Properties

Label 725.2.e.a.157.1
Level $725$
Weight $2$
Character 725.157
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(157,725)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("725.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 725.e (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 157.1
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 725.157
Dual form 725.2.e.a.568.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.23607i q^{2} -3.00000 q^{4} +(2.23607 + 2.23607i) q^{7} +2.23607i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-2.23607i q^{2} -3.00000 q^{4} +(2.23607 + 2.23607i) q^{7} +2.23607i q^{8} -3.00000 q^{9} +(4.00000 + 4.00000i) q^{11} +(4.47214 + 4.47214i) q^{13} +(5.00000 - 5.00000i) q^{14} -1.00000 q^{16} +4.47214i q^{17} +6.70820i q^{18} +(-2.00000 + 2.00000i) q^{19} +(8.94427 - 8.94427i) q^{22} +(-2.23607 + 2.23607i) q^{23} +(10.0000 - 10.0000i) q^{26} +(-6.70820 - 6.70820i) q^{28} +(2.00000 - 5.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} +6.70820i q^{32} +10.0000 q^{34} +9.00000 q^{36} -4.47214 q^{37} +(4.47214 + 4.47214i) q^{38} +(1.00000 - 1.00000i) q^{41} +4.47214 q^{43} +(-12.0000 - 12.0000i) q^{44} +(5.00000 + 5.00000i) q^{46} +4.47214 q^{47} +3.00000i q^{49} +(-13.4164 - 13.4164i) q^{52} +(8.94427 - 8.94427i) q^{53} +(-5.00000 + 5.00000i) q^{56} +(-11.1803 - 4.47214i) q^{58} +(-9.00000 - 9.00000i) q^{61} +(-8.94427 + 8.94427i) q^{62} +(-6.70820 - 6.70820i) q^{63} +13.0000 q^{64} +(-2.23607 + 2.23607i) q^{67} -13.4164i q^{68} +12.0000i q^{71} -6.70820i q^{72} -4.47214i q^{73} +10.0000i q^{74} +(6.00000 - 6.00000i) q^{76} +17.8885i q^{77} +(-2.00000 + 2.00000i) q^{79} +9.00000 q^{81} +(-2.23607 - 2.23607i) q^{82} +(6.70820 - 6.70820i) q^{83} -10.0000i q^{86} +(-8.94427 + 8.94427i) q^{88} +(-7.00000 + 7.00000i) q^{89} +20.0000i q^{91} +(6.70820 - 6.70820i) q^{92} -10.0000i q^{94} +4.47214 q^{97} +6.70820 q^{98} +(-12.0000 - 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{4} - 12 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/725\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23607i 1.58114i −0.612372 0.790569i \(-0.709785\pi\)
0.612372 0.790569i \(-0.290215\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) −3.00000 −1.50000
\(5\) 0 0
\(6\) 0 0
\(7\) 2.23607 + 2.23607i 0.845154 + 0.845154i 0.989524 0.144370i \(-0.0461154\pi\)
−0.144370 + 0.989524i \(0.546115\pi\)
\(8\) 2.23607i 0.790569i
\(9\) −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 0.959857 + 0.280491i \(0.0904971\pi\)
0.280491 + 0.959857i \(0.409503\pi\)
\(14\) 5.00000 5.00000i 1.33631 1.33631i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 4.47214i 1.08465i 0.840168 + 0.542326i \(0.182456\pi\)
−0.840168 + 0.542326i \(0.817544\pi\)
\(18\) 6.70820i 1.58114i
\(19\) −2.00000 + 2.00000i −0.458831 + 0.458831i −0.898272 0.439440i \(-0.855177\pi\)
0.439440 + 0.898272i \(0.355177\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 8.94427 8.94427i 1.90693 1.90693i
\(23\) −2.23607 + 2.23607i −0.466252 + 0.466252i −0.900698 0.434446i \(-0.856944\pi\)
0.434446 + 0.900698i \(0.356944\pi\)
\(24\) 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 \(0.919615\pi\)
\(32\) 6.70820i 1.18585i
\(33\) 0 0
\(34\) 10.0000 1.71499
\(35\) 0 0
\(36\) 9.00000 1.50000
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) 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
\(43\) 4.47214 0.681994 0.340997 0.940064i \(-0.389235\pi\)
0.340997 + 0.940064i \(0.389235\pi\)
\(44\) −12.0000 12.0000i −1.80907 1.80907i
\(45\) 0 0
\(46\) 5.00000 + 5.00000i 0.737210 + 0.737210i
\(47\) 4.47214 0.652328 0.326164 0.945313i \(-0.394244\pi\)
0.326164 + 0.945313i \(0.394244\pi\)
\(48\) 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 0.264093 0.964497i \(-0.414927\pi\)
0.964497 0.264093i \(-0.0850726\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −5.00000 + 5.00000i −0.668153 + 0.668153i
\(57\) 0 0
\(58\) −11.1803 4.47214i −1.46805 0.587220i
\(59\) 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 \(-0.811876\pi\)
0.557199 + 0.830379i \(0.311876\pi\)
\(68\) 13.4164i 1.62698i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) 6.70820i 0.790569i
\(73\) 4.47214i 0.523424i −0.965146 0.261712i \(-0.915713\pi\)
0.965146 0.261712i \(-0.0842870\pi\)
\(74\) 10.0000i 1.16248i
\(75\) 0 0
\(76\) 6.00000 6.00000i 0.688247 0.688247i
\(77\) 17.8885i 2.03859i
\(78\) 0 0
\(79\) −2.00000 + 2.00000i −0.225018 + 0.225018i −0.810607 0.585590i \(-0.800863\pi\)
0.585590 + 0.810607i \(0.300863\pi\)
\(80\) 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 −0.235543 0.971864i \(-0.575687\pi\)
0.971864 + 0.235543i \(0.0756868\pi\)
\(84\) 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 −0.972962 0.230964i \(-0.925812\pi\)
0.230964 + 0.972962i \(0.425812\pi\)
\(90\) 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
\(97\) 4.47214 0.454077 0.227038 0.973886i \(-0.427096\pi\)
0.227038 + 0.973886i \(0.427096\pi\)
\(98\) 6.70820 0.677631
\(99\) −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 −0.955611 0.294632i \(-0.904803\pi\)
0.294632 + 0.955611i \(0.404803\pi\)
\(104\) −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 0.952632 0.304125i \(-0.0983642\pi\)
−0.304125 + 0.952632i \(0.598364\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.23607 2.23607i −0.211289 0.211289i
\(113\) 4.47214i 0.420703i −0.977626 0.210352i \(-0.932539\pi\)
0.977626 0.210352i \(-0.0674609\pi\)
\(114\) 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
\(127\) 4.47214i 0.396838i 0.980117 + 0.198419i \(0.0635807\pi\)
−0.980117 + 0.198419i \(0.936419\pi\)
\(128\) 15.6525i 1.38350i
\(129\) 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
\(133\) −8.94427 −0.775567
\(134\) 5.00000 + 5.00000i 0.431934 + 0.431934i
\(135\) 0 0
\(136\) −10.0000 −0.857493
\(137\) 13.4164i 1.14624i −0.819471 0.573121i \(-0.805733\pi\)
0.819471 0.573121i \(-0.194267\pi\)
\(138\) 0 0
\(139\) 4.00000i 0.339276i −0.985506 0.169638i \(-0.945740\pi\)
0.985506 0.169638i \(-0.0542598\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 26.8328 2.25176
\(143\) 35.7771i 2.99183i
\(144\) 3.00000 0.250000
\(145\) 0 0
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) 13.4164 1.10282
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 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
\(153\) 13.4164i 1.08465i
\(154\) 40.0000 3.22329
\(155\) 0 0
\(156\) 0 0
\(157\) 13.4164 1.07075 0.535373 0.844616i \(-0.320171\pi\)
0.535373 + 0.844616i \(0.320171\pi\)
\(158\) 4.47214 + 4.47214i 0.355784 + 0.355784i
\(159\) 0 0
\(160\) 0 0
\(161\) −10.0000 −0.788110
\(162\) 20.1246i 1.58114i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −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 \(-0.630366\pi\)
0.917298 + 0.398202i \(0.130366\pi\)
\(168\) 0 0
\(169\) 27.0000i 2.07692i
\(170\) 0 0
\(171\) 6.00000 6.00000i 0.458831 0.458831i
\(172\) −13.4164 −1.02299
\(173\) 13.4164 + 13.4164i 1.02003 + 1.02003i 0.999795 + 0.0202354i \(0.00644155\pi\)
0.0202354 + 0.999795i \(0.493558\pi\)
\(174\) 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 \(0.766738\pi\)
\(182\) 44.7214 3.31497
\(183\) 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
\(188\) −13.4164 −0.978492
\(189\) 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
\(193\) −4.47214 −0.321911 −0.160956 0.986962i \(-0.551458\pi\)
−0.160956 + 0.986962i \(0.551458\pi\)
\(194\) 10.0000i 0.717958i
\(195\) 0 0
\(196\) 9.00000i 0.642857i
\(197\) 13.4164 + 13.4164i 0.955879 + 0.955879i 0.999067 0.0431875i \(-0.0137513\pi\)
−0.0431875 + 0.999067i \(0.513751\pi\)
\(198\) −26.8328 + 26.8328i −1.90693 + 1.90693i
\(199\) 20.0000i 1.41776i −0.705328 0.708881i \(-0.749200\pi\)
0.705328 0.708881i \(-0.250800\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.23607 + 2.23607i −0.157329 + 0.157329i
\(203\) 15.6525 6.70820i 1.09859 0.470824i
\(204\) 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
\(217\) 17.8885i 1.21435i
\(218\) 22.3607i 1.51446i
\(219\) 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 −0.225542 0.974233i \(-0.572415\pi\)
0.974233 + 0.225542i \(0.0724154\pi\)
\(224\) −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 0.448529 0.893768i \(-0.351948\pi\)
−0.893768 + 0.448529i \(0.851948\pi\)
\(228\) 0 0
\(229\) −3.00000 3.00000i −0.198246 0.198246i 0.601002 0.799248i \(-0.294768\pi\)
−0.799248 + 0.601002i \(0.794768\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 11.1803 + 4.47214i 0.734025 + 0.293610i
\(233\) −8.94427 + 8.94427i −0.585959 + 0.585959i −0.936534 0.350576i \(-0.885986\pi\)
0.350576 + 0.936534i \(0.385986\pi\)
\(234\) −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 \(0.917048\pi\)
\(242\) 46.9574 3.01854
\(243\) 0 0
\(244\) 27.0000 + 27.0000i 1.72850 + 1.72850i
\(245\) 0 0
\(246\) 0 0
\(247\) −17.8885 −1.13822
\(248\) 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
\(253\) −17.8885 −1.12464
\(254\) 10.0000 0.627456
\(255\) 0 0
\(256\) −9.00000 −0.562500
\(257\) −4.47214 4.47214i −0.278964 0.278964i 0.553731 0.832695i \(-0.313203\pi\)
−0.832695 + 0.553731i \(0.813203\pi\)
\(258\) 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
\(263\) −8.94427 −0.551527 −0.275764 0.961225i \(-0.588931\pi\)
−0.275764 + 0.961225i \(0.588931\pi\)
\(264\) 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 0.460738 0.887536i \(-0.347585\pi\)
−0.887536 + 0.460738i \(0.847585\pi\)
\(270\) 0 0
\(271\) 14.0000 14.0000i 0.850439 0.850439i −0.139748 0.990187i \(-0.544629\pi\)
0.990187 + 0.139748i \(0.0446292\pi\)
\(272\) 4.47214i 0.271163i
\(273\) 0 0
\(274\) −30.0000 −1.81237
\(275\) 0 0
\(276\) 0 0
\(277\) −8.94427 8.94427i −0.537409 0.537409i 0.385358 0.922767i \(-0.374078\pi\)
−0.922767 + 0.385358i \(0.874078\pi\)
\(278\) −8.94427 −0.536442
\(279\) 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 \(-0.405726\pi\)
−0.956461 + 0.291859i \(0.905726\pi\)
\(284\) 36.0000i 2.13621i
\(285\) 0 0
\(286\) 80.0000 4.73050
\(287\) 4.47214 0.263982
\(288\) 20.1246i 1.18585i
\(289\) −3.00000 −0.176471
\(290\) 0 0
\(291\) 0 0
\(292\) 13.4164i 0.785136i
\(293\) −4.47214 −0.261265 −0.130632 0.991431i \(-0.541701\pi\)
−0.130632 + 0.991431i \(0.541701\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 10.0000i 0.581238i
\(297\) 0 0
\(298\) 44.7214i 2.59064i
\(299\) −20.0000 −1.15663
\(300\) 0 0
\(301\) 10.0000 + 10.0000i 0.576390 + 0.576390i
\(302\) −26.8328 −1.54406
\(303\) 0 0
\(304\) 2.00000 2.00000i 0.114708 0.114708i
\(305\) 0 0
\(306\) −30.0000 −1.71499
\(307\) 31.3050i 1.78667i −0.449393 0.893334i \(-0.648360\pi\)
0.449393 0.893334i \(-0.351640\pi\)
\(308\) 53.6656i 3.05788i
\(309\) 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 −0.314714 + 0.949187i \(0.601909\pi\)
−0.949187 + 0.314714i \(0.898091\pi\)
\(314\) 30.0000i 1.69300i
\(315\) 0 0
\(316\) 6.00000 6.00000i 0.337526 0.337526i
\(317\) −31.3050 −1.75826 −0.879131 0.476581i \(-0.841876\pi\)
−0.879131 + 0.476581i \(0.841876\pi\)
\(318\) 0 0
\(319\) 28.0000 12.0000i 1.56770 0.671871i
\(320\) 0 0
\(321\) 0 0
\(322\) 22.3607i 1.24611i
\(323\) −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
\(333\) 13.4164 0.735215
\(334\) −15.0000 15.0000i −0.820763 0.820763i
\(335\) 0 0
\(336\) 0 0
\(337\) 13.4164 0.730838 0.365419 0.930843i \(-0.380926\pi\)
0.365419 + 0.930843i \(0.380926\pi\)
\(338\) 60.3738 3.28390
\(339\) 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 \(-0.547485\pi\)
0.988894 + 0.148625i \(0.0474846\pi\)
\(348\) 0 0
\(349\) 30.0000i 1.60586i 0.596071 + 0.802932i \(0.296728\pi\)
−0.596071 + 0.802932i \(0.703272\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −26.8328 + 26.8328i −1.43019 + 1.43019i
\(353\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(354\) 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 −0.315567 0.948903i \(-0.602195\pi\)
0.948903 + 0.315567i \(0.102195\pi\)
\(360\) 0 0
\(361\) 11.0000i 0.578947i
\(362\) 44.7214i 2.35050i
\(363\) 0 0
\(364\) 60.0000i 3.14485i
\(365\) 0 0
\(366\) 0 0
\(367\) 26.8328i 1.40066i 0.713818 + 0.700331i \(0.246964\pi\)
−0.713818 + 0.700331i \(0.753036\pi\)
\(368\) 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 −0.963257 0.268582i \(-0.913445\pi\)
0.268582 + 0.963257i \(0.413445\pi\)
\(374\) 40.0000 + 40.0000i 2.06835 + 2.06835i
\(375\) 0 0
\(376\) 10.0000i 0.515711i
\(377\) 31.3050 13.4164i 1.61229 0.690980i
\(378\) 0 0
\(379\) 12.0000 12.0000i 0.616399 0.616399i −0.328207 0.944606i \(-0.606444\pi\)
0.944606 + 0.328207i \(0.106444\pi\)
\(380\) 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 \(-0.382367\pi\)
−0.932488 + 0.361200i \(0.882367\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000i 0.508987i
\(387\) −13.4164 −0.681994
\(388\) −13.4164 −0.681115
\(389\) 7.00000 + 7.00000i 0.354914 + 0.354914i 0.861934 0.507020i \(-0.169253\pi\)
−0.507020 + 0.861934i \(0.669253\pi\)
\(390\) 0 0
\(391\) −10.0000 10.0000i −0.505722 0.505722i
\(392\) −6.70820 −0.338815
\(393\) 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 0.958487 0.285137i \(-0.0920390\pi\)
−0.285137 + 0.958487i \(0.592039\pi\)
\(398\) −44.7214 −2.24168
\(399\) 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
\(403\) 35.7771i 1.78218i
\(404\) 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 −0.629036 0.777376i \(-0.716550\pi\)
0.777376 + 0.629036i \(0.216550\pi\)
\(410\) 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
\(418\) 35.7771i 1.74991i
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 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
\(423\) −13.4164 −0.652328
\(424\) 20.0000 + 20.0000i 0.971286 + 0.971286i
\(425\) 0 0
\(426\) 0 0
\(427\) 40.2492i 1.94780i
\(428\) −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
\(433\) 22.3607i 1.07459i −0.843396 0.537293i \(-0.819447\pi\)
0.843396 0.537293i \(-0.180553\pi\)
\(434\) −40.0000 −1.92006
\(435\) 0 0
\(436\) 30.0000 1.43674
\(437\) 8.94427i 0.427863i
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) 9.00000i 0.428571i
\(442\) 44.7214 + 44.7214i 2.12718 + 2.12718i
\(443\) 31.3050i 1.48734i 0.668545 + 0.743672i \(0.266917\pi\)
−0.668545 + 0.743672i \(0.733083\pi\)
\(444\) 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 −0.330350 0.943858i \(-0.607167\pi\)
0.943858 + 0.330350i \(0.107167\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) 13.4164i 0.631055i
\(453\) 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 \(-0.548457\pi\)
0.988435 + 0.151644i \(0.0484568\pi\)
\(458\) −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 \(-0.273411\pi\)
−0.757155 + 0.653236i \(0.773411\pi\)
\(464\) −2.00000 + 5.00000i −0.0928477 + 0.232119i
\(465\) 0 0
\(466\) 20.0000 + 20.0000i 0.926482 + 0.926482i
\(467\) 13.4164i 0.620837i 0.950600 + 0.310419i \(0.100469\pi\)
−0.950600 + 0.310419i \(0.899531\pi\)
\(468\) 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 0.164017 0.986458i \(-0.447555\pi\)
−0.986458 + 0.164017i \(0.947555\pi\)
\(480\) 0 0
\(481\) −20.0000 20.0000i −0.911922 0.911922i
\(482\) 17.8885 0.814801
\(483\) 0 0
\(484\) 63.0000i 2.86364i
\(485\) 0 0
\(486\) 0 0
\(487\) −20.1246 20.1246i −0.911933 0.911933i 0.0844910 0.996424i \(-0.473074\pi\)
−0.996424 + 0.0844910i \(0.973074\pi\)
\(488\) 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
\(493\) 22.3607 + 8.94427i 1.00707 + 0.402830i
\(494\) 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 \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 8.94427 8.94427i 0.399202 0.399202i
\(503\) 22.3607i 0.997013i −0.866886 0.498507i \(-0.833882\pi\)
0.866886 0.498507i \(-0.166118\pi\)
\(504\) 15.0000 15.0000i 0.668153 0.668153i
\(505\) 0 0
\(506\) 40.0000i 1.77822i
\(507\) 0 0
\(508\) 13.4164i 0.595257i
\(509\) 24.0000i 1.06378i −0.846813 0.531891i \(-0.821482\pi\)
0.846813 0.531891i \(-0.178518\pi\)
\(510\) 0 0
\(511\) 10.0000 10.0000i 0.442374 0.442374i
\(512\) 11.1803i 0.494106i
\(513\) 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 \(-0.0702971\pi\)
\(522\) 33.5410 + 13.4164i 1.46805 + 0.587220i
\(523\) −15.6525 + 15.6525i −0.684435 + 0.684435i −0.960996 0.276561i \(-0.910805\pi\)
0.276561 + 0.960996i \(0.410805\pi\)
\(524\) −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
\(532\) 26.8328 1.16335
\(533\) 8.94427 0.387419
\(534\) 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 0.957543 0.288291i \(-0.0930871\pi\)
−0.288291 + 0.957543i \(0.593087\pi\)
\(548\) 40.2492i 1.71936i
\(549\) 27.0000 + 27.0000i 1.15233 + 1.15233i
\(550\) 0 0
\(551\) 6.00000 + 14.0000i 0.255609 + 0.596420i
\(552\) 0 0
\(553\) −8.94427 −0.380349
\(554\) −20.0000 + 20.0000i −0.849719 + 0.849719i
\(555\) 0 0
\(556\) 12.0000i 0.508913i
\(557\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(558\) 26.8328 26.8328i 1.13592 1.13592i
\(559\) 20.0000 + 20.0000i 0.845910 + 0.845910i
\(560\) 0 0
\(561\) 0 0
\(562\) 26.8328i 1.13187i
\(563\) 35.7771i 1.50782i 0.656975 + 0.753912i \(0.271836\pi\)
−0.656975 + 0.753912i \(0.728164\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −25.0000 + 25.0000i −1.05083 + 1.05083i
\(567\) 20.1246 + 20.1246i 0.845154 + 0.845154i
\(568\) −26.8328 −1.12588
\(569\) −7.00000 7.00000i −0.293455 0.293455i 0.544988 0.838444i \(-0.316534\pi\)
−0.838444 + 0.544988i \(0.816534\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 107.331i 4.48775i
\(573\) 0 0
\(574\) 10.0000i 0.417392i
\(575\) 0 0
\(576\) −39.0000 −1.62500
\(577\) −40.2492 −1.67560 −0.837799 0.545979i \(-0.816158\pi\)
−0.837799 + 0.545979i \(0.816158\pi\)
\(578\) 6.70820i 0.279024i
\(579\) 0 0
\(580\) 0 0
\(581\) 30.0000 1.24461
\(582\) 0 0
\(583\) 71.5542 2.96347
\(584\) 10.0000 0.413803
\(585\) 0 0
\(586\) 10.0000i 0.413096i
\(587\) 20.1246 + 20.1246i 0.830632 + 0.830632i 0.987603 0.156972i \(-0.0501731\pi\)
−0.156972 + 0.987603i \(0.550173\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) 0 0
\(592\) 4.47214 0.183804
\(593\) 8.94427 + 8.94427i 0.367297 + 0.367297i 0.866491 0.499193i \(-0.166370\pi\)
−0.499193 + 0.866491i \(0.666370\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −60.0000 −2.45770
\(597\) 0 0
\(598\) 44.7214i 1.82879i
\(599\) 22.0000 22.0000i 0.898896 0.898896i −0.0964429 0.995339i \(-0.530747\pi\)
0.995339 + 0.0964429i \(0.0307465\pi\)
\(600\) 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
\(607\) 13.4164 0.544555 0.272278 0.962219i \(-0.412223\pi\)
0.272278 + 0.962219i \(0.412223\pi\)
\(608\) −13.4164 13.4164i −0.544107 0.544107i
\(609\) 0 0
\(610\) 0 0
\(611\) 20.0000 + 20.0000i 0.809113 + 0.809113i
\(612\) 40.2492i 1.62698i
\(613\) −8.94427 8.94427i −0.361256 0.361256i 0.503019 0.864275i \(-0.332222\pi\)
−0.864275 + 0.503019i \(0.832222\pi\)
\(614\) −70.0000 −2.82497
\(615\) 0 0
\(616\) −40.0000 −1.61165
\(617\) 40.2492 1.62037 0.810186 0.586172i \(-0.199366\pi\)
0.810186 + 0.586172i \(0.199366\pi\)
\(618\) 0 0
\(619\) −12.0000 12.0000i −0.482321 0.482321i 0.423551 0.905872i \(-0.360783\pi\)
−0.905872 + 0.423551i \(0.860783\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −8.94427 + 8.94427i −0.358633 + 0.358633i
\(623\) −31.3050 −1.25421
\(624\) 0 0
\(625\) 0 0
\(626\) 50.0000 + 50.0000i 1.99840 + 1.99840i
\(627\) 0 0
\(628\) −40.2492 −1.60612
\(629\) 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
\(638\) −26.8328 62.6099i −1.06232 2.47875i
\(639\) 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 0.987262 + 0.159103i \(0.0508601\pi\)
0.159103 + 0.987262i \(0.449140\pi\)
\(644\) 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 \(-0.809709\pi\)
0.562839 + 0.826566i \(0.309709\pi\)
\(648\) 20.1246i 0.790569i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 31.3050i 1.22506i 0.790448 + 0.612529i \(0.209848\pi\)
−0.790448 + 0.612529i \(0.790152\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 + 1.00000i −0.0390434 + 0.0390434i
\(657\) 13.4164i 0.523424i
\(658\) 22.3607 22.3607i 0.871710 0.871710i
\(659\) 2.00000 2.00000i 0.0779089 0.0779089i −0.667078 0.744987i \(-0.732455\pi\)
0.744987 + 0.667078i \(0.232455\pi\)
\(660\) 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
\(667\) 6.70820 + 15.6525i 0.259743 + 0.606066i
\(668\) −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 \(-0.288898\pi\)
−0.788028 + 0.615640i \(0.788898\pi\)
\(674\) 30.0000i 1.15556i
\(675\) 0 0
\(676\) 81.0000i 3.11538i
\(677\) 4.47214 0.171878 0.0859391 0.996300i \(-0.472611\pi\)
0.0859391 + 0.996300i \(0.472611\pi\)
\(678\) 0 0
\(679\) 10.0000 + 10.0000i 0.383765 + 0.383765i
\(680\) 0 0
\(681\) 0 0
\(682\) −71.5542 −2.73995
\(683\) −33.5410 + 33.5410i −1.28341 + 1.28341i −0.344698 + 0.938714i \(0.612019\pi\)
−0.938714 + 0.344698i \(0.887981\pi\)
\(684\) −18.0000 + 18.0000i −0.688247 + 0.688247i
\(685\) 0 0
\(686\) −20.0000 20.0000i −0.763604 0.763604i
\(687\) 0 0
\(688\) −4.47214 −0.170499
\(689\) 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
\(693\) 53.6656i 2.03859i
\(694\) −35.0000 35.0000i −1.32858 1.32858i
\(695\) 0 0
\(696\) 0 0
\(697\) 4.47214 + 4.47214i 0.169394 + 0.169394i
\(698\) 67.0820 2.53909
\(699\) 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
\(707\) 4.47214i 0.168192i
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 6.00000 6.00000i 0.225018 0.225018i
\(712\) −15.6525 15.6525i −0.586601 0.586601i
\(713\) 17.8885 0.669931
\(714\) 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 \(0.121649\pi\)
−0.927857 + 0.372937i \(0.878351\pi\)
\(720\) 0 0
\(721\) −30.0000 −1.11726
\(722\) 24.5967 0.915396
\(723\) 0 0
\(724\) 60.0000 2.22988
\(725\) 0 0
\(726\) 0 0
\(727\) 44.7214i 1.65862i 0.558786 + 0.829312i \(0.311267\pi\)
−0.558786 + 0.829312i \(0.688733\pi\)
\(728\) −44.7214 −1.65748
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 20.0000i 0.739727i
\(732\) 0 0
\(733\) 4.47214i 0.165182i −0.996584 0.0825911i \(-0.973680\pi\)
0.996584 0.0825911i \(-0.0263195\pi\)
\(734\) 60.0000 2.21464
\(735\) 0 0
\(736\) −15.0000 15.0000i −0.552907 0.552907i
\(737\) −17.8885 −0.658933
\(738\) 6.70820 + 6.70820i 0.246932 + 0.246932i
\(739\) −18.0000 + 18.0000i −0.662141 + 0.662141i −0.955884 0.293744i \(-0.905099\pi\)
0.293744 + 0.955884i \(0.405099\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 89.4427i 3.28355i
\(743\) 22.3607i 0.820334i −0.912010 0.410167i \(-0.865470\pi\)
0.912010 0.410167i \(-0.134530\pi\)
\(744\) 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 \(0.0374308\pi\)
\(752\) −4.47214 −0.163082
\(753\) 0 0
\(754\) −30.0000 70.0000i −1.09254 2.54925i
\(755\) 0 0
\(756\) 0 0
\(757\) 40.2492i 1.46288i −0.681904 0.731441i \(-0.738848\pi\)
0.681904 0.731441i \(-0.261152\pi\)
\(758\) −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 0.999662 0.0260166i \(-0.00828228\pi\)
−0.0260166 + 0.999662i \(0.508282\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13.4164 0.482867
\(773\) 13.4164 0.482555 0.241277 0.970456i \(-0.422434\pi\)
0.241277 + 0.970456i \(0.422434\pi\)
\(774\) 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 −0.220140 + 0.975468i \(0.570651\pi\)