Properties

Label 441.2.h.g.373.5
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.5
Root \(1.82904 + 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.g.214.5

$q$-expansion

\(f(q)\) \(=\) \(q+2.46050 q^{2} +(-1.25233 - 1.19652i) q^{3} +4.05408 q^{4} +(1.82904 + 3.16799i) q^{5} +(-3.08137 - 2.94405i) q^{6} +5.05408 q^{8} +(0.136673 + 2.99689i) q^{9} +O(q^{10})\) \(q+2.46050 q^{2} +(-1.25233 - 1.19652i) q^{3} +4.05408 q^{4} +(1.82904 + 3.16799i) q^{5} +(-3.08137 - 2.94405i) q^{6} +5.05408 q^{8} +(0.136673 + 2.99689i) q^{9} +(4.50036 + 7.79485i) q^{10} +(-0.203210 + 0.351971i) q^{11} +(-5.07706 - 4.85080i) q^{12} +(0.243398 - 0.421578i) q^{13} +(1.50000 - 6.15585i) q^{15} +4.32743 q^{16} +(-2.42792 - 4.20528i) q^{17} +(0.336285 + 7.37385i) q^{18} +(0.986757 - 1.70911i) q^{19} +(7.41507 + 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-2.32383 - 4.02499i) q^{23} +(-6.32939 - 6.04732i) q^{24} +(-4.19076 + 7.25860i) q^{25} +(0.598883 - 1.03729i) q^{26} +(3.41468 - 3.91663i) q^{27} +(-3.82383 - 6.62307i) q^{29} +(3.69076 - 15.1465i) q^{30} +7.02720 q^{31} +0.539495 q^{32} +(0.675627 - 0.197639i) q^{33} +(-5.97391 - 10.3471i) q^{34} +(0.554084 + 12.1496i) q^{36} +(-1.16372 + 2.01561i) q^{37} +(2.42792 - 4.20528i) q^{38} +(-0.809243 + 0.236725i) q^{39} +(9.24411 + 16.0113i) q^{40} +(-3.75700 + 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +(-0.823832 + 1.42692i) q^{44} +(-9.24411 + 5.91439i) q^{45} +(-5.71780 - 9.90352i) q^{46} -6.31623 q^{47} +(-5.41938 - 5.17786i) q^{48} +(-10.3114 + 17.8598i) q^{50} +(-1.99115 + 8.17147i) q^{51} +(0.986757 - 1.70911i) q^{52} +(1.78434 + 3.09056i) q^{53} +(8.40183 - 9.63688i) q^{54} -1.48672 q^{55} +(-3.28074 + 0.959702i) q^{57} +(-9.40856 - 16.2961i) q^{58} +6.11839 q^{59} +(6.08113 - 24.9564i) q^{60} -8.02712 q^{61} +17.2905 q^{62} -7.32743 q^{64} +1.78074 q^{65} +(1.66238 - 0.486291i) q^{66} +3.60078 q^{67} +(-9.84299 - 17.0486i) q^{68} +(-1.90578 + 7.82115i) q^{69} +8.46050 q^{71} +(0.690757 + 15.1465i) q^{72} +(-0.986757 - 1.70911i) q^{73} +(-2.86333 + 4.95943i) q^{74} +(13.9333 - 4.07586i) q^{75} +(4.00040 - 6.92889i) q^{76} +(-1.99115 + 0.582462i) q^{78} +8.16225 q^{79} +(7.91503 + 13.7092i) q^{80} +(-8.96264 + 0.819187i) q^{81} +(-9.24411 + 16.0113i) q^{82} +(-6.08600 - 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} +(2.86333 + 4.95943i) q^{86} +(-3.13594 + 12.8696i) q^{87} +(-1.02704 + 1.77889i) q^{88} +(-7.41507 + 12.8433i) q^{89} +(-22.7452 + 14.5524i) q^{90} +(-9.42101 - 16.3177i) q^{92} +(-8.80039 - 8.40819i) q^{93} -15.5411 q^{94} +7.21926 q^{95} +(-0.675627 - 0.645517i) q^{96} +(4.74375 + 8.21642i) q^{97} +(-1.08259 - 0.560893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{2} + 12q^{4} + 24q^{8} + O(q^{10}) \) \( 12q + 4q^{2} + 12q^{4} + 24q^{8} - 8q^{11} + 18q^{15} + 12q^{16} + 24q^{18} - 6q^{22} - 4q^{23} - 12q^{25} - 22q^{29} + 6q^{30} + 32q^{32} - 30q^{36} + 6q^{37} - 48q^{39} - 6q^{43} + 14q^{44} - 12q^{46} - 56q^{50} + 36q^{51} - 28q^{53} - 6q^{57} - 18q^{58} + 18q^{60} - 48q^{64} - 12q^{65} + 76q^{71} - 30q^{72} - 36q^{74} + 36q^{78} - 12q^{79} + 24q^{81} + 30q^{85} + 36q^{86} + 6q^{88} - 62q^{92} - 84q^{93} + 120q^{95} - 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
</
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.46050 1.73984 0.869920 0.493193i \(-0.164170\pi\)
0.869920 + 0.493193i \(0.164170\pi\)
\(3\) −1.25233 1.19652i −0.723034 0.690812i
\(4\) 4.05408 2.02704
\(5\) 1.82904 + 3.16799i 0.817970 + 1.41677i 0.907175 + 0.420753i \(0.138234\pi\)
−0.0892047 + 0.996013i \(0.528433\pi\)
\(6\) −3.08137 2.94405i −1.25796 1.20190i
\(7\) 0 0
\(8\) 5.05408 1.78689
\(9\) 0.136673 + 2.99689i 0.0455577 + 0.998962i
\(10\) 4.50036 + 7.79485i 1.42314 + 2.46495i
\(11\) −0.203210 + 0.351971i −0.0612702 + 0.106123i −0.895033 0.445999i \(-0.852848\pi\)
0.833763 + 0.552122i \(0.186182\pi\)
\(12\) −5.07706 4.85080i −1.46562 1.40030i
\(13\) 0.243398 0.421578i 0.0675065 0.116925i −0.830297 0.557322i \(-0.811829\pi\)
0.897803 + 0.440397i \(0.145162\pi\)
\(14\) 0 0
\(15\) 1.50000 6.15585i 0.387298 1.58943i
\(16\) 4.32743 1.08186
\(17\) −2.42792 4.20528i −0.588857 1.01993i −0.994382 0.105847i \(-0.966245\pi\)
0.405525 0.914084i \(-0.367089\pi\)
\(18\) 0.336285 + 7.37385i 0.0792631 + 1.73803i
\(19\) 0.986757 1.70911i 0.226378 0.392097i −0.730354 0.683069i \(-0.760645\pi\)
0.956732 + 0.290971i \(0.0939784\pi\)
\(20\) 7.41507 + 12.8433i 1.65806 + 2.87185i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −2.32383 4.02499i −0.484552 0.839269i 0.515290 0.857016i \(-0.327684\pi\)
−0.999843 + 0.0177464i \(0.994351\pi\)
\(24\) −6.32939 6.04732i −1.29198 1.23440i
\(25\) −4.19076 + 7.25860i −0.838151 + 1.45172i
\(26\) 0.598883 1.03729i 0.117451 0.203430i
\(27\) 3.41468 3.91663i 0.657155 0.753756i
\(28\) 0 0
\(29\) −3.82383 6.62307i −0.710068 1.22987i −0.964831 0.262870i \(-0.915331\pi\)
0.254764 0.967003i \(-0.418002\pi\)
\(30\) 3.69076 15.1465i 0.673837 2.76536i
\(31\) 7.02720 1.26212 0.631061 0.775733i \(-0.282620\pi\)
0.631061 + 0.775733i \(0.282620\pi\)
\(32\) 0.539495 0.0953702
\(33\) 0.675627 0.197639i 0.117612 0.0344045i
\(34\) −5.97391 10.3471i −1.02452 1.77452i
\(35\) 0 0
\(36\) 0.554084 + 12.1496i 0.0923474 + 2.02494i
\(37\) −1.16372 + 2.01561i −0.191314 + 0.331365i −0.945686 0.325082i \(-0.894608\pi\)
0.754372 + 0.656447i \(0.227941\pi\)
\(38\) 2.42792 4.20528i 0.393861 0.682187i
\(39\) −0.809243 + 0.236725i −0.129583 + 0.0379063i
\(40\) 9.24411 + 16.0113i 1.46162 + 2.53160i
\(41\) −3.75700 + 6.50731i −0.586744 + 1.01627i 0.407911 + 0.913022i \(0.366257\pi\)
−0.994655 + 0.103249i \(0.967076\pi\)
\(42\) 0 0
\(43\) 1.16372 + 2.01561i 0.177465 + 0.307378i 0.941012 0.338374i \(-0.109877\pi\)
−0.763547 + 0.645753i \(0.776544\pi\)
\(44\) −0.823832 + 1.42692i −0.124197 + 0.215116i
\(45\) −9.24411 + 5.91439i −1.37803 + 0.881666i
\(46\) −5.71780 9.90352i −0.843044 1.46019i
\(47\) −6.31623 −0.921317 −0.460658 0.887578i \(-0.652387\pi\)
−0.460658 + 0.887578i \(0.652387\pi\)
\(48\) −5.41938 5.17786i −0.782220 0.747360i
\(49\) 0 0
\(50\) −10.3114 + 17.8598i −1.45825 + 2.52576i
\(51\) −1.99115 + 8.17147i −0.278816 + 1.14423i
\(52\) 0.986757 1.70911i 0.136839 0.237011i
\(53\) 1.78434 + 3.09056i 0.245097 + 0.424521i 0.962159 0.272489i \(-0.0878467\pi\)
−0.717062 + 0.697010i \(0.754513\pi\)
\(54\) 8.40183 9.63688i 1.14334 1.31141i
\(55\) −1.48672 −0.200469
\(56\) 0 0
\(57\) −3.28074 + 0.959702i −0.434544 + 0.127116i
\(58\) −9.40856 16.2961i −1.23540 2.13978i
\(59\) 6.11839 0.796546 0.398273 0.917267i \(-0.369610\pi\)
0.398273 + 0.917267i \(0.369610\pi\)
\(60\) 6.08113 24.9564i 0.785070 3.22185i
\(61\) −8.02712 −1.02777 −0.513884 0.857860i \(-0.671794\pi\)
−0.513884 + 0.857860i \(0.671794\pi\)
\(62\) 17.2905 2.19589
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) 1.78074 0.220873
\(66\) 1.66238 0.486291i 0.204625 0.0598583i
\(67\) 3.60078 0.439905 0.219952 0.975511i \(-0.429410\pi\)
0.219952 + 0.975511i \(0.429410\pi\)
\(68\) −9.84299 17.0486i −1.19364 2.06744i
\(69\) −1.90578 + 7.82115i −0.229429 + 0.941555i
\(70\) 0 0
\(71\) 8.46050 1.00408 0.502039 0.864845i \(-0.332584\pi\)
0.502039 + 0.864845i \(0.332584\pi\)
\(72\) 0.690757 + 15.1465i 0.0814065 + 1.78503i
\(73\) −0.986757 1.70911i −0.115491 0.200037i 0.802485 0.596673i \(-0.203511\pi\)
−0.917976 + 0.396636i \(0.870178\pi\)
\(74\) −2.86333 + 4.95943i −0.332855 + 0.576522i
\(75\) 13.9333 4.07586i 1.60888 0.470639i
\(76\) 4.00040 6.92889i 0.458877 0.794798i
\(77\) 0 0
\(78\) −1.99115 + 0.582462i −0.225453 + 0.0659509i
\(79\) 8.16225 0.918325 0.459163 0.888352i \(-0.348150\pi\)
0.459163 + 0.888352i \(0.348150\pi\)
\(80\) 7.91503 + 13.7092i 0.884928 + 1.53274i
\(81\) −8.96264 + 0.819187i −0.995849 + 0.0910208i
\(82\) −9.24411 + 16.0113i −1.02084 + 1.76815i
\(83\) −6.08600 10.5413i −0.668025 1.15705i −0.978456 0.206457i \(-0.933807\pi\)
0.310431 0.950596i \(-0.399527\pi\)
\(84\) 0 0
\(85\) 8.88151 15.3832i 0.963336 1.66855i
\(86\) 2.86333 + 4.95943i 0.308760 + 0.534789i
\(87\) −3.13594 + 12.8696i −0.336208 + 1.37976i
\(88\) −1.02704 + 1.77889i −0.109483 + 0.189630i
\(89\) −7.41507 + 12.8433i −0.785996 + 1.36139i 0.142406 + 0.989808i \(0.454516\pi\)
−0.928402 + 0.371577i \(0.878817\pi\)
\(90\) −22.7452 + 14.5524i −2.39755 + 1.53396i
\(91\) 0 0
\(92\) −9.42101 16.3177i −0.982208 1.70123i
\(93\) −8.80039 8.40819i −0.912558 0.871889i
\(94\) −15.5411 −1.60294
\(95\) 7.21926 0.740681
\(96\) −0.675627 0.645517i −0.0689559 0.0658829i
\(97\) 4.74375 + 8.21642i 0.481655 + 0.834251i 0.999778 0.0210547i \(-0.00670241\pi\)
−0.518123 + 0.855306i \(0.673369\pi\)
\(98\) 0 0
\(99\) −1.08259 0.560893i −0.108804 0.0563719i
\(100\) −16.9897 + 29.4270i −1.69897 + 2.94270i
\(101\) −4.35588 + 7.54461i −0.433426 + 0.750716i −0.997166 0.0752364i \(-0.976029\pi\)
0.563739 + 0.825953i \(0.309362\pi\)
\(102\) −4.89922 + 20.1059i −0.485095 + 1.99078i
\(103\) −4.01356 6.95169i −0.395468 0.684970i 0.597693 0.801725i \(-0.296084\pi\)
−0.993161 + 0.116755i \(0.962751\pi\)
\(104\) 1.23016 2.13069i 0.120627 0.208931i
\(105\) 0 0
\(106\) 4.39037 + 7.60434i 0.426430 + 0.738599i
\(107\) −6.42101 + 11.1215i −0.620742 + 1.07516i 0.368605 + 0.929586i \(0.379835\pi\)
−0.989348 + 0.145571i \(0.953498\pi\)
\(108\) 13.8434 15.8783i 1.33208 1.52789i
\(109\) −1.30039 2.25234i −0.124555 0.215735i 0.797004 0.603974i \(-0.206417\pi\)
−0.921559 + 0.388239i \(0.873084\pi\)
\(110\) −3.65808 −0.348784
\(111\) 3.86908 1.13181i 0.367237 0.107427i
\(112\) 0 0
\(113\) 6.97509 12.0812i 0.656162 1.13651i −0.325440 0.945563i \(-0.605512\pi\)
0.981601 0.190942i \(-0.0611544\pi\)
\(114\) −8.07227 + 2.36135i −0.756038 + 0.221161i
\(115\) 8.50075 14.7237i 0.792699 1.37300i
\(116\) −15.5021 26.8505i −1.43934 2.49301i
\(117\) 1.29669 + 0.671818i 0.119879 + 0.0621096i
\(118\) 15.0543 1.38586
\(119\) 0 0
\(120\) 7.58113 31.1122i 0.692059 2.84014i
\(121\) 5.41741 + 9.38323i 0.492492 + 0.853021i
\(122\) −19.7508 −1.78815
\(123\) 12.4911 3.65399i 1.12629 0.329469i
\(124\) 28.4889 2.55837
\(125\) −12.3698 −1.10639
\(126\) 0 0
\(127\) −15.5438 −1.37929 −0.689643 0.724149i \(-0.742233\pi\)
−0.689643 + 0.724149i \(0.742233\pi\)
\(128\) −19.1082 −1.68894
\(129\) 0.954367 3.91663i 0.0840273 0.344840i
\(130\) 4.38151 0.384284
\(131\) 4.25696 + 7.37327i 0.371932 + 0.644205i 0.989863 0.142027i \(-0.0453621\pi\)
−0.617931 + 0.786233i \(0.712029\pi\)
\(132\) 2.73905 0.801244i 0.238404 0.0697393i
\(133\) 0 0
\(134\) 8.85973 0.765364
\(135\) 18.6534 + 3.65399i 1.60543 + 0.314485i
\(136\) −12.2709 21.2538i −1.05222 1.82250i
\(137\) −0.188621 + 0.326702i −0.0161150 + 0.0279120i −0.873970 0.485979i \(-0.838463\pi\)
0.857855 + 0.513891i \(0.171796\pi\)
\(138\) −4.68919 + 19.2440i −0.399170 + 1.63816i
\(139\) 9.50067 16.4556i 0.805837 1.39575i −0.109888 0.993944i \(-0.535049\pi\)
0.915725 0.401806i \(-0.131617\pi\)
\(140\) 0 0
\(141\) 7.91002 + 7.55750i 0.666144 + 0.636457i
\(142\) 20.8171 1.74693
\(143\) 0.0989221 + 0.171338i 0.00827228 + 0.0143280i
\(144\) 0.591443 + 12.9688i 0.0492869 + 1.08073i
\(145\) 13.9879 24.2277i 1.16163 2.01200i
\(146\) −2.42792 4.20528i −0.200936 0.348032i
\(147\) 0 0
\(148\) −4.71780 + 8.17147i −0.387801 + 0.671691i
\(149\) 4.85087 + 8.40196i 0.397399 + 0.688315i 0.993404 0.114665i \(-0.0365795\pi\)
−0.596005 + 0.802981i \(0.703246\pi\)
\(150\) 34.2829 10.0287i 2.79919 0.818837i
\(151\) 6.41741 11.1153i 0.522242 0.904549i −0.477424 0.878673i \(-0.658429\pi\)
0.999665 0.0258756i \(-0.00823738\pi\)
\(152\) 4.98715 8.63800i 0.404511 0.700634i
\(153\) 12.2709 7.85095i 0.992045 0.634711i
\(154\) 0 0
\(155\) 12.8530 + 22.2621i 1.03238 + 1.78813i
\(156\) −3.28074 + 0.959702i −0.262669 + 0.0768377i
\(157\) 20.9485 1.67187 0.835937 0.548825i \(-0.184925\pi\)
0.835937 + 0.548825i \(0.184925\pi\)
\(158\) 20.0833 1.59774
\(159\) 1.46334 6.00541i 0.116050 0.476260i
\(160\) 0.986757 + 1.70911i 0.0780100 + 0.135117i
\(161\) 0 0
\(162\) −22.0526 + 2.01561i −1.73262 + 0.158362i
\(163\) 5.58113 9.66679i 0.437148 0.757162i −0.560321 0.828276i \(-0.689322\pi\)
0.997468 + 0.0711140i \(0.0226554\pi\)
\(164\) −15.2312 + 26.3812i −1.18936 + 2.06002i
\(165\) 1.86186 + 1.77889i 0.144946 + 0.138486i
\(166\) −14.9746 25.9368i −1.16226 2.01309i
\(167\) −1.73012 + 2.99665i −0.133880 + 0.231888i −0.925169 0.379555i \(-0.876077\pi\)
0.791289 + 0.611443i \(0.209410\pi\)
\(168\) 0 0
\(169\) 6.38151 + 11.0531i 0.490886 + 0.850239i
\(170\) 21.8530 37.8505i 1.67605 2.90300i
\(171\) 5.25688 + 2.72361i 0.402004 + 0.208279i
\(172\) 4.71780 + 8.17147i 0.359729 + 0.623069i
\(173\) −6.05361 −0.460247 −0.230124 0.973161i \(-0.573913\pi\)
−0.230124 + 0.973161i \(0.573913\pi\)
\(174\) −7.71599 + 31.6657i −0.584948 + 2.40057i
\(175\) 0 0
\(176\) −0.879379 + 1.52313i −0.0662857 + 0.114810i
\(177\) −7.66225 7.32078i −0.575930 0.550263i
\(178\) −18.2448 + 31.6010i −1.36751 + 2.36859i
\(179\) −4.56654 7.90947i −0.341319 0.591182i 0.643359 0.765565i \(-0.277540\pi\)
−0.984678 + 0.174383i \(0.944207\pi\)
\(180\) −37.4764 + 23.9775i −2.79333 + 1.78717i
\(181\) 11.9478 0.888074 0.444037 0.896008i \(-0.353546\pi\)
0.444037 + 0.896008i \(0.353546\pi\)
\(182\) 0 0
\(183\) 10.0526 + 9.60462i 0.743111 + 0.709994i
\(184\) −11.7448 20.3427i −0.865841 1.49968i
\(185\) −8.51392 −0.625956
\(186\) −21.6534 20.6884i −1.58770 1.51695i
\(187\) 1.97351 0.144318
\(188\) −25.6065 −1.86755
\(189\) 0 0
\(190\) 17.7630 1.28867
\(191\) 9.14027 0.661367 0.330683 0.943742i \(-0.392721\pi\)
0.330683 + 0.943742i \(0.392721\pi\)
\(192\) 9.17638 + 8.76743i 0.662248 + 0.632735i
\(193\) 16.9430 1.21958 0.609792 0.792562i \(-0.291253\pi\)
0.609792 + 0.792562i \(0.291253\pi\)
\(194\) 11.6720 + 20.2165i 0.838003 + 1.45146i
\(195\) −2.23008 2.13069i −0.159699 0.152582i
\(196\) 0 0
\(197\) −21.3173 −1.51880 −0.759398 0.650627i \(-0.774506\pi\)
−0.759398 + 0.650627i \(0.774506\pi\)
\(198\) −2.66372 1.38008i −0.189302 0.0980780i
\(199\) −4.98715 8.63800i −0.353530 0.612332i 0.633335 0.773877i \(-0.281685\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(200\) −21.1804 + 36.6856i −1.49768 + 2.59406i
\(201\) −4.50937 4.30841i −0.318066 0.303892i
\(202\) −10.7177 + 18.5635i −0.754092 + 1.30613i
\(203\) 0 0
\(204\) −8.07227 + 33.1278i −0.565172 + 2.31941i
\(205\) −27.4868 −1.91976
\(206\) −9.87538 17.1047i −0.688051 1.19174i
\(207\) 11.7448 7.51437i 0.816323 0.522284i
\(208\) 1.05329 1.82435i 0.0730324 0.126496i
\(209\) 0.401038 + 0.694619i 0.0277404 + 0.0480478i
\(210\) 0 0
\(211\) −2.44592 + 4.23645i −0.168384 + 0.291649i −0.937852 0.347036i \(-0.887188\pi\)
0.769468 + 0.638685i \(0.220521\pi\)
\(212\) 7.23385 + 12.5294i 0.496823 + 0.860523i
\(213\) −10.5954 10.1232i −0.725982 0.693629i
\(214\) −15.7989 + 27.3645i −1.07999 + 1.87060i
\(215\) −4.25696 + 7.37327i −0.290322 + 0.502853i
\(216\) 17.2581 19.7950i 1.17426 1.34688i
\(217\) 0 0
\(218\) −3.19961 5.54189i −0.216705 0.375344i
\(219\) −0.809243 + 3.32105i −0.0546836 + 0.224416i
\(220\) −6.02728 −0.406359
\(221\) −2.36381 −0.159007
\(222\) 9.51990 2.78482i 0.638934 0.186905i
\(223\) 11.7044 + 20.2727i 0.783786 + 1.35756i 0.929722 + 0.368263i \(0.120047\pi\)
−0.145936 + 0.989294i \(0.546619\pi\)
\(224\) 0 0
\(225\) −22.3260 11.5672i −1.48840 0.771144i
\(226\) 17.1623 29.7259i 1.14162 1.97734i
\(227\) 3.05919 5.29868i 0.203046 0.351686i −0.746463 0.665427i \(-0.768249\pi\)
0.949508 + 0.313742i \(0.101583\pi\)
\(228\) −13.3004 + 3.89071i −0.880840 + 0.257669i
\(229\) −0.730195 1.26473i −0.0482526 0.0835760i 0.840890 0.541206i \(-0.182032\pi\)
−0.889143 + 0.457630i \(0.848699\pi\)
\(230\) 20.9161 36.2278i 1.37917 2.38879i
\(231\) 0 0
\(232\) −19.3260 33.4736i −1.26881 2.19765i
\(233\) 6.62422 11.4735i 0.433967 0.751653i −0.563244 0.826291i \(-0.690447\pi\)
0.997211 + 0.0746378i \(0.0237801\pi\)
\(234\) 3.19050 + 1.65301i 0.208570 + 0.108061i
\(235\) −11.5526 20.0097i −0.753610 1.30529i
\(236\) 24.8045 1.61463
\(237\) −10.2219 9.76631i −0.663981 0.634390i
\(238\) 0 0
\(239\) −9.69436 + 16.7911i −0.627076 + 1.08613i 0.361060 + 0.932543i \(0.382415\pi\)
−0.988136 + 0.153584i \(0.950918\pi\)
\(240\) 6.49115 26.6390i 0.419002 1.71954i
\(241\) 2.52684 4.37662i 0.162768 0.281923i −0.773092 0.634294i \(-0.781291\pi\)
0.935860 + 0.352371i \(0.114624\pi\)
\(242\) 13.3296 + 23.0875i 0.856857 + 1.48412i
\(243\) 12.2044 + 9.69810i 0.782911 + 0.622133i
\(244\) −32.5426 −2.08333
\(245\) 0 0
\(246\) 30.7345 8.99066i 1.95956 0.573223i
\(247\) −0.480350 0.831990i −0.0305639 0.0529383i
\(248\) 35.5161 2.25527
\(249\) −4.99115 + 20.4832i −0.316301 + 1.29807i
\(250\) −30.4360 −1.92494
\(251\) −15.0928 −0.952647 −0.476324 0.879270i \(-0.658031\pi\)
−0.476324 + 0.879270i \(0.658031\pi\)
\(252\) 0 0
\(253\) 1.88891 0.118755
\(254\) −38.2455 −2.39974
\(255\) −29.5290 + 8.63800i −1.84918 + 0.540933i
\(256\) −32.3609 −2.02256
\(257\) 3.85592 + 6.67865i 0.240526 + 0.416603i 0.960864 0.277020i \(-0.0893469\pi\)
−0.720338 + 0.693623i \(0.756014\pi\)
\(258\) 2.34822 9.63688i 0.146194 0.599966i
\(259\) 0 0
\(260\) 7.21926 0.447720
\(261\) 19.3260 12.3648i 1.19625 0.765361i
\(262\) 10.4743 + 18.1420i 0.647102 + 1.12081i
\(263\) −2.10603 + 3.64776i −0.129864 + 0.224930i −0.923624 0.383301i \(-0.874787\pi\)
0.793760 + 0.608231i \(0.208121\pi\)
\(264\) 3.41468 0.998883i 0.210159 0.0614770i
\(265\) −6.52724 + 11.3055i −0.400965 + 0.694492i
\(266\) 0 0
\(267\) 24.6534 7.21177i 1.50876 0.441353i
\(268\) 14.5979 0.891706
\(269\) 10.3753 + 17.9706i 0.632596 + 1.09569i 0.987019 + 0.160603i \(0.0513439\pi\)
−0.354423 + 0.935085i \(0.615323\pi\)
\(270\) 45.8968 + 8.99066i 2.79319 + 0.547154i
\(271\) −14.2444 + 24.6721i −0.865287 + 1.49872i 0.00147433 + 0.999999i \(0.499531\pi\)
−0.866762 + 0.498723i \(0.833803\pi\)
\(272\) −10.5067 18.1981i −0.637060 1.10342i
\(273\) 0 0
\(274\) −0.464103 + 0.803851i −0.0280375 + 0.0485624i
\(275\) −1.70321 2.95005i −0.102707 0.177895i
\(276\) −7.72620 + 31.7076i −0.465063 + 1.90857i
\(277\) −8.58113 + 14.8629i −0.515590 + 0.893028i 0.484246 + 0.874932i \(0.339094\pi\)
−0.999836 + 0.0180962i \(0.994239\pi\)
\(278\) 23.3765 40.4892i 1.40203 2.42838i
\(279\) 0.960429 + 21.0597i 0.0574994 + 1.26081i
\(280\) 0 0
\(281\) −4.72140 8.17770i −0.281655 0.487841i 0.690138 0.723678i \(-0.257550\pi\)
−0.971793 + 0.235837i \(0.924217\pi\)
\(282\) 19.4626 + 18.5953i 1.15898 + 1.10733i
\(283\) −16.8684 −1.00272 −0.501362 0.865237i \(-0.667168\pi\)
−0.501362 + 0.865237i \(0.667168\pi\)
\(284\) 34.2996 2.03531
\(285\) −9.04092 8.63800i −0.535538 0.511671i
\(286\) 0.243398 + 0.421578i 0.0143924 + 0.0249284i
\(287\) 0 0
\(288\) 0.0737345 + 1.61680i 0.00434485 + 0.0952711i
\(289\) −3.28959 + 5.69774i −0.193505 + 0.335161i
\(290\) 34.4172 59.6124i 2.02105 3.50056i
\(291\) 3.89037 15.9657i 0.228057 0.935926i
\(292\) −4.00040 6.92889i −0.234105 0.405483i
\(293\) −1.86143 + 3.22409i −0.108746 + 0.188353i −0.915262 0.402858i \(-0.868017\pi\)
0.806517 + 0.591211i \(0.201350\pi\)
\(294\) 0 0
\(295\) 11.1908 + 19.3830i 0.651551 + 1.12852i
\(296\) −5.88151 + 10.1871i −0.341856 + 0.592112i
\(297\) 0.684641 + 1.99777i 0.0397269 + 0.115922i
\(298\) 11.9356 + 20.6731i 0.691411 + 1.19756i
\(299\) −2.26247 −0.130842
\(300\) 56.4868 16.5239i 3.26126 0.954006i
\(301\) 0 0
\(302\) 15.7901 27.3492i 0.908617 1.57377i
\(303\) 14.4823 4.23645i 0.831986 0.243378i
\(304\) 4.27012 7.39607i 0.244908 0.424194i
\(305\) −14.6819 25.4298i −0.840683 1.45611i
\(306\) 30.1926 19.3173i 1.72600 1.10430i
\(307\) −30.5691 −1.74467 −0.872335 0.488908i \(-0.837395\pi\)
−0.872335 + 0.488908i \(0.837395\pi\)
\(308\) 0 0
\(309\) −3.29153 + 13.5081i −0.187249 + 0.768451i
\(310\) 31.6249 + 54.7759i 1.79617 + 3.11106i
\(311\) 10.4348 0.591702 0.295851 0.955234i \(-0.404397\pi\)
0.295851 + 0.955234i \(0.404397\pi\)
\(312\) −4.08998 + 1.19643i −0.231550 + 0.0677343i
\(313\) 0.619860 0.0350366 0.0175183 0.999847i \(-0.494423\pi\)
0.0175183 + 0.999847i \(0.494423\pi\)
\(314\) 51.5440 2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) 10.2484 0.575610 0.287805 0.957689i \(-0.407075\pi\)
0.287805 + 0.957689i \(0.407075\pi\)
\(318\) 3.60056 14.7763i 0.201909 0.828616i
\(319\) 3.10817 0.174024
\(320\) −13.4021 23.2132i −0.749203 1.29766i
\(321\) 21.3484 6.24496i 1.19155 0.348560i
\(322\) 0 0
\(323\) −9.58307 −0.533216
\(324\) −36.3353 + 3.32105i −2.01863 + 0.184503i
\(325\) 2.04005 + 3.53346i 0.113161 + 0.196001i
\(326\) 13.7324 23.7852i 0.760567 1.31734i
\(327\) −1.06645 + 4.37662i −0.0589750 + 0.242028i
\(328\) −18.9882 + 32.8885i −1.04845 + 1.81596i
\(329\) 0 0
\(330\) 4.58113 + 4.37697i 0.252183 + 0.240944i
\(331\) −20.3638 −1.11930 −0.559648 0.828730i \(-0.689064\pi\)
−0.559648 + 0.828730i \(0.689064\pi\)
\(332\) −24.6731 42.7351i −1.35411 2.34539i
\(333\) −6.19961 3.21204i −0.339737 0.176019i
\(334\) −4.25696 + 7.37327i −0.232930 + 0.403447i
\(335\) 6.58596 + 11.4072i 0.359829 + 0.623242i
\(336\) 0 0
\(337\) 2.85594 4.94662i 0.155573 0.269460i −0.777695 0.628642i \(-0.783611\pi\)
0.933267 + 0.359182i \(0.116944\pi\)
\(338\) 15.7017 + 27.1962i 0.854062 + 1.47928i
\(339\) −23.1906 + 6.78385i −1.25954 + 0.368448i
\(340\) 36.0064 62.3649i 1.95272 3.38221i
\(341\) −1.42800 + 2.47337i −0.0773305 + 0.133940i
\(342\) 12.9346 + 6.70145i 0.699422 + 0.362373i
\(343\) 0 0
\(344\) 5.88151 + 10.1871i 0.317110 + 0.549251i
\(345\) −28.2630 + 8.26768i −1.52163 + 0.445117i
\(346\) −14.8949 −0.800756
\(347\) 8.88132 0.476774 0.238387 0.971170i \(-0.423381\pi\)
0.238387 + 0.971170i \(0.423381\pi\)
\(348\) −12.7134 + 52.1744i −0.681507 + 2.79684i
\(349\) −10.4874 18.1648i −0.561379 0.972337i −0.997376 0.0723893i \(-0.976938\pi\)
0.435997 0.899948i \(-0.356396\pi\)
\(350\) 0 0
\(351\) −0.820039 2.39285i −0.0437704 0.127721i
\(352\) −0.109631 + 0.189886i −0.00584335 + 0.0101210i
\(353\) 7.38268 12.7872i 0.392941 0.680593i −0.599895 0.800078i \(-0.704791\pi\)
0.992836 + 0.119485i \(0.0381245\pi\)
\(354\) −18.8530 18.0128i −1.00203 0.957370i
\(355\) 15.4746 + 26.8028i 0.821306 + 1.42254i
\(356\) −30.0613 + 52.0677i −1.59325 + 2.75959i
\(357\) 0 0
\(358\) −11.2360 19.4613i −0.593840 1.02856i
\(359\) −3.60603 + 6.24583i −0.190319 + 0.329642i −0.945356 0.326040i \(-0.894286\pi\)
0.755037 + 0.655682i \(0.227619\pi\)
\(360\) −46.7205 + 29.8918i −2.46239 + 1.57544i
\(361\) 7.55262 + 13.0815i 0.397506 + 0.688501i
\(362\) 29.3977 1.54511
\(363\) 4.44284 18.2330i 0.233188 0.956983i
\(364\) 0 0
\(365\) 3.60963 6.25206i 0.188937 0.327248i
\(366\) 24.7345 + 23.6322i 1.29289 + 1.23528i
\(367\) 5.48711 9.50396i 0.286425 0.496103i −0.686529 0.727103i \(-0.740866\pi\)
0.972954 + 0.231000i \(0.0741998\pi\)
\(368\) −10.0562 17.4179i −0.524217 0.907970i
\(369\) −20.0151 10.3699i −1.04195 0.539836i
\(370\) −20.9485 −1.08906
\(371\) 0 0
\(372\) −35.6775 34.0875i −1.84979 1.76736i
\(373\) 0.271884 + 0.470916i 0.0140776 + 0.0243831i 0.872978 0.487759i \(-0.162185\pi\)
−0.858901 + 0.512142i \(0.828852\pi\)
\(374\) 4.85584 0.251090
\(375\) 15.4911 + 14.8008i 0.799959 + 0.764309i
\(376\) −31.9228 −1.64629
\(377\) −3.72286 −0.191737
\(378\) 0 0
\(379\) −22.6912 −1.16557 −0.582785 0.812626i \(-0.698037\pi\)
−0.582785 + 0.812626i \(0.698037\pi\)
\(380\) 29.2675 1.50139
\(381\) 19.4660 + 18.5985i 0.997272 + 0.952827i
\(382\) 22.4897 1.15067
\(383\) −17.8569 30.9291i −0.912447 1.58041i −0.810596 0.585606i \(-0.800857\pi\)
−0.101851 0.994800i \(-0.532477\pi\)
\(384\) 23.9298 + 22.8633i 1.22116 + 1.16674i
\(385\) 0 0
\(386\) 41.6883 2.12188
\(387\) −5.88151 + 3.76300i −0.298974 + 0.191284i
\(388\) 19.2316 + 33.3101i 0.976336 + 1.69106i
\(389\) −19.3296 + 33.4798i −0.980048 + 1.69749i −0.317892 + 0.948127i \(0.602975\pi\)
−0.662156 + 0.749366i \(0.730359\pi\)
\(390\) −5.48711 5.24258i −0.277851 0.265468i
\(391\) −11.2842 + 19.5447i −0.570664 + 0.988420i
\(392\) 0 0
\(393\) 3.49115 14.3273i 0.176105 0.722718i
\(394\) −52.4513 −2.64246
\(395\) 14.9291 + 25.8579i 0.751163 + 1.30105i
\(396\) −4.38891 2.27391i −0.220551 0.114268i
\(397\) 5.97391 10.3471i 0.299822 0.519307i −0.676273 0.736651i \(-0.736406\pi\)
0.976095 + 0.217344i \(0.0697394\pi\)
\(398\) −12.2709 21.2538i −0.615085 1.06536i
\(399\) 0 0
\(400\) −18.1352 + 31.4111i −0.906761 + 1.57056i
\(401\) −16.1783 28.0216i −0.807906 1.39933i −0.914312 0.405011i \(-0.867268\pi\)
0.106406 0.994323i \(-0.466066\pi\)
\(402\) −11.0953 10.6009i −0.553385 0.528723i
\(403\) 1.71041 2.96251i 0.0852015 0.147573i
\(404\) −17.6591 + 30.5865i −0.878573 + 1.52173i
\(405\) −18.9882 26.8952i −0.943530 1.33643i
\(406\) 0 0
\(407\) −0.472958 0.819187i −0.0234437 0.0406056i
\(408\) −10.0634 + 41.2993i −0.498213 + 2.04462i
\(409\) 18.9750 0.938254 0.469127 0.883131i \(-0.344569\pi\)
0.469127 + 0.883131i \(0.344569\pi\)
\(410\) −67.6313 −3.34007
\(411\) 0.627122 0.183450i 0.0309336 0.00904890i
\(412\) −16.2713 28.1827i −0.801630 1.38846i
\(413\) 0 0
\(414\) 28.8982 18.4891i 1.42027 0.908691i
\(415\) 22.2630 38.5607i 1.09285 1.89287i
\(416\) 0.131312 0.227439i 0.00643811 0.0111511i
\(417\) −31.5875 + 9.24018i −1.54685 + 0.452494i
\(418\) 0.986757 + 1.70911i 0.0482639 + 0.0835955i
\(419\) 8.64523 14.9740i 0.422347 0.731526i −0.573822 0.818980i \(-0.694540\pi\)
0.996169 + 0.0874539i \(0.0278730\pi\)
\(420\) 0 0
\(421\) −9.30039 16.1087i −0.453273 0.785092i 0.545314 0.838232i \(-0.316410\pi\)
−0.998587 + 0.0531397i \(0.983077\pi\)
\(422\) −6.01819 + 10.4238i −0.292961 + 0.507423i
\(423\) −0.863259 18.9290i −0.0419731 0.920360i
\(424\) 9.01819 + 15.6200i 0.437962 + 0.758572i
\(425\) 40.6993 1.97421
\(426\) −26.0699 24.9081i −1.26309 1.20680i
\(427\) 0 0
\(428\) −26.0313 + 45.0876i −1.25827 + 2.17939i
\(429\) 0.0811263 0.332935i 0.00391682 0.0160742i
\(430\) −10.4743 + 18.1420i −0.505114 + 0.874883i
\(431\) 7.93920 + 13.7511i 0.382418 + 0.662367i 0.991407 0.130811i \(-0.0417582\pi\)
−0.608990 + 0.793178i \(0.708425\pi\)
\(432\) 14.7768 16.9489i 0.710948 0.815456i
\(433\) 40.4367 1.94326 0.971631 0.236501i \(-0.0760007\pi\)
0.971631 + 0.236501i \(0.0760007\pi\)
\(434\) 0 0
\(435\) −46.5064 + 13.6043i −2.22981 + 0.652278i
\(436\) −5.27188 9.13117i −0.252477 0.437304i
\(437\) −9.17223 −0.438767
\(438\) −1.99115 + 8.17147i −0.0951406 + 0.390448i
\(439\) 12.4609 0.594728 0.297364 0.954764i \(-0.403892\pi\)
0.297364 + 0.954764i \(0.403892\pi\)
\(440\) −7.51399 −0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) −8.23073 −0.391054 −0.195527 0.980698i \(-0.562642\pi\)
−0.195527 + 0.980698i \(0.562642\pi\)
\(444\) 15.6856 4.58845i 0.744405 0.217758i
\(445\) −54.2498 −2.57169
\(446\) 28.7988 + 49.8810i 1.36366 + 2.36193i
\(447\) 3.97822 16.3262i 0.188163 0.772204i
\(448\) 0 0
\(449\) 5.64474 0.266392 0.133196 0.991090i \(-0.457476\pi\)
0.133196 + 0.991090i \(0.457476\pi\)
\(450\) −54.9332 28.4611i −2.58957 1.34167i
\(451\) −1.52692 2.64471i −0.0718999 0.124534i
\(452\) 28.2776 48.9783i 1.33007 2.30374i
\(453\) −21.3364 + 6.24146i −1.00247 + 0.293249i
\(454\) 7.52716 13.0374i 0.353267 0.611876i
\(455\) 0 0
\(456\) −16.5811 + 4.85041i −0.776482 + 0.227141i
\(457\) 5.06887 0.237112 0.118556 0.992947i \(-0.462174\pi\)
0.118556 + 0.992947i \(0.462174\pi\)
\(458\) −1.79665 3.11188i −0.0839518 0.145409i
\(459\) −24.7611 4.85041i −1.15575 0.226398i
\(460\) 34.4628 59.6913i 1.60683 2.78312i
\(461\) 3.88831 + 6.73475i 0.181097 + 0.313669i 0.942254 0.334898i \(-0.108702\pi\)
−0.761158 + 0.648567i \(0.775369\pi\)
\(462\) 0 0
\(463\) 4.58998 7.95008i 0.213314 0.369472i −0.739435 0.673228i \(-0.764907\pi\)
0.952750 + 0.303756i \(0.0982408\pi\)
\(464\) −16.5474 28.6609i −0.768192 1.33055i
\(465\) 10.5408 43.2584i 0.488818 2.00606i
\(466\) 16.2989 28.2306i 0.755033 1.30776i
\(467\) 6.88272 11.9212i 0.318494 0.551648i −0.661680 0.749787i \(-0.730156\pi\)
0.980174 + 0.198138i \(0.0634895\pi\)
\(468\) 5.25688 + 2.72361i 0.242999 + 0.125899i
\(469\) 0 0
\(470\) −28.4253 49.2340i −1.31116 2.27100i
\(471\) −26.2345 25.0654i −1.20882 1.15495i
\(472\) 30.9228 1.42334
\(473\) −0.945916 −0.0434933
\(474\) −25.1509 24.0301i −1.15522 1.10374i
\(475\) 8.27052 + 14.3250i 0.379477 + 0.657274i
\(476\) 0 0
\(477\) −9.01819 + 5.76985i −0.412914 + 0.264183i
\(478\) −23.8530 + 41.3146i −1.09101 + 1.88969i
\(479\) −4.35588 + 7.54461i −0.199025 + 0.344722i −0.948213 0.317636i \(-0.897111\pi\)
0.749187 + 0.662358i \(0.230444\pi\)
\(480\) 0.809243 3.32105i 0.0369367 0.151585i
\(481\) 0.566492 + 0.981194i 0.0258298 + 0.0447386i
\(482\) 6.21731 10.7687i 0.283191 0.490501i
\(483\) 0 0
\(484\) 21.9626 + 38.0404i 0.998302 + 1.72911i
\(485\) −17.3530 + 30.0563i −0.787960 + 1.36479i
\(486\) 30.0289 + 23.8622i 1.36214 + 1.08241i
\(487\) 9.01819 + 15.6200i 0.408653 + 0.707808i 0.994739 0.102441i \(-0.0326653\pi\)
−0.586086 + 0.810249i \(0.699332\pi\)
\(488\) −40.5697 −1.83651
\(489\) −18.5560 + 5.42810i −0.839129 + 0.245467i
\(490\) 0 0
\(491\) −1.02344 + 1.77266i −0.0461874 + 0.0799989i −0.888195 0.459467i \(-0.848040\pi\)
0.842007 + 0.539466i \(0.181374\pi\)
\(492\) 50.6402 14.8136i 2.28303 0.667848i
\(493\) −18.5679 + 32.1606i −0.836257 + 1.44844i
\(494\) −1.18190 2.04712i −0.0531763 0.0921041i
\(495\) −0.203194 4.45552i −0.00913290 0.200261i
\(496\) 30.4097 1.36544
\(497\) 0 0
\(498\) −12.2807 + 50.3990i −0.550313 + 2.25843i
\(499\) 19.5438 + 33.8508i 0.874899 + 1.51537i 0.856870 + 0.515532i \(0.172406\pi\)
0.0180291 + 0.999837i \(0.494261\pi\)
\(500\) −50.1484 −2.24270
\(501\) 5.75223 1.68268i 0.256991 0.0751766i
\(502\) −37.1358 −1.65745
\(503\) 5.11846 0.228221 0.114111 0.993468i \(-0.463598\pi\)
0.114111 + 0.993468i \(0.463598\pi\)
\(504\) 0 0
\(505\) −31.8683 −1.41812
\(506\) 4.64766 0.206614
\(507\) 5.23350 21.4778i 0.232428 0.953862i
\(508\) −63.0157 −2.79587
\(509\) 14.7636 + 25.5713i 0.654386 + 1.13343i 0.982047 + 0.188634i \(0.0604060\pi\)
−0.327662 + 0.944795i \(0.606261\pi\)
\(510\) −72.6562 + 21.2538i −3.21727 + 0.941136i
\(511\) 0 0
\(512\) −41.4078 −1.82998
\(513\) −3.32451 9.70083i −0.146780 0.428302i
\(514\) 9.48751 + 16.4328i 0.418476 + 0.724822i
\(515\) 14.6819 25.4298i 0.646962 1.12057i
\(516\) 3.86908 15.8783i 0.170327 0.699005i
\(517\) 1.28352 2.22313i 0.0564493 0.0977730i
\(518\) 0 0
\(519\) 7.58113 + 7.24327i 0.332775 + 0.317944i
\(520\) 9.00000 0.394676
\(521\) −0.532351 0.922058i −0.0233227 0.0403961i 0.854128 0.520062i \(-0.174091\pi\)
−0.877451 + 0.479666i \(0.840758\pi\)
\(522\) 47.5516 30.4236i 2.08128 1.33160i
\(523\) −6.69094 + 11.5890i −0.292574 + 0.506754i −0.974418 0.224745i \(-0.927845\pi\)
0.681843 + 0.731498i \(0.261179\pi\)
\(524\) 17.2581 + 29.8918i 0.753922 + 1.30583i
\(525\) 0 0
\(526\) −5.18190 + 8.97532i −0.225942 + 0.391343i
\(527\) −17.0615 29.5513i −0.743210 1.28728i
\(528\) 2.92373 0.855268i 0.127239 0.0372208i
\(529\) 0.699612 1.21176i 0.0304179 0.0526853i
\(530\) −16.0603 + 27.8173i −0.697615 + 1.20830i
\(531\) 0.836219 + 18.3361i 0.0362888 + 0.795719i
\(532\) 0 0
\(533\) 1.82889 + 3.16774i 0.0792181 + 0.137210i
\(534\) 60.6598 17.7446i 2.62501 0.767883i
\(535\) −46.9771 −2.03100
\(536\) 18.1986 0.786061
\(537\) −3.74503 + 15.3693i −0.161610 + 0.663232i
\(538\) 25.5286 + 44.2168i 1.10062 + 1.90632i
\(539\) 0 0
\(540\) 75.6224 + 14.8136i 3.25427 + 0.637475i
\(541\) 17.0438 29.5207i 0.732769 1.26919i −0.222927 0.974835i \(-0.571561\pi\)
0.955695 0.294358i \(-0.0951056\pi\)
\(542\) −35.0485 + 60.7058i −1.50546 + 2.60754i
\(543\) −14.9626 14.2958i −0.642108 0.613492i
\(544\) −1.30985 2.26873i −0.0561594 0.0972709i
\(545\) 4.75692 8.23922i 0.203764 0.352930i
\(546\) 0 0
\(547\) 2.97150 + 5.14678i 0.127052 + 0.220060i 0.922533 0.385918i \(-0.126115\pi\)
−0.795481 + 0.605978i \(0.792782\pi\)
\(548\) −0.764686 + 1.32448i −0.0326658 + 0.0565788i
\(549\) −1.09709 24.0564i −0.0468227 1.02670i
\(550\) −4.19076 7.25860i −0.178694 0.309508i
\(551\) −15.0928 −0.642974
\(552\) −9.63198 + 39.5287i −0.409964 + 1.68245i
\(553\) 0 0
\(554\) −21.1139 + 36.5704i −0.897044 + 1.55373i
\(555\) 10.6623 + 10.1871i 0.452587 + 0.432418i
\(556\) 38.5165 66.7126i 1.63346 2.82924i
\(557\) 15.0402 + 26.0503i 0.637272 + 1.10379i 0.986029 + 0.166575i \(0.0532707\pi\)
−0.348756 + 0.937213i \(0.613396\pi\)
\(558\) 2.36314 + 51.8175i 0.100040 + 2.19361i
\(559\) 1.13298 0.0479202
\(560\) 0 0
\(561\) −2.47150 2.36135i −0.104347 0.0996963i
\(562\) −11.6170 20.1213i −0.490035 0.848765i
\(563\) 19.6212 0.826935 0.413468 0.910519i \(-0.364317\pi\)
0.413468 + 0.910519i \(0.364317\pi\)
\(564\) 32.0679 + 30.6388i 1.35030 + 1.29012i
\(565\) 51.0308 2.14688
\(566\) −41.5049 −1.74458
\(567\) 0 0
\(568\) 42.7601 1.79417
\(569\) −1.37432 −0.0576144 −0.0288072 0.999585i \(-0.509171\pi\)
−0.0288072 + 0.999585i \(0.509171\pi\)
\(570\) −22.2452 21.2538i −0.931750 0.890226i
\(571\) 17.3815 0.727394 0.363697 0.931517i \(-0.381514\pi\)
0.363697 + 0.931517i \(0.381514\pi\)
\(572\) 0.401038 + 0.694619i 0.0167683 + 0.0290435i
\(573\) −11.4467 10.9365i −0.478191 0.456880i
\(574\) 0 0
\(575\) 38.9545 1.62451
\(576\) −1.00146 21.9595i −0.0417276 0.914978i
\(577\) −13.5274 23.4301i −0.563153 0.975409i −0.997219 0.0745283i \(-0.976255\pi\)
0.434066 0.900881i \(-0.357078\pi\)
\(578\) −8.09406 + 14.0193i −0.336668 + 0.583127i
\(579\) −21.2183 20.2727i −0.881801 0.842503i
\(580\) 56.7080 98.2211i 2.35467 4.07841i
\(581\) 0 0
\(582\) 9.57227 39.2837i 0.396783 1.62836i
\(583\) −1.45038 −0.0600687
\(584\) −4.98715 8.63800i −0.206370 0.357443i
\(585\) 0.243379 + 5.33667i 0.0100625 + 0.220644i
\(586\) −4.58005 + 7.93288i −0.189200 + 0.327704i
\(587\) 3.75700 + 6.50731i 0.155068 + 0.268585i 0.933084 0.359659i \(-0.117107\pi\)
−0.778016 + 0.628245i \(0.783774\pi\)
\(588\) 0 0
\(589\) 6.93414 12.0103i 0.285716 0.494875i
\(590\) 27.5349 + 47.6919i 1.13359 + 1.96344i
\(591\) 26.6964 + 25.5066i 1.09814 + 1.04920i
\(592\) −5.03590 + 8.72243i −0.206974 + 0.358490i
\(593\) 17.7904 30.8139i 0.730565 1.26538i −0.226077 0.974109i \(-0.572590\pi\)
0.956642 0.291266i \(-0.0940765\pi\)
\(594\) 1.68456 + 4.91551i 0.0691184 + 0.201686i
\(595\) 0 0
\(596\) 19.6659 + 34.0623i 0.805545 + 1.39524i
\(597\) −4.08998 + 16.7849i −0.167392 + 0.686960i
\(598\) −5.56681 −0.227644
\(599\) −11.4821 −0.469146 −0.234573 0.972099i \(-0.575369\pi\)
−0.234573 + 0.972099i \(0.575369\pi\)
\(600\) 70.4201 20.5997i 2.87489 0.840980i
\(601\) −0.190030 0.329142i −0.00775150 0.0134260i 0.862124 0.506698i \(-0.169134\pi\)
−0.869875 + 0.493272i \(0.835801\pi\)
\(602\) 0 0
\(603\) 0.492129 + 10.7911i 0.0200411 + 0.439448i
\(604\) 26.0167 45.0623i 1.05861 1.83356i
\(605\) −19.8173 + 34.3246i −0.805688 + 1.39549i
\(606\) 35.6337 10.4238i 1.44752 0.423438i
\(607\) −9.27044 16.0569i −0.376275 0.651728i 0.614242 0.789118i \(-0.289462\pi\)
−0.990517 + 0.137390i \(0.956129\pi\)
\(608\) 0.532351 0.922058i 0.0215897 0.0373944i
\(609\) 0 0
\(610\) −36.1249 62.5702i −1.46265 2.53339i
\(611\) −1.53736 + 2.66278i −0.0621949 + 0.107725i
\(612\) 49.7473 31.8284i 2.01092 1.28659i
\(613\) −3.66225 6.34321i −0.147917 0.256200i 0.782540 0.622600i \(-0.213924\pi\)
−0.930457 + 0.366400i \(0.880590\pi\)
\(614\) −75.2154 −3.03545
\(615\) 34.4226 + 32.8885i 1.38805 + 1.32619i
\(616\) 0 0
\(617\) 12.7427 22.0710i 0.513002 0.888546i −0.486884 0.873466i \(-0.661867\pi\)
0.999886 0.0150791i \(-0.00480000\pi\)
\(618\) −8.09884 + 33.2368i −0.325783 + 1.33698i
\(619\) 16.4482 28.4891i 0.661108 1.14507i −0.319217 0.947682i \(-0.603420\pi\)
0.980325 0.197391i \(-0.0632468\pi\)
\(620\) 52.1072 + 90.2523i 2.09267 + 3.62462i
\(621\) −23.6995 4.64247i −0.951030 0.186296i
\(622\) 25.6748 1.02947
\(623\) 0 0
\(624\) −3.50194 + 1.02441i −0.140190 + 0.0410092i
\(625\) −1.67111 2.89444i −0.0668443 0.115778i
\(626\) 1.52517 0.0609580
\(627\) 0.328893 1.34974i 0.0131347 0.0539036i
\(628\) 84.9271 3.38896
\(629\) 11.3016 0.450626
\(630\) 0 0
\(631\) 29.8683 1.18904 0.594519 0.804082i \(-0.297343\pi\)
0.594519 + 0.804082i \(0.297343\pi\)
\(632\) 41.2527 1.64094
\(633\) 8.13210 2.37885i 0.323222 0.0945509i
\(634\) 25.2163 1.00147
\(635\) −28.4301 49.2424i −1.12822 1.95413i
\(636\) 5.93251 24.3464i 0.235239 0.965399i
\(637\) 0 0
\(638\) 7.64766 0.302774
\(639\) 1.15632 + 25.3552i 0.0457434 + 1.00303i
\(640\) −34.9496 60.5344i −1.38150 2.39283i
\(641\) −5.73025 + 9.92509i −0.226331 + 0.392017i −0.956718 0.291016i \(-0.906007\pi\)
0.730387 + 0.683034i \(0.239340\pi\)
\(642\) 52.5278 15.3658i 2.07311 0.606438i
\(643\) −8.69078 + 15.0529i −0.342731 + 0.593627i −0.984939 0.172903i \(-0.944685\pi\)
0.642208 + 0.766531i \(0.278019\pi\)
\(644\) 0 0
\(645\) 14.1534 4.14024i 0.557290 0.163022i
\(646\) −23.5792 −0.927711
\(647\) 12.6720 + 21.9485i 0.498186 + 0.862883i 0.999998 0.00209358i \(-0.000666408\pi\)
−0.501812 + 0.864977i \(0.667333\pi\)
\(648\) −45.2979 + 4.14024i −1.77947 + 0.162644i
\(649\) −1.24332 + 2.15349i −0.0488045 + 0.0845320i
\(650\) 5.01954 + 8.69410i 0.196883 + 0.341011i
\(651\) 0 0
\(652\) 22.6264 39.1900i 0.886116 1.53480i
\(653\) −7.04163 12.1965i −0.275560 0.477284i 0.694716 0.719284i \(-0.255530\pi\)
−0.970276 + 0.242000i \(0.922197\pi\)
\(654\) −2.62401 + 10.7687i −0.102607 + 0.421089i
\(655\) −15.5723 + 26.9720i −0.608459 + 1.05388i
\(656\) −16.2581 + 28.1599i −0.634774 + 1.09946i
\(657\) 4.98715 3.19079i 0.194567 0.124484i
\(658\) 0 0
\(659\) −19.0854 33.0569i −0.743462 1.28771i −0.950910 0.309467i \(-0.899849\pi\)
0.207449 0.978246i \(-0.433484\pi\)
\(660\) 7.54815 + 7.21177i 0.293812 + 0.280718i
\(661\) 0.353732 0.0137586 0.00687930 0.999976i \(-0.497810\pi\)
0.00687930 + 0.999976i \(0.497810\pi\)
\(662\) −50.1052 −1.94740
\(663\) 2.96027 + 2.82834i 0.114967 + 0.109844i
\(664\) −30.7591 53.2764i −1.19369 2.06752i
\(665\) 0 0
\(666\) −15.2542 7.90324i −0.591087 0.306244i
\(667\) −17.7719 + 30.7818i −0.688130 + 1.19188i
\(668\) −7.01403 + 12.1487i −0.271381 + 0.470046i
\(669\) 9.59884 39.3927i 0.371112 1.52301i
\(670\) 16.2048 + 28.0675i 0.626045 + 1.08434i
\(671\) 1.63119 2.82531i 0.0629715 0.109070i
\(672\) 0 0
\(673\) 10.5555 + 18.2827i 0.406886 + 0.704748i 0.994539 0.104365i \(-0.0332811\pi\)
−0.587653 + 0.809113i \(0.699948\pi\)
\(674\) 7.02704 12.1712i 0.270672 0.468817i
\(675\) 14.1192 + 41.1994i 0.543447 + 1.58577i
\(676\) 25.8712 + 44.8102i 0.995046 + 1.72347i
\(677\) −21.1464 −0.812721 −0.406361 0.913713i \(-0.633202\pi\)
−0.406361 + 0.913713i \(0.633202\pi\)
\(678\) −57.0605 + 16.6917i −2.19140 + 0.641041i
\(679\) 0 0
\(680\) 44.8879 77.7482i 1.72137 2.98151i
\(681\) −10.1711 + 2.97532i −0.389758 + 0.114014i
\(682\) −3.51360 + 6.08573i −0.134543 + 0.233035i
\(683\) −17.3858 30.1131i −0.665249 1.15224i −0.979218 0.202811i \(-0.934992\pi\)
0.313969 0.949433i \(-0.398341\pi\)
\(684\) 21.3118 + 11.0417i 0.814878 + 0.422191i
\(685\) −1.37998 −0.0527264
\(686\) 0 0
\(687\) −0.598835 + 2.45756i −0.0228470 + 0.0937618i
\(688\) 5.03590 + 8.72243i 0.191992 + 0.332539i
\(689\) 1.73722 0.0661827
\(690\) −69.5413 + 20.3427i −2.64739 + 0.774432i
\(691\) −34.6492 −1.31812 −0.659059 0.752091i \(-0.729045\pi\)
−0.659059 + 0.752091i \(0.729045\pi\)
\(692\) −24.5418 −0.932940
\(693\) 0 0
\(694\) 21.8525 0.829511
\(695\) 69.5083 2.63660
\(696\) −15.8493 + 65.0440i −0.600766 + 2.46548i
\(697\) 36.4868 1.38203
\(698\) −25.8044 44.6945i −0.976710 1.69171i
\(699\) −22.0240 + 6.44260i −0.833024 + 0.243681i
\(700\) 0 0
\(701\) −48.6050 −1.83579 −0.917894 0.396826i \(-0.870111\pi\)
−0.917894 + 0.396826i \(0.870111\pi\)
\(702\) −2.01771 5.88763i −0.0761535 0.222214i
\(703\) 2.29661 + 3.97784i 0.0866182 + 0.150027i
\(704\) 1.48901 2.57904i 0.0561192 0.0972012i
\(705\) −9.47434 + 38.8818i −0.356824 + 1.46437i
\(706\) 18.1651 31.4629i 0.683654 1.18412i
\(707\) 0 0
\(708\) −31.0634 29.6791i −1.16743 1.11541i
\(709\) 4.10817 0.154286 0.0771428 0.997020i \(-0.475420\pi\)
0.0771428 + 0.997020i \(0.475420\pi\)
\(710\) 38.0753 + 65.9483i 1.42894 + 2.47500i
\(711\) 1.11556 + 24.4613i 0.0418368 + 0.917372i
\(712\) −37.4764 + 64.9110i −1.40449 + 2.43264i
\(713\) −16.3300 28.2844i −0.611564 1.05926i
\(714\) 0 0
\(715\) −0.361864 + 0.626767i −0.0135330 + 0.0234398i
\(716\) −18.5131 32.0657i −0.691868 1.19835i
\(717\) 32.2315 9.42856i 1.20371 0.352116i
\(718\) −8.87266 + 15.3679i −0.331125 + 0.573525i
\(719\) 24.1408 41.8131i 0.900299 1.55936i 0.0731939 0.997318i \(-0.476681\pi\)
0.827106 0.562047i \(-0.189986\pi\)
\(720\) −40.0032 + 25.5941i −1.49083 + 0.953837i
\(721\) 0 0
\(722\) 18.5833 + 32.1872i 0.691597 + 1.19788i
\(723\) −8.40116 + 2.45756i −0.312443 + 0.0913977i
\(724\) 48.4375 1.80016
\(725\) 64.0990 2.38058
\(726\) 10.9316 44.8623i 0.405711 1.66500i
\(727\) −20.5151 35.5332i −0.760863 1.31785i −0.942406 0.334470i \(-0.891443\pi\)
0.181543 0.983383i \(-0.441891\pi\)
\(728\) 0 0
\(729\) −3.67996 26.7480i −0.136295 0.990668i
\(730\) 8.88151 15.3832i 0.328720 0.569359i
\(731\) 5.65082 9.78750i 0.209003 0.362004i
\(732\) 40.7542 + 38.9379i 1.50632 + 1.43919i
\(733\) 15.2714 + 26.4508i 0.564062 + 0.976983i 0.997136 + 0.0756253i \(0.0240953\pi\)
−0.433075 + 0.901358i \(0.642571\pi\)
\(734\) 13.5011 23.3845i 0.498334 0.863139i
\(735\) 0 0
\(736\) −1.25370 2.17147i −0.0462118 0.0800413i
\(737\) −0.731715 + 1.26737i −0.0269531 + 0.0466841i
\(738\) −49.2474 25.5152i −1.81282 0.939228i
\(739\) −11.9100 20.6288i −0.438117 0.758841i 0.559427 0.828880i \(-0.311021\pi\)
−0.997544 + 0.0700384i \(0.977688\pi\)
\(740\) −34.5161 −1.26884
\(741\) −0.393936 + 1.61668i −0.0144716 + 0.0593901i
\(742\) 0 0
\(743\) −5.26089 + 9.11213i −0.193003 + 0.334292i −0.946244 0.323453i \(-0.895156\pi\)
0.753241 + 0.657745i \(0.228490\pi\)
\(744\) −44.4779 42.4957i −1.63064 1.55797i
\(745\) −17.7449 + 30.7350i −0.650121 + 1.12604i
\(746\) 0.668971 + 1.15869i 0.0244928 + 0.0424227i
\(747\) 30.7591 19.6797i 1.12542 0.720044i
\(748\) 8.00079 0.292538
\(749\) 0 0
\(750\) 38.1160 + 36.4174i 1.39180 + 1.32977i
\(751\) 5.13521 + 8.89445i 0.187386 + 0.324563i 0.944378 0.328862i \(-0.106665\pi\)
−0.756992 + 0.653425i \(0.773332\pi\)
\(752\) −27.3330 −0.996734
\(753\) 18.9012 + 18.0588i 0.688797 + 0.658100i
\(754\) −9.16010 −0.333591
\(755\) 46.9507 1.70871
\(756\) 0 0
\(757\) 8.03930 0.292193 0.146097 0.989270i \(-0.453329\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(758\) −55.8319 −2.02791
\(759\) −2.36554 2.26012i −0.0858636 0.0820371i
\(760\) 36.4868 1.32351
\(761\) 13.8302 + 23.9547i 0.501345 + 0.868355i 0.999999 + 0.00155404i \(0.000494668\pi\)
−0.498654 + 0.866801i \(0.666172\pi\)
\(762\) 47.8961 + 45.7616i 1.73509 + 1.65777i
\(763\) 0 0
\(764\) 37.0554 1.34062
\(765\) 47.3157 + 24.5144i 1.71070 + 0.886320i
\(766\) −43.9371 76.1013i −1.58751 2.74965i
\(767\) 1.48920 2.57938i 0.0537720 0.0931359i
\(768\) 40.5266 + 38.7205i 1.46238 + 1.39721i
\(769\) −16.9613 + 29.3778i −0.611640 + 1.05939i 0.379324 + 0.925264i \(0.376157\pi\)
−0.990964 + 0.134128i \(0.957177\pi\)
\(770\) 0 0
\(771\) 3.16225 12.9776i 0.113886 0.467376i
\(772\) 68.6883 2.47215
\(773\) −14.2978 24.7645i −0.514256 0.890717i −0.999863 0.0165403i \(-0.994735\pi\)
0.485607 0.874177i \(-0.338599\pi\)
\(774\) −14.4715 + 9.25888i −0.520167 + 0.332804i
\(775\) −29.4493 + 51.0077i −1.05785 + 1.83225i
\(776\) 23.9753 + 41.5265i 0.860664 + 1.49071i
\(777\) 0 0
\(778\) −47.5605 + 82.3772i −1.70513 + 2.95337i
\(779\) 7.41449 + 12.8423i 0.265652 + 0.460122i
\(780\) −9.04092 8.63800i −0.323717 0.309290i
\(781\) −1.71926 + 2.97785i −0.0615200 + 0.106556i