Properties

Label 300.2.m.a.121.1
Level $300$
Weight $2$
Character 300.121
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\Q(\zeta_{15})\)
Defining polynomial: \(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 121.1
Root \(0.669131 + 0.743145i\) of defining polynomial
Character \(\chi\) \(=\) 300.121
Dual form 300.2.m.a.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{3} +(-0.233733 + 2.22382i) q^{5} -0.511170 q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{3} +(-0.233733 + 2.22382i) q^{5} -0.511170 q^{7} +(0.309017 + 0.951057i) q^{9} +(-0.564602 + 1.73767i) q^{11} +(1.89169 + 5.82203i) q^{13} +(1.49622 - 1.66172i) q^{15} +(-2.09007 + 1.51852i) q^{17} +(3.93444 - 2.85854i) q^{19} +(0.413545 + 0.300458i) q^{21} +(-2.04965 + 6.30818i) q^{23} +(-4.89074 - 1.03956i) q^{25} +(0.309017 - 0.951057i) q^{27} +(6.46980 + 4.70059i) q^{29} +(3.95252 - 2.87167i) q^{31} +(1.47815 - 1.07394i) q^{33} +(0.119477 - 1.13675i) q^{35} +(-2.29833 - 7.07355i) q^{37} +(1.89169 - 5.82203i) q^{39} +(1.77084 + 5.45007i) q^{41} -2.05126 q^{43} +(-2.18720 + 0.464905i) q^{45} +(-6.43523 - 4.67547i) q^{47} -6.73870 q^{49} +2.58347 q^{51} +(-1.07528 - 0.781240i) q^{53} +(-3.73229 - 1.66172i) q^{55} -4.86324 q^{57} +(-3.11882 - 9.59875i) q^{59} +(1.47437 - 4.53764i) q^{61} +(-0.157960 - 0.486152i) q^{63} +(-13.3893 + 2.84598i) q^{65} +(11.5960 - 8.42500i) q^{67} +(5.36606 - 3.89867i) q^{69} +(4.34421 + 3.15625i) q^{71} +(-1.07559 + 3.31031i) q^{73} +(3.34565 + 3.71572i) q^{75} +(0.288608 - 0.888244i) q^{77} +(1.06789 + 0.775869i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.738301 + 0.536407i) q^{83} +(-2.88840 - 5.00286i) q^{85} +(-2.47124 - 7.60571i) q^{87} +(3.63893 - 11.1995i) q^{89} +(-0.966977 - 2.97605i) q^{91} -4.88558 q^{93} +(5.43727 + 9.41762i) q^{95} +(5.98660 + 4.34952i) q^{97} -1.82709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} - 2q^{11} - 5q^{15} + 7q^{17} + 5q^{19} - 3q^{21} + 7q^{23} + 5q^{25} - 2q^{27} + 27q^{29} - 3q^{31} + 3q^{33} + 20q^{35} - 9q^{37} + 20q^{41} - 68q^{43} - 5q^{45} - 7q^{47} - 8q^{49} - 8q^{51} - 11q^{53} + 5q^{55} - 10q^{57} + 2q^{59} - 14q^{61} + 7q^{63} - 35q^{65} + 28q^{67} + 2q^{69} - 15q^{71} + 6q^{73} + 5q^{75} + 17q^{77} + 24q^{79} - 2q^{81} + 2q^{83} + 10q^{85} - 23q^{87} + 5q^{91} - 18q^{93} + 5q^{95} + 34q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.809017 0.587785i −0.467086 0.339358i
\(4\) 0 0
\(5\) −0.233733 + 2.22382i −0.104528 + 0.994522i
\(6\) 0 0
\(7\) −0.511170 −0.193204 −0.0966021 0.995323i \(-0.530797\pi\)
−0.0966021 + 0.995323i \(0.530797\pi\)
\(8\) 0 0
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0 0
\(11\) −0.564602 + 1.73767i −0.170234 + 0.523926i −0.999384 0.0351002i \(-0.988825\pi\)
0.829150 + 0.559026i \(0.188825\pi\)
\(12\) 0 0
\(13\) 1.89169 + 5.82203i 0.524661 + 1.61474i 0.764985 + 0.644048i \(0.222746\pi\)
−0.240323 + 0.970693i \(0.577254\pi\)
\(14\) 0 0
\(15\) 1.49622 1.66172i 0.386323 0.429055i
\(16\) 0 0
\(17\) −2.09007 + 1.51852i −0.506916 + 0.368296i −0.811652 0.584141i \(-0.801432\pi\)
0.304736 + 0.952437i \(0.401432\pi\)
\(18\) 0 0
\(19\) 3.93444 2.85854i 0.902623 0.655794i −0.0365153 0.999333i \(-0.511626\pi\)
0.939138 + 0.343539i \(0.111626\pi\)
\(20\) 0 0
\(21\) 0.413545 + 0.300458i 0.0902430 + 0.0655654i
\(22\) 0 0
\(23\) −2.04965 + 6.30818i −0.427382 + 1.31535i 0.473312 + 0.880895i \(0.343058\pi\)
−0.900695 + 0.434453i \(0.856942\pi\)
\(24\) 0 0
\(25\) −4.89074 1.03956i −0.978148 0.207912i
\(26\) 0 0
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 0 0
\(29\) 6.46980 + 4.70059i 1.20141 + 0.872877i 0.994423 0.105466i \(-0.0336336\pi\)
0.206989 + 0.978343i \(0.433634\pi\)
\(30\) 0 0
\(31\) 3.95252 2.87167i 0.709893 0.515767i −0.173246 0.984879i \(-0.555426\pi\)
0.883139 + 0.469111i \(0.155426\pi\)
\(32\) 0 0
\(33\) 1.47815 1.07394i 0.257312 0.186948i
\(34\) 0 0
\(35\) 0.119477 1.13675i 0.0201953 0.192146i
\(36\) 0 0
\(37\) −2.29833 7.07355i −0.377844 1.16288i −0.941540 0.336902i \(-0.890621\pi\)
0.563696 0.825982i \(-0.309379\pi\)
\(38\) 0 0
\(39\) 1.89169 5.82203i 0.302913 0.932271i
\(40\) 0 0
\(41\) 1.77084 + 5.45007i 0.276558 + 0.851158i 0.988803 + 0.149227i \(0.0476786\pi\)
−0.712245 + 0.701931i \(0.752321\pi\)
\(42\) 0 0
\(43\) −2.05126 −0.312814 −0.156407 0.987693i \(-0.549991\pi\)
−0.156407 + 0.987693i \(0.549991\pi\)
\(44\) 0 0
\(45\) −2.18720 + 0.464905i −0.326049 + 0.0693039i
\(46\) 0 0
\(47\) −6.43523 4.67547i −0.938675 0.681987i 0.00942623 0.999956i \(-0.496999\pi\)
−0.948101 + 0.317968i \(0.896999\pi\)
\(48\) 0 0
\(49\) −6.73870 −0.962672
\(50\) 0 0
\(51\) 2.58347 0.361758
\(52\) 0 0
\(53\) −1.07528 0.781240i −0.147702 0.107312i 0.511480 0.859295i \(-0.329097\pi\)
−0.659182 + 0.751983i \(0.729097\pi\)
\(54\) 0 0
\(55\) −3.73229 1.66172i −0.503262 0.224067i
\(56\) 0 0
\(57\) −4.86324 −0.644152
\(58\) 0 0
\(59\) −3.11882 9.59875i −0.406036 1.24965i −0.920027 0.391855i \(-0.871833\pi\)
0.513991 0.857796i \(-0.328167\pi\)
\(60\) 0 0
\(61\) 1.47437 4.53764i 0.188774 0.580985i −0.811219 0.584742i \(-0.801196\pi\)
0.999993 + 0.00375653i \(0.00119574\pi\)
\(62\) 0 0
\(63\) −0.157960 0.486152i −0.0199011 0.0612494i
\(64\) 0 0
\(65\) −13.3893 + 2.84598i −1.66074 + 0.353001i
\(66\) 0 0
\(67\) 11.5960 8.42500i 1.41668 1.02928i 0.424370 0.905489i \(-0.360495\pi\)
0.992309 0.123789i \(-0.0395045\pi\)
\(68\) 0 0
\(69\) 5.36606 3.89867i 0.645998 0.469345i
\(70\) 0 0
\(71\) 4.34421 + 3.15625i 0.515563 + 0.374578i 0.814930 0.579560i \(-0.196775\pi\)
−0.299367 + 0.954138i \(0.596775\pi\)
\(72\) 0 0
\(73\) −1.07559 + 3.31031i −0.125888 + 0.387443i −0.994062 0.108817i \(-0.965294\pi\)
0.868174 + 0.496260i \(0.165294\pi\)
\(74\) 0 0
\(75\) 3.34565 + 3.71572i 0.386323 + 0.429055i
\(76\) 0 0
\(77\) 0.288608 0.888244i 0.0328899 0.101225i
\(78\) 0 0
\(79\) 1.06789 + 0.775869i 0.120147 + 0.0872921i 0.646236 0.763137i \(-0.276342\pi\)
−0.526089 + 0.850430i \(0.676342\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0 0
\(83\) −0.738301 + 0.536407i −0.0810391 + 0.0588783i −0.627567 0.778562i \(-0.715949\pi\)
0.546528 + 0.837441i \(0.315949\pi\)
\(84\) 0 0
\(85\) −2.88840 5.00286i −0.313291 0.542636i
\(86\) 0 0
\(87\) −2.47124 7.60571i −0.264945 0.815417i
\(88\) 0 0
\(89\) 3.63893 11.1995i 0.385726 1.18714i −0.550226 0.835016i \(-0.685459\pi\)
0.935952 0.352127i \(-0.114541\pi\)
\(90\) 0 0
\(91\) −0.966977 2.97605i −0.101367 0.311975i
\(92\) 0 0
\(93\) −4.88558 −0.506611
\(94\) 0 0
\(95\) 5.43727 + 9.41762i 0.557852 + 0.966228i
\(96\) 0 0
\(97\) 5.98660 + 4.34952i 0.607847 + 0.441627i 0.848655 0.528946i \(-0.177413\pi\)
−0.240809 + 0.970573i \(0.577413\pi\)
\(98\) 0 0
\(99\) −1.82709 −0.183630
\(100\) 0 0
\(101\) 13.0962 1.30312 0.651561 0.758596i \(-0.274114\pi\)
0.651561 + 0.758596i \(0.274114\pi\)
\(102\) 0 0
\(103\) 8.92360 + 6.48337i 0.879268 + 0.638826i 0.933058 0.359727i \(-0.117130\pi\)
−0.0537897 + 0.998552i \(0.517130\pi\)
\(104\) 0 0
\(105\) −0.764824 + 0.849423i −0.0746392 + 0.0828952i
\(106\) 0 0
\(107\) −8.08083 −0.781203 −0.390602 0.920560i \(-0.627733\pi\)
−0.390602 + 0.920560i \(0.627733\pi\)
\(108\) 0 0
\(109\) 3.49904 + 10.7690i 0.335148 + 1.03148i 0.966649 + 0.256104i \(0.0824390\pi\)
−0.631502 + 0.775375i \(0.717561\pi\)
\(110\) 0 0
\(111\) −2.29833 + 7.07355i −0.218148 + 0.671391i
\(112\) 0 0
\(113\) 1.16456 + 3.58415i 0.109553 + 0.337169i 0.990772 0.135539i \(-0.0432766\pi\)
−0.881219 + 0.472708i \(0.843277\pi\)
\(114\) 0 0
\(115\) −13.5492 6.03249i −1.26347 0.562532i
\(116\) 0 0
\(117\) −4.95252 + 3.59821i −0.457860 + 0.332655i
\(118\) 0 0
\(119\) 1.06838 0.776224i 0.0979383 0.0711563i
\(120\) 0 0
\(121\) 6.19848 + 4.50346i 0.563498 + 0.409405i
\(122\) 0 0
\(123\) 1.77084 5.45007i 0.159671 0.491416i
\(124\) 0 0
\(125\) 3.45492 10.6331i 0.309017 0.951057i
\(126\) 0 0
\(127\) −1.28920 + 3.96774i −0.114398 + 0.352080i −0.991821 0.127637i \(-0.959261\pi\)
0.877423 + 0.479717i \(0.159261\pi\)
\(128\) 0 0
\(129\) 1.65951 + 1.20570i 0.146111 + 0.106156i
\(130\) 0 0
\(131\) −11.9660 + 8.69382i −1.04548 + 0.759583i −0.971347 0.237666i \(-0.923618\pi\)
−0.0741292 + 0.997249i \(0.523618\pi\)
\(132\) 0 0
\(133\) −2.01117 + 1.46120i −0.174391 + 0.126702i
\(134\) 0 0
\(135\) 2.04275 + 0.909491i 0.175812 + 0.0782765i
\(136\) 0 0
\(137\) −0.379143 1.16688i −0.0323923 0.0996934i 0.933553 0.358439i \(-0.116691\pi\)
−0.965946 + 0.258746i \(0.916691\pi\)
\(138\) 0 0
\(139\) 2.80764 8.64102i 0.238141 0.732922i −0.758549 0.651616i \(-0.774091\pi\)
0.996689 0.0813051i \(-0.0259088\pi\)
\(140\) 0 0
\(141\) 2.45804 + 7.56507i 0.207004 + 0.637094i
\(142\) 0 0
\(143\) −11.1848 −0.935320
\(144\) 0 0
\(145\) −11.9655 + 13.2890i −0.993677 + 1.10359i
\(146\) 0 0
\(147\) 5.45173 + 3.96091i 0.449651 + 0.326690i
\(148\) 0 0
\(149\) 1.90097 0.155733 0.0778666 0.996964i \(-0.475189\pi\)
0.0778666 + 0.996964i \(0.475189\pi\)
\(150\) 0 0
\(151\) −4.60292 −0.374580 −0.187290 0.982305i \(-0.559970\pi\)
−0.187290 + 0.982305i \(0.559970\pi\)
\(152\) 0 0
\(153\) −2.09007 1.51852i −0.168972 0.122765i
\(154\) 0 0
\(155\) 5.46224 + 9.46088i 0.438738 + 0.759916i
\(156\) 0 0
\(157\) 3.96076 0.316103 0.158052 0.987431i \(-0.449479\pi\)
0.158052 + 0.987431i \(0.449479\pi\)
\(158\) 0 0
\(159\) 0.410722 + 1.26407i 0.0325724 + 0.100247i
\(160\) 0 0
\(161\) 1.04772 3.22456i 0.0825721 0.254131i
\(162\) 0 0
\(163\) 6.48302 + 19.9527i 0.507789 + 1.56281i 0.796031 + 0.605256i \(0.206929\pi\)
−0.288241 + 0.957558i \(0.593071\pi\)
\(164\) 0 0
\(165\) 2.04275 + 3.53815i 0.159028 + 0.275444i
\(166\) 0 0
\(167\) 14.5925 10.6021i 1.12920 0.820413i 0.143624 0.989632i \(-0.454125\pi\)
0.985578 + 0.169219i \(0.0541246\pi\)
\(168\) 0 0
\(169\) −19.8003 + 14.3858i −1.52310 + 1.10660i
\(170\) 0 0
\(171\) 3.93444 + 2.85854i 0.300874 + 0.218598i
\(172\) 0 0
\(173\) 7.91007 24.3447i 0.601391 1.85089i 0.0814747 0.996675i \(-0.474037\pi\)
0.519917 0.854217i \(-0.325963\pi\)
\(174\) 0 0
\(175\) 2.50000 + 0.531391i 0.188982 + 0.0401694i
\(176\) 0 0
\(177\) −3.11882 + 9.59875i −0.234425 + 0.721486i
\(178\) 0 0
\(179\) 6.81056 + 4.94816i 0.509045 + 0.369843i 0.812461 0.583015i \(-0.198127\pi\)
−0.303416 + 0.952858i \(0.598127\pi\)
\(180\) 0 0
\(181\) 16.2350 11.7955i 1.20674 0.876749i 0.211811 0.977311i \(-0.432064\pi\)
0.994931 + 0.100561i \(0.0320639\pi\)
\(182\) 0 0
\(183\) −3.85995 + 2.80442i −0.285336 + 0.207308i
\(184\) 0 0
\(185\) 16.2675 3.45776i 1.19601 0.254220i
\(186\) 0 0
\(187\) −1.45863 4.48920i −0.106666 0.328283i
\(188\) 0 0
\(189\) −0.157960 + 0.486152i −0.0114899 + 0.0353623i
\(190\) 0 0
\(191\) 1.19381 + 3.67416i 0.0863808 + 0.265853i 0.984912 0.173057i \(-0.0553646\pi\)
−0.898531 + 0.438910i \(0.855365\pi\)
\(192\) 0 0
\(193\) 10.6925 0.769662 0.384831 0.922987i \(-0.374260\pi\)
0.384831 + 0.922987i \(0.374260\pi\)
\(194\) 0 0
\(195\) 12.5050 + 5.56758i 0.895501 + 0.398703i
\(196\) 0 0
\(197\) 3.36909 + 2.44778i 0.240037 + 0.174397i 0.701300 0.712866i \(-0.252603\pi\)
−0.461263 + 0.887264i \(0.652603\pi\)
\(198\) 0 0
\(199\) −27.5965 −1.95627 −0.978134 0.207978i \(-0.933312\pi\)
−0.978134 + 0.207978i \(0.933312\pi\)
\(200\) 0 0
\(201\) −14.3335 −1.01100
\(202\) 0 0
\(203\) −3.30717 2.40280i −0.232118 0.168643i
\(204\) 0 0
\(205\) −12.5339 + 2.66416i −0.875404 + 0.186073i
\(206\) 0 0
\(207\) −6.63282 −0.461013
\(208\) 0 0
\(209\) 2.74580 + 8.45069i 0.189931 + 0.584546i
\(210\) 0 0
\(211\) 0.597913 1.84019i 0.0411621 0.126684i −0.928364 0.371673i \(-0.878784\pi\)
0.969526 + 0.244989i \(0.0787843\pi\)
\(212\) 0 0
\(213\) −1.65934 5.10692i −0.113696 0.349921i
\(214\) 0 0
\(215\) 0.479447 4.56163i 0.0326980 0.311101i
\(216\) 0 0
\(217\) −2.02041 + 1.46791i −0.137154 + 0.0996484i
\(218\) 0 0
\(219\) 2.81592 2.04589i 0.190282 0.138248i
\(220\) 0 0
\(221\) −12.7947 9.29586i −0.860662 0.625307i
\(222\) 0 0
\(223\) −5.68828 + 17.5067i −0.380916 + 1.17234i 0.558485 + 0.829515i \(0.311383\pi\)
−0.939400 + 0.342823i \(0.888617\pi\)
\(224\) 0 0
\(225\) −0.522642 4.97261i −0.0348428 0.331507i
\(226\) 0 0
\(227\) −5.95154 + 18.3170i −0.395018 + 1.21574i 0.533930 + 0.845529i \(0.320714\pi\)
−0.928948 + 0.370211i \(0.879286\pi\)
\(228\) 0 0
\(229\) 21.3918 + 15.5420i 1.41361 + 1.02705i 0.992785 + 0.119905i \(0.0382589\pi\)
0.420824 + 0.907142i \(0.361741\pi\)
\(230\) 0 0
\(231\) −0.755585 + 0.548965i −0.0497139 + 0.0361192i
\(232\) 0 0
\(233\) 12.7508 9.26399i 0.835332 0.606904i −0.0857308 0.996318i \(-0.527323\pi\)
0.921063 + 0.389414i \(0.127323\pi\)
\(234\) 0 0
\(235\) 11.9015 13.2180i 0.776370 0.862246i
\(236\) 0 0
\(237\) −0.407899 1.25538i −0.0264959 0.0815459i
\(238\) 0 0
\(239\) 5.67518 17.4664i 0.367097 1.12981i −0.581561 0.813503i \(-0.697558\pi\)
0.948658 0.316305i \(-0.102442\pi\)
\(240\) 0 0
\(241\) −7.81517 24.0526i −0.503419 1.54936i −0.803412 0.595423i \(-0.796984\pi\)
0.299993 0.953941i \(-0.403016\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 1.57506 14.9857i 0.100627 0.957399i
\(246\) 0 0
\(247\) 24.0853 + 17.4990i 1.53251 + 1.11343i
\(248\) 0 0
\(249\) 0.912590 0.0578331
\(250\) 0 0
\(251\) −17.4297 −1.10015 −0.550076 0.835115i \(-0.685401\pi\)
−0.550076 + 0.835115i \(0.685401\pi\)
\(252\) 0 0
\(253\) −9.80428 7.12323i −0.616390 0.447834i
\(254\) 0 0
\(255\) −0.603841 + 5.74516i −0.0378140 + 0.359776i
\(256\) 0 0
\(257\) −29.6169 −1.84745 −0.923727 0.383052i \(-0.874873\pi\)
−0.923727 + 0.383052i \(0.874873\pi\)
\(258\) 0 0
\(259\) 1.17484 + 3.61579i 0.0730010 + 0.224674i
\(260\) 0 0
\(261\) −2.47124 + 7.60571i −0.152966 + 0.470781i
\(262\) 0 0
\(263\) −5.17140 15.9159i −0.318882 0.981419i −0.974127 0.226002i \(-0.927434\pi\)
0.655244 0.755417i \(-0.272566\pi\)
\(264\) 0 0
\(265\) 1.98866 2.20864i 0.122163 0.135675i
\(266\) 0 0
\(267\) −9.52685 + 6.92166i −0.583034 + 0.423599i
\(268\) 0 0
\(269\) 10.3471 7.51758i 0.630872 0.458355i −0.225830 0.974167i \(-0.572509\pi\)
0.856702 + 0.515811i \(0.172509\pi\)
\(270\) 0 0
\(271\) −23.1964 16.8532i −1.40908 1.02376i −0.993455 0.114224i \(-0.963562\pi\)
−0.415628 0.909535i \(-0.636438\pi\)
\(272\) 0 0
\(273\) −0.966977 + 2.97605i −0.0585241 + 0.180119i
\(274\) 0 0
\(275\) 4.56773 7.91154i 0.275444 0.477084i
\(276\) 0 0
\(277\) 1.64932 5.07610i 0.0990983 0.304993i −0.889202 0.457515i \(-0.848739\pi\)
0.988300 + 0.152522i \(0.0487395\pi\)
\(278\) 0 0
\(279\) 3.95252 + 2.87167i 0.236631 + 0.171922i
\(280\) 0 0
\(281\) 5.19975 3.77784i 0.310191 0.225367i −0.421787 0.906695i \(-0.638597\pi\)
0.731979 + 0.681328i \(0.238597\pi\)
\(282\) 0 0
\(283\) 8.46527 6.15038i 0.503208 0.365602i −0.307033 0.951699i \(-0.599336\pi\)
0.810241 + 0.586097i \(0.199336\pi\)
\(284\) 0 0
\(285\) 1.13670 10.8150i 0.0673322 0.640623i
\(286\) 0 0
\(287\) −0.905199 2.78591i −0.0534322 0.164447i
\(288\) 0 0
\(289\) −3.19082 + 9.82033i −0.187695 + 0.577666i
\(290\) 0 0
\(291\) −2.28668 7.03767i −0.134047 0.412555i
\(292\) 0 0
\(293\) 4.63761 0.270932 0.135466 0.990782i \(-0.456747\pi\)
0.135466 + 0.990782i \(0.456747\pi\)
\(294\) 0 0
\(295\) 22.0749 4.69216i 1.28525 0.273188i
\(296\) 0 0
\(297\) 1.47815 + 1.07394i 0.0857708 + 0.0623162i
\(298\) 0 0
\(299\) −40.6038 −2.34818
\(300\) 0 0
\(301\) 1.04854 0.0604371
\(302\) 0 0
\(303\) −10.5951 7.69776i −0.608670 0.442225i
\(304\) 0 0
\(305\) 9.74628 + 4.33932i 0.558071 + 0.248469i
\(306\) 0 0
\(307\) 17.5664 1.00257 0.501285 0.865282i \(-0.332861\pi\)
0.501285 + 0.865282i \(0.332861\pi\)
\(308\) 0 0
\(309\) −3.40851 10.4903i −0.193903 0.596773i
\(310\) 0 0
\(311\) 5.67507 17.4661i 0.321803 0.990409i −0.651059 0.759027i \(-0.725675\pi\)
0.972863 0.231382i \(-0.0743249\pi\)
\(312\) 0 0
\(313\) −7.83472 24.1128i −0.442845 1.36294i −0.884830 0.465914i \(-0.845726\pi\)
0.441986 0.897022i \(-0.354274\pi\)
\(314\) 0 0
\(315\) 1.11803 0.237645i 0.0629941 0.0133898i
\(316\) 0 0
\(317\) 19.1343 13.9019i 1.07469 0.780808i 0.0979401 0.995192i \(-0.468775\pi\)
0.976749 + 0.214385i \(0.0687747\pi\)
\(318\) 0 0
\(319\) −11.8209 + 8.58840i −0.661844 + 0.480858i
\(320\) 0 0
\(321\) 6.53753 + 4.74979i 0.364889 + 0.265108i
\(322\) 0 0
\(323\) −3.88249 + 11.9491i −0.216028 + 0.664865i
\(324\) 0 0
\(325\) −3.19943 30.4406i −0.177473 1.68854i
\(326\) 0 0
\(327\) 3.49904 10.7690i 0.193498 0.595524i
\(328\) 0 0
\(329\) 3.28950 + 2.38996i 0.181356 + 0.131763i
\(330\) 0 0
\(331\) −26.6188 + 19.3397i −1.46310 + 1.06301i −0.480561 + 0.876961i \(0.659567\pi\)
−0.982541 + 0.186045i \(0.940433\pi\)
\(332\) 0 0
\(333\) 6.01712 4.37169i 0.329736 0.239567i
\(334\) 0 0
\(335\) 16.0253 + 27.7566i 0.875556 + 1.51651i
\(336\) 0 0
\(337\) 1.60814 + 4.94935i 0.0876011 + 0.269608i 0.985255 0.171093i \(-0.0547298\pi\)
−0.897654 + 0.440701i \(0.854730\pi\)
\(338\) 0 0
\(339\) 1.16456 3.58415i 0.0632503 0.194665i
\(340\) 0 0
\(341\) 2.75841 + 8.48951i 0.149376 + 0.459733i
\(342\) 0 0
\(343\) 7.02282 0.379197
\(344\) 0 0
\(345\) 7.41572 + 12.8444i 0.399249 + 0.691519i
\(346\) 0 0
\(347\) −2.70449 1.96493i −0.145185 0.105483i 0.512822 0.858495i \(-0.328600\pi\)
−0.658007 + 0.753012i \(0.728600\pi\)
\(348\) 0 0
\(349\) −28.9138 −1.54772 −0.773859 0.633358i \(-0.781676\pi\)
−0.773859 + 0.633358i \(0.781676\pi\)
\(350\) 0 0
\(351\) 6.12165 0.326749
\(352\) 0 0
\(353\) −16.4521 11.9531i −0.875656 0.636201i 0.0564426 0.998406i \(-0.482024\pi\)
−0.932099 + 0.362204i \(0.882024\pi\)
\(354\) 0 0
\(355\) −8.03432 + 8.92301i −0.426417 + 0.473584i
\(356\) 0 0
\(357\) −1.32059 −0.0698931
\(358\) 0 0
\(359\) 11.4959 + 35.3806i 0.606729 + 1.86732i 0.484439 + 0.874825i \(0.339024\pi\)
0.122289 + 0.992494i \(0.460976\pi\)
\(360\) 0 0
\(361\) 1.43727 4.42345i 0.0756456 0.232813i
\(362\) 0 0
\(363\) −2.36761 7.28675i −0.124267 0.382455i
\(364\) 0 0
\(365\) −7.11014 3.16564i −0.372162 0.165697i
\(366\) 0 0
\(367\) −2.97782 + 2.16352i −0.155441 + 0.112935i −0.662787 0.748808i \(-0.730627\pi\)
0.507346 + 0.861742i \(0.330627\pi\)
\(368\) 0 0
\(369\) −4.63611 + 3.36833i −0.241346 + 0.175348i
\(370\) 0 0
\(371\) 0.549653 + 0.399347i 0.0285366 + 0.0207330i
\(372\) 0 0
\(373\) 6.29124 19.3625i 0.325748 1.00255i −0.645353 0.763884i \(-0.723290\pi\)
0.971102 0.238666i \(-0.0767101\pi\)
\(374\) 0 0
\(375\) −9.04508 + 6.57164i −0.467086 + 0.339358i
\(376\) 0 0
\(377\) −15.1281 + 46.5595i −0.779136 + 2.39793i
\(378\) 0 0
\(379\) 5.17476 + 3.75968i 0.265809 + 0.193122i 0.712704 0.701465i \(-0.247470\pi\)
−0.446895 + 0.894586i \(0.647470\pi\)
\(380\) 0 0
\(381\) 3.37516 2.45220i 0.172915 0.125630i
\(382\) 0 0
\(383\) 1.99777 1.45146i 0.102081 0.0741663i −0.535574 0.844488i \(-0.679905\pi\)
0.637655 + 0.770322i \(0.279905\pi\)
\(384\) 0 0
\(385\) 1.90784 + 0.849423i 0.0972323 + 0.0432906i
\(386\) 0 0
\(387\) −0.633875 1.95087i −0.0322217 0.0991681i
\(388\) 0 0
\(389\) 4.50293 13.8586i 0.228307 0.702658i −0.769632 0.638488i \(-0.779560\pi\)
0.997939 0.0641697i \(-0.0204399\pi\)
\(390\) 0 0
\(391\) −5.29521 16.2970i −0.267790 0.824174i
\(392\) 0 0
\(393\) 14.7908 0.746098
\(394\) 0 0
\(395\) −1.97499 + 2.19345i −0.0993727 + 0.110365i
\(396\) 0 0
\(397\) 20.0023 + 14.5325i 1.00389 + 0.729365i 0.962918 0.269795i \(-0.0869560\pi\)
0.0409675 + 0.999160i \(0.486956\pi\)
\(398\) 0 0
\(399\) 2.48594 0.124453
\(400\) 0 0
\(401\) 6.50743 0.324966 0.162483 0.986711i \(-0.448050\pi\)
0.162483 + 0.986711i \(0.448050\pi\)
\(402\) 0 0
\(403\) 24.1959 + 17.5794i 1.20528 + 0.875690i
\(404\) 0 0
\(405\) −1.11803 1.93649i −0.0555556 0.0962250i
\(406\) 0 0
\(407\) 13.5891 0.673587
\(408\) 0 0
\(409\) 3.41434 + 10.5082i 0.168828 + 0.519599i 0.999298 0.0374642i \(-0.0119280\pi\)
−0.830470 + 0.557063i \(0.811928\pi\)
\(410\) 0 0
\(411\) −0.379143 + 1.16688i −0.0187017 + 0.0575580i
\(412\) 0 0
\(413\) 1.59425 + 4.90660i 0.0784479 + 0.241438i
\(414\) 0 0
\(415\) −1.02031 1.76722i −0.0500849 0.0867496i
\(416\) 0 0
\(417\) −7.35049 + 5.34044i −0.359955 + 0.261523i
\(418\) 0 0
\(419\) −15.0550 + 10.9381i −0.735483 + 0.534360i −0.891293 0.453427i \(-0.850201\pi\)
0.155810 + 0.987787i \(0.450201\pi\)
\(420\) 0 0
\(421\) 11.0426 + 8.02291i 0.538183 + 0.391013i 0.823410 0.567447i \(-0.192069\pi\)
−0.285227 + 0.958460i \(0.592069\pi\)
\(422\) 0 0
\(423\) 2.45804 7.56507i 0.119514 0.367826i
\(424\) 0 0
\(425\) 11.8006 5.25395i 0.572412 0.254854i
\(426\) 0 0
\(427\) −0.753654 + 2.31951i −0.0364719 + 0.112249i
\(428\) 0 0
\(429\) 9.04870 + 6.57426i 0.436875 + 0.317408i
\(430\) 0 0
\(431\) −27.6903 + 20.1182i −1.33379 + 0.969058i −0.334146 + 0.942521i \(0.608448\pi\)
−0.999648 + 0.0265371i \(0.991552\pi\)
\(432\) 0 0
\(433\) −7.29864 + 5.30277i −0.350750 + 0.254835i −0.749184 0.662362i \(-0.769554\pi\)
0.398434 + 0.917197i \(0.369554\pi\)
\(434\) 0 0
\(435\) 17.4913 3.71790i 0.838645 0.178259i
\(436\) 0 0
\(437\) 9.96795 + 30.6782i 0.476832 + 1.46754i
\(438\) 0 0
\(439\) 5.87343 18.0766i 0.280324 0.862747i −0.707438 0.706776i \(-0.750149\pi\)
0.987761 0.155972i \(-0.0498509\pi\)
\(440\) 0 0
\(441\) −2.08237 6.40889i −0.0991607 0.305185i
\(442\) 0 0
\(443\) −1.68124 −0.0798779 −0.0399390 0.999202i \(-0.512716\pi\)
−0.0399390 + 0.999202i \(0.512716\pi\)
\(444\) 0 0
\(445\) 24.0551 + 10.7100i 1.14032 + 0.507703i
\(446\) 0 0
\(447\) −1.53791 1.11736i −0.0727408 0.0528493i
\(448\) 0 0
\(449\) −14.1334 −0.666997 −0.333499 0.942751i \(-0.608229\pi\)
−0.333499 + 0.942751i \(0.608229\pi\)
\(450\) 0 0
\(451\) −10.4702 −0.493024
\(452\) 0 0
\(453\) 3.72384 + 2.70553i 0.174961 + 0.127117i
\(454\) 0 0
\(455\) 6.84421 1.45478i 0.320862 0.0682012i
\(456\) 0 0
\(457\) −24.8188 −1.16097 −0.580487 0.814269i \(-0.697138\pi\)
−0.580487 + 0.814269i \(0.697138\pi\)
\(458\) 0 0
\(459\) 0.798335 + 2.45702i 0.0372631 + 0.114684i
\(460\) 0 0
\(461\) −10.4642 + 32.2054i −0.487365 + 1.49996i 0.341161 + 0.940005i \(0.389180\pi\)
−0.828526 + 0.559951i \(0.810820\pi\)
\(462\) 0 0
\(463\) 0.846018 + 2.60378i 0.0393178 + 0.121008i 0.968789 0.247887i \(-0.0797362\pi\)
−0.929471 + 0.368895i \(0.879736\pi\)
\(464\) 0 0
\(465\) 1.14192 10.8646i 0.0529553 0.503836i
\(466\) 0 0
\(467\) 28.0538 20.3823i 1.29817 0.943179i 0.298239 0.954491i \(-0.403601\pi\)
0.999936 + 0.0113121i \(0.00360084\pi\)
\(468\) 0 0
\(469\) −5.92754 + 4.30661i −0.273708 + 0.198861i
\(470\) 0 0
\(471\) −3.20432 2.32808i −0.147647 0.107272i
\(472\) 0 0
\(473\) 1.15815 3.56441i 0.0532516 0.163892i
\(474\) 0 0
\(475\) −22.2139 + 9.89029i −1.01925 + 0.453797i
\(476\) 0 0
\(477\) 0.410722 1.26407i 0.0188057 0.0578779i
\(478\) 0 0
\(479\) −4.41726 3.20933i −0.201830 0.146638i 0.482280 0.876017i \(-0.339809\pi\)
−0.684109 + 0.729379i \(0.739809\pi\)
\(480\) 0 0
\(481\) 36.8347 26.7620i 1.67952 1.22024i
\(482\) 0 0
\(483\) −2.74297 + 1.99289i −0.124810 + 0.0906794i
\(484\) 0 0
\(485\) −11.0718 + 12.2965i −0.502745 + 0.558354i
\(486\) 0 0
\(487\) −7.29352 22.4471i −0.330501 1.01718i −0.968896 0.247468i \(-0.920401\pi\)
0.638395 0.769709i \(-0.279599\pi\)
\(488\) 0 0
\(489\) 6.48302 19.9527i 0.293172 0.902291i
\(490\) 0 0
\(491\) 4.07930 + 12.5548i 0.184096 + 0.566590i 0.999932 0.0116942i \(-0.00372245\pi\)
−0.815835 + 0.578284i \(0.803722\pi\)
\(492\) 0 0
\(493\) −20.6603 −0.930492
\(494\) 0 0
\(495\) 0.427051 4.06312i 0.0191945 0.182624i
\(496\) 0 0
\(497\) −2.22063 1.61338i −0.0996089 0.0723701i
\(498\) 0 0
\(499\) 25.5183 1.14235 0.571177 0.820827i \(-0.306487\pi\)
0.571177 + 0.820827i \(0.306487\pi\)
\(500\) 0 0
\(501\) −18.0373 −0.805848
\(502\) 0 0
\(503\) 23.6136 + 17.1563i 1.05288 + 0.764960i 0.972757 0.231826i \(-0.0744699\pi\)
0.0801193 + 0.996785i \(0.474470\pi\)
\(504\) 0 0
\(505\) −3.06101 + 29.1236i −0.136213 + 1.29598i
\(506\) 0 0
\(507\) 24.4746 1.08695
\(508\) 0 0
\(509\) 8.87540 + 27.3157i 0.393395 + 1.21075i 0.930204 + 0.367042i \(0.119630\pi\)
−0.536809 + 0.843704i \(0.680370\pi\)
\(510\) 0 0
\(511\) 0.549808 1.69213i 0.0243221 0.0748556i
\(512\) 0 0
\(513\) −1.50282 4.62521i −0.0663513 0.204208i
\(514\) 0 0
\(515\) −16.5036 + 18.3291i −0.727235 + 0.807676i
\(516\) 0 0
\(517\) 11.7578 8.54251i 0.517105 0.375699i
\(518\) 0 0
\(519\) −20.7088 + 15.0458i −0.909017 + 0.660439i
\(520\) 0 0
\(521\) −27.6502 20.0890i −1.21138 0.880116i −0.216021 0.976389i \(-0.569308\pi\)
−0.995355 + 0.0962724i \(0.969308\pi\)
\(522\) 0 0
\(523\) 4.65282 14.3199i 0.203454 0.626166i −0.796320 0.604876i \(-0.793223\pi\)
0.999773 0.0212901i \(-0.00677737\pi\)
\(524\) 0 0
\(525\) −1.71020 1.89937i −0.0746392 0.0828952i
\(526\) 0 0
\(527\) −3.90033 + 12.0040i −0.169901 + 0.522901i
\(528\) 0 0
\(529\) −16.9847 12.3401i −0.738466 0.536527i
\(530\) 0 0
\(531\) 8.16519 5.93236i 0.354339 0.257442i
\(532\) 0 0
\(533\) −28.3806 + 20.6197i −1.22930 + 0.893139i
\(534\) 0 0
\(535\) 1.88875 17.9703i 0.0816580 0.776924i
\(536\) 0 0
\(537\) −2.60140 8.00630i −0.112259 0.345497i
\(538\) 0 0
\(539\) 3.80469 11.7096i 0.163879 0.504369i
\(540\) 0 0
\(541\) 13.5497 + 41.7016i 0.582546 + 1.79289i 0.608909 + 0.793240i \(0.291607\pi\)
−0.0263633 + 0.999652i \(0.508393\pi\)
\(542\) 0 0
\(543\) −20.0676 −0.861184
\(544\) 0 0
\(545\) −24.7660 + 5.26418i −1.06086 + 0.225493i
\(546\) 0 0
\(547\) 8.39025 + 6.09587i 0.358741 + 0.260641i 0.752527 0.658562i \(-0.228835\pi\)
−0.393786 + 0.919202i \(0.628835\pi\)
\(548\) 0 0
\(549\) 4.77116 0.203628
\(550\) 0 0
\(551\) 38.8919 1.65685
\(552\) 0 0
\(553\) −0.545875 0.396601i −0.0232130 0.0168652i
\(554\) 0 0
\(555\) −15.1931 6.76440i −0.644911 0.287133i
\(556\) 0 0
\(557\) −24.3856 −1.03325 −0.516625 0.856212i \(-0.672812\pi\)
−0.516625 + 0.856212i \(0.672812\pi\)
\(558\) 0 0
\(559\) −3.88036 11.9425i −0.164122 0.505114i
\(560\) 0 0
\(561\) −1.45863 + 4.48920i −0.0615834 + 0.189534i
\(562\) 0 0
\(563\) −8.88197 27.3359i −0.374330 1.15207i −0.943929 0.330147i \(-0.892902\pi\)
0.569599 0.821923i \(-0.307098\pi\)
\(564\) 0 0
\(565\) −8.24270 + 1.75204i −0.346773 + 0.0737089i
\(566\) 0 0
\(567\) 0.413545 0.300458i 0.0173673 0.0126181i
\(568\) 0 0
\(569\) −14.1571 + 10.2858i −0.593498 + 0.431202i −0.843565 0.537027i \(-0.819547\pi\)
0.250067 + 0.968229i \(0.419547\pi\)
\(570\) 0 0
\(571\) 15.5117 + 11.2699i 0.649146 + 0.471632i 0.862980 0.505238i \(-0.168595\pi\)
−0.213834 + 0.976870i \(0.568595\pi\)
\(572\) 0 0
\(573\) 1.19381 3.67416i 0.0498720 0.153490i
\(574\) 0 0
\(575\) 16.5820 28.7209i 0.691519 1.19775i
\(576\) 0 0
\(577\) 2.86928 8.83072i 0.119450 0.367628i −0.873400 0.487004i \(-0.838090\pi\)
0.992849 + 0.119377i \(0.0380896\pi\)
\(578\) 0 0
\(579\) −8.65040 6.28489i −0.359498 0.261191i
\(580\) 0 0
\(581\) 0.377398 0.274195i 0.0156571 0.0113755i
\(582\) 0 0
\(583\) 1.96464 1.42740i 0.0813672 0.0591167i
\(584\) 0 0
\(585\) −6.84421 11.8545i −0.282973 0.490124i
\(586\) 0 0
\(587\) −5.47068 16.8370i −0.225799 0.694938i −0.998210 0.0598141i \(-0.980949\pi\)
0.772411 0.635123i \(-0.219051\pi\)
\(588\) 0 0
\(589\) 7.34216 22.5969i 0.302529 0.931087i
\(590\) 0 0
\(591\) −1.28688 3.96060i −0.0529350 0.162917i
\(592\) 0 0
\(593\) 25.8975 1.06348 0.531742 0.846907i \(-0.321538\pi\)
0.531742 + 0.846907i \(0.321538\pi\)
\(594\) 0 0
\(595\) 1.47647 + 2.55731i 0.0605292 + 0.104840i
\(596\) 0 0
\(597\) 22.3261 + 16.2208i 0.913745 + 0.663875i
\(598\) 0 0
\(599\) 10.0259 0.409646 0.204823 0.978799i \(-0.434338\pi\)
0.204823 + 0.978799i \(0.434338\pi\)
\(600\) 0 0
\(601\) −1.69846 −0.0692818 −0.0346409 0.999400i \(-0.511029\pi\)
−0.0346409 + 0.999400i \(0.511029\pi\)
\(602\) 0 0
\(603\) 11.5960 + 8.42500i 0.472226 + 0.343092i
\(604\) 0 0
\(605\) −11.4637 + 12.7317i −0.466064 + 0.517617i
\(606\) 0 0
\(607\) −13.3043 −0.540005 −0.270002 0.962860i \(-0.587024\pi\)
−0.270002 + 0.962860i \(0.587024\pi\)
\(608\) 0 0
\(609\) 1.26323 + 3.88781i 0.0511885 + 0.157542i
\(610\) 0 0
\(611\) 15.0473 46.3107i 0.608747 1.87353i
\(612\) 0 0
\(613\) −2.17187 6.68433i −0.0877210 0.269977i 0.897567 0.440877i \(-0.145333\pi\)
−0.985288 + 0.170900i \(0.945333\pi\)
\(614\) 0 0
\(615\) 11.7061 + 5.21188i 0.472034 + 0.210163i
\(616\) 0 0
\(617\) 8.04174 5.84267i 0.323748 0.235217i −0.414025 0.910266i \(-0.635877\pi\)
0.737773 + 0.675049i \(0.235877\pi\)
\(618\) 0 0
\(619\) 20.2765 14.7317i 0.814980 0.592118i −0.100290 0.994958i \(-0.531977\pi\)
0.915270 + 0.402840i \(0.131977\pi\)
\(620\) 0 0
\(621\) 5.36606 + 3.89867i 0.215333 + 0.156448i
\(622\) 0 0
\(623\) −1.86011 + 5.72484i −0.0745239 + 0.229361i
\(624\) 0 0
\(625\) 22.8386 + 10.1684i 0.913545 + 0.406737i
\(626\) 0 0
\(627\) 2.74580 8.45069i 0.109656 0.337488i
\(628\) 0 0
\(629\) 15.5450 + 11.2941i 0.619821 + 0.450326i
\(630\) 0 0
\(631\) −8.20614 + 5.96211i −0.326681 + 0.237348i −0.739021 0.673682i \(-0.764712\pi\)
0.412340 + 0.911030i \(0.364712\pi\)
\(632\) 0 0
\(633\) −1.56536 + 1.13730i −0.0622174 + 0.0452036i
\(634\) 0 0
\(635\) −8.52221 3.79433i −0.338194 0.150574i
\(636\) 0 0
\(637\) −12.7476 39.2330i −0.505077 1.55447i
\(638\) 0 0
\(639\) −1.65934 + 5.10692i −0.0656425 + 0.202027i
\(640\) 0 0
\(641\) 4.53631 + 13.9613i 0.179174 + 0.551440i 0.999799 0.0200262i \(-0.00637497\pi\)
−0.820626 + 0.571466i \(0.806375\pi\)
\(642\) 0 0
\(643\) 8.52311 0.336119 0.168059 0.985777i \(-0.446250\pi\)
0.168059 + 0.985777i \(0.446250\pi\)
\(644\) 0 0
\(645\) −3.06914 + 3.40863i −0.120847 + 0.134215i
\(646\) 0 0
\(647\) −30.9405 22.4796i −1.21640 0.883764i −0.220600 0.975364i \(-0.570802\pi\)
−0.995796 + 0.0916006i \(0.970802\pi\)
\(648\) 0 0
\(649\) 18.4403 0.723846
\(650\) 0 0
\(651\) 2.49736 0.0978794
\(652\) 0 0
\(653\) 6.79344 + 4.93572i 0.265848 + 0.193150i 0.712721 0.701448i \(-0.247463\pi\)
−0.446873 + 0.894597i \(0.647463\pi\)
\(654\) 0 0
\(655\) −16.5366 28.6423i −0.646140 1.11915i
\(656\) 0 0
\(657\) −3.48067 −0.135794
\(658\) 0 0
\(659\) −14.5953 44.9197i −0.568552 1.74982i −0.657153 0.753757i \(-0.728240\pi\)
0.0886012 0.996067i \(-0.471760\pi\)
\(660\) 0 0
\(661\) −7.82323 + 24.0774i −0.304288 + 0.936503i 0.675654 + 0.737219i \(0.263862\pi\)
−0.979942 + 0.199284i \(0.936138\pi\)
\(662\) 0 0
\(663\) 4.88712 + 15.0410i 0.189800 + 0.584145i
\(664\) 0 0
\(665\) −2.77937 4.81401i −0.107779 0.186679i
\(666\) 0 0
\(667\) −42.9130 + 31.1781i −1.66160 + 1.20722i
\(668\) 0 0
\(669\) 14.8921 10.8198i 0.575763 0.418316i
\(670\) 0 0
\(671\) 7.05248 + 5.12392i 0.272258 + 0.197807i
\(672\) 0 0
\(673\) −4.89943 + 15.0789i −0.188859 + 0.581248i −0.999993 0.00361149i \(-0.998850\pi\)
0.811135 + 0.584860i \(0.198850\pi\)
\(674\) 0 0
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) 0 0
\(677\) 10.6671 32.8299i 0.409970 1.26176i −0.506704 0.862120i \(-0.669136\pi\)
0.916674 0.399637i \(-0.130864\pi\)
\(678\) 0 0
\(679\) −3.06017 2.22334i −0.117439 0.0853241i
\(680\) 0 0
\(681\) 15.5813 11.3205i 0.597078 0.433803i
\(682\) 0 0
\(683\) −20.2580 + 14.7183i −0.775152 + 0.563181i −0.903520 0.428546i \(-0.859026\pi\)
0.128368 + 0.991727i \(0.459026\pi\)
\(684\) 0 0
\(685\) 2.68355 0.570406i 0.102533 0.0217941i
\(686\) 0 0
\(687\) −8.17094 25.1476i −0.311741 0.959439i
\(688\) 0 0
\(689\) 2.51430 7.73821i 0.0957870 0.294802i
\(690\) 0 0
\(691\) −8.49860 26.1560i −0.323302 0.995021i −0.972201 0.234147i \(-0.924770\pi\)
0.648899 0.760874i \(-0.275230\pi\)
\(692\) 0 0
\(693\) 0.933955 0.0354780
\(694\) 0 0
\(695\) 18.5598 + 8.26336i 0.704014 + 0.313447i
\(696\) 0 0
\(697\) −11.9772 8.70196i −0.453670 0.329610i
\(698\) 0 0
\(699\) −15.7608 −0.596130
\(700\) 0 0
\(701\) −5.38643 −0.203443 −0.101721 0.994813i \(-0.532435\pi\)
−0.101721 + 0.994813i \(0.532435\pi\)
\(702\) 0 0
\(703\) −29.2627 21.2606i −1.10366 0.801858i
\(704\) 0 0
\(705\) −17.3979 + 3.69803i −0.655242 + 0.139276i
\(706\) 0 0
\(707\) −6.69440 −0.251769
\(708\) 0 0
\(709\) 6.33013 + 19.4821i 0.237733 + 0.731667i 0.996747 + 0.0805929i \(0.0256814\pi\)
−0.759014 + 0.651074i \(0.774319\pi\)
\(710\) 0 0
\(711\) −0.407899 + 1.25538i −0.0152974 + 0.0470805i
\(712\) 0 0
\(713\) 10.0137 + 30.8191i 0.375018 + 1.15419i
\(714\) 0 0
\(715\) 2.61426 24.8730i 0.0977676 0.930197i
\(716\) 0 0
\(717\) −14.8578 + 10.7948i −0.554875 + 0.403141i
\(718\) 0 0
\(719\) 27.6232 20.0694i 1.03017 0.748464i 0.0618291 0.998087i \(-0.480307\pi\)
0.968343 + 0.249623i \(0.0803066\pi\)
\(720\) 0 0
\(721\) −4.56148 3.31411i −0.169878 0.123424i
\(722\) 0 0
\(723\) −7.81517 + 24.0526i −0.290649 + 0.894526i
\(724\) 0 0
\(725\) −26.7556 29.7151i −0.993677 1.10359i
\(726\) 0 0
\(727\) −9.46652 + 29.1350i −0.351094 + 1.08056i 0.607146 + 0.794590i \(0.292314\pi\)
−0.958240 + 0.285966i \(0.907686\pi\)
\(728\) 0 0
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 0 0
\(731\) 4.28728 3.11489i 0.158571 0.115208i
\(732\) 0 0
\(733\) −29.9046 + 21.7270i −1.10455 + 0.802505i −0.981797 0.189932i \(-0.939173\pi\)
−0.122756 + 0.992437i \(0.539173\pi\)
\(734\) 0 0
\(735\) −10.0826 + 11.1979i −0.371902 + 0.413039i
\(736\) 0 0
\(737\) 8.09270 + 24.9068i 0.298099 + 0.917453i
\(738\) 0 0
\(739\) 10.2391 31.5127i 0.376652 1.15922i −0.565706 0.824607i \(-0.691396\pi\)
0.942357 0.334608i \(-0.108604\pi\)
\(740\) 0 0
\(741\) −9.19975 28.3139i −0.337961 1.04014i
\(742\) 0 0
\(743\) 18.9855 0.696512 0.348256 0.937400i \(-0.386774\pi\)
0.348256 + 0.937400i \(0.386774\pi\)
\(744\) 0 0
\(745\) −0.444318 + 4.22740i −0.0162786 + 0.154880i
\(746\) 0 0
\(747\) −0.738301 0.536407i −0.0270130 0.0196261i
\(748\) 0 0
\(749\) 4.13068 0.150932
\(750\) 0 0
\(751\) −7.10651 −0.259320 −0.129660 0.991559i \(-0.541389\pi\)
−0.129660 + 0.991559i \(0.541389\pi\)
\(752\) 0 0
\(753\) 14.1009 + 10.2449i 0.513866 + 0.373345i
\(754\) 0 0
\(755\) 1.07585 10.2361i 0.0391543 0.372528i
\(756\) 0 0
\(757\) −8.77180 −0.318817 −0.159408 0.987213i \(-0.550959\pi\)
−0.159408 + 0.987213i \(0.550959\pi\)
\(758\) 0 0
\(759\) 3.74490 + 11.5256i 0.135931 + 0.418354i
\(760\) 0 0
\(761\) 6.40922 19.7255i 0.232334 0.715050i −0.765130 0.643876i \(-0.777325\pi\)
0.997464 0.0711744i \(-0.0226747\pi\)
\(762\) 0 0
\(763\) −1.78861 5.50477i −0.0647520 0.199286i
\(764\) 0 0
\(765\) 3.86544 4.29300i 0.139755 0.155214i
\(766\) 0 0
\(767\) 49.9844 36.3158i 1.80483 1.31129i
\(768\) 0 0
\(769\) 11.0923 8.05906i 0.400000 0.290617i −0.369541 0.929214i \(-0.620485\pi\)
0.769541 + 0.638597i \(0.220485\pi\)
\(770\) 0 0
\(771\) 23.9606 + 17.4084i 0.862920 + 0.626948i
\(772\) 0 0
\(773\) −8.30485 + 25.5597i −0.298705 + 0.919318i 0.683247 + 0.730187i \(0.260567\pi\)
−0.981952 + 0.189131i \(0.939433\pi\)
\(774\) 0 0
\(775\) −22.3160 + 9.93572i −0.801614 + 0.356902i
\(776\) 0 0
\(777\) 1.17484 3.61579i 0.0421472 0.129716i
\(778\) 0 0
\(779\) 22.5465 + 16.3810i 0.807812 + 0.586910i
\(780\) 0 0
\(781\) −7.93727 + 5.76676i −0.284018 + 0.206351i
\(782\) 0 0
\(783\) 6.46980 4.70059i 0.231212 0.167985i
\(784\) 0 0
\(785\) −0.925760 + 8.80802i −0.0330418 + 0.314372i
\(786\) 0 0
\(787\) −0.449069 1.38209i −0.0160076 0.0492662i 0.942734 0.333546i \(-0.108245\pi\)
−0.958741 + 0.284280i \(0.908245\pi\)
\(788\) 0 0
\(789\) −5.17140 + 15.9159i −0.184107 + 0.566623i
\(790\) 0 0
\(791\) −0.595290 1.83211i −0.0211661 0.0651424i
\(792\) 0 0
\(793\) 29.2074 1.03718
\(794\) 0 0
\(795\) −2.90707 + 0.617916i −0.103103