Properties

Label 168.2.q.c.121.2
Level $168$
Weight $2$
Character 168.121
Analytic conductor $1.341$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) Copy content Toggle raw display
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 \(2.13746 - 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 168.121
Dual form 168.2.q.c.25.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(2.13746 - 3.70219i) q^{5} +(-1.50000 - 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(2.13746 - 3.70219i) q^{5} +(-1.50000 - 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.13746 + 3.70219i) q^{11} -1.27492 q^{13} +4.27492 q^{15} +(2.00000 + 3.46410i) q^{17} +(-0.637459 + 1.10411i) q^{19} +(1.13746 - 2.38876i) q^{21} +(-2.00000 + 3.46410i) q^{23} +(-6.63746 - 11.4964i) q^{25} -1.00000 q^{27} -2.27492 q^{29} +(0.500000 + 0.866025i) q^{31} +(-2.13746 + 3.70219i) q^{33} +(-11.2749 + 0.894797i) q^{35} +(-2.63746 + 4.56821i) q^{37} +(-0.637459 - 1.10411i) q^{39} +10.5498 q^{41} -7.27492 q^{43} +(2.13746 + 3.70219i) q^{45} +(3.00000 - 5.19615i) q^{47} +(-2.50000 + 6.53835i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-0.862541 - 1.49397i) q^{53} +18.2749 q^{55} -1.27492 q^{57} +(-3.13746 - 5.43424i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(2.63746 - 0.209313i) q^{63} +(-2.72508 + 4.71998i) q^{65} +(-3.63746 - 6.30026i) q^{67} -4.00000 q^{69} +2.00000 q^{71} +(-1.63746 - 2.83616i) q^{73} +(6.63746 - 11.4964i) q^{75} +(4.86254 - 10.2118i) q^{77} +(1.77492 - 3.07425i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.274917 q^{83} +17.0997 q^{85} +(-1.13746 - 1.97014i) q^{87} +(-2.27492 + 3.94027i) q^{89} +(1.91238 + 2.77862i) q^{91} +(-0.500000 + 0.866025i) q^{93} +(2.72508 + 4.71998i) q^{95} +16.2749 q^{97} -4.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + q^{5} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + q^{5} - 6 q^{7} - 2 q^{9} + q^{11} + 10 q^{13} + 2 q^{15} + 8 q^{17} + 5 q^{19} - 3 q^{21} - 8 q^{23} - 19 q^{25} - 4 q^{27} + 6 q^{29} + 2 q^{31} - q^{33} - 30 q^{35} - 3 q^{37} + 5 q^{39} + 12 q^{41} - 14 q^{43} + q^{45} + 12 q^{47} - 10 q^{49} - 8 q^{51} - 11 q^{53} + 58 q^{55} + 10 q^{57} - 5 q^{59} - 20 q^{61} + 3 q^{63} - 26 q^{65} - 7 q^{67} - 16 q^{69} + 8 q^{71} + q^{73} + 19 q^{75} + 27 q^{77} - 8 q^{79} - 2 q^{81} + 14 q^{83} + 8 q^{85} + 3 q^{87} + 6 q^{89} - 15 q^{91} - 2 q^{93} + 26 q^{95} + 50 q^{97} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 2.13746 3.70219i 0.955901 1.65567i 0.223607 0.974679i \(-0.428217\pi\)
0.732294 0.680989i \(-0.238450\pi\)
\(6\) 0 0
\(7\) −1.50000 2.17945i −0.566947 0.823754i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.13746 + 3.70219i 0.644468 + 1.11625i 0.984424 + 0.175810i \(0.0562545\pi\)
−0.339956 + 0.940441i \(0.610412\pi\)
\(12\) 0 0
\(13\) −1.27492 −0.353598 −0.176799 0.984247i \(-0.556574\pi\)
−0.176799 + 0.984247i \(0.556574\pi\)
\(14\) 0 0
\(15\) 4.27492 1.10378
\(16\) 0 0
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 0 0
\(19\) −0.637459 + 1.10411i −0.146243 + 0.253300i −0.929836 0.367974i \(-0.880051\pi\)
0.783593 + 0.621275i \(0.213385\pi\)
\(20\) 0 0
\(21\) 1.13746 2.38876i 0.248214 0.521271i
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) −6.63746 11.4964i −1.32749 2.29928i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.27492 −0.422442 −0.211221 0.977438i \(-0.567744\pi\)
−0.211221 + 0.977438i \(0.567744\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) −2.13746 + 3.70219i −0.372084 + 0.644468i
\(34\) 0 0
\(35\) −11.2749 + 0.894797i −1.90581 + 0.151248i
\(36\) 0 0
\(37\) −2.63746 + 4.56821i −0.433596 + 0.751009i −0.997180 0.0750491i \(-0.976089\pi\)
0.563584 + 0.826059i \(0.309422\pi\)
\(38\) 0 0
\(39\) −0.637459 1.10411i −0.102075 0.176799i
\(40\) 0 0
\(41\) 10.5498 1.64761 0.823804 0.566875i \(-0.191848\pi\)
0.823804 + 0.566875i \(0.191848\pi\)
\(42\) 0 0
\(43\) −7.27492 −1.10941 −0.554707 0.832046i \(-0.687170\pi\)
−0.554707 + 0.832046i \(0.687170\pi\)
\(44\) 0 0
\(45\) 2.13746 + 3.70219i 0.318634 + 0.551889i
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −2.50000 + 6.53835i −0.357143 + 0.934050i
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) −0.862541 1.49397i −0.118479 0.205212i 0.800686 0.599084i \(-0.204469\pi\)
−0.919165 + 0.393872i \(0.871135\pi\)
\(54\) 0 0
\(55\) 18.2749 2.46419
\(56\) 0 0
\(57\) −1.27492 −0.168867
\(58\) 0 0
\(59\) −3.13746 5.43424i −0.408462 0.707477i 0.586255 0.810126i \(-0.300602\pi\)
−0.994718 + 0.102649i \(0.967268\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 0 0
\(63\) 2.63746 0.209313i 0.332289 0.0263710i
\(64\) 0 0
\(65\) −2.72508 + 4.71998i −0.338005 + 0.585442i
\(66\) 0 0
\(67\) −3.63746 6.30026i −0.444386 0.769700i 0.553623 0.832767i \(-0.313245\pi\)
−0.998009 + 0.0630678i \(0.979912\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −1.63746 2.83616i −0.191650 0.331948i 0.754147 0.656705i \(-0.228051\pi\)
−0.945797 + 0.324758i \(0.894717\pi\)
\(74\) 0 0
\(75\) 6.63746 11.4964i 0.766428 1.32749i
\(76\) 0 0
\(77\) 4.86254 10.2118i 0.554138 1.16374i
\(78\) 0 0
\(79\) 1.77492 3.07425i 0.199694 0.345880i −0.748735 0.662869i \(-0.769339\pi\)
0.948429 + 0.316989i \(0.102672\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −0.274917 −0.0301761 −0.0150880 0.999886i \(-0.504803\pi\)
−0.0150880 + 0.999886i \(0.504803\pi\)
\(84\) 0 0
\(85\) 17.0997 1.85472
\(86\) 0 0
\(87\) −1.13746 1.97014i −0.121948 0.211221i
\(88\) 0 0
\(89\) −2.27492 + 3.94027i −0.241141 + 0.417668i −0.961040 0.276411i \(-0.910855\pi\)
0.719899 + 0.694079i \(0.244188\pi\)
\(90\) 0 0
\(91\) 1.91238 + 2.77862i 0.200471 + 0.291278i
\(92\) 0 0
\(93\) −0.500000 + 0.866025i −0.0518476 + 0.0898027i
\(94\) 0 0
\(95\) 2.72508 + 4.71998i 0.279588 + 0.484260i
\(96\) 0 0
\(97\) 16.2749 1.65247 0.826234 0.563327i \(-0.190479\pi\)
0.826234 + 0.563327i \(0.190479\pi\)
\(98\) 0 0
\(99\) −4.27492 −0.429645
\(100\) 0 0
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) 5.91238 10.2405i 0.582564 1.00903i −0.412611 0.910907i \(-0.635383\pi\)
0.995174 0.0981224i \(-0.0312837\pi\)
\(104\) 0 0
\(105\) −6.41238 9.31697i −0.625784 0.909243i
\(106\) 0 0
\(107\) −3.41238 + 5.91041i −0.329887 + 0.571381i −0.982489 0.186320i \(-0.940344\pi\)
0.652602 + 0.757701i \(0.273677\pi\)
\(108\) 0 0
\(109\) 2.91238 + 5.04438i 0.278955 + 0.483164i 0.971125 0.238570i \(-0.0766786\pi\)
−0.692170 + 0.721734i \(0.743345\pi\)
\(110\) 0 0
\(111\) −5.27492 −0.500673
\(112\) 0 0
\(113\) 10.5498 0.992445 0.496222 0.868195i \(-0.334720\pi\)
0.496222 + 0.868195i \(0.334720\pi\)
\(114\) 0 0
\(115\) 8.54983 + 14.8087i 0.797276 + 1.38092i
\(116\) 0 0
\(117\) 0.637459 1.10411i 0.0589331 0.102075i
\(118\) 0 0
\(119\) 4.54983 9.55505i 0.417083 0.875910i
\(120\) 0 0
\(121\) −3.63746 + 6.30026i −0.330678 + 0.572751i
\(122\) 0 0
\(123\) 5.27492 + 9.13642i 0.475623 + 0.823804i
\(124\) 0 0
\(125\) −35.3746 −3.16400
\(126\) 0 0
\(127\) −21.5498 −1.91224 −0.956119 0.292978i \(-0.905354\pi\)
−0.956119 + 0.292978i \(0.905354\pi\)
\(128\) 0 0
\(129\) −3.63746 6.30026i −0.320260 0.554707i
\(130\) 0 0
\(131\) 0.137459 0.238085i 0.0120098 0.0208016i −0.859958 0.510365i \(-0.829510\pi\)
0.871968 + 0.489563i \(0.162844\pi\)
\(132\) 0 0
\(133\) 3.36254 0.266857i 0.291569 0.0231395i
\(134\) 0 0
\(135\) −2.13746 + 3.70219i −0.183963 + 0.318634i
\(136\) 0 0
\(137\) −8.27492 14.3326i −0.706974 1.22451i −0.965974 0.258638i \(-0.916726\pi\)
0.259001 0.965877i \(-0.416607\pi\)
\(138\) 0 0
\(139\) 0.725083 0.0615007 0.0307504 0.999527i \(-0.490210\pi\)
0.0307504 + 0.999527i \(0.490210\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) −2.72508 4.71998i −0.227883 0.394705i
\(144\) 0 0
\(145\) −4.86254 + 8.42217i −0.403812 + 0.699423i
\(146\) 0 0
\(147\) −6.91238 + 1.10411i −0.570123 + 0.0910655i
\(148\) 0 0
\(149\) −0.274917 + 0.476171i −0.0225221 + 0.0390094i −0.877067 0.480368i \(-0.840503\pi\)
0.854545 + 0.519378i \(0.173836\pi\)
\(150\) 0 0
\(151\) 7.68729 + 13.3148i 0.625583 + 1.08354i 0.988428 + 0.151692i \(0.0484722\pi\)
−0.362845 + 0.931850i \(0.618194\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) 4.27492 0.343370
\(156\) 0 0
\(157\) −7.27492 12.6005i −0.580602 1.00563i −0.995408 0.0957218i \(-0.969484\pi\)
0.414807 0.909910i \(-0.363849\pi\)
\(158\) 0 0
\(159\) 0.862541 1.49397i 0.0684040 0.118479i
\(160\) 0 0
\(161\) 10.5498 0.837253i 0.831443 0.0659848i
\(162\) 0 0
\(163\) 6.00000 10.3923i 0.469956 0.813988i −0.529454 0.848339i \(-0.677603\pi\)
0.999410 + 0.0343508i \(0.0109363\pi\)
\(164\) 0 0
\(165\) 9.13746 + 15.8265i 0.711350 + 1.23209i
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) −11.3746 −0.874968
\(170\) 0 0
\(171\) −0.637459 1.10411i −0.0487477 0.0844335i
\(172\) 0 0
\(173\) 3.72508 6.45203i 0.283213 0.490539i −0.688961 0.724798i \(-0.741933\pi\)
0.972174 + 0.234259i \(0.0752664\pi\)
\(174\) 0 0
\(175\) −15.0997 + 31.7106i −1.14143 + 2.39710i
\(176\) 0 0
\(177\) 3.13746 5.43424i 0.235826 0.408462i
\(178\) 0 0
\(179\) 0.725083 + 1.25588i 0.0541952 + 0.0938689i 0.891850 0.452331i \(-0.149407\pi\)
−0.837655 + 0.546200i \(0.816074\pi\)
\(180\) 0 0
\(181\) 3.82475 0.284292 0.142146 0.989846i \(-0.454600\pi\)
0.142146 + 0.989846i \(0.454600\pi\)
\(182\) 0 0
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) 11.2749 + 19.5287i 0.828948 + 1.43578i
\(186\) 0 0
\(187\) −8.54983 + 14.8087i −0.625226 + 1.08292i
\(188\) 0 0
\(189\) 1.50000 + 2.17945i 0.109109 + 0.158532i
\(190\) 0 0
\(191\) 5.27492 9.13642i 0.381680 0.661088i −0.609623 0.792692i \(-0.708679\pi\)
0.991302 + 0.131603i \(0.0420124\pi\)
\(192\) 0 0
\(193\) −7.77492 13.4666i −0.559651 0.969344i −0.997525 0.0703075i \(-0.977602\pi\)
0.437875 0.899036i \(-0.355731\pi\)
\(194\) 0 0
\(195\) −5.45017 −0.390294
\(196\) 0 0
\(197\) −16.5498 −1.17913 −0.589563 0.807722i \(-0.700700\pi\)
−0.589563 + 0.807722i \(0.700700\pi\)
\(198\) 0 0
\(199\) −12.5498 21.7370i −0.889634 1.54089i −0.840308 0.542109i \(-0.817626\pi\)
−0.0493259 0.998783i \(-0.515707\pi\)
\(200\) 0 0
\(201\) 3.63746 6.30026i 0.256567 0.444386i
\(202\) 0 0
\(203\) 3.41238 + 4.95807i 0.239502 + 0.347988i
\(204\) 0 0
\(205\) 22.5498 39.0575i 1.57495 2.72789i
\(206\) 0 0
\(207\) −2.00000 3.46410i −0.139010 0.240772i
\(208\) 0 0
\(209\) −5.45017 −0.376996
\(210\) 0 0
\(211\) 17.6495 1.21504 0.607521 0.794304i \(-0.292164\pi\)
0.607521 + 0.794304i \(0.292164\pi\)
\(212\) 0 0
\(213\) 1.00000 + 1.73205i 0.0685189 + 0.118678i
\(214\) 0 0
\(215\) −15.5498 + 26.9331i −1.06049 + 1.83682i
\(216\) 0 0
\(217\) 1.13746 2.38876i 0.0772157 0.162160i
\(218\) 0 0
\(219\) 1.63746 2.83616i 0.110649 0.191650i
\(220\) 0 0
\(221\) −2.54983 4.41644i −0.171520 0.297082i
\(222\) 0 0
\(223\) 6.27492 0.420200 0.210100 0.977680i \(-0.432621\pi\)
0.210100 + 0.977680i \(0.432621\pi\)
\(224\) 0 0
\(225\) 13.2749 0.884994
\(226\) 0 0
\(227\) 1.86254 + 3.22602i 0.123621 + 0.214118i 0.921193 0.389106i \(-0.127216\pi\)
−0.797572 + 0.603224i \(0.793883\pi\)
\(228\) 0 0
\(229\) −5.36254 + 9.28819i −0.354367 + 0.613781i −0.987009 0.160663i \(-0.948637\pi\)
0.632643 + 0.774444i \(0.281970\pi\)
\(230\) 0 0
\(231\) 11.2749 0.894797i 0.741835 0.0588733i
\(232\) 0 0
\(233\) −7.27492 + 12.6005i −0.476596 + 0.825488i −0.999640 0.0268173i \(-0.991463\pi\)
0.523045 + 0.852305i \(0.324796\pi\)
\(234\) 0 0
\(235\) −12.8248 22.2131i −0.836595 1.44902i
\(236\) 0 0
\(237\) 3.54983 0.230587
\(238\) 0 0
\(239\) 30.5498 1.97610 0.988052 0.154119i \(-0.0492540\pi\)
0.988052 + 0.154119i \(0.0492540\pi\)
\(240\) 0 0
\(241\) 6.41238 + 11.1066i 0.413057 + 0.715436i 0.995222 0.0976343i \(-0.0311275\pi\)
−0.582165 + 0.813071i \(0.697794\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 18.8625 + 23.2309i 1.20508 + 1.48417i
\(246\) 0 0
\(247\) 0.812707 1.40765i 0.0517113 0.0895666i
\(248\) 0 0
\(249\) −0.137459 0.238085i −0.00871109 0.0150880i
\(250\) 0 0
\(251\) 19.3746 1.22291 0.611457 0.791278i \(-0.290584\pi\)
0.611457 + 0.791278i \(0.290584\pi\)
\(252\) 0 0
\(253\) −17.0997 −1.07505
\(254\) 0 0
\(255\) 8.54983 + 14.8087i 0.535411 + 0.927360i
\(256\) 0 0
\(257\) 9.54983 16.5408i 0.595702 1.03179i −0.397745 0.917496i \(-0.630207\pi\)
0.993447 0.114291i \(-0.0364595\pi\)
\(258\) 0 0
\(259\) 13.9124 1.10411i 0.864473 0.0686061i
\(260\) 0 0
\(261\) 1.13746 1.97014i 0.0704069 0.121948i
\(262\) 0 0
\(263\) 12.2749 + 21.2608i 0.756904 + 1.31100i 0.944422 + 0.328735i \(0.106622\pi\)
−0.187518 + 0.982261i \(0.560044\pi\)
\(264\) 0 0
\(265\) −7.37459 −0.453017
\(266\) 0 0
\(267\) −4.54983 −0.278445
\(268\) 0 0
\(269\) −14.1375 24.4868i −0.861976 1.49299i −0.870019 0.493019i \(-0.835893\pi\)
0.00804266 0.999968i \(-0.497440\pi\)
\(270\) 0 0
\(271\) 3.13746 5.43424i 0.190587 0.330106i −0.754858 0.655888i \(-0.772294\pi\)
0.945445 + 0.325782i \(0.105628\pi\)
\(272\) 0 0
\(273\) −1.45017 + 3.04547i −0.0877680 + 0.184321i
\(274\) 0 0
\(275\) 28.3746 49.1462i 1.71105 2.96363i
\(276\) 0 0
\(277\) 2.08762 + 3.61587i 0.125433 + 0.217257i 0.921902 0.387423i \(-0.126635\pi\)
−0.796469 + 0.604679i \(0.793301\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) −11.4502 −0.683060 −0.341530 0.939871i \(-0.610945\pi\)
−0.341530 + 0.939871i \(0.610945\pi\)
\(282\) 0 0
\(283\) −13.4622 23.3172i −0.800245 1.38607i −0.919454 0.393196i \(-0.871369\pi\)
0.119209 0.992869i \(-0.461964\pi\)
\(284\) 0 0
\(285\) −2.72508 + 4.71998i −0.161420 + 0.279588i
\(286\) 0 0
\(287\) −15.8248 22.9928i −0.934106 1.35722i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 8.13746 + 14.0945i 0.477026 + 0.826234i
\(292\) 0 0
\(293\) −5.17525 −0.302341 −0.151171 0.988508i \(-0.548304\pi\)
−0.151171 + 0.988508i \(0.548304\pi\)
\(294\) 0 0
\(295\) −26.8248 −1.56180
\(296\) 0 0
\(297\) −2.13746 3.70219i −0.124028 0.214823i
\(298\) 0 0
\(299\) 2.54983 4.41644i 0.147461 0.255409i
\(300\) 0 0
\(301\) 10.9124 + 15.8553i 0.628979 + 0.913885i
\(302\) 0 0
\(303\) −3.00000 + 5.19615i −0.172345 + 0.298511i
\(304\) 0 0
\(305\) 21.3746 + 37.0219i 1.22391 + 2.11987i
\(306\) 0 0
\(307\) −26.3746 −1.50528 −0.752639 0.658434i \(-0.771219\pi\)
−0.752639 + 0.658434i \(0.771219\pi\)
\(308\) 0 0
\(309\) 11.8248 0.672687
\(310\) 0 0
\(311\) −5.27492 9.13642i −0.299113 0.518079i 0.676820 0.736148i \(-0.263357\pi\)
−0.975933 + 0.218069i \(0.930024\pi\)
\(312\) 0 0
\(313\) 2.22508 3.85396i 0.125769 0.217838i −0.796264 0.604949i \(-0.793193\pi\)
0.922033 + 0.387111i \(0.126527\pi\)
\(314\) 0 0
\(315\) 4.86254 10.2118i 0.273973 0.575368i
\(316\) 0 0
\(317\) 2.58762 4.48190i 0.145335 0.251728i −0.784163 0.620555i \(-0.786907\pi\)
0.929498 + 0.368827i \(0.120241\pi\)
\(318\) 0 0
\(319\) −4.86254 8.42217i −0.272250 0.471551i
\(320\) 0 0
\(321\) −6.82475 −0.380920
\(322\) 0 0
\(323\) −5.09967 −0.283753
\(324\) 0 0
\(325\) 8.46221 + 14.6570i 0.469399 + 0.813023i
\(326\) 0 0
\(327\) −2.91238 + 5.04438i −0.161055 + 0.278955i
\(328\) 0 0
\(329\) −15.8248 + 1.25588i −0.872447 + 0.0692389i
\(330\) 0 0
\(331\) −11.9124 + 20.6328i −0.654763 + 1.13408i 0.327190 + 0.944959i \(0.393898\pi\)
−0.981953 + 0.189125i \(0.939435\pi\)
\(332\) 0 0
\(333\) −2.63746 4.56821i −0.144532 0.250336i
\(334\) 0 0
\(335\) −31.0997 −1.69916
\(336\) 0 0
\(337\) 6.09967 0.332270 0.166135 0.986103i \(-0.446871\pi\)
0.166135 + 0.986103i \(0.446871\pi\)
\(338\) 0 0
\(339\) 5.27492 + 9.13642i 0.286494 + 0.496222i
\(340\) 0 0
\(341\) −2.13746 + 3.70219i −0.115750 + 0.200485i
\(342\) 0 0
\(343\) 18.0000 4.35890i 0.971909 0.235358i
\(344\) 0 0
\(345\) −8.54983 + 14.8087i −0.460308 + 0.797276i
\(346\) 0 0
\(347\) 15.0997 + 26.1534i 0.810593 + 1.40399i 0.912450 + 0.409189i \(0.134188\pi\)
−0.101857 + 0.994799i \(0.532478\pi\)
\(348\) 0 0
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 0 0
\(351\) 1.27492 0.0680500
\(352\) 0 0
\(353\) 2.72508 + 4.71998i 0.145042 + 0.251219i 0.929388 0.369103i \(-0.120335\pi\)
−0.784347 + 0.620322i \(0.787002\pi\)
\(354\) 0 0
\(355\) 4.27492 7.40437i 0.226889 0.392983i
\(356\) 0 0
\(357\) 10.5498 0.837253i 0.558356 0.0443122i
\(358\) 0 0
\(359\) −12.8248 + 22.2131i −0.676865 + 1.17236i 0.299056 + 0.954236i \(0.403328\pi\)
−0.975920 + 0.218128i \(0.930005\pi\)
\(360\) 0 0
\(361\) 8.68729 + 15.0468i 0.457226 + 0.791939i
\(362\) 0 0
\(363\) −7.27492 −0.381834
\(364\) 0 0
\(365\) −14.0000 −0.732793
\(366\) 0 0
\(367\) 4.04983 + 7.01452i 0.211400 + 0.366155i 0.952153 0.305622i \(-0.0988645\pi\)
−0.740753 + 0.671777i \(0.765531\pi\)
\(368\) 0 0
\(369\) −5.27492 + 9.13642i −0.274601 + 0.475623i
\(370\) 0 0
\(371\) −1.96221 + 4.12081i −0.101873 + 0.213942i
\(372\) 0 0
\(373\) −0.637459 + 1.10411i −0.0330064 + 0.0571687i −0.882057 0.471143i \(-0.843841\pi\)
0.849050 + 0.528312i \(0.177175\pi\)
\(374\) 0 0
\(375\) −17.6873 30.6353i −0.913368 1.58200i
\(376\) 0 0
\(377\) 2.90033 0.149375
\(378\) 0 0
\(379\) 35.8248 1.84019 0.920097 0.391691i \(-0.128110\pi\)
0.920097 + 0.391691i \(0.128110\pi\)
\(380\) 0 0
\(381\) −10.7749 18.6627i −0.552016 0.956119i
\(382\) 0 0
\(383\) 2.27492 3.94027i 0.116243 0.201339i −0.802033 0.597280i \(-0.796248\pi\)
0.918276 + 0.395941i \(0.129582\pi\)
\(384\) 0 0
\(385\) −27.4124 39.8293i −1.39706 2.02989i
\(386\) 0 0
\(387\) 3.63746 6.30026i 0.184902 0.320260i
\(388\) 0 0
\(389\) 1.00000 + 1.73205i 0.0507020 + 0.0878185i 0.890263 0.455448i \(-0.150521\pi\)
−0.839561 + 0.543266i \(0.817187\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0.274917 0.0138677
\(394\) 0 0
\(395\) −7.58762 13.1422i −0.381775 0.661253i
\(396\) 0 0
\(397\) −17.1873 + 29.7693i −0.862606 + 1.49408i 0.00679974 + 0.999977i \(0.497836\pi\)
−0.869405 + 0.494100i \(0.835498\pi\)
\(398\) 0 0
\(399\) 1.91238 + 2.77862i 0.0957385 + 0.139105i
\(400\) 0 0
\(401\) −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i \(0.371202\pi\)
−0.992932 + 0.118686i \(0.962132\pi\)
\(402\) 0 0
\(403\) −0.637459 1.10411i −0.0317541 0.0549997i
\(404\) 0 0
\(405\) −4.27492 −0.212422
\(406\) 0 0
\(407\) −22.5498 −1.11775
\(408\) 0 0
\(409\) −12.7749 22.1268i −0.631679 1.09410i −0.987208 0.159435i \(-0.949033\pi\)
0.355529 0.934665i \(-0.384301\pi\)
\(410\) 0 0
\(411\) 8.27492 14.3326i 0.408172 0.706974i
\(412\) 0 0
\(413\) −7.13746 + 14.9893i −0.351211 + 0.737575i
\(414\) 0 0
\(415\) −0.587624 + 1.01779i −0.0288453 + 0.0499616i
\(416\) 0 0
\(417\) 0.362541 + 0.627940i 0.0177537 + 0.0307504i
\(418\) 0 0
\(419\) 13.4502 0.657084 0.328542 0.944489i \(-0.393443\pi\)
0.328542 + 0.944489i \(0.393443\pi\)
\(420\) 0 0
\(421\) −13.8248 −0.673777 −0.336889 0.941545i \(-0.609375\pi\)
−0.336889 + 0.941545i \(0.609375\pi\)
\(422\) 0 0
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 0 0
\(425\) 26.5498 45.9857i 1.28786 2.23063i
\(426\) 0 0
\(427\) 26.3746 2.09313i 1.27636 0.101294i
\(428\) 0 0
\(429\) 2.72508 4.71998i 0.131568 0.227883i
\(430\) 0 0
\(431\) −13.8248 23.9452i −0.665915 1.15340i −0.979036 0.203685i \(-0.934708\pi\)
0.313122 0.949713i \(-0.398625\pi\)
\(432\) 0 0
\(433\) 25.8248 1.24106 0.620529 0.784183i \(-0.286918\pi\)
0.620529 + 0.784183i \(0.286918\pi\)
\(434\) 0 0
\(435\) −9.72508 −0.466282
\(436\) 0 0
\(437\) −2.54983 4.41644i −0.121975 0.211267i
\(438\) 0 0
\(439\) −4.86254 + 8.42217i −0.232076 + 0.401968i −0.958419 0.285365i \(-0.907885\pi\)
0.726343 + 0.687333i \(0.241219\pi\)
\(440\) 0 0
\(441\) −4.41238 5.43424i −0.210113 0.258773i
\(442\) 0 0
\(443\) −15.6873 + 27.1712i −0.745326 + 1.29094i 0.204717 + 0.978821i \(0.434373\pi\)
−0.950042 + 0.312121i \(0.898961\pi\)
\(444\) 0 0
\(445\) 9.72508 + 16.8443i 0.461013 + 0.798498i
\(446\) 0 0
\(447\) −0.549834 −0.0260063
\(448\) 0 0
\(449\) 5.45017 0.257209 0.128605 0.991696i \(-0.458950\pi\)
0.128605 + 0.991696i \(0.458950\pi\)
\(450\) 0 0
\(451\) 22.5498 + 39.0575i 1.06183 + 1.83914i
\(452\) 0 0
\(453\) −7.68729 + 13.3148i −0.361181 + 0.625583i
\(454\) 0 0
\(455\) 14.3746 1.14079i 0.673891 0.0534812i
\(456\) 0 0
\(457\) 4.32475 7.49069i 0.202303 0.350400i −0.746967 0.664861i \(-0.768491\pi\)
0.949270 + 0.314462i \(0.101824\pi\)
\(458\) 0 0
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 41.6495 1.93981 0.969905 0.243482i \(-0.0782897\pi\)
0.969905 + 0.243482i \(0.0782897\pi\)
\(462\) 0 0
\(463\) 35.8248 1.66492 0.832459 0.554087i \(-0.186933\pi\)
0.832459 + 0.554087i \(0.186933\pi\)
\(464\) 0 0
\(465\) 2.13746 + 3.70219i 0.0991223 + 0.171685i
\(466\) 0 0
\(467\) −12.7251 + 22.0405i −0.588847 + 1.01991i 0.405537 + 0.914079i \(0.367084\pi\)
−0.994384 + 0.105834i \(0.966249\pi\)
\(468\) 0 0
\(469\) −8.27492 + 17.3781i −0.382100 + 0.802444i
\(470\) 0 0
\(471\) 7.27492 12.6005i 0.335210 0.580602i
\(472\) 0 0
\(473\) −15.5498 26.9331i −0.714982 1.23839i
\(474\) 0 0
\(475\) 16.9244 0.776546
\(476\) 0 0
\(477\) 1.72508 0.0789861
\(478\) 0 0
\(479\) 10.2749 + 17.7967i 0.469473 + 0.813151i 0.999391 0.0348979i \(-0.0111106\pi\)
−0.529918 + 0.848049i \(0.677777\pi\)
\(480\) 0 0
\(481\) 3.36254 5.82409i 0.153319 0.265556i
\(482\) 0 0
\(483\) 6.00000 + 8.71780i 0.273009 + 0.396674i
\(484\) 0 0
\(485\) 34.7870 60.2528i 1.57959 2.73594i
\(486\) 0 0
\(487\) −0.500000 0.866025i −0.0226572 0.0392434i 0.854475 0.519493i \(-0.173879\pi\)
−0.877132 + 0.480250i \(0.840546\pi\)
\(488\) 0 0
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −15.9244 −0.718659 −0.359330 0.933211i \(-0.616995\pi\)
−0.359330 + 0.933211i \(0.616995\pi\)
\(492\) 0 0
\(493\) −4.54983 7.88054i −0.204914 0.354922i
\(494\) 0 0
\(495\) −9.13746 + 15.8265i −0.410698 + 0.711350i
\(496\) 0 0
\(497\) −3.00000 4.35890i −0.134568 0.195523i
\(498\) 0 0
\(499\) −12.3625 + 21.4125i −0.553423 + 0.958557i 0.444601 + 0.895729i \(0.353345\pi\)
−0.998024 + 0.0628286i \(0.979988\pi\)
\(500\) 0 0
\(501\) −3.00000 5.19615i −0.134030 0.232147i
\(502\) 0 0
\(503\) 7.64950 0.341074 0.170537 0.985351i \(-0.445450\pi\)
0.170537 + 0.985351i \(0.445450\pi\)
\(504\) 0 0
\(505\) 25.6495 1.14139
\(506\) 0 0
\(507\) −5.68729 9.85068i −0.252582 0.437484i
\(508\) 0 0
\(509\) 1.86254 3.22602i 0.0825557 0.142991i −0.821791 0.569789i \(-0.807025\pi\)
0.904347 + 0.426798i \(0.140358\pi\)
\(510\) 0 0
\(511\) −3.72508 + 7.82300i −0.164788 + 0.346069i
\(512\) 0 0
\(513\) 0.637459 1.10411i 0.0281445 0.0487477i
\(514\) 0 0
\(515\) −25.2749 43.7774i −1.11375 1.92906i
\(516\) 0 0
\(517\) 25.6495 1.12806
\(518\) 0 0
\(519\) 7.45017 0.327026
\(520\) 0 0
\(521\) −0.274917 0.476171i −0.0120443 0.0208614i 0.859940 0.510394i \(-0.170501\pi\)
−0.871985 + 0.489533i \(0.837167\pi\)
\(522\) 0 0
\(523\) 12.6375 21.8887i 0.552597 0.957127i −0.445489 0.895288i \(-0.646970\pi\)
0.998086 0.0618393i \(-0.0196966\pi\)
\(524\) 0 0
\(525\) −35.0120 + 2.77862i −1.52805 + 0.121269i
\(526\) 0 0
\(527\) −2.00000 + 3.46410i −0.0871214 + 0.150899i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 6.27492 0.272308
\(532\) 0 0
\(533\) −13.4502 −0.582591
\(534\) 0 0
\(535\) 14.5876 + 25.2665i 0.630678 + 1.09237i
\(536\) 0 0
\(537\) −0.725083 + 1.25588i −0.0312896 + 0.0541952i
\(538\) 0 0
\(539\) −29.5498 + 4.71998i −1.27280 + 0.203304i
\(540\) 0 0
\(541\) 0.362541 0.627940i 0.0155869 0.0269973i −0.858127 0.513438i \(-0.828372\pi\)
0.873714 + 0.486441i \(0.161705\pi\)
\(542\) 0 0
\(543\) 1.91238 + 3.31233i 0.0820679 + 0.142146i
\(544\) 0 0
\(545\) 24.9003 1.06661
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) −5.00000 8.66025i −0.213395 0.369611i
\(550\) 0 0
\(551\) 1.45017 2.51176i 0.0617791 0.107005i
\(552\) 0 0
\(553\) −9.36254 + 0.743028i −0.398136 + 0.0315968i
\(554\) 0 0
\(555\) −11.2749 + 19.5287i −0.478594 + 0.828948i
\(556\) 0 0
\(557\) 3.58762 + 6.21395i 0.152013 + 0.263293i 0.931967 0.362543i \(-0.118091\pi\)
−0.779955 + 0.625836i \(0.784758\pi\)
\(558\) 0 0
\(559\) 9.27492 0.392287
\(560\) 0 0
\(561\) −17.0997 −0.721949
\(562\) 0 0
\(563\) −3.86254 6.69012i −0.162787 0.281955i 0.773080 0.634308i \(-0.218715\pi\)
−0.935867 + 0.352353i \(0.885382\pi\)
\(564\) 0 0
\(565\) 22.5498 39.0575i 0.948679 1.64316i
\(566\) 0 0
\(567\) −1.13746 + 2.38876i −0.0477688 + 0.100319i
\(568\) 0 0
\(569\) −13.2749 + 22.9928i −0.556513 + 0.963910i 0.441271 + 0.897374i \(0.354528\pi\)
−0.997784 + 0.0665355i \(0.978805\pi\)
\(570\) 0 0
\(571\) −0.362541 0.627940i −0.0151719 0.0262785i 0.858340 0.513082i \(-0.171496\pi\)
−0.873512 + 0.486803i \(0.838163\pi\)
\(572\) 0 0
\(573\) 10.5498 0.440726
\(574\) 0 0
\(575\) 53.0997 2.21441
\(576\) 0 0
\(577\) 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) 0 0
\(579\) 7.77492 13.4666i 0.323115 0.559651i
\(580\) 0 0
\(581\) 0.412376 + 0.599168i 0.0171082 + 0.0248577i
\(582\) 0 0
\(583\) 3.68729 6.38658i 0.152712 0.264505i
\(584\) 0 0
\(585\) −2.72508 4.71998i −0.112668 0.195147i
\(586\) 0 0
\(587\) 1.72508 0.0712018 0.0356009 0.999366i \(-0.488665\pi\)
0.0356009 + 0.999366i \(0.488665\pi\)
\(588\) 0 0
\(589\) −1.27492 −0.0525320
\(590\) 0 0
\(591\) −8.27492 14.3326i −0.340385 0.589563i
\(592\) 0 0
\(593\) −7.27492 + 12.6005i −0.298745 + 0.517442i −0.975849 0.218446i \(-0.929901\pi\)
0.677104 + 0.735887i \(0.263235\pi\)
\(594\) 0 0
\(595\) −25.6495 37.2679i −1.05153 1.52783i
\(596\) 0 0
\(597\) 12.5498 21.7370i 0.513631 0.889634i
\(598\) 0 0
\(599\) −3.72508 6.45203i −0.152203 0.263623i 0.779834 0.625986i \(-0.215303\pi\)
−0.932037 + 0.362363i \(0.881970\pi\)
\(600\) 0 0
\(601\) −26.0997 −1.06463 −0.532314 0.846547i \(-0.678677\pi\)
−0.532314 + 0.846547i \(0.678677\pi\)
\(602\) 0 0
\(603\) 7.27492 0.296258
\(604\) 0 0
\(605\) 15.5498 + 26.9331i 0.632191 + 1.09499i
\(606\) 0 0
\(607\) 3.50000 6.06218i 0.142061 0.246056i −0.786212 0.617957i \(-0.787961\pi\)
0.928272 + 0.371901i \(0.121294\pi\)
\(608\) 0 0
\(609\) −2.58762 + 5.43424i −0.104856 + 0.220206i
\(610\) 0 0
\(611\) −3.82475 + 6.62466i −0.154733 + 0.268005i
\(612\) 0 0
\(613\) −3.27492 5.67232i −0.132273 0.229103i 0.792280 0.610158i \(-0.208894\pi\)
−0.924552 + 0.381055i \(0.875561\pi\)
\(614\) 0 0
\(615\) 45.0997 1.81859
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) −3.08762 5.34792i −0.124102 0.214951i 0.797280 0.603610i \(-0.206272\pi\)
−0.921382 + 0.388659i \(0.872938\pi\)
\(620\) 0 0
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) 0 0
\(623\) 12.0000 0.952341i 0.480770 0.0381547i
\(624\) 0 0
\(625\) −42.4244 + 73.4813i −1.69698 + 2.93925i
\(626\) 0 0
\(627\) −2.72508 4.71998i −0.108829 0.188498i
\(628\) 0 0
\(629\) −21.0997 −0.841299
\(630\) 0 0
\(631\) −2.82475 −0.112452 −0.0562258 0.998418i \(-0.517907\pi\)
−0.0562258 + 0.998418i \(0.517907\pi\)
\(632\) 0 0
\(633\) 8.82475 + 15.2849i 0.350752 + 0.607521i
\(634\) 0 0
\(635\) −46.0619 + 79.7815i −1.82791 + 3.16603i
\(636\) 0 0
\(637\) 3.18729 8.33585i 0.126285 0.330279i
\(638\) 0 0
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) −20.8248 36.0695i −0.822528 1.42466i −0.903794 0.427968i \(-0.859230\pi\)
0.0812655 0.996692i \(-0.474104\pi\)
\(642\) 0 0
\(643\) −32.3746 −1.27673 −0.638365 0.769734i \(-0.720389\pi\)
−0.638365 + 0.769734i \(0.720389\pi\)
\(644\) 0 0
\(645\) −31.0997 −1.22455
\(646\) 0 0
\(647\) 17.0000 + 29.4449i 0.668339 + 1.15760i 0.978368 + 0.206870i \(0.0663277\pi\)
−0.310029 + 0.950727i \(0.600339\pi\)
\(648\) 0 0
\(649\) 13.4124 23.2309i 0.526482 0.911893i
\(650\) 0 0
\(651\) 2.63746 0.209313i 0.103370 0.00820364i
\(652\) 0 0
\(653\) −22.9622 + 39.7717i −0.898581 + 1.55639i −0.0692713 + 0.997598i \(0.522067\pi\)
−0.829309 + 0.558790i \(0.811266\pi\)
\(654\) 0 0
\(655\) −0.587624 1.01779i −0.0229604 0.0397685i
\(656\) 0 0
\(657\) 3.27492 0.127767
\(658\) 0 0
\(659\) 18.1993 0.708946 0.354473 0.935066i \(-0.384660\pi\)
0.354473 + 0.935066i \(0.384660\pi\)
\(660\) 0 0
\(661\) −14.9124 25.8290i −0.580024 1.00463i −0.995476 0.0950161i \(-0.969710\pi\)
0.415452 0.909615i \(-0.363624\pi\)
\(662\) 0 0
\(663\) 2.54983 4.41644i 0.0990274 0.171520i
\(664\) 0 0
\(665\) 6.19934 13.0192i 0.240400 0.504861i
\(666\) 0 0
\(667\) 4.54983 7.88054i 0.176170 0.305136i
\(668\) 0 0
\(669\) 3.13746 + 5.43424i 0.121301 + 0.210100i
\(670\) 0 0
\(671\) −42.7492 −1.65031
\(672\) 0 0
\(673\) 26.4502 1.01958 0.509789 0.860299i \(-0.329723\pi\)
0.509789 + 0.860299i \(0.329723\pi\)
\(674\) 0 0
\(675\) 6.63746 + 11.4964i 0.255476 + 0.442497i
\(676\) 0 0
\(677\) 2.86254 4.95807i 0.110016 0.190554i −0.805760 0.592242i \(-0.798243\pi\)
0.915777 + 0.401688i \(0.131576\pi\)
\(678\) 0 0
\(679\) −24.4124 35.4704i −0.936861 1.36123i
\(680\) 0 0
\(681\) −1.86254 + 3.22602i −0.0713727 + 0.123621i
\(682\) 0 0
\(683\) −17.4124 30.1591i −0.666266 1.15401i −0.978940 0.204146i \(-0.934558\pi\)
0.312674 0.949860i \(-0.398775\pi\)
\(684\) 0 0
\(685\) −70.7492 −2.70319
\(686\) 0 0
\(687\) −10.7251 −0.409187
\(688\) 0 0
\(689\) 1.09967 + 1.90468i 0.0418940 + 0.0725626i
\(690\) 0 0
\(691\) −5.91238 + 10.2405i −0.224917 + 0.389568i −0.956295 0.292405i \(-0.905545\pi\)
0.731377 + 0.681973i \(0.238878\pi\)
\(692\) 0 0
\(693\) 6.41238 + 9.31697i 0.243586 + 0.353922i
\(694\) 0 0
\(695\) 1.54983 2.68439i 0.0587886 0.101825i
\(696\) 0 0
\(697\) 21.0997 + 36.5457i 0.799207 + 1.38427i
\(698\) 0 0
\(699\) −14.5498 −0.550325
\(700\) 0 0
\(701\) 39.9244 1.50792 0.753962 0.656918i \(-0.228140\pi\)
0.753962 + 0.656918i \(0.228140\pi\)
\(702\) 0 0
\(703\) −3.36254 5.82409i −0.126821 0.219660i
\(704\) 0 0
\(705\) 12.8248 22.2131i 0.483008 0.836595i
\(706\) 0 0
\(707\) 6.82475 14.3326i 0.256671 0.539032i
\(708\) 0 0
\(709\) −16.0997 + 27.8854i −0.604636 + 1.04726i 0.387473 + 0.921881i \(0.373348\pi\)
−0.992109 + 0.125379i \(0.959985\pi\)
\(710\) 0 0
\(711\) 1.77492 + 3.07425i 0.0665646 + 0.115293i
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) −23.2990 −0.871333
\(716\) 0 0
\(717\) 15.2749 + 26.4569i 0.570452 + 0.988052i
\(718\) 0 0
\(719\) 16.0997 27.8854i 0.600416 1.03995i −0.392342 0.919820i \(-0.628335\pi\)
0.992758 0.120132i \(-0.0383318\pi\)
\(720\) 0 0
\(721\) −31.1873 + 2.47508i −1.16148 + 0.0921767i
\(722\) 0 0
\(723\) −6.41238 + 11.1066i −0.238479 + 0.413057i
\(724\) 0 0
\(725\) 15.0997 + 26.1534i 0.560788 + 0.971313i
\(726\) 0 0
\(727\) 16.4502 0.610103 0.305051 0.952336i \(-0.401326\pi\)
0.305051 + 0.952336i \(0.401326\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −14.5498 25.2011i −0.538145 0.932095i
\(732\) 0 0
\(733\) 23.4622 40.6377i 0.866597 1.50099i 0.00114334 0.999999i \(-0.499636\pi\)
0.865453 0.500990i \(-0.167031\pi\)
\(734\) 0 0
\(735\) −10.6873 + 27.9509i −0.394207 + 1.03098i
\(736\) 0 0
\(737\) 15.5498 26.9331i 0.572786 0.992094i
\(738\) 0 0
\(739\) 18.1873 + 31.5013i 0.669030 + 1.15879i 0.978176 + 0.207780i \(0.0666237\pi\)
−0.309145 + 0.951015i \(0.600043\pi\)
\(740\) 0 0
\(741\) 1.62541 0.0597111
\(742\) 0 0
\(743\) 16.1993 0.594296 0.297148 0.954831i \(-0.403965\pi\)
0.297148 + 0.954831i \(0.403965\pi\)
\(744\) 0 0
\(745\) 1.17525 + 2.03559i 0.0430578 + 0.0745782i
\(746\) 0 0
\(747\) 0.137459 0.238085i 0.00502935 0.00871109i
\(748\) 0 0
\(749\) 18.0000 1.42851i 0.657706 0.0521967i
\(750\) 0 0
\(751\) 12.7749 22.1268i 0.466163 0.807419i −0.533090 0.846059i \(-0.678969\pi\)
0.999253 + 0.0386400i \(0.0123026\pi\)
\(752\) 0 0
\(753\) 9.68729 + 16.7789i 0.353025 + 0.611457i
\(754\) 0 0
\(755\) 65.7251 2.39198
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) −8.54983 14.8087i −0.310339 0.537523i
\(760\) 0 0
\(761\) −2.54983 + 4.41644i −0.0924314 + 0.160096i −0.908534 0.417812i \(-0.862797\pi\)
0.816102 + 0.577907i \(0.196131\pi\)
\(762\) 0 0
\(763\) 6.62541 13.9140i 0.239856 0.503719i
\(764\) 0 0
\(765\) −8.54983 + 14.8087i −0.309120 + 0.535411i
\(766\) 0 0
\(767\) 4.00000 + 6.92820i 0.144432 + 0.250163i
\(768\) 0 0
\(769\) 12.6495 0.456153 0.228076 0.973643i \(-0.426756\pi\)
0.228076 + 0.973643i \(0.426756\pi\)
\(770\) 0 0
\(771\) 19.0997 0.687858
\(772\) 0 0
\(773\) 13.5498 + 23.4690i 0.487354 + 0.844121i 0.999894 0.0145417i \(-0.00462892\pi\)
−0.512541 + 0.858663i \(0.671296\pi\)
\(774\) 0 0
\(775\) 6.63746 11.4964i 0.238425 0.412963i
\(776\) 0 0
\(777\) 7.91238 + 11.4964i 0.283855 + 0.412432i
\(778\) 0 0
\(779\) −6.72508 + 11.6482i −0.240951 + 0.417340i
\(780\) 0 0
\(781\) 4.27492 + 7.40437i 0.152969 + 0.264949i
\(782\) 0 0
\(783\) 2.27492 0.0812989
\(784\) 0 0
\(785\) −62.1993 −2.21999
\(786\) 0 0
\(787\) 6.27492 + 10.8685i 0.223677 + 0.387419i 0.955922 0.293622i \(-0.0948607\pi\)
−0.732245 + 0.681041i \(0.761527\pi\)
\(788\) 0 0
\(789\) −12.2749 + 21.2608i −0.436999 + 0.756904i
\(790\) 0 0
\(791\) −15.8248 22.9928i −0.562663 0.817531i
\(792\) 0 0
\(793\) 6.37459 11.0411i 0.226368 0.392081i
\(794\) 0 0
\(795\)