Properties

Label 675.2.l.a.601.1
Level $675$
Weight $2$
Character 675.601
Analytic conductor $5.390$
Analytic rank $1$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(76,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\), degree \(6\), 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: \(5.38990213644\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 601.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 675.601
Dual form 675.2.l.a.301.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.826352 + 0.300767i) q^{2} +(0.592396 - 1.62760i) q^{3} +(-0.939693 + 0.788496i) q^{4} +1.52314i q^{6} +(-2.87939 - 2.41609i) q^{7} +(1.41875 - 2.45734i) q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\) \(q+(-0.826352 + 0.300767i) q^{2} +(0.592396 - 1.62760i) q^{3} +(-0.939693 + 0.788496i) q^{4} +1.52314i q^{6} +(-2.87939 - 2.41609i) q^{7} +(1.41875 - 2.45734i) q^{8} +(-2.29813 - 1.92836i) q^{9} +(-0.180922 + 1.02606i) q^{11} +(0.726682 + 1.99654i) q^{12} +(2.99273 + 1.08926i) q^{13} +(3.10607 + 1.13052i) q^{14} +(-0.00727396 + 0.0412527i) q^{16} +(-0.233956 - 0.405223i) q^{17} +(2.47906 + 0.902302i) q^{18} +(-2.34730 + 4.06564i) q^{19} +(-5.63816 + 3.25519i) q^{21} +(-0.159100 - 0.902302i) q^{22} +(-4.11334 + 3.45150i) q^{23} +(-3.15910 - 3.76487i) q^{24} -2.80066 q^{26} +(-4.50000 + 2.59808i) q^{27} +4.61081 q^{28} +(-5.45084 + 1.98394i) q^{29} +(-3.14543 + 2.63933i) q^{31} +(0.979055 + 5.55250i) q^{32} +(1.56283 + 0.902302i) q^{33} +(0.315207 + 0.264490i) q^{34} +3.68004 q^{36} +(2.23783 + 3.87603i) q^{37} +(0.716881 - 4.06564i) q^{38} +(3.54576 - 4.22567i) q^{39} +(-7.52481 - 2.73881i) q^{41} +(3.68004 - 4.38571i) q^{42} +(2.11334 - 11.9854i) q^{43} +(-0.639033 - 1.10684i) q^{44} +(2.36097 - 4.08931i) q^{46} +(-2.65657 - 2.22913i) q^{47} +(0.0628336 + 0.0362770i) q^{48} +(1.23783 + 7.02006i) q^{49} +(-0.798133 + 0.140732i) q^{51} +(-3.67112 + 1.33618i) q^{52} -8.83750 q^{53} +(2.93717 - 3.50038i) q^{54} +(-10.0223 + 3.64781i) q^{56} +(5.22668 + 6.22892i) q^{57} +(3.90760 - 3.27887i) q^{58} +(2.36959 + 13.4386i) q^{59} +(7.46064 + 6.26022i) q^{61} +(1.80541 - 3.12706i) q^{62} +(1.95811 + 11.1050i) q^{63} +(-2.52094 - 4.36640i) q^{64} +(-1.56283 - 0.275570i) q^{66} +(-1.71301 - 0.623485i) q^{67} +(0.539363 + 0.196312i) q^{68} +(3.18092 + 8.73951i) q^{69} +(-3.85117 - 6.67042i) q^{71} +(-7.99912 + 2.91144i) q^{72} +(0.407604 - 0.705990i) q^{73} +(-3.01501 - 2.52990i) q^{74} +(-1.00000 - 5.67128i) q^{76} +(3.00000 - 2.51730i) q^{77} +(-1.65910 + 4.55834i) q^{78} +(3.81180 - 1.38738i) q^{79} +(1.56283 + 8.86327i) q^{81} +7.04189 q^{82} +(-15.9820 + 5.81699i) q^{83} +(2.73143 - 7.50454i) q^{84} +(1.85844 + 10.5397i) q^{86} +10.0470i q^{87} +(2.26470 + 1.90031i) q^{88} +(5.19846 - 9.00400i) q^{89} +(-5.98545 - 10.3671i) q^{91} +(1.14378 - 6.48670i) q^{92} +(2.43242 + 6.68302i) q^{93} +(2.86571 + 1.04303i) q^{94} +(9.61721 + 1.69577i) q^{96} +(1.06283 - 6.02763i) q^{97} +(-3.13429 - 5.42874i) q^{98} +(2.39440 - 2.00914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8} - 18 q^{11} - 9 q^{12} - 6 q^{14} - 18 q^{16} - 6 q^{17} + 18 q^{18} - 12 q^{19} + 36 q^{22} - 18 q^{23} + 18 q^{24} + 12 q^{26} - 27 q^{27} + 36 q^{28} - 21 q^{29} - 3 q^{31} + 9 q^{32} + 9 q^{34} - 18 q^{36} - 6 q^{37} - 12 q^{38} - 9 q^{39} - 18 q^{41} - 18 q^{42} + 6 q^{43} - 27 q^{44} - 9 q^{46} + 6 q^{47} - 9 q^{48} - 12 q^{49} + 9 q^{51} - 36 q^{52} - 48 q^{53} + 27 q^{54} - 48 q^{56} + 18 q^{57} + 27 q^{58} + 36 q^{61} + 15 q^{62} + 18 q^{63} - 12 q^{64} - 18 q^{67} + 12 q^{68} + 36 q^{69} + 3 q^{71} + 9 q^{72} + 6 q^{73} + 12 q^{74} - 6 q^{76} + 18 q^{77} + 27 q^{78} - 12 q^{79} + 36 q^{82} - 18 q^{83} + 36 q^{84} + 3 q^{86} + 18 q^{88} + 3 q^{89} + 63 q^{92} - 9 q^{93} + 27 q^{94} + 27 q^{96} - 3 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.826352 + 0.300767i −0.584319 + 0.212675i −0.617229 0.786784i \(-0.711745\pi\)
0.0329100 + 0.999458i \(0.489523\pi\)
\(3\) 0.592396 1.62760i 0.342020 0.939693i
\(4\) −0.939693 + 0.788496i −0.469846 + 0.394248i
\(5\) 0 0
\(6\) 1.52314i 0.621819i
\(7\) −2.87939 2.41609i −1.08831 0.913197i −0.0917216 0.995785i \(-0.529237\pi\)
−0.996584 + 0.0825881i \(0.973681\pi\)
\(8\) 1.41875 2.45734i 0.501603 0.868802i
\(9\) −2.29813 1.92836i −0.766044 0.642788i
\(10\) 0 0
\(11\) −0.180922 + 1.02606i −0.0545501 + 0.309369i −0.999859 0.0168083i \(-0.994649\pi\)
0.945309 + 0.326177i \(0.105761\pi\)
\(12\) 0.726682 + 1.99654i 0.209775 + 0.576352i
\(13\) 2.99273 + 1.08926i 0.830033 + 0.302107i 0.721872 0.692026i \(-0.243282\pi\)
0.108160 + 0.994133i \(0.465504\pi\)
\(14\) 3.10607 + 1.13052i 0.830131 + 0.302143i
\(15\) 0 0
\(16\) −0.00727396 + 0.0412527i −0.00181849 + 0.0103132i
\(17\) −0.233956 0.405223i −0.0567426 0.0982810i 0.836259 0.548335i \(-0.184738\pi\)
−0.893001 + 0.450054i \(0.851405\pi\)
\(18\) 2.47906 + 0.902302i 0.584319 + 0.212675i
\(19\) −2.34730 + 4.06564i −0.538507 + 0.932721i 0.460478 + 0.887671i \(0.347678\pi\)
−0.998985 + 0.0450499i \(0.985655\pi\)
\(20\) 0 0
\(21\) −5.63816 + 3.25519i −1.23035 + 0.710341i
\(22\) −0.159100 0.902302i −0.0339203 0.192372i
\(23\) −4.11334 + 3.45150i −0.857691 + 0.719688i −0.961469 0.274912i \(-0.911351\pi\)
0.103778 + 0.994600i \(0.466907\pi\)
\(24\) −3.15910 3.76487i −0.644849 0.768501i
\(25\) 0 0
\(26\) −2.80066 −0.549255
\(27\) −4.50000 + 2.59808i −0.866025 + 0.500000i
\(28\) 4.61081 0.871362
\(29\) −5.45084 + 1.98394i −1.01220 + 0.368409i −0.794275 0.607558i \(-0.792149\pi\)
−0.217920 + 0.975967i \(0.569927\pi\)
\(30\) 0 0
\(31\) −3.14543 + 2.63933i −0.564936 + 0.474037i −0.879961 0.475046i \(-0.842431\pi\)
0.315025 + 0.949083i \(0.397987\pi\)
\(32\) 0.979055 + 5.55250i 0.173074 + 0.981553i
\(33\) 1.56283 + 0.902302i 0.272054 + 0.157071i
\(34\) 0.315207 + 0.264490i 0.0540576 + 0.0453597i
\(35\) 0 0
\(36\) 3.68004 0.613341
\(37\) 2.23783 + 3.87603i 0.367896 + 0.637215i 0.989236 0.146326i \(-0.0467448\pi\)
−0.621340 + 0.783541i \(0.713411\pi\)
\(38\) 0.716881 4.06564i 0.116294 0.659533i
\(39\) 3.54576 4.22567i 0.567776 0.676649i
\(40\) 0 0
\(41\) −7.52481 2.73881i −1.17518 0.427730i −0.320682 0.947187i \(-0.603912\pi\)
−0.854497 + 0.519457i \(0.826134\pi\)
\(42\) 3.68004 4.38571i 0.567843 0.676729i
\(43\) 2.11334 11.9854i 0.322281 1.82775i −0.205847 0.978584i \(-0.565995\pi\)
0.528128 0.849165i \(-0.322894\pi\)
\(44\) −0.639033 1.10684i −0.0963379 0.166862i
\(45\) 0 0
\(46\) 2.36097 4.08931i 0.348106 0.602937i
\(47\) −2.65657 2.22913i −0.387501 0.325152i 0.428138 0.903714i \(-0.359170\pi\)
−0.815639 + 0.578561i \(0.803614\pi\)
\(48\) 0.0628336 + 0.0362770i 0.00906925 + 0.00523613i
\(49\) 1.23783 + 7.02006i 0.176832 + 1.00287i
\(50\) 0 0
\(51\) −0.798133 + 0.140732i −0.111761 + 0.0197065i
\(52\) −3.67112 + 1.33618i −0.509093 + 0.185295i
\(53\) −8.83750 −1.21392 −0.606962 0.794731i \(-0.707612\pi\)
−0.606962 + 0.794731i \(0.707612\pi\)
\(54\) 2.93717 3.50038i 0.399698 0.476341i
\(55\) 0 0
\(56\) −10.0223 + 3.64781i −1.33928 + 0.487460i
\(57\) 5.22668 + 6.22892i 0.692291 + 0.825040i
\(58\) 3.90760 3.27887i 0.513094 0.430537i
\(59\) 2.36959 + 13.4386i 0.308494 + 1.74955i 0.606586 + 0.795018i \(0.292538\pi\)
−0.298093 + 0.954537i \(0.596350\pi\)
\(60\) 0 0
\(61\) 7.46064 + 6.26022i 0.955237 + 0.801539i 0.980172 0.198150i \(-0.0634934\pi\)
−0.0249349 + 0.999689i \(0.507938\pi\)
\(62\) 1.80541 3.12706i 0.229287 0.397137i
\(63\) 1.95811 + 11.1050i 0.246699 + 1.39910i
\(64\) −2.52094 4.36640i −0.315118 0.545801i
\(65\) 0 0
\(66\) −1.56283 0.275570i −0.192372 0.0339203i
\(67\) −1.71301 0.623485i −0.209278 0.0761708i 0.235254 0.971934i \(-0.424408\pi\)
−0.444532 + 0.895763i \(0.646630\pi\)
\(68\) 0.539363 + 0.196312i 0.0654074 + 0.0238063i
\(69\) 3.18092 + 8.73951i 0.382938 + 1.05211i
\(70\) 0 0
\(71\) −3.85117 6.67042i −0.457049 0.791633i 0.541754 0.840537i \(-0.317760\pi\)
−0.998803 + 0.0489043i \(0.984427\pi\)
\(72\) −7.99912 + 2.91144i −0.942706 + 0.343117i
\(73\) 0.407604 0.705990i 0.0477064 0.0826299i −0.841186 0.540746i \(-0.818142\pi\)
0.888893 + 0.458116i \(0.151475\pi\)
\(74\) −3.01501 2.52990i −0.350488 0.294095i
\(75\) 0 0
\(76\) −1.00000 5.67128i −0.114708 0.650541i
\(77\) 3.00000 2.51730i 0.341882 0.286873i
\(78\) −1.65910 + 4.55834i −0.187856 + 0.516130i
\(79\) 3.81180 1.38738i 0.428861 0.156093i −0.118566 0.992946i \(-0.537830\pi\)
0.547427 + 0.836853i \(0.315607\pi\)
\(80\) 0 0
\(81\) 1.56283 + 8.86327i 0.173648 + 0.984808i
\(82\) 7.04189 0.777647
\(83\) −15.9820 + 5.81699i −1.75426 + 0.638498i −0.999840 0.0178968i \(-0.994303\pi\)
−0.754418 + 0.656394i \(0.772081\pi\)
\(84\) 2.73143 7.50454i 0.298023 0.818812i
\(85\) 0 0
\(86\) 1.85844 + 10.5397i 0.200401 + 1.13653i
\(87\) 10.0470i 1.07716i
\(88\) 2.26470 + 1.90031i 0.241418 + 0.202574i
\(89\) 5.19846 9.00400i 0.551036 0.954422i −0.447164 0.894452i \(-0.647566\pi\)
0.998200 0.0599704i \(-0.0191006\pi\)
\(90\) 0 0
\(91\) −5.98545 10.3671i −0.627446 1.08677i
\(92\) 1.14378 6.48670i 0.119247 0.676286i
\(93\) 2.43242 + 6.68302i 0.252230 + 0.692996i
\(94\) 2.86571 + 1.04303i 0.295576 + 0.107581i
\(95\) 0 0
\(96\) 9.61721 + 1.69577i 0.981553 + 0.173074i
\(97\) 1.06283 6.02763i 0.107914 0.612013i −0.882102 0.471059i \(-0.843872\pi\)
0.990016 0.140954i \(-0.0450170\pi\)
\(98\) −3.13429 5.42874i −0.316611 0.548386i
\(99\) 2.39440 2.00914i 0.240646 0.201926i
\(100\) 0 0
\(101\) 1.51501 + 1.27125i 0.150750 + 0.126494i 0.715043 0.699080i \(-0.246407\pi\)
−0.564294 + 0.825574i \(0.690851\pi\)
\(102\) 0.617211 0.356347i 0.0611130 0.0352836i
\(103\) 2.07650 + 11.7764i 0.204604 + 1.16037i 0.898062 + 0.439870i \(0.144975\pi\)
−0.693458 + 0.720497i \(0.743914\pi\)
\(104\) 6.92262 5.80877i 0.678819 0.569596i
\(105\) 0 0
\(106\) 7.30288 2.65803i 0.709319 0.258171i
\(107\) −20.6382 −1.99517 −0.997583 0.0694862i \(-0.977864\pi\)
−0.997583 + 0.0694862i \(0.977864\pi\)
\(108\) 2.18004 5.98962i 0.209775 0.576352i
\(109\) 0.433763 0.0415469 0.0207735 0.999784i \(-0.493387\pi\)
0.0207735 + 0.999784i \(0.493387\pi\)
\(110\) 0 0
\(111\) 7.63429 1.34613i 0.724614 0.127769i
\(112\) 0.120615 0.101208i 0.0113970 0.00956324i
\(113\) −0.998656 5.66366i −0.0939456 0.532792i −0.995065 0.0992218i \(-0.968365\pi\)
0.901120 0.433570i \(-0.142746\pi\)
\(114\) −6.19253 3.57526i −0.579984 0.334854i
\(115\) 0 0
\(116\) 3.55778 6.16226i 0.330332 0.572151i
\(117\) −4.77719 8.27433i −0.441651 0.764962i
\(118\) −6.00000 10.3923i −0.552345 0.956689i
\(119\) −0.305407 + 1.73205i −0.0279966 + 0.158777i
\(120\) 0 0
\(121\) 9.31655 + 3.39095i 0.846959 + 0.308268i
\(122\) −8.04798 2.92923i −0.728630 0.265200i
\(123\) −8.91534 + 10.6249i −0.803870 + 0.958014i
\(124\) 0.874638 4.96032i 0.0785448 0.445450i
\(125\) 0 0
\(126\) −4.95811 8.58770i −0.441704 0.765053i
\(127\) 9.80587 16.9843i 0.870131 1.50711i 0.00826966 0.999966i \(-0.497368\pi\)
0.861861 0.507145i \(-0.169299\pi\)
\(128\) −5.24170 4.39831i −0.463305 0.388759i
\(129\) −18.2554 10.5397i −1.60730 0.927972i
\(130\) 0 0
\(131\) 13.8701 11.6384i 1.21183 1.01685i 0.212621 0.977135i \(-0.431800\pi\)
0.999211 0.0397131i \(-0.0126444\pi\)
\(132\) −2.18004 + 0.384401i −0.189749 + 0.0334578i
\(133\) 16.5817 6.03525i 1.43782 0.523323i
\(134\) 1.60307 0.138484
\(135\) 0 0
\(136\) −1.32770 −0.113849
\(137\) 13.7208 4.99395i 1.17224 0.426662i 0.318787 0.947826i \(-0.396725\pi\)
0.853456 + 0.521165i \(0.174502\pi\)
\(138\) −5.25712 6.26519i −0.447516 0.533329i
\(139\) −16.9440 + 14.2177i −1.43717 + 1.20593i −0.495859 + 0.868403i \(0.665147\pi\)
−0.941315 + 0.337529i \(0.890409\pi\)
\(140\) 0 0
\(141\) −5.20187 + 3.00330i −0.438076 + 0.252923i
\(142\) 5.18866 + 4.35381i 0.435423 + 0.365363i
\(143\) −1.65910 + 2.87365i −0.138741 + 0.240306i
\(144\) 0.0962667 0.0807773i 0.00802222 0.00673144i
\(145\) 0 0
\(146\) −0.124485 + 0.705990i −0.0103025 + 0.0584282i
\(147\) 12.1591 + 2.14398i 1.00287 + 0.176832i
\(148\) −5.15910 1.87776i −0.424075 0.154351i
\(149\) 13.3969 + 4.87608i 1.09752 + 0.399464i 0.826401 0.563082i \(-0.190384\pi\)
0.271118 + 0.962546i \(0.412607\pi\)
\(150\) 0 0
\(151\) 0.805407 4.56769i 0.0655431 0.371713i −0.934339 0.356384i \(-0.884009\pi\)
0.999883 0.0153290i \(-0.00487956\pi\)
\(152\) 6.66044 + 11.5362i 0.540233 + 0.935712i
\(153\) −0.243756 + 1.38241i −0.0197065 + 0.111761i
\(154\) −1.72193 + 2.98248i −0.138757 + 0.240335i
\(155\) 0 0
\(156\) 6.76665i 0.541765i
\(157\) −2.18392 12.3856i −0.174295 0.988478i −0.938954 0.344043i \(-0.888203\pi\)
0.764659 0.644436i \(-0.222908\pi\)
\(158\) −2.73261 + 2.29293i −0.217395 + 0.182416i
\(159\) −5.23530 + 14.3839i −0.415186 + 1.14071i
\(160\) 0 0
\(161\) 20.1830 1.59065
\(162\) −3.95723 6.85413i −0.310910 0.538511i
\(163\) −6.40373 −0.501579 −0.250790 0.968042i \(-0.580690\pi\)
−0.250790 + 0.968042i \(0.580690\pi\)
\(164\) 9.23055 3.35965i 0.720785 0.262344i
\(165\) 0 0
\(166\) 11.4572 9.61376i 0.889254 0.746173i
\(167\) −1.55303 8.80769i −0.120177 0.681560i −0.984056 0.177859i \(-0.943083\pi\)
0.863879 0.503700i \(-0.168028\pi\)
\(168\) 18.4732i 1.42524i
\(169\) −2.18866 1.83651i −0.168359 0.141270i
\(170\) 0 0
\(171\) 13.2344 4.81694i 1.01206 0.368360i
\(172\) 7.46451 + 12.9289i 0.569163 + 0.985820i
\(173\) 1.05391 5.97702i 0.0801274 0.454425i −0.918175 0.396176i \(-0.870337\pi\)
0.998302 0.0582491i \(-0.0185518\pi\)
\(174\) −3.02182 8.30239i −0.229084 0.629402i
\(175\) 0 0
\(176\) −0.0410117 0.0149270i −0.00309137 0.00112517i
\(177\) 23.2763 + 4.10424i 1.74955 + 0.308494i
\(178\) −1.58765 + 9.00400i −0.118999 + 0.674878i
\(179\) −1.80200 3.12116i −0.134688 0.233287i 0.790790 0.612087i \(-0.209670\pi\)
−0.925478 + 0.378801i \(0.876337\pi\)
\(180\) 0 0
\(181\) −5.56283 + 9.63511i −0.413482 + 0.716172i −0.995268 0.0971701i \(-0.969021\pi\)
0.581786 + 0.813342i \(0.302354\pi\)
\(182\) 8.06418 + 6.76665i 0.597757 + 0.501577i
\(183\) 14.6088 8.43437i 1.07991 0.623486i
\(184\) 2.64573 + 15.0047i 0.195046 + 1.10616i
\(185\) 0 0
\(186\) −4.02007 4.79093i −0.294766 0.351288i
\(187\) 0.458111 0.166739i 0.0335004 0.0121931i
\(188\) 4.25402 0.310256
\(189\) 19.2344 + 3.39155i 1.39910 + 0.246699i
\(190\) 0 0
\(191\) −9.53596 + 3.47081i −0.689998 + 0.251139i −0.663134 0.748500i \(-0.730774\pi\)
−0.0268635 + 0.999639i \(0.508552\pi\)
\(192\) −8.60014 + 1.51644i −0.620661 + 0.109439i
\(193\) 0.269915 0.226485i 0.0194289 0.0163028i −0.633021 0.774134i \(-0.718186\pi\)
0.652450 + 0.757831i \(0.273741\pi\)
\(194\) 0.934640 + 5.30061i 0.0671033 + 0.380561i
\(195\) 0 0
\(196\) −6.69846 5.62068i −0.478462 0.401477i
\(197\) −10.8268 + 18.7526i −0.771379 + 1.33607i 0.165428 + 0.986222i \(0.447099\pi\)
−0.936807 + 0.349846i \(0.886234\pi\)
\(198\) −1.37433 + 2.38041i −0.0976696 + 0.169169i
\(199\) −12.0209 20.8209i −0.852142 1.47595i −0.879271 0.476322i \(-0.841970\pi\)
0.0271290 0.999632i \(-0.491364\pi\)
\(200\) 0 0
\(201\) −2.02956 + 2.41874i −0.143154 + 0.170605i
\(202\) −1.63429 0.594831i −0.114988 0.0418522i
\(203\) 20.4884 + 7.45718i 1.43801 + 0.523392i
\(204\) 0.639033 0.761570i 0.0447413 0.0533206i
\(205\) 0 0
\(206\) −5.25789 9.10694i −0.366335 0.634510i
\(207\) 16.1088 1.11964
\(208\) −0.0667040 + 0.115535i −0.00462509 + 0.00801089i
\(209\) −3.74691 3.14403i −0.259179 0.217477i
\(210\) 0 0
\(211\) −1.12789 6.39657i −0.0776471 0.440358i −0.998702 0.0509266i \(-0.983783\pi\)
0.921055 0.389432i \(-0.127329\pi\)
\(212\) 8.30453 6.96833i 0.570357 0.478587i
\(213\) −13.1382 + 2.31661i −0.900212 + 0.158732i
\(214\) 17.0544 6.20729i 1.16581 0.424321i
\(215\) 0 0
\(216\) 14.7441i 1.00321i
\(217\) 15.4338 1.04771
\(218\) −0.358441 + 0.130462i −0.0242767 + 0.00883598i
\(219\) −0.907604 1.08164i −0.0613302 0.0730905i
\(220\) 0 0
\(221\) −0.258770 1.46756i −0.0174068 0.0987188i
\(222\) −5.90373 + 3.40852i −0.396233 + 0.228765i
\(223\) −4.43763 3.72362i −0.297166 0.249352i 0.481998 0.876173i \(-0.339911\pi\)
−0.779164 + 0.626821i \(0.784356\pi\)
\(224\) 10.5963 18.3533i 0.707993 1.22628i
\(225\) 0 0
\(226\) 2.52869 + 4.37981i 0.168206 + 0.291341i
\(227\) 2.24510 12.7326i 0.149013 0.845092i −0.815045 0.579398i \(-0.803288\pi\)
0.964057 0.265694i \(-0.0856011\pi\)
\(228\) −9.82295 1.73205i −0.650541 0.114708i
\(229\) 1.17365 + 0.427173i 0.0775569 + 0.0282284i 0.380507 0.924778i \(-0.375749\pi\)
−0.302950 + 0.953006i \(0.597972\pi\)
\(230\) 0 0
\(231\) −2.31996 6.37402i −0.152642 0.419380i
\(232\) −2.85814 + 16.2093i −0.187646 + 1.06419i
\(233\) 0.190722 + 0.330341i 0.0124946 + 0.0216413i 0.872205 0.489140i \(-0.162689\pi\)
−0.859710 + 0.510782i \(0.829356\pi\)
\(234\) 6.43629 + 5.40069i 0.420753 + 0.353054i
\(235\) 0 0
\(236\) −12.8229 10.7597i −0.834703 0.700399i
\(237\) 7.02595i 0.456385i
\(238\) −0.268571 1.52314i −0.0174089 0.0987305i
\(239\) −2.40760 + 2.02022i −0.155735 + 0.130677i −0.717326 0.696738i \(-0.754634\pi\)
0.561591 + 0.827415i \(0.310190\pi\)
\(240\) 0 0
\(241\) 7.05778 2.56882i 0.454632 0.165472i −0.104546 0.994520i \(-0.533339\pi\)
0.559178 + 0.829048i \(0.311117\pi\)
\(242\) −8.71864 −0.560455
\(243\) 15.3516 + 2.70691i 0.984808 + 0.173648i
\(244\) −11.9469 −0.764819
\(245\) 0 0
\(246\) 4.17159 11.4613i 0.265971 0.730749i
\(247\) −11.4534 + 9.61051i −0.728760 + 0.611502i
\(248\) 2.02317 + 11.4739i 0.128471 + 0.728596i
\(249\) 29.4583i 1.86684i
\(250\) 0 0
\(251\) −7.68732 + 13.3148i −0.485219 + 0.840424i −0.999856 0.0169841i \(-0.994594\pi\)
0.514637 + 0.857408i \(0.327927\pi\)
\(252\) −10.5963 8.89132i −0.667502 0.560101i
\(253\) −2.79726 4.84499i −0.175862 0.304602i
\(254\) −2.99479 + 16.9843i −0.187910 + 1.06569i
\(255\) 0 0
\(256\) 15.1300 + 5.50687i 0.945625 + 0.344179i
\(257\) −16.8084 6.11776i −1.04848 0.381615i −0.240391 0.970676i \(-0.577276\pi\)
−0.808089 + 0.589061i \(0.799498\pi\)
\(258\) 18.2554 + 3.21891i 1.13653 + 0.200401i
\(259\) 2.92127 16.5674i 0.181519 1.02945i
\(260\) 0 0
\(261\) 16.3525 + 5.95183i 1.01220 + 0.368409i
\(262\) −7.96110 + 13.7890i −0.491839 + 0.851890i
\(263\) 2.97178 + 2.49362i 0.183248 + 0.153763i 0.729797 0.683664i \(-0.239614\pi\)
−0.546549 + 0.837427i \(0.684059\pi\)
\(264\) 4.43453 2.56028i 0.272927 0.157574i
\(265\) 0 0
\(266\) −11.8871 + 9.97448i −0.728846 + 0.611575i
\(267\) −11.5753 13.7949i −0.708398 0.844236i
\(268\) 2.10132 0.764818i 0.128358 0.0467187i
\(269\) −19.8084 −1.20774 −0.603870 0.797083i \(-0.706375\pi\)
−0.603870 + 0.797083i \(0.706375\pi\)
\(270\) 0 0
\(271\) −14.7888 −0.898356 −0.449178 0.893442i \(-0.648283\pi\)
−0.449178 + 0.893442i \(0.648283\pi\)
\(272\) 0.0184183 0.00670372i 0.00111677 0.000406473i
\(273\) −20.4192 + 3.60046i −1.23583 + 0.217910i
\(274\) −9.83615 + 8.25351i −0.594224 + 0.498613i
\(275\) 0 0
\(276\) −9.88016 5.70431i −0.594716 0.343359i
\(277\) −13.4422 11.2794i −0.807665 0.677711i 0.142385 0.989811i \(-0.454523\pi\)
−0.950049 + 0.312100i \(0.898967\pi\)
\(278\) 9.72550 16.8451i 0.583297 1.01030i
\(279\) 12.3182 0.737471
\(280\) 0 0
\(281\) 1.08853 6.17334i 0.0649360 0.368270i −0.934972 0.354721i \(-0.884576\pi\)
0.999908 0.0135494i \(-0.00431304\pi\)
\(282\) 3.39528 4.04633i 0.202186 0.240956i
\(283\) −5.95084 2.16593i −0.353741 0.128751i 0.159037 0.987273i \(-0.449161\pi\)
−0.512777 + 0.858522i \(0.671383\pi\)
\(284\) 8.87851 + 3.23151i 0.526843 + 0.191755i
\(285\) 0 0
\(286\) 0.506701 2.87365i 0.0299619 0.169922i
\(287\) 15.0496 + 26.0667i 0.888352 + 1.53867i
\(288\) 8.45723 14.6484i 0.498347 0.863163i
\(289\) 8.39053 14.5328i 0.493561 0.854872i
\(290\) 0 0
\(291\) −9.18092 5.30061i −0.538195 0.310727i
\(292\) 0.173648 + 0.984808i 0.0101620 + 0.0576315i
\(293\) 3.50593 2.94182i 0.204819 0.171863i −0.534608 0.845100i \(-0.679541\pi\)
0.739427 + 0.673237i \(0.235096\pi\)
\(294\) −10.6925 + 1.88538i −0.623601 + 0.109958i
\(295\) 0 0
\(296\) 12.6996 0.738152
\(297\) −1.85163 5.08732i −0.107443 0.295196i
\(298\) −12.5371 −0.726257
\(299\) −16.0697 + 5.84889i −0.929335 + 0.338250i
\(300\) 0 0
\(301\) −35.0428 + 29.4044i −2.01983 + 1.69484i
\(302\) 0.708263 + 4.01676i 0.0407560 + 0.231139i
\(303\) 2.96657 1.71275i 0.170425 0.0983948i
\(304\) −0.150644 0.126406i −0.00864004 0.00724985i
\(305\) 0 0
\(306\) −0.214355 1.21567i −0.0122539 0.0694952i
\(307\) −2.02481 3.50708i −0.115562 0.200160i 0.802442 0.596730i \(-0.203534\pi\)
−0.918004 + 0.396570i \(0.870200\pi\)
\(308\) −0.834198 + 4.73097i −0.0475329 + 0.269572i
\(309\) 20.3974 + 3.59661i 1.16037 + 0.204604i
\(310\) 0 0
\(311\) 4.63088 + 1.68550i 0.262593 + 0.0955761i 0.469962 0.882687i \(-0.344268\pi\)
−0.207369 + 0.978263i \(0.566490\pi\)
\(312\) −5.35339 14.7083i −0.303076 0.832694i
\(313\) 2.40033 13.6129i 0.135675 0.769449i −0.838713 0.544574i \(-0.816691\pi\)
0.974388 0.224875i \(-0.0721975\pi\)
\(314\) 5.52987 + 9.57801i 0.312068 + 0.540518i
\(315\) 0 0
\(316\) −2.48798 + 4.30930i −0.139960 + 0.242417i
\(317\) 11.8669 + 9.95751i 0.666511 + 0.559269i 0.912031 0.410122i \(-0.134514\pi\)
−0.245519 + 0.969392i \(0.578958\pi\)
\(318\) 13.4607i 0.754841i
\(319\) −1.04947 5.95183i −0.0587589 0.333238i
\(320\) 0 0
\(321\) −12.2260 + 33.5906i −0.682387 + 1.87484i
\(322\) −16.6783 + 6.07040i −0.929445 + 0.338290i
\(323\) 2.19665 0.122225
\(324\) −8.45723 7.09646i −0.469846 0.394248i
\(325\) 0 0
\(326\) 5.29174 1.92603i 0.293082 0.106673i
\(327\) 0.256959 0.705990i 0.0142099 0.0390414i
\(328\) −17.4060 + 14.6054i −0.961086 + 0.806447i
\(329\) 2.26352 + 12.8370i 0.124792 + 0.707729i
\(330\) 0 0
\(331\) −6.24170 5.23741i −0.343075 0.287874i 0.454927 0.890529i \(-0.349665\pi\)
−0.798002 + 0.602655i \(0.794110\pi\)
\(332\) 10.4315 18.0680i 0.572505 0.991608i
\(333\) 2.33157 13.2230i 0.127769 0.724614i
\(334\) 3.93242 + 6.81115i 0.215172 + 0.372689i
\(335\) 0 0
\(336\) −0.0932736 0.256267i −0.00508849 0.0139805i
\(337\) 5.35369 + 1.94858i 0.291634 + 0.106146i 0.483694 0.875237i \(-0.339295\pi\)
−0.192060 + 0.981383i \(0.561517\pi\)
\(338\) 2.36097 + 0.859322i 0.128420 + 0.0467409i
\(339\) −9.80974 1.72972i −0.532792 0.0939456i
\(340\) 0 0
\(341\) −2.13903 3.70491i −0.115835 0.200632i
\(342\) −9.48751 + 7.96097i −0.513026 + 0.430480i
\(343\) 0.241230 0.417822i 0.0130252 0.0225603i
\(344\) −26.4538 22.1974i −1.42629 1.19680i
\(345\) 0 0
\(346\) 0.926794 + 5.25611i 0.0498247 + 0.282570i
\(347\) −20.4158 + 17.1309i −1.09598 + 0.919635i −0.997148 0.0754694i \(-0.975954\pi\)
−0.0988301 + 0.995104i \(0.531510\pi\)
\(348\) −7.92205 9.44113i −0.424666 0.506098i
\(349\) 7.47906 2.72215i 0.400345 0.145714i −0.133998 0.990982i \(-0.542782\pi\)
0.534342 + 0.845268i \(0.320559\pi\)
\(350\) 0 0
\(351\) −16.2973 + 2.87365i −0.869883 + 0.153384i
\(352\) −5.87433 −0.313103
\(353\) −13.4966 + 4.91236i −0.718351 + 0.261459i −0.675226 0.737611i \(-0.735954\pi\)
−0.0431256 + 0.999070i \(0.513732\pi\)
\(354\) −20.4688 + 3.60921i −1.08791 + 0.191827i
\(355\) 0 0
\(356\) 2.21466 + 12.5600i 0.117377 + 0.665677i
\(357\) 2.63816 + 1.52314i 0.139626 + 0.0806131i
\(358\) 2.42783 + 2.03719i 0.128315 + 0.107669i
\(359\) 10.3341 17.8992i 0.545413 0.944682i −0.453168 0.891425i \(-0.649706\pi\)
0.998581 0.0532573i \(-0.0169603\pi\)
\(360\) 0 0
\(361\) −1.51960 2.63203i −0.0799790 0.138528i
\(362\) 1.69893 9.63511i 0.0892938 0.506410i
\(363\) 11.0382 13.1548i 0.579354 0.690447i
\(364\) 13.7989 + 5.02239i 0.723259 + 0.263245i
\(365\) 0 0
\(366\) −9.53519 + 11.3636i −0.498412 + 0.593985i
\(367\) −1.15002 + 6.52206i −0.0600303 + 0.340449i −1.00000 0.000810039i \(-0.999742\pi\)
0.939969 + 0.341259i \(0.110853\pi\)
\(368\) −0.112463 0.194792i −0.00586256 0.0101543i
\(369\) 12.0116 + 20.8047i 0.625300 + 1.08305i
\(370\) 0 0
\(371\) 25.4466 + 21.3522i 1.32112 + 1.10855i
\(372\) −7.55525 4.36203i −0.391722 0.226161i
\(373\) 5.52023 + 31.3068i 0.285827 + 1.62100i 0.702318 + 0.711864i \(0.252149\pi\)
−0.416491 + 0.909140i \(0.636740\pi\)
\(374\) −0.328411 + 0.275570i −0.0169817 + 0.0142494i
\(375\) 0 0
\(376\) −9.24675 + 3.36554i −0.476865 + 0.173565i
\(377\) −18.4739 −0.951454
\(378\) −16.9145 + 2.98248i −0.869986 + 0.153402i
\(379\) −34.1925 −1.75635 −0.878176 0.478337i \(-0.841240\pi\)
−0.878176 + 0.478337i \(0.841240\pi\)
\(380\) 0 0
\(381\) −21.8346 26.0214i −1.11862 1.33312i
\(382\) 6.83615 5.73621i 0.349768 0.293490i
\(383\) 4.13294 + 23.4391i 0.211183 + 1.19768i 0.887408 + 0.460985i \(0.152504\pi\)
−0.676224 + 0.736696i \(0.736385\pi\)
\(384\) −10.2638 + 5.92582i −0.523774 + 0.302401i
\(385\) 0 0
\(386\) −0.154925 + 0.268338i −0.00788548 + 0.0136581i
\(387\) −27.9688 + 23.4686i −1.42174 + 1.19298i
\(388\) 3.75402 + 6.50216i 0.190582 + 0.330097i
\(389\) 0.769915 4.36640i 0.0390362 0.221385i −0.959049 0.283241i \(-0.908591\pi\)
0.998085 + 0.0618550i \(0.0197016\pi\)
\(390\) 0 0
\(391\) 2.36097 + 0.859322i 0.119399 + 0.0434578i
\(392\) 19.0069 + 6.91793i 0.959992 + 0.349408i
\(393\) −10.7260 29.4694i −0.541053 1.48653i
\(394\) 3.30659 18.7526i 0.166584 0.944742i
\(395\) 0 0
\(396\) −0.665802 + 3.77595i −0.0334578 + 0.189749i
\(397\) −9.41875 + 16.3138i −0.472713 + 0.818764i −0.999512 0.0312263i \(-0.990059\pi\)
0.526799 + 0.849990i \(0.323392\pi\)
\(398\) 16.1958 + 13.5899i 0.811821 + 0.681199i
\(399\) 30.5636i 1.53009i
\(400\) 0 0
\(401\) −7.00387 + 5.87695i −0.349757 + 0.293481i −0.800692 0.599076i \(-0.795535\pi\)
0.450936 + 0.892556i \(0.351090\pi\)
\(402\) 0.949655 2.60916i 0.0473645 0.130133i
\(403\) −12.2883 + 4.47259i −0.612125 + 0.222795i
\(404\) −2.42602 −0.120699
\(405\) 0 0
\(406\) −19.1735 −0.951567
\(407\) −4.38191 + 1.59489i −0.217203 + 0.0790555i
\(408\) −0.786522 + 2.16095i −0.0389386 + 0.106983i
\(409\) 21.2920 17.8661i 1.05282 0.883424i 0.0594360 0.998232i \(-0.481070\pi\)
0.993388 + 0.114808i \(0.0366253\pi\)
\(410\) 0 0
\(411\) 25.2902i 1.24747i
\(412\) −11.2369 9.42892i −0.553605 0.464530i
\(413\) 25.6459 44.4200i 1.26195 2.18577i
\(414\) −13.3115 + 4.84499i −0.654224 + 0.238118i
\(415\) 0 0
\(416\) −3.11809 + 17.6836i −0.152877 + 0.867008i
\(417\) 13.1031 + 36.0006i 0.641663 + 1.76295i
\(418\) 4.04189 + 1.47113i 0.197695 + 0.0719552i
\(419\) −7.55943 2.75141i −0.369302 0.134415i 0.150701 0.988579i \(-0.451847\pi\)
−0.520003 + 0.854164i \(0.674069\pi\)
\(420\) 0 0
\(421\) −3.44862 + 19.5581i −0.168075 + 0.953202i 0.777762 + 0.628559i \(0.216355\pi\)
−0.945837 + 0.324643i \(0.894756\pi\)
\(422\) 2.85591 + 4.94659i 0.139024 + 0.240796i
\(423\) 1.80659 + 10.2457i 0.0878394 + 0.498162i
\(424\) −12.5382 + 21.7168i −0.608908 + 1.05466i
\(425\) 0 0
\(426\) 10.1600 5.86587i 0.492253 0.284202i
\(427\) −6.35679 36.0512i −0.307627 1.74464i
\(428\) 19.3935 16.2731i 0.937421 0.786590i
\(429\) 3.69429 + 4.40268i 0.178362 + 0.212563i
\(430\) 0 0
\(431\) −5.89393 −0.283901 −0.141950 0.989874i \(-0.545337\pi\)
−0.141950 + 0.989874i \(0.545337\pi\)
\(432\) −0.0744448 0.204535i −0.00358173 0.00984071i
\(433\) −3.82201 −0.183674 −0.0918372 0.995774i \(-0.529274\pi\)
−0.0918372 + 0.995774i \(0.529274\pi\)
\(434\) −12.7537 + 4.64197i −0.612198 + 0.222822i
\(435\) 0 0
\(436\) −0.407604 + 0.342020i −0.0195207 + 0.0163798i
\(437\) −4.37733 24.8250i −0.209396 1.18754i
\(438\) 1.07532 + 0.620838i 0.0513809 + 0.0296648i
\(439\) 29.3200 + 24.6024i 1.39937 + 1.17421i 0.961379 + 0.275229i \(0.0887536\pi\)
0.437989 + 0.898980i \(0.355691\pi\)
\(440\) 0 0
\(441\) 10.6925 18.5200i 0.509168 0.881905i
\(442\) 0.655230 + 1.13489i 0.0311661 + 0.0539813i
\(443\) −2.31892 + 13.1512i −0.110175 + 0.624834i 0.878852 + 0.477095i \(0.158310\pi\)
−0.989027 + 0.147738i \(0.952801\pi\)
\(444\) −6.11246 + 7.28455i −0.290085 + 0.345709i
\(445\) 0 0
\(446\) 4.78699 + 1.74232i 0.226670 + 0.0825013i
\(447\) 15.8726 18.9162i 0.750747 0.894706i
\(448\) −3.29086 + 18.6634i −0.155478 + 0.881762i
\(449\) −3.45929 5.99167i −0.163254 0.282764i 0.772780 0.634674i \(-0.218866\pi\)
−0.936034 + 0.351910i \(0.885532\pi\)
\(450\) 0 0
\(451\) 4.17159 7.22540i 0.196432 0.340231i
\(452\) 5.40420 + 4.53466i 0.254192 + 0.213293i
\(453\) −6.95723 4.01676i −0.326879 0.188724i
\(454\) 1.97431 + 11.1969i 0.0926589 + 0.525494i
\(455\) 0 0
\(456\) 22.7219 4.00649i 1.06405 0.187621i
\(457\) −7.80928 + 2.84234i −0.365303 + 0.132959i −0.518148 0.855291i \(-0.673378\pi\)
0.152846 + 0.988250i \(0.451156\pi\)
\(458\) −1.09833 −0.0513214
\(459\) 2.10560 + 1.21567i 0.0982810 + 0.0567426i
\(460\) 0 0
\(461\) 23.2319 8.45572i 1.08202 0.393822i 0.261359 0.965242i \(-0.415829\pi\)
0.820658 + 0.571420i \(0.193607\pi\)
\(462\) 3.83420 + 4.56942i 0.178383 + 0.212589i
\(463\) −0.0983261 + 0.0825054i −0.00456960 + 0.00383435i −0.645070 0.764124i \(-0.723172\pi\)
0.640500 + 0.767958i \(0.278727\pi\)
\(464\) −0.0421938 0.239293i −0.00195880 0.0111089i
\(465\) 0 0
\(466\) −0.256959 0.215615i −0.0119034 0.00998815i
\(467\) 19.9577 34.5678i 0.923532 1.59960i 0.129627 0.991563i \(-0.458622\pi\)
0.793905 0.608042i \(-0.208045\pi\)
\(468\) 11.0134 + 4.00854i 0.509093 + 0.185295i
\(469\) 3.42602 + 5.93404i 0.158199 + 0.274009i
\(470\) 0 0
\(471\) −21.4525 3.78265i −0.988478 0.174295i
\(472\) 36.3851 + 13.2431i 1.67476 + 0.609562i
\(473\) 11.9153 + 4.33683i 0.547868 + 0.199408i
\(474\) 2.11318 + 5.80591i 0.0970615 + 0.266674i
\(475\) 0 0
\(476\) −1.07873 1.86841i −0.0494433 0.0856383i
\(477\) 20.3097 + 17.0419i 0.929919 + 0.780295i
\(478\) 1.38191 2.39354i 0.0632072 0.109478i
\(479\) −6.30200 5.28801i −0.287946 0.241615i 0.487360 0.873201i \(-0.337960\pi\)
−0.775306 + 0.631586i \(0.782404\pi\)
\(480\) 0 0
\(481\) 2.47519 + 14.0375i 0.112859 + 0.640054i
\(482\) −5.05959 + 4.24550i −0.230458 + 0.193377i
\(483\) 11.9564 32.8498i 0.544033 1.49472i
\(484\) −11.4284 + 4.15961i −0.519475 + 0.189073i
\(485\) 0 0
\(486\) −13.5000 + 2.38041i −0.612372 + 0.107978i
\(487\) 2.84760 0.129037 0.0645186 0.997917i \(-0.479449\pi\)
0.0645186 + 0.997917i \(0.479449\pi\)
\(488\) 25.9683 9.45168i 1.17553 0.427857i
\(489\) −3.79355 + 10.4227i −0.171550 + 0.471330i
\(490\) 0 0
\(491\) −6.89481 39.1024i −0.311158 1.76467i −0.592996 0.805205i \(-0.702055\pi\)
0.281838 0.959462i \(-0.409056\pi\)
\(492\) 17.0138i 0.767043i
\(493\) 2.07919 + 1.74465i 0.0936421 + 0.0785751i
\(494\) 6.57398 11.3865i 0.295777 0.512301i
\(495\) 0 0
\(496\) −0.0859997 0.148956i −0.00386150 0.00668831i
\(497\) −5.02734 + 28.5115i −0.225507 + 1.27891i
\(498\) −8.86009 24.3429i −0.397030 1.09083i
\(499\) 36.4962 + 13.2835i 1.63379 + 0.594652i 0.985938 0.167111i \(-0.0534438\pi\)
0.647856 + 0.761763i \(0.275666\pi\)
\(500\) 0 0
\(501\) −15.2554 2.68993i −0.681560 0.120177i
\(502\) 2.34776 13.3148i 0.104786 0.594270i
\(503\) 13.5530 + 23.4745i 0.604300 + 1.04668i 0.992162 + 0.124961i \(0.0398804\pi\)
−0.387862 + 0.921718i \(0.626786\pi\)
\(504\) 30.0669 + 10.9434i 1.33928 + 0.487460i
\(505\) 0 0
\(506\) 3.76873 + 3.16234i 0.167541 + 0.140583i
\(507\) −4.28564 + 2.47432i −0.190332 + 0.109888i
\(508\) 4.17752 + 23.6919i 0.185347 + 1.05116i
\(509\) −14.8105 + 12.4275i −0.656462 + 0.550837i −0.909024 0.416744i \(-0.863171\pi\)
0.252562 + 0.967581i \(0.418727\pi\)
\(510\) 0 0
\(511\) −2.87939 + 1.04801i −0.127377 + 0.0463613i
\(512\) −0.473897 −0.0209435
\(513\) 24.3938i 1.07701i
\(514\) 15.7297 0.693806
\(515\) 0 0
\(516\) 25.4650 4.49016i 1.12103 0.197668i
\(517\) 2.76786 2.32251i 0.121730 0.102144i
\(518\) 2.56893 + 14.5691i 0.112872 + 0.640130i
\(519\) −9.10385 5.25611i −0.399614 0.230718i
\(520\) 0 0
\(521\) −12.2618 + 21.2380i −0.537198 + 0.930454i 0.461856 + 0.886955i \(0.347184\pi\)
−0.999053 + 0.0434986i \(0.986150\pi\)
\(522\) −15.3030 −0.669796
\(523\) 4.31521 + 7.47416i 0.188691 + 0.326822i 0.944814 0.327607i \(-0.106242\pi\)
−0.756123 + 0.654429i \(0.772909\pi\)
\(524\) −3.85679 + 21.8730i −0.168485 + 0.955524i
\(525\) 0 0
\(526\) −3.20574 1.16679i −0.139777 0.0508746i
\(527\) 1.80541 + 0.657115i 0.0786448 + 0.0286244i
\(528\) −0.0485904 + 0.0579078i −0.00211462 + 0.00252011i
\(529\) 1.01279 5.74384i 0.0440345 0.249732i
\(530\) 0 0
\(531\) 20.4688 35.4531i 0.888272 1.53853i
\(532\) −10.8229 + 18.7459i −0.469234 + 0.812738i
\(533\) −19.5364 16.3930i −0.846217 0.710060i
\(534\) 13.7144 + 7.91799i 0.593478 + 0.342645i
\(535\) 0 0
\(536\) −3.96245 + 3.32489i −0.171152 + 0.143613i
\(537\) −6.14749 + 1.08397i −0.265284 + 0.0467767i
\(538\) 16.3687 5.95772i 0.705705 0.256856i
\(539\) −7.42696 −0.319902
\(540\) 0 0
\(541\) 21.5722 0.927462 0.463731 0.885976i \(-0.346510\pi\)
0.463731 + 0.885976i \(0.346510\pi\)
\(542\) 12.2208 4.44799i 0.524926 0.191058i
\(543\) 12.3867 + 14.7618i 0.531562 + 0.633491i
\(544\) 2.02094 1.69577i 0.0866473 0.0727057i
\(545\) 0 0
\(546\) 15.7906 9.11668i 0.675773 0.390158i
\(547\) 17.3289 + 14.5407i 0.740929 + 0.621714i 0.933087 0.359651i \(-0.117104\pi\)
−0.192158 + 0.981364i \(0.561549\pi\)
\(548\) −8.95558 + 15.5115i −0.382564 + 0.662620i
\(549\) −5.07357 28.7736i −0.216535 1.22803i
\(550\) 0 0
\(551\) 4.72874 26.8180i 0.201451 1.14249i
\(552\) 25.9889 + 4.58255i 1.10616 + 0.195046i
\(553\) −14.3277 5.21485i −0.609276 0.221758i
\(554\) 14.5005 + 5.27774i 0.616066 + 0.224230i
\(555\) 0 0
\(556\) 4.71156 26.7206i 0.199815 1.13321i
\(557\) 22.9807 + 39.8037i 0.973724 + 1.68654i 0.684084 + 0.729403i \(0.260202\pi\)
0.289640 + 0.957136i \(0.406465\pi\)
\(558\) −10.1792 + 3.70491i −0.430919 + 0.156842i
\(559\) 19.3799 33.5669i 0.819680 1.41973i
\(560\) 0 0
\(561\) 0.844395i 0.0356504i
\(562\) 0.957234 + 5.42874i 0.0403785 + 0.228998i
\(563\) −2.20645 + 1.85143i −0.0929909 + 0.0780286i −0.688098 0.725618i \(-0.741554\pi\)
0.595107 + 0.803646i \(0.297110\pi\)
\(564\) 2.52007 6.92383i 0.106114 0.291546i
\(565\) 0 0
\(566\) 5.56893 0.234079
\(567\) 16.9145 29.2967i 0.710341 1.23035i
\(568\) −21.8553 −0.917030
\(569\) −35.1472 + 12.7925i −1.47345 + 0.536292i −0.949035 0.315172i \(-0.897938\pi\)
−0.524414 + 0.851463i \(0.675716\pi\)
\(570\) 0 0
\(571\) −19.2324 + 16.1379i −0.804849 + 0.675349i −0.949372 0.314153i \(-0.898280\pi\)
0.144523 + 0.989501i \(0.453835\pi\)
\(572\) −0.706813 4.00854i −0.0295533 0.167605i
\(573\) 17.5768i 0.734280i
\(574\) −20.2763 17.0138i −0.846317 0.710144i
\(575\) 0 0
\(576\) −2.62654 + 14.8959i −0.109439 + 0.620661i
\(577\) 2.39053 + 4.14052i 0.0995190 + 0.172372i 0.911486 0.411332i \(-0.134936\pi\)
−0.811967 + 0.583704i \(0.801603\pi\)
\(578\) −2.56253 + 14.5328i −0.106587 + 0.604486i
\(579\) −0.208730 0.573481i −0.00867453 0.0238331i
\(580\) 0 0
\(581\) 60.0729 + 21.8647i 2.49224 + 0.907102i
\(582\) 9.18092 + 1.61884i 0.380561 + 0.0671033i
\(583\) 1.59890 9.06781i 0.0662196 0.375550i
\(584\) −1.15657 2.00324i −0.0478594 0.0828949i
\(585\) 0 0
\(586\) −2.01233 + 3.48545i −0.0831284 + 0.143983i
\(587\) −18.0116 15.1135i −0.743419 0.623802i 0.190335 0.981719i \(-0.439043\pi\)
−0.933753 + 0.357917i \(0.883487\pi\)
\(588\) −13.1163 + 7.57272i −0.540908 + 0.312294i
\(589\) −3.34730 18.9835i −0.137923 0.782200i
\(590\) 0 0
\(591\) 24.1079 + 28.7307i 0.991666 + 1.18182i
\(592\) −0.176174 + 0.0641222i −0.00724072 + 0.00263541i
\(593\) 2.98276 0.122487 0.0612437 0.998123i \(-0.480493\pi\)
0.0612437 + 0.998123i \(0.480493\pi\)
\(594\) 3.06020 + 3.64701i 0.125562 + 0.149638i
\(595\) 0 0
\(596\) −16.4338 + 5.98140i −0.673153 + 0.245008i
\(597\) −41.0091 + 7.23102i −1.67839 + 0.295946i
\(598\) 11.5201 9.66648i 0.471091 0.395292i
\(599\) −5.51930 31.3015i −0.225512 1.27894i −0.861703 0.507412i \(-0.830602\pi\)
0.636191 0.771532i \(-0.280509\pi\)
\(600\) 0 0
\(601\) 28.2763 + 23.7266i 1.15341 + 0.967830i 0.999794 0.0202999i \(-0.00646211\pi\)
0.153621 + 0.988130i \(0.450907\pi\)
\(602\) 20.1138 34.8381i 0.819778 1.41990i
\(603\) 2.73442 + 4.73616i 0.111354 + 0.192871i
\(604\) 2.84477 + 4.92729i 0.115752 + 0.200488i
\(605\) 0 0
\(606\) −1.93629 + 2.30758i −0.0786564 + 0.0937390i
\(607\) −29.5355 10.7501i −1.19881 0.436331i −0.336002 0.941861i \(-0.609075\pi\)
−0.862809 + 0.505530i \(0.831297\pi\)
\(608\) −24.8726 9.05288i −1.00872 0.367143i
\(609\) 24.2746 28.9293i 0.983655 1.17227i
\(610\) 0 0
\(611\) −5.52229 9.56488i −0.223408 0.386954i
\(612\) −0.860967 1.49124i −0.0348025 0.0602797i
\(613\) −12.7057 + 22.0070i −0.513180 + 0.888854i 0.486703 + 0.873567i \(0.338199\pi\)
−0.999883 + 0.0152863i \(0.995134\pi\)
\(614\) 2.72803 + 2.28909i 0.110094 + 0.0923800i
\(615\) 0 0
\(616\) −1.92962 10.9434i −0.0777468 0.440924i
\(617\) 16.7422 14.0483i 0.674014 0.565565i −0.240236 0.970714i \(-0.577225\pi\)
0.914250 + 0.405149i \(0.132781\pi\)
\(618\) −17.9372 + 3.16281i −0.721539 + 0.127227i
\(619\) 37.8619 13.7806i 1.52180 0.553889i 0.560202 0.828356i \(-0.310724\pi\)
0.961597 + 0.274467i \(0.0885014\pi\)
\(620\) 0 0
\(621\) 9.54277 26.2185i 0.382938 1.05211i
\(622\) −4.33368 −0.173765
\(623\) −36.7229 + 13.3660i −1.47127 + 0.535499i
\(624\) 0.148529 + 0.177009i 0.00594590 + 0.00708605i
\(625\) 0 0
\(626\) 2.11081 + 11.9710i 0.0843651 + 0.478458i
\(627\) −7.33687 + 4.23594i −0.293006 + 0.169167i
\(628\) 11.8182 + 9.91665i 0.471598 + 0.395717i
\(629\) 1.04710 1.81364i 0.0417508 0.0723144i
\(630\) 0 0
\(631\) 13.9650 + 24.1880i 0.555937 + 0.962911i 0.997830 + 0.0658432i \(0.0209737\pi\)
−0.441893 + 0.897068i \(0.645693\pi\)
\(632\) 1.99871 11.3353i 0.0795045 0.450892i
\(633\) −11.0792 1.95356i −0.440358 0.0776471i
\(634\) −12.8011 4.65923i −0.508398 0.185042i
\(635\) 0 0
\(636\) −6.42205 17.6444i −0.254651 0.699647i
\(637\) −3.94222 + 22.3574i −0.156196 + 0.885834i
\(638\) 2.65735 + 4.60266i 0.105205 + 0.182221i
\(639\) −4.01249 + 22.7560i −0.158732 + 0.900212i
\(640\) 0 0
\(641\) −23.7230 19.9060i −0.937003 0.786239i 0.0400580 0.999197i \(-0.487246\pi\)
−0.977061 + 0.212958i \(0.931690\pi\)
\(642\) 31.4348i 1.24063i
\(643\) −5.70068 32.3302i −0.224813 1.27498i −0.863042 0.505132i \(-0.831444\pi\)
0.638229 0.769846i \(-0.279667\pi\)
\(644\) −18.9659 + 15.9142i −0.747359 + 0.627109i
\(645\) 0 0
\(646\) −1.81521 + 0.660681i −0.0714184 + 0.0259942i
\(647\) −11.1310 −0.437606 −0.218803 0.975769i \(-0.570215\pi\)
−0.218803 + 0.975769i \(0.570215\pi\)
\(648\) 23.9974 + 8.73433i 0.942706 + 0.343117i
\(649\) −14.2175 −0.558086
\(650\) 0 0
\(651\) 9.14290 25.1199i 0.358339 0.984527i
\(652\) 6.01754 5.04932i 0.235665 0.197746i
\(653\) −0.866592 4.91469i −0.0339124 0.192327i 0.963145 0.268982i \(-0.0866871\pi\)
−0.997058 + 0.0766550i \(0.975576\pi\)
\(654\) 0.660681i 0.0258347i
\(655\) 0 0
\(656\) 0.167718 0.290497i 0.00654830 0.0113420i
\(657\) −2.29813 + 0.836452i −0.0896587 + 0.0326331i
\(658\) −5.73143 9.92713i −0.223434 0.387000i
\(659\) 3.68825 20.9171i 0.143674 0.814815i −0.824748 0.565500i \(-0.808683\pi\)
0.968422 0.249315i \(-0.0802056\pi\)
\(660\) 0 0
\(661\) −1.06506 0.387648i −0.0414258 0.0150778i 0.321224 0.947003i \(-0.395906\pi\)
−0.362650 + 0.931925i \(0.618128\pi\)
\(662\) 6.73308 + 2.45064i 0.261689 + 0.0952468i
\(663\) −2.54189 0.448204i −0.0987188 0.0174068i
\(664\) −8.38016 + 47.5262i −0.325213 + 1.84438i
\(665\) 0 0
\(666\) 2.05035 + 11.6281i 0.0794493 + 0.450579i
\(667\) 15.5736 26.9742i 0.603011 1.04445i
\(668\) 8.40420 + 7.05196i 0.325168 + 0.272849i
\(669\) −8.68938 + 5.01681i −0.335951 + 0.193961i
\(670\) 0 0
\(671\) −7.77316 + 6.52245i −0.300079 + 0.251796i
\(672\) −23.5945 28.1188i −0.910178 1.08471i
\(673\) −41.2083 + 14.9986i −1.58846 + 0.578154i −0.977023 0.213136i \(-0.931632\pi\)
−0.611441 + 0.791290i \(0.709410\pi\)
\(674\) −5.01010 −0.192982
\(675\) 0 0
\(676\) 3.50475 0.134798
\(677\) 9.53033 3.46876i 0.366280 0.133315i −0.152321 0.988331i \(-0.548675\pi\)
0.518602 + 0.855016i \(0.326453\pi\)
\(678\) 8.62654 1.52109i 0.331300 0.0584172i
\(679\) −17.6236 + 14.7880i −0.676332 + 0.567510i
\(680\) 0 0
\(681\) −19.3935 11.1969i −0.743161 0.429064i
\(682\) 2.88191 + 2.41821i 0.110354 + 0.0925981i
\(683\) −2.53091 + 4.38366i −0.0968425 + 0.167736i −0.910376 0.413782i \(-0.864208\pi\)
0.813534 + 0.581518i \(0.197541\pi\)
\(684\) −8.63816 + 14.9617i −0.330288 + 0.572076i
\(685\) 0 0
\(686\) −0.0736733 + 0.417822i −0.00281286 + 0.0159525i
\(687\) 1.39053 1.65717i 0.0530520 0.0632249i
\(688\) 0.479055 + 0.174362i 0.0182638 + 0.00664749i
\(689\) −26.4482 9.62636i −1.00760 0.366735i
\(690\) 0 0
\(691\) 4.22147 23.9411i 0.160592 0.910763i −0.792901 0.609350i \(-0.791430\pi\)
0.953494 0.301413i \(-0.0974584\pi\)
\(692\) 3.72251 + 6.44757i 0.141508 + 0.245100i
\(693\) −11.7487 −0.446295
\(694\) 11.7182 20.2966i 0.444818 0.770447i
\(695\) 0 0
\(696\) 24.6890 + 14.2542i 0.935835 + 0.540305i
\(697\) 0.650644 + 3.68999i 0.0246449 + 0.139768i
\(698\) −5.36160 + 4.49891i −0.202939 + 0.170286i
\(699\) 0.650644 0.114726i 0.0246096 0.00433934i
\(700\) 0 0
\(701\) 46.7256 1.76480 0.882400 0.470500i \(-0.155926\pi\)
0.882400 + 0.470500i \(0.155926\pi\)
\(702\) 12.6030 7.27633i 0.475668 0.274627i
\(703\) −21.0114 −0.792459
\(704\) 4.93629 1.79666i 0.186043 0.0677143i
\(705\) 0 0
\(706\) 9.67546 8.11867i 0.364141 0.305550i
\(707\) −1.29086 7.32083i −0.0485478 0.275328i
\(708\) −25.1088 + 14.4965i −0.943645 + 0.544814i
\(709\) −6.47044 5.42934i −0.243002 0.203903i 0.513150 0.858299i \(-0.328479\pi\)
−0.756152 + 0.654396i \(0.772923\pi\)
\(710\) 0 0
\(711\) −11.4354 4.16215i −0.428861 0.156093i
\(712\) −14.7506 25.5488i −0.552803 0.957483i
\(713\) 3.82857 21.7129i 0.143381 0.813155i
\(714\) −2.63816 0.465178i −0.0987305 0.0174089i
\(715\) 0 0
\(716\) 4.15435 + 1.51206i 0.155255 + 0.0565084i
\(717\) 1.86184 + 5.11538i 0.0695318 + 0.191037i
\(718\) −3.15611 + 17.8992i −0.117785 + 0.667991i
\(719\) 12.5924 + 21.8107i 0.469617 + 0.813401i 0.999397 0.0347347i \(-0.0110586\pi\)
−0.529779 + 0.848135i \(0.677725\pi\)
\(720\) 0 0
\(721\) 22.4739 38.9259i 0.836972 1.44968i
\(722\) 2.04735 + 1.71793i 0.0761946 + 0.0639348i
\(723\) 13.0090i 0.483809i
\(724\) −2.36989 13.4403i −0.0880763 0.499505i
\(725\) 0 0
\(726\) −5.16489 + 14.1904i −0.191687 + 0.526656i
\(727\) 11.3375 4.12651i 0.420484 0.153044i −0.123108 0.992393i \(-0.539286\pi\)
0.543592 + 0.839349i \(0.317064\pi\)
\(728\) −33.9674 −1.25892
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) 0 0
\(731\) −5.35117 + 1.94767i −0.197920 + 0.0720370i
\(732\) −7.07728 + 19.4447i −0.261584 + 0.718695i
\(733\) 30.9818 25.9968i 1.14434 0.960214i 0.144767 0.989466i \(-0.453757\pi\)
0.999572 + 0.0292515i \(0.00931236\pi\)
\(734\) −1.01131 5.73540i −0.0373280 0.211698i
\(735\) 0 0
\(736\) −23.1917 19.4601i −0.854856 0.717309i
\(737\) 0.949655 1.64485i 0.0349810 0.0605889i
\(738\) −16.1832 13.5793i −0.595712 0.499862i
\(739\) −4.33140 7.50221i −0.159333 0.275973i 0.775295 0.631599i \(-0.217601\pi\)
−0.934628 + 0.355626i \(0.884268\pi\)
\(740\) 0 0
\(741\) 8.85710 + 24.3347i 0.325374 + 0.893957i
\(742\) −27.4499 9.99093i −1.00772 0.366779i
\(743\) −16.4804 5.99837i −0.604607 0.220059i 0.0215347 0.999768i \(-0.493145\pi\)
−0.626142 + 0.779709i \(0.715367\pi\)
\(744\) 19.8735 + 3.50423i 0.728596 + 0.128471i
\(745\) 0 0
\(746\) −13.9777 24.2101i −0.511760 0.886395i
\(747\) 47.9461 + 17.4510i 1.75426 + 0.638498i
\(748\) −0.299011 + 0.517902i −0.0109329 + 0.0189364i
\(749\) 59.4252 + 49.8637i 2.17135 + 1.82198i
\(750\) 0 0
\(751\) −5.13253 29.1080i −0.187289 1.06217i −0.922979 0.384849i \(-0.874253\pi\)
0.735691 0.677318i \(-0.236858\pi\)
\(752\) 0.111281 0.0933762i 0.00405802 0.00340508i
\(753\) 17.1172 + 20.3995i 0.623786 + 0.743399i
\(754\) 15.2659 5.55635i 0.555953 0.202350i
\(755\) 0 0
\(756\) −20.7487 + 11.9792i −0.754622 + 0.435681i
\(757\) −26.1165 −0.949220 −0.474610 0.880196i \(-0.657411\pi\)
−0.474610 + 0.880196i \(0.657411\pi\)
\(758\) 28.2551 10.2840i 1.02627 0.373532i
\(759\) −9.54277 + 1.68265i −0.346380 + 0.0610762i
\(760\) 0 0
\(761\) −1.78136 10.1026i −0.0645744 0.366220i −0.999922 0.0124897i \(-0.996024\pi\)
0.935348 0.353730i \(-0.115087\pi\)
\(762\) 25.8694 + 14.9357i 0.937150 + 0.541064i
\(763\) −1.24897 1.04801i −0.0452158 0.0379405i
\(764\) 6.22416 10.7806i 0.225182 0.390027i
\(765\) 0 0
\(766\) −10.4650 18.1259i −0.378115 0.654914i
\(767\) −7.54664 + 42.7991i −0.272493 + 1.54539i
\(768\) 17.9259 21.3633i 0.646846 0.770881i
\(769\) −26.7520 9.73692i −0.964700 0.351122i −0.188827 0.982010i \(-0.560468\pi\)
−0.775874 + 0.630888i \(0.782691\pi\)
\(770\) 0 0
\(771\) −19.9145 + 23.7331i −0.717202 + 0.854728i
\(772\) −0.0750542 + 0.425653i −0.00270126 + 0.0153196i