Properties

Label 495.2.n.h.361.4
Level $495$
Weight $2$
Character 495.361
Analytic conductor $3.953$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} - 172 x^{7} + 471 x^{6} - 430 x^{5} + 383 x^{4} + 70 x^{3} + 17 x^{2} + 4 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.4
Root \(2.46673 + 1.79218i\) of defining polynomial
Character \(\chi\) \(=\) 495.361
Dual form 495.2.n.h.181.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.633189 - 1.94876i) q^{2} +(-1.77869 - 1.29229i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.477268 + 0.346756i) q^{7} +(-0.329192 + 0.239172i) q^{8} +O(q^{10})\) \(q+(0.633189 - 1.94876i) q^{2} +(-1.77869 - 1.29229i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.477268 + 0.346756i) q^{7} +(-0.329192 + 0.239172i) q^{8} -2.04904 q^{10} +(0.933738 - 3.18247i) q^{11} +(0.465044 - 1.43126i) q^{13} +(0.977943 - 0.710517i) q^{14} +(-1.10115 - 3.38900i) q^{16} +(-1.52036 - 4.67919i) q^{17} +(-5.51798 + 4.00905i) q^{19} +(-0.679399 + 2.09098i) q^{20} +(-5.61063 - 3.83474i) q^{22} +0.0822934 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-2.49471 - 1.81252i) q^{26} +(-0.400802 - 1.23354i) q^{28} +(6.81551 + 4.95175i) q^{29} +(-0.611585 + 1.88227i) q^{31} -8.11537 q^{32} -10.0813 q^{34} +(0.182300 - 0.561062i) q^{35} +(2.89625 + 2.10425i) q^{37} +(4.31873 + 13.2917i) q^{38} +(0.329192 + 0.239172i) q^{40} +(3.29530 - 2.39417i) q^{41} +4.86148 q^{43} +(-5.77352 + 4.45397i) q^{44} +(0.0521073 - 0.160370i) q^{46} +(4.67492 - 3.39653i) q^{47} +(-2.05557 - 6.32640i) q^{49} +(0.633189 + 1.94876i) q^{50} +(-2.67678 + 1.94479i) q^{52} +(-2.09317 + 6.44213i) q^{53} +(-3.31525 + 0.0954005i) q^{55} -0.240047 q^{56} +(13.9653 - 10.1464i) q^{58} +(-4.51758 - 3.28221i) q^{59} +(-0.296732 - 0.913248i) q^{61} +(3.28083 + 2.38366i) q^{62} +(-2.93627 + 9.03690i) q^{64} -1.50491 q^{65} +13.6559 q^{67} +(-3.34264 + 10.2876i) q^{68} +(-0.977943 - 0.710517i) q^{70} +(0.396714 + 1.22096i) q^{71} +(12.6426 + 9.18538i) q^{73} +(5.93455 - 4.31171i) q^{74} +14.9956 q^{76} +(1.54918 - 1.19511i) q^{77} +(-3.44622 + 10.6064i) q^{79} +(-2.88285 + 2.09451i) q^{80} +(-2.57911 - 7.93770i) q^{82} +(1.23982 + 3.81578i) q^{83} +(-3.98036 + 2.89190i) q^{85} +(3.07824 - 9.47385i) q^{86} +(0.453779 + 1.27097i) q^{88} -6.08177 q^{89} +(0.718247 - 0.521837i) q^{91} +(-0.146374 - 0.106347i) q^{92} +(-3.65890 - 11.2609i) q^{94} +(5.51798 + 4.00905i) q^{95} +(-2.07220 + 6.37757i) q^{97} -13.6302 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.633189 1.94876i 0.447733 1.37798i −0.431726 0.902005i \(-0.642095\pi\)
0.879459 0.475975i \(-0.157905\pi\)
\(3\) 0 0
\(4\) −1.77869 1.29229i −0.889345 0.646147i
\(5\) −0.309017 0.951057i −0.138197 0.425325i
\(6\) 0 0
\(7\) 0.477268 + 0.346756i 0.180390 + 0.131061i 0.674316 0.738443i \(-0.264439\pi\)
−0.493926 + 0.869504i \(0.664439\pi\)
\(8\) −0.329192 + 0.239172i −0.116387 + 0.0845600i
\(9\) 0 0
\(10\) −2.04904 −0.647965
\(11\) 0.933738 3.18247i 0.281533 0.959552i
\(12\) 0 0
\(13\) 0.465044 1.43126i 0.128980 0.396960i −0.865625 0.500693i \(-0.833079\pi\)
0.994605 + 0.103733i \(0.0330787\pi\)
\(14\) 0.977943 0.710517i 0.261366 0.189894i
\(15\) 0 0
\(16\) −1.10115 3.38900i −0.275288 0.847249i
\(17\) −1.52036 4.67919i −0.368742 1.13487i −0.947604 0.319446i \(-0.896503\pi\)
0.578862 0.815425i \(-0.303497\pi\)
\(18\) 0 0
\(19\) −5.51798 + 4.00905i −1.26591 + 0.919739i −0.999032 0.0439914i \(-0.985993\pi\)
−0.266880 + 0.963730i \(0.585993\pi\)
\(20\) −0.679399 + 2.09098i −0.151918 + 0.467556i
\(21\) 0 0
\(22\) −5.61063 3.83474i −1.19619 0.817569i
\(23\) 0.0822934 0.0171594 0.00857968 0.999963i \(-0.497269\pi\)
0.00857968 + 0.999963i \(0.497269\pi\)
\(24\) 0 0
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) −2.49471 1.81252i −0.489253 0.355463i
\(27\) 0 0
\(28\) −0.400802 1.23354i −0.0757444 0.233117i
\(29\) 6.81551 + 4.95175i 1.26561 + 0.919518i 0.999019 0.0442926i \(-0.0141034\pi\)
0.266589 + 0.963810i \(0.414103\pi\)
\(30\) 0 0
\(31\) −0.611585 + 1.88227i −0.109844 + 0.338065i −0.990837 0.135065i \(-0.956876\pi\)
0.880993 + 0.473130i \(0.156876\pi\)
\(32\) −8.11537 −1.43461
\(33\) 0 0
\(34\) −10.0813 −1.72893
\(35\) 0.182300 0.561062i 0.0308144 0.0948368i
\(36\) 0 0
\(37\) 2.89625 + 2.10425i 0.476141 + 0.345937i 0.799830 0.600227i \(-0.204923\pi\)
−0.323689 + 0.946164i \(0.604923\pi\)
\(38\) 4.31873 + 13.2917i 0.700591 + 2.15620i
\(39\) 0 0
\(40\) 0.329192 + 0.239172i 0.0520498 + 0.0378164i
\(41\) 3.29530 2.39417i 0.514639 0.373907i −0.299942 0.953958i \(-0.596967\pi\)
0.814581 + 0.580050i \(0.196967\pi\)
\(42\) 0 0
\(43\) 4.86148 0.741369 0.370685 0.928759i \(-0.379123\pi\)
0.370685 + 0.928759i \(0.379123\pi\)
\(44\) −5.77352 + 4.45397i −0.870391 + 0.671461i
\(45\) 0 0
\(46\) 0.0521073 0.160370i 0.00768280 0.0236452i
\(47\) 4.67492 3.39653i 0.681908 0.495435i −0.192082 0.981379i \(-0.561524\pi\)
0.873990 + 0.485944i \(0.161524\pi\)
\(48\) 0 0
\(49\) −2.05557 6.32640i −0.293653 0.903772i
\(50\) 0.633189 + 1.94876i 0.0895465 + 0.275596i
\(51\) 0 0
\(52\) −2.67678 + 1.94479i −0.371202 + 0.269694i
\(53\) −2.09317 + 6.44213i −0.287520 + 0.884894i 0.698112 + 0.715988i \(0.254024\pi\)
−0.985632 + 0.168906i \(0.945976\pi\)
\(54\) 0 0
\(55\) −3.31525 + 0.0954005i −0.447029 + 0.0128638i
\(56\) −0.240047 −0.0320776
\(57\) 0 0
\(58\) 13.9653 10.1464i 1.83373 1.33228i
\(59\) −4.51758 3.28221i −0.588138 0.427308i 0.253511 0.967333i \(-0.418415\pi\)
−0.841649 + 0.540025i \(0.818415\pi\)
\(60\) 0 0
\(61\) −0.296732 0.913248i −0.0379927 0.116929i 0.930261 0.366897i \(-0.119580\pi\)
−0.968254 + 0.249968i \(0.919580\pi\)
\(62\) 3.28083 + 2.38366i 0.416666 + 0.302725i
\(63\) 0 0
\(64\) −2.93627 + 9.03690i −0.367033 + 1.12961i
\(65\) −1.50491 −0.186662
\(66\) 0 0
\(67\) 13.6559 1.66834 0.834168 0.551511i \(-0.185948\pi\)
0.834168 + 0.551511i \(0.185948\pi\)
\(68\) −3.34264 + 10.2876i −0.405355 + 1.24755i
\(69\) 0 0
\(70\) −0.977943 0.710517i −0.116887 0.0849231i
\(71\) 0.396714 + 1.22096i 0.0470813 + 0.144901i 0.971834 0.235668i \(-0.0757279\pi\)
−0.924752 + 0.380570i \(0.875728\pi\)
\(72\) 0 0
\(73\) 12.6426 + 9.18538i 1.47970 + 1.07507i 0.977652 + 0.210230i \(0.0674214\pi\)
0.502052 + 0.864837i \(0.332579\pi\)
\(74\) 5.93455 4.31171i 0.689878 0.501226i
\(75\) 0 0
\(76\) 14.9956 1.72012
\(77\) 1.54918 1.19511i 0.176546 0.136196i
\(78\) 0 0
\(79\) −3.44622 + 10.6064i −0.387730 + 1.19331i 0.546751 + 0.837295i \(0.315865\pi\)
−0.934481 + 0.356014i \(0.884135\pi\)
\(80\) −2.88285 + 2.09451i −0.322313 + 0.234174i
\(81\) 0 0
\(82\) −2.57911 7.93770i −0.284816 0.876572i
\(83\) 1.23982 + 3.81578i 0.136088 + 0.418837i 0.995758 0.0920140i \(-0.0293305\pi\)
−0.859669 + 0.510851i \(0.829330\pi\)
\(84\) 0 0
\(85\) −3.98036 + 2.89190i −0.431731 + 0.313671i
\(86\) 3.07824 9.47385i 0.331935 1.02159i
\(87\) 0 0
\(88\) 0.453779 + 1.27097i 0.0483730 + 0.135486i
\(89\) −6.08177 −0.644667 −0.322333 0.946626i \(-0.604467\pi\)
−0.322333 + 0.946626i \(0.604467\pi\)
\(90\) 0 0
\(91\) 0.718247 0.521837i 0.0752928 0.0547034i
\(92\) −0.146374 0.106347i −0.0152606 0.0110875i
\(93\) 0 0
\(94\) −3.65890 11.2609i −0.377387 1.16148i
\(95\) 5.51798 + 4.00905i 0.566133 + 0.411320i
\(96\) 0 0
\(97\) −2.07220 + 6.37757i −0.210400 + 0.647544i 0.789048 + 0.614331i \(0.210574\pi\)
−0.999448 + 0.0332133i \(0.989426\pi\)
\(98\) −13.6302 −1.37686
\(99\) 0 0
\(100\) 2.19858 0.219858
\(101\) 1.83730 5.65462i 0.182818 0.562656i −0.817086 0.576516i \(-0.804412\pi\)
0.999904 + 0.0138601i \(0.00441195\pi\)
\(102\) 0 0
\(103\) −1.56592 1.13771i −0.154294 0.112101i 0.507959 0.861381i \(-0.330400\pi\)
−0.662254 + 0.749280i \(0.730400\pi\)
\(104\) 0.189228 + 0.582384i 0.0185553 + 0.0571074i
\(105\) 0 0
\(106\) 11.2288 + 8.15818i 1.09063 + 0.792392i
\(107\) 6.70449 4.87110i 0.648148 0.470907i −0.214492 0.976726i \(-0.568810\pi\)
0.862640 + 0.505819i \(0.168810\pi\)
\(108\) 0 0
\(109\) 3.18782 0.305338 0.152669 0.988277i \(-0.451213\pi\)
0.152669 + 0.988277i \(0.451213\pi\)
\(110\) −1.91327 + 6.52103i −0.182423 + 0.621756i
\(111\) 0 0
\(112\) 0.649609 1.99929i 0.0613822 0.188915i
\(113\) 9.29605 6.75398i 0.874499 0.635361i −0.0572913 0.998358i \(-0.518246\pi\)
0.931790 + 0.362997i \(0.118246\pi\)
\(114\) 0 0
\(115\) −0.0254300 0.0782656i −0.00237136 0.00729831i
\(116\) −5.72355 17.6153i −0.531418 1.63554i
\(117\) 0 0
\(118\) −9.25671 + 6.72540i −0.852150 + 0.619123i
\(119\) 0.896916 2.76042i 0.0822202 0.253048i
\(120\) 0 0
\(121\) −9.25627 5.94319i −0.841479 0.540290i
\(122\) −1.96759 −0.178137
\(123\) 0 0
\(124\) 3.52026 2.55762i 0.316129 0.229681i
\(125\) 0.809017 + 0.587785i 0.0723607 + 0.0525731i
\(126\) 0 0
\(127\) 5.62146 + 17.3011i 0.498824 + 1.53522i 0.810911 + 0.585170i \(0.198972\pi\)
−0.312087 + 0.950054i \(0.601028\pi\)
\(128\) 2.62055 + 1.90394i 0.231626 + 0.168286i
\(129\) 0 0
\(130\) −0.952896 + 2.93271i −0.0835745 + 0.257216i
\(131\) −18.7758 −1.64045 −0.820225 0.572041i \(-0.806152\pi\)
−0.820225 + 0.572041i \(0.806152\pi\)
\(132\) 0 0
\(133\) −4.02371 −0.348900
\(134\) 8.64678 26.6121i 0.746968 2.29893i
\(135\) 0 0
\(136\) 1.61962 + 1.17672i 0.138881 + 0.100903i
\(137\) 1.46073 + 4.49567i 0.124799 + 0.384091i 0.993864 0.110606i \(-0.0352791\pi\)
−0.869066 + 0.494697i \(0.835279\pi\)
\(138\) 0 0
\(139\) 14.9456 + 10.8586i 1.26767 + 0.921013i 0.999107 0.0422509i \(-0.0134529\pi\)
0.268558 + 0.963264i \(0.413453\pi\)
\(140\) −1.04931 + 0.762370i −0.0886831 + 0.0644321i
\(141\) 0 0
\(142\) 2.63055 0.220751
\(143\) −4.12071 2.81641i −0.344591 0.235520i
\(144\) 0 0
\(145\) 2.60329 8.01211i 0.216192 0.665369i
\(146\) 25.9052 18.8213i 2.14393 1.55766i
\(147\) 0 0
\(148\) −2.43223 7.48563i −0.199928 0.615315i
\(149\) −4.79009 14.7424i −0.392420 1.20774i −0.930953 0.365140i \(-0.881021\pi\)
0.538533 0.842604i \(-0.318979\pi\)
\(150\) 0 0
\(151\) −4.49360 + 3.26479i −0.365684 + 0.265685i −0.755419 0.655242i \(-0.772567\pi\)
0.389735 + 0.920927i \(0.372567\pi\)
\(152\) 0.857623 2.63949i 0.0695624 0.214091i
\(153\) 0 0
\(154\) −1.34806 3.77571i −0.108630 0.304256i
\(155\) 1.97913 0.158968
\(156\) 0 0
\(157\) 14.9761 10.8808i 1.19522 0.868381i 0.201418 0.979505i \(-0.435445\pi\)
0.993807 + 0.111124i \(0.0354451\pi\)
\(158\) 18.4871 + 13.4317i 1.47076 + 1.06857i
\(159\) 0 0
\(160\) 2.50779 + 7.71818i 0.198258 + 0.610176i
\(161\) 0.0392760 + 0.0285357i 0.00309538 + 0.00224893i
\(162\) 0 0
\(163\) 2.41484 7.43210i 0.189145 0.582127i −0.810851 0.585253i \(-0.800995\pi\)
0.999995 + 0.00312615i \(0.000995086\pi\)
\(164\) −8.95529 −0.699291
\(165\) 0 0
\(166\) 8.22108 0.638080
\(167\) −1.84233 + 5.67010i −0.142564 + 0.438766i −0.996690 0.0813005i \(-0.974093\pi\)
0.854126 + 0.520066i \(0.174093\pi\)
\(168\) 0 0
\(169\) 8.68499 + 6.31001i 0.668076 + 0.485386i
\(170\) 3.11529 + 9.58788i 0.238932 + 0.735357i
\(171\) 0 0
\(172\) −8.64707 6.28247i −0.659333 0.479034i
\(173\) −13.4085 + 9.74186i −1.01943 + 0.740660i −0.966166 0.257920i \(-0.916963\pi\)
−0.0532650 + 0.998580i \(0.516963\pi\)
\(174\) 0 0
\(175\) −0.589936 −0.0445949
\(176\) −11.8136 + 0.339950i −0.890482 + 0.0256247i
\(177\) 0 0
\(178\) −3.85092 + 11.8519i −0.288638 + 0.888337i
\(179\) −17.4300 + 12.6637i −1.30278 + 0.946526i −0.999979 0.00652751i \(-0.997922\pi\)
−0.302802 + 0.953053i \(0.597922\pi\)
\(180\) 0 0
\(181\) −6.23300 19.1832i −0.463295 1.42588i −0.861114 0.508411i \(-0.830233\pi\)
0.397819 0.917464i \(-0.369767\pi\)
\(182\) −0.562147 1.73011i −0.0416691 0.128244i
\(183\) 0 0
\(184\) −0.0270903 + 0.0196823i −0.00199712 + 0.00145100i
\(185\) 1.10627 3.40475i 0.0813346 0.250322i
\(186\) 0 0
\(187\) −16.3110 + 0.469370i −1.19278 + 0.0343237i
\(188\) −12.7046 −0.926575
\(189\) 0 0
\(190\) 11.3066 8.21471i 0.820266 0.595958i
\(191\) 13.1782 + 9.57452i 0.953541 + 0.692788i 0.951642 0.307210i \(-0.0993954\pi\)
0.00189928 + 0.999998i \(0.499395\pi\)
\(192\) 0 0
\(193\) 1.03505 + 3.18555i 0.0745043 + 0.229301i 0.981373 0.192113i \(-0.0615340\pi\)
−0.906868 + 0.421414i \(0.861534\pi\)
\(194\) 11.1162 + 8.07642i 0.798100 + 0.579853i
\(195\) 0 0
\(196\) −4.51935 + 13.9091i −0.322811 + 0.993509i
\(197\) 9.78158 0.696909 0.348454 0.937326i \(-0.386707\pi\)
0.348454 + 0.937326i \(0.386707\pi\)
\(198\) 0 0
\(199\) 9.89054 0.701121 0.350561 0.936540i \(-0.385991\pi\)
0.350561 + 0.936540i \(0.385991\pi\)
\(200\) 0.125740 0.386988i 0.00889117 0.0273642i
\(201\) 0 0
\(202\) −9.85612 7.16089i −0.693474 0.503838i
\(203\) 1.53577 + 4.72663i 0.107790 + 0.331744i
\(204\) 0 0
\(205\) −3.29530 2.39417i −0.230154 0.167216i
\(206\) −3.20863 + 2.33121i −0.223556 + 0.162423i
\(207\) 0 0
\(208\) −5.36261 −0.371830
\(209\) 7.60634 + 21.3042i 0.526141 + 1.47364i
\(210\) 0 0
\(211\) −6.85049 + 21.0836i −0.471607 + 1.45146i 0.378873 + 0.925449i \(0.376312\pi\)
−0.850480 + 0.526008i \(0.823688\pi\)
\(212\) 12.0482 8.75355i 0.827476 0.601197i
\(213\) 0 0
\(214\) −5.24737 16.1497i −0.358703 1.10397i
\(215\) −1.50228 4.62355i −0.102455 0.315323i
\(216\) 0 0
\(217\) −0.944576 + 0.686275i −0.0641220 + 0.0465874i
\(218\) 2.01850 6.21229i 0.136710 0.420750i
\(219\) 0 0
\(220\) 6.02009 + 4.11459i 0.405875 + 0.277406i
\(221\) −7.40417 −0.498058
\(222\) 0 0
\(223\) −9.98313 + 7.25317i −0.668520 + 0.485708i −0.869529 0.493881i \(-0.835578\pi\)
0.201010 + 0.979589i \(0.435578\pi\)
\(224\) −3.87321 2.81405i −0.258790 0.188022i
\(225\) 0 0
\(226\) −7.27570 22.3923i −0.483972 1.48951i
\(227\) −6.65140 4.83252i −0.441469 0.320746i 0.344750 0.938695i \(-0.387964\pi\)
−0.786218 + 0.617949i \(0.787964\pi\)
\(228\) 0 0
\(229\) 8.35722 25.7209i 0.552261 1.69968i −0.150810 0.988563i \(-0.548188\pi\)
0.703070 0.711120i \(-0.251812\pi\)
\(230\) −0.168623 −0.0111187
\(231\) 0 0
\(232\) −3.42793 −0.225055
\(233\) −7.72672 + 23.7804i −0.506194 + 1.55791i 0.292559 + 0.956247i \(0.405493\pi\)
−0.798753 + 0.601659i \(0.794507\pi\)
\(234\) 0 0
\(235\) −4.67492 3.39653i −0.304958 0.221565i
\(236\) 3.79379 + 11.6761i 0.246955 + 0.760048i
\(237\) 0 0
\(238\) −4.81148 3.49574i −0.311882 0.226595i
\(239\) −16.7638 + 12.1796i −1.08436 + 0.787835i −0.978438 0.206539i \(-0.933780\pi\)
−0.105924 + 0.994374i \(0.533780\pi\)
\(240\) 0 0
\(241\) −23.4295 −1.50923 −0.754615 0.656168i \(-0.772176\pi\)
−0.754615 + 0.656168i \(0.772176\pi\)
\(242\) −17.4428 + 14.2750i −1.12127 + 0.917635i
\(243\) 0 0
\(244\) −0.652390 + 2.00785i −0.0417650 + 0.128539i
\(245\) −5.38156 + 3.90993i −0.343815 + 0.249796i
\(246\) 0 0
\(247\) 3.17188 + 9.76204i 0.201822 + 0.621144i
\(248\) −0.248856 0.765901i −0.0158024 0.0486347i
\(249\) 0 0
\(250\) 1.65771 1.20440i 0.104843 0.0761728i
\(251\) 3.17352 9.76710i 0.200311 0.616494i −0.799563 0.600583i \(-0.794935\pi\)
0.999873 0.0159107i \(-0.00506475\pi\)
\(252\) 0 0
\(253\) 0.0768405 0.261896i 0.00483092 0.0164653i
\(254\) 37.2751 2.33885
\(255\) 0 0
\(256\) −10.0049 + 7.26896i −0.625304 + 0.454310i
\(257\) −1.57711 1.14584i −0.0983774 0.0714753i 0.537509 0.843258i \(-0.319365\pi\)
−0.635886 + 0.771783i \(0.719365\pi\)
\(258\) 0 0
\(259\) 0.652629 + 2.00858i 0.0405524 + 0.124807i
\(260\) 2.67678 + 1.94479i 0.166007 + 0.120611i
\(261\) 0 0
\(262\) −11.8886 + 36.5895i −0.734483 + 2.26051i
\(263\) −8.80234 −0.542775 −0.271388 0.962470i \(-0.587483\pi\)
−0.271388 + 0.962470i \(0.587483\pi\)
\(264\) 0 0
\(265\) 6.77365 0.416102
\(266\) −2.54777 + 7.84124i −0.156214 + 0.480777i
\(267\) 0 0
\(268\) −24.2896 17.6475i −1.48373 1.07799i
\(269\) 3.76512 + 11.5878i 0.229563 + 0.706523i 0.997796 + 0.0663529i \(0.0211363\pi\)
−0.768233 + 0.640171i \(0.778864\pi\)
\(270\) 0 0
\(271\) −10.0039 7.26827i −0.607694 0.441516i 0.240907 0.970548i \(-0.422555\pi\)
−0.848602 + 0.529032i \(0.822555\pi\)
\(272\) −14.1836 + 10.3050i −0.860008 + 0.624833i
\(273\) 0 0
\(274\) 9.68590 0.585146
\(275\) 1.11520 + 3.12351i 0.0672491 + 0.188355i
\(276\) 0 0
\(277\) 6.34377 19.5241i 0.381160 1.17309i −0.558067 0.829796i \(-0.688457\pi\)
0.939228 0.343295i \(-0.111543\pi\)
\(278\) 30.6241 22.2497i 1.83671 1.33445i
\(279\) 0 0
\(280\) 0.0741786 + 0.228298i 0.00443302 + 0.0136434i
\(281\) 3.53113 + 10.8677i 0.210650 + 0.648313i 0.999434 + 0.0336429i \(0.0107109\pi\)
−0.788784 + 0.614670i \(0.789289\pi\)
\(282\) 0 0
\(283\) −23.8919 + 17.3585i −1.42023 + 1.03186i −0.428493 + 0.903545i \(0.640956\pi\)
−0.991734 + 0.128311i \(0.959044\pi\)
\(284\) 0.872208 2.68438i 0.0517560 0.159289i
\(285\) 0 0
\(286\) −8.09769 + 6.24694i −0.478826 + 0.369389i
\(287\) 2.40293 0.141841
\(288\) 0 0
\(289\) −5.83007 + 4.23579i −0.342945 + 0.249164i
\(290\) −13.9653 10.1464i −0.820069 0.595815i
\(291\) 0 0
\(292\) −10.6170 32.6759i −0.621316 1.91221i
\(293\) −9.38171 6.81621i −0.548085 0.398207i 0.278994 0.960293i \(-0.409999\pi\)
−0.827079 + 0.562086i \(0.809999\pi\)
\(294\) 0 0
\(295\) −1.72556 + 5.31073i −0.100466 + 0.309203i
\(296\) −1.45670 −0.0846690
\(297\) 0 0
\(298\) −31.7624 −1.83995
\(299\) 0.0382700 0.117783i 0.00221321 0.00681157i
\(300\) 0 0
\(301\) 2.32023 + 1.68575i 0.133736 + 0.0971648i
\(302\) 3.51699 + 10.8242i 0.202380 + 0.622861i
\(303\) 0 0
\(304\) 19.6628 + 14.2858i 1.12774 + 0.819349i
\(305\) −0.776855 + 0.564418i −0.0444826 + 0.0323185i
\(306\) 0 0
\(307\) 1.27309 0.0726593 0.0363296 0.999340i \(-0.488433\pi\)
0.0363296 + 0.999340i \(0.488433\pi\)
\(308\) −4.29996 + 0.123737i −0.245013 + 0.00705054i
\(309\) 0 0
\(310\) 1.25317 3.85685i 0.0711750 0.219054i
\(311\) −3.96859 + 2.88335i −0.225038 + 0.163500i −0.694592 0.719404i \(-0.744415\pi\)
0.469553 + 0.882904i \(0.344415\pi\)
\(312\) 0 0
\(313\) −4.76494 14.6650i −0.269331 0.828914i −0.990664 0.136326i \(-0.956470\pi\)
0.721333 0.692588i \(-0.243530\pi\)
\(314\) −11.7213 36.0744i −0.661470 2.03580i
\(315\) 0 0
\(316\) 19.8363 14.4119i 1.11588 0.810734i
\(317\) 10.3782 31.9408i 0.582897 1.79397i −0.0246573 0.999696i \(-0.507849\pi\)
0.607555 0.794278i \(-0.292151\pi\)
\(318\) 0 0
\(319\) 22.1227 17.0665i 1.23863 0.955542i
\(320\) 9.50196 0.531175
\(321\) 0 0
\(322\) 0.0804782 0.0584709i 0.00448488 0.00325845i
\(323\) 27.1484 + 19.7245i 1.51058 + 1.09750i
\(324\) 0 0
\(325\) 0.465044 + 1.43126i 0.0257960 + 0.0793919i
\(326\) −12.9543 9.41186i −0.717473 0.521275i
\(327\) 0 0
\(328\) −0.512166 + 1.57628i −0.0282796 + 0.0870358i
\(329\) 3.40896 0.187942
\(330\) 0 0
\(331\) −9.50564 −0.522477 −0.261239 0.965274i \(-0.584131\pi\)
−0.261239 + 0.965274i \(0.584131\pi\)
\(332\) 2.72585 8.38932i 0.149601 0.460424i
\(333\) 0 0
\(334\) 9.88310 + 7.18050i 0.540779 + 0.392899i
\(335\) −4.21991 12.9875i −0.230558 0.709586i
\(336\) 0 0
\(337\) −20.7225 15.0557i −1.12882 0.820138i −0.143301 0.989679i \(-0.545772\pi\)
−0.985523 + 0.169541i \(0.945772\pi\)
\(338\) 17.7959 12.9295i 0.967971 0.703272i
\(339\) 0 0
\(340\) 10.8170 0.586635
\(341\) 5.41920 + 3.70390i 0.293466 + 0.200577i
\(342\) 0 0
\(343\) 2.48876 7.65961i 0.134380 0.413580i
\(344\) −1.60036 + 1.16273i −0.0862856 + 0.0626902i
\(345\) 0 0
\(346\) 10.4944 + 32.2984i 0.564182 + 1.73637i
\(347\) −8.62415 26.5424i −0.462969 1.42487i −0.861520 0.507724i \(-0.830487\pi\)
0.398551 0.917146i \(-0.369513\pi\)
\(348\) 0 0
\(349\) 8.58282 6.23578i 0.459428 0.333794i −0.333879 0.942616i \(-0.608358\pi\)
0.793307 + 0.608822i \(0.208358\pi\)
\(350\) −0.373541 + 1.14964i −0.0199666 + 0.0614509i
\(351\) 0 0
\(352\) −7.57763 + 25.8270i −0.403889 + 1.37658i
\(353\) −29.0702 −1.54725 −0.773627 0.633642i \(-0.781559\pi\)
−0.773627 + 0.633642i \(0.781559\pi\)
\(354\) 0 0
\(355\) 1.03861 0.754594i 0.0551237 0.0400497i
\(356\) 10.8176 + 7.85944i 0.573331 + 0.416550i
\(357\) 0 0
\(358\) 13.6419 + 41.9854i 0.720995 + 2.21900i
\(359\) 24.4571 + 17.7692i 1.29080 + 0.937820i 0.999821 0.0189094i \(-0.00601942\pi\)
0.290978 + 0.956730i \(0.406019\pi\)
\(360\) 0 0
\(361\) 8.50432 26.1736i 0.447596 1.37756i
\(362\) −41.3300 −2.17226
\(363\) 0 0
\(364\) −1.95191 −0.102308
\(365\) 4.82904 14.8623i 0.252764 0.777926i
\(366\) 0 0
\(367\) 19.1378 + 13.9044i 0.998984 + 0.725805i 0.961870 0.273506i \(-0.0881835\pi\)
0.0371142 + 0.999311i \(0.488183\pi\)
\(368\) −0.0906175 0.278892i −0.00472376 0.0145382i
\(369\) 0 0
\(370\) −5.93455 4.31171i −0.308523 0.224155i
\(371\) −3.23285 + 2.34880i −0.167841 + 0.121944i
\(372\) 0 0
\(373\) −14.5998 −0.755949 −0.377974 0.925816i \(-0.623379\pi\)
−0.377974 + 0.925816i \(0.623379\pi\)
\(374\) −9.41328 + 32.0834i −0.486749 + 1.65899i
\(375\) 0 0
\(376\) −0.726592 + 2.23622i −0.0374711 + 0.115324i
\(377\) 10.2567 7.45196i 0.528249 0.383796i
\(378\) 0 0
\(379\) 2.07156 + 6.37559i 0.106409 + 0.327492i 0.990058 0.140656i \(-0.0449212\pi\)
−0.883650 + 0.468148i \(0.844921\pi\)
\(380\) −4.63391 14.2617i −0.237715 0.731610i
\(381\) 0 0
\(382\) 27.0027 19.6186i 1.38158 1.00378i
\(383\) 9.74277 29.9852i 0.497832 1.53217i −0.314663 0.949203i \(-0.601892\pi\)
0.812496 0.582967i \(-0.198108\pi\)
\(384\) 0 0
\(385\) −1.61534 1.10405i −0.0823256 0.0562676i
\(386\) 6.86324 0.349330
\(387\) 0 0
\(388\) 11.9275 8.66584i 0.605527 0.439941i
\(389\) −31.5385 22.9141i −1.59907 1.16179i −0.889271 0.457380i \(-0.848788\pi\)
−0.709794 0.704409i \(-0.751212\pi\)
\(390\) 0 0
\(391\) −0.125116 0.385067i −0.00632737 0.0194737i
\(392\) 2.18978 + 1.59097i 0.110600 + 0.0803559i
\(393\) 0 0
\(394\) 6.19359 19.0619i 0.312029 0.960326i
\(395\) 11.1522 0.561128
\(396\) 0 0
\(397\) 27.1682 1.36353 0.681766 0.731570i \(-0.261212\pi\)
0.681766 + 0.731570i \(0.261212\pi\)
\(398\) 6.26258 19.2742i 0.313915 0.966131i
\(399\) 0 0
\(400\) 2.88285 + 2.09451i 0.144143 + 0.104726i
\(401\) −4.07725 12.5485i −0.203608 0.626641i −0.999768 0.0215543i \(-0.993139\pi\)
0.796160 0.605087i \(-0.206861\pi\)
\(402\) 0 0
\(403\) 2.40959 + 1.75067i 0.120030 + 0.0872072i
\(404\) −10.5754 + 7.68349i −0.526146 + 0.382268i
\(405\) 0 0
\(406\) 10.1835 0.505398
\(407\) 9.40107 7.25243i 0.465994 0.359490i
\(408\) 0 0
\(409\) −3.06772 + 9.44146i −0.151689 + 0.466850i −0.997810 0.0661398i \(-0.978932\pi\)
0.846122 + 0.532990i \(0.178932\pi\)
\(410\) −6.75221 + 4.90577i −0.333468 + 0.242279i
\(411\) 0 0
\(412\) 1.31503 + 4.04725i 0.0647870 + 0.199394i
\(413\) −1.01797 3.13299i −0.0500910 0.154164i
\(414\) 0 0
\(415\) 3.24590 2.35828i 0.159335 0.115764i
\(416\) −3.77401 + 11.6152i −0.185036 + 0.569482i
\(417\) 0 0
\(418\) 46.3330 1.33329i 2.26622 0.0652133i
\(419\) 26.4274 1.29107 0.645533 0.763733i \(-0.276635\pi\)
0.645533 + 0.763733i \(0.276635\pi\)
\(420\) 0 0
\(421\) −11.1232 + 8.08146i −0.542111 + 0.393866i −0.824868 0.565325i \(-0.808751\pi\)
0.282758 + 0.959191i \(0.408751\pi\)
\(422\) 36.7492 + 26.6999i 1.78892 + 1.29973i
\(423\) 0 0
\(424\) −0.851720 2.62132i −0.0413632 0.127303i
\(425\) 3.98036 + 2.89190i 0.193076 + 0.140278i
\(426\) 0 0
\(427\) 0.175053 0.538758i 0.00847141 0.0260723i
\(428\) −18.2201 −0.880702
\(429\) 0 0
\(430\) −9.96139 −0.480381
\(431\) −6.17164 + 18.9944i −0.297278 + 0.914927i 0.685169 + 0.728384i \(0.259728\pi\)
−0.982447 + 0.186543i \(0.940272\pi\)
\(432\) 0 0
\(433\) −13.4316 9.75862i −0.645481 0.468969i 0.216248 0.976338i \(-0.430618\pi\)
−0.861729 + 0.507369i \(0.830618\pi\)
\(434\) 0.739287 + 2.27529i 0.0354869 + 0.109218i
\(435\) 0 0
\(436\) −5.67015 4.11961i −0.271551 0.197293i
\(437\) −0.454093 + 0.329918i −0.0217222 + 0.0157821i
\(438\) 0 0
\(439\) −28.3645 −1.35376 −0.676882 0.736091i \(-0.736669\pi\)
−0.676882 + 0.736091i \(0.736669\pi\)
\(440\) 1.06854 0.824320i 0.0509405 0.0392979i
\(441\) 0 0
\(442\) −4.68824 + 14.4289i −0.222997 + 0.686314i
\(443\) 18.3506 13.3325i 0.871865 0.633447i −0.0592220 0.998245i \(-0.518862\pi\)
0.931087 + 0.364798i \(0.118862\pi\)
\(444\) 0 0
\(445\) 1.87937 + 5.78411i 0.0890908 + 0.274193i
\(446\) 7.81345 + 24.0473i 0.369977 + 1.13867i
\(447\) 0 0
\(448\) −4.53498 + 3.29486i −0.214258 + 0.155667i
\(449\) −1.41587 + 4.35761i −0.0668192 + 0.205648i −0.978891 0.204381i \(-0.934482\pi\)
0.912072 + 0.410030i \(0.134482\pi\)
\(450\) 0 0
\(451\) −4.54245 12.7227i −0.213896 0.599090i
\(452\) −25.2629 −1.18827
\(453\) 0 0
\(454\) −13.6290 + 9.90205i −0.639641 + 0.464726i
\(455\) −0.718247 0.521837i −0.0336719 0.0244641i
\(456\) 0 0
\(457\) 2.07841 + 6.39668i 0.0972238 + 0.299224i 0.987827 0.155557i \(-0.0497174\pi\)
−0.890603 + 0.454781i \(0.849717\pi\)
\(458\) −44.8320 32.5724i −2.09486 1.52201i
\(459\) 0 0
\(460\) −0.0559101 + 0.172073i −0.00260682 + 0.00802297i
\(461\) 2.83529 0.132053 0.0660263 0.997818i \(-0.478968\pi\)
0.0660263 + 0.997818i \(0.478968\pi\)
\(462\) 0 0
\(463\) 20.5498 0.955029 0.477515 0.878624i \(-0.341538\pi\)
0.477515 + 0.878624i \(0.341538\pi\)
\(464\) 9.27657 28.5504i 0.430654 1.32542i
\(465\) 0 0
\(466\) 41.4497 + 30.1150i 1.92012 + 1.39505i
\(467\) 3.63384 + 11.1838i 0.168154 + 0.517525i 0.999255 0.0385968i \(-0.0122888\pi\)
−0.831101 + 0.556122i \(0.812289\pi\)
\(468\) 0 0
\(469\) 6.51753 + 4.73526i 0.300952 + 0.218654i
\(470\) −9.57912 + 6.95964i −0.441852 + 0.321024i
\(471\) 0 0
\(472\) 2.27216 0.104585
\(473\) 4.53935 15.4715i 0.208720 0.711382i
\(474\) 0 0
\(475\) 2.10768 6.48677i 0.0967070 0.297634i
\(476\) −5.16262 + 3.75086i −0.236628 + 0.171920i
\(477\) 0 0
\(478\) 13.1205 + 40.3806i 0.600116 + 1.84697i
\(479\) −0.470421 1.44781i −0.0214941 0.0661519i 0.939734 0.341906i \(-0.111072\pi\)
−0.961228 + 0.275754i \(0.911072\pi\)
\(480\) 0 0
\(481\) 4.35861 3.16672i 0.198736 0.144390i
\(482\) −14.8353 + 45.6585i −0.675731 + 2.07969i
\(483\) 0 0
\(484\) 8.78368 + 22.5329i 0.399258 + 1.02422i
\(485\) 6.70578 0.304494
\(486\) 0 0
\(487\) −28.7184 + 20.8652i −1.30136 + 0.945491i −0.999968 0.00801039i \(-0.997450\pi\)
−0.301389 + 0.953501i \(0.597450\pi\)
\(488\) 0.316105 + 0.229664i 0.0143094 + 0.0103964i
\(489\) 0 0
\(490\) 4.21196 + 12.9631i 0.190277 + 0.585612i
\(491\) 10.2562 + 7.45159i 0.462858 + 0.336286i 0.794651 0.607066i \(-0.207654\pi\)
−0.331794 + 0.943352i \(0.607654\pi\)
\(492\) 0 0
\(493\) 12.8082 39.4195i 0.576852 1.77537i
\(494\) 21.0322 0.946285
\(495\) 0 0
\(496\) 7.05244 0.316664
\(497\) −0.234036 + 0.720288i −0.0104979 + 0.0323093i
\(498\) 0 0
\(499\) −17.0361 12.3774i −0.762640 0.554090i 0.137079 0.990560i \(-0.456229\pi\)
−0.899719 + 0.436470i \(0.856229\pi\)
\(500\) −0.679399 2.09098i −0.0303837 0.0935113i
\(501\) 0 0
\(502\) −17.0243 12.3688i −0.759830 0.552049i
\(503\) 20.2875 14.7398i 0.904576 0.657213i −0.0350612 0.999385i \(-0.511163\pi\)
0.939637 + 0.342172i \(0.111163\pi\)
\(504\) 0 0
\(505\) −5.94562 −0.264577
\(506\) −0.461718 0.315573i −0.0205259 0.0140289i
\(507\) 0 0
\(508\) 12.3593 38.0379i 0.548353 1.68766i
\(509\) −29.6791 + 21.5631i −1.31550 + 0.955767i −0.315524 + 0.948917i \(0.602180\pi\)
−0.999977 + 0.00684995i \(0.997820\pi\)
\(510\) 0 0
\(511\) 2.84882 + 8.76778i 0.126025 + 0.387864i
\(512\) 9.83238 + 30.2610i 0.434534 + 1.33736i
\(513\) 0 0
\(514\) −3.23157 + 2.34787i −0.142538 + 0.103560i
\(515\) −0.598127 + 1.84085i −0.0263566 + 0.0811174i
\(516\) 0 0
\(517\) −6.44421 18.0493i −0.283416 0.793807i
\(518\) 4.32748 0.190139
\(519\) 0 0
\(520\) 0.495405 0.359933i 0.0217250 0.0157841i
\(521\) 22.9371 + 16.6648i 1.00489 + 0.730099i 0.963132 0.269029i \(-0.0867027\pi\)
0.0417626 + 0.999128i \(0.486703\pi\)
\(522\) 0 0
\(523\) 8.27685 + 25.4735i 0.361922 + 1.11388i 0.951886 + 0.306451i \(0.0991416\pi\)
−0.589965 + 0.807429i \(0.700858\pi\)
\(524\) 33.3964 + 24.2639i 1.45893 + 1.05997i
\(525\) 0 0
\(526\) −5.57355 + 17.1536i −0.243018 + 0.747933i
\(527\) 9.73732 0.424164
\(528\) 0 0
\(529\) −22.9932 −0.999706
\(530\) 4.28901 13.2002i 0.186303 0.573380i
\(531\) 0 0
\(532\) 7.15694 + 5.19982i 0.310293 + 0.225441i
\(533\) −1.89422 5.82982i −0.0820479 0.252517i
\(534\) 0 0
\(535\) −6.70449 4.87110i −0.289860 0.210596i
\(536\) −4.49542 + 3.26611i −0.194172 + 0.141074i
\(537\) 0 0
\(538\) 24.9659 1.07636
\(539\) −22.0530 + 0.634602i −0.949889 + 0.0273342i
\(540\) 0 0
\(541\) 5.17081 15.9141i 0.222311 0.684201i −0.776243 0.630434i \(-0.782877\pi\)
0.998553 0.0537675i \(-0.0171230\pi\)
\(542\) −20.4985 + 14.8930i −0.880484 + 0.639709i
\(543\) 0 0
\(544\) 12.3383 + 37.9734i 0.529001 + 1.62810i
\(545\) −0.985092 3.03180i −0.0421967 0.129868i
\(546\) 0 0
\(547\) 17.3143 12.5796i 0.740305 0.537863i −0.152502 0.988303i \(-0.548733\pi\)
0.892807 + 0.450440i \(0.148733\pi\)
\(548\) 3.21154 9.88411i 0.137190 0.422228i
\(549\) 0 0
\(550\) 6.79310 0.195480i 0.289659 0.00833529i
\(551\) −57.4596 −2.44786
\(552\) 0 0
\(553\) −5.32259 + 3.86709i −0.226339 + 0.164445i
\(554\) −34.0310 24.7249i −1.44584 1.05046i
\(555\) 0 0
\(556\) −12.5510 38.6281i −0.532282 1.63820i
\(557\) 34.7026 + 25.2129i 1.47040 + 1.06830i 0.980499 + 0.196524i \(0.0629655\pi\)
0.489897 + 0.871781i \(0.337035\pi\)
\(558\) 0 0
\(559\) 2.26080 6.95804i 0.0956218 0.294294i
\(560\) −2.10218 −0.0888332
\(561\) 0 0
\(562\) 23.4144 0.987677
\(563\) −10.1843 + 31.3440i −0.429216 + 1.32099i 0.469682 + 0.882835i \(0.344368\pi\)
−0.898899 + 0.438157i \(0.855632\pi\)
\(564\) 0 0
\(565\) −9.29605 6.75398i −0.391088 0.284142i
\(566\) 18.6994 + 57.5508i 0.785994 + 2.41904i
\(567\) 0 0
\(568\) −0.422614 0.307047i −0.0177325 0.0128834i
\(569\) 2.72574 1.98036i 0.114269 0.0830212i −0.529183 0.848508i \(-0.677502\pi\)
0.643452 + 0.765486i \(0.277502\pi\)
\(570\) 0 0
\(571\) −0.267599 −0.0111987 −0.00559934 0.999984i \(-0.501782\pi\)
−0.00559934 + 0.999984i \(0.501782\pi\)
\(572\) 3.68984 + 10.3347i 0.154280 + 0.432115i
\(573\) 0 0
\(574\) 1.52151 4.68273i 0.0635067 0.195453i
\(575\) −0.0665767 + 0.0483708i −0.00277644 + 0.00201720i
\(576\) 0 0
\(577\) 11.7100 + 36.0396i 0.487493 + 1.50035i 0.828337 + 0.560230i \(0.189287\pi\)
−0.340844 + 0.940120i \(0.610713\pi\)
\(578\) 4.56299 + 14.0434i 0.189795 + 0.584130i
\(579\) 0 0
\(580\) −14.9844 + 10.8868i −0.622195 + 0.452051i
\(581\) −0.731416 + 2.25107i −0.0303443 + 0.0933900i
\(582\) 0 0
\(583\) 18.5474 + 12.6767i 0.768156 + 0.525017i
\(584\) −6.35872 −0.263126
\(585\) 0 0
\(586\) −19.2235 + 13.9667i −0.794117 + 0.576960i
\(587\) −13.6375 9.90825i −0.562881 0.408957i 0.269631 0.962964i \(-0.413098\pi\)
−0.832512 + 0.554006i \(0.813098\pi\)
\(588\) 0 0
\(589\) −4.17138 12.8382i −0.171879 0.528988i
\(590\) 9.25671 + 6.72540i 0.381093 + 0.276880i
\(591\) 0 0
\(592\) 3.94209 12.1325i 0.162019 0.498642i
\(593\) −11.0211 −0.452580 −0.226290 0.974060i \(-0.572660\pi\)
−0.226290 + 0.974060i \(0.572660\pi\)
\(594\) 0 0
\(595\) −2.90248 −0.118990
\(596\) −10.5314 + 32.4124i −0.431384 + 1.32766i
\(597\) 0 0
\(598\) −0.205298 0.149158i −0.00839527 0.00609952i
\(599\) −5.15906 15.8779i −0.210793 0.648755i −0.999426 0.0338901i \(-0.989210\pi\)
0.788632 0.614865i \(-0.210790\pi\)
\(600\) 0 0
\(601\) 6.27526 + 4.55925i 0.255973 + 0.185976i 0.708370 0.705841i \(-0.249431\pi\)
−0.452397 + 0.891817i \(0.649431\pi\)
\(602\) 4.75425 3.45417i 0.193769 0.140781i
\(603\) 0 0
\(604\) 12.2118 0.496891
\(605\) −2.79197 + 10.6398i −0.113510 + 0.432569i
\(606\) 0 0
\(607\) 9.85634 30.3347i 0.400057 1.23125i −0.524896 0.851166i \(-0.675896\pi\)
0.924953 0.380082i \(-0.124104\pi\)
\(608\) 44.7805 32.5349i 1.81609 1.31946i
\(609\) 0 0
\(610\) 0.608018 + 1.87129i 0.0246179 + 0.0757662i
\(611\) −2.68727 8.27056i −0.108715 0.334591i
\(612\) 0 0
\(613\) 34.6283 25.1589i 1.39862 1.01616i 0.403766 0.914862i \(-0.367701\pi\)
0.994856 0.101296i \(-0.0322991\pi\)
\(614\) 0.806109 2.48095i 0.0325319 0.100123i
\(615\) 0 0
\(616\) −0.224141 + 0.763943i −0.00903089 + 0.0307801i
\(617\) 21.7979 0.877550 0.438775 0.898597i \(-0.355412\pi\)
0.438775 + 0.898597i \(0.355412\pi\)
\(618\) 0 0
\(619\) −27.2098 + 19.7691i −1.09366 + 0.794587i −0.980013 0.198935i \(-0.936252\pi\)
−0.113642 + 0.993522i \(0.536252\pi\)
\(620\) −3.52026 2.55762i −0.141377 0.102717i
\(621\) 0 0
\(622\) 3.10608 + 9.55953i 0.124542 + 0.383302i
\(623\) −2.90264 2.10889i −0.116292 0.0844908i
\(624\) 0 0
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) −31.5956 −1.26281
\(627\) 0 0
\(628\) −40.6990 −1.62407
\(629\) 5.44285 16.7514i 0.217021 0.667921i
\(630\) 0 0
\(631\) 17.3577 + 12.6111i 0.690997 + 0.502039i 0.876988 0.480513i \(-0.159549\pi\)
−0.185991 + 0.982552i \(0.559549\pi\)
\(632\) −1.40228 4.31577i −0.0557796 0.171672i
\(633\) 0 0
\(634\) −55.6735 40.4492i −2.21108 1.60644i
\(635\) 14.7172 10.6927i 0.584034 0.424325i
\(636\) 0 0
\(637\) −10.0107 −0.396636
\(638\) −19.2506 53.9181i −0.762139 2.13464i
\(639\) 0 0
\(640\) 1.00096 3.08064i 0.0395665 0.121773i
\(641\) 36.1507 26.2650i 1.42787 1.03740i 0.437456 0.899240i \(-0.355880\pi\)
0.990409 0.138165i \(-0.0441205\pi\)
\(642\) 0 0
\(643\) 2.65477 + 8.17053i 0.104694 + 0.322214i 0.989658 0.143444i \(-0.0458176\pi\)
−0.884965 + 0.465658i \(0.845818\pi\)
\(644\) −0.0329833 0.101512i −0.00129973 0.00400014i
\(645\) 0 0
\(646\) 55.6284 40.4164i 2.18867 1.59016i
\(647\) −2.76396 + 8.50658i −0.108662 + 0.334428i −0.990573 0.136989i \(-0.956257\pi\)
0.881910 + 0.471417i \(0.156257\pi\)
\(648\) 0 0
\(649\) −14.6638 + 11.3123i −0.575604 + 0.444048i
\(650\) 3.08363 0.120950
\(651\) 0 0
\(652\) −13.8997 + 10.0987i −0.544355 + 0.395497i
\(653\) −11.2834 8.19784i −0.441552 0.320806i 0.344699 0.938713i \(-0.387981\pi\)
−0.786251 + 0.617907i \(0.787981\pi\)
\(654\) 0 0
\(655\) 5.80204 + 17.8569i 0.226705 + 0.697725i
\(656\) −11.7425 8.53140i −0.458466 0.333095i
\(657\) 0 0
\(658\) 2.15852 6.64323i 0.0841477 0.258980i
\(659\) 6.61492 0.257681 0.128840 0.991665i \(-0.458875\pi\)
0.128840 + 0.991665i \(0.458875\pi\)
\(660\) 0 0
\(661\) 23.5635 0.916515 0.458257 0.888820i \(-0.348474\pi\)
0.458257 + 0.888820i \(0.348474\pi\)
\(662\) −6.01887 + 18.5242i −0.233930 + 0.719962i
\(663\) 0 0
\(664\) −1.32077 0.959594i −0.0512557 0.0372395i
\(665\) 1.24340 + 3.82678i 0.0482168 + 0.148396i
\(666\) 0 0
\(667\) 0.560871 + 0.407497i 0.0217170 + 0.0157783i
\(668\) 10.6044 7.70452i 0.410295 0.298097i
\(669\) 0 0
\(670\) −27.9816 −1.08102
\(671\) −3.18346 + 0.0916079i −0.122896 + 0.00353649i
\(672\) 0 0
\(673\) 1.30209 4.00742i 0.0501919 0.154475i −0.922819 0.385234i \(-0.874121\pi\)
0.973011 + 0.230759i \(0.0741209\pi\)
\(674\) −42.4612 + 30.8499i −1.63554 + 1.18829i
\(675\) 0 0
\(676\) −7.29351 22.4471i −0.280520 0.863351i
\(677\) 5.25436 + 16.1713i 0.201942 + 0.621512i 0.999825 + 0.0187007i \(0.00595297\pi\)
−0.797884 + 0.602812i \(0.794047\pi\)
\(678\) 0 0
\(679\) −3.20045 + 2.32527i −0.122822 + 0.0892355i
\(680\) 0.618641 1.90398i 0.0237238 0.0730143i
\(681\) 0 0
\(682\) 10.6494 8.21544i 0.407786 0.314585i
\(683\) −19.6114 −0.750409 −0.375204 0.926942i \(-0.622427\pi\)
−0.375204 + 0.926942i \(0.622427\pi\)
\(684\) 0 0
\(685\) 3.82425 2.77848i 0.146117 0.106160i
\(686\) −13.3509 9.69997i −0.509738 0.370346i
\(687\) 0 0
\(688\) −5.35323 16.4755i −0.204090 0.628124i
\(689\) 8.24693 + 5.99175i 0.314183 + 0.228267i
\(690\) 0 0
\(691\) 2.37016 7.29459i 0.0901650 0.277499i −0.895799 0.444460i \(-0.853395\pi\)
0.985963 + 0.166961i \(0.0533954\pi\)
\(692\) 36.4390 1.38520
\(693\) 0 0
\(694\) −57.1854 −2.17073
\(695\) 5.70869 17.5695i 0.216543 0.666451i
\(696\) 0 0
\(697\) −16.2129 11.7793i −0.614106 0.446174i
\(698\) −6.71747 20.6743i −0.254260 0.782532i
\(699\) 0 0
\(700\) 1.04931 + 0.762370i 0.0396603 + 0.0288149i
\(701\) 17.7443 12.8920i 0.670192 0.486923i −0.199897 0.979817i \(-0.564061\pi\)
0.870090 + 0.492894i \(0.164061\pi\)
\(702\) 0 0
\(703\) −24.4175 −0.920924
\(704\) 26.0180 + 17.7827i 0.980589 + 0.670210i
\(705\) 0 0
\(706\) −18.4070 + 56.6508i −0.692756 + 2.13208i
\(707\) 2.83765 2.06168i 0.106721 0.0775373i
\(708\) 0 0
\(709\) −2.23257 6.87116i −0.0838461 0.258052i 0.900341 0.435186i \(-0.143317\pi\)
−0.984187 + 0.177134i \(0.943317\pi\)
\(710\) −0.812884 2.50180i −0.0305070 0.0938909i
\(711\) 0 0
\(712\) 2.00207 1.45459i 0.0750307 0.0545130i
\(713\) −0.0503294 + 0.154898i −0.00188485 + 0.00580098i
\(714\) 0 0
\(715\) −1.40520 + 4.78935i −0.0525513 + 0.179111i
\(716\) 47.3678 1.77022
\(717\) 0 0
\(718\) 50.1138 36.4098i 1.87023 1.35880i
\(719\) −15.5513 11.2987i −0.579967 0.421371i 0.258745 0.965946i \(-0.416691\pi\)
−0.838712 + 0.544575i \(0.816691\pi\)
\(720\) 0 0
\(721\) −0.352857 1.08598i −0.0131411 0.0404440i
\(722\) −45.6212 33.1457i −1.69784 1.23356i
\(723\) 0 0
\(724\) −13.7038 + 42.1758i −0.509296 + 1.56745i
\(725\) −8.42443 −0.312875
\(726\) 0 0
\(727\) −33.9775 −1.26015 −0.630077 0.776532i \(-0.716977\pi\)
−0.630077 + 0.776532i \(0.716977\pi\)
\(728\) −0.111632 + 0.343569i −0.00413737 + 0.0127335i
\(729\) 0 0
\(730\) −25.9052 18.8213i −0.958796 0.696606i
\(731\) −7.39122 22.7478i −0.273374 0.841359i
\(732\) 0 0
\(733\) −5.25720 3.81958i −0.194179 0.141079i 0.486448 0.873710i \(-0.338292\pi\)
−0.680627 + 0.732630i \(0.738292\pi\)
\(734\) 39.2142 28.4908i 1.44742 1.05161i
\(735\) 0 0
\(736\) −0.667841 −0.0246170
\(737\) 12.7510 43.4596i 0.469691 1.60085i
\(738\) 0 0
\(739\) −5.78294 + 17.7981i −0.212729 + 0.654712i 0.786578 + 0.617491i \(0.211851\pi\)
−0.999307 + 0.0372216i \(0.988149\pi\)
\(740\) −6.36765 + 4.62637i −0.234080 + 0.170069i
\(741\) 0 0
\(742\) 2.53024 + 7.78727i 0.0928880 + 0.285880i
\(743\) −2.71901 8.36824i −0.0997506 0.307001i 0.888712 0.458466i \(-0.151601\pi\)
−0.988463 + 0.151465i \(0.951601\pi\)
\(744\) 0 0
\(745\) −12.5406 + 9.11130i −0.459453 + 0.333812i
\(746\) −9.24443 + 28.4514i −0.338463 + 1.04168i
\(747\) 0 0
\(748\) 29.6188 + 20.2438i 1.08297 + 0.740186i
\(749\) 4.88892 0.178637
\(750\) 0 0
\(751\) −20.8619 + 15.1571i −0.761261 + 0.553089i −0.899297 0.437339i \(-0.855921\pi\)
0.138036 + 0.990427i \(0.455921\pi\)
\(752\) −16.6586 12.1032i −0.607478 0.441358i
\(753\) 0 0
\(754\) −8.02760 24.7064i −0.292348 0.899754i
\(755\) 4.49360 + 3.26479i 0.163539 + 0.118818i
\(756\) 0 0
\(757\) 12.3823 38.1087i 0.450041 1.38508i −0.426818 0.904338i \(-0.640366\pi\)
0.876859 0.480747i \(-0.159634\pi\)
\(758\) 13.7362 0.498920
\(759\) 0 0
\(760\) −2.77532 −0.100672
\(761\) −5.54238 + 17.0577i −0.200911 + 0.618340i 0.798946 + 0.601403i \(0.205392\pi\)
−0.999857 + 0.0169371i \(0.994608\pi\)
\(762\) 0 0
\(763\) 1.52145 + 1.10540i 0.0550801 + 0.0400180i
\(764\) −11.0668 34.0602i −0.400384 1.23226i
\(765\) 0 0
\(766\) −52.2648 37.9726i −1.88840 1.37201i
\(767\) −6.79856 + 4.93945i −0.245482 + 0.178353i
\(768\) 0 0
\(769\) −10.8431 −0.391011 −0.195506 0.980703i \(-0.562635\pi\)
−0.195506 + 0.980703i \(0.562635\pi\)
\(770\) −3.17435 + 2.44884i −0.114395 + 0.0882501i
\(771\) 0 0
\(772\) 2.27564 7.00369i 0.0819020 0.252068i
\(773\) −5.55690 + 4.03732i −0.199868 + 0.145212i −0.683218 0.730215i \(-0.739420\pi\)
0.483350 + 0.875427i \(0.339420\pi\)
\(774\) 0 0
\(775\) −0.611585 1.88227i −0.0219688 0.0676130i
\(776\) −0.843185 2.59506i −0.0302686 0.0931571i
\(777\) 0 0
\(778\) −64.6238 + 46.9519i −2.31687 + 1.68331i
\(779\) −8.58503 + 26.4220i −0.307591 + 0.946667i
\(780\) 0 0
\(781\) 4.25610 0.122474i 0.152295 0.00438248i
\(782\) −0.829623 −0.0296673
\(783\) 0 0
\(784\) −19.1767 + 13.9327i −0.684881 + 0.497595i
\(785\) −14.9761 10.8808i −0.534521