Properties

Label 220.2.l.a.67.1
Level $220$
Weight $2$
Character 220.67
Analytic conductor $1.757$
Analytic rank $1$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [220,2,Mod(23,220)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(220, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("220.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 220.l (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: \(1.75670884447\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 67.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 220.67
Dual form 220.2.l.a.23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} -2.00000i q^{4} +(-1.00000 - 2.00000i) q^{5} +4.00000 q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +5.00000i q^{9} +(3.00000 + 1.00000i) q^{10} -1.00000i q^{11} +(-4.00000 + 4.00000i) q^{12} +(-4.00000 + 4.00000i) q^{13} -2.00000i q^{14} +(-2.00000 + 6.00000i) q^{15} -4.00000 q^{16} +(2.00000 + 2.00000i) q^{17} +(-5.00000 - 5.00000i) q^{18} +2.00000 q^{19} +(-4.00000 + 2.00000i) q^{20} +4.00000 q^{21} +(1.00000 + 1.00000i) q^{22} +(-4.00000 - 4.00000i) q^{23} -8.00000i q^{24} +(-3.00000 + 4.00000i) q^{25} -8.00000i q^{26} +(4.00000 - 4.00000i) q^{27} +(2.00000 + 2.00000i) q^{28} -2.00000i q^{29} +(-4.00000 - 8.00000i) q^{30} +8.00000i q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.00000 + 2.00000i) q^{33} -4.00000 q^{34} +(3.00000 + 1.00000i) q^{35} +10.0000 q^{36} +(-5.00000 - 5.00000i) q^{37} +(-2.00000 + 2.00000i) q^{38} +16.0000 q^{39} +(2.00000 - 6.00000i) q^{40} -6.00000 q^{41} +(-4.00000 + 4.00000i) q^{42} +(1.00000 + 1.00000i) q^{43} -2.00000 q^{44} +(10.0000 - 5.00000i) q^{45} +8.00000 q^{46} +(-4.00000 + 4.00000i) q^{47} +(8.00000 + 8.00000i) q^{48} +5.00000i q^{49} +(-1.00000 - 7.00000i) q^{50} -8.00000i q^{51} +(8.00000 + 8.00000i) q^{52} +(9.00000 - 9.00000i) q^{53} +8.00000i q^{54} +(-2.00000 + 1.00000i) q^{55} -4.00000 q^{56} +(-4.00000 - 4.00000i) q^{57} +(2.00000 + 2.00000i) q^{58} -8.00000 q^{59} +(12.0000 + 4.00000i) q^{60} -10.0000 q^{61} +(-8.00000 - 8.00000i) q^{62} +(-5.00000 - 5.00000i) q^{63} +8.00000i q^{64} +(12.0000 + 4.00000i) q^{65} -4.00000i q^{66} +(4.00000 - 4.00000i) q^{68} +16.0000i q^{69} +(-4.00000 + 2.00000i) q^{70} -12.0000i q^{71} +(-10.0000 + 10.0000i) q^{72} +(2.00000 - 2.00000i) q^{73} +10.0000 q^{74} +(14.0000 - 2.00000i) q^{75} -4.00000i q^{76} +(1.00000 + 1.00000i) q^{77} +(-16.0000 + 16.0000i) q^{78} -10.0000 q^{79} +(4.00000 + 8.00000i) q^{80} -1.00000 q^{81} +(6.00000 - 6.00000i) q^{82} +(1.00000 + 1.00000i) q^{83} -8.00000i q^{84} +(2.00000 - 6.00000i) q^{85} -2.00000 q^{86} +(-4.00000 + 4.00000i) q^{87} +(2.00000 - 2.00000i) q^{88} -6.00000i q^{89} +(-5.00000 + 15.0000i) q^{90} -8.00000i q^{91} +(-8.00000 + 8.00000i) q^{92} +(16.0000 - 16.0000i) q^{93} -8.00000i q^{94} +(-2.00000 - 4.00000i) q^{95} -16.0000 q^{96} +(-3.00000 - 3.00000i) q^{97} +(-5.00000 - 5.00000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{3} - 2 q^{5} + 8 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{10} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 8 q^{16} + 4 q^{17} - 10 q^{18} + 4 q^{19} - 8 q^{20} + 8 q^{21} + 2 q^{22} - 8 q^{23} - 6 q^{25}+ \cdots + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/220\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(111\) \(177\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i
\(3\) −2.00000 2.00000i −1.15470 1.15470i −0.985599 0.169102i \(-0.945913\pi\)
−0.169102 0.985599i \(-0.554087\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 4.00000 1.63299
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 5.00000i 1.66667i
\(10\) 3.00000 + 1.00000i 0.948683 + 0.316228i
\(11\) 1.00000i 0.301511i
\(12\) −4.00000 + 4.00000i −1.15470 + 1.15470i
\(13\) −4.00000 + 4.00000i −1.10940 + 1.10940i −0.116171 + 0.993229i \(0.537062\pi\)
−0.993229 + 0.116171i \(0.962938\pi\)
\(14\) 2.00000i 0.534522i
\(15\) −2.00000 + 6.00000i −0.516398 + 1.54919i
\(16\) −4.00000 −1.00000
\(17\) 2.00000 + 2.00000i 0.485071 + 0.485071i 0.906747 0.421676i \(-0.138558\pi\)
−0.421676 + 0.906747i \(0.638558\pi\)
\(18\) −5.00000 5.00000i −1.17851 1.17851i
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −4.00000 + 2.00000i −0.894427 + 0.447214i
\(21\) 4.00000 0.872872
\(22\) 1.00000 + 1.00000i 0.213201 + 0.213201i
\(23\) −4.00000 4.00000i −0.834058 0.834058i 0.154011 0.988069i \(-0.450781\pi\)
−0.988069 + 0.154011i \(0.950781\pi\)
\(24\) 8.00000i 1.63299i
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 8.00000i 1.56893i
\(27\) 4.00000 4.00000i 0.769800 0.769800i
\(28\) 2.00000 + 2.00000i 0.377964 + 0.377964i
\(29\) 2.00000i 0.371391i −0.982607 0.185695i \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) −4.00000 8.00000i −0.730297 1.46059i
\(31\) 8.00000i 1.43684i 0.695608 + 0.718421i \(0.255135\pi\)
−0.695608 + 0.718421i \(0.744865\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) −2.00000 + 2.00000i −0.348155 + 0.348155i
\(34\) −4.00000 −0.685994
\(35\) 3.00000 + 1.00000i 0.507093 + 0.169031i
\(36\) 10.0000 1.66667
\(37\) −5.00000 5.00000i −0.821995 0.821995i 0.164399 0.986394i \(-0.447432\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) −2.00000 + 2.00000i −0.324443 + 0.324443i
\(39\) 16.0000 2.56205
\(40\) 2.00000 6.00000i 0.316228 0.948683i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) −4.00000 + 4.00000i −0.617213 + 0.617213i
\(43\) 1.00000 + 1.00000i 0.152499 + 0.152499i 0.779233 0.626734i \(-0.215609\pi\)
−0.626734 + 0.779233i \(0.715609\pi\)
\(44\) −2.00000 −0.301511
\(45\) 10.0000 5.00000i 1.49071 0.745356i
\(46\) 8.00000 1.17954
\(47\) −4.00000 + 4.00000i −0.583460 + 0.583460i −0.935852 0.352392i \(-0.885368\pi\)
0.352392 + 0.935852i \(0.385368\pi\)
\(48\) 8.00000 + 8.00000i 1.15470 + 1.15470i
\(49\) 5.00000i 0.714286i
\(50\) −1.00000 7.00000i −0.141421 0.989949i
\(51\) 8.00000i 1.12022i
\(52\) 8.00000 + 8.00000i 1.10940 + 1.10940i
\(53\) 9.00000 9.00000i 1.23625 1.23625i 0.274721 0.961524i \(-0.411414\pi\)
0.961524 0.274721i \(-0.0885855\pi\)
\(54\) 8.00000i 1.08866i
\(55\) −2.00000 + 1.00000i −0.269680 + 0.134840i
\(56\) −4.00000 −0.534522
\(57\) −4.00000 4.00000i −0.529813 0.529813i
\(58\) 2.00000 + 2.00000i 0.262613 + 0.262613i
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 12.0000 + 4.00000i 1.54919 + 0.516398i
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −8.00000 8.00000i −1.01600 1.01600i
\(63\) −5.00000 5.00000i −0.629941 0.629941i
\(64\) 8.00000i 1.00000i
\(65\) 12.0000 + 4.00000i 1.48842 + 0.496139i
\(66\) 4.00000i 0.492366i
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 4.00000 4.00000i 0.485071 0.485071i
\(69\) 16.0000i 1.92617i
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) −10.0000 + 10.0000i −1.17851 + 1.17851i
\(73\) 2.00000 2.00000i 0.234082 0.234082i −0.580312 0.814394i \(-0.697069\pi\)
0.814394 + 0.580312i \(0.197069\pi\)
\(74\) 10.0000 1.16248
\(75\) 14.0000 2.00000i 1.61658 0.230940i
\(76\) 4.00000i 0.458831i
\(77\) 1.00000 + 1.00000i 0.113961 + 0.113961i
\(78\) −16.0000 + 16.0000i −1.81164 + 1.81164i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 4.00000 + 8.00000i 0.447214 + 0.894427i
\(81\) −1.00000 −0.111111
\(82\) 6.00000 6.00000i 0.662589 0.662589i
\(83\) 1.00000 + 1.00000i 0.109764 + 0.109764i 0.759856 0.650092i \(-0.225269\pi\)
−0.650092 + 0.759856i \(0.725269\pi\)
\(84\) 8.00000i 0.872872i
\(85\) 2.00000 6.00000i 0.216930 0.650791i
\(86\) −2.00000 −0.215666
\(87\) −4.00000 + 4.00000i −0.428845 + 0.428845i
\(88\) 2.00000 2.00000i 0.213201 0.213201i
\(89\) 6.00000i 0.635999i −0.948091 0.317999i \(-0.896989\pi\)
0.948091 0.317999i \(-0.103011\pi\)
\(90\) −5.00000 + 15.0000i −0.527046 + 1.58114i
\(91\) 8.00000i 0.838628i
\(92\) −8.00000 + 8.00000i −0.834058 + 0.834058i
\(93\) 16.0000 16.0000i 1.65912 1.65912i
\(94\) 8.00000i 0.825137i
\(95\) −2.00000 4.00000i −0.205196 0.410391i
\(96\) −16.0000 −1.63299
\(97\) −3.00000 3.00000i −0.304604 0.304604i 0.538208 0.842812i \(-0.319101\pi\)
−0.842812 + 0.538208i \(0.819101\pi\)
\(98\) −5.00000 5.00000i −0.505076 0.505076i
\(99\) 5.00000 0.502519
\(100\) 8.00000 + 6.00000i 0.800000 + 0.600000i
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 8.00000 + 8.00000i 0.792118 + 0.792118i
\(103\) −6.00000 6.00000i −0.591198 0.591198i 0.346757 0.937955i \(-0.387283\pi\)
−0.937955 + 0.346757i \(0.887283\pi\)
\(104\) −16.0000 −1.56893
\(105\) −4.00000 8.00000i −0.390360 0.780720i
\(106\) 18.0000i 1.74831i
\(107\) −13.0000 + 13.0000i −1.25676 + 1.25676i −0.304125 + 0.952632i \(0.598364\pi\)
−0.952632 + 0.304125i \(0.901636\pi\)
\(108\) −8.00000 8.00000i −0.769800 0.769800i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 1.00000 3.00000i 0.0953463 0.286039i
\(111\) 20.0000i 1.89832i
\(112\) 4.00000 4.00000i 0.377964 0.377964i
\(113\) −1.00000 + 1.00000i −0.0940721 + 0.0940721i −0.752577 0.658505i \(-0.771189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 8.00000 0.749269
\(115\) −4.00000 + 12.0000i −0.373002 + 1.11901i
\(116\) −4.00000 −0.371391
\(117\) −20.0000 20.0000i −1.84900 1.84900i
\(118\) 8.00000 8.00000i 0.736460 0.736460i
\(119\) −4.00000 −0.366679
\(120\) −16.0000 + 8.00000i −1.46059 + 0.730297i
\(121\) −1.00000 −0.0909091
\(122\) 10.0000 10.0000i 0.905357 0.905357i
\(123\) 12.0000 + 12.0000i 1.08200 + 1.08200i
\(124\) 16.0000 1.43684
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 10.0000 0.890871
\(127\) 1.00000 1.00000i 0.0887357 0.0887357i −0.661346 0.750081i \(-0.730014\pi\)
0.750081 + 0.661346i \(0.230014\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) 4.00000i 0.352180i
\(130\) −16.0000 + 8.00000i −1.40329 + 0.701646i
\(131\) 6.00000i 0.524222i −0.965038 0.262111i \(-0.915581\pi\)
0.965038 0.262111i \(-0.0844187\pi\)
\(132\) 4.00000 + 4.00000i 0.348155 + 0.348155i
\(133\) −2.00000 + 2.00000i −0.173422 + 0.173422i
\(134\) 0 0
\(135\) −12.0000 4.00000i −1.03280 0.344265i
\(136\) 8.00000i 0.685994i
\(137\) 7.00000 + 7.00000i 0.598050 + 0.598050i 0.939793 0.341743i \(-0.111017\pi\)
−0.341743 + 0.939793i \(0.611017\pi\)
\(138\) −16.0000 16.0000i −1.36201 1.36201i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 2.00000 6.00000i 0.169031 0.507093i
\(141\) 16.0000 1.34744
\(142\) 12.0000 + 12.0000i 1.00702 + 1.00702i
\(143\) 4.00000 + 4.00000i 0.334497 + 0.334497i
\(144\) 20.0000i 1.66667i
\(145\) −4.00000 + 2.00000i −0.332182 + 0.166091i
\(146\) 4.00000i 0.331042i
\(147\) 10.0000 10.0000i 0.824786 0.824786i
\(148\) −10.0000 + 10.0000i −0.821995 + 0.821995i
\(149\) 18.0000i 1.47462i 0.675556 + 0.737309i \(0.263904\pi\)
−0.675556 + 0.737309i \(0.736096\pi\)
\(150\) −12.0000 + 16.0000i −0.979796 + 1.30639i
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 4.00000 + 4.00000i 0.324443 + 0.324443i
\(153\) −10.0000 + 10.0000i −0.808452 + 0.808452i
\(154\) −2.00000 −0.161165
\(155\) 16.0000 8.00000i 1.28515 0.642575i
\(156\) 32.0000i 2.56205i
\(157\) 3.00000 + 3.00000i 0.239426 + 0.239426i 0.816612 0.577186i \(-0.195849\pi\)
−0.577186 + 0.816612i \(0.695849\pi\)
\(158\) 10.0000 10.0000i 0.795557 0.795557i
\(159\) −36.0000 −2.85499
\(160\) −12.0000 4.00000i −0.948683 0.316228i
\(161\) 8.00000 0.630488
\(162\) 1.00000 1.00000i 0.0785674 0.0785674i
\(163\) 6.00000 + 6.00000i 0.469956 + 0.469956i 0.901900 0.431944i \(-0.142172\pi\)
−0.431944 + 0.901900i \(0.642172\pi\)
\(164\) 12.0000i 0.937043i
\(165\) 6.00000 + 2.00000i 0.467099 + 0.155700i
\(166\) −2.00000 −0.155230
\(167\) 3.00000 3.00000i 0.232147 0.232147i −0.581441 0.813588i \(-0.697511\pi\)
0.813588 + 0.581441i \(0.197511\pi\)
\(168\) 8.00000 + 8.00000i 0.617213 + 0.617213i
\(169\) 19.0000i 1.46154i
\(170\) 4.00000 + 8.00000i 0.306786 + 0.613572i
\(171\) 10.0000i 0.764719i
\(172\) 2.00000 2.00000i 0.152499 0.152499i
\(173\) −2.00000 + 2.00000i −0.152057 + 0.152057i −0.779036 0.626979i \(-0.784291\pi\)
0.626979 + 0.779036i \(0.284291\pi\)
\(174\) 8.00000i 0.606478i
\(175\) −1.00000 7.00000i −0.0755929 0.529150i
\(176\) 4.00000i 0.301511i
\(177\) 16.0000 + 16.0000i 1.20263 + 1.20263i
\(178\) 6.00000 + 6.00000i 0.449719 + 0.449719i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −10.0000 20.0000i −0.745356 1.49071i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 8.00000 + 8.00000i 0.592999 + 0.592999i
\(183\) 20.0000 + 20.0000i 1.47844 + 1.47844i
\(184\) 16.0000i 1.17954i
\(185\) −5.00000 + 15.0000i −0.367607 + 1.10282i
\(186\) 32.0000i 2.34635i
\(187\) 2.00000 2.00000i 0.146254 0.146254i
\(188\) 8.00000 + 8.00000i 0.583460 + 0.583460i
\(189\) 8.00000i 0.581914i
\(190\) 6.00000 + 2.00000i 0.435286 + 0.145095i
\(191\) 4.00000i 0.289430i −0.989473 0.144715i \(-0.953773\pi\)
0.989473 0.144715i \(-0.0462265\pi\)
\(192\) 16.0000 16.0000i 1.15470 1.15470i
\(193\) 10.0000 10.0000i 0.719816 0.719816i −0.248752 0.968567i \(-0.580020\pi\)
0.968567 + 0.248752i \(0.0800203\pi\)
\(194\) 6.00000 0.430775
\(195\) −16.0000 32.0000i −1.14578 2.29157i
\(196\) 10.0000 0.714286
\(197\) −2.00000 2.00000i −0.142494 0.142494i 0.632261 0.774755i \(-0.282127\pi\)
−0.774755 + 0.632261i \(0.782127\pi\)
\(198\) −5.00000 + 5.00000i −0.355335 + 0.355335i
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) −14.0000 + 2.00000i −0.989949 + 0.141421i
\(201\) 0 0
\(202\) 14.0000 14.0000i 0.985037 0.985037i
\(203\) 2.00000 + 2.00000i 0.140372 + 0.140372i
\(204\) −16.0000 −1.12022
\(205\) 6.00000 + 12.0000i 0.419058 + 0.838116i
\(206\) 12.0000 0.836080
\(207\) 20.0000 20.0000i 1.39010 1.39010i
\(208\) 16.0000 16.0000i 1.10940 1.10940i
\(209\) 2.00000i 0.138343i
\(210\) 12.0000 + 4.00000i 0.828079 + 0.276026i
\(211\) 22.0000i 1.51454i −0.653101 0.757271i \(-0.726532\pi\)
0.653101 0.757271i \(-0.273468\pi\)
\(212\) −18.0000 18.0000i −1.23625 1.23625i
\(213\) −24.0000 + 24.0000i −1.64445 + 1.64445i
\(214\) 26.0000i 1.77732i
\(215\) 1.00000 3.00000i 0.0681994 0.204598i
\(216\) 16.0000 1.08866
\(217\) −8.00000 8.00000i −0.543075 0.543075i
\(218\) 2.00000 + 2.00000i 0.135457 + 0.135457i
\(219\) −8.00000 −0.540590
\(220\) 2.00000 + 4.00000i 0.134840 + 0.269680i
\(221\) −16.0000 −1.07628
\(222\) −20.0000 20.0000i −1.34231 1.34231i
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 8.00000i 0.534522i
\(225\) −20.0000 15.0000i −1.33333 1.00000i
\(226\) 2.00000i 0.133038i
\(227\) −5.00000 + 5.00000i −0.331862 + 0.331862i −0.853293 0.521431i \(-0.825398\pi\)
0.521431 + 0.853293i \(0.325398\pi\)
\(228\) −8.00000 + 8.00000i −0.529813 + 0.529813i
\(229\) 4.00000i 0.264327i 0.991228 + 0.132164i \(0.0421925\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) −8.00000 16.0000i −0.527504 1.05501i
\(231\) 4.00000i 0.263181i
\(232\) 4.00000 4.00000i 0.262613 0.262613i
\(233\) 20.0000 20.0000i 1.31024 1.31024i 0.389010 0.921234i \(-0.372817\pi\)
0.921234 0.389010i \(-0.127183\pi\)
\(234\) 40.0000 2.61488
\(235\) 12.0000 + 4.00000i 0.782794 + 0.260931i
\(236\) 16.0000i 1.04151i
\(237\) 20.0000 + 20.0000i 1.29914 + 1.29914i
\(238\) 4.00000 4.00000i 0.259281 0.259281i
\(239\) 22.0000 1.42306 0.711531 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 8.00000 24.0000i 0.516398 1.54919i
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 1.00000 1.00000i 0.0642824 0.0642824i
\(243\) −10.0000 10.0000i −0.641500 0.641500i
\(244\) 20.0000i 1.28037i
\(245\) 10.0000 5.00000i 0.638877 0.319438i
\(246\) −24.0000 −1.53018
\(247\) −8.00000 + 8.00000i −0.509028 + 0.509028i
\(248\) −16.0000 + 16.0000i −1.01600 + 1.01600i
\(249\) 4.00000i 0.253490i
\(250\) −13.0000 + 9.00000i −0.822192 + 0.569210i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −10.0000 + 10.0000i −0.629941 + 0.629941i
\(253\) −4.00000 + 4.00000i −0.251478 + 0.251478i
\(254\) 2.00000i 0.125491i
\(255\) −16.0000 + 8.00000i −1.00196 + 0.500979i
\(256\) 16.0000 1.00000
\(257\) 1.00000 + 1.00000i 0.0623783 + 0.0623783i 0.737608 0.675229i \(-0.235955\pi\)
−0.675229 + 0.737608i \(0.735955\pi\)
\(258\) 4.00000 + 4.00000i 0.249029 + 0.249029i
\(259\) 10.0000 0.621370
\(260\) 8.00000 24.0000i 0.496139 1.48842i
\(261\) 10.0000 0.618984
\(262\) 6.00000 + 6.00000i 0.370681 + 0.370681i
\(263\) −5.00000 5.00000i −0.308313 0.308313i 0.535942 0.844255i \(-0.319957\pi\)
−0.844255 + 0.535942i \(0.819957\pi\)
\(264\) −8.00000 −0.492366
\(265\) −27.0000 9.00000i −1.65860 0.552866i
\(266\) 4.00000i 0.245256i
\(267\) −12.0000 + 12.0000i −0.734388 + 0.734388i
\(268\) 0 0
\(269\) 26.0000i 1.58525i 0.609711 + 0.792624i \(0.291286\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) 16.0000 8.00000i 0.973729 0.486864i
\(271\) 14.0000i 0.850439i 0.905090 + 0.425220i \(0.139803\pi\)
−0.905090 + 0.425220i \(0.860197\pi\)
\(272\) −8.00000 8.00000i −0.485071 0.485071i
\(273\) −16.0000 + 16.0000i −0.968364 + 0.968364i
\(274\) −14.0000 −0.845771
\(275\) 4.00000 + 3.00000i 0.241209 + 0.180907i
\(276\) 32.0000 1.92617
\(277\) −8.00000 8.00000i −0.480673 0.480673i 0.424673 0.905347i \(-0.360389\pi\)
−0.905347 + 0.424673i \(0.860389\pi\)
\(278\) −20.0000 + 20.0000i −1.19952 + 1.19952i
\(279\) −40.0000 −2.39474
\(280\) 4.00000 + 8.00000i 0.239046 + 0.478091i
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) −16.0000 + 16.0000i −0.952786 + 0.952786i
\(283\) −21.0000 21.0000i −1.24832 1.24832i −0.956461 0.291859i \(-0.905726\pi\)
−0.291859 0.956461i \(-0.594274\pi\)
\(284\) −24.0000 −1.42414
\(285\) −4.00000 + 12.0000i −0.236940 + 0.710819i
\(286\) −8.00000 −0.473050
\(287\) 6.00000 6.00000i 0.354169 0.354169i
\(288\) 20.0000 + 20.0000i 1.17851 + 1.17851i
\(289\) 9.00000i 0.529412i
\(290\) 2.00000 6.00000i 0.117444 0.352332i
\(291\) 12.0000i 0.703452i
\(292\) −4.00000 4.00000i −0.234082 0.234082i
\(293\) −8.00000 + 8.00000i −0.467365 + 0.467365i −0.901060 0.433695i \(-0.857210\pi\)
0.433695 + 0.901060i \(0.357210\pi\)
\(294\) 20.0000i 1.16642i
\(295\) 8.00000 + 16.0000i 0.465778 + 0.931556i
\(296\) 20.0000i 1.16248i
\(297\) −4.00000 4.00000i −0.232104 0.232104i
\(298\) −18.0000 18.0000i −1.04271 1.04271i
\(299\) 32.0000 1.85061
\(300\) −4.00000 28.0000i −0.230940 1.61658i
\(301\) −2.00000 −0.115278
\(302\) −10.0000 10.0000i −0.575435 0.575435i
\(303\) 28.0000 + 28.0000i 1.60856 + 1.60856i
\(304\) −8.00000 −0.458831
\(305\) 10.0000 + 20.0000i 0.572598 + 1.14520i
\(306\) 20.0000i 1.14332i
\(307\) 15.0000 15.0000i 0.856095 0.856095i −0.134780 0.990876i \(-0.543033\pi\)
0.990876 + 0.134780i \(0.0430329\pi\)
\(308\) 2.00000 2.00000i 0.113961 0.113961i
\(309\) 24.0000i 1.36531i
\(310\) −8.00000 + 24.0000i −0.454369 + 1.36311i
\(311\) 4.00000i 0.226819i −0.993548 0.113410i \(-0.963823\pi\)
0.993548 0.113410i \(-0.0361772\pi\)
\(312\) 32.0000 + 32.0000i 1.81164 + 1.81164i
\(313\) −9.00000 + 9.00000i −0.508710 + 0.508710i −0.914130 0.405420i \(-0.867125\pi\)
0.405420 + 0.914130i \(0.367125\pi\)
\(314\) −6.00000 −0.338600
\(315\) −5.00000 + 15.0000i −0.281718 + 0.845154i
\(316\) 20.0000i 1.12509i
\(317\) −21.0000 21.0000i −1.17948 1.17948i −0.979877 0.199600i \(-0.936036\pi\)
−0.199600 0.979877i \(-0.563964\pi\)
\(318\) 36.0000 36.0000i 2.01878 2.01878i
\(319\) −2.00000 −0.111979
\(320\) 16.0000 8.00000i 0.894427 0.447214i
\(321\) 52.0000 2.90236
\(322\) −8.00000 + 8.00000i −0.445823 + 0.445823i
\(323\) 4.00000 + 4.00000i 0.222566 + 0.222566i
\(324\) 2.00000i 0.111111i
\(325\) −4.00000 28.0000i −0.221880 1.55316i
\(326\) −12.0000 −0.664619
\(327\) −4.00000 + 4.00000i −0.221201 + 0.221201i
\(328\) −12.0000 12.0000i −0.662589 0.662589i
\(329\) 8.00000i 0.441054i
\(330\) −8.00000 + 4.00000i −0.440386 + 0.220193i
\(331\) 8.00000i 0.439720i 0.975531 + 0.219860i \(0.0705600\pi\)
−0.975531 + 0.219860i \(0.929440\pi\)
\(332\) 2.00000 2.00000i 0.109764 0.109764i
\(333\) 25.0000 25.0000i 1.36999 1.36999i
\(334\) 6.00000i 0.328305i
\(335\) 0 0
\(336\) −16.0000 −0.872872
\(337\) 18.0000 + 18.0000i 0.980522 + 0.980522i 0.999814 0.0192914i \(-0.00614103\pi\)
−0.0192914 + 0.999814i \(0.506141\pi\)
\(338\) 19.0000 + 19.0000i 1.03346 + 1.03346i
\(339\) 4.00000 0.217250
\(340\) −12.0000 4.00000i −0.650791 0.216930i
\(341\) 8.00000 0.433224
\(342\) −10.0000 10.0000i −0.540738 0.540738i
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 4.00000i 0.215666i
\(345\) 32.0000 16.0000i 1.72282 0.861411i
\(346\) 4.00000i 0.215041i
\(347\) 5.00000 5.00000i 0.268414 0.268414i −0.560047 0.828461i \(-0.689217\pi\)
0.828461 + 0.560047i \(0.189217\pi\)
\(348\) 8.00000 + 8.00000i 0.428845 + 0.428845i
\(349\) 6.00000i 0.321173i −0.987022 0.160586i \(-0.948662\pi\)
0.987022 0.160586i \(-0.0513385\pi\)
\(350\) 8.00000 + 6.00000i 0.427618 + 0.320713i
\(351\) 32.0000i 1.70803i
\(352\) −4.00000 4.00000i −0.213201 0.213201i
\(353\) 13.0000 13.0000i 0.691920 0.691920i −0.270734 0.962654i \(-0.587266\pi\)
0.962654 + 0.270734i \(0.0872664\pi\)
\(354\) −32.0000 −1.70078
\(355\) −24.0000 + 12.0000i −1.27379 + 0.636894i
\(356\) −12.0000 −0.635999
\(357\) 8.00000 + 8.00000i 0.423405 + 0.423405i
\(358\) 12.0000 12.0000i 0.634220 0.634220i
\(359\) −22.0000 −1.16112 −0.580558 0.814219i \(-0.697165\pi\)
−0.580558 + 0.814219i \(0.697165\pi\)
\(360\) 30.0000 + 10.0000i 1.58114 + 0.527046i
\(361\) −15.0000 −0.789474
\(362\) 16.0000 16.0000i 0.840941 0.840941i
\(363\) 2.00000 + 2.00000i 0.104973 + 0.104973i
\(364\) −16.0000 −0.838628
\(365\) −6.00000 2.00000i −0.314054 0.104685i
\(366\) −40.0000 −2.09083
\(367\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(368\) 16.0000 + 16.0000i 0.834058 + 0.834058i
\(369\) 30.0000i 1.56174i
\(370\) −10.0000 20.0000i −0.519875 1.03975i
\(371\) 18.0000i 0.934513i
\(372\) −32.0000 32.0000i −1.65912 1.65912i
\(373\) −14.0000 + 14.0000i −0.724893 + 0.724893i −0.969598 0.244705i \(-0.921309\pi\)
0.244705 + 0.969598i \(0.421309\pi\)
\(374\) 4.00000i 0.206835i
\(375\) −18.0000 26.0000i −0.929516 1.34263i
\(376\) −16.0000 −0.825137
\(377\) 8.00000 + 8.00000i 0.412021 + 0.412021i
\(378\) −8.00000 8.00000i −0.411476 0.411476i
\(379\) 24.0000 1.23280 0.616399 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) −8.00000 + 4.00000i −0.410391 + 0.205196i
\(381\) −4.00000 −0.204926
\(382\) 4.00000 + 4.00000i 0.204658 + 0.204658i
\(383\) 2.00000 + 2.00000i 0.102195 + 0.102195i 0.756356 0.654161i \(-0.226978\pi\)
−0.654161 + 0.756356i \(0.726978\pi\)
\(384\) 32.0000i 1.63299i
\(385\) 1.00000 3.00000i 0.0509647 0.152894i
\(386\) 20.0000i 1.01797i
\(387\) −5.00000 + 5.00000i −0.254164 + 0.254164i
\(388\) −6.00000 + 6.00000i −0.304604 + 0.304604i
\(389\) 26.0000i 1.31825i −0.752032 0.659126i \(-0.770926\pi\)
0.752032 0.659126i \(-0.229074\pi\)
\(390\) 48.0000 + 16.0000i 2.43057 + 0.810191i
\(391\) 16.0000i 0.809155i
\(392\) −10.0000 + 10.0000i −0.505076 + 0.505076i
\(393\) −12.0000 + 12.0000i −0.605320 + 0.605320i
\(394\) 4.00000 0.201517
\(395\) 10.0000 + 20.0000i 0.503155 + 1.00631i
\(396\) 10.0000i 0.502519i
\(397\) −9.00000 9.00000i −0.451697 0.451697i 0.444220 0.895918i \(-0.353481\pi\)
−0.895918 + 0.444220i \(0.853481\pi\)
\(398\) −4.00000 + 4.00000i −0.200502 + 0.200502i
\(399\) 8.00000 0.400501
\(400\) 12.0000 16.0000i 0.600000 0.800000i
\(401\) 8.00000 0.399501 0.199750 0.979847i \(-0.435987\pi\)
0.199750 + 0.979847i \(0.435987\pi\)
\(402\) 0 0
\(403\) −32.0000 32.0000i −1.59403 1.59403i
\(404\) 28.0000i 1.39305i
\(405\) 1.00000 + 2.00000i 0.0496904 + 0.0993808i
\(406\) −4.00000 −0.198517
\(407\) −5.00000 + 5.00000i −0.247841 + 0.247841i
\(408\) 16.0000 16.0000i 0.792118 0.792118i
\(409\) 6.00000i 0.296681i 0.988936 + 0.148340i \(0.0473931\pi\)
−0.988936 + 0.148340i \(0.952607\pi\)
\(410\) −18.0000 6.00000i −0.888957 0.296319i
\(411\) 28.0000i 1.38114i
\(412\) −12.0000 + 12.0000i −0.591198 + 0.591198i
\(413\) 8.00000 8.00000i 0.393654 0.393654i
\(414\) 40.0000i 1.96589i
\(415\) 1.00000 3.00000i 0.0490881 0.147264i
\(416\) 32.0000i 1.56893i
\(417\) −40.0000 40.0000i −1.95881 1.95881i
\(418\) 2.00000 + 2.00000i 0.0978232 + 0.0978232i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −16.0000 + 8.00000i −0.780720 + 0.390360i
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 22.0000 + 22.0000i 1.07094 + 1.07094i
\(423\) −20.0000 20.0000i −0.972433 0.972433i
\(424\) 36.0000 1.74831
\(425\) −14.0000 + 2.00000i −0.679100 + 0.0970143i
\(426\) 48.0000i 2.32561i
\(427\) 10.0000 10.0000i 0.483934 0.483934i
\(428\) 26.0000 + 26.0000i 1.25676 + 1.25676i
\(429\) 16.0000i 0.772487i
\(430\) 2.00000 + 4.00000i 0.0964486 + 0.192897i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −16.0000 + 16.0000i −0.769800 + 0.769800i
\(433\) −21.0000 + 21.0000i −1.00920 + 1.00920i −0.00923827 + 0.999957i \(0.502941\pi\)
−0.999957 + 0.00923827i \(0.997059\pi\)
\(434\) 16.0000 0.768025
\(435\) 12.0000 + 4.00000i 0.575356 + 0.191785i
\(436\) −4.00000 −0.191565
\(437\) −8.00000 8.00000i −0.382692 0.382692i
\(438\) 8.00000 8.00000i 0.382255 0.382255i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) −6.00000 2.00000i −0.286039 0.0953463i
\(441\) −25.0000 −1.19048
\(442\) 16.0000 16.0000i 0.761042 0.761042i
\(443\) −10.0000 10.0000i −0.475114 0.475114i 0.428451 0.903565i \(-0.359060\pi\)
−0.903565 + 0.428451i \(0.859060\pi\)
\(444\) 40.0000 1.89832
\(445\) −12.0000 + 6.00000i −0.568855 + 0.284427i
\(446\) 0 0
\(447\) 36.0000 36.0000i 1.70274 1.70274i
\(448\) −8.00000 8.00000i −0.377964 0.377964i
\(449\) 12.0000i 0.566315i −0.959073 0.283158i \(-0.908618\pi\)
0.959073 0.283158i \(-0.0913819\pi\)
\(450\) 35.0000 5.00000i 1.64992 0.235702i
\(451\) 6.00000i 0.282529i
\(452\) 2.00000 + 2.00000i 0.0940721 + 0.0940721i
\(453\) 20.0000 20.0000i 0.939682 0.939682i
\(454\) 10.0000i 0.469323i
\(455\) −16.0000 + 8.00000i −0.750092 + 0.375046i
\(456\) 16.0000i 0.749269i
\(457\) 16.0000 + 16.0000i 0.748448 + 0.748448i 0.974188 0.225739i \(-0.0724798\pi\)
−0.225739 + 0.974188i \(0.572480\pi\)
\(458\) −4.00000 4.00000i −0.186908 0.186908i
\(459\) 16.0000 0.746816
\(460\) 24.0000 + 8.00000i 1.11901 + 0.373002i
\(461\) 10.0000 0.465746 0.232873 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 4.00000 + 4.00000i 0.186097 + 0.186097i
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) 8.00000i 0.371391i
\(465\) −48.0000 16.0000i −2.22595 0.741982i
\(466\) 40.0000i 1.85296i
\(467\) 12.0000 12.0000i 0.555294 0.555294i −0.372670 0.927964i \(-0.621558\pi\)
0.927964 + 0.372670i \(0.121558\pi\)
\(468\) −40.0000 + 40.0000i −1.84900 + 1.84900i
\(469\) 0 0
\(470\) −16.0000 + 8.00000i −0.738025 + 0.369012i
\(471\) 12.0000i 0.552931i
\(472\) −16.0000 16.0000i −0.736460 0.736460i
\(473\) 1.00000 1.00000i 0.0459800 0.0459800i
\(474\) −40.0000 −1.83726
\(475\) −6.00000 + 8.00000i −0.275299 + 0.367065i
\(476\) 8.00000i 0.366679i
\(477\) 45.0000 + 45.0000i 2.06041 + 2.06041i
\(478\) −22.0000 + 22.0000i −1.00626 + 1.00626i
\(479\) 18.0000 0.822441 0.411220 0.911536i \(-0.365103\pi\)
0.411220 + 0.911536i \(0.365103\pi\)
\(480\) 16.0000 + 32.0000i 0.730297 + 1.46059i
\(481\) 40.0000 1.82384
\(482\) −10.0000 + 10.0000i −0.455488 + 0.455488i
\(483\) −16.0000 16.0000i −0.728025 0.728025i
\(484\) 2.00000i 0.0909091i
\(485\) −3.00000 + 9.00000i −0.136223 + 0.408669i
\(486\) 20.0000 0.907218
\(487\) 16.0000 16.0000i 0.725029 0.725029i −0.244596 0.969625i \(-0.578655\pi\)
0.969625 + 0.244596i \(0.0786553\pi\)
\(488\) −20.0000 20.0000i −0.905357 0.905357i
\(489\) 24.0000i 1.08532i
\(490\) −5.00000 + 15.0000i −0.225877 + 0.677631i
\(491\) 12.0000i 0.541552i 0.962642 + 0.270776i \(0.0872803\pi\)
−0.962642 + 0.270776i \(0.912720\pi\)
\(492\) 24.0000 24.0000i 1.08200 1.08200i
\(493\) 4.00000 4.00000i 0.180151 0.180151i
\(494\) 16.0000i 0.719874i
\(495\) −5.00000 10.0000i −0.224733 0.449467i
\(496\) 32.0000i 1.43684i
\(497\) 12.0000 + 12.0000i 0.538274 + 0.538274i
\(498\) 4.00000 + 4.00000i 0.179244 + 0.179244i
\(499\) 8.00000 0.358129 0.179065 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) 4.00000 22.0000i 0.178885 0.983870i
\(501\) −12.0000 −0.536120
\(502\) 0 0
\(503\) 19.0000 + 19.0000i 0.847168 + 0.847168i 0.989779 0.142611i \(-0.0455497\pi\)
−0.142611 + 0.989779i \(0.545550\pi\)
\(504\) 20.0000i 0.890871i
\(505\) 14.0000 + 28.0000i 0.622992 + 1.24598i
\(506\) 8.00000i 0.355643i
\(507\) −38.0000 + 38.0000i −1.68764 + 1.68764i
\(508\) −2.00000 2.00000i −0.0887357 0.0887357i
\(509\) 28.0000i 1.24108i −0.784176 0.620539i \(-0.786914\pi\)
0.784176 0.620539i \(-0.213086\pi\)
\(510\) 8.00000 24.0000i 0.354246 1.06274i
\(511\) 4.00000i 0.176950i
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 8.00000 8.00000i 0.353209 0.353209i
\(514\) −2.00000 −0.0882162
\(515\) −6.00000 + 18.0000i −0.264392 + 0.793175i
\(516\) −8.00000 −0.352180
\(517\) 4.00000 + 4.00000i 0.175920 + 0.175920i
\(518\) −10.0000 + 10.0000i −0.439375 + 0.439375i
\(519\) 8.00000 0.351161
\(520\) 16.0000 + 32.0000i 0.701646 + 1.40329i
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) −10.0000 + 10.0000i −0.437688 + 0.437688i
\(523\) −3.00000 3.00000i −0.131181 0.131181i 0.638468 0.769649i \(-0.279569\pi\)
−0.769649 + 0.638468i \(0.779569\pi\)
\(524\) −12.0000 −0.524222
\(525\) −12.0000 + 16.0000i −0.523723 + 0.698297i
\(526\) 10.0000 0.436021
\(527\) −16.0000 + 16.0000i −0.696971 + 0.696971i
\(528\) 8.00000 8.00000i 0.348155 0.348155i
\(529\) 9.00000i 0.391304i
\(530\) 36.0000 18.0000i 1.56374 0.781870i
\(531\) 40.0000i 1.73585i
\(532\) 4.00000 + 4.00000i 0.173422 + 0.173422i
\(533\) 24.0000 24.0000i 1.03956 1.03956i
\(534\) 24.0000i 1.03858i
\(535\) 39.0000 + 13.0000i 1.68612 + 0.562039i
\(536\) 0 0
\(537\) 24.0000 + 24.0000i 1.03568 + 1.03568i
\(538\) −26.0000 26.0000i −1.12094 1.12094i
\(539\) 5.00000 0.215365
\(540\) −8.00000 + 24.0000i −0.344265 + 1.03280i
\(541\) 6.00000 0.257960 0.128980 0.991647i \(-0.458830\pi\)
0.128980 + 0.991647i \(0.458830\pi\)
\(542\) −14.0000 14.0000i −0.601351 0.601351i
\(543\) 32.0000 + 32.0000i 1.37325 + 1.37325i
\(544\) 16.0000 0.685994
\(545\) −4.00000 + 2.00000i −0.171341 + 0.0856706i
\(546\) 32.0000i 1.36947i
\(547\) −31.0000 + 31.0000i −1.32546 + 1.32546i −0.416184 + 0.909281i \(0.636633\pi\)
−0.909281 + 0.416184i \(0.863367\pi\)
\(548\) 14.0000 14.0000i 0.598050 0.598050i
\(549\) 50.0000i 2.13395i
\(550\) −7.00000 + 1.00000i −0.298481 + 0.0426401i
\(551\) 4.00000i 0.170406i
\(552\) −32.0000 + 32.0000i −1.36201 + 1.36201i
\(553\) 10.0000 10.0000i 0.425243 0.425243i
\(554\) 16.0000 0.679775
\(555\) 40.0000 20.0000i 1.69791 0.848953i
\(556\) 40.0000i 1.69638i
\(557\) 10.0000 + 10.0000i 0.423714 + 0.423714i 0.886480 0.462767i \(-0.153143\pi\)
−0.462767 + 0.886480i \(0.653143\pi\)
\(558\) 40.0000 40.0000i 1.69334 1.69334i
\(559\) −8.00000 −0.338364
\(560\) −12.0000 4.00000i −0.507093 0.169031i
\(561\) −8.00000 −0.337760
\(562\) 10.0000 10.0000i 0.421825 0.421825i
\(563\) 9.00000 + 9.00000i 0.379305 + 0.379305i 0.870851 0.491547i \(-0.163568\pi\)
−0.491547 + 0.870851i \(0.663568\pi\)
\(564\) 32.0000i 1.34744i
\(565\) 3.00000 + 1.00000i 0.126211 + 0.0420703i
\(566\) 42.0000 1.76539
\(567\) 1.00000 1.00000i 0.0419961 0.0419961i
\(568\) 24.0000 24.0000i 1.00702 1.00702i
\(569\) 10.0000i 0.419222i −0.977785 0.209611i \(-0.932780\pi\)
0.977785 0.209611i \(-0.0672197\pi\)
\(570\) −8.00000 16.0000i −0.335083 0.670166i
\(571\) 4.00000i 0.167395i 0.996491 + 0.0836974i \(0.0266729\pi\)
−0.996491 + 0.0836974i \(0.973327\pi\)
\(572\) 8.00000 8.00000i 0.334497 0.334497i
\(573\) −8.00000 + 8.00000i −0.334205 + 0.334205i
\(574\) 12.0000i 0.500870i
\(575\) 28.0000 4.00000i 1.16768 0.166812i
\(576\) −40.0000 −1.66667
\(577\) 13.0000 + 13.0000i 0.541197 + 0.541197i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(578\) 9.00000 + 9.00000i 0.374351 + 0.374351i
\(579\) −40.0000 −1.66234
\(580\) 4.00000 + 8.00000i 0.166091 + 0.332182i
\(581\) −2.00000 −0.0829740
\(582\) −12.0000 12.0000i −0.497416 0.497416i
\(583\) −9.00000 9.00000i −0.372742 0.372742i
\(584\) 8.00000 0.331042
\(585\) −20.0000 + 60.0000i −0.826898 + 2.48069i
\(586\) 16.0000i 0.660954i
\(587\) −24.0000 + 24.0000i −0.990586 + 0.990586i −0.999956 0.00937009i \(-0.997017\pi\)
0.00937009 + 0.999956i \(0.497017\pi\)
\(588\) −20.0000 20.0000i −0.824786 0.824786i
\(589\) 16.0000i 0.659269i
\(590\) −24.0000 8.00000i −0.988064 0.329355i
\(591\) 8.00000i 0.329076i
\(592\) 20.0000 + 20.0000i 0.821995 + 0.821995i
\(593\) −22.0000 + 22.0000i −0.903432 + 0.903432i −0.995731 0.0922996i \(-0.970578\pi\)
0.0922996 + 0.995731i \(0.470578\pi\)
\(594\) 8.00000 0.328244
\(595\) 4.00000 + 8.00000i 0.163984 + 0.327968i
\(596\) 36.0000 1.47462
\(597\) −8.00000 8.00000i −0.327418 0.327418i
\(598\) −32.0000 + 32.0000i −1.30858 + 1.30858i
\(599\) −20.0000 −0.817178 −0.408589 0.912719i \(-0.633979\pi\)
−0.408589 + 0.912719i \(0.633979\pi\)
\(600\) 32.0000 + 24.0000i 1.30639 + 0.979796i
\(601\) 34.0000 1.38689 0.693444 0.720510i \(-0.256092\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(602\) 2.00000 2.00000i 0.0815139 0.0815139i
\(603\) 0 0
\(604\) 20.0000 0.813788
\(605\) 1.00000 + 2.00000i 0.0406558 + 0.0813116i
\(606\) −56.0000 −2.27484
\(607\) −15.0000 + 15.0000i −0.608831 + 0.608831i −0.942641 0.333809i \(-0.891666\pi\)
0.333809 + 0.942641i \(0.391666\pi\)
\(608\) 8.00000 8.00000i 0.324443 0.324443i
\(609\) 8.00000i 0.324176i
\(610\) −30.0000 10.0000i −1.21466 0.404888i
\(611\) 32.0000i 1.29458i
\(612\) 20.0000 + 20.0000i 0.808452 + 0.808452i
\(613\) −2.00000 + 2.00000i −0.0807792 + 0.0807792i −0.746342 0.665563i \(-0.768192\pi\)
0.665563 + 0.746342i \(0.268192\pi\)
\(614\) 30.0000i 1.21070i
\(615\) 12.0000 36.0000i 0.483887 1.45166i
\(616\) 4.00000i 0.161165i
\(617\) 11.0000 + 11.0000i 0.442843 + 0.442843i 0.892966 0.450123i \(-0.148620\pi\)
−0.450123 + 0.892966i \(0.648620\pi\)
\(618\) −24.0000 24.0000i −0.965422 0.965422i
\(619\) −36.0000 −1.44696 −0.723481 0.690344i \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(620\) −16.0000 32.0000i −0.642575 1.28515i
\(621\) −32.0000 −1.28412
\(622\) 4.00000 + 4.00000i 0.160385 + 0.160385i
\(623\) 6.00000 + 6.00000i 0.240385 + 0.240385i
\(624\) −64.0000 −2.56205
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 18.0000i 0.719425i
\(627\) −4.00000 + 4.00000i −0.159745 + 0.159745i
\(628\) 6.00000 6.00000i 0.239426 0.239426i
\(629\) 20.0000i 0.797452i
\(630\) −10.0000 20.0000i −0.398410 0.796819i
\(631\) 28.0000i 1.11466i −0.830290 0.557331i \(-0.811825\pi\)
0.830290 0.557331i \(-0.188175\pi\)
\(632\) −20.0000 20.0000i −0.795557 0.795557i
\(633\) −44.0000 + 44.0000i −1.74884 + 1.74884i
\(634\) 42.0000 1.66803
\(635\) −3.00000 1.00000i −0.119051 0.0396838i
\(636\) 72.0000i 2.85499i
\(637\) −20.0000 20.0000i −0.792429 0.792429i
\(638\) 2.00000 2.00000i 0.0791808 0.0791808i
\(639\) 60.0000 2.37356
\(640\) −8.00000 + 24.0000i −0.316228 + 0.948683i
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −52.0000 + 52.0000i −2.05228 + 2.05228i
\(643\) 10.0000 + 10.0000i 0.394362 + 0.394362i 0.876239 0.481877i \(-0.160045\pi\)
−0.481877 + 0.876239i \(0.660045\pi\)
\(644\) 16.0000i 0.630488i
\(645\) −8.00000 + 4.00000i −0.315000 + 0.157500i
\(646\) −8.00000 −0.314756
\(647\) −30.0000 + 30.0000i −1.17942 + 1.17942i −0.199530 + 0.979892i \(0.563942\pi\)
−0.979892 + 0.199530i \(0.936058\pi\)
\(648\) −2.00000 2.00000i −0.0785674 0.0785674i
\(649\) 8.00000i 0.314027i
\(650\) 32.0000 + 24.0000i 1.25514 + 0.941357i
\(651\) 32.0000i 1.25418i
\(652\) 12.0000 12.0000i 0.469956 0.469956i
\(653\) −19.0000 + 19.0000i −0.743527 + 0.743527i −0.973255 0.229728i \(-0.926216\pi\)
0.229728 + 0.973255i \(0.426216\pi\)
\(654\) 8.00000i 0.312825i
\(655\) −12.0000 + 6.00000i −0.468879 + 0.234439i
\(656\) 24.0000 0.937043
\(657\) 10.0000 + 10.0000i 0.390137 + 0.390137i
\(658\) 8.00000 + 8.00000i 0.311872 + 0.311872i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 4.00000 12.0000i 0.155700 0.467099i
\(661\) 40.0000 1.55582 0.777910 0.628376i \(-0.216280\pi\)
0.777910 + 0.628376i \(0.216280\pi\)
\(662\) −8.00000 8.00000i −0.310929 0.310929i
\(663\) 32.0000 + 32.0000i 1.24278 + 1.24278i
\(664\) 4.00000i 0.155230i
\(665\) 6.00000 + 2.00000i 0.232670 + 0.0775567i
\(666\) 50.0000i 1.93746i
\(667\) −8.00000 + 8.00000i −0.309761 + 0.309761i
\(668\) −6.00000 6.00000i −0.232147 0.232147i
\(669\) 0 0
\(670\) 0 0
\(671\) 10.0000i 0.386046i
\(672\) 16.0000 16.0000i 0.617213 0.617213i
\(673\) −30.0000 + 30.0000i −1.15642 + 1.15642i −0.171174 + 0.985241i \(0.554756\pi\)
−0.985241 + 0.171174i \(0.945244\pi\)
\(674\) −36.0000 −1.38667
\(675\) 4.00000 + 28.0000i 0.153960 + 1.07772i
\(676\) −38.0000 −1.46154
\(677\) 16.0000 + 16.0000i 0.614930 + 0.614930i 0.944227 0.329297i \(-0.106812\pi\)
−0.329297 + 0.944227i \(0.606812\pi\)
\(678\) −4.00000 + 4.00000i −0.153619 + 0.153619i
\(679\) 6.00000 0.230259
\(680\) 16.0000 8.00000i 0.613572 0.306786i
\(681\) 20.0000 0.766402
\(682\) −8.00000 + 8.00000i −0.306336 + 0.306336i
\(683\) 4.00000 + 4.00000i 0.153056 + 0.153056i 0.779481 0.626426i \(-0.215483\pi\)
−0.626426 + 0.779481i \(0.715483\pi\)
\(684\) 20.0000 0.764719
\(685\) 7.00000 21.0000i 0.267456 0.802369i
\(686\) 24.0000 0.916324
\(687\) 8.00000 8.00000i 0.305219 0.305219i
\(688\) −4.00000 4.00000i −0.152499 0.152499i
\(689\) 72.0000i 2.74298i
\(690\) −16.0000 + 48.0000i −0.609110 + 1.82733i
\(691\) 8.00000i 0.304334i −0.988355 0.152167i \(-0.951375\pi\)
0.988355 0.152167i \(-0.0486252\pi\)
\(692\) 4.00000 + 4.00000i 0.152057 + 0.152057i
\(693\) −5.00000 + 5.00000i −0.189934 + 0.189934i
\(694\) 10.0000i 0.379595i
\(695\) −20.0000 40.0000i −0.758643 1.51729i
\(696\) −16.0000 −0.606478
\(697\) −12.0000 12.0000i −0.454532 0.454532i
\(698\) 6.00000 + 6.00000i 0.227103 + 0.227103i
\(699\) −80.0000 −3.02588
\(700\) −14.0000 + 2.00000i −0.529150 + 0.0755929i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −32.0000 32.0000i −1.20776 1.20776i
\(703\) −10.0000 10.0000i −0.377157 0.377157i
\(704\) 8.00000 0.301511
\(705\) −16.0000 32.0000i −0.602595 1.20519i
\(706\) 26.0000i 0.978523i
\(707\) 14.0000 14.0000i 0.526524 0.526524i
\(708\) 32.0000 32.0000i 1.20263 1.20263i
\(709\) 38.0000i 1.42712i 0.700594 + 0.713560i \(0.252918\pi\)
−0.700594 + 0.713560i \(0.747082\pi\)
\(710\) 12.0000 36.0000i 0.450352 1.35106i
\(711\) 50.0000i 1.87515i
\(712\) 12.0000 12.0000i 0.449719 0.449719i
\(713\) 32.0000 32.0000i 1.19841 1.19841i
\(714\) −16.0000 −0.598785
\(715\) 4.00000 12.0000i 0.149592 0.448775i
\(716\) 24.0000i 0.896922i
\(717\) −44.0000 44.0000i −1.64321 1.64321i
\(718\) 22.0000 22.0000i 0.821033 0.821033i
\(719\) −20.0000 −0.745874 −0.372937 0.927857i \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) −40.0000 + 20.0000i −1.49071 + 0.745356i
\(721\) 12.0000 0.446903
\(722\) 15.0000 15.0000i 0.558242 0.558242i
\(723\) −20.0000 20.0000i −0.743808 0.743808i
\(724\) 32.0000i 1.18927i
\(725\) 8.00000 + 6.00000i 0.297113 + 0.222834i
\(726\) −4.00000 −0.148454
\(727\) 2.00000 2.00000i 0.0741759 0.0741759i −0.669046 0.743221i \(-0.733297\pi\)
0.743221 + 0.669046i \(0.233297\pi\)
\(728\) 16.0000 16.0000i 0.592999 0.592999i
\(729\) 43.0000i 1.59259i
\(730\) 8.00000 4.00000i 0.296093 0.148047i
\(731\) 4.00000i 0.147945i
\(732\) 40.0000 40.0000i 1.47844 1.47844i
\(733\) 6.00000 6.00000i 0.221615 0.221615i −0.587563 0.809178i \(-0.699913\pi\)
0.809178 + 0.587563i \(0.199913\pi\)
\(734\) 0 0
\(735\) −30.0000 10.0000i −1.10657 0.368856i
\(736\) −32.0000 −1.17954
\(737\) 0 0
\(738\) 30.0000 + 30.0000i 1.10432 + 1.10432i
\(739\) 36.0000 1.32428 0.662141 0.749380i \(-0.269648\pi\)
0.662141 + 0.749380i \(0.269648\pi\)
\(740\) 30.0000 + 10.0000i 1.10282 + 0.367607i
\(741\) 32.0000 1.17555
\(742\) −18.0000 18.0000i −0.660801 0.660801i
\(743\) −19.0000 19.0000i −0.697042 0.697042i 0.266729 0.963772i \(-0.414057\pi\)
−0.963772 + 0.266729i \(0.914057\pi\)
\(744\) 64.0000 2.34635
\(745\) 36.0000 18.0000i 1.31894 0.659469i
\(746\) 28.0000i 1.02515i
\(747\) −5.00000 + 5.00000i −0.182940 + 0.182940i
\(748\) −4.00000 4.00000i −0.146254 0.146254i
\(749\) 26.0000i 0.950019i
\(750\) 44.0000 + 8.00000i 1.60665 + 0.292119i
\(751\) 32.0000i 1.16770i 0.811863 + 0.583848i \(0.198454\pi\)
−0.811863 + 0.583848i \(0.801546\pi\)
\(752\) 16.0000 16.0000i 0.583460 0.583460i
\(753\) 0 0
\(754\) −16.0000 −0.582686
\(755\) 20.0000 10.0000i 0.727875 0.363937i
\(756\) 16.0000 0.581914
\(757\) −15.0000 15.0000i −0.545184 0.545184i 0.379860 0.925044i \(-0.375972\pi\)
−0.925044 + 0.379860i \(0.875972\pi\)
\(758\) −24.0000 + 24.0000i −0.871719 + 0.871719i
\(759\) 16.0000 0.580763
\(760\) 4.00000 12.0000i 0.145095 0.435286i
\(761\) −22.0000 −0.797499 −0.398750 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 4.00000 4.00000i 0.144905 0.144905i
\(763\) 2.00000 + 2.00000i 0.0724049 + 0.0724049i
\(764\) −8.00000 −0.289430
\(765\) 30.0000 + 10.0000i 1.08465 + 0.361551i
\(766\) −4.00000 −0.144526
\(767\) 32.0000 32.0000i 1.15545 1.15545i
\(768\) −32.0000 32.0000i −1.15470 1.15470i
\(769\) 10.0000i 0.360609i 0.983611 + 0.180305i \(0.0577084\pi\)
−0.983611 + 0.180305i \(0.942292\pi\)
\(770\) 2.00000 + 4.00000i 0.0720750 + 0.144150i
\(771\) 4.00000i 0.144056i
\(772\) −20.0000 20.0000i −0.719816 0.719816i