Properties

Label 1134.2.f.t.757.2
Level $1134$
Weight $2$
Character 1134.757
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 757.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.757
Dual form 1134.2.f.t.379.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.73205 q^{10} +(0.633975 + 1.09808i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +0.464102 q^{17} +4.19615 q^{19} +(0.866025 + 1.50000i) q^{20} +(-0.633975 + 1.09808i) q^{22} +(2.36603 - 4.09808i) q^{23} +(1.00000 + 1.73205i) q^{25} +1.00000 q^{26} +1.00000 q^{28} +(-0.232051 - 0.401924i) q^{29} +(3.09808 - 5.36603i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.232051 + 0.401924i) q^{34} -1.73205 q^{35} +7.19615 q^{37} +(2.09808 + 3.63397i) q^{38} +(-0.866025 + 1.50000i) q^{40} +(4.73205 - 8.19615i) q^{41} +(4.19615 + 7.26795i) q^{43} -1.26795 q^{44} +4.73205 q^{46} +(-4.09808 - 7.09808i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-1.00000 + 1.73205i) q^{50} +(0.500000 + 0.866025i) q^{52} -2.53590 q^{53} +2.19615 q^{55} +(0.500000 + 0.866025i) q^{56} +(0.232051 - 0.401924i) q^{58} +(1.09808 - 1.90192i) q^{59} +(5.69615 + 9.86603i) q^{61} +6.19615 q^{62} +1.00000 q^{64} +(-0.866025 - 1.50000i) q^{65} +(3.09808 - 5.36603i) q^{67} +(-0.232051 + 0.401924i) q^{68} +(-0.866025 - 1.50000i) q^{70} -16.3923 q^{71} +1.19615 q^{73} +(3.59808 + 6.23205i) q^{74} +(-2.09808 + 3.63397i) q^{76} +(0.633975 - 1.09808i) q^{77} +(-2.09808 - 3.63397i) q^{79} -1.73205 q^{80} +9.46410 q^{82} +(2.36603 + 4.09808i) q^{83} +(0.401924 - 0.696152i) q^{85} +(-4.19615 + 7.26795i) q^{86} +(-0.633975 - 1.09808i) q^{88} +5.53590 q^{89} -1.00000 q^{91} +(2.36603 + 4.09808i) q^{92} +(4.09808 - 7.09808i) q^{94} +(3.63397 - 6.29423i) q^{95} +(8.00000 + 13.8564i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 2q^{7} - 4q^{8} + 6q^{11} + 2q^{13} + 2q^{14} - 2q^{16} - 12q^{17} - 4q^{19} - 6q^{22} + 6q^{23} + 4q^{25} + 4q^{26} + 4q^{28} + 6q^{29} + 2q^{31} + 2q^{32} - 6q^{34} + 8q^{37} - 2q^{38} + 12q^{41} - 4q^{43} - 12q^{44} + 12q^{46} - 6q^{47} - 2q^{49} - 4q^{50} + 2q^{52} - 24q^{53} - 12q^{55} + 2q^{56} - 6q^{58} - 6q^{59} + 2q^{61} + 4q^{62} + 4q^{64} + 2q^{67} + 6q^{68} - 24q^{71} - 16q^{73} + 4q^{74} + 2q^{76} + 6q^{77} + 2q^{79} + 24q^{82} + 6q^{83} + 12q^{85} + 4q^{86} - 6q^{88} + 36q^{89} - 4q^{91} + 6q^{92} + 6q^{94} + 18q^{95} + 32q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.866025 1.50000i 0.387298 0.670820i −0.604787 0.796387i \(-0.706742\pi\)
0.992085 + 0.125567i \(0.0400750\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.73205 0.547723
\(11\) 0.633975 + 1.09808i 0.191151 + 0.331082i 0.945632 0.325239i \(-0.105445\pi\)
−0.754481 + 0.656322i \(0.772111\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.464102 0.112561 0.0562806 0.998415i \(-0.482076\pi\)
0.0562806 + 0.998415i \(0.482076\pi\)
\(18\) 0 0
\(19\) 4.19615 0.962663 0.481332 0.876539i \(-0.340153\pi\)
0.481332 + 0.876539i \(0.340153\pi\)
\(20\) 0.866025 + 1.50000i 0.193649 + 0.335410i
\(21\) 0 0
\(22\) −0.633975 + 1.09808i −0.135164 + 0.234111i
\(23\) 2.36603 4.09808i 0.493350 0.854508i −0.506620 0.862169i \(-0.669105\pi\)
0.999971 + 0.00766135i \(0.00243871\pi\)
\(24\) 0 0
\(25\) 1.00000 + 1.73205i 0.200000 + 0.346410i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −0.232051 0.401924i −0.0430908 0.0746354i 0.843676 0.536853i \(-0.180387\pi\)
−0.886766 + 0.462218i \(0.847054\pi\)
\(30\) 0 0
\(31\) 3.09808 5.36603i 0.556431 0.963767i −0.441360 0.897330i \(-0.645504\pi\)
0.997791 0.0664364i \(-0.0211629\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0.232051 + 0.401924i 0.0397964 + 0.0689294i
\(35\) −1.73205 −0.292770
\(36\) 0 0
\(37\) 7.19615 1.18304 0.591520 0.806290i \(-0.298528\pi\)
0.591520 + 0.806290i \(0.298528\pi\)
\(38\) 2.09808 + 3.63397i 0.340353 + 0.589509i
\(39\) 0 0
\(40\) −0.866025 + 1.50000i −0.136931 + 0.237171i
\(41\) 4.73205 8.19615i 0.739022 1.28002i −0.213914 0.976853i \(-0.568621\pi\)
0.952936 0.303171i \(-0.0980455\pi\)
\(42\) 0 0
\(43\) 4.19615 + 7.26795i 0.639907 + 1.10835i 0.985453 + 0.169950i \(0.0543606\pi\)
−0.345545 + 0.938402i \(0.612306\pi\)
\(44\) −1.26795 −0.191151
\(45\) 0 0
\(46\) 4.73205 0.697703
\(47\) −4.09808 7.09808i −0.597766 1.03536i −0.993150 0.116845i \(-0.962722\pi\)
0.395384 0.918516i \(-0.370611\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −1.00000 + 1.73205i −0.141421 + 0.244949i
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −2.53590 −0.348332 −0.174166 0.984716i \(-0.555723\pi\)
−0.174166 + 0.984716i \(0.555723\pi\)
\(54\) 0 0
\(55\) 2.19615 0.296129
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 0.232051 0.401924i 0.0304698 0.0527752i
\(59\) 1.09808 1.90192i 0.142957 0.247609i −0.785652 0.618669i \(-0.787672\pi\)
0.928609 + 0.371060i \(0.121005\pi\)
\(60\) 0 0
\(61\) 5.69615 + 9.86603i 0.729318 + 1.26322i 0.957172 + 0.289520i \(0.0934956\pi\)
−0.227854 + 0.973695i \(0.573171\pi\)
\(62\) 6.19615 0.786912
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.866025 1.50000i −0.107417 0.186052i
\(66\) 0 0
\(67\) 3.09808 5.36603i 0.378490 0.655564i −0.612353 0.790585i \(-0.709777\pi\)
0.990843 + 0.135020i \(0.0431100\pi\)
\(68\) −0.232051 + 0.401924i −0.0281403 + 0.0487404i
\(69\) 0 0
\(70\) −0.866025 1.50000i −0.103510 0.179284i
\(71\) −16.3923 −1.94541 −0.972704 0.232048i \(-0.925457\pi\)
−0.972704 + 0.232048i \(0.925457\pi\)
\(72\) 0 0
\(73\) 1.19615 0.139999 0.0699995 0.997547i \(-0.477700\pi\)
0.0699995 + 0.997547i \(0.477700\pi\)
\(74\) 3.59808 + 6.23205i 0.418268 + 0.724461i
\(75\) 0 0
\(76\) −2.09808 + 3.63397i −0.240666 + 0.416845i
\(77\) 0.633975 1.09808i 0.0722481 0.125137i
\(78\) 0 0
\(79\) −2.09808 3.63397i −0.236052 0.408854i 0.723526 0.690297i \(-0.242520\pi\)
−0.959578 + 0.281443i \(0.909187\pi\)
\(80\) −1.73205 −0.193649
\(81\) 0 0
\(82\) 9.46410 1.04514
\(83\) 2.36603 + 4.09808i 0.259705 + 0.449822i 0.966163 0.257933i \(-0.0830413\pi\)
−0.706458 + 0.707755i \(0.749708\pi\)
\(84\) 0 0
\(85\) 0.401924 0.696152i 0.0435948 0.0755083i
\(86\) −4.19615 + 7.26795i −0.452483 + 0.783723i
\(87\) 0 0
\(88\) −0.633975 1.09808i −0.0675819 0.117055i
\(89\) 5.53590 0.586804 0.293402 0.955989i \(-0.405213\pi\)
0.293402 + 0.955989i \(0.405213\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 2.36603 + 4.09808i 0.246675 + 0.427254i
\(93\) 0 0
\(94\) 4.09808 7.09808i 0.422684 0.732111i
\(95\) 3.63397 6.29423i 0.372838 0.645774i
\(96\) 0 0
\(97\) 8.00000 + 13.8564i 0.812277 + 1.40690i 0.911267 + 0.411816i \(0.135106\pi\)
−0.0989899 + 0.995088i \(0.531561\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) −0.464102 0.803848i −0.0461798 0.0799858i 0.842012 0.539459i \(-0.181371\pi\)
−0.888191 + 0.459474i \(0.848038\pi\)
\(102\) 0 0
\(103\) −6.19615 + 10.7321i −0.610525 + 1.05746i 0.380627 + 0.924729i \(0.375708\pi\)
−0.991152 + 0.132732i \(0.957625\pi\)
\(104\) −0.500000 + 0.866025i −0.0490290 + 0.0849208i
\(105\) 0 0
\(106\) −1.26795 2.19615i −0.123154 0.213309i
\(107\) −13.8564 −1.33955 −0.669775 0.742564i \(-0.733609\pi\)
−0.669775 + 0.742564i \(0.733609\pi\)
\(108\) 0 0
\(109\) −15.1962 −1.45553 −0.727764 0.685828i \(-0.759440\pi\)
−0.727764 + 0.685828i \(0.759440\pi\)
\(110\) 1.09808 + 1.90192i 0.104697 + 0.181341i
\(111\) 0 0
\(112\) −0.500000 + 0.866025i −0.0472456 + 0.0818317i
\(113\) −6.86603 + 11.8923i −0.645901 + 1.11873i 0.338191 + 0.941077i \(0.390185\pi\)
−0.984093 + 0.177657i \(0.943148\pi\)
\(114\) 0 0
\(115\) −4.09808 7.09808i −0.382148 0.661899i
\(116\) 0.464102 0.0430908
\(117\) 0 0
\(118\) 2.19615 0.202172
\(119\) −0.232051 0.401924i −0.0212721 0.0368443i
\(120\) 0 0
\(121\) 4.69615 8.13397i 0.426923 0.739452i
\(122\) −5.69615 + 9.86603i −0.515705 + 0.893228i
\(123\) 0 0
\(124\) 3.09808 + 5.36603i 0.278215 + 0.481883i
\(125\) 12.1244 1.08444
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0.866025 1.50000i 0.0759555 0.131559i
\(131\) −4.73205 + 8.19615i −0.413441 + 0.716101i −0.995263 0.0972148i \(-0.969007\pi\)
0.581822 + 0.813316i \(0.302340\pi\)
\(132\) 0 0
\(133\) −2.09808 3.63397i −0.181926 0.315106i
\(134\) 6.19615 0.535266
\(135\) 0 0
\(136\) −0.464102 −0.0397964
\(137\) 7.33013 + 12.6962i 0.626255 + 1.08471i 0.988297 + 0.152544i \(0.0487465\pi\)
−0.362042 + 0.932162i \(0.617920\pi\)
\(138\) 0 0
\(139\) 3.90192 6.75833i 0.330957 0.573234i −0.651743 0.758440i \(-0.725962\pi\)
0.982700 + 0.185206i \(0.0592952\pi\)
\(140\) 0.866025 1.50000i 0.0731925 0.126773i
\(141\) 0 0
\(142\) −8.19615 14.1962i −0.687806 1.19131i
\(143\) 1.26795 0.106031
\(144\) 0 0
\(145\) −0.803848 −0.0667559
\(146\) 0.598076 + 1.03590i 0.0494971 + 0.0857316i
\(147\) 0 0
\(148\) −3.59808 + 6.23205i −0.295760 + 0.512271i
\(149\) 4.96410 8.59808i 0.406675 0.704382i −0.587840 0.808977i \(-0.700021\pi\)
0.994515 + 0.104596i \(0.0333548\pi\)
\(150\) 0 0
\(151\) −4.29423 7.43782i −0.349459 0.605281i 0.636694 0.771116i \(-0.280301\pi\)
−0.986154 + 0.165835i \(0.946968\pi\)
\(152\) −4.19615 −0.340353
\(153\) 0 0
\(154\) 1.26795 0.102174
\(155\) −5.36603 9.29423i −0.431010 0.746530i
\(156\) 0 0
\(157\) 2.69615 4.66987i 0.215176 0.372696i −0.738151 0.674636i \(-0.764301\pi\)
0.953327 + 0.301939i \(0.0976340\pi\)
\(158\) 2.09808 3.63397i 0.166914 0.289103i
\(159\) 0 0
\(160\) −0.866025 1.50000i −0.0684653 0.118585i
\(161\) −4.73205 −0.372938
\(162\) 0 0
\(163\) 3.60770 0.282576 0.141288 0.989969i \(-0.454876\pi\)
0.141288 + 0.989969i \(0.454876\pi\)
\(164\) 4.73205 + 8.19615i 0.369511 + 0.640012i
\(165\) 0 0
\(166\) −2.36603 + 4.09808i −0.183639 + 0.318072i
\(167\) −5.36603 + 9.29423i −0.415236 + 0.719209i −0.995453 0.0952525i \(-0.969634\pi\)
0.580218 + 0.814461i \(0.302967\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0.803848 0.0616523
\(171\) 0 0
\(172\) −8.39230 −0.639907
\(173\) −11.5981 20.0885i −0.881785 1.52730i −0.849354 0.527823i \(-0.823008\pi\)
−0.0324311 0.999474i \(-0.510325\pi\)
\(174\) 0 0
\(175\) 1.00000 1.73205i 0.0755929 0.130931i
\(176\) 0.633975 1.09808i 0.0477876 0.0827706i
\(177\) 0 0
\(178\) 2.76795 + 4.79423i 0.207467 + 0.359343i
\(179\) −10.7321 −0.802151 −0.401076 0.916045i \(-0.631364\pi\)
−0.401076 + 0.916045i \(0.631364\pi\)
\(180\) 0 0
\(181\) −20.3923 −1.51575 −0.757874 0.652401i \(-0.773762\pi\)
−0.757874 + 0.652401i \(0.773762\pi\)
\(182\) −0.500000 0.866025i −0.0370625 0.0641941i
\(183\) 0 0
\(184\) −2.36603 + 4.09808i −0.174426 + 0.302114i
\(185\) 6.23205 10.7942i 0.458189 0.793607i
\(186\) 0 0
\(187\) 0.294229 + 0.509619i 0.0215161 + 0.0372670i
\(188\) 8.19615 0.597766
\(189\) 0 0
\(190\) 7.26795 0.527272
\(191\) −3.29423 5.70577i −0.238362 0.412855i 0.721882 0.692016i \(-0.243277\pi\)
−0.960244 + 0.279161i \(0.909944\pi\)
\(192\) 0 0
\(193\) 9.50000 16.4545i 0.683825 1.18442i −0.289980 0.957033i \(-0.593649\pi\)
0.973805 0.227387i \(-0.0730182\pi\)
\(194\) −8.00000 + 13.8564i −0.574367 + 0.994832i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 0 0
\(199\) −10.5885 −0.750596 −0.375298 0.926904i \(-0.622460\pi\)
−0.375298 + 0.926904i \(0.622460\pi\)
\(200\) −1.00000 1.73205i −0.0707107 0.122474i
\(201\) 0 0
\(202\) 0.464102 0.803848i 0.0326541 0.0565585i
\(203\) −0.232051 + 0.401924i −0.0162868 + 0.0282095i
\(204\) 0 0
\(205\) −8.19615 14.1962i −0.572444 0.991502i
\(206\) −12.3923 −0.863413
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 2.66025 + 4.60770i 0.184014 + 0.318721i
\(210\) 0 0
\(211\) −11.0981 + 19.2224i −0.764023 + 1.32333i 0.176738 + 0.984258i \(0.443445\pi\)
−0.940762 + 0.339069i \(0.889888\pi\)
\(212\) 1.26795 2.19615i 0.0870831 0.150832i
\(213\) 0 0
\(214\) −6.92820 12.0000i −0.473602 0.820303i
\(215\) 14.5359 0.991340
\(216\) 0 0
\(217\) −6.19615 −0.420622
\(218\) −7.59808 13.1603i −0.514607 0.891325i
\(219\) 0 0
\(220\) −1.09808 + 1.90192i −0.0740323 + 0.128228i
\(221\) 0.232051 0.401924i 0.0156094 0.0270363i
\(222\) 0 0
\(223\) 4.19615 + 7.26795i 0.280995 + 0.486698i 0.971630 0.236506i \(-0.0760022\pi\)
−0.690635 + 0.723204i \(0.742669\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −13.7321 −0.913442
\(227\) −9.46410 16.3923i −0.628154 1.08800i −0.987922 0.154953i \(-0.950477\pi\)
0.359767 0.933042i \(-0.382856\pi\)
\(228\) 0 0
\(229\) −9.89230 + 17.1340i −0.653702 + 1.13224i 0.328516 + 0.944499i \(0.393452\pi\)
−0.982218 + 0.187746i \(0.939882\pi\)
\(230\) 4.09808 7.09808i 0.270219 0.468033i
\(231\) 0 0
\(232\) 0.232051 + 0.401924i 0.0152349 + 0.0263876i
\(233\) −10.2679 −0.672676 −0.336338 0.941741i \(-0.609188\pi\)
−0.336338 + 0.941741i \(0.609188\pi\)
\(234\) 0 0
\(235\) −14.1962 −0.926055
\(236\) 1.09808 + 1.90192i 0.0714787 + 0.123805i
\(237\) 0 0
\(238\) 0.232051 0.401924i 0.0150416 0.0260528i
\(239\) −4.56218 + 7.90192i −0.295103 + 0.511133i −0.975009 0.222166i \(-0.928687\pi\)
0.679906 + 0.733299i \(0.262021\pi\)
\(240\) 0 0
\(241\) −8.79423 15.2321i −0.566486 0.981183i −0.996910 0.0785557i \(-0.974969\pi\)
0.430424 0.902627i \(-0.358364\pi\)
\(242\) 9.39230 0.603760
\(243\) 0 0
\(244\) −11.3923 −0.729318
\(245\) 0.866025 + 1.50000i 0.0553283 + 0.0958315i
\(246\) 0 0
\(247\) 2.09808 3.63397i 0.133497 0.231224i
\(248\) −3.09808 + 5.36603i −0.196728 + 0.340743i
\(249\) 0 0
\(250\) 6.06218 + 10.5000i 0.383406 + 0.664078i
\(251\) 14.1962 0.896053 0.448027 0.894020i \(-0.352127\pi\)
0.448027 + 0.894020i \(0.352127\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) −2.00000 3.46410i −0.125491 0.217357i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.03590 + 12.1865i −0.438887 + 0.760175i −0.997604 0.0691835i \(-0.977961\pi\)
0.558717 + 0.829359i \(0.311294\pi\)
\(258\) 0 0
\(259\) −3.59808 6.23205i −0.223574 0.387241i
\(260\) 1.73205 0.107417
\(261\) 0 0
\(262\) −9.46410 −0.584694
\(263\) −4.56218 7.90192i −0.281316 0.487253i 0.690393 0.723434i \(-0.257438\pi\)
−0.971709 + 0.236181i \(0.924104\pi\)
\(264\) 0 0
\(265\) −2.19615 + 3.80385i −0.134909 + 0.233668i
\(266\) 2.09808 3.63397i 0.128641 0.222813i
\(267\) 0 0
\(268\) 3.09808 + 5.36603i 0.189245 + 0.327782i
\(269\) 29.4449 1.79529 0.897643 0.440724i \(-0.145278\pi\)
0.897643 + 0.440724i \(0.145278\pi\)
\(270\) 0 0
\(271\) 17.8038 1.08151 0.540753 0.841181i \(-0.318139\pi\)
0.540753 + 0.841181i \(0.318139\pi\)
\(272\) −0.232051 0.401924i −0.0140701 0.0243702i
\(273\) 0 0
\(274\) −7.33013 + 12.6962i −0.442829 + 0.767003i
\(275\) −1.26795 + 2.19615i −0.0764602 + 0.132433i
\(276\) 0 0
\(277\) −11.3923 19.7321i −0.684497 1.18558i −0.973595 0.228284i \(-0.926688\pi\)
0.289097 0.957300i \(-0.406645\pi\)
\(278\) 7.80385 0.468044
\(279\) 0 0
\(280\) 1.73205 0.103510
\(281\) −5.13397 8.89230i −0.306267 0.530470i 0.671275 0.741208i \(-0.265747\pi\)
−0.977543 + 0.210738i \(0.932413\pi\)
\(282\) 0 0
\(283\) −12.1962 + 21.1244i −0.724986 + 1.25571i 0.233994 + 0.972238i \(0.424820\pi\)
−0.958980 + 0.283475i \(0.908513\pi\)
\(284\) 8.19615 14.1962i 0.486352 0.842387i
\(285\) 0 0
\(286\) 0.633975 + 1.09808i 0.0374877 + 0.0649306i
\(287\) −9.46410 −0.558648
\(288\) 0 0
\(289\) −16.7846 −0.987330
\(290\) −0.401924 0.696152i −0.0236018 0.0408795i
\(291\) 0 0
\(292\) −0.598076 + 1.03590i −0.0349998 + 0.0606214i
\(293\) −4.66987 + 8.08846i −0.272817 + 0.472533i −0.969582 0.244767i \(-0.921289\pi\)
0.696765 + 0.717299i \(0.254622\pi\)
\(294\) 0 0
\(295\) −1.90192 3.29423i −0.110734 0.191797i
\(296\) −7.19615 −0.418268
\(297\) 0 0
\(298\) 9.92820 0.575125
\(299\) −2.36603 4.09808i −0.136831 0.236998i
\(300\) 0 0
\(301\) 4.19615 7.26795i 0.241862 0.418918i
\(302\) 4.29423 7.43782i 0.247105 0.427999i
\(303\) 0 0
\(304\) −2.09808 3.63397i −0.120333 0.208423i
\(305\) 19.7321 1.12985
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0.633975 + 1.09808i 0.0361241 + 0.0625687i
\(309\) 0 0
\(310\) 5.36603 9.29423i 0.304770 0.527877i
\(311\) 14.4904 25.0981i 0.821674 1.42318i −0.0827607 0.996569i \(-0.526374\pi\)
0.904435 0.426612i \(-0.140293\pi\)
\(312\) 0 0
\(313\) 14.9904 + 25.9641i 0.847306 + 1.46758i 0.883603 + 0.468237i \(0.155111\pi\)
−0.0362966 + 0.999341i \(0.511556\pi\)
\(314\) 5.39230 0.304305
\(315\) 0 0
\(316\) 4.19615 0.236052
\(317\) 9.69615 + 16.7942i 0.544590 + 0.943258i 0.998633 + 0.0522778i \(0.0166481\pi\)
−0.454042 + 0.890980i \(0.650019\pi\)
\(318\) 0 0
\(319\) 0.294229 0.509619i 0.0164736 0.0285332i
\(320\) 0.866025 1.50000i 0.0484123 0.0838525i
\(321\) 0 0
\(322\) −2.36603 4.09808i −0.131853 0.228377i
\(323\) 1.94744 0.108359
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 1.80385 + 3.12436i 0.0999059 + 0.173042i
\(327\) 0 0
\(328\) −4.73205 + 8.19615i −0.261284 + 0.452557i
\(329\) −4.09808 + 7.09808i −0.225934 + 0.391330i
\(330\) 0 0
\(331\) −16.5885 28.7321i −0.911784 1.57926i −0.811543 0.584293i \(-0.801372\pi\)
−0.100241 0.994963i \(-0.531962\pi\)
\(332\) −4.73205 −0.259705
\(333\) 0 0
\(334\) −10.7321 −0.587232
\(335\) −5.36603 9.29423i −0.293177 0.507798i
\(336\) 0 0
\(337\) 5.80385 10.0526i 0.316156 0.547598i −0.663527 0.748153i \(-0.730941\pi\)
0.979682 + 0.200555i \(0.0642745\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 0 0
\(340\) 0.401924 + 0.696152i 0.0217974 + 0.0377542i
\(341\) 7.85641 0.425448
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.19615 7.26795i −0.226241 0.391862i
\(345\) 0 0
\(346\) 11.5981 20.0885i 0.623516 1.07996i
\(347\) −2.19615 + 3.80385i −0.117896 + 0.204201i −0.918934 0.394412i \(-0.870948\pi\)
0.801038 + 0.598614i \(0.204281\pi\)
\(348\) 0 0
\(349\) 4.19615 + 7.26795i 0.224615 + 0.389044i 0.956204 0.292702i \(-0.0945543\pi\)
−0.731589 + 0.681746i \(0.761221\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 1.26795 0.0675819
\(353\) 15.9282 + 27.5885i 0.847773 + 1.46839i 0.883191 + 0.469013i \(0.155390\pi\)
−0.0354186 + 0.999373i \(0.511276\pi\)
\(354\) 0 0
\(355\) −14.1962 + 24.5885i −0.753454 + 1.30502i
\(356\) −2.76795 + 4.79423i −0.146701 + 0.254094i
\(357\) 0 0
\(358\) −5.36603 9.29423i −0.283603 0.491215i
\(359\) −5.07180 −0.267679 −0.133840 0.991003i \(-0.542731\pi\)
−0.133840 + 0.991003i \(0.542731\pi\)
\(360\) 0 0
\(361\) −1.39230 −0.0732792
\(362\) −10.1962 17.6603i −0.535898 0.928202i
\(363\) 0 0
\(364\) 0.500000 0.866025i 0.0262071 0.0453921i
\(365\) 1.03590 1.79423i 0.0542214 0.0939142i
\(366\) 0 0
\(367\) −13.2942 23.0263i −0.693953 1.20196i −0.970532 0.240971i \(-0.922534\pi\)
0.276579 0.960991i \(-0.410799\pi\)
\(368\) −4.73205 −0.246675
\(369\) 0 0
\(370\) 12.4641 0.647978
\(371\) 1.26795 + 2.19615i 0.0658286 + 0.114019i
\(372\) 0 0
\(373\) −10.0000 + 17.3205i −0.517780 + 0.896822i 0.482006 + 0.876168i \(0.339908\pi\)
−0.999787 + 0.0206542i \(0.993425\pi\)
\(374\) −0.294229 + 0.509619i −0.0152142 + 0.0263518i
\(375\) 0 0
\(376\) 4.09808 + 7.09808i 0.211342 + 0.366055i
\(377\) −0.464102 −0.0239024
\(378\) 0 0
\(379\) 14.5885 0.749359 0.374679 0.927154i \(-0.377753\pi\)
0.374679 + 0.927154i \(0.377753\pi\)
\(380\) 3.63397 + 6.29423i 0.186419 + 0.322887i
\(381\) 0 0
\(382\) 3.29423 5.70577i 0.168547 0.291933i
\(383\) −18.9282 + 32.7846i −0.967186 + 1.67522i −0.263562 + 0.964642i \(0.584898\pi\)
−0.703624 + 0.710573i \(0.748436\pi\)
\(384\) 0 0
\(385\) −1.09808 1.90192i −0.0559631 0.0969310i
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) −16.0000 −0.812277
\(389\) 9.12436 + 15.8038i 0.462623 + 0.801287i 0.999091 0.0426341i \(-0.0135750\pi\)
−0.536468 + 0.843921i \(0.680242\pi\)
\(390\) 0 0
\(391\) 1.09808 1.90192i 0.0555321 0.0961844i
\(392\) 0.500000 0.866025i 0.0252538 0.0437409i
\(393\) 0 0
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) −7.26795 −0.365690
\(396\) 0 0
\(397\) −8.60770 −0.432008 −0.216004 0.976392i \(-0.569302\pi\)
−0.216004 + 0.976392i \(0.569302\pi\)
\(398\) −5.29423 9.16987i −0.265376 0.459644i
\(399\) 0 0
\(400\) 1.00000 1.73205i 0.0500000 0.0866025i
\(401\) 12.8660 22.2846i 0.642499 1.11284i −0.342375 0.939564i \(-0.611231\pi\)
0.984873 0.173277i \(-0.0554355\pi\)
\(402\) 0 0
\(403\) −3.09808 5.36603i −0.154326 0.267301i
\(404\) 0.928203 0.0461798
\(405\) 0 0
\(406\) −0.464102 −0.0230330
\(407\) 4.56218 + 7.90192i 0.226139 + 0.391684i
\(408\) 0 0
\(409\) 5.40192 9.35641i 0.267108 0.462645i −0.701006 0.713156i \(-0.747265\pi\)
0.968114 + 0.250511i \(0.0805986\pi\)
\(410\) 8.19615 14.1962i 0.404779 0.701098i
\(411\) 0 0
\(412\) −6.19615 10.7321i −0.305263 0.528730i
\(413\) −2.19615 −0.108066
\(414\) 0 0
\(415\) 8.19615 0.402333
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 0 0
\(418\) −2.66025 + 4.60770i −0.130117 + 0.225370i
\(419\) −5.66025 + 9.80385i −0.276522 + 0.478949i −0.970518 0.241029i \(-0.922515\pi\)
0.693996 + 0.719979i \(0.255848\pi\)
\(420\) 0 0
\(421\) −1.40192 2.42820i −0.0683256 0.118343i 0.829839 0.558003i \(-0.188432\pi\)
−0.898164 + 0.439660i \(0.855099\pi\)
\(422\) −22.1962 −1.08049
\(423\) 0 0
\(424\) 2.53590 0.123154
\(425\) 0.464102 + 0.803848i 0.0225122 + 0.0389923i
\(426\) 0 0
\(427\) 5.69615 9.86603i 0.275656 0.477450i
\(428\) 6.92820 12.0000i 0.334887 0.580042i
\(429\) 0 0
\(430\) 7.26795 + 12.5885i 0.350492 + 0.607069i
\(431\) −35.3205 −1.70133 −0.850665 0.525709i \(-0.823800\pi\)
−0.850665 + 0.525709i \(0.823800\pi\)
\(432\) 0 0
\(433\) −0.411543 −0.0197775 −0.00988874 0.999951i \(-0.503148\pi\)
−0.00988874 + 0.999951i \(0.503148\pi\)
\(434\) −3.09808 5.36603i −0.148712 0.257577i
\(435\) 0 0
\(436\) 7.59808 13.1603i 0.363882 0.630262i
\(437\) 9.92820 17.1962i 0.474930 0.822604i
\(438\) 0 0
\(439\) 20.5885 + 35.6603i 0.982633 + 1.70197i 0.652014 + 0.758207i \(0.273924\pi\)
0.330619 + 0.943764i \(0.392742\pi\)
\(440\) −2.19615 −0.104697
\(441\) 0 0
\(442\) 0.464102 0.0220751
\(443\) −4.09808 7.09808i −0.194705 0.337240i 0.752098 0.659051i \(-0.229042\pi\)
−0.946804 + 0.321811i \(0.895708\pi\)
\(444\) 0 0
\(445\) 4.79423 8.30385i 0.227268 0.393640i
\(446\) −4.19615 + 7.26795i −0.198694 + 0.344147i
\(447\) 0 0
\(448\) −0.500000 0.866025i −0.0236228 0.0409159i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 12.0000 0.565058
\(452\) −6.86603 11.8923i −0.322951 0.559367i
\(453\) 0 0
\(454\) 9.46410 16.3923i 0.444172 0.769329i
\(455\) −0.866025 + 1.50000i −0.0405999 + 0.0703211i
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) −19.7846 −0.924474
\(459\) 0 0
\(460\) 8.19615 0.382148
\(461\) 12.4641 + 21.5885i 0.580511 + 1.00547i 0.995419 + 0.0956112i \(0.0304805\pi\)
−0.414908 + 0.909864i \(0.636186\pi\)
\(462\) 0 0
\(463\) −8.09808 + 14.0263i −0.376350 + 0.651856i −0.990528 0.137311i \(-0.956154\pi\)
0.614179 + 0.789167i \(0.289487\pi\)
\(464\) −0.232051 + 0.401924i −0.0107727 + 0.0186588i
\(465\) 0 0
\(466\) −5.13397 8.89230i −0.237827 0.411928i
\(467\) 4.73205 0.218973 0.109487 0.993988i \(-0.465079\pi\)
0.109487 + 0.993988i \(0.465079\pi\)
\(468\) 0 0
\(469\) −6.19615 −0.286112
\(470\) −7.09808 12.2942i −0.327410 0.567090i
\(471\) 0 0
\(472\) −1.09808 + 1.90192i −0.0505431 + 0.0875431i
\(473\) −5.32051 + 9.21539i −0.244637 + 0.423724i
\(474\) 0 0
\(475\) 4.19615 + 7.26795i 0.192533 + 0.333476i
\(476\) 0.464102 0.0212721
\(477\) 0 0
\(478\) −9.12436 −0.417338
\(479\) 6.63397 + 11.4904i 0.303114 + 0.525009i 0.976840 0.213973i \(-0.0686404\pi\)
−0.673726 + 0.738982i \(0.735307\pi\)
\(480\) 0 0
\(481\) 3.59808 6.23205i 0.164058 0.284157i
\(482\) 8.79423 15.2321i 0.400566 0.693801i
\(483\) 0 0
\(484\) 4.69615 + 8.13397i 0.213461 + 0.369726i
\(485\) 27.7128 1.25837
\(486\) 0 0
\(487\) 4.19615 0.190146 0.0950729 0.995470i \(-0.469692\pi\)
0.0950729 + 0.995470i \(0.469692\pi\)
\(488\) −5.69615 9.86603i −0.257853 0.446614i
\(489\) 0 0
\(490\) −0.866025 + 1.50000i −0.0391230 + 0.0677631i
\(491\) −11.6603 + 20.1962i −0.526220 + 0.911440i 0.473313 + 0.880894i \(0.343058\pi\)
−0.999533 + 0.0305455i \(0.990276\pi\)
\(492\) 0 0
\(493\) −0.107695 0.186533i −0.00485035 0.00840105i
\(494\) 4.19615 0.188794
\(495\) 0 0
\(496\) −6.19615 −0.278215
\(497\) 8.19615 + 14.1962i 0.367648 + 0.636784i
\(498\) 0 0
\(499\) 5.29423 9.16987i 0.237002 0.410500i −0.722850 0.691004i \(-0.757168\pi\)
0.959853 + 0.280505i \(0.0905018\pi\)
\(500\) −6.06218 + 10.5000i −0.271109 + 0.469574i
\(501\) 0 0
\(502\) 7.09808 + 12.2942i 0.316803 + 0.548718i
\(503\) −28.9808 −1.29219 −0.646094 0.763258i \(-0.723599\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(504\) 0 0
\(505\) −1.60770 −0.0715415
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) 0 0
\(508\) 2.00000 3.46410i 0.0887357 0.153695i
\(509\) 16.8564 29.1962i 0.747147 1.29410i −0.202038 0.979378i \(-0.564756\pi\)
0.949185 0.314719i \(-0.101910\pi\)
\(510\) 0 0
\(511\) −0.598076 1.03590i −0.0264573 0.0458254i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −14.0718 −0.620680
\(515\) 10.7321 + 18.5885i 0.472911 + 0.819105i
\(516\) 0 0
\(517\) 5.19615 9.00000i 0.228527 0.395820i
\(518\) 3.59808 6.23205i 0.158090 0.273821i
\(519\) 0 0
\(520\) 0.866025 + 1.50000i 0.0379777 + 0.0657794i
\(521\) −16.1436 −0.707264 −0.353632 0.935385i \(-0.615053\pi\)
−0.353632 + 0.935385i \(0.615053\pi\)
\(522\) 0 0
\(523\) 36.3923 1.59132 0.795662 0.605741i \(-0.207123\pi\)
0.795662 + 0.605741i \(0.207123\pi\)
\(524\) −4.73205 8.19615i −0.206721 0.358051i
\(525\) 0 0
\(526\) 4.56218 7.90192i 0.198920 0.344540i
\(527\) 1.43782 2.49038i 0.0626325 0.108483i
\(528\) 0 0
\(529\) 0.303848 + 0.526279i 0.0132108 + 0.0228817i
\(530\) −4.39230 −0.190790
\(531\) 0 0
\(532\) 4.19615 0.181926
\(533\) −4.73205 8.19615i −0.204968 0.355015i
\(534\) 0 0
\(535\) −12.0000 + 20.7846i −0.518805 + 0.898597i
\(536\) −3.09808 + 5.36603i −0.133817 + 0.231777i
\(537\) 0 0
\(538\) 14.7224 + 25.5000i 0.634729 + 1.09938i
\(539\) −1.26795 −0.0546144
\(540\) 0 0
\(541\) −0.411543 −0.0176936 −0.00884680 0.999961i \(-0.502816\pi\)
−0.00884680 + 0.999961i \(0.502816\pi\)
\(542\) 8.90192 + 15.4186i 0.382370 + 0.662285i
\(543\) 0 0
\(544\) 0.232051 0.401924i 0.00994910 0.0172323i
\(545\) −13.1603 + 22.7942i −0.563723 + 0.976397i
\(546\) 0 0
\(547\) 15.0981 + 26.1506i 0.645547 + 1.11812i 0.984175 + 0.177200i \(0.0567039\pi\)
−0.338628 + 0.940920i \(0.609963\pi\)
\(548\) −14.6603 −0.626255
\(549\) 0 0
\(550\) −2.53590 −0.108131
\(551\) −0.973721 1.68653i −0.0414819 0.0718487i
\(552\) 0 0
\(553\) −2.09808 + 3.63397i −0.0892193 + 0.154532i
\(554\) 11.3923 19.7321i 0.484013 0.838335i
\(555\) 0 0
\(556\) 3.90192 + 6.75833i 0.165478 + 0.286617i
\(557\) −13.1436 −0.556912 −0.278456 0.960449i \(-0.589823\pi\)
−0.278456 + 0.960449i \(0.589823\pi\)
\(558\) 0 0
\(559\) 8.39230 0.354957
\(560\) 0.866025 + 1.50000i 0.0365963 + 0.0633866i
\(561\) 0 0
\(562\) 5.13397 8.89230i 0.216564 0.375099i
\(563\) 12.0000 20.7846i 0.505740 0.875967i −0.494238 0.869326i \(-0.664553\pi\)
0.999978 0.00664037i \(-0.00211371\pi\)
\(564\) 0 0
\(565\) 11.8923 + 20.5981i 0.500313 + 0.866568i
\(566\) −24.3923 −1.02529
\(567\) 0 0
\(568\) 16.3923 0.687806
\(569\) 21.9904 + 38.0885i 0.921885 + 1.59675i 0.796496 + 0.604643i \(0.206684\pi\)
0.125388 + 0.992108i \(0.459982\pi\)
\(570\) 0 0
\(571\) 15.0981 26.1506i 0.631835 1.09437i −0.355342 0.934737i \(-0.615635\pi\)
0.987176 0.159633i \(-0.0510312\pi\)
\(572\) −0.633975 + 1.09808i −0.0265078 + 0.0459129i
\(573\) 0 0
\(574\) −4.73205 8.19615i −0.197512 0.342101i
\(575\) 9.46410 0.394680
\(576\) 0 0
\(577\) 20.8038 0.866076 0.433038 0.901376i \(-0.357442\pi\)
0.433038 + 0.901376i \(0.357442\pi\)
\(578\) −8.39230 14.5359i −0.349074 0.604614i
\(579\) 0 0
\(580\) 0.401924 0.696152i 0.0166890 0.0289062i
\(581\) 2.36603 4.09808i 0.0981593 0.170017i
\(582\) 0 0
\(583\) −1.60770 2.78461i −0.0665839 0.115327i
\(584\) −1.19615 −0.0494971
\(585\) 0 0
\(586\) −9.33975 −0.385821
\(587\) −3.63397 6.29423i −0.149990 0.259791i 0.781233 0.624239i \(-0.214591\pi\)
−0.931224 + 0.364448i \(0.881258\pi\)
\(588\) 0 0
\(589\) 13.0000 22.5167i 0.535656 0.927783i
\(590\) 1.90192 3.29423i 0.0783010 0.135621i
\(591\) 0 0
\(592\) −3.59808 6.23205i −0.147880 0.256136i
\(593\) 13.1436 0.539743 0.269871 0.962896i \(-0.413019\pi\)
0.269871 + 0.962896i \(0.413019\pi\)
\(594\) 0 0
\(595\) −0.803848 −0.0329545
\(596\) 4.96410 + 8.59808i 0.203338 + 0.352191i
\(597\) 0 0
\(598\) 2.36603 4.09808i 0.0967540 0.167583i
\(599\) −7.09808 + 12.2942i −0.290020 + 0.502329i −0.973814 0.227346i \(-0.926995\pi\)
0.683794 + 0.729675i \(0.260328\pi\)
\(600\) 0 0
\(601\) −0.598076 1.03590i −0.0243960 0.0422552i 0.853570 0.520979i \(-0.174433\pi\)
−0.877966 + 0.478724i \(0.841100\pi\)
\(602\) 8.39230 0.342045
\(603\) 0 0
\(604\) 8.58846 0.349459
\(605\) −8.13397 14.0885i −0.330693 0.572777i
\(606\) 0 0
\(607\) −1.29423 + 2.24167i −0.0525311 + 0.0909866i −0.891095 0.453816i \(-0.850062\pi\)
0.838564 + 0.544803i \(0.183396\pi\)
\(608\) 2.09808 3.63397i 0.0850882 0.147377i
\(609\) 0 0
\(610\) 9.86603 + 17.0885i 0.399464 + 0.691891i
\(611\) −8.19615 −0.331581
\(612\) 0 0
\(613\) 34.7846 1.40494 0.702469 0.711715i \(-0.252081\pi\)
0.702469 + 0.711715i \(0.252081\pi\)
\(614\) 4.00000 + 6.92820i 0.161427 + 0.279600i
\(615\) 0 0
\(616\) −0.633975 + 1.09808i −0.0255436 + 0.0442428i
\(617\) −14.2583 + 24.6962i −0.574019 + 0.994230i 0.422129 + 0.906536i \(0.361283\pi\)
−0.996147 + 0.0876938i \(0.972050\pi\)
\(618\) 0 0
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 10.7321 0.431010
\(621\) 0 0
\(622\) 28.9808 1.16202
\(623\) −2.76795 4.79423i −0.110896 0.192077i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −14.9904 + 25.9641i −0.599136 + 1.03773i
\(627\) 0 0
\(628\) 2.69615 + 4.66987i 0.107588 + 0.186348i
\(629\) 3.33975 0.133164
\(630\) 0 0
\(631\) 8.58846 0.341901 0.170951 0.985280i \(-0.445316\pi\)
0.170951 + 0.985280i \(0.445316\pi\)
\(632\) 2.09808 + 3.63397i 0.0834570 + 0.144552i
\(633\) 0 0
\(634\) −9.69615 + 16.7942i −0.385083 + 0.666984i
\(635\) −3.46410 + 6.00000i −0.137469 + 0.238103i
\(636\) 0 0
\(637\) 0.500000 + 0.866025i 0.0198107 + 0.0343132i
\(638\) 0.588457 0.0232972
\(639\) 0 0
\(640\) 1.73205 0.0684653
\(641\) 13.3301 + 23.0885i 0.526508 + 0.911939i 0.999523 + 0.0308846i \(0.00983245\pi\)
−0.473015 + 0.881055i \(0.656834\pi\)
\(642\) 0 0
\(643\) −14.0981 + 24.4186i −0.555974 + 0.962975i 0.441853 + 0.897087i \(0.354321\pi\)
−0.997827 + 0.0658876i \(0.979012\pi\)
\(644\) 2.36603 4.09808i 0.0932345 0.161487i
\(645\) 0 0
\(646\) 0.973721 + 1.68653i 0.0383105 + 0.0663558i
\(647\) −11.3205 −0.445055 −0.222528 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(648\) 0 0
\(649\) 2.78461 0.109305
\(650\) 1.00000 + 1.73205i 0.0392232 + 0.0679366i
\(651\) 0 0
\(652\) −1.80385 + 3.12436i −0.0706441 + 0.122359i
\(653\) −0.339746 + 0.588457i −0.0132953 + 0.0230281i −0.872597 0.488442i \(-0.837565\pi\)
0.859301 + 0.511470i \(0.170899\pi\)
\(654\) 0 0
\(655\) 8.19615 + 14.1962i 0.320250 + 0.554690i
\(656\) −9.46410 −0.369511
\(657\) 0 0
\(658\) −8.19615 −0.319519
\(659\) 17.6603 + 30.5885i 0.687946 + 1.19156i 0.972501 + 0.232898i \(0.0748207\pi\)
−0.284555 + 0.958660i \(0.591846\pi\)
\(660\) 0 0
\(661\) −6.30385 + 10.9186i −0.245191 + 0.424684i −0.962185 0.272396i \(-0.912184\pi\)
0.716994 + 0.697079i \(0.245517\pi\)
\(662\) 16.5885 28.7321i 0.644729 1.11670i
\(663\) 0 0
\(664\) −2.36603 4.09808i −0.0918196 0.159036i
\(665\) −7.26795 −0.281839
\(666\) 0 0
\(667\) −2.19615 −0.0850354
\(668\) −5.36603 9.29423i −0.207618 0.359605i
\(669\) 0 0
\(670\) 5.36603 9.29423i 0.207308 0.359067i
\(671\) −7.22243 + 12.5096i −0.278819 + 0.482928i
\(672\) 0 0
\(673\) 22.0885 + 38.2583i 0.851447 + 1.47475i 0.879902 + 0.475155i \(0.157608\pi\)
−0.0284546 + 0.999595i \(0.509059\pi\)
\(674\) 11.6077 0.447112
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 1.60770 + 2.78461i 0.0617887 + 0.107021i 0.895265 0.445534i \(-0.146986\pi\)
−0.833476 + 0.552555i \(0.813653\pi\)
\(678\) 0 0
\(679\) 8.00000 13.8564i 0.307012 0.531760i
\(680\) −0.401924 + 0.696152i −0.0154131 + 0.0266962i
\(681\) 0 0
\(682\) 3.92820 + 6.80385i 0.150419 + 0.260533i
\(683\) −15.7128 −0.601234 −0.300617 0.953745i \(-0.597193\pi\)
−0.300617 + 0.953745i \(0.597193\pi\)
\(684\) 0 0
\(685\) 25.3923 0.970190
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) 4.19615 7.26795i 0.159977 0.277088i
\(689\) −1.26795 + 2.19615i −0.0483050 + 0.0836667i
\(690\) 0 0
\(691\) −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i \(-0.851021\pi\)
0.0555386 0.998457i \(-0.482312\pi\)
\(692\) 23.1962 0.881785
\(693\) 0 0
\(694\) −4.39230 −0.166730
\(695\) −6.75833 11.7058i −0.256358 0.444025i
\(696\) 0 0
\(697\) 2.19615 3.80385i 0.0831852 0.144081i
\(698\) −4.19615 + 7.26795i −0.158827 + 0.275096i
\(699\) 0 0
\(700\) 1.00000 + 1.73205i 0.0377964 + 0.0654654i
\(701\) 16.1769 0.610994 0.305497 0.952193i \(-0.401177\pi\)
0.305497 + 0.952193i \(0.401177\pi\)
\(702\) 0 0
\(703\) 30.1962 1.13887
\(704\) 0.633975 + 1.09808i 0.0238938 + 0.0413853i
\(705\) 0 0
\(706\) −15.9282 + 27.5885i −0.599466 + 1.03831i
\(707\) −0.464102 + 0.803848i −0.0174543 + 0.0302318i
\(708\) 0 0
\(709\) −11.7942 20.4282i −0.442942 0.767197i 0.554965 0.831874i \(-0.312732\pi\)
−0.997906 + 0.0646766i \(0.979398\pi\)
\(710\) −28.3923 −1.06554
\(711\) 0 0
\(712\) −5.53590 −0.207467
\(713\) −14.6603 25.3923i −0.549031 0.950949i
\(714\) 0 0
\(715\) 1.09808 1.90192i 0.0410657 0.0711279i
\(716\) 5.36603 9.29423i 0.200538 0.347342i
\(717\) 0 0
\(718\) −2.53590 4.39230i −0.0946389 0.163919i
\(719\) 11.3205 0.422184 0.211092 0.977466i \(-0.432298\pi\)
0.211092 + 0.977466i \(0.432298\pi\)
\(720\) 0 0
\(721\) 12.3923 0.461514
\(722\) −0.696152 1.20577i −0.0259081 0.0448742i
\(723\) 0 0
\(724\) 10.1962 17.6603i 0.378937 0.656338i
\(725\) 0.464102 0.803848i 0.0172363 0.0298541i
\(726\) 0 0
\(727\) −18.1962 31.5167i −0.674858 1.16889i −0.976510 0.215470i \(-0.930872\pi\)
0.301652 0.953418i \(-0.402462\pi\)
\(728\) 1.00000 0.0370625
\(729\) 0 0
\(730\) 2.07180 0.0766806
\(731\) 1.94744 + 3.37307i 0.0720287 + 0.124757i
\(732\) 0 0
\(733\) −16.5885 + 28.7321i −0.612709 + 1.06124i 0.378073 + 0.925776i \(0.376587\pi\)
−0.990782 + 0.135467i \(0.956747\pi\)
\(734\) 13.2942 23.0263i 0.490699 0.849915i
\(735\) 0 0
\(736\) −2.36603 4.09808i −0.0872129 0.151057i
\(737\) 7.85641 0.289394
\(738\) 0 0
\(739\) −13.8038 −0.507783 −0.253891 0.967233i \(-0.581711\pi\)
−0.253891 + 0.967233i \(0.581711\pi\)
\(740\) 6.23205 + 10.7942i 0.229095 + 0.396804i
\(741\) 0 0
\(742\) −1.26795 + 2.19615i −0.0465479 + 0.0806233i
\(743\) −7.26795 + 12.5885i −0.266635 + 0.461826i −0.967991 0.250986i \(-0.919245\pi\)
0.701356 + 0.712812i \(0.252579\pi\)
\(744\) 0 0
\(745\) −8.59808 14.8923i −0.315009 0.545612i
\(746\) −20.0000 −0.732252
\(747\) 0 0
\(748\) −0.588457 −0.0215161
\(749\) 6.92820 + 12.0000i 0.253151 + 0.438470i
\(750\) 0 0
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) −4.09808 + 7.09808i −0.149441 + 0.258840i
\(753\) 0 0
\(754\) −0.232051 0.401924i −0.00845079 0.0146372i
\(755\) −14.8756 −0.541380
\(756\) 0 0
\(757\) −36.7846 −1.33696 −0.668480 0.743730i \(-0.733055\pi\)
−0.668480 + 0.743730i \(0.733055\pi\)
\(758\) 7.29423 + 12.6340i 0.264938 + 0.458887i
\(759\) 0 0
\(760\) −3.63397 + 6.29423i −0.131818 + 0.228316i
\(761\) 13.1603 22.7942i 0.477059 0.826290i −0.522596 0.852581i \(-0.675036\pi\)
0.999654 + 0.0262906i \(0.00836952\pi\)
\(762\) 0 0
\(763\) 7.59808 + 13.1603i 0.275069 + 0.476433i
\(764\) 6.58846 0.238362
\(765\) 0 0
\(766\) −37.8564 −1.36781
\(767\) −1.09808 1.90192i −0.0396492 0.0686745i
\(768\) 0 0
\(769\) 1.59808 2.76795i 0.0576281 0.0998148i −0.835772 0.549076i \(-0.814980\pi\)
0.893400 + 0.449262i \(0.148313\pi\)
\(770\) 1.09808 1.90192i 0.0395719 0.0685406i
\(771\) 0 0
\(772\) 9.50000 + 16.4545i 0.341912 + 0.592210i
\(773\) 38.6603 1.39051 0.695256 0.718762i \(-0.255291\pi\)
0.695256 + 0.718762i \(0.255291\pi\)
\(774\) 0 0
\(775\) 12.3923 0.445145
\(776\) −8.00000 13.8564i −0.287183 0.497416i
\(777\) 0 0
\(778\) −9.12436 + 15.8038i −0.327124 + 0.566595i
\(779\) 19.8564 34.3923i 0.711430 1.23223i
\(780\) 0 0
\(781\) −10.3923 18.0000i −0.371866 0.644091i
\(782\) 2.19615 0.0785343
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) −4.66987 8.08846i −0.166675 0.288689i
\(786\) 0 0
\(787\) 8.58846 14.8756i 0.306145 0.530259i −0.671370 0.741122i \(-0.734294\pi\)
0.977516 + 0.210863i \(0.0676273\pi\)
\(788\) −7.50000 + 12.9904i −0.267176 + 0.462763i
\(789\) 0 0
\(790\) −3.63397 6.29423i −0.129291 0.223939i
\(791\) 13.7321