164i 1.07075i −0.844616 0.535373i \(-0.820171\pi\)
0.844616 0.535373i \(-0.179829\pi\)
\(158\) −4.47214 + 4.47214i −0.355784 + 0.355784i
\(159\) 0 0
\(160\) 0 0
\(161\) −10.0000 −0.788110
\(162\) −20.1246 −1.58114
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 3.00000 3.00000i 0.234261 0.234261i
\(165\) 0 0
\(166\) −15.0000 15.0000i −1.16423 1.16423i
\(167\) −6.70820 6.70820i −0.519096 0.519096i 0.398202 0.917298i \(-0.369634\pi\)
−0.917298 + 0.398202i \(0.869634\pi\)
\(168\) 0 0
\(169\) 27.0000i 2.07692i
\(170\) 0 0
\(171\) 6.00000 6.00000i 0.458831 0.458831i
\(172\) 13.4164i 1.02299i
\(173\) −13.4164 + 13.4164i −1.02003 + 1.02003i −0.0202354 + 0.999795i \(0.506442\pi\)
−0.999795 + 0.0202354i \(0.993558\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 4.00000i −0.301511 0.301511i
\(177\) 0 0
\(178\) −15.6525 + 15.6525i −1.17320 + 1.17320i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 44.7214i 3.31497i
\(183\) 0 0
\(184\) 5.00000 + 5.00000i 0.368605 + 0.368605i
\(185\) 0 0
\(186\) 0 0
\(187\) 17.8885 + 17.8885i 1.30814 + 1.30814i
\(188\) 13.4164i 0.978492i
\(189\) 0 0
\(190\) 0 0
\(191\) 6.00000 + 6.00000i 0.434145 + 0.434145i 0.890036 0.455891i \(-0.150679\pi\)
−0.455891 + 0.890036i \(0.650679\pi\)
\(192\) 0 0
\(193\) 4.47214i 0.321911i −0.986962 0.160956i \(-0.948542\pi\)
0.986962 0.160956i \(-0.0514576\pi\)
\(194\) 10.0000i 0.717958i
\(195\) 0 0
\(196\) 9.00000i 0.642857i
\(197\) 13.4164 13.4164i 0.955879 0.955879i −0.0431875 0.999067i \(-0.513751\pi\)
0.999067 + 0.0431875i \(0.0137513\pi\)
\(198\) −26.8328 26.8328i −1.90693 1.90693i
\(199\) 20.0000i 1.41776i 0.705328 + 0.708881i \(0.250800\pi\)
−0.705328 + 0.708881i \(0.749200\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2.23607 + 2.23607i 0.157329 + 0.157329i
\(203\) 6.70820 + 15.6525i 0.470824 + 1.09859i
\(204\) 0 0
\(205\) 0 0
\(206\) 15.0000 + 15.0000i 1.04510 + 1.04510i
\(207\) −6.70820 6.70820i −0.466252 0.466252i
\(208\) 4.47214 4.47214i 0.310087 0.310087i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 16.0000 16.0000i 1.10149 1.10149i 0.107254 0.994232i \(-0.465794\pi\)
0.994232 0.107254i \(-0.0342057\pi\)
\(212\) 26.8328 + 26.8328i 1.84289 + 1.84289i
\(213\) 0 0
\(214\) −15.0000 + 15.0000i −1.02538 + 1.02538i
\(215\) 0 0
\(216\) 0 0
\(217\) −17.8885 −1.21435
\(218\) −22.3607 −1.51446
\(219\) 0 0
\(220\) 0 0
\(221\) −20.0000 + 20.0000i −1.34535 + 1.34535i
\(222\) 0 0
\(223\) 11.1803 + 11.1803i 0.748691 + 0.748691i 0.974233 0.225542i \(-0.0724154\pi\)
−0.225542 + 0.974233i \(0.572415\pi\)
\(224\) 15.0000 15.0000i 1.00223 1.00223i
\(225\) 0 0
\(226\) −10.0000 −0.665190
\(227\) −6.70820 + 6.70820i −0.445239 + 0.445239i −0.893768 0.448529i \(-0.851948\pi\)
0.448529 + 0.893768i \(0.351948\pi\)
\(228\) 0 0
\(229\) 3.00000 + 3.00000i 0.198246 + 0.198246i 0.799248 0.601002i \(-0.205232\pi\)
−0.601002 + 0.799248i \(0.705232\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.47214 11.1803i 0.293610 0.734025i
\(233\) −8.94427 8.94427i −0.585959 0.585959i 0.350576 0.936534i \(-0.385986\pi\)
−0.936534 + 0.350576i \(0.885986\pi\)
\(234\) 30.0000 30.0000i 1.96116 1.96116i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −22.3607 + 22.3607i −1.44943 + 1.44943i
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 8.00000i 0.515325i 0.966235 + 0.257663i \(0.0829523\pi\)
−0.966235 + 0.257663i \(0.917048\pi\)
\(242\) 46.9574i 3.01854i
\(243\) 0 0
\(244\) −27.0000 27.0000i −1.72850 1.72850i
\(245\) 0 0
\(246\) 0 0
\(247\) 17.8885i 1.13822i
\(248\) 8.94427 + 8.94427i 0.567962 + 0.567962i
\(249\) 0 0
\(250\) 0 0
\(251\) 4.00000 + 4.00000i 0.252478 + 0.252478i 0.821986 0.569508i \(-0.192866\pi\)
−0.569508 + 0.821986i \(0.692866\pi\)
\(252\) 20.1246 20.1246i 1.26773 1.26773i
\(253\) 17.8885i 1.12464i
\(254\) −10.0000 −0.627456
\(255\) 0 0
\(256\) −9.00000 −0.562500
\(257\) −4.47214 + 4.47214i −0.278964 + 0.278964i −0.832695 0.553731i \(-0.813203\pi\)
0.553731 + 0.832695i \(0.313203\pi\)
\(258\) 0 0
\(259\) 10.0000 + 10.0000i 0.621370 + 0.621370i
\(260\) 0 0
\(261\) −6.00000 + 15.0000i −0.371391 + 0.928477i
\(262\) −31.3050 + 31.3050i −1.93403 + 1.93403i
\(263\) 8.94427i 0.551527i −0.961225 0.275764i \(-0.911069\pi\)
0.961225 0.275764i \(-0.0889307\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 20.0000i 1.22628i
\(267\) 0 0
\(268\) 6.70820 + 6.70820i 0.409769 + 0.409769i
\(269\) 7.00000 + 7.00000i 0.426798 + 0.426798i 0.887536 0.460738i \(-0.152415\pi\)
−0.460738 + 0.887536i \(0.652415\pi\)
\(270\) 0 0
\(271\) 14.0000 14.0000i 0.850439 0.850439i −0.139748 0.990187i \(-0.544629\pi\)
0.990187 + 0.139748i \(0.0446292\pi\)
\(272\) −4.47214 −0.271163
\(273\) 0 0
\(274\) 30.0000 1.81237
\(275\) 0 0
\(276\) 0 0
\(277\) −8.94427 + 8.94427i −0.537409 + 0.537409i −0.922767 0.385358i \(-0.874078\pi\)
0.385358 + 0.922767i \(0.374078\pi\)
\(278\) 8.94427i 0.536442i
\(279\) −12.0000 12.0000i −0.718421 0.718421i
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 0 0
\(283\) 11.1803 11.1803i 0.664602 0.664602i −0.291859 0.956461i \(-0.594274\pi\)
0.956461 + 0.291859i \(0.0942738\pi\)
\(284\) 36.0000i 2.13621i
\(285\) 0 0
\(286\) 80.0000 4.73050
\(287\) 4.47214i 0.263982i
\(288\) 20.1246 1.18585
\(289\) 3.00000 0.176471
\(290\) 0 0
\(291\) 0 0
\(292\) 13.4164 0.785136
\(293\) 4.47214i 0.261265i −0.991431 0.130632i \(-0.958299\pi\)
0.991431 0.130632i \(-0.0417008\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 10.0000i 0.581238i
\(297\) 0 0
\(298\) 44.7214 2.59064
\(299\) 20.0000 1.15663
\(300\) 0 0
\(301\) 10.0000 + 10.0000i 0.576390 + 0.576390i
\(302\) 26.8328i 1.54406i
\(303\) 0 0
\(304\) −2.00000 + 2.00000i −0.114708 + 0.114708i
\(305\) 0 0
\(306\) −30.0000 −1.71499
\(307\) −31.3050 −1.78667 −0.893334 0.449393i \(-0.851640\pi\)
−0.893334 + 0.449393i \(0.851640\pi\)
\(308\) 53.6656 3.05788
\(309\) 0 0
\(310\) 0 0
\(311\) −4.00000 4.00000i −0.226819 0.226819i 0.584543 0.811363i \(-0.301274\pi\)
−0.811363 + 0.584543i \(0.801274\pi\)
\(312\) 0 0
\(313\) −22.3607 22.3607i −1.26390 1.26390i −0.949187 0.314714i \(-0.898091\pi\)
−0.314714 0.949187i \(-0.601909\pi\)
\(314\) 30.0000i 1.69300i
\(315\) 0 0
\(316\) 6.00000 6.00000i 0.337526 0.337526i
\(317\) 31.3050i 1.75826i 0.476581 + 0.879131i \(0.341876\pi\)
−0.476581 + 0.879131i \(0.658124\pi\)
\(318\) 0 0
\(319\) −28.0000 + 12.0000i −1.56770 + 0.671871i
\(320\) 0 0
\(321\) 0 0
\(322\) 22.3607 1.24611
\(323\) 8.94427 8.94427i 0.497673 0.497673i
\(324\) 27.0000 1.50000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −2.23607 + 2.23607i −0.123466 + 0.123466i
\(329\) −10.0000 10.0000i −0.551318 0.551318i
\(330\) 0 0
\(331\) −6.00000 + 6.00000i −0.329790 + 0.329790i −0.852506 0.522717i \(-0.824919\pi\)
0.522717 + 0.852506i \(0.324919\pi\)
\(332\) 20.1246 + 20.1246i 1.10448 + 1.10448i
\(333\) 13.4164i 0.735215i
\(334\) 15.0000 + 15.0000i 0.820763 + 0.820763i
\(335\) 0 0
\(336\) 0 0
\(337\) 13.4164i 0.730838i −0.930843 0.365419i \(-0.880926\pi\)
0.930843 0.365419i \(-0.119074\pi\)
\(338\) 60.3738i 3.28390i
\(339\) 0 0
\(340\) 0 0
\(341\) 32.0000i 1.73290i
\(342\) −13.4164 + 13.4164i −0.725476 + 0.725476i
\(343\) 8.94427 + 8.94427i 0.482945 + 0.482945i
\(344\) 10.0000i 0.539164i
\(345\) 0 0
\(346\) 30.0000 30.0000i 1.61281 1.61281i
\(347\) −15.6525 15.6525i −0.840269 0.840269i 0.148625 0.988894i \(-0.452515\pi\)
−0.988894 + 0.148625i \(0.952515\pi\)
\(348\) 0 0
\(349\) 30.0000i 1.60586i −0.596071 0.802932i \(-0.703272\pi\)
0.596071 0.802932i \(-0.296728\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 26.8328 + 26.8328i 1.43019 + 1.43019i
\(353\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 21.0000 21.0000i 1.11300 1.11300i
\(357\) 0 0
\(358\) 0 0
\(359\) −12.0000 + 12.0000i −0.633336 + 0.633336i −0.948903 0.315567i \(-0.897805\pi\)
0.315567 + 0.948903i \(0.397805\pi\)
\(360\) 0 0
\(361\) 11.0000i 0.578947i
\(362\) 44.7214 2.35050
\(363\) 0 0
\(364\) 60.0000i 3.14485i
\(365\) 0 0
\(366\) 0 0
\(367\) 26.8328 1.40066 0.700331 0.713818i \(-0.253036\pi\)
0.700331 + 0.713818i \(0.253036\pi\)
\(368\) 2.23607 + 2.23607i 0.116563 + 0.116563i
\(369\) 3.00000 3.00000i 0.156174 0.156174i
\(370\) 0 0
\(371\) 40.0000 2.07670
\(372\) 0 0
\(373\) −13.4164 13.4164i −0.694675 0.694675i 0.268582 0.963257i \(-0.413445\pi\)
−0.963257 + 0.268582i \(0.913445\pi\)
\(374\) −40.0000 40.0000i −2.06835 2.06835i
\(375\) 0 0
\(376\) 10.0000i 0.515711i
\(377\) −13.4164 31.3050i −0.690980 1.61229i
\(378\) 0 0
\(379\) −12.0000 + 12.0000i −0.616399 + 0.616399i −0.944606 0.328207i \(-0.893556\pi\)
0.328207 + 0.944606i \(0.393556\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −13.4164 13.4164i −0.686443 0.686443i
\(383\) 11.1803 11.1803i 0.571289 0.571289i −0.361200 0.932488i \(-0.617633\pi\)
0.932488 + 0.361200i \(0.117633\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000i 0.508987i
\(387\) 13.4164i 0.681994i
\(388\) 13.4164i 0.681115i
\(389\) −7.00000 7.00000i −0.354914 0.354914i 0.507020 0.861934i \(-0.330747\pi\)
−0.861934 + 0.507020i \(0.830747\pi\)
\(390\) 0 0
\(391\) −10.0000 10.0000i −0.505722 0.505722i
\(392\) 6.70820i 0.338815i
\(393\) 0 0
\(394\) −30.0000 + 30.0000i −1.51138 + 1.51138i
\(395\) 0 0
\(396\) 36.0000 + 36.0000i 1.80907 + 1.80907i
\(397\) 13.4164 13.4164i 0.673350 0.673350i −0.285137 0.958487i \(-0.592039\pi\)
0.958487 + 0.285137i \(0.0920390\pi\)
\(398\) 44.7214i 2.24168i
\(399\) 0 0
\(400\) 0 0
\(401\) −20.0000 −0.998752 −0.499376 0.866385i \(-0.666437\pi\)
−0.499376 + 0.866385i \(0.666437\pi\)
\(402\) 0 0
\(403\) 35.7771 1.78218
\(404\) −3.00000 3.00000i −0.149256 0.149256i
\(405\) 0 0
\(406\) −15.0000 35.0000i −0.744438 1.73702i
\(407\) −17.8885 + 17.8885i −0.886702 + 0.886702i
\(408\) 0 0
\(409\) −3.00000 + 3.00000i −0.148340 + 0.148340i −0.777376 0.629036i \(-0.783450\pi\)
0.629036 + 0.777376i \(0.283450\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −20.1246 20.1246i −0.991468 0.991468i
\(413\) 0 0
\(414\) 15.0000 + 15.0000i 0.737210 + 0.737210i
\(415\) 0 0
\(416\) −30.0000 + 30.0000i −1.47087 + 1.47087i
\(417\) 0 0
\(418\) −35.7771 −1.74991
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 9.00000 9.00000i 0.438633 0.438633i −0.452919 0.891552i \(-0.649617\pi\)
0.891552 + 0.452919i \(0.149617\pi\)
\(422\) −35.7771 + 35.7771i −1.74160 + 1.74160i
\(423\) 13.4164i 0.652328i
\(424\) −20.0000 20.0000i −0.971286 0.971286i
\(425\) 0 0
\(426\) 0 0
\(427\) −40.2492 −1.94780
\(428\) 20.1246 20.1246i 0.972760 0.972760i
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 0 0
\(433\) 22.3607 1.07459 0.537293 0.843396i \(-0.319447\pi\)
0.537293 + 0.843396i \(0.319447\pi\)
\(434\) 40.0000 1.92006
\(435\) 0 0
\(436\) 30.0000 1.43674
\(437\) −8.94427 −0.427863
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) 9.00000i 0.428571i
\(442\) 44.7214 44.7214i 2.12718 2.12718i
\(443\) −31.3050 −1.48734 −0.743672 0.668545i \(-0.766917\pi\)
−0.743672 + 0.668545i \(0.766917\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −25.0000 25.0000i −1.18378 1.18378i
\(447\) 0 0
\(448\) −29.0689 + 29.0689i −1.37338 + 1.37338i
\(449\) −13.0000 + 13.0000i −0.613508 + 0.613508i −0.943858 0.330350i \(-0.892833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) 13.4164 0.631055
\(453\) 0 0
\(454\) 15.0000 15.0000i 0.703985 0.703985i
\(455\) 0 0
\(456\) 0 0
\(457\) −17.8885 17.8885i −0.836791 0.836791i 0.151644 0.988435i \(-0.451543\pi\)
−0.988435 + 0.151644i \(0.951543\pi\)
\(458\) −6.70820 6.70820i −0.313454 0.313454i
\(459\) 0 0
\(460\) 0 0
\(461\) −9.00000 + 9.00000i −0.419172 + 0.419172i −0.884918 0.465746i \(-0.845786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 0 0
\(463\) 2.23607 2.23607i 0.103919 0.103919i −0.653236 0.757155i \(-0.726589\pi\)
0.757155 + 0.653236i \(0.226589\pi\)
\(464\) 2.00000 5.00000i 0.0928477 0.232119i
\(465\) 0 0
\(466\) 20.0000 + 20.0000i 0.926482 + 0.926482i
\(467\) 13.4164 0.620837 0.310419 0.950600i \(-0.399531\pi\)
0.310419 + 0.950600i \(0.399531\pi\)
\(468\) −40.2492 + 40.2492i −1.86052 + 1.86052i
\(469\) 10.0000 0.461757
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −17.8885 + 17.8885i −0.822516 + 0.822516i
\(474\) 0 0
\(475\) 0 0
\(476\) 30.0000 30.0000i 1.37505 1.37505i
\(477\) 26.8328 + 26.8328i 1.22859 + 1.22859i
\(478\) 0 0
\(479\) 18.0000 + 18.0000i 0.822441 + 0.822441i 0.986458 0.164017i \(-0.0524451\pi\)
−0.164017 + 0.986458i \(0.552445\pi\)
\(480\) 0 0
\(481\) −20.0000 20.0000i −0.911922 0.911922i
\(482\) 17.8885i 0.814801i
\(483\) 0 0
\(484\) 63.0000i 2.86364i
\(485\) 0 0
\(486\) 0 0
\(487\) −20.1246 + 20.1246i −0.911933 + 0.911933i −0.996424 0.0844910i \(-0.973074\pi\)
0.0844910 + 0.996424i \(0.473074\pi\)
\(488\) 20.1246 + 20.1246i 0.910998 + 0.910998i
\(489\) 0 0
\(490\) 0 0
\(491\) −6.00000 + 6.00000i −0.270776 + 0.270776i −0.829413 0.558636i \(-0.811325\pi\)
0.558636 + 0.829413i \(0.311325\pi\)
\(492\) 0 0
\(493\) −8.94427 + 22.3607i −0.402830 + 1.00707i
\(494\) 40.0000i 1.79969i
\(495\) 0 0
\(496\) 4.00000 + 4.00000i 0.179605 + 0.179605i
\(497\) 26.8328 + 26.8328i 1.20362 + 1.20362i
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −8.94427 8.94427i −0.399202 0.399202i
\(503\) 22.3607 0.997013 0.498507 0.866886i \(-0.333882\pi\)
0.498507 + 0.866886i \(0.333882\pi\)
\(504\) −15.0000 + 15.0000i −0.668153 + 0.668153i
\(505\) 0 0
\(506\) 40.0000i 1.77822i
\(507\) 0 0
\(508\) 13.4164 0.595257
\(509\) 24.0000i 1.06378i 0.846813 + 0.531891i \(0.178518\pi\)
−0.846813 + 0.531891i \(0.821482\pi\)
\(510\) 0 0
\(511\) 10.0000 10.0000i 0.442374 0.442374i
\(512\) −11.1803 −0.494106
\(513\) 0 0
\(514\) 10.0000 10.0000i 0.441081 0.441081i
\(515\) 0 0
\(516\) 0 0
\(517\) 17.8885 17.8885i 0.786737 0.786737i
\(518\) −22.3607 22.3607i −0.982472 0.982472i
\(519\) 0 0
\(520\) 0 0
\(521\) 10.0000i 0.438108i −0.975713 0.219054i \(-0.929703\pi\)
0.975713 0.219054i \(-0.0702971\pi\)
\(522\) 13.4164 33.5410i 0.587220 1.46805i
\(523\) −15.6525 15.6525i −0.684435 0.684435i 0.276561 0.960996i \(-0.410805\pi\)
−0.960996 + 0.276561i \(0.910805\pi\)
\(524\) 42.0000 42.0000i 1.83478 1.83478i
\(525\) 0 0
\(526\) 20.0000i 0.872041i
\(527\) −17.8885 17.8885i −0.779237 0.779237i
\(528\) 0 0
\(529\) 13.0000i 0.565217i
\(530\) 0 0
\(531\) 0 0
\(532\) 26.8328i 1.16335i
\(533\) 8.94427i 0.387419i
\(534\) 0 0
\(535\) 0 0
\(536\) −5.00000 5.00000i −0.215967 0.215967i
\(537\) 0 0
\(538\) −15.6525 15.6525i −0.674826 0.674826i
\(539\) 12.0000 12.0000i 0.516877 0.516877i
\(540\) 0 0
\(541\) −9.00000 9.00000i −0.386940 0.386940i 0.486654 0.873595i \(-0.338217\pi\)
−0.873595 + 0.486654i \(0.838217\pi\)
\(542\) −31.3050 + 31.3050i −1.34466 + 1.34466i
\(543\) 0 0
\(544\) 30.0000 1.28624
\(545\) 0 0
\(546\) 0 0
\(547\) 15.6525 15.6525i 0.669252 0.669252i −0.288291 0.957543i \(-0.593087\pi\)
0.957543 + 0.288291i \(0.0930871\pi\)
\(548\) −40.2492 −1.71936
\(549\) −27.0000 27.0000i −1.15233 1.15233i
\(550\) 0 0
\(551\) 6.00000 + 14.0000i 0.255609 + 0.596420i
\(552\) 0 0
\(553\) 8.94427i 0.380349i
\(554\) 20.0000 20.0000i 0.849719 0.849719i
\(555\) 0 0
\(556\) 12.0000i 0.508913i
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 26.8328 + 26.8328i 1.13592 + 1.13592i
\(559\) −20.0000 20.0000i −0.845910 0.845910i
\(560\) 0 0
\(561\) 0 0
\(562\) 26.8328 1.13187
\(563\) −35.7771 −1.50782 −0.753912 0.656975i \(-0.771836\pi\)
−0.753912 + 0.656975i \(0.771836\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −25.0000 + 25.0000i −1.05083 + 1.05083i
\(567\) 20.1246 20.1246i 0.845154 0.845154i
\(568\) 26.8328i 1.12588i
\(569\) 7.00000 + 7.00000i 0.293455 + 0.293455i 0.838444 0.544988i \(-0.183466\pi\)
−0.544988 + 0.838444i \(0.683466\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) −107.331 −4.48775
\(573\) 0 0
\(574\) 10.0000i 0.417392i
\(575\) 0 0
\(576\) −39.0000 −1.62500
\(577\) 40.2492i 1.67560i 0.545979 + 0.837799i \(0.316158\pi\)
−0.545979 + 0.837799i \(0.683842\pi\)
\(578\) −6.70820 −0.279024
\(579\) 0 0
\(580\) 0 0
\(581\) 30.0000 1.24461
\(582\) 0 0
\(583\) 71.5542i 2.96347i
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) 10.0000i 0.413096i
\(587\) 20.1246 20.1246i 0.830632 0.830632i −0.156972 0.987603i \(-0.550173\pi\)
0.987603 + 0.156972i \(0.0501731\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) 0 0
\(591\) 0 0
\(592\) 4.47214i 0.183804i
\(593\) −8.94427 + 8.94427i −0.367297 + 0.367297i −0.866491 0.499193i \(-0.833630\pi\)
0.499193 + 0.866491i \(0.333630\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −60.0000 −2.45770
\(597\) 0 0
\(598\) −44.7214 −1.82879
\(599\) −22.0000 + 22.0000i −0.898896 + 0.898896i −0.995339 0.0964429i \(-0.969253\pi\)
0.0964429 + 0.995339i \(0.469253\pi\)
\(600\) 0 0
\(601\) −21.0000 21.0000i −0.856608 0.856608i 0.134329 0.990937i \(-0.457112\pi\)
−0.990937 + 0.134329i \(0.957112\pi\)
\(602\) −22.3607 22.3607i −0.911353 0.911353i
\(603\) 6.70820 + 6.70820i 0.273179 + 0.273179i
\(604\) 36.0000i 1.46482i
\(605\) 0 0
\(606\) 0 0
\(607\) 13.4164i 0.544555i −0.962219 0.272278i \(-0.912223\pi\)
0.962219 0.272278i \(-0.0877769\pi\)
\(608\) 13.4164 13.4164i 0.544107 0.544107i
\(609\) 0 0
\(610\) 0 0
\(611\) 20.0000 + 20.0000i 0.809113 + 0.809113i
\(612\) 40.2492 1.62698
\(613\) 8.94427 8.94427i 0.361256 0.361256i −0.503019 0.864275i \(-0.667778\pi\)
0.864275 + 0.503019i \(0.167778\pi\)
\(614\) 70.0000 2.82497
\(615\) 0 0
\(616\) −40.0000 −1.61165
\(617\) 40.2492i 1.62037i −0.586172 0.810186i \(-0.699366\pi\)
0.586172 0.810186i \(-0.300634\pi\)
\(618\) 0 0
\(619\) 12.0000 + 12.0000i 0.482321 + 0.482321i 0.905872 0.423551i \(-0.139217\pi\)
−0.423551 + 0.905872i \(0.639217\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 8.94427 + 8.94427i 0.358633 + 0.358633i
\(623\) 31.3050i 1.25421i
\(624\) 0 0
\(625\) 0 0
\(626\) 50.0000 + 50.0000i 1.99840 + 1.99840i
\(627\) 0 0
\(628\) 40.2492i 1.60612i
\(629\) 20.0000i 0.797452i
\(630\) 0 0
\(631\) 40.0000i 1.59237i 0.605050 + 0.796187i \(0.293153\pi\)
−0.605050 + 0.796187i \(0.706847\pi\)
\(632\) −4.47214 + 4.47214i −0.177892 + 0.177892i
\(633\) 0 0
\(634\) 70.0000i 2.78006i
\(635\) 0 0
\(636\) 0 0
\(637\) 13.4164 + 13.4164i 0.531577 + 0.531577i
\(638\) 62.6099 26.8328i 2.47875 1.06232i
\(639\) 36.0000i 1.42414i
\(640\) 0 0
\(641\) 1.00000 + 1.00000i 0.0394976 + 0.0394976i 0.726580 0.687082i \(-0.241109\pi\)
−0.687082 + 0.726580i \(0.741109\pi\)
\(642\) 0 0
\(643\) −29.0689 + 29.0689i −1.14636 + 1.14636i −0.159103 + 0.987262i \(0.550860\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) −30.0000 −1.18217
\(645\) 0 0
\(646\) −20.0000 + 20.0000i −0.786889 + 0.786889i
\(647\) 6.70820 + 6.70820i 0.263727 + 0.263727i 0.826566 0.562839i \(-0.190291\pi\)
−0.562839 + 0.826566i \(0.690291\pi\)
\(648\) −20.1246 −0.790569
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.3050 −1.22506 −0.612529 0.790448i \(-0.709848\pi\)
−0.612529 + 0.790448i \(0.709848\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 + 1.00000i −0.0390434 + 0.0390434i
\(657\) 13.4164 0.523424
\(658\) 22.3607 + 22.3607i 0.871710 + 0.871710i
\(659\) −2.00000 + 2.00000i −0.0779089 + 0.0779089i −0.744987 0.667078i \(-0.767545\pi\)
0.667078 + 0.744987i \(0.267545\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 13.4164 13.4164i 0.521443 0.521443i
\(663\) 0 0
\(664\) −15.0000 15.0000i −0.582113 0.582113i
\(665\) 0 0
\(666\) 30.0000i 1.16248i
\(667\) 15.6525 6.70820i 0.606066 0.259743i
\(668\) −20.1246 20.1246i −0.778645 0.778645i
\(669\) 0 0
\(670\) 0 0
\(671\) 72.0000i 2.77953i
\(672\) 0 0
\(673\) 4.47214 4.47214i 0.172388 0.172388i −0.615640 0.788028i \(-0.711102\pi\)
0.788028 + 0.615640i \(0.211102\pi\)
\(674\) 30.0000i 1.15556i
\(675\) 0 0
\(676\) 81.0000i 3.11538i
\(677\) 4.47214i 0.171878i −0.996300 0.0859391i \(-0.972611\pi\)
0.996300 0.0859391i \(-0.0273890\pi\)
\(678\) 0 0
\(679\) −10.0000 10.0000i −0.383765 0.383765i
\(680\) 0 0
\(681\) 0 0
\(682\) 71.5542i 2.73995i
\(683\) −33.5410 33.5410i −1.28341 1.28341i −0.938714 0.344698i \(-0.887981\pi\)
−0.344698 0.938714i \(-0.612019\pi\)
\(684\) 18.0000 18.0000i 0.688247 0.688247i
\(685\) 0 0
\(686\) −20.0000 20.0000i −0.763604 0.763604i
\(687\) 0 0
\(688\) 4.47214i 0.170499i
\(689\) −80.0000 −3.04776
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −40.2492 + 40.2492i −1.53005 + 1.53005i
\(693\) 53.6656 2.03859
\(694\) 35.0000 + 35.0000i 1.32858 + 1.32858i
\(695\) 0 0
\(696\) 0 0
\(697\) 4.47214 4.47214i 0.169394 0.169394i
\(698\) 67.0820i 2.53909i
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000i 0.679851i −0.940452 0.339925i \(-0.889598\pi\)
0.940452 0.339925i \(-0.110402\pi\)
\(702\) 0 0
\(703\) 8.94427 + 8.94427i 0.337340 + 0.337340i
\(704\) −52.0000 52.0000i −1.95982 1.95982i
\(705\) 0 0
\(706\) 0 0
\(707\) −4.47214 −0.168192
\(708\) 0 0
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 0 0
\(711\) 6.00000 6.00000i 0.225018 0.225018i
\(712\) −15.6525 + 15.6525i −0.586601 + 0.586601i
\(713\) 17.8885i 0.669931i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 26.8328 26.8328i 1.00139 1.00139i
\(719\) 20.0000i 0.745874i −0.927857 0.372937i \(-0.878351\pi\)
0.927857 0.372937i \(-0.121649\pi\)
\(720\) 0 0
\(721\) −30.0000 −1.11726
\(722\) 24.5967i 0.915396i
\(723\) 0 0
\(724\) −60.0000 −2.22988
\(725\) 0 0
\(726\) 0 0
\(727\) 44.7214 1.65862 0.829312 0.558786i \(-0.188733\pi\)
0.829312 + 0.558786i \(0.188733\pi\)
\(728\) 44.7214i 1.65748i
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 20.0000i 0.739727i
\(732\) 0 0
\(733\) 4.47214 0.165182 0.0825911 0.996584i \(-0.473680\pi\)
0.0825911 + 0.996584i \(0.473680\pi\)
\(734\) −60.0000 −2.21464
\(735\) 0 0
\(736\) −15.0000 15.0000i −0.552907 0.552907i
\(737\) 17.8885i 0.658933i
\(738\) −6.70820 + 6.70820i −0.246932 + 0.246932i
\(739\) 18.0000 18.0000i 0.662141 0.662141i −0.293744 0.955884i \(-0.594901\pi\)
0.955884 + 0.293744i \(0.0949012\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −89.4427 −3.28355
\(743\) 22.3607 0.820334 0.410167 0.912010i \(-0.365470\pi\)
0.410167 + 0.912010i \(0.365470\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 30.0000 + 30.0000i 1.09838 + 1.09838i
\(747\) 20.1246 + 20.1246i 0.736321 + 0.736321i
\(748\) 53.6656 + 53.6656i 1.96221 + 1.96221i
\(749\) 30.0000i 1.09618i
\(750\) 0 0
\(751\) 24.0000 24.0000i 0.875772 0.875772i −0.117322 0.993094i \(-0.537431\pi\)
0.993094 + 0.117322i \(0.0374308\pi\)
\(752\) 4.47214i 0.163082i
\(753\) 0 0
\(754\) 30.0000 + 70.0000i 1.09254 + 2.54925i
\(755\) 0 0
\(756\) 0 0
\(757\) −40.2492 −1.46288 −0.731441 0.681904i \(-0.761152\pi\)
−0.731441 + 0.681904i \(0.761152\pi\)
\(758\) 26.8328 26.8328i 0.974612 0.974612i
\(759\) 0 0
\(760\) 0 0
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) 22.3607 22.3607i 0.809511 0.809511i
\(764\) 18.0000 + 18.0000i 0.651217 + 0.651217i
\(765\) 0 0
\(766\) −25.0000 + 25.0000i −0.903287 + 0.903287i
\(767\) 0 0
\(768\) 0 0
\(769\) −27.0000 27.0000i −0.973645 0.973645i 0.0260166 0.999662i \(-0.491718\pi\)
−0.999662 + 0.0260166i \(0.991718\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13.4164i 0.482867i
\(773\) 13.4164i 0.482555i 0.970456 + 0.241277i \(0.0775663\pi\)
−0.970456 + 0.241277i \(0.922434\pi\)
\(774\) 30.0000i 1.07833i
\(775\) 0 0
\(776\) 10.0000i 0.358979i
\(777\) 0 0
\(778\) 15.6525 + 15.6525i 0.561168 + 0.561168i
\(779\) 4.00000i 0.143315i
\(780\) 0 0
\(781\) −48.0000 + 48.0000i −1.71758 + 1.71758i
\(782\) 22.3607 + 22.3607i 0.799616 + 0.799616i
\(783\) 0 0
\(784\) 3.00000i 0.107143i
\(785\) 0 0
\(786\) 0 0
\(787\) 33.5410 + 33.5410i 1.19561 + 1.19561i