Properties

Label 441.2.h.g.214.6
Level $441$
Weight $2$
Character 441.214
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 214.6
Root \(-1.82904 + 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.g.373.6

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.0892047 + 0.996013i \(0.471567\pi\)
−0.907175 + 0.420753i \(0.861766\pi\)
\(6\) 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 0.833763 0.552122i \(-0.186182\pi\)
−0.895033 + 0.445999i \(0.852848\pi\)
\(12\) 5.07706 4.85080i 1.46562 1.40030i
\(13\) −0.243398 0.421578i −0.0675065 0.116925i 0.830297 0.557322i \(-0.188171\pi\)
−0.897803 + 0.440397i \(0.854838\pi\)
\(14\) 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 −0.405525 0.914084i \(-0.632911\pi\)
0.994382 0.105847i \(-0.0337553\pi\)
\(18\) 0.336285 7.37385i 0.0792631 1.73803i
\(19\) −0.986757 1.70911i −0.226378 0.392097i 0.730354 0.683069i \(-0.239355\pi\)
−0.956732 + 0.290971i \(0.906022\pi\)
\(20\) −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 −0.999843 0.0177464i \(-0.994351\pi\)
0.515290 + 0.857016i \(0.327684\pi\)
\(24\) 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 0.254764 + 0.967003i \(0.418002\pi\)
−0.964831 + 0.262870i \(0.915331\pi\)
\(30\) 3.69076 + 15.1465i 0.673837 + 2.76536i
\(31\) −7.02720 −1.26212 −0.631061 0.775733i \(-0.717380\pi\)
−0.631061 + 0.775733i \(0.717380\pi\)
\(32\) 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 0.754372 0.656447i \(-0.227941\pi\)
−0.945686 + 0.325082i \(0.894608\pi\)
\(38\) −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 0.994655 + 0.103249i \(0.0329240\pi\)
−0.407911 + 0.913022i \(0.633743\pi\)
\(42\) 0 0
\(43\) 1.16372 2.01561i 0.177465 0.307378i −0.763547 0.645753i \(-0.776544\pi\)
0.941012 + 0.338374i \(0.109877\pi\)
\(44\) −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 \(-0.347613\pi\)
0.460658 + 0.887578i \(0.347613\pi\)
\(48\) 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 −0.717062 0.697010i \(-0.754513\pi\)
0.962159 + 0.272489i \(0.0878467\pi\)
\(54\) −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 \(-0.630390\pi\)
−0.398273 + 0.917267i \(0.630390\pi\)
\(60\) 6.08113 + 24.9564i 0.785070 + 3.22185i
\(61\) 8.02712 1.02777 0.513884 0.857860i \(-0.328206\pi\)
0.513884 + 0.857860i \(0.328206\pi\)
\(62\) −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 \(-0.796489\pi\)
0.917976 + 0.396636i \(0.129822\pi\)
\(74\) −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 −0.310431 0.950596i \(-0.600473\pi\)
0.978456 0.206457i \(-0.0661933\pi\)
\(84\) 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 0.928402 + 0.371577i \(0.121183\pi\)
−0.142406 + 0.989808i \(0.545484\pi\)
\(90\) 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 \(-0.993298\pi\)
0.518123 + 0.855306i \(0.326631\pi\)
\(98\) 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 \(-0.0239711\pi\)
−0.563739 + 0.825953i \(0.690638\pi\)
\(102\) −4.89922 20.1059i −0.485095 1.99078i
\(103\) 4.01356 6.95169i 0.395468 0.684970i −0.597693 0.801725i \(-0.703916\pi\)
0.993161 + 0.116755i \(0.0372492\pi\)
\(104\) −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 −0.989348 0.145571i \(-0.953498\pi\)
0.368605 0.929586i \(-0.379835\pi\)
\(108\) −13.8434 15.8783i −1.33208 1.52789i
\(109\) −1.30039 + 2.25234i −0.124555 + 0.215735i −0.921559 0.388239i \(-0.873084\pi\)
0.797004 + 0.603974i \(0.206417\pi\)
\(110\) 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 0.981601 + 0.190942i \(0.0611544\pi\)
−0.325440 + 0.945563i \(0.605512\pi\)
\(114\) −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 \(-0.954638\pi\)
0.617931 + 0.786233i \(0.287971\pi\)
\(132\) −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 0.857855 0.513891i \(-0.171796\pi\)
−0.873970 + 0.485979i \(0.838463\pi\)
\(138\) 4.68919 + 19.2440i 0.399170 + 1.63816i
\(139\) −9.50067 16.4556i −0.805837 1.39575i −0.915725 0.401806i \(-0.868383\pi\)
0.109888 0.993944i \(-0.464951\pi\)
\(140\) 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 −0.596005 0.802981i \(-0.703246\pi\)
0.993404 + 0.114665i \(0.0365795\pi\)
\(150\) −34.2829 10.0287i −2.79919 0.818837i
\(151\) 6.41741 + 11.1153i 0.522242 + 0.904549i 0.999665 + 0.0258756i \(0.00823738\pi\)
−0.477424 + 0.878673i \(0.658429\pi\)
\(152\) −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 \(-0.815075\pi\)
−0.835937 + 0.548825i \(0.815075\pi\)
\(158\) 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 0.997468 0.0711140i \(-0.0226554\pi\)
−0.560321 + 0.828276i \(0.689322\pi\)
\(164\) 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 \(-0.123923\pi\)
−0.791289 + 0.611443i \(0.790590\pi\)
\(168\) 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 \(-0.426087\pi\)
0.230124 + 0.973161i \(0.426087\pi\)
\(174\) 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 −0.984678 0.174383i \(-0.944207\pi\)
0.643359 + 0.765565i \(0.277540\pi\)
\(180\) 37.4764 + 23.9775i 2.79333 + 1.78717i
\(181\) −11.9478 −0.888074 −0.444037 0.896008i \(-0.646454\pi\)
−0.444037 + 0.896008i \(0.646454\pi\)
\(182\) 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 \(-0.718315\pi\)
0.986865 + 0.161546i \(0.0516479\pi\)
\(200\) −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 0.769468 0.638685i \(-0.220521\pi\)
−0.937852 + 0.347036i \(0.887188\pi\)
\(212\) 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 0.145936 + 0.989294i \(0.453381\pi\)
−0.929722 + 0.368263i \(0.879953\pi\)
\(224\) 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 \(-0.231751\pi\)
−0.949508 + 0.313742i \(0.898417\pi\)
\(228\) −13.3004 3.89071i −0.880840 0.257669i
\(229\) 0.730195 1.26473i 0.0482526 0.0835760i −0.840890 0.541206i \(-0.817968\pi\)
0.889143 + 0.457630i \(0.151301\pi\)
\(230\) −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 0.997211 0.0746378i \(-0.0237801\pi\)
−0.563244 + 0.826291i \(0.690447\pi\)
\(234\) −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 −0.988136 0.153584i \(-0.950918\pi\)
0.361060 0.932543i \(-0.382415\pi\)
\(240\) 6.49115 + 26.6390i 0.419002 + 1.71954i
\(241\) −2.52684 4.37662i −0.162768 0.281923i 0.773092 0.634294i \(-0.218709\pi\)
−0.935860 + 0.352371i \(0.885376\pi\)
\(242\) 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 \(-0.341969\pi\)
0.476324 + 0.879270i \(0.341969\pi\)
\(252\) 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 \(-0.910653\pi\)
0.720338 + 0.693623i \(0.243986\pi\)
\(258\) −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 0.793760 0.608231i \(-0.208121\pi\)
−0.923624 + 0.383301i \(0.874787\pi\)
\(264\) −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 0.354423 + 0.935085i \(0.384677\pi\)
−0.987019 + 0.160603i \(0.948656\pi\)
\(270\) 45.8968 8.99066i 2.79319 0.547154i
\(271\) 14.2444 + 24.6721i 0.865287 + 1.49872i 0.866762 + 0.498723i \(0.166197\pi\)
−0.00147433 + 0.999999i \(0.500469\pi\)
\(272\) 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 −0.999836 0.0180962i \(-0.994239\pi\)
0.484246 0.874932i \(-0.339094\pi\)
\(278\) −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 −0.971793 0.235837i \(-0.924217\pi\)
0.690138 + 0.723678i \(0.257550\pi\)
\(282\) 19.4626 18.5953i 1.15898 1.10733i
\(283\) 16.8684 1.00272 0.501362 0.865237i \(-0.332832\pi\)
0.501362 + 0.865237i \(0.332832\pi\)
\(284\) 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 \(-0.131983\pi\)
−0.806517 + 0.591211i \(0.798650\pi\)
\(294\) 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 \(-0.162605\pi\)
0.872335 + 0.488908i \(0.162605\pi\)
\(308\) 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 \(-0.595603\pi\)
−0.295851 + 0.955234i \(0.595603\pi\)
\(312\) −4.08998 1.19643i −0.231550 0.0677343i
\(313\) −0.619860 −0.0350366 −0.0175183 0.999847i \(-0.505577\pi\)
−0.0175183 + 0.999847i \(0.505577\pi\)
\(314\) −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 0.933267 0.359182i \(-0.116944\pi\)
−0.777695 + 0.628642i \(0.783611\pi\)
\(338\) 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 −0.435997 0.899948i \(-0.643604\pi\)
0.997376 0.0723893i \(-0.0230624\pi\)
\(350\) 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 \(-0.295209\pi\)
−0.992836 + 0.119485i \(0.961876\pi\)
\(354\) −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 0.755037 0.655682i \(-0.227619\pi\)
−0.945356 + 0.326040i \(0.894286\pi\)
\(360\) 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 \(-0.259134\pi\)
−0.972954 + 0.231000i \(0.925800\pi\)
\(368\) −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 −0.858901 0.512142i \(-0.828852\pi\)
0.872978 + 0.487759i \(0.162185\pi\)
\(374\) −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 0.101851 0.994800i \(-0.467523\pi\)
0.810596 0.585606i \(-0.199143\pi\)
\(384\) −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 −0.662156 0.749366i \(-0.730359\pi\)
−0.317892 0.948127i \(-0.602975\pi\)
\(390\) 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 \(-0.263594\pi\)
−0.976095 + 0.217344i \(0.930261\pi\)
\(398\) 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 0.106406 + 0.994323i \(0.466066\pi\)
−0.914312 + 0.405011i \(0.867268\pi\)
\(402\) 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 \(-0.655431\pi\)
−0.469127 + 0.883131i \(0.655431\pi\)
\(410\) −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 \(-0.305460\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(420\) 0 0
\(421\) −9.30039 + 16.1087i −0.453273 + 0.785092i −0.998587 0.0531397i \(-0.983077\pi\)
0.545314 + 0.838232i \(0.316410\pi\)
\(422\) −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 −0.608990 0.793178i \(-0.708425\pi\)
0.991407 + 0.130811i \(0.0417582\pi\)
\(432\) −14.7768 16.9489i −0.710948 0.815456i
\(433\) −40.4367 −1.94326 −0.971631 0.236501i \(-0.923999\pi\)
−0.971631 + 0.236501i \(0.923999\pi\)
\(434\) 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 \(-0.596108\pi\)
−0.297364 + 0.954764i \(0.596108\pi\)
\(440\) 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 \(-0.891298\pi\)
0.761158 + 0.648567i \(0.224631\pi\)
\(462\) 0 0
\(463\) 4.58998 + 7.95008i 0.213314 + 0.369472i 0.952750 0.303756i \(-0.0982408\pi\)
−0.739435 + 0.673228i \(0.764907\pi\)
\(464\) −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 \(-0.269844\pi\)
−0.980174 + 0.198138i \(0.936511\pi\)
\(468\) −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 \(-0.102889\pi\)
−0.749187 + 0.662358i \(0.769556\pi\)
\(480\) 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 −0.586086 0.810249i \(-0.699332\pi\)
0.994739 + 0.102441i \(0.0326653\pi\)
\(488\) 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 0.842007 0.539466i \(-0.181374\pi\)
−0.888195 + 0.459467i \(0.848040\pi\)
\(492\) 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 0.0180291 0.999837i \(-0.494261\pi\)
0.856870 0.515532i \(-0.172406\pi\)
\(500\) 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 \(-0.536402\pi\)
−0.114111 + 0.993468i \(0.536402\pi\)
\(504\) 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 0.327662 + 0.944795i \(0.393739\pi\)
−0.982047 + 0.188634i \(0.939594\pi\)
\(510\) 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 \(-0.825909\pi\)
0.877451 + 0.479666i \(0.159242\pi\)
\(522\) 47.5516 + 30.4236i 2.08128 + 1.33160i
\(523\) 6.69094 + 11.5890i 0.292574 + 0.506754i 0.974418 0.224745i \(-0.0721548\pi\)
−0.681843 + 0.731498i \(0.738821\pi\)
\(524\) −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 0.955695 + 0.294358i \(0.0951056\pi\)
−0.222927 + 0.974835i \(0.571561\pi\)
\(542\) 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 −0.795481 0.605978i \(-0.792782\pi\)
0.922533 + 0.385918i \(0.126115\pi\)
\(548\) −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 −0.348756 0.937213i \(-0.613396\pi\)
0.986029 0.166575i \(-0.0532707\pi\)
\(558\) −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 \(-0.635683\pi\)
−0.413468 + 0.910519i \(0.635683\pi\)
\(564\) 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 −0.434066 0.900881i \(-0.642922\pi\)
0.997219 0.0745283i \(-0.0237451\pi\)
\(578\) −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 \(-0.882893\pi\)
0.778016 + 0.628245i \(0.216226\pi\)
\(588\) 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 −0.956642 0.291266i \(-0.905924\pi\)
0.226077 0.974109i \(-0.427410\pi\)
\(594\) −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 \(-0.830866\pi\)
0.869875 + 0.493272i \(0.164199\pi\)
\(602\) 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 \(-0.710538\pi\)
0.990517 + 0.137390i \(0.0438713\pi\)
\(608\) −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 −0.930457 0.366400i \(-0.880590\pi\)
0.782540 + 0.622600i \(0.213924\pi\)
\(614\) 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 0.999886 + 0.0150791i \(0.00480000\pi\)
−0.486884 + 0.873466i \(0.661867\pi\)
\(618\) −8.09884 33.2368i −0.325783 1.33698i
\(619\) −16.4482 28.4891i −0.661108 1.14507i −0.980325 0.197391i \(-0.936753\pi\)
0.319217 0.947682i \(-0.396580\pi\)
\(620\) 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 0.730387 0.683034i \(-0.239340\pi\)
−0.956718 + 0.291016i \(0.906007\pi\)
\(642\) −52.5278 15.3658i −2.07311 0.606438i
\(643\) 8.69078 + 15.0529i 0.342731 + 0.593627i 0.984939 0.172903i \(-0.0553147\pi\)
−0.642208 + 0.766531i \(0.721981\pi\)
\(644\) 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 \(-0.999334\pi\)
0.501812 + 0.864977i \(0.332667\pi\)
\(648\) −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 −0.970276 0.242000i \(-0.922197\pi\)
0.694716 + 0.719284i \(0.255530\pi\)
\(654\) 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 0.207449 + 0.978246i \(0.433484\pi\)
−0.950910 + 0.309467i \(0.899849\pi\)
\(660\) 7.54815 7.21177i 0.293812 0.280718i
\(661\) −0.353732 −0.0137586 −0.00687930 0.999976i \(-0.502190\pi\)
−0.00687930 + 0.999976i \(0.502190\pi\)
\(662\) −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 −0.587653 0.809113i \(-0.699948\pi\)
0.994539 + 0.104365i \(0.0332811\pi\)
\(674\) 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 \(-0.366798\pi\)
0.406361 + 0.913713i \(0.366798\pi\)
\(678\) 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 0.313969 + 0.949433i \(0.398341\pi\)
−0.979218 + 0.202811i \(0.934992\pi\)
\(684\) −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 \(-0.270955\pi\)
0.659059 + 0.752091i \(0.270955\pi\)
\(692\) 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 −0.827106 0.562047i \(-0.810014\pi\)
−0.0731939 0.997318i \(-0.523319\pi\)
\(720\) 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 −0.181543 0.983383i \(-0.558109\pi\)
0.942406 0.334470i \(-0.108557\pi\)
\(728\) 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 0.433075 + 0.901358i \(0.357429\pi\)
−0.997136 + 0.0756253i \(0.975905\pi\)
\(734\) −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 −0.997544 0.0700384i \(-0.977688\pi\)
0.559427 + 0.828880i \(0.311021\pi\)
\(740\) 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 0.753241 0.657745i \(-0.228490\pi\)
−0.946244 + 0.323453i \(0.895156\pi\)
\(744\) −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 −0.756992 0.653425i \(-0.773332\pi\)
0.944378 + 0.328862i \(0.106665\pi\)
\(752\) 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 0.498654 + 0.866801i \(0.333828\pi\)
−0.999999 + 0.00155404i \(0.999505\pi\)
\(762\) −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 0.990964 + 0.134128i \(0.0428233\pi\)
−0.379324 + 0.925264i \(0.623843\pi\)
\(770\) 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 −0.485607 0.874177i \(-0.661401\pi\)
0.999863 0.0165403i \(-0.00526518\pi\)
\(774\) −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