Properties

Label 570.2.i.i.121.2
Level $570$
Weight $2$
Character 570.121
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \(x^{4} + 7 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.2
Root \(-1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.2.i.i.391.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.64575 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.64575 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +4.29150 q^{11} -1.00000 q^{12} +(1.32288 + 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.177124 + 0.306788i) q^{17} -1.00000 q^{18} +(-4.32288 - 0.559237i) q^{19} -1.00000 q^{20} +(1.32288 + 2.29129i) q^{21} +(2.14575 + 3.71655i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +(-1.32288 + 2.29129i) q^{28} +(-0.822876 + 1.42526i) q^{29} -1.00000 q^{30} -3.29150 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.14575 + 3.71655i) q^{33} +(-0.177124 + 0.306788i) q^{34} +(1.32288 + 2.29129i) q^{35} +(-0.500000 - 0.866025i) q^{36} -2.29150 q^{37} +(-1.67712 - 4.02334i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(1.67712 + 2.90486i) q^{41} +(-1.32288 + 2.29129i) q^{42} +(-3.00000 - 5.19615i) q^{43} +(-2.14575 + 3.71655i) q^{44} -1.00000 q^{45} -1.00000 q^{46} +(4.29150 - 7.43310i) q^{47} +(0.500000 - 0.866025i) q^{48} -1.00000 q^{50} +(-0.177124 + 0.306788i) q^{51} +(-0.322876 + 0.559237i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.14575 + 3.71655i) q^{55} -2.64575 q^{56} +(-1.67712 - 4.02334i) q^{57} -1.64575 q^{58} +(2.64575 + 4.58258i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(4.46863 - 7.73989i) q^{61} +(-1.64575 - 2.85052i) q^{62} +(-1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(-2.14575 + 3.71655i) q^{66} +(2.17712 - 3.77089i) q^{67} -0.354249 q^{68} -1.00000 q^{69} +(-1.32288 + 2.29129i) q^{70} +(4.17712 + 7.23499i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-4.17712 - 7.23499i) q^{73} +(-1.14575 - 1.98450i) q^{74} -1.00000 q^{75} +(2.64575 - 3.46410i) q^{76} +11.3542 q^{77} +(2.64575 + 4.58258i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.67712 + 2.90486i) q^{82} -4.58301 q^{83} -2.64575 q^{84} +(-0.177124 + 0.306788i) q^{85} +(3.00000 - 5.19615i) q^{86} -1.64575 q^{87} -4.29150 q^{88} +(6.61438 - 11.4564i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-0.500000 - 0.866025i) q^{92} +(-1.64575 - 2.85052i) q^{93} +8.58301 q^{94} +(-1.67712 - 4.02334i) q^{95} +1.00000 q^{96} +(-1.82288 - 3.15731i) q^{97} +(-2.14575 + 3.71655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} + 2q^{5} - 2q^{6} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} + 2q^{5} - 2q^{6} - 4q^{8} - 2q^{9} - 2q^{10} - 4q^{11} - 4q^{12} - 2q^{15} - 2q^{16} + 6q^{17} - 4q^{18} - 12q^{19} - 4q^{20} - 2q^{22} - 2q^{23} - 2q^{24} - 2q^{25} - 4q^{27} + 2q^{29} - 4q^{30} + 8q^{31} + 2q^{32} - 2q^{33} - 6q^{34} - 2q^{36} + 12q^{37} - 12q^{38} - 2q^{40} + 12q^{41} - 12q^{43} + 2q^{44} - 4q^{45} - 4q^{46} - 4q^{47} + 2q^{48} - 4q^{50} - 6q^{51} + 4q^{53} - 2q^{54} - 2q^{55} - 12q^{57} + 4q^{58} - 2q^{60} + 2q^{61} + 4q^{62} + 4q^{64} + 2q^{66} + 14q^{67} - 12q^{68} - 4q^{69} + 22q^{71} + 2q^{72} - 22q^{73} + 6q^{74} - 4q^{75} + 56q^{77} + 2q^{80} - 2q^{81} - 12q^{82} + 24q^{83} - 6q^{85} + 12q^{86} + 4q^{87} + 4q^{88} - 2q^{90} - 2q^{92} + 4q^{93} - 8q^{94} - 12q^{95} + 4q^{96} - 2q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 2.64575 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 4.29150 1.29394 0.646968 0.762517i \(-0.276037\pi\)
0.646968 + 0.762517i \(0.276037\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(14\) 1.32288 + 2.29129i 0.353553 + 0.612372i
\(15\) −0.500000 + 0.866025i −0.129099 + 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.177124 + 0.306788i 0.0429590 + 0.0744071i 0.886705 0.462335i \(-0.152988\pi\)
−0.843746 + 0.536742i \(0.819655\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.32288 0.559237i −0.991736 0.128298i
\(20\) −1.00000 −0.223607
\(21\) 1.32288 + 2.29129i 0.288675 + 0.500000i
\(22\) 2.14575 + 3.71655i 0.457476 + 0.792371i
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.32288 + 2.29129i −0.250000 + 0.433013i
\(29\) −0.822876 + 1.42526i −0.152804 + 0.264665i −0.932257 0.361796i \(-0.882164\pi\)
0.779453 + 0.626461i \(0.215497\pi\)
\(30\) −1.00000 −0.182574
\(31\) −3.29150 −0.591171 −0.295586 0.955316i \(-0.595515\pi\)
−0.295586 + 0.955316i \(0.595515\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 2.14575 + 3.71655i 0.373527 + 0.646968i
\(34\) −0.177124 + 0.306788i −0.0303766 + 0.0526138i
\(35\) 1.32288 + 2.29129i 0.223607 + 0.387298i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −2.29150 −0.376721 −0.188360 0.982100i \(-0.560317\pi\)
−0.188360 + 0.982100i \(0.560317\pi\)
\(38\) −1.67712 4.02334i −0.272065 0.652672i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 1.67712 + 2.90486i 0.261923 + 0.453664i 0.966753 0.255713i \(-0.0823101\pi\)
−0.704830 + 0.709376i \(0.748977\pi\)
\(42\) −1.32288 + 2.29129i −0.204124 + 0.353553i
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) −2.14575 + 3.71655i −0.323484 + 0.560291i
\(45\) −1.00000 −0.149071
\(46\) −1.00000 −0.147442
\(47\) 4.29150 7.43310i 0.625980 1.08423i −0.362370 0.932034i \(-0.618032\pi\)
0.988350 0.152195i \(-0.0486342\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) −0.177124 + 0.306788i −0.0248024 + 0.0429590i
\(52\) 0 0
\(53\) −0.322876 + 0.559237i −0.0443504 + 0.0768171i −0.887348 0.461099i \(-0.847455\pi\)
0.842998 + 0.537917i \(0.180788\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 2.14575 + 3.71655i 0.289333 + 0.501140i
\(56\) −2.64575 −0.353553
\(57\) −1.67712 4.02334i −0.222141 0.532904i
\(58\) −1.64575 −0.216098
\(59\) 2.64575 + 4.58258i 0.344447 + 0.596601i 0.985253 0.171103i \(-0.0547329\pi\)
−0.640806 + 0.767703i \(0.721400\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) 4.46863 7.73989i 0.572149 0.990991i −0.424196 0.905570i \(-0.639443\pi\)
0.996345 0.0854208i \(-0.0272235\pi\)
\(62\) −1.64575 2.85052i −0.209011 0.362017i
\(63\) −1.32288 + 2.29129i −0.166667 + 0.288675i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.14575 + 3.71655i −0.264124 + 0.457476i
\(67\) 2.17712 3.77089i 0.265978 0.460688i −0.701841 0.712333i \(-0.747638\pi\)
0.967819 + 0.251646i \(0.0809718\pi\)
\(68\) −0.354249 −0.0429590
\(69\) −1.00000 −0.120386
\(70\) −1.32288 + 2.29129i −0.158114 + 0.273861i
\(71\) 4.17712 + 7.23499i 0.495733 + 0.858636i 0.999988 0.00491959i \(-0.00156596\pi\)
−0.504254 + 0.863555i \(0.668233\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −4.17712 7.23499i −0.488895 0.846792i 0.511023 0.859567i \(-0.329267\pi\)
−0.999918 + 0.0127753i \(0.995933\pi\)
\(74\) −1.14575 1.98450i −0.133191 0.230693i
\(75\) −1.00000 −0.115470
\(76\) 2.64575 3.46410i 0.303488 0.397360i
\(77\) 11.3542 1.29394
\(78\) 0 0
\(79\) 2.64575 + 4.58258i 0.297670 + 0.515580i 0.975603 0.219544i \(-0.0704571\pi\)
−0.677932 + 0.735124i \(0.737124\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.67712 + 2.90486i −0.185207 + 0.320789i
\(83\) −4.58301 −0.503050 −0.251525 0.967851i \(-0.580932\pi\)
−0.251525 + 0.967851i \(0.580932\pi\)
\(84\) −2.64575 −0.288675
\(85\) −0.177124 + 0.306788i −0.0192118 + 0.0332759i
\(86\) 3.00000 5.19615i 0.323498 0.560316i
\(87\) −1.64575 −0.176443
\(88\) −4.29150 −0.457476
\(89\) 6.61438 11.4564i 0.701123 1.21438i −0.266950 0.963710i \(-0.586016\pi\)
0.968073 0.250670i \(-0.0806508\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) 0 0
\(92\) −0.500000 0.866025i −0.0521286 0.0902894i
\(93\) −1.64575 2.85052i −0.170656 0.295586i
\(94\) 8.58301 0.885269
\(95\) −1.67712 4.02334i −0.172069 0.412786i
\(96\) 1.00000 0.102062
\(97\) −1.82288 3.15731i −0.185085 0.320577i 0.758520 0.651650i \(-0.225923\pi\)
−0.943605 + 0.331073i \(0.892589\pi\)
\(98\) 0 0
\(99\) −2.14575 + 3.71655i −0.215656 + 0.373527i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 9.93725 17.2118i 0.988794 1.71264i 0.365109 0.930965i \(-0.381032\pi\)
0.623684 0.781676i \(-0.285635\pi\)
\(102\) −0.354249 −0.0350758
\(103\) −13.9373 −1.37328 −0.686639 0.726998i \(-0.740915\pi\)
−0.686639 + 0.726998i \(0.740915\pi\)
\(104\) 0 0
\(105\) −1.32288 + 2.29129i −0.129099 + 0.223607i
\(106\) −0.645751 −0.0627209
\(107\) 9.64575 0.932490 0.466245 0.884656i \(-0.345607\pi\)
0.466245 + 0.884656i \(0.345607\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 2.82288 + 4.88936i 0.270382 + 0.468316i 0.968960 0.247218i \(-0.0795165\pi\)
−0.698577 + 0.715535i \(0.746183\pi\)
\(110\) −2.14575 + 3.71655i −0.204589 + 0.354359i
\(111\) −1.14575 1.98450i −0.108750 0.188360i
\(112\) −1.32288 2.29129i −0.125000 0.216506i
\(113\) −0.354249 −0.0333249 −0.0166625 0.999861i \(-0.505304\pi\)
−0.0166625 + 0.999861i \(0.505304\pi\)
\(114\) 2.64575 3.46410i 0.247797 0.324443i
\(115\) −1.00000 −0.0932505
\(116\) −0.822876 1.42526i −0.0764021 0.132332i
\(117\) 0 0
\(118\) −2.64575 + 4.58258i −0.243561 + 0.421860i
\(119\) 0.468627 + 0.811686i 0.0429590 + 0.0744071i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) 7.41699 0.674272
\(122\) 8.93725 0.809141
\(123\) −1.67712 + 2.90486i −0.151221 + 0.261923i
\(124\) 1.64575 2.85052i 0.147793 0.255985i
\(125\) −1.00000 −0.0894427
\(126\) −2.64575 −0.235702
\(127\) −7.61438 + 13.1885i −0.675667 + 1.17029i 0.300607 + 0.953748i \(0.402811\pi\)
−0.976274 + 0.216541i \(0.930522\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 3.00000 5.19615i 0.264135 0.457496i
\(130\) 0 0
\(131\) 9.14575 + 15.8409i 0.799068 + 1.38403i 0.920224 + 0.391393i \(0.128007\pi\)
−0.121156 + 0.992634i \(0.538660\pi\)
\(132\) −4.29150 −0.373527
\(133\) −11.4373 1.47960i −0.991736 0.128298i
\(134\) 4.35425 0.376150
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) −0.177124 0.306788i −0.0151883 0.0263069i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) −0.500000 0.866025i −0.0425628 0.0737210i
\(139\) 3.64575 6.31463i 0.309229 0.535600i −0.668965 0.743294i \(-0.733263\pi\)
0.978194 + 0.207694i \(0.0665958\pi\)
\(140\) −2.64575 −0.223607
\(141\) 8.58301 0.722819
\(142\) −4.17712 + 7.23499i −0.350536 + 0.607147i
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −1.64575 −0.136672
\(146\) 4.17712 7.23499i 0.345701 0.598772i
\(147\) 0 0
\(148\) 1.14575 1.98450i 0.0941802 0.163125i
\(149\) −5.11438 8.85836i −0.418986 0.725705i 0.576852 0.816849i \(-0.304281\pi\)
−0.995838 + 0.0911436i \(0.970948\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 6.22876 0.506889 0.253445 0.967350i \(-0.418436\pi\)
0.253445 + 0.967350i \(0.418436\pi\)
\(152\) 4.32288 + 0.559237i 0.350632 + 0.0453601i
\(153\) −0.354249 −0.0286393
\(154\) 5.67712 + 9.83307i 0.457476 + 0.792371i
\(155\) −1.64575 2.85052i −0.132190 0.228960i
\(156\) 0 0
\(157\) −9.43725 16.3458i −0.753175 1.30454i −0.946277 0.323358i \(-0.895188\pi\)
0.193102 0.981179i \(-0.438145\pi\)
\(158\) −2.64575 + 4.58258i −0.210485 + 0.364570i
\(159\) −0.645751 −0.0512114
\(160\) 1.00000 0.0790569
\(161\) −1.32288 + 2.29129i −0.104257 + 0.180579i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −13.2915 −1.04107 −0.520535 0.853840i \(-0.674268\pi\)
−0.520535 + 0.853840i \(0.674268\pi\)
\(164\) −3.35425 −0.261923
\(165\) −2.14575 + 3.71655i −0.167047 + 0.289333i
\(166\) −2.29150 3.96900i −0.177855 0.308054i
\(167\) 1.79150 3.10297i 0.138631 0.240115i −0.788348 0.615230i \(-0.789063\pi\)
0.926979 + 0.375114i \(0.122397\pi\)
\(168\) −1.32288 2.29129i −0.102062 0.176777i
\(169\) 6.50000 + 11.2583i 0.500000 + 0.866025i
\(170\) −0.354249 −0.0271696
\(171\) 2.64575 3.46410i 0.202326 0.264906i
\(172\) 6.00000 0.457496
\(173\) 3.96863 + 6.87386i 0.301729 + 0.522610i 0.976528 0.215392i \(-0.0691028\pi\)
−0.674799 + 0.738002i \(0.735770\pi\)
\(174\) −0.822876 1.42526i −0.0623820 0.108049i
\(175\) −1.32288 + 2.29129i −0.100000 + 0.173205i
\(176\) −2.14575 3.71655i −0.161742 0.280146i
\(177\) −2.64575 + 4.58258i −0.198867 + 0.344447i
\(178\) 13.2288 0.991537
\(179\) −17.5830 −1.31422 −0.657108 0.753797i \(-0.728220\pi\)
−0.657108 + 0.753797i \(0.728220\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 9.82288 17.0137i 0.730129 1.26462i −0.226699 0.973965i \(-0.572793\pi\)
0.956828 0.290655i \(-0.0938732\pi\)
\(182\) 0 0
\(183\) 8.93725 0.660661
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −1.14575 1.98450i −0.0842373 0.145903i
\(186\) 1.64575 2.85052i 0.120672 0.209011i
\(187\) 0.760130 + 1.31658i 0.0555862 + 0.0962781i
\(188\) 4.29150 + 7.43310i 0.312990 + 0.542115i
\(189\) −2.64575 −0.192450
\(190\) 2.64575 3.46410i 0.191943 0.251312i
\(191\) 16.5830 1.19990 0.599952 0.800036i \(-0.295186\pi\)
0.599952 + 0.800036i \(0.295186\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −3.17712 5.50294i −0.228694 0.396110i 0.728727 0.684804i \(-0.240112\pi\)
−0.957421 + 0.288694i \(0.906779\pi\)
\(194\) 1.82288 3.15731i 0.130875 0.226682i
\(195\) 0 0
\(196\) 0 0
\(197\) 2.64575 0.188502 0.0942510 0.995548i \(-0.469954\pi\)
0.0942510 + 0.995548i \(0.469954\pi\)
\(198\) −4.29150 −0.304984
\(199\) −9.46863 + 16.4001i −0.671213 + 1.16258i 0.306347 + 0.951920i \(0.400893\pi\)
−0.977560 + 0.210655i \(0.932440\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 4.35425 0.307125
\(202\) 19.8745 1.39837
\(203\) −2.17712 + 3.77089i −0.152804 + 0.264665i
\(204\) −0.177124 0.306788i −0.0124012 0.0214795i
\(205\) −1.67712 + 2.90486i −0.117135 + 0.202885i
\(206\) −6.96863 12.0700i −0.485527 0.840958i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 0 0
\(209\) −18.5516 2.39997i −1.28324 0.166009i
\(210\) −2.64575 −0.182574
\(211\) −9.26013 16.0390i −0.637494 1.10417i −0.985981 0.166858i \(-0.946638\pi\)
0.348487 0.937313i \(-0.386695\pi\)
\(212\) −0.322876 0.559237i −0.0221752 0.0384086i
\(213\) −4.17712 + 7.23499i −0.286212 + 0.495733i
\(214\) 4.82288 + 8.35347i 0.329685 + 0.571031i
\(215\) 3.00000 5.19615i 0.204598 0.354375i
\(216\) 1.00000 0.0680414
\(217\) −8.70850 −0.591171
\(218\) −2.82288 + 4.88936i −0.191189 + 0.331150i
\(219\) 4.17712 7.23499i 0.282264 0.488895i
\(220\) −4.29150 −0.289333
\(221\) 0 0
\(222\) 1.14575 1.98450i 0.0768978 0.133191i
\(223\) −0.677124 1.17281i −0.0453436 0.0785374i 0.842463 0.538754i \(-0.181105\pi\)
−0.887806 + 0.460217i \(0.847772\pi\)
\(224\) 1.32288 2.29129i 0.0883883 0.153093i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −0.177124 0.306788i −0.0117821 0.0204073i
\(227\) −24.8118 −1.64681 −0.823407 0.567451i \(-0.807930\pi\)
−0.823407 + 0.567451i \(0.807930\pi\)
\(228\) 4.32288 + 0.559237i 0.286289 + 0.0370364i
\(229\) 25.2915 1.67131 0.835655 0.549255i \(-0.185088\pi\)
0.835655 + 0.549255i \(0.185088\pi\)
\(230\) −0.500000 0.866025i −0.0329690 0.0571040i
\(231\) 5.67712 + 9.83307i 0.373527 + 0.646968i
\(232\) 0.822876 1.42526i 0.0540244 0.0935731i
\(233\) 0.291503 + 0.504897i 0.0190970 + 0.0330769i 0.875416 0.483370i \(-0.160588\pi\)
−0.856319 + 0.516447i \(0.827254\pi\)
\(234\) 0 0
\(235\) 8.58301 0.559894
\(236\) −5.29150 −0.344447
\(237\) −2.64575 + 4.58258i −0.171860 + 0.297670i
\(238\) −0.468627 + 0.811686i −0.0303766 + 0.0526138i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 1.00000 0.0645497
\(241\) −11.2915 + 19.5575i −0.727350 + 1.25981i 0.230650 + 0.973037i \(0.425915\pi\)
−0.958000 + 0.286770i \(0.907419\pi\)
\(242\) 3.70850 + 6.42331i 0.238391 + 0.412906i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 4.46863 + 7.73989i 0.286075 + 0.495496i
\(245\) 0 0
\(246\) −3.35425 −0.213859
\(247\) 0 0
\(248\) 3.29150 0.209011
\(249\) −2.29150 3.96900i −0.145218 0.251525i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −9.29150 + 16.0934i −0.586474 + 1.01580i 0.408215 + 0.912886i \(0.366151\pi\)
−0.994690 + 0.102918i \(0.967182\pi\)
\(252\) −1.32288 2.29129i −0.0833333 0.144338i
\(253\) −2.14575 + 3.71655i −0.134902 + 0.233658i
\(254\) −15.2288 −0.955537
\(255\) −0.354249 −0.0221839
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 6.00000 0.373544
\(259\) −6.06275 −0.376721
\(260\) 0 0
\(261\) −0.822876 1.42526i −0.0509347 0.0882215i
\(262\) −9.14575 + 15.8409i −0.565026 + 0.978654i
\(263\) 3.14575 + 5.44860i 0.193975 + 0.335975i 0.946564 0.322516i \(-0.104528\pi\)
−0.752589 + 0.658491i \(0.771195\pi\)
\(264\) −2.14575 3.71655i −0.132062 0.228738i
\(265\) −0.645751 −0.0396682
\(266\) −4.43725 10.6448i −0.272065 0.652672i
\(267\) 13.2288 0.809587
\(268\) 2.17712 + 3.77089i 0.132989 + 0.230344i
\(269\) 1.46863 + 2.54374i 0.0895438 + 0.155094i 0.907318 0.420444i \(-0.138126\pi\)
−0.817775 + 0.575539i \(0.804792\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 9.93725 + 17.2118i 0.603645 + 1.04554i 0.992264 + 0.124146i \(0.0396190\pi\)
−0.388619 + 0.921399i \(0.627048\pi\)
\(272\) 0.177124 0.306788i 0.0107397 0.0186018i
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) −2.14575 + 3.71655i −0.129394 + 0.224116i
\(276\) 0.500000 0.866025i 0.0300965 0.0521286i
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) 7.29150 0.437315
\(279\) 1.64575 2.85052i 0.0985286 0.170656i
\(280\) −1.32288 2.29129i −0.0790569 0.136931i
\(281\) −13.9059 + 24.0857i −0.829555 + 1.43683i 0.0688322 + 0.997628i \(0.478073\pi\)
−0.898388 + 0.439204i \(0.855261\pi\)
\(282\) 4.29150 + 7.43310i 0.255555 + 0.442635i
\(283\) 5.93725 + 10.2836i 0.352933 + 0.611298i 0.986762 0.162175i \(-0.0518510\pi\)
−0.633829 + 0.773473i \(0.718518\pi\)
\(284\) −8.35425 −0.495733
\(285\) 2.64575 3.46410i 0.156721 0.205196i
\(286\) 0 0
\(287\) 4.43725 + 7.68555i 0.261923 + 0.453664i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 8.43725 14.6138i 0.496309 0.859632i
\(290\) −0.822876 1.42526i −0.0483209 0.0836943i
\(291\) 1.82288 3.15731i 0.106859 0.185085i
\(292\) 8.35425 0.488895
\(293\) −14.6458 −0.855614 −0.427807 0.903870i \(-0.640714\pi\)
−0.427807 + 0.903870i \(0.640714\pi\)
\(294\) 0 0
\(295\) −2.64575 + 4.58258i −0.154042 + 0.266808i
\(296\) 2.29150 0.133191
\(297\) −4.29150 −0.249018
\(298\) 5.11438 8.85836i 0.296268 0.513151i
\(299\) 0 0
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) −7.93725 13.7477i −0.457496 0.792406i
\(302\) 3.11438 + 5.39426i 0.179212 + 0.310405i
\(303\) 19.8745 1.14176
\(304\) 1.67712 + 4.02334i 0.0961897 + 0.230754i
\(305\) 8.93725 0.511746
\(306\) −0.177124 0.306788i −0.0101255 0.0175379i
\(307\) −5.76013 9.97684i −0.328748 0.569408i 0.653516 0.756913i \(-0.273293\pi\)
−0.982264 + 0.187505i \(0.939960\pi\)
\(308\) −5.67712 + 9.83307i −0.323484 + 0.560291i
\(309\) −6.96863 12.0700i −0.396431 0.686639i
\(310\) 1.64575 2.85052i 0.0934724 0.161899i
\(311\) 17.1660 0.973395 0.486698 0.873571i \(-0.338201\pi\)
0.486698 + 0.873571i \(0.338201\pi\)
\(312\) 0 0
\(313\) −9.29150 + 16.0934i −0.525187 + 0.909650i 0.474383 + 0.880319i \(0.342671\pi\)
−0.999570 + 0.0293316i \(0.990662\pi\)
\(314\) 9.43725 16.3458i 0.532575 0.922447i
\(315\) −2.64575 −0.149071
\(316\) −5.29150 −0.297670
\(317\) −9.96863 + 17.2662i −0.559894 + 0.969765i 0.437611 + 0.899164i \(0.355825\pi\)
−0.997505 + 0.0706001i \(0.977509\pi\)
\(318\) −0.322876 0.559237i −0.0181060 0.0313605i
\(319\) −3.53137 + 6.11652i −0.197719 + 0.342459i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 4.82288 + 8.35347i 0.269187 + 0.466245i
\(322\) −2.64575 −0.147442
\(323\) −0.594119 1.42526i −0.0330577 0.0793037i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.64575 11.5108i −0.368074 0.637523i
\(327\) −2.82288 + 4.88936i −0.156105 + 0.270382i
\(328\) −1.67712 2.90486i −0.0926037 0.160394i
\(329\) 11.3542 19.6661i 0.625980 1.08423i
\(330\) −4.29150 −0.236239
\(331\) −13.3542 −0.734016 −0.367008 0.930218i \(-0.619618\pi\)
−0.367008 + 0.930218i \(0.619618\pi\)
\(332\) 2.29150 3.96900i 0.125763 0.217827i
\(333\) 1.14575 1.98450i 0.0627868 0.108750i
\(334\) 3.58301 0.196053
\(335\) 4.35425 0.237898
\(336\) 1.32288 2.29129i 0.0721688 0.125000i
\(337\) −8.64575 14.9749i −0.470964 0.815734i 0.528484 0.848943i \(-0.322761\pi\)
−0.999448 + 0.0332093i \(0.989427\pi\)
\(338\) −6.50000 + 11.2583i −0.353553 + 0.612372i
\(339\) −0.177124 0.306788i −0.00962007 0.0166625i
\(340\) −0.177124 0.306788i −0.00960592 0.0166379i
\(341\) −14.1255 −0.764938
\(342\) 4.32288 + 0.559237i 0.233754 + 0.0302401i
\(343\) −18.5203 −1.00000
\(344\) 3.00000 + 5.19615i 0.161749 + 0.280158i
\(345\) −0.500000 0.866025i −0.0269191 0.0466252i
\(346\) −3.96863 + 6.87386i −0.213355 + 0.369541i
\(347\) 4.29150 + 7.43310i 0.230380 + 0.399030i 0.957920 0.287036i \(-0.0926698\pi\)
−0.727540 + 0.686065i \(0.759336\pi\)
\(348\) 0.822876 1.42526i 0.0441108 0.0764021i
\(349\) 32.9373 1.76309 0.881545 0.472099i \(-0.156504\pi\)
0.881545 + 0.472099i \(0.156504\pi\)
\(350\) −2.64575 −0.141421
\(351\) 0 0
\(352\) 2.14575 3.71655i 0.114369 0.198093i
\(353\) −22.9373 −1.22083 −0.610413 0.792083i \(-0.708997\pi\)
−0.610413 + 0.792083i \(0.708997\pi\)
\(354\) −5.29150 −0.281240
\(355\) −4.17712 + 7.23499i −0.221699 + 0.383993i
\(356\) 6.61438 + 11.4564i 0.350561 + 0.607190i
\(357\) −0.468627 + 0.811686i −0.0248024 + 0.0429590i
\(358\) −8.79150 15.2273i −0.464645 0.804789i
\(359\) 5.46863 + 9.47194i 0.288623 + 0.499910i 0.973481 0.228766i \(-0.0734692\pi\)
−0.684858 + 0.728676i \(0.740136\pi\)
\(360\) 1.00000 0.0527046
\(361\) 18.3745 + 4.83502i 0.967079 + 0.254475i
\(362\) 19.6458 1.03256
\(363\) 3.70850 + 6.42331i 0.194646 + 0.337136i
\(364\) 0 0
\(365\) 4.17712 7.23499i 0.218641 0.378697i
\(366\) 4.46863 + 7.73989i 0.233579 + 0.404570i
\(367\) −14.9373 + 25.8721i −0.779718 + 1.35051i 0.152386 + 0.988321i \(0.451304\pi\)
−0.932104 + 0.362191i \(0.882029\pi\)
\(368\) 1.00000 0.0521286
\(369\) −3.35425 −0.174615
\(370\) 1.14575 1.98450i 0.0595648 0.103169i
\(371\) −0.854249 + 1.47960i −0.0443504 + 0.0768171i
\(372\) 3.29150 0.170656
\(373\) 7.70850 0.399131 0.199565 0.979885i \(-0.436047\pi\)
0.199565 + 0.979885i \(0.436047\pi\)
\(374\) −0.760130 + 1.31658i −0.0393054 + 0.0680789i
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) −4.29150 + 7.43310i −0.221317 + 0.383333i
\(377\) 0 0
\(378\) −1.32288 2.29129i −0.0680414 0.117851i
\(379\) −13.8745 −0.712686 −0.356343 0.934355i \(-0.615976\pi\)
−0.356343 + 0.934355i \(0.615976\pi\)
\(380\) 4.32288 + 0.559237i 0.221759 + 0.0286883i
\(381\) −15.2288 −0.780193
\(382\) 8.29150 + 14.3613i 0.424230 + 0.734788i
\(383\) 7.70850 + 13.3515i 0.393886 + 0.682230i 0.992958 0.118465i \(-0.0377972\pi\)
−0.599072 + 0.800695i \(0.704464\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 5.67712 + 9.83307i 0.289333 + 0.501140i
\(386\) 3.17712 5.50294i 0.161711 0.280092i
\(387\) 6.00000 0.304997
\(388\) 3.64575 0.185085
\(389\) −9.76013 + 16.9050i −0.494858 + 0.857120i −0.999982 0.00592708i \(-0.998113\pi\)
0.505124 + 0.863047i \(0.331447\pi\)
\(390\) 0 0
\(391\) −0.354249 −0.0179151
\(392\) 0 0
\(393\) −9.14575 + 15.8409i −0.461342 + 0.799068i
\(394\) 1.32288 + 2.29129i 0.0666455 + 0.115433i
\(395\) −2.64575 + 4.58258i −0.133122 + 0.230574i
\(396\) −2.14575 3.71655i −0.107828 0.186764i
\(397\) −12.7288 22.0469i −0.638838 1.10650i −0.985688 0.168579i \(-0.946082\pi\)
0.346850 0.937921i \(-0.387251\pi\)
\(398\) −18.9373 −0.949239
\(399\) −4.43725 10.6448i −0.222141 0.532904i
\(400\) 1.00000 0.0500000
\(401\) −3.00000 5.19615i −0.149813 0.259483i 0.781345 0.624099i \(-0.214534\pi\)
−0.931158 + 0.364615i \(0.881200\pi\)
\(402\) 2.17712 + 3.77089i 0.108585 + 0.188075i
\(403\) 0 0
\(404\) 9.93725 + 17.2118i 0.494397 + 0.856320i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) −4.35425 −0.216098
\(407\) −9.83399 −0.487453
\(408\) 0.177124 0.306788i 0.00876896 0.0151883i
\(409\) 19.7915 34.2799i 0.978627 1.69503i 0.311220 0.950338i \(-0.399262\pi\)
0.667407 0.744694i \(-0.267404\pi\)
\(410\) −3.35425 −0.165655
\(411\) 12.0000 0.591916
\(412\) 6.96863 12.0700i 0.343320 0.594647i
\(413\) 7.00000 + 12.1244i 0.344447 + 0.596601i
\(414\) 0.500000 0.866025i 0.0245737 0.0425628i
\(415\) −2.29150 3.96900i −0.112485 0.194830i
\(416\) 0 0
\(417\) 7.29150 0.357066
\(418\) −7.19738 17.2662i −0.352036 0.844516i
\(419\) −4.16601 −0.203523 −0.101761 0.994809i \(-0.532448\pi\)
−0.101761 + 0.994809i \(0.532448\pi\)
\(420\) −1.32288 2.29129i −0.0645497 0.111803i
\(421\) 1.53137 + 2.65242i 0.0746346 + 0.129271i 0.900927 0.433970i \(-0.142888\pi\)
−0.826293 + 0.563241i \(0.809554\pi\)
\(422\) 9.26013 16.0390i 0.450776 0.780767i
\(423\) 4.29150 + 7.43310i 0.208660 + 0.361410i
\(424\) 0.322876 0.559237i 0.0156802 0.0271590i
\(425\) −0.354249 −0.0171836
\(426\) −8.35425 −0.404765
\(427\) 11.8229 20.4778i 0.572149 0.990991i
\(428\) −4.82288 + 8.35347i −0.233122 + 0.403780i
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) −16.8229 + 29.1381i −0.810329 + 1.40353i 0.102304 + 0.994753i \(0.467378\pi\)
−0.912634 + 0.408779i \(0.865955\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 5.46863 9.47194i 0.262805 0.455192i −0.704181 0.710021i \(-0.748686\pi\)
0.966986 + 0.254828i \(0.0820189\pi\)
\(434\) −4.35425 7.54178i −0.209011 0.362017i
\(435\) −0.822876 1.42526i −0.0394539 0.0683361i
\(436\) −5.64575 −0.270382
\(437\) 2.64575 3.46410i 0.126563 0.165710i
\(438\) 8.35425 0.399181
\(439\) 9.46863 + 16.4001i 0.451913 + 0.782736i 0.998505 0.0546630i \(-0.0174084\pi\)
−0.546592 + 0.837399i \(0.684075\pi\)
\(440\) −2.14575 3.71655i −0.102295 0.177180i
\(441\) 0 0
\(442\) 0 0
\(443\) 20.4686 35.4527i 0.972494 1.68441i 0.284525 0.958669i \(-0.408164\pi\)
0.687969 0.725740i \(-0.258502\pi\)
\(444\) 2.29150 0.108750
\(445\) 13.2288 0.627103
\(446\) 0.677124 1.17281i 0.0320628 0.0555343i
\(447\) 5.11438 8.85836i 0.241902 0.418986i
\(448\) 2.64575 0.125000
\(449\) −22.6458 −1.06872 −0.534360 0.845257i \(-0.679447\pi\)
−0.534360 + 0.845257i \(0.679447\pi\)
\(450\) 0.500000 0.866025i 0.0235702 0.0408248i
\(451\) 7.19738 + 12.4662i 0.338912 + 0.587012i
\(452\) 0.177124 0.306788i 0.00833123 0.0144301i
\(453\) 3.11438 + 5.39426i 0.146326 + 0.253445i
\(454\) −12.4059 21.4876i −0.582237 1.00846i
\(455\) 0 0
\(456\) 1.67712 + 4.02334i 0.0785385 + 0.188410i
\(457\) 28.2288 1.32049 0.660243 0.751052i \(-0.270453\pi\)
0.660243 + 0.751052i \(0.270453\pi\)
\(458\) 12.6458 + 21.9031i 0.590897 + 1.02346i
\(459\) −0.177124 0.306788i −0.00826746 0.0143197i
\(460\) 0.500000 0.866025i 0.0233126 0.0403786i
\(461\) −3.58301 6.20595i −0.166877 0.289040i 0.770443 0.637509i \(-0.220035\pi\)
−0.937320 + 0.348469i \(0.886702\pi\)
\(462\) −5.67712 + 9.83307i −0.264124 + 0.457476i
\(463\) 34.6458 1.61012 0.805062 0.593190i \(-0.202132\pi\)
0.805062 + 0.593190i \(0.202132\pi\)
\(464\) 1.64575 0.0764021
\(465\) 1.64575 2.85052i 0.0763199 0.132190i
\(466\) −0.291503 + 0.504897i −0.0135036 + 0.0233889i
\(467\) −21.5203 −0.995839 −0.497919 0.867223i \(-0.665902\pi\)
−0.497919 + 0.867223i \(0.665902\pi\)
\(468\) 0 0
\(469\) 5.76013 9.97684i 0.265978 0.460688i
\(470\) 4.29150 + 7.43310i 0.197952 + 0.342863i
\(471\) 9.43725 16.3458i 0.434846 0.753175i
\(472\) −2.64575 4.58258i −0.121781 0.210930i
\(473\) −12.8745 22.2993i −0.591971 1.02532i
\(474\) −5.29150 −0.243047
\(475\) 2.64575 3.46410i 0.121395 0.158944i
\(476\) −0.937254 −0.0429590
\(477\) −0.322876 0.559237i −0.0147835 0.0256057i
\(478\) −12.0000 20.7846i −0.548867 0.950666i
\(479\) 5.46863 9.47194i 0.249868 0.432784i −0.713621 0.700532i \(-0.752946\pi\)
0.963489 + 0.267748i \(0.0862795\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) 0 0
\(482\) −22.5830 −1.02863
\(483\) −2.64575 −0.120386
\(484\) −3.70850 + 6.42331i −0.168568 + 0.291968i
\(485\) 1.82288 3.15731i 0.0827725 0.143366i
\(486\) 1.00000 0.0453609
\(487\) 15.3542 0.695767 0.347884 0.937538i \(-0.386900\pi\)
0.347884 + 0.937538i \(0.386900\pi\)
\(488\) −4.46863 + 7.73989i −0.202285 + 0.350368i
\(489\) −6.64575 11.5108i −0.300531 0.520535i
\(490\) 0 0
\(491\) 6.72876 + 11.6545i 0.303665 + 0.525962i 0.976963 0.213408i \(-0.0684565\pi\)
−0.673299 + 0.739371i \(0.735123\pi\)
\(492\) −1.67712 2.90486i −0.0756106 0.130961i
\(493\) −0.583005 −0.0262572
\(494\) 0 0
\(495\) −4.29150 −0.192889
\(496\) 1.64575 + 2.85052i 0.0738964 + 0.127992i
\(497\) 11.0516 + 19.1420i 0.495733 + 0.858636i
\(498\) 2.29150 3.96900i 0.102685 0.177855i
\(499\) −6.32288 10.9515i −0.283051 0.490258i 0.689084 0.724682i \(-0.258013\pi\)
−0.972135 + 0.234423i \(0.924680\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 3.58301 0.160077
\(502\) −18.5830 −0.829400
\(503\) 18.3745 31.8256i 0.819279 1.41903i −0.0869355 0.996214i \(-0.527707\pi\)
0.906214 0.422819i \(-0.138959\pi\)
\(504\) 1.32288 2.29129i 0.0589256 0.102062i
\(505\) 19.8745 0.884404
\(506\) −4.29150 −0.190781
\(507\) −6.50000 + 11.2583i −0.288675 + 0.500000i
\(508\) −7.61438 13.1885i −0.337833 0.585145i
\(509\) 6.64575 11.5108i 0.294568 0.510206i −0.680317 0.732918i \(-0.738158\pi\)
0.974884 + 0.222712i \(0.0714910\pi\)
\(510\) −0.177124 0.306788i −0.00784320 0.0135848i
\(511\) −11.0516 19.1420i −0.488895 0.846792i
\(512\) −1.00000 −0.0441942
\(513\) 4.32288 + 0.559237i 0.190860 + 0.0246909i
\(514\) −6.00000 −0.264649
\(515\) −6.96863 12.0700i −0.307074 0.531868i
\(516\) 3.00000 + 5.19615i 0.132068 + 0.228748i
\(517\) 18.4170 31.8992i 0.809979 1.40292i
\(518\) −3.03137 5.25049i −0.133191 0.230693i
\(519\) −3.96863 + 6.87386i −0.174203 + 0.301729i
\(520\) 0 0
\(521\) −30.4575 −1.33437 −0.667184 0.744893i \(-0.732501\pi\)
−0.667184 + 0.744893i \(0.732501\pi\)
\(522\) 0.822876 1.42526i 0.0360163 0.0623820i
\(523\) 20.1144 34.8391i 0.879540 1.52341i 0.0276942 0.999616i \(-0.491184\pi\)
0.851846 0.523792i \(-0.175483\pi\)
\(524\) −18.2915 −0.799068
\(525\) −2.64575 −0.115470
\(526\) −3.14575 + 5.44860i −0.137161 + 0.237570i
\(527\) −0.583005 1.00979i −0.0253961 0.0439873i
\(528\) 2.14575 3.71655i 0.0933818 0.161742i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −0.322876 0.559237i −0.0140248 0.0242917i
\(531\) −5.29150 −0.229632
\(532\) 7.00000 9.16515i 0.303488 0.397360i
\(533\) 0 0
\(534\) 6.61438 + 11.4564i 0.286232 + 0.495769i
\(535\) 4.82288 + 8.35347i 0.208511 + 0.361152i
\(536\) −2.17712 + 3.77089i −0.0940374 + 0.162878i
\(537\) −8.79150 15.2273i −0.379381 0.657108i
\(538\) −1.46863 + 2.54374i −0.0633170 + 0.109668i
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 6.93725 12.0157i 0.298256 0.516594i −0.677481 0.735540i \(-0.736928\pi\)
0.975737 + 0.218946i \(0.0702618\pi\)
\(542\) −9.93725 + 17.2118i −0.426842 + 0.739311i
\(543\) 19.6458 0.843080
\(544\) 0.354249 0.0151883
\(545\) −2.82288 + 4.88936i −0.120919 + 0.209437i
\(546\) 0 0
\(547\) −14.6458 + 25.3672i −0.626207 + 1.08462i 0.362099 + 0.932140i \(0.382060\pi\)
−0.988306 + 0.152483i \(0.951273\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) 4.46863 + 7.73989i 0.190716 + 0.330330i
\(550\) −4.29150 −0.182990
\(551\) 4.35425 5.70105i 0.185497 0.242873i
\(552\) 1.00000 0.0425628
\(553\) 7.00000 + 12.1244i 0.297670 + 0.515580i
\(554\) −4.00000 6.92820i −0.169944 0.294351i
\(555\) 1.14575 1.98450i 0.0486344 0.0842373i
\(556\) 3.64575 + 6.31463i 0.154614 + 0.267800i
\(557\) −6.26013 + 10.8429i −0.265250 + 0.459427i −0.967629 0.252376i \(-0.918788\pi\)
0.702379 + 0.711803i \(0.252121\pi\)
\(558\) 3.29150 0.139340
\(559\) 0 0
\(560\) 1.32288 2.29129i 0.0559017 0.0968246i
\(561\) −0.760130 + 1.31658i −0.0320927 + 0.0555862i
\(562\) −27.8118 −1.17317
\(563\) 42.5830 1.79466 0.897330 0.441361i \(-0.145504\pi\)
0.897330 + 0.441361i \(0.145504\pi\)
\(564\) −4.29150 + 7.43310i −0.180705 + 0.312990i
\(565\) −0.177124 0.306788i −0.00745168 0.0129067i
\(566\) −5.93725 + 10.2836i −0.249561 + 0.432253i
\(567\) −1.32288 2.29129i −0.0555556 0.0962250i
\(568\) −4.17712 7.23499i −0.175268 0.303574i
\(569\) 10.6458 0.446293 0.223147 0.974785i \(-0.428367\pi\)
0.223147 + 0.974785i \(0.428367\pi\)
\(570\) 4.32288 + 0.559237i 0.181065 + 0.0234239i
\(571\) −26.4575 −1.10721 −0.553606 0.832779i \(-0.686749\pi\)
−0.553606 + 0.832779i \(0.686749\pi\)
\(572\) 0 0
\(573\) 8.29150 + 14.3613i 0.346382 + 0.599952i
\(574\) −4.43725 + 7.68555i −0.185207 + 0.320789i
\(575\) −0.500000 0.866025i −0.0208514 0.0361158i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −12.9373 −0.538585 −0.269292 0.963058i \(-0.586790\pi\)
−0.269292 + 0.963058i \(0.586790\pi\)
\(578\) 16.8745 0.701887
\(579\) 3.17712 5.50294i 0.132037 0.228694i
\(580\) 0.822876 1.42526i 0.0341681 0.0591808i
\(581\) −12.1255 −0.503050
\(582\) 3.64575 0.151121
\(583\) −1.38562 + 2.39997i −0.0573866 + 0.0993965i
\(584\) 4.17712 + 7.23499i 0.172851 + 0.299386i
\(585\) 0 0
\(586\) −7.32288 12.6836i −0.302505 0.523954i
\(587\) −21.6458 37.4915i −0.893416 1.54744i −0.835753 0.549105i \(-0.814969\pi\)
−0.0576626 0.998336i \(-0.518365\pi\)
\(588\) 0 0
\(589\) 14.2288 + 1.84073i 0.586286 + 0.0758460i
\(590\) −5.29150 −0.217848
\(591\) 1.32288 + 2.29129i 0.0544158 + 0.0942510i
\(592\) 1.14575 + 1.98450i 0.0470901 + 0.0815624i
\(593\) 15.1771 26.2876i 0.623250 1.07950i −0.365627 0.930762i \(-0.619145\pi\)
0.988877 0.148739i \(-0.0475213\pi\)
\(594\) −2.14575 3.71655i −0.0880412 0.152492i
\(595\) −0.468627 + 0.811686i −0.0192118 + 0.0332759i
\(596\) 10.2288 0.418986
\(597\) −18.9373 −0.775050
\(598\) 0 0
\(599\) −9.76013 + 16.9050i −0.398788 + 0.690721i −0.993577 0.113161i \(-0.963902\pi\)
0.594789 + 0.803882i \(0.297236\pi\)
\(600\) 1.00000 0.0408248
\(601\) −5.70850 −0.232854 −0.116427 0.993199i \(-0.537144\pi\)
−0.116427 + 0.993199i \(0.537144\pi\)
\(602\) 7.93725 13.7477i 0.323498 0.560316i
\(603\) 2.17712 + 3.77089i 0.0886594 + 0.153563i
\(604\) −3.11438 + 5.39426i −0.126722 + 0.219489i
\(605\) 3.70850 + 6.42331i 0.150772 + 0.261145i
\(606\) 9.93725 + 17.2118i 0.403673 + 0.699183i
\(607\) 19.2288 0.780471 0.390236 0.920715i \(-0.372394\pi\)
0.390236 + 0.920715i \(0.372394\pi\)
\(608\) −2.64575 + 3.46410i −0.107299 + 0.140488i
\(609\) −4.35425 −0.176443
\(610\) 4.46863 + 7.73989i 0.180929 + 0.313379i
\(611\) 0 0
\(612\) 0.177124 0.306788i 0.00715983 0.0124012i
\(613\) −1.43725 2.48940i −0.0580501 0.100546i 0.835540 0.549430i \(-0.185155\pi\)
−0.893590 + 0.448884i \(0.851822\pi\)
\(614\) 5.76013 9.97684i 0.232460 0.402632i
\(615\) −3.35425 −0.135256
\(616\) −11.3542 −0.457476
\(617\) −9.29150 + 16.0934i −0.374062 + 0.647894i −0.990186 0.139755i \(-0.955369\pi\)
0.616124 + 0.787649i \(0.288702\pi\)
\(618\) 6.96863 12.0700i 0.280319 0.485527i
\(619\) −33.9373 −1.36405 −0.682027 0.731327i \(-0.738901\pi\)
−0.682027 + 0.731327i \(0.738901\pi\)
\(620\) 3.29150 0.132190
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) 8.58301 + 14.8662i 0.344147 + 0.596080i
\(623\) 17.5000 30.3109i 0.701123 1.21438i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −18.5830 −0.742726
\(627\) −7.19738 17.2662i −0.287436 0.689544i
\(628\) 18.8745 0.753175
\(629\) −0.405881 0.703006i −0.0161835 0.0280307i
\(630\) −1.32288 2.29129i −0.0527046 0.0912871i
\(631\) −10.8229 + 18.7458i −0.430852 + 0.746257i −0.996947 0.0780827i \(-0.975120\pi\)
0.566095 + 0.824340i \(0.308454\pi\)
\(632\) −2.64575 4.58258i −0.105242 0.182285i
\(633\) 9.26013 16.0390i 0.368057 0.637494i
\(634\) −19.9373 −0.791810
\(635\) −15.2288 −0.604335
\(636\) 0.322876 0.559237i 0.0128029 0.0221752i
\(637\) 0 0
\(638\) −7.06275 −0.279617
\(639\) −8.35425 −0.330489
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 5.35425 + 9.27383i 0.211480 + 0.366294i 0.952178 0.305544i \(-0.0988383\pi\)
−0.740698 + 0.671838i \(0.765505\pi\)
\(642\) −4.82288 + 8.35347i −0.190344 + 0.329685i
\(643\) −24.4059 42.2722i −0.962474 1.66705i −0.716254 0.697840i \(-0.754145\pi\)
−0.246220 0.969214i \(-0.579189\pi\)
\(644\) −1.32288 2.29129i −0.0521286 0.0902894i
\(645\) 6.00000 0.236250
\(646\) 0.937254 1.22715i 0.0368758 0.0482817i
\(647\) 5.12549 0.201504 0.100752 0.994912i \(-0.467875\pi\)
0.100752 + 0.994912i \(0.467875\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 11.3542 + 19.6661i 0.445693 + 0.771963i
\(650\) 0 0
\(651\) −4.35425 7.54178i −0.170656 0.295586i
\(652\) 6.64575 11.5108i 0.260268 0.450797i
\(653\) 10.0627 0.393786 0.196893 0.980425i \(-0.436915\pi\)
0.196893 + 0.980425i \(0.436915\pi\)
\(654\) −5.64575 −0.220766
\(655\) −9.14575 + 15.8409i −0.357354 + 0.618955i
\(656\) 1.67712 2.90486i 0.0654807 0.113416i
\(657\) 8.35425 0.325930
\(658\) 22.7085 0.885269
\(659\) 5.79150 10.0312i 0.225605 0.390759i −0.730896 0.682489i \(-0.760897\pi\)
0.956501 + 0.291730i \(0.0942308\pi\)
\(660\) −2.14575 3.71655i −0.0835233 0.144667i
\(661\) 6.70850 11.6195i 0.260930 0.451945i −0.705559 0.708651i \(-0.749304\pi\)
0.966489 + 0.256707i \(0.0826374\pi\)
\(662\) −6.67712 11.5651i −0.259514 0.449491i
\(663\) 0 0
\(664\) 4.58301 0.177855
\(665\) −4.43725 10.6448i −0.172069 0.412786i
\(666\) 2.29150 0.0887939
\(667\) −0.822876 1.42526i −0.0318619 0.0551864i
\(668\) 1.79150 + 3.10297i 0.0693153 + 0.120058i
\(669\) 0.677124 1.17281i 0.0261791 0.0453436i
\(670\) 2.17712 + 3.77089i 0.0841097 + 0.145682i
\(671\) 19.1771 33.2158i 0.740325 1.28228i
\(672\) 2.64575 0.102062
\(673\) −6.12549 −0.236120 −0.118060 0.993006i \(-0.537668\pi\)
−0.118060 + 0.993006i \(0.537668\pi\)
\(674\) 8.64575 14.9749i 0.333022 0.576811i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) −13.0000 −0.500000
\(677\) −41.2288 −1.58455 −0.792275 0.610164i \(-0.791103\pi\)
−0.792275 + 0.610164i \(0.791103\pi\)
\(678\) 0.177124 0.306788i 0.00680242 0.0117821i
\(679\) −4.82288 8.35347i −0.185085 0.320577i
\(680\) 0.177124 0.306788i 0.00679241 0.0117648i
\(681\) −12.4059 21.4876i −0.475394 0.823407i
\(682\) −7.06275 12.2330i −0.270447 0.468427i
\(683\) 28.9373 1.10725 0.553627 0.832765i \(-0.313243\pi\)
0.553627 + 0.832765i \(0.313243\pi\)
\(684\) 1.67712 + 4.02334i 0.0641265 + 0.153836i
\(685\) 12.0000 0.458496
\(686\) −9.26013 16.0390i −0.353553 0.612372i
\(687\) 12.6458 + 21.9031i 0.482466 + 0.835655i
\(688\) −3.00000 + 5.19615i −0.114374 + 0.198101i
\(689\) 0 0
\(690\) 0.500000 0.866025i 0.0190347 0.0329690i
\(691\) −13.8118 −0.525424 −0.262712 0.964874i \(-0.584617\pi\)
−0.262712 + 0.964874i \(0.584617\pi\)
\(692\) −7.93725 −0.301729
\(693\) −5.67712 + 9.83307i −0.215656 + 0.373527i
\(694\) −4.29150 + 7.43310i −0.162903 + 0.282157i
\(695\) 7.29150 0.276582
\(696\) 1.64575 0.0623820
\(697\) −0.594119 + 1.02904i −0.0225039 + 0.0389778i
\(698\) 16.4686 + 28.5245i 0.623347 + 1.07967i
\(699\) −0.291503 + 0.504897i −0.0110256 + 0.0190970i
\(700\) −1.32288 2.29129i −0.0500000 0.0866025i
\(701\) 20.1660 + 34.9286i 0.761660 + 1.31923i 0.941995 + 0.335628i \(0.108949\pi\)
−0.180335 + 0.983605i \(0.557718\pi\)
\(702\) 0 0
\(703\) 9.90588 + 1.28149i 0.373607 + 0.0483324i
\(704\) 4.29150 0.161742
\(705\) 4.29150 + 7.43310i 0.161627 + 0.279947i
\(706\) −11.4686 19.8642i −0.431627 0.747601i
\(707\) 26.2915 45.5382i 0.988794 1.71264i
\(708\) −2.64575 4.58258i −0.0994334 0.172224i
\(709\) −12.4686 + 21.5963i −0.468269 + 0.811066i −0.999342 0.0362600i \(-0.988456\pi\)
0.531073 + 0.847326i \(0.321789\pi\)
\(710\) −8.35425 −0.313529
\(711\) −5.29150 −0.198447
\(712\) −6.61438 + 11.4564i −0.247884 + 0.429348i
\(713\) 1.64575 2.85052i 0.0616339 0.106753i
\(714\) −0.937254 −0.0350758
\(715\) 0 0
\(716\) 8.79150 15.2273i 0.328554 0.569072i
\(717\) −12.0000 20.7846i −0.448148 0.776215i
\(718\) −5.46863 + 9.47194i −0.204087 + 0.353490i
\(719\) 11.6458 + 20.1710i 0.434313 + 0.752253i 0.997239 0.0742547i \(-0.0236578\pi\)
−0.562926 + 0.826507i \(0.690324\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −36.8745 −1.37328
\(722\) 5.00000 + 18.3303i 0.186081 + 0.682183i
\(723\) −22.5830 −0.839871
\(724\) 9.82288 + 17.0137i 0.365064 + 0.632310i
\(725\) −0.822876 1.42526i −0.0305608 0.0529329i
\(726\) −3.70850 + 6.42331i −0.137635 + 0.238391i
\(727\) 9.93725 + 17.2118i 0.368552 + 0.638351i 0.989339 0.145628i \(-0.0465202\pi\)
−0.620787 + 0.783979i \(0.713187\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 8.35425 0.309205
\(731\) 1.06275 1.84073i 0.0393071 0.0680819i
\(732\) −4.46863 + 7.73989i −0.165165 + 0.286075i
\(733\) −1.70850 −0.0631048 −0.0315524 0.999502i \(-0.510045\pi\)
−0.0315524 + 0.999502i \(0.510045\pi\)
\(734\) −29.8745 −1.10269
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) 9.34313 16.1828i 0.344159 0.596101i
\(738\) −1.67712 2.90486i −0.0617358 0.106930i
\(739\) 25.4889 + 44.1480i 0.937624 + 1.62401i 0.769887 + 0.638180i \(0.220313\pi\)
0.167737 + 0.985832i \(0.446354\pi\)
\(740\) 2.29150 0.0842373
\(741\) 0 0
\(742\) −1.70850 −0.0627209
\(743\) 10.2085 + 17.6816i 0.374513 + 0.648676i 0.990254 0.139273i \(-0.0444764\pi\)
−0.615741 + 0.787949i \(0.711143\pi\)
\(744\) 1.64575 + 2.85052i 0.0603362 + 0.104505i
\(745\) 5.11438 8.85836i 0.187376 0.324545i
\(746\) 3.85425 + 6.67575i 0.141114 + 0.244417i
\(747\) 2.29150 3.96900i 0.0838417 0.145218i
\(748\) −1.52026 −0.0555862
\(749\) 25.5203 0.932490
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) 22.0000 38.1051i 0.802791 1.39048i −0.114981 0.993368i \(-0.536681\pi\)
0.917772 0.397108i \(-0.129986\pi\)
\(752\) −8.58301 −0.312990
\(753\) −18.5830 −0.677202
\(754\) 0 0
\(755\) 3.11438 + 5.39426i 0.113344 + 0.196317i
\(756\) 1.32288 2.29129i 0.0481125 0.0833333i
\(757\) 14.7288 + 25.5110i 0.535326 + 0.927211i 0.999147 + 0.0412829i \(0.0131445\pi\)
−0.463822 + 0.885929i \(0.653522\pi\)
\(758\) −6.93725 12.0157i −0.251972 0.436429i
\(759\) −4.29150 −0.155772
\(760\) 1.67712 + 4.02334i 0.0608357 + 0.145942i
\(761\) 16.5203 0.598859 0.299429 0.954118i \(-0.403204\pi\)
0.299429 + 0.954118i \(0.403204\pi\)
\(762\) −7.61438 13.1885i −0.275840 0.477769i
\(763\) 7.46863 + 12.9360i 0.270382 + 0.468316i
\(764\) −8.29150 + 14.3613i −0.299976 + 0.519574i
\(765\) −0.177124 0.306788i −0.00640394 0.0110920i
\(766\) −7.70850 + 13.3515i −0.278519 + 0.482410i
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −4.35425 + 7.54178i −0.157018 + 0.271964i −0.933792 0.357816i \(-0.883521\pi\)
0.776774 + 0.629780i \(0.216855\pi\)
\(770\) −5.67712 + 9.83307i −0.204589 + 0.354359i
\(771\) −6.00000 −0.216085
\(772\) 6.35425 0.228694
\(773\) −6.96863 + 12.0700i −0.250644 + 0.434128i −0.963703 0.266976i \(-0.913976\pi\)
0.713059 + 0.701104i \(0.247309\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) 1.64575 2.85052i 0.0591171 0.102394i
\(776\) 1.82288 + 3.15731i 0.0654374 + 0.113341i
\(777\) −3.03137 5.25049i −0.108750 0.188360i
\(778\) −19.5203 −0.699835
\(779\) −5.62549 13.4953i −0.201554 0.483519i
\(780\) 0 0
\(781\) 17.9261 + 31.0490i 0.641448 + 1.11102i