Properties

Label 1134.2.f.t.379.1
Level $1134$
Weight $2$
Character 1134.379
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 379.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.t.757.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -1.73205 q^{10} +(2.36603 - 4.09808i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.46410 q^{17} -6.19615 q^{19} +(-0.866025 + 1.50000i) q^{20} +(-2.36603 - 4.09808i) q^{22} +(0.633975 + 1.09808i) q^{23} +(1.00000 - 1.73205i) q^{25} +1.00000 q^{26} +1.00000 q^{28} +(3.23205 - 5.59808i) q^{29} +(-2.09808 - 3.63397i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.23205 + 5.59808i) q^{34} +1.73205 q^{35} -3.19615 q^{37} +(-3.09808 + 5.36603i) q^{38} +(0.866025 + 1.50000i) q^{40} +(1.26795 + 2.19615i) q^{41} +(-6.19615 + 10.7321i) q^{43} -4.73205 q^{44} +1.26795 q^{46} +(1.09808 - 1.90192i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-1.00000 - 1.73205i) q^{50} +(0.500000 - 0.866025i) q^{52} -9.46410 q^{53} -8.19615 q^{55} +(0.500000 - 0.866025i) q^{56} +(-3.23205 - 5.59808i) q^{58} +(-4.09808 - 7.09808i) q^{59} +(-4.69615 + 8.13397i) q^{61} -4.19615 q^{62} +1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +(-2.09808 - 3.63397i) q^{67} +(3.23205 + 5.59808i) q^{68} +(0.866025 - 1.50000i) q^{70} +4.39230 q^{71} -9.19615 q^{73} +(-1.59808 + 2.76795i) q^{74} +(3.09808 + 5.36603i) q^{76} +(2.36603 + 4.09808i) q^{77} +(3.09808 - 5.36603i) q^{79} +1.73205 q^{80} +2.53590 q^{82} +(0.633975 - 1.09808i) q^{83} +(5.59808 + 9.69615i) q^{85} +(6.19615 + 10.7321i) q^{86} +(-2.36603 + 4.09808i) q^{88} +12.4641 q^{89} -1.00000 q^{91} +(0.633975 - 1.09808i) q^{92} +(-1.09808 - 1.90192i) q^{94} +(5.36603 + 9.29423i) q^{95} +(8.00000 - 13.8564i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 2q^{7} - 4q^{8} + 6q^{11} + 2q^{13} + 2q^{14} - 2q^{16} - 12q^{17} - 4q^{19} - 6q^{22} + 6q^{23} + 4q^{25} + 4q^{26} + 4q^{28} + 6q^{29} + 2q^{31} + 2q^{32} - 6q^{34} + 8q^{37} - 2q^{38} + 12q^{41} - 4q^{43} - 12q^{44} + 12q^{46} - 6q^{47} - 2q^{49} - 4q^{50} + 2q^{52} - 24q^{53} - 12q^{55} + 2q^{56} - 6q^{58} - 6q^{59} + 2q^{61} + 4q^{62} + 4q^{64} + 2q^{67} + 6q^{68} - 24q^{71} - 16q^{73} + 4q^{74} + 2q^{76} + 6q^{77} + 2q^{79} + 24q^{82} + 6q^{83} + 12q^{85} + 4q^{86} - 6q^{88} + 36q^{89} - 4q^{91} + 6q^{92} + 6q^{94} + 18q^{95} + 32q^{97} - 4q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.293258\pi\)
−0.992085 + 0.125567i \(0.959925\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.73205 −0.547723
\(11\) 2.36603 4.09808i 0.713384 1.23562i −0.250196 0.968195i \(-0.580495\pi\)
0.963580 0.267421i \(-0.0861715\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −6.46410 −1.56777 −0.783887 0.620903i \(-0.786766\pi\)
−0.783887 + 0.620903i \(0.786766\pi\)
\(18\) 0 0
\(19\) −6.19615 −1.42149 −0.710747 0.703447i \(-0.751643\pi\)
−0.710747 + 0.703447i \(0.751643\pi\)
\(20\) −0.866025 + 1.50000i −0.193649 + 0.335410i
\(21\) 0 0
\(22\) −2.36603 4.09808i −0.504438 0.873713i
\(23\) 0.633975 + 1.09808i 0.132193 + 0.228965i 0.924522 0.381130i \(-0.124465\pi\)
−0.792329 + 0.610094i \(0.791132\pi\)
\(24\) 0 0
\(25\) 1.00000 1.73205i 0.200000 0.346410i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 3.23205 5.59808i 0.600177 1.03954i −0.392617 0.919702i \(-0.628430\pi\)
0.992794 0.119835i \(-0.0382364\pi\)
\(30\) 0 0
\(31\) −2.09808 3.63397i −0.376826 0.652681i 0.613773 0.789483i \(-0.289651\pi\)
−0.990598 + 0.136802i \(0.956318\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.23205 + 5.59808i −0.554292 + 0.960062i
\(35\) 1.73205 0.292770
\(36\) 0 0
\(37\) −3.19615 −0.525444 −0.262722 0.964872i \(-0.584620\pi\)
−0.262722 + 0.964872i \(0.584620\pi\)
\(38\) −3.09808 + 5.36603i −0.502574 + 0.870484i
\(39\) 0 0
\(40\) 0.866025 + 1.50000i 0.136931 + 0.237171i
\(41\) 1.26795 + 2.19615i 0.198020 + 0.342981i 0.947886 0.318608i \(-0.103215\pi\)
−0.749866 + 0.661590i \(0.769882\pi\)
\(42\) 0 0
\(43\) −6.19615 + 10.7321i −0.944904 + 1.63662i −0.188962 + 0.981984i \(0.560512\pi\)
−0.755943 + 0.654638i \(0.772821\pi\)
\(44\) −4.73205 −0.713384
\(45\) 0 0
\(46\) 1.26795 0.186949
\(47\) 1.09808 1.90192i 0.160171 0.277424i −0.774759 0.632257i \(-0.782129\pi\)
0.934930 + 0.354833i \(0.115462\pi\)
\(48\) 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
\(53\) −9.46410 −1.29999 −0.649997 0.759937i \(-0.725230\pi\)
−0.649997 + 0.759937i \(0.725230\pi\)
\(54\) 0 0
\(55\) −8.19615 −1.10517
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 0 0
\(58\) −3.23205 5.59808i −0.424389 0.735063i
\(59\) −4.09808 7.09808i −0.533524 0.924091i −0.999233 0.0391530i \(-0.987534\pi\)
0.465709 0.884938i \(-0.345799\pi\)
\(60\) 0 0
\(61\) −4.69615 + 8.13397i −0.601281 + 1.04145i 0.391347 + 0.920243i \(0.372009\pi\)
−0.992627 + 0.121205i \(0.961324\pi\)
\(62\) −4.19615 −0.532912
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.866025 1.50000i 0.107417 0.186052i
\(66\) 0 0
\(67\) −2.09808 3.63397i −0.256321 0.443961i 0.708933 0.705276i \(-0.249177\pi\)
−0.965253 + 0.261316i \(0.915844\pi\)
\(68\) 3.23205 + 5.59808i 0.391944 + 0.678866i
\(69\) 0 0
\(70\) 0.866025 1.50000i 0.103510 0.179284i
\(71\) 4.39230 0.521271 0.260635 0.965437i \(-0.416068\pi\)
0.260635 + 0.965437i \(0.416068\pi\)
\(72\) 0 0
\(73\) −9.19615 −1.07633 −0.538164 0.842840i \(-0.680882\pi\)
−0.538164 + 0.842840i \(0.680882\pi\)
\(74\) −1.59808 + 2.76795i −0.185773 + 0.321768i
\(75\) 0 0
\(76\) 3.09808 + 5.36603i 0.355374 + 0.615525i
\(77\) 2.36603 + 4.09808i 0.269634 + 0.467019i
\(78\) 0 0
\(79\) 3.09808 5.36603i 0.348561 0.603725i −0.637433 0.770506i \(-0.720004\pi\)
0.985994 + 0.166781i \(0.0533372\pi\)
\(80\) 1.73205 0.193649
\(81\) 0 0
\(82\) 2.53590 0.280043
\(83\) 0.633975 1.09808i 0.0695878 0.120530i −0.829132 0.559053i \(-0.811165\pi\)
0.898720 + 0.438523i \(0.144498\pi\)
\(84\) 0 0
\(85\) 5.59808 + 9.69615i 0.607197 + 1.05170i
\(86\) 6.19615 + 10.7321i 0.668148 + 1.15727i
\(87\) 0 0
\(88\) −2.36603 + 4.09808i −0.252219 + 0.436856i
\(89\) 12.4641 1.32119 0.660596 0.750742i \(-0.270304\pi\)
0.660596 + 0.750742i \(0.270304\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0.633975 1.09808i 0.0660964 0.114482i
\(93\) 0 0
\(94\) −1.09808 1.90192i −0.113258 0.196168i
\(95\) 5.36603 + 9.29423i 0.550543 + 0.953568i
\(96\) 0 0
\(97\) 8.00000 13.8564i 0.812277 1.40690i −0.0989899 0.995088i \(-0.531561\pi\)
0.911267 0.411816i \(-0.135106\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) 6.46410 11.1962i 0.643202 1.11406i −0.341511 0.939878i \(-0.610939\pi\)
0.984714 0.174181i \(-0.0557278\pi\)
\(102\) 0 0
\(103\) 4.19615 + 7.26795i 0.413459 + 0.716132i 0.995265 0.0971952i \(-0.0309871\pi\)
−0.581806 + 0.813327i \(0.697654\pi\)
\(104\) −0.500000 0.866025i −0.0490290 0.0849208i
\(105\) 0 0
\(106\) −4.73205 + 8.19615i −0.459617 + 0.796081i
\(107\) 13.8564 1.33955 0.669775 0.742564i \(-0.266391\pi\)
0.669775 + 0.742564i \(0.266391\pi\)
\(108\) 0 0
\(109\) −4.80385 −0.460125 −0.230063 0.973176i \(-0.573893\pi\)
−0.230063 + 0.973176i \(0.573893\pi\)
\(110\) −4.09808 + 7.09808i −0.390736 + 0.676775i
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −5.13397 8.89230i −0.482964 0.836518i 0.516845 0.856079i \(-0.327106\pi\)
−0.999809 + 0.0195613i \(0.993773\pi\)
\(114\) 0 0
\(115\) 1.09808 1.90192i 0.102396 0.177355i
\(116\) −6.46410 −0.600177
\(117\) 0 0
\(118\) −8.19615 −0.754517
\(119\) 3.23205 5.59808i 0.296282 0.513175i
\(120\) 0 0
\(121\) −5.69615 9.86603i −0.517832 0.896911i
\(122\) 4.69615 + 8.13397i 0.425170 + 0.736415i
\(123\) 0 0
\(124\) −2.09808 + 3.63397i −0.188413 + 0.326341i
\(125\) −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
\(131\) −1.26795 2.19615i −0.110781 0.191879i 0.805304 0.592862i \(-0.202002\pi\)
−0.916085 + 0.400983i \(0.868669\pi\)
\(132\) 0 0
\(133\) 3.09808 5.36603i 0.268637 0.465293i
\(134\) −4.19615 −0.362492
\(135\) 0 0
\(136\) 6.46410 0.554292
\(137\) −1.33013 + 2.30385i −0.113640 + 0.196831i −0.917235 0.398345i \(-0.869585\pi\)
0.803595 + 0.595176i \(0.202918\pi\)
\(138\) 0 0
\(139\) 9.09808 + 15.7583i 0.771689 + 1.33660i 0.936637 + 0.350302i \(0.113921\pi\)
−0.164948 + 0.986302i \(0.552746\pi\)
\(140\) −0.866025 1.50000i −0.0731925 0.126773i
\(141\) 0 0
\(142\) 2.19615 3.80385i 0.184297 0.319212i
\(143\) 4.73205 0.395714
\(144\) 0 0
\(145\) −11.1962 −0.929790
\(146\) −4.59808 + 7.96410i −0.380539 + 0.659114i
\(147\) 0 0
\(148\) 1.59808 + 2.76795i 0.131361 + 0.227524i
\(149\) −1.96410 3.40192i −0.160905 0.278696i 0.774288 0.632833i \(-0.218108\pi\)
−0.935194 + 0.354137i \(0.884775\pi\)
\(150\) 0 0
\(151\) 11.2942 19.5622i 0.919111 1.59195i 0.118343 0.992973i \(-0.462242\pi\)
0.800768 0.598975i \(-0.204425\pi\)
\(152\) 6.19615 0.502574
\(153\) 0 0
\(154\) 4.73205 0.381320
\(155\) −3.63397 + 6.29423i −0.291888 + 0.505565i
\(156\) 0 0
\(157\) −7.69615 13.3301i −0.614220 1.06386i −0.990521 0.137362i \(-0.956137\pi\)
0.376301 0.926497i \(-0.377196\pi\)
\(158\) −3.09808 5.36603i −0.246470 0.426898i
\(159\) 0 0
\(160\) 0.866025 1.50000i 0.0684653 0.118585i
\(161\) −1.26795 −0.0999284
\(162\) 0 0
\(163\) 24.3923 1.91055 0.955276 0.295714i \(-0.0955577\pi\)
0.955276 + 0.295714i \(0.0955577\pi\)
\(164\) 1.26795 2.19615i 0.0990102 0.171491i
\(165\) 0 0
\(166\) −0.633975 1.09808i −0.0492060 0.0852272i
\(167\) −3.63397 6.29423i −0.281205 0.487062i 0.690477 0.723355i \(-0.257401\pi\)
−0.971682 + 0.236293i \(0.924068\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 11.1962 0.858706
\(171\) 0 0
\(172\) 12.3923 0.944904
\(173\) −6.40192 + 11.0885i −0.486729 + 0.843040i −0.999884 0.0152565i \(-0.995144\pi\)
0.513154 + 0.858296i \(0.328477\pi\)
\(174\) 0 0
\(175\) 1.00000 + 1.73205i 0.0755929 + 0.130931i
\(176\) 2.36603 + 4.09808i 0.178346 + 0.308904i
\(177\) 0 0
\(178\) 6.23205 10.7942i 0.467112 0.809062i
\(179\) −7.26795 −0.543232 −0.271616 0.962406i \(-0.587558\pi\)
−0.271616 + 0.962406i \(0.587558\pi\)
\(180\) 0 0
\(181\) 0.392305 0.0291598 0.0145799 0.999894i \(-0.495359\pi\)
0.0145799 + 0.999894i \(0.495359\pi\)
\(182\) −0.500000 + 0.866025i −0.0370625 + 0.0641941i
\(183\) 0 0
\(184\) −0.633975 1.09808i −0.0467372 0.0809513i
\(185\) 2.76795 + 4.79423i 0.203504 + 0.352479i
\(186\) 0 0
\(187\) −15.2942 + 26.4904i −1.11842 + 1.93717i
\(188\) −2.19615 −0.160171
\(189\) 0 0
\(190\) 10.7321 0.778585
\(191\) 12.2942 21.2942i 0.889579 1.54080i 0.0492056 0.998789i \(-0.484331\pi\)
0.840374 0.542008i \(-0.182336\pi\)
\(192\) 0 0
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) −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
\(199\) 20.5885 1.45948 0.729739 0.683726i \(-0.239642\pi\)
0.729739 + 0.683726i \(0.239642\pi\)
\(200\) −1.00000 + 1.73205i −0.0707107 + 0.122474i
\(201\) 0 0
\(202\) −6.46410 11.1962i −0.454813 0.787759i
\(203\) 3.23205 + 5.59808i 0.226845 + 0.392908i
\(204\) 0 0
\(205\) 2.19615 3.80385i 0.153386 0.265672i
\(206\) 8.39230 0.584720
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) −14.6603 + 25.3923i −1.01407 + 1.75642i
\(210\) 0 0
\(211\) −5.90192 10.2224i −0.406305 0.703741i 0.588167 0.808739i \(-0.299850\pi\)
−0.994472 + 0.104998i \(0.966516\pi\)
\(212\) 4.73205 + 8.19615i 0.324999 + 0.562914i
\(213\) 0 0
\(214\) 6.92820 12.0000i 0.473602 0.820303i
\(215\) 21.4641 1.46384
\(216\) 0 0
\(217\) 4.19615 0.284853
\(218\) −2.40192 + 4.16025i −0.162679 + 0.281768i
\(219\) 0 0
\(220\) 4.09808 + 7.09808i 0.276292 + 0.478552i
\(221\) −3.23205 5.59808i −0.217411 0.376567i
\(222\) 0 0
\(223\) −6.19615 + 10.7321i −0.414925 + 0.718671i −0.995421 0.0955922i \(-0.969526\pi\)
0.580496 + 0.814263i \(0.302859\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −10.2679 −0.683014
\(227\) −2.53590 + 4.39230i −0.168313 + 0.291528i −0.937827 0.347103i \(-0.887165\pi\)
0.769514 + 0.638631i \(0.220499\pi\)
\(228\) 0 0
\(229\) 10.8923 + 18.8660i 0.719784 + 1.24670i 0.961085 + 0.276252i \(0.0890924\pi\)
−0.241302 + 0.970450i \(0.577574\pi\)
\(230\) −1.09808 1.90192i −0.0724050 0.125409i
\(231\) 0 0
\(232\) −3.23205 + 5.59808i −0.212195 + 0.367532i
\(233\) −13.7321 −0.899617 −0.449808 0.893125i \(-0.648508\pi\)
−0.449808 + 0.893125i \(0.648508\pi\)
\(234\) 0 0
\(235\) −3.80385 −0.248136
\(236\) −4.09808 + 7.09808i −0.266762 + 0.462045i
\(237\) 0 0
\(238\) −3.23205 5.59808i −0.209503 0.362869i
\(239\) 7.56218 + 13.0981i 0.489157 + 0.847244i 0.999922 0.0124759i \(-0.00397131\pi\)
−0.510766 + 0.859720i \(0.670638\pi\)
\(240\) 0 0
\(241\) 6.79423 11.7679i 0.437655 0.758040i −0.559853 0.828592i \(-0.689143\pi\)
0.997508 + 0.0705514i \(0.0224759\pi\)
\(242\) −11.3923 −0.732325
\(243\) 0 0
\(244\) 9.39230 0.601281
\(245\) −0.866025 + 1.50000i −0.0553283 + 0.0958315i
\(246\) 0 0
\(247\) −3.09808 5.36603i −0.197126 0.341432i
\(248\) 2.09808 + 3.63397i 0.133228 + 0.230758i
\(249\) 0 0
\(250\) −6.06218 + 10.5000i −0.383406 + 0.664078i
\(251\) 3.80385 0.240097 0.120048 0.992768i \(-0.461695\pi\)
0.120048 + 0.992768i \(0.461695\pi\)
\(252\) 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
\(257\) −13.9641 24.1865i −0.871057 1.50871i −0.860905 0.508766i \(-0.830102\pi\)
−0.0101519 0.999948i \(-0.503232\pi\)
\(258\) 0 0
\(259\) 1.59808 2.76795i 0.0992996 0.171992i
\(260\) −1.73205 −0.107417
\(261\) 0 0
\(262\) −2.53590 −0.156668
\(263\) 7.56218 13.0981i 0.466304 0.807662i −0.532955 0.846143i \(-0.678919\pi\)
0.999259 + 0.0384813i \(0.0122520\pi\)
\(264\) 0 0
\(265\) 8.19615 + 14.1962i 0.503486 + 0.872063i
\(266\) −3.09808 5.36603i −0.189955 0.329012i
\(267\) 0 0
\(268\) −2.09808 + 3.63397i −0.128160 + 0.221980i
\(269\) −29.4449 −1.79529 −0.897643 0.440724i \(-0.854722\pi\)
−0.897643 + 0.440724i \(0.854722\pi\)
\(270\) 0 0
\(271\) 28.1962 1.71279 0.856397 0.516318i \(-0.172698\pi\)
0.856397 + 0.516318i \(0.172698\pi\)
\(272\) 3.23205 5.59808i 0.195972 0.339433i
\(273\) 0 0
\(274\) 1.33013 + 2.30385i 0.0803559 + 0.139181i
\(275\) −4.73205 8.19615i −0.285353 0.494247i
\(276\) 0 0
\(277\) 9.39230 16.2679i 0.564329 0.977446i −0.432783 0.901498i \(-0.642468\pi\)
0.997112 0.0759481i \(-0.0241983\pi\)
\(278\) 18.1962 1.09133
\(279\) 0 0
\(280\) −1.73205 −0.103510
\(281\) −6.86603 + 11.8923i −0.409593 + 0.709435i −0.994844 0.101417i \(-0.967663\pi\)
0.585251 + 0.810852i \(0.300996\pi\)
\(282\) 0 0
\(283\) −1.80385 3.12436i −0.107228 0.185724i 0.807419 0.589979i \(-0.200864\pi\)
−0.914646 + 0.404255i \(0.867531\pi\)
\(284\) −2.19615 3.80385i −0.130318 0.225717i
\(285\) 0 0
\(286\) 2.36603 4.09808i 0.139906 0.242324i
\(287\) −2.53590 −0.149689
\(288\) 0 0
\(289\) 24.7846 1.45792
\(290\) −5.59808 + 9.69615i −0.328730 + 0.569378i
\(291\) 0 0
\(292\) 4.59808 + 7.96410i 0.269082 + 0.466064i
\(293\) −13.3301 23.0885i −0.778754 1.34884i −0.932660 0.360757i \(-0.882519\pi\)
0.153906 0.988086i \(-0.450815\pi\)
\(294\) 0 0
\(295\) −7.09808 + 12.2942i −0.413266 + 0.715798i
\(296\) 3.19615 0.185773
\(297\) 0 0
\(298\) −3.92820 −0.227555
\(299\) −0.633975 + 1.09808i −0.0366637 + 0.0635034i
\(300\) 0 0
\(301\) −6.19615 10.7321i −0.357140 0.618585i
\(302\) −11.2942 19.5622i −0.649910 1.12568i
\(303\) 0 0
\(304\) 3.09808 5.36603i 0.177687 0.307763i
\(305\) 16.2679 0.931500
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 2.36603 4.09808i 0.134817 0.233510i
\(309\) 0 0
\(310\) 3.63397 + 6.29423i 0.206396 + 0.357488i
\(311\) −11.4904 19.9019i −0.651560 1.12853i −0.982744 0.184969i \(-0.940782\pi\)
0.331185 0.943566i \(-0.392552\pi\)
\(312\) 0 0
\(313\) −10.9904 + 19.0359i −0.621213 + 1.07597i 0.368047 + 0.929807i \(0.380027\pi\)
−0.989260 + 0.146165i \(0.953307\pi\)
\(314\) −15.3923 −0.868638
\(315\) 0 0
\(316\) −6.19615 −0.348561
\(317\) −0.696152 + 1.20577i −0.0390998 + 0.0677229i −0.884913 0.465756i \(-0.845782\pi\)
0.845813 + 0.533479i \(0.179116\pi\)
\(318\) 0 0
\(319\) −15.2942 26.4904i −0.856312 1.48318i
\(320\) −0.866025 1.50000i −0.0484123 0.0838525i
\(321\) 0 0
\(322\) −0.633975 + 1.09808i −0.0353300 + 0.0611934i
\(323\) 40.0526 2.22858
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 12.1962 21.1244i 0.675482 1.16997i
\(327\) 0 0
\(328\) −1.26795 2.19615i −0.0700108 0.121262i
\(329\) 1.09808 + 1.90192i 0.0605389 + 0.104856i
\(330\) 0 0
\(331\) 14.5885 25.2679i 0.801854 1.38885i −0.116540 0.993186i \(-0.537180\pi\)
0.918394 0.395666i \(-0.129486\pi\)
\(332\) −1.26795 −0.0695878
\(333\) 0 0
\(334\) −7.26795 −0.397684
\(335\) −3.63397 + 6.29423i −0.198545 + 0.343890i
\(336\) 0 0
\(337\) 16.1962 + 28.0526i 0.882261 + 1.52812i 0.848822 + 0.528679i \(0.177313\pi\)
0.0334391 + 0.999441i \(0.489354\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 0 0
\(340\) 5.59808 9.69615i 0.303598 0.525848i
\(341\) −19.8564 −1.07528
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 6.19615 10.7321i 0.334074 0.578633i
\(345\) 0 0
\(346\) 6.40192 + 11.0885i 0.344170 + 0.596119i
\(347\) 8.19615 + 14.1962i 0.439993 + 0.762089i 0.997688 0.0679560i \(-0.0216478\pi\)
−0.557696 + 0.830045i \(0.688314\pi\)
\(348\) 0 0
\(349\) −6.19615 + 10.7321i −0.331672 + 0.574474i −0.982840 0.184461i \(-0.940946\pi\)
0.651167 + 0.758934i \(0.274280\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 4.73205 0.252219
\(353\) 2.07180 3.58846i 0.110271 0.190994i −0.805609 0.592448i \(-0.798162\pi\)
0.915879 + 0.401454i \(0.131495\pi\)
\(354\) 0 0
\(355\) −3.80385 6.58846i −0.201887 0.349679i
\(356\) −6.23205 10.7942i −0.330298 0.572093i
\(357\) 0 0
\(358\) −3.63397 + 6.29423i −0.192062 + 0.332660i
\(359\) −18.9282 −0.998992 −0.499496 0.866316i \(-0.666482\pi\)
−0.499496 + 0.866316i \(0.666482\pi\)
\(360\) 0 0
\(361\) 19.3923 1.02065
\(362\) 0.196152 0.339746i 0.0103095 0.0178567i
\(363\) 0 0
\(364\) 0.500000 + 0.866025i 0.0262071 + 0.0453921i
\(365\) 7.96410 + 13.7942i 0.416860 + 0.722023i
\(366\) 0 0
\(367\) 2.29423 3.97372i 0.119758 0.207427i −0.799914 0.600115i \(-0.795122\pi\)
0.919672 + 0.392688i \(0.128455\pi\)
\(368\) −1.26795 −0.0660964
\(369\) 0 0
\(370\) 5.53590 0.287798
\(371\) 4.73205 8.19615i 0.245676 0.425523i
\(372\) 0 0
\(373\) −10.0000 17.3205i −0.517780 0.896822i −0.999787 0.0206542i \(-0.993425\pi\)
0.482006 0.876168i \(-0.339908\pi\)
\(374\) 15.2942 + 26.4904i 0.790846 + 1.36978i
\(375\) 0 0
\(376\) −1.09808 + 1.90192i −0.0566290 + 0.0980842i
\(377\) 6.46410 0.332918
\(378\) 0 0
\(379\) −16.5885 −0.852092 −0.426046 0.904702i \(-0.640094\pi\)
−0.426046 + 0.904702i \(0.640094\pi\)
\(380\) 5.36603 9.29423i 0.275271 0.476784i
\(381\) 0 0
\(382\) −12.2942 21.2942i −0.629027 1.08951i
\(383\) −5.07180 8.78461i −0.259157 0.448873i 0.706860 0.707354i \(-0.250111\pi\)
−0.966016 + 0.258481i \(0.916778\pi\)
\(384\) 0 0
\(385\) 4.09808 7.09808i 0.208857 0.361751i
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) −16.0000 −0.812277
\(389\) −15.1244 + 26.1962i −0.766835 + 1.32820i 0.172436 + 0.985021i \(0.444836\pi\)
−0.939271 + 0.343177i \(0.888497\pi\)
\(390\) 0 0
\(391\) −4.09808 7.09808i −0.207249 0.358965i
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) 7.50000 12.9904i 0.377845 0.654446i
\(395\) −10.7321 −0.539988
\(396\) 0 0
\(397\) −29.3923 −1.47516 −0.737579 0.675261i \(-0.764031\pi\)
−0.737579 + 0.675261i \(0.764031\pi\)
\(398\) 10.2942 17.8301i 0.516003 0.893744i
\(399\) 0 0
\(400\) 1.00000 + 1.73205i 0.0500000 + 0.0866025i
\(401\) 11.1340 + 19.2846i 0.556004 + 0.963027i 0.997825 + 0.0659240i \(0.0209995\pi\)
−0.441820 + 0.897103i \(0.645667\pi\)
\(402\) 0 0
\(403\) 2.09808 3.63397i 0.104513 0.181021i
\(404\) −12.9282 −0.643202
\(405\) 0 0
\(406\) 6.46410 0.320808
\(407\) −7.56218 + 13.0981i −0.374843 + 0.649248i
\(408\) 0 0
\(409\) 10.5981 + 18.3564i 0.524041 + 0.907666i 0.999608 + 0.0279865i \(0.00890953\pi\)
−0.475567 + 0.879679i \(0.657757\pi\)
\(410\) −2.19615 3.80385i −0.108460 0.187859i
\(411\) 0 0
\(412\) 4.19615 7.26795i 0.206730 0.358066i
\(413\) 8.19615 0.403306
\(414\) 0 0
\(415\) −2.19615 −0.107805
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) 14.6603 + 25.3923i 0.717056 + 1.24198i
\(419\) 11.6603 + 20.1962i 0.569641 + 0.986647i 0.996601 + 0.0823764i \(0.0262510\pi\)
−0.426961 + 0.904270i \(0.640416\pi\)
\(420\) 0 0
\(421\) −6.59808 + 11.4282i −0.321571 + 0.556977i −0.980812 0.194955i \(-0.937544\pi\)
0.659242 + 0.751931i \(0.270877\pi\)
\(422\) −11.8038 −0.574602
\(423\) 0 0
\(424\) 9.46410 0.459617
\(425\) −6.46410 + 11.1962i −0.313555 + 0.543093i
\(426\) 0 0
\(427\) −4.69615 8.13397i −0.227263 0.393631i
\(428\) −6.92820 12.0000i −0.334887 0.580042i
\(429\) 0 0
\(430\) 10.7321 18.5885i 0.517545 0.896415i
\(431\) −0.679492 −0.0327300 −0.0163650 0.999866i \(-0.505209\pi\)
−0.0163650 + 0.999866i \(0.505209\pi\)
\(432\) 0 0
\(433\) −31.5885 −1.51804 −0.759022 0.651065i \(-0.774323\pi\)
−0.759022 + 0.651065i \(0.774323\pi\)
\(434\) 2.09808 3.63397i 0.100711 0.174436i
\(435\) 0 0
\(436\) 2.40192 + 4.16025i 0.115031 + 0.199240i
\(437\) −3.92820 6.80385i −0.187911 0.325472i
\(438\) 0 0
\(439\) −10.5885 + 18.3397i −0.505359 + 0.875308i 0.494621 + 0.869109i \(0.335307\pi\)
−0.999981 + 0.00619971i \(0.998027\pi\)
\(440\) 8.19615 0.390736
\(441\) 0 0
\(442\) −6.46410 −0.307466
\(443\) 1.09808 1.90192i 0.0521712 0.0903631i −0.838760 0.544501i \(-0.816719\pi\)
0.890932 + 0.454138i \(0.150053\pi\)
\(444\) 0 0
\(445\) −10.7942 18.6962i −0.511696 0.886283i
\(446\) 6.19615 + 10.7321i 0.293396 + 0.508177i
\(447\) 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
\(452\) −5.13397 + 8.89230i −0.241482 + 0.418259i
\(453\) 0 0
\(454\) 2.53590 + 4.39230i 0.119016 + 0.206141i
\(455\) 0.866025 + 1.50000i 0.0405999 + 0.0703211i
\(456\) 0 0
\(457\) 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) 21.7846 1.01793
\(459\) 0 0
\(460\) −2.19615 −0.102396
\(461\) 5.53590 9.58846i 0.257832 0.446579i −0.707829 0.706384i \(-0.750325\pi\)
0.965661 + 0.259805i \(0.0836584\pi\)
\(462\) 0 0
\(463\) −2.90192 5.02628i −0.134864 0.233591i 0.790682 0.612228i \(-0.209726\pi\)
−0.925545 + 0.378637i \(0.876393\pi\)
\(464\) 3.23205 + 5.59808i 0.150044 + 0.259884i
\(465\) 0 0
\(466\) −6.86603 + 11.8923i −0.318062 + 0.550900i
\(467\) 1.26795 0.0586737 0.0293368 0.999570i \(-0.490660\pi\)
0.0293368 + 0.999570i \(0.490660\pi\)
\(468\) 0 0
\(469\) 4.19615 0.193760
\(470\) −1.90192 + 3.29423i −0.0877292 + 0.151951i
\(471\) 0 0
\(472\) 4.09808 + 7.09808i 0.188629 + 0.326715i
\(473\) 29.3205 + 50.7846i 1.34816 + 2.33508i
\(474\) 0 0
\(475\) −6.19615 + 10.7321i −0.284299 + 0.492420i
\(476\) −6.46410 −0.296282
\(477\) 0 0
\(478\) 15.1244 0.691772
\(479\) 8.36603 14.4904i 0.382253 0.662082i −0.609131 0.793070i \(-0.708481\pi\)
0.991384 + 0.130988i \(0.0418148\pi\)
\(480\) 0 0
\(481\) −1.59808 2.76795i −0.0728660 0.126208i
\(482\) −6.79423 11.7679i −0.309469 0.536015i
\(483\) 0 0
\(484\) −5.69615 + 9.86603i −0.258916 + 0.448456i
\(485\) −27.7128 −1.25837
\(486\) 0 0
\(487\) −6.19615 −0.280774 −0.140387 0.990097i \(-0.544835\pi\)
−0.140387 + 0.990097i \(0.544835\pi\)
\(488\) 4.69615 8.13397i 0.212585 0.368208i
\(489\) 0 0
\(490\) 0.866025 + 1.50000i 0.0391230 + 0.0677631i
\(491\) 5.66025 + 9.80385i 0.255444 + 0.442441i 0.965016 0.262191i \(-0.0844451\pi\)
−0.709572 + 0.704633i \(0.751112\pi\)
\(492\) 0 0
\(493\) −20.8923 + 36.1865i −0.940942 + 1.62976i
\(494\) −6.19615 −0.278778
\(495\) 0 0
\(496\) 4.19615 0.188413
\(497\) −2.19615 + 3.80385i −0.0985109 + 0.170626i
\(498\) 0 0
\(499\) −10.2942 17.8301i −0.460833 0.798186i 0.538170 0.842836i \(-0.319116\pi\)
−0.999003 + 0.0446504i \(0.985783\pi\)
\(500\) 6.06218 + 10.5000i 0.271109 + 0.469574i
\(501\) 0 0
\(502\) 1.90192 3.29423i 0.0848870 0.147029i
\(503\) 22.9808 1.02466 0.512331 0.858788i \(-0.328782\pi\)
0.512331 + 0.858788i \(0.328782\pi\)
\(504\) 0 0
\(505\) −22.3923 −0.996444
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) 0 0
\(508\) 2.00000 + 3.46410i 0.0887357 + 0.153695i
\(509\) −10.8564 18.8038i −0.481202 0.833466i 0.518566 0.855038i \(-0.326466\pi\)
−0.999767 + 0.0215720i \(0.993133\pi\)
\(510\) 0 0
\(511\) 4.59808 7.96410i 0.203407 0.352311i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −27.9282 −1.23186
\(515\) 7.26795 12.5885i 0.320264 0.554714i
\(516\) 0 0
\(517\) −5.19615 9.00000i −0.228527 0.395820i
\(518\) −1.59808 2.76795i −0.0702154 0.121617i
\(519\) 0 0
\(520\) −0.866025 + 1.50000i −0.0379777 + 0.0657794i
\(521\) −43.8564 −1.92138 −0.960692 0.277616i \(-0.910456\pi\)
−0.960692 + 0.277616i \(0.910456\pi\)
\(522\) 0 0
\(523\) 15.6077 0.682477 0.341238 0.939977i \(-0.389154\pi\)
0.341238 + 0.939977i \(0.389154\pi\)
\(524\) −1.26795 + 2.19615i −0.0553906 + 0.0959394i
\(525\) 0 0
\(526\) −7.56218 13.0981i −0.329727 0.571103i
\(527\) 13.5622 + 23.4904i 0.590778 + 1.02326i
\(528\) 0 0
\(529\) 10.6962 18.5263i 0.465050 0.805490i
\(530\) 16.3923 0.712036
\(531\) 0 0
\(532\) −6.19615 −0.268637
\(533\) −1.26795 + 2.19615i −0.0549210 + 0.0951259i
\(534\) 0 0
\(535\) −12.0000 20.7846i −0.518805 0.898597i
\(536\) 2.09808 + 3.63397i 0.0906231 + 0.156964i
\(537\) 0 0
\(538\) −14.7224 + 25.5000i −0.634729 + 1.09938i
\(539\) −4.73205 −0.203824
\(540\) 0 0
\(541\) −31.5885 −1.35809 −0.679047 0.734095i \(-0.737607\pi\)
−0.679047 + 0.734095i \(0.737607\pi\)
\(542\) 14.0981 24.4186i 0.605564 1.04887i
\(543\) 0 0
\(544\) −3.23205 5.59808i −0.138573 0.240016i
\(545\) 4.16025 + 7.20577i 0.178206 + 0.308661i
\(546\) 0 0
\(547\) 9.90192 17.1506i 0.423376 0.733308i −0.572892 0.819631i \(-0.694178\pi\)
0.996267 + 0.0863230i \(0.0275117\pi\)
\(548\) 2.66025 0.113640
\(549\) 0 0
\(550\) −9.46410 −0.403551
\(551\) −20.0263 + 34.6865i −0.853148 + 1.47770i
\(552\) 0 0
\(553\) 3.09808 + 5.36603i 0.131744 + 0.228187i
\(554\) −9.39230 16.2679i −0.399041 0.691159i
\(555\) 0 0
\(556\) 9.09808 15.7583i 0.385844 0.668302i
\(557\) −40.8564 −1.73114 −0.865571 0.500787i \(-0.833044\pi\)
−0.865571 + 0.500787i \(0.833044\pi\)
\(558\) 0 0
\(559\) −12.3923 −0.524139
\(560\) −0.866025 + 1.50000i −0.0365963 + 0.0633866i
\(561\) 0 0
\(562\) 6.86603 + 11.8923i 0.289626 + 0.501647i
\(563\) 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i \(0.00211371\pi\)
−0.494238 + 0.869326i \(0.664553\pi\)
\(564\) 0 0
\(565\) −8.89230 + 15.4019i −0.374102 + 0.647964i
\(566\) −3.60770 −0.151643
\(567\) 0 0
\(568\) −4.39230 −0.184297
\(569\) −3.99038 + 6.91154i −0.167285 + 0.289747i −0.937465 0.348081i \(-0.886833\pi\)
0.770179 + 0.637828i \(0.220167\pi\)
\(570\) 0 0
\(571\) 9.90192 + 17.1506i 0.414383 + 0.717732i 0.995363 0.0961855i \(-0.0306642\pi\)
−0.580981 + 0.813917i \(0.697331\pi\)
\(572\) −2.36603 4.09808i −0.0989285 0.171349i
\(573\) 0 0
\(574\) −1.26795 + 2.19615i −0.0529232 + 0.0916656i
\(575\) 2.53590 0.105754
\(576\) 0 0
\(577\) 31.1962 1.29871 0.649356 0.760484i \(-0.275038\pi\)
0.649356 + 0.760484i \(0.275038\pi\)
\(578\) 12.3923 21.4641i 0.515452 0.892789i
\(579\) 0 0
\(580\) 5.59808 + 9.69615i 0.232447 + 0.402611i
\(581\) 0.633975 + 1.09808i 0.0263017 + 0.0455559i
\(582\) 0 0
\(583\) −22.3923 + 38.7846i −0.927395 + 1.60629i
\(584\) 9.19615 0.380539
\(585\) 0 0
\(586\) −26.6603 −1.10132
\(587\) −5.36603 + 9.29423i −0.221480 + 0.383614i −0.955257 0.295776i \(-0.904422\pi\)
0.733778 + 0.679389i \(0.237755\pi\)
\(588\) 0 0
\(589\) 13.0000 + 22.5167i 0.535656 + 0.927783i
\(590\) 7.09808 + 12.2942i 0.292223 + 0.506145i
\(591\) 0 0
\(592\) 1.59808 2.76795i 0.0656805 0.113762i
\(593\) 40.8564 1.67777 0.838886 0.544308i \(-0.183208\pi\)
0.838886 + 0.544308i \(0.183208\pi\)
\(594\) 0 0
\(595\) −11.1962 −0.458997
\(596\) −1.96410 + 3.40192i −0.0804527 + 0.139348i
\(597\) 0 0
\(598\) 0.633975 + 1.09808i 0.0259251 + 0.0449037i
\(599\) −1.90192 3.29423i −0.0777105 0.134599i 0.824551 0.565787i \(-0.191428\pi\)
−0.902262 + 0.431189i \(0.858094\pi\)
\(600\) 0 0
\(601\) 4.59808 7.96410i 0.187559 0.324862i −0.756877 0.653558i \(-0.773276\pi\)
0.944436 + 0.328695i \(0.106609\pi\)
\(602\) −12.3923 −0.505073
\(603\) 0 0
\(604\) −22.5885 −0.919111
\(605\) −9.86603 + 17.0885i −0.401111 + 0.694745i
\(606\) 0 0
\(607\) 14.2942 + 24.7583i 0.580185 + 1.00491i 0.995457 + 0.0952124i \(0.0303530\pi\)
−0.415272 + 0.909697i \(0.636314\pi\)
\(608\) −3.09808 5.36603i −0.125644 0.217621i
\(609\) 0 0
\(610\) 8.13397 14.0885i 0.329335 0.570425i
\(611\) 2.19615 0.0888468
\(612\) 0 0
\(613\) −6.78461 −0.274028 −0.137014 0.990569i \(-0.543751\pi\)
−0.137014 + 0.990569i \(0.543751\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 0 0
\(616\) −2.36603 4.09808i −0.0953299 0.165116i
\(617\) 8.25833 + 14.3038i 0.332468 + 0.575851i 0.982995 0.183632i \(-0.0587854\pi\)
−0.650527 + 0.759483i \(0.725452\pi\)
\(618\) 0 0
\(619\) 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i \(-0.807718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(620\) 7.26795 0.291888
\(621\) 0 0
\(622\) −22.9808 −0.921445
\(623\) −6.23205 + 10.7942i −0.249682 + 0.432462i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 10.9904 + 19.0359i 0.439264 + 0.760828i
\(627\) 0 0
\(628\) −7.69615 + 13.3301i −0.307110 + 0.531930i
\(629\) 20.6603 0.823778
\(630\) 0 0
\(631\) −22.5885 −0.899232 −0.449616 0.893222i \(-0.648439\pi\)
−0.449616 + 0.893222i \(0.648439\pi\)
\(632\) −3.09808 + 5.36603i −0.123235 + 0.213449i
\(633\) 0 0
\(634\) 0.696152 + 1.20577i 0.0276477 + 0.0478873i
\(635\) 3.46410 + 6.00000i 0.137469 + 0.238103i
\(636\) 0 0
\(637\) 0.500000 0.866025i 0.0198107 0.0343132i
\(638\) −30.5885 −1.21101
\(639\) 0 0
\(640\) −1.73205 −0.0684653
\(641\) 4.66987 8.08846i 0.184449 0.319475i −0.758942 0.651158i \(-0.774283\pi\)
0.943391 + 0.331684i \(0.107617\pi\)
\(642\) 0 0
\(643\) −8.90192 15.4186i −0.351058 0.608050i 0.635377 0.772202i \(-0.280845\pi\)
−0.986435 + 0.164152i \(0.947511\pi\)
\(644\) 0.633975 + 1.09808i 0.0249821 + 0.0432703i
\(645\) 0 0
\(646\) 20.0263 34.6865i 0.787923 1.36472i
\(647\) 23.3205 0.916824 0.458412 0.888740i \(-0.348418\pi\)
0.458412 + 0.888740i \(0.348418\pi\)
\(648\) 0 0
\(649\) −38.7846 −1.52243
\(650\) 1.00000 1.73205i 0.0392232 0.0679366i
\(651\) 0 0
\(652\) −12.1962 21.1244i −0.477638 0.827294i
\(653\) −17.6603 30.5885i −0.691099 1.19702i −0.971478 0.237129i \(-0.923793\pi\)
0.280379 0.959889i \(-0.409540\pi\)
\(654\) 0 0
\(655\) −2.19615 + 3.80385i −0.0858108 + 0.148629i
\(656\) −2.53590 −0.0990102
\(657\) 0 0
\(658\) 2.19615 0.0856149
\(659\) 0.339746 0.588457i 0.0132346 0.0229230i −0.859332 0.511418i \(-0.829120\pi\)
0.872567 + 0.488495i \(0.162454\pi\)
\(660\) 0 0
\(661\) −16.6962 28.9186i −0.649405 1.12480i −0.983265 0.182180i \(-0.941685\pi\)
0.333860 0.942623i \(-0.391649\pi\)
\(662\) −14.5885 25.2679i −0.566996 0.982067i
\(663\) 0 0
\(664\) −0.633975 + 1.09808i −0.0246030 + 0.0426136i
\(665\) −10.7321 −0.416171
\(666\) 0 0
\(667\) 8.19615 0.317356
\(668\) −3.63397 + 6.29423i −0.140603 + 0.243531i
\(669\) 0 0
\(670\) 3.63397 + 6.29423i 0.140393 + 0.243167i
\(671\) 22.2224 + 38.4904i 0.857887 + 1.48590i
\(672\) 0 0
\(673\) −9.08846 + 15.7417i −0.350334 + 0.606797i −0.986308 0.164914i \(-0.947265\pi\)
0.635974 + 0.771711i \(0.280599\pi\)
\(674\) 32.3923 1.24770
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 22.3923 38.7846i 0.860606 1.49061i −0.0107386 0.999942i \(-0.503418\pi\)
0.871345 0.490671i \(-0.163248\pi\)
\(678\) 0 0
\(679\) 8.00000 + 13.8564i 0.307012 + 0.531760i
\(680\) −5.59808 9.69615i −0.214676 0.371830i
\(681\) 0 0
\(682\) −9.92820 + 17.1962i −0.380171 + 0.658475i
\(683\) 39.7128 1.51957 0.759784 0.650175i \(-0.225305\pi\)
0.759784 + 0.650175i \(0.225305\pi\)
\(684\) 0 0
\(685\) 4.60770 0.176051
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 0 0
\(688\) −6.19615 10.7321i −0.236226 0.409156i
\(689\) −4.73205 8.19615i −0.180277 0.312249i
\(690\) 0 0
\(691\) −22.0000 + 38.1051i −0.836919 + 1.44959i 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) 12.8038 0.486729
\(693\) 0 0
\(694\) 16.3923 0.622243
\(695\) 15.7583 27.2942i 0.597748 1.03533i
\(696\) 0 0
\(697\) −8.19615 14.1962i −0.310451 0.537718i
\(698\) 6.19615 + 10.7321i 0.234528 + 0.406214i
\(699\) 0 0
\(700\) 1.00000 1.73205i 0.0377964 0.0654654i
\(701\) −46.1769 −1.74408 −0.872039 0.489436i \(-0.837203\pi\)
−0.872039 + 0.489436i \(0.837203\pi\)
\(702\) 0 0
\(703\) 19.8038 0.746916
\(704\) 2.36603 4.09808i 0.0891729 0.154452i
\(705\) 0 0
\(706\) −2.07180 3.58846i −0.0779731 0.135053i
\(707\) 6.46410 + 11.1962i 0.243108 + 0.421075i
\(708\) 0 0
\(709\) 3.79423 6.57180i 0.142495 0.246809i −0.785940 0.618302i \(-0.787821\pi\)
0.928436 + 0.371493i \(0.121154\pi\)
\(710\) −7.60770 −0.285512
\(711\) 0 0
\(712\) −12.4641 −0.467112
\(713\) 2.66025 4.60770i 0.0996273 0.172560i
\(714\) 0 0
\(715\) −4.09808 7.09808i −0.153259 0.265453i
\(716\) 3.63397 + 6.29423i 0.135808 + 0.235226i
\(717\) 0 0
\(718\) −9.46410 + 16.3923i −0.353197 + 0.611755i
\(719\) −23.3205 −0.869708 −0.434854 0.900501i \(-0.643200\pi\)
−0.434854 + 0.900501i \(0.643200\pi\)
\(720\) 0 0
\(721\) −8.39230 −0.312546
\(722\) 9.69615 16.7942i 0.360853 0.625016i
\(723\) 0 0
\(724\) −0.196152 0.339746i −0.00728995 0.0126266i
\(725\) −6.46410 11.1962i −0.240071 0.415815i
\(726\) 0 0
\(727\) −7.80385 + 13.5167i −0.289429 + 0.501305i −0.973673 0.227947i \(-0.926799\pi\)
0.684245 + 0.729252i \(0.260132\pi\)
\(728\) 1.00000 0.0370625
\(729\) 0 0
\(730\) 15.9282 0.589529
\(731\) 40.0526 69.3731i 1.48140 2.56586i
\(732\) 0 0
\(733\) 14.5885 + 25.2679i 0.538837 + 0.933293i 0.998967 + 0.0454415i \(0.0144694\pi\)
−0.460130 + 0.887852i \(0.652197\pi\)
\(734\) −2.29423 3.97372i −0.0846815 0.146673i
\(735\) 0 0
\(736\) −0.633975 + 1.09808i −0.0233686 + 0.0404756i
\(737\) −19.8564 −0.731420
\(738\) 0 0
\(739\) −24.1962 −0.890070 −0.445035 0.895513i \(-0.646809\pi\)
−0.445035 + 0.895513i \(0.646809\pi\)
\(740\) 2.76795 4.79423i 0.101752 0.176239i
\(741\) 0 0
\(742\) −4.73205 8.19615i −0.173719 0.300890i
\(743\) −10.7321 18.5885i −0.393721 0.681944i 0.599216 0.800587i \(-0.295479\pi\)
−0.992937 + 0.118643i \(0.962146\pi\)
\(744\) 0 0
\(745\) −3.40192 + 5.89230i −0.124637 + 0.215877i
\(746\) −20.0000 −0.732252
\(747\) 0 0
\(748\) 30.5885 1.11842
\(749\) −6.92820 + 12.0000i −0.253151 + 0.438470i
\(750\) 0 0
\(751\) 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i \(-0.143415\pi\)
−0.827225 + 0.561870i \(0.810082\pi\)
\(752\) 1.09808 + 1.90192i 0.0400427 + 0.0693560i
\(753\) 0 0
\(754\) 3.23205 5.59808i 0.117704 0.203870i
\(755\) −39.1244 −1.42388
\(756\) 0 0
\(757\) 4.78461 0.173900 0.0869498 0.996213i \(-0.472288\pi\)
0.0869498 + 0.996213i \(0.472288\pi\)
\(758\) −8.29423 + 14.3660i −0.301260 + 0.521798i
\(759\) 0 0
\(760\) −5.36603 9.29423i −0.194646 0.337137i
\(761\) −4.16025 7.20577i −0.150809 0.261209i 0.780716 0.624886i \(-0.214855\pi\)
−0.931525 + 0.363677i \(0.881521\pi\)
\(762\) 0 0
\(763\) 2.40192 4.16025i 0.0869555 0.150611i
\(764\) −24.5885 −0.889579
\(765\) 0 0
\(766\) −10.1436 −0.366503
\(767\) 4.09808 7.09808i 0.147973 0.256297i
\(768\) 0 0
\(769\) −3.59808 6.23205i −0.129750 0.224733i 0.793830 0.608140i \(-0.208084\pi\)
−0.923580 + 0.383407i \(0.874751\pi\)
\(770\) −4.09808 7.09808i −0.147684 0.255797i
\(771\) 0 0
\(772\) 9.50000 16.4545i 0.341912 0.592210i
\(773\) 21.3397 0.767537 0.383769 0.923429i \(-0.374626\pi\)
0.383769 + 0.923429i \(0.374626\pi\)
\(774\) 0 0
\(775\) −8.39230 −0.301460
\(776\) −8.00000 + 13.8564i −0.287183 + 0.497416i
\(777\) 0 0
\(778\) 15.1244 + 26.1962i 0.542234 + 0.939178i
\(779\) −7.85641 13.6077i −0.281485 0.487546i
\(780\) 0 0
\(781\) 10.3923 18.0000i 0.371866 0.644091i
\(782\) −8.19615 −0.293094
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) −13.3301 + 23.0885i −0.475773 + 0.824062i
\(786\) 0 0
\(787\) −22.5885 39.1244i −0.805192 1.39463i −0.916162 0.400809i \(-0.868729\pi\)
0.110970 0.993824i \(-0.464604\pi\)
\(788\) −7.50000 12.9904i −0.267176 0.462763i
\(789\) 0 0
\(790\) −5.36603 + 9.29423i −0.190915 + 0.330674i
\(791\)