Properties

Label 1960.2.q.y.961.3
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.21913473024.16
Defining polynomial: \(x^{8} - 2 x^{7} + 11 x^{6} - 2 x^{5} + 51 x^{4} + 162 x^{2} + 112 x + 196\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.3
Root \(1.09199 + 1.89138i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.y.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.09199 + 1.89138i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.884883 + 1.53266i) q^{9} +O(q^{10})\) \(q+(1.09199 + 1.89138i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.884883 + 1.53266i) q^{9} +(-1.79910 - 3.11613i) q^{11} -5.85838 q^{13} +2.18398 q^{15} +(-3.18060 - 5.50897i) q^{17} +(2.25141 - 3.89956i) q^{19} +(-1.31407 + 2.27604i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.68681 q^{27} +2.05866 q^{29} +(-3.31407 - 5.74014i) q^{31} +(3.92919 - 6.80556i) q^{33} +(2.95852 - 5.12431i) q^{37} +(-6.39729 - 11.0804i) q^{39} -7.22348 q^{41} -5.34880 q^{43} +(0.884883 + 1.53266i) q^{45} +(1.15942 - 2.00818i) q^{47} +(6.94637 - 12.0315i) q^{51} +(2.05389 + 3.55744i) q^{53} -3.59819 q^{55} +9.83408 q^{57} +(-2.53553 - 4.39167i) q^{59} +(-3.68681 + 6.38574i) q^{61} +(-2.92919 + 5.07351i) q^{65} +(-1.69833 - 2.94160i) q^{67} -5.73981 q^{69} +16.7224 q^{71} +(7.35919 + 12.7465i) q^{73} +(1.09199 - 1.89138i) q^{75} +(1.62752 - 2.81895i) q^{79} +(5.58861 + 9.67976i) q^{81} -10.6936 q^{83} -6.36121 q^{85} +(2.24804 + 3.89371i) q^{87} +(5.57701 - 9.65967i) q^{89} +(7.23787 - 12.5364i) q^{93} +(-2.25141 - 3.89956i) q^{95} -17.1896 q^{97} +6.36796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 4q^{5} - 6q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 4q^{5} - 6q^{9} - 2q^{11} - 20q^{13} + 4q^{15} + 6q^{17} + 4q^{23} - 4q^{25} - 28q^{27} - 4q^{29} - 12q^{31} + 18q^{33} - 14q^{39} - 24q^{41} - 16q^{43} + 6q^{45} - 2q^{47} - 2q^{51} + 4q^{53} - 4q^{55} - 16q^{57} + 8q^{59} + 20q^{61} - 10q^{65} + 8q^{67} - 48q^{69} + 8q^{71} + 16q^{73} + 2q^{75} - 22q^{79} + 20q^{81} - 72q^{83} + 12q^{85} - 18q^{87} + 40q^{89} + 32q^{93} - 52q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.09199 + 1.89138i 0.630461 + 1.09199i 0.987458 + 0.157884i \(0.0504673\pi\)
−0.356997 + 0.934105i \(0.616199\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.884883 + 1.53266i −0.294961 + 0.510887i
\(10\) 0 0
\(11\) −1.79910 3.11613i −0.542448 0.939547i −0.998763 0.0497290i \(-0.984164\pi\)
0.456315 0.889818i \(-0.349169\pi\)
\(12\) 0 0
\(13\) −5.85838 −1.62482 −0.812411 0.583085i \(-0.801845\pi\)
−0.812411 + 0.583085i \(0.801845\pi\)
\(14\) 0 0
\(15\) 2.18398 0.563901
\(16\) 0 0
\(17\) −3.18060 5.50897i −0.771410 1.33612i −0.936791 0.349891i \(-0.886219\pi\)
0.165381 0.986230i \(-0.447115\pi\)
\(18\) 0 0
\(19\) 2.25141 3.89956i 0.516510 0.894621i −0.483307 0.875451i \(-0.660564\pi\)
0.999816 0.0191698i \(-0.00610231\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.31407 + 2.27604i −0.274003 + 0.474587i −0.969883 0.243571i \(-0.921681\pi\)
0.695880 + 0.718158i \(0.255015\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 2.68681 0.517076
\(28\) 0 0
\(29\) 2.05866 0.382284 0.191142 0.981562i \(-0.438781\pi\)
0.191142 + 0.981562i \(0.438781\pi\)
\(30\) 0 0
\(31\) −3.31407 5.74014i −0.595225 1.03096i −0.993515 0.113700i \(-0.963730\pi\)
0.398290 0.917259i \(-0.369604\pi\)
\(32\) 0 0
\(33\) 3.92919 6.80556i 0.683984 1.18470i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.95852 5.12431i 0.486378 0.842431i −0.513500 0.858090i \(-0.671651\pi\)
0.999877 + 0.0156589i \(0.00498458\pi\)
\(38\) 0 0
\(39\) −6.39729 11.0804i −1.02439 1.77429i
\(40\) 0 0
\(41\) −7.22348 −1.12812 −0.564059 0.825734i \(-0.690761\pi\)
−0.564059 + 0.825734i \(0.690761\pi\)
\(42\) 0 0
\(43\) −5.34880 −0.815684 −0.407842 0.913052i \(-0.633719\pi\)
−0.407842 + 0.913052i \(0.633719\pi\)
\(44\) 0 0
\(45\) 0.884883 + 1.53266i 0.131911 + 0.228476i
\(46\) 0 0
\(47\) 1.15942 2.00818i 0.169119 0.292923i −0.768991 0.639259i \(-0.779241\pi\)
0.938110 + 0.346336i \(0.112574\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 6.94637 12.0315i 0.972686 1.68474i
\(52\) 0 0
\(53\) 2.05389 + 3.55744i 0.282123 + 0.488651i 0.971907 0.235363i \(-0.0756280\pi\)
−0.689784 + 0.724015i \(0.742295\pi\)
\(54\) 0 0
\(55\) −3.59819 −0.485180
\(56\) 0 0
\(57\) 9.83408 1.30256
\(58\) 0 0
\(59\) −2.53553 4.39167i −0.330098 0.571747i 0.652432 0.757847i \(-0.273749\pi\)
−0.982531 + 0.186100i \(0.940415\pi\)
\(60\) 0 0
\(61\) −3.68681 + 6.38574i −0.472047 + 0.817610i −0.999488 0.0319818i \(-0.989818\pi\)
0.527441 + 0.849591i \(0.323151\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.92919 + 5.07351i −0.363321 + 0.629291i
\(66\) 0 0
\(67\) −1.69833 2.94160i −0.207485 0.359374i 0.743437 0.668806i \(-0.233194\pi\)
−0.950921 + 0.309432i \(0.899861\pi\)
\(68\) 0 0
\(69\) −5.73981 −0.690992
\(70\) 0 0
\(71\) 16.7224 1.98459 0.992293 0.123917i \(-0.0395457\pi\)
0.992293 + 0.123917i \(0.0395457\pi\)
\(72\) 0 0
\(73\) 7.35919 + 12.7465i 0.861328 + 1.49186i 0.870648 + 0.491907i \(0.163700\pi\)
−0.00932043 + 0.999957i \(0.502967\pi\)
\(74\) 0 0
\(75\) 1.09199 1.89138i 0.126092 0.218398i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.62752 2.81895i 0.183111 0.317157i −0.759828 0.650125i \(-0.774717\pi\)
0.942938 + 0.332968i \(0.108050\pi\)
\(80\) 0 0
\(81\) 5.58861 + 9.67976i 0.620957 + 1.07553i
\(82\) 0 0
\(83\) −10.6936 −1.17377 −0.586885 0.809670i \(-0.699646\pi\)
−0.586885 + 0.809670i \(0.699646\pi\)
\(84\) 0 0
\(85\) −6.36121 −0.689970
\(86\) 0 0
\(87\) 2.24804 + 3.89371i 0.241015 + 0.417450i
\(88\) 0 0
\(89\) 5.57701 9.65967i 0.591162 1.02392i −0.402914 0.915238i \(-0.632003\pi\)
0.994076 0.108685i \(-0.0346641\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 7.23787 12.5364i 0.750532 1.29996i
\(94\) 0 0
\(95\) −2.25141 3.89956i −0.230990 0.400087i
\(96\) 0 0
\(97\) −17.1896 −1.74534 −0.872671 0.488308i \(-0.837614\pi\)
−0.872671 + 0.488308i \(0.837614\pi\)
\(98\) 0 0
\(99\) 6.36796 0.640004
\(100\) 0 0
\(101\) 1.72065 + 2.98026i 0.171212 + 0.296547i 0.938844 0.344344i \(-0.111899\pi\)
−0.767632 + 0.640891i \(0.778565\pi\)
\(102\) 0 0
\(103\) −5.98785 + 10.3713i −0.590000 + 1.02191i 0.404231 + 0.914657i \(0.367539\pi\)
−0.994232 + 0.107254i \(0.965794\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.33801 9.24570i 0.516045 0.893815i −0.483782 0.875189i \(-0.660737\pi\)
0.999827 0.0186269i \(-0.00592946\pi\)
\(108\) 0 0
\(109\) 4.16706 + 7.21755i 0.399131 + 0.691316i 0.993619 0.112789i \(-0.0359784\pi\)
−0.594487 + 0.804105i \(0.702645\pi\)
\(110\) 0 0
\(111\) 12.9227 1.22657
\(112\) 0 0
\(113\) −12.1542 −1.14337 −0.571684 0.820474i \(-0.693710\pi\)
−0.571684 + 0.820474i \(0.693710\pi\)
\(114\) 0 0
\(115\) 1.31407 + 2.27604i 0.122538 + 0.212242i
\(116\) 0 0
\(117\) 5.18398 8.97892i 0.479259 0.830101i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.973496 + 1.68614i −0.0884996 + 0.153286i
\(122\) 0 0
\(123\) −7.88797 13.6624i −0.711234 1.23189i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.82453 −0.871786 −0.435893 0.899998i \(-0.643567\pi\)
−0.435893 + 0.899998i \(0.643567\pi\)
\(128\) 0 0
\(129\) −5.84083 10.1166i −0.514257 0.890719i
\(130\) 0 0
\(131\) 2.47687 4.29007i 0.216405 0.374825i −0.737301 0.675564i \(-0.763900\pi\)
0.953706 + 0.300739i \(0.0972334\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.34340 2.32684i 0.115622 0.200263i
\(136\) 0 0
\(137\) 5.65685 + 9.79796i 0.483298 + 0.837096i 0.999816 0.0191800i \(-0.00610555\pi\)
−0.516518 + 0.856276i \(0.672772\pi\)
\(138\) 0 0
\(139\) −8.70311 −0.738188 −0.369094 0.929392i \(-0.620332\pi\)
−0.369094 + 0.929392i \(0.620332\pi\)
\(140\) 0 0
\(141\) 5.06431 0.426492
\(142\) 0 0
\(143\) 10.5398 + 18.2554i 0.881381 + 1.52660i
\(144\) 0 0
\(145\) 1.02933 1.78285i 0.0854813 0.148058i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.22634 5.58818i 0.264312 0.457802i −0.703071 0.711119i \(-0.748189\pi\)
0.967383 + 0.253318i \(0.0815218\pi\)
\(150\) 0 0
\(151\) 2.01303 + 3.48667i 0.163818 + 0.283741i 0.936235 0.351375i \(-0.114286\pi\)
−0.772417 + 0.635116i \(0.780952\pi\)
\(152\) 0 0
\(153\) 11.2578 0.910143
\(154\) 0 0
\(155\) −6.62814 −0.532385
\(156\) 0 0
\(157\) 7.76301 + 13.4459i 0.619556 + 1.07310i 0.989567 + 0.144075i \(0.0460206\pi\)
−0.370011 + 0.929027i \(0.620646\pi\)
\(158\) 0 0
\(159\) −4.48565 + 7.76937i −0.355735 + 0.616151i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.4805 21.6169i 0.977549 1.69316i 0.306294 0.951937i \(-0.400911\pi\)
0.671254 0.741227i \(-0.265756\pi\)
\(164\) 0 0
\(165\) −3.92919 6.80556i −0.305887 0.529812i
\(166\) 0 0
\(167\) 16.0739 1.24384 0.621919 0.783082i \(-0.286353\pi\)
0.621919 + 0.783082i \(0.286353\pi\)
\(168\) 0 0
\(169\) 21.3206 1.64005
\(170\) 0 0
\(171\) 3.98447 + 6.90131i 0.304700 + 0.527757i
\(172\) 0 0
\(173\) −0.0178027 + 0.0308352i −0.00135351 + 0.00234436i −0.866701 0.498827i \(-0.833764\pi\)
0.865348 + 0.501172i \(0.167098\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.53755 9.59132i 0.416228 0.720928i
\(178\) 0 0
\(179\) 2.22634 + 3.85613i 0.166404 + 0.288221i 0.937153 0.348918i \(-0.113451\pi\)
−0.770749 + 0.637139i \(0.780118\pi\)
\(180\) 0 0
\(181\) 22.7377 1.69008 0.845039 0.534705i \(-0.179577\pi\)
0.845039 + 0.534705i \(0.179577\pi\)
\(182\) 0 0
\(183\) −16.1038 −1.19043
\(184\) 0 0
\(185\) −2.95852 5.12431i −0.217515 0.376747i
\(186\) 0 0
\(187\) −11.4444 + 19.8223i −0.836899 + 1.44955i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.7760 22.1288i 0.924442 1.60118i 0.131985 0.991252i \(-0.457865\pi\)
0.792456 0.609929i \(-0.208802\pi\)
\(192\) 0 0
\(193\) −10.5452 18.2648i −0.759059 1.31473i −0.943331 0.331854i \(-0.892326\pi\)
0.184272 0.982875i \(-0.441007\pi\)
\(194\) 0 0
\(195\) −12.7946 −0.916239
\(196\) 0 0
\(197\) 16.4622 1.17288 0.586442 0.809991i \(-0.300528\pi\)
0.586442 + 0.809991i \(0.300528\pi\)
\(198\) 0 0
\(199\) −12.9709 22.4663i −0.919485 1.59259i −0.800199 0.599734i \(-0.795273\pi\)
−0.119285 0.992860i \(-0.538060\pi\)
\(200\) 0 0
\(201\) 3.70913 6.42440i 0.261622 0.453142i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.61174 + 6.25572i −0.252255 + 0.436918i
\(206\) 0 0
\(207\) −2.32560 4.02806i −0.161640 0.279969i
\(208\) 0 0
\(209\) −16.2020 −1.12072
\(210\) 0 0
\(211\) 8.84877 0.609174 0.304587 0.952484i \(-0.401481\pi\)
0.304587 + 0.952484i \(0.401481\pi\)
\(212\) 0 0
\(213\) 18.2607 + 31.6285i 1.25120 + 2.16715i
\(214\) 0 0
\(215\) −2.67440 + 4.63220i −0.182393 + 0.315913i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −16.0723 + 27.8381i −1.08607 + 1.88112i
\(220\) 0 0
\(221\) 18.6332 + 32.2736i 1.25340 + 2.17096i
\(222\) 0 0
\(223\) −4.06042 −0.271906 −0.135953 0.990715i \(-0.543410\pi\)
−0.135953 + 0.990715i \(0.543410\pi\)
\(224\) 0 0
\(225\) 1.76977 0.117984
\(226\) 0 0
\(227\) −5.98032 10.3582i −0.396928 0.687499i 0.596417 0.802674i \(-0.296590\pi\)
−0.993345 + 0.115175i \(0.963257\pi\)
\(228\) 0 0
\(229\) 5.65208 9.78969i 0.373500 0.646921i −0.616601 0.787276i \(-0.711491\pi\)
0.990101 + 0.140355i \(0.0448243\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.6530 + 18.4515i −0.697898 + 1.20880i 0.271295 + 0.962496i \(0.412548\pi\)
−0.969194 + 0.246299i \(0.920785\pi\)
\(234\) 0 0
\(235\) −1.15942 2.00818i −0.0756325 0.130999i
\(236\) 0 0
\(237\) 7.10896 0.461776
\(238\) 0 0
\(239\) −22.5361 −1.45774 −0.728871 0.684651i \(-0.759955\pi\)
−0.728871 + 0.684651i \(0.759955\pi\)
\(240\) 0 0
\(241\) −6.42386 11.1265i −0.413798 0.716718i 0.581504 0.813544i \(-0.302465\pi\)
−0.995301 + 0.0968253i \(0.969131\pi\)
\(242\) 0 0
\(243\) −8.17521 + 14.1599i −0.524440 + 0.908356i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −13.1896 + 22.8451i −0.839236 + 1.45360i
\(248\) 0 0
\(249\) −11.6773 20.2256i −0.740016 1.28175i
\(250\) 0 0
\(251\) −23.7361 −1.49821 −0.749103 0.662453i \(-0.769515\pi\)
−0.749103 + 0.662453i \(0.769515\pi\)
\(252\) 0 0
\(253\) 9.45657 0.594530
\(254\) 0 0
\(255\) −6.94637 12.0315i −0.434999 0.753440i
\(256\) 0 0
\(257\) 6.60697 11.4436i 0.412131 0.713832i −0.582991 0.812478i \(-0.698118\pi\)
0.995123 + 0.0986462i \(0.0314512\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.82167 + 3.15523i −0.112759 + 0.195304i
\(262\) 0 0
\(263\) 14.4266 + 24.9876i 0.889584 + 1.54080i 0.840368 + 0.542016i \(0.182339\pi\)
0.0492151 + 0.998788i \(0.484328\pi\)
\(264\) 0 0
\(265\) 4.10777 0.252338
\(266\) 0 0
\(267\) 24.3602 1.49082
\(268\) 0 0
\(269\) 1.28536 + 2.22631i 0.0783700 + 0.135741i 0.902547 0.430592i \(-0.141695\pi\)
−0.824177 + 0.566333i \(0.808362\pi\)
\(270\) 0 0
\(271\) 3.37361 5.84327i 0.204932 0.354953i −0.745179 0.666865i \(-0.767636\pi\)
0.950111 + 0.311911i \(0.100969\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.79910 + 3.11613i −0.108490 + 0.187909i
\(276\) 0 0
\(277\) 1.62727 + 2.81851i 0.0977730 + 0.169348i 0.910763 0.412931i \(-0.135495\pi\)
−0.812990 + 0.582278i \(0.802161\pi\)
\(278\) 0 0
\(279\) 11.7303 0.702273
\(280\) 0 0
\(281\) −2.55422 −0.152372 −0.0761860 0.997094i \(-0.524274\pi\)
−0.0761860 + 0.997094i \(0.524274\pi\)
\(282\) 0 0
\(283\) −6.25681 10.8371i −0.371929 0.644199i 0.617933 0.786230i \(-0.287970\pi\)
−0.989862 + 0.142031i \(0.954637\pi\)
\(284\) 0 0
\(285\) 4.91704 8.51656i 0.291260 0.504478i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −11.7325 + 20.3212i −0.690145 + 1.19537i
\(290\) 0 0
\(291\) −18.7709 32.5122i −1.10037 1.90590i
\(292\) 0 0
\(293\) 25.6574 1.49892 0.749460 0.662050i \(-0.230313\pi\)
0.749460 + 0.662050i \(0.230313\pi\)
\(294\) 0 0
\(295\) −5.07107 −0.295249
\(296\) 0 0
\(297\) −4.83382 8.37243i −0.280487 0.485818i
\(298\) 0 0
\(299\) 7.69833 13.3339i 0.445206 0.771120i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −3.75787 + 6.50883i −0.215884 + 0.373922i
\(304\) 0 0
\(305\) 3.68681 + 6.38574i 0.211106 + 0.365646i
\(306\) 0 0
\(307\) 11.9391 0.681398 0.340699 0.940172i \(-0.389336\pi\)
0.340699 + 0.940172i \(0.389336\pi\)
\(308\) 0 0
\(309\) −26.1547 −1.48789
\(310\) 0 0
\(311\) 4.24939 + 7.36017i 0.240961 + 0.417357i 0.960988 0.276589i \(-0.0892041\pi\)
−0.720027 + 0.693946i \(0.755871\pi\)
\(312\) 0 0
\(313\) −0.878058 + 1.52084i −0.0496308 + 0.0859631i −0.889774 0.456402i \(-0.849138\pi\)
0.840143 + 0.542365i \(0.182471\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.98245 + 5.16576i −0.167511 + 0.290138i −0.937544 0.347866i \(-0.886906\pi\)
0.770033 + 0.638004i \(0.220240\pi\)
\(318\) 0 0
\(319\) −3.70373 6.41505i −0.207369 0.359174i
\(320\) 0 0
\(321\) 23.3162 1.30138
\(322\) 0 0
\(323\) −28.6434 −1.59376
\(324\) 0 0
\(325\) 2.92919 + 5.07351i 0.162482 + 0.281427i
\(326\) 0 0
\(327\) −9.10076 + 15.7630i −0.503273 + 0.871695i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7.05191 12.2143i 0.387608 0.671357i −0.604519 0.796590i \(-0.706635\pi\)
0.992127 + 0.125234i \(0.0399681\pi\)
\(332\) 0 0
\(333\) 5.23589 + 9.06882i 0.286925 + 0.496968i
\(334\) 0 0
\(335\) −3.39667 −0.185580
\(336\) 0 0
\(337\) −22.8876 −1.24677 −0.623384 0.781916i \(-0.714242\pi\)
−0.623384 + 0.781916i \(0.714242\pi\)
\(338\) 0 0
\(339\) −13.2722 22.9882i −0.720849 1.24855i
\(340\) 0 0
\(341\) −11.9247 + 20.6541i −0.645757 + 1.11848i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.86991 + 4.97082i −0.154511 + 0.267620i
\(346\) 0 0
\(347\) 11.8293 + 20.4890i 0.635030 + 1.09990i 0.986509 + 0.163709i \(0.0523458\pi\)
−0.351478 + 0.936196i \(0.614321\pi\)
\(348\) 0 0
\(349\) −27.7912 −1.48763 −0.743814 0.668386i \(-0.766985\pi\)
−0.743814 + 0.668386i \(0.766985\pi\)
\(350\) 0 0
\(351\) −15.7403 −0.840157
\(352\) 0 0
\(353\) 10.5840 + 18.3321i 0.563331 + 0.975717i 0.997203 + 0.0747430i \(0.0238136\pi\)
−0.433872 + 0.900974i \(0.642853\pi\)
\(354\) 0 0
\(355\) 8.36121 14.4820i 0.443767 0.768627i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −18.1421 + 31.4231i −0.957505 + 1.65845i −0.228977 + 0.973432i \(0.573538\pi\)
−0.728528 + 0.685016i \(0.759795\pi\)
\(360\) 0 0
\(361\) −0.637724 1.10457i −0.0335644 0.0581353i
\(362\) 0 0
\(363\) −4.25219 −0.223182
\(364\) 0 0
\(365\) 14.7184 0.770395
\(366\) 0 0
\(367\) −15.5793 26.9841i −0.813232 1.40856i −0.910590 0.413310i \(-0.864372\pi\)
0.0973579 0.995249i \(-0.468961\pi\)
\(368\) 0 0
\(369\) 6.39194 11.0712i 0.332751 0.576341i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3.33639 5.77880i 0.172752 0.299215i −0.766629 0.642090i \(-0.778067\pi\)
0.939381 + 0.342875i \(0.111401\pi\)
\(374\) 0 0
\(375\) −1.09199 1.89138i −0.0563901 0.0976705i
\(376\) 0 0
\(377\) −12.0604 −0.621143
\(378\) 0 0
\(379\) 21.3984 1.09916 0.549582 0.835440i \(-0.314787\pi\)
0.549582 + 0.835440i \(0.314787\pi\)
\(380\) 0 0
\(381\) −10.7283 18.5819i −0.549627 0.951981i
\(382\) 0 0
\(383\) 1.81726 3.14759i 0.0928578 0.160834i −0.815855 0.578257i \(-0.803733\pi\)
0.908713 + 0.417422i \(0.137066\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.73306 8.19790i 0.240595 0.416723i
\(388\) 0 0
\(389\) −10.9476 18.9618i −0.555066 0.961403i −0.997898 0.0647981i \(-0.979360\pi\)
0.442832 0.896604i \(-0.353974\pi\)
\(390\) 0 0
\(391\) 16.7182 0.845474
\(392\) 0 0
\(393\) 10.8189 0.545740
\(394\) 0 0
\(395\) −1.62752 2.81895i −0.0818896 0.141837i
\(396\) 0 0
\(397\) −8.98785 + 15.5674i −0.451087 + 0.781306i −0.998454 0.0555869i \(-0.982297\pi\)
0.547367 + 0.836893i \(0.315630\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.8172 + 23.9320i −0.689996 + 1.19511i 0.281843 + 0.959461i \(0.409054\pi\)
−0.971839 + 0.235647i \(0.924279\pi\)
\(402\) 0 0
\(403\) 19.4151 + 33.6279i 0.967135 + 1.67513i
\(404\) 0 0
\(405\) 11.1772 0.555401
\(406\) 0 0
\(407\) −21.2907 −1.05534
\(408\) 0 0
\(409\) −19.9630 34.5770i −0.987108 1.70972i −0.632164 0.774834i \(-0.717833\pi\)
−0.354944 0.934887i \(-0.615500\pi\)
\(410\) 0 0
\(411\) −12.3545 + 21.3985i −0.609400 + 1.05551i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −5.34678 + 9.26089i −0.262463 + 0.454599i
\(416\) 0 0
\(417\) −9.50371 16.4609i −0.465398 0.806094i
\(418\) 0 0
\(419\) −2.89384 −0.141373 −0.0706867 0.997499i \(-0.522519\pi\)
−0.0706867 + 0.997499i \(0.522519\pi\)
\(420\) 0 0
\(421\) −33.5744 −1.63632 −0.818158 0.574993i \(-0.805005\pi\)
−0.818158 + 0.574993i \(0.805005\pi\)
\(422\) 0 0
\(423\) 2.05191 + 3.55401i 0.0997672 + 0.172802i
\(424\) 0 0
\(425\) −3.18060 + 5.50897i −0.154282 + 0.267224i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −23.0187 + 39.8695i −1.11135 + 1.92492i
\(430\) 0 0
\(431\) −0.165441 0.286552i −0.00796902 0.0138027i 0.862013 0.506885i \(-0.169203\pi\)
−0.869982 + 0.493083i \(0.835870\pi\)
\(432\) 0 0
\(433\) 0.573752 0.0275727 0.0137864 0.999905i \(-0.495612\pi\)
0.0137864 + 0.999905i \(0.495612\pi\)
\(434\) 0 0
\(435\) 4.49607 0.215570
\(436\) 0 0
\(437\) 5.91704 + 10.2486i 0.283050 + 0.490258i
\(438\) 0 0
\(439\) −13.7582 + 23.8300i −0.656645 + 1.13734i 0.324834 + 0.945771i \(0.394692\pi\)
−0.981479 + 0.191571i \(0.938642\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.85838 17.0752i 0.468386 0.811268i −0.530961 0.847396i \(-0.678169\pi\)
0.999347 + 0.0361281i \(0.0115024\pi\)
\(444\) 0 0
\(445\) −5.57701 9.65967i −0.264376 0.457912i
\(446\) 0 0
\(447\) 14.0925 0.666553
\(448\) 0 0
\(449\) 32.6751 1.54203 0.771016 0.636816i \(-0.219749\pi\)
0.771016 + 0.636816i \(0.219749\pi\)
\(450\) 0 0
\(451\) 12.9957 + 22.5093i 0.611945 + 1.05992i
\(452\) 0 0
\(453\) −4.39641 + 7.61481i −0.206561 + 0.357775i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.87556 + 3.24857i −0.0877350 + 0.151962i −0.906553 0.422091i \(-0.861296\pi\)
0.818818 + 0.574053i \(0.194630\pi\)
\(458\) 0 0
\(459\) −8.54566 14.8015i −0.398877 0.690876i
\(460\) 0 0
\(461\) −8.77983 −0.408917 −0.204459 0.978875i \(-0.565543\pi\)
−0.204459 + 0.978875i \(0.565543\pi\)
\(462\) 0 0
\(463\) −4.78203 −0.222240 −0.111120 0.993807i \(-0.535444\pi\)
−0.111120 + 0.993807i \(0.535444\pi\)
\(464\) 0 0
\(465\) −7.23787 12.5364i −0.335648 0.581359i
\(466\) 0 0
\(467\) 10.9599 18.9831i 0.507165 0.878435i −0.492801 0.870142i \(-0.664027\pi\)
0.999966 0.00829277i \(-0.00263970\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −16.9543 + 29.3656i −0.781211 + 1.35310i
\(472\) 0 0
\(473\) 9.62301 + 16.6675i 0.442466 + 0.766374i
\(474\) 0 0
\(475\) −4.50283 −0.206604
\(476\) 0 0
\(477\) −7.26980 −0.332861
\(478\) 0 0
\(479\) 2.54431 + 4.40687i 0.116252 + 0.201355i 0.918280 0.395932i \(-0.129579\pi\)
−0.802027 + 0.597287i \(0.796245\pi\)
\(480\) 0 0
\(481\) −17.3321 + 30.0201i −0.790277 + 1.36880i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.59482 + 14.8867i −0.390271 + 0.675968i
\(486\) 0 0
\(487\) −4.02518 6.97181i −0.182398 0.315923i 0.760299 0.649574i \(-0.225053\pi\)
−0.942697 + 0.333651i \(0.891719\pi\)
\(488\) 0 0
\(489\) 54.5143 2.46522
\(490\) 0 0
\(491\) 12.8081 0.578021 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(492\) 0 0
\(493\) −6.54778 11.3411i −0.294897 0.510777i
\(494\) 0 0
\(495\) 3.18398 5.51481i 0.143109 0.247872i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 14.2642 24.7063i 0.638552 1.10601i −0.347198 0.937792i \(-0.612867\pi\)
0.985751 0.168213i \(-0.0537997\pi\)
\(500\) 0 0
\(501\) 17.5526 + 30.4019i 0.784191 + 1.35826i
\(502\) 0 0
\(503\) 6.56948 0.292919 0.146459 0.989217i \(-0.453212\pi\)
0.146459 + 0.989217i \(0.453212\pi\)
\(504\) 0 0
\(505\) 3.44131 0.153136
\(506\) 0 0
\(507\) 23.2819 + 40.3254i 1.03398 + 1.79091i
\(508\) 0 0
\(509\) 12.0787 20.9209i 0.535379 0.927304i −0.463766 0.885958i \(-0.653502\pi\)
0.999145 0.0413458i \(-0.0131645\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 6.04911 10.4774i 0.267075 0.462587i
\(514\) 0 0
\(515\) 5.98785 + 10.3713i 0.263856 + 0.457012i
\(516\) 0 0
\(517\) −8.34366 −0.366954
\(518\) 0 0
\(519\) −0.0777615 −0.00341335
\(520\) 0 0
\(521\) 10.4315 + 18.0679i 0.457012 + 0.791568i 0.998801 0.0489461i \(-0.0155863\pi\)
−0.541789 + 0.840514i \(0.682253\pi\)
\(522\) 0 0
\(523\) −6.43539 + 11.1464i −0.281400 + 0.487399i −0.971730 0.236096i \(-0.924132\pi\)
0.690330 + 0.723495i \(0.257465\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.0815 + 36.5142i −0.918324 + 1.59058i
\(528\) 0 0
\(529\) 8.04643 + 13.9368i 0.349845 + 0.605949i
\(530\) 0 0
\(531\) 8.97460 0.389465
\(532\) 0 0
\(533\) 42.3179 1.83299
\(534\) 0 0
\(535\) −5.33801 9.24570i −0.230782 0.399726i
\(536\) 0 0
\(537\) −4.86228 + 8.42171i −0.209823 + 0.363424i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.2681 21.2489i 0.527446 0.913563i −0.472043 0.881576i \(-0.656483\pi\)
0.999488 0.0319870i \(-0.0101835\pi\)
\(542\) 0 0
\(543\) 24.8293 + 43.0056i 1.06553 + 1.84555i
\(544\) 0 0
\(545\) 8.33411 0.356994
\(546\) 0 0
\(547\) −27.5781 −1.17916 −0.589578 0.807711i \(-0.700706\pi\)
−0.589578 + 0.807711i \(0.700706\pi\)
\(548\) 0 0
\(549\) −6.52478 11.3013i −0.278471 0.482326i
\(550\) 0 0
\(551\) 4.63490 8.02788i 0.197453 0.341999i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.46135 11.1914i 0.274269 0.475048i
\(556\) 0 0
\(557\) 3.30130 + 5.71802i 0.139881 + 0.242280i 0.927451 0.373944i \(-0.121995\pi\)
−0.787571 + 0.616224i \(0.788661\pi\)
\(558\) 0 0
\(559\) 31.3353 1.32534
\(560\) 0 0
\(561\) −49.9888 −2.11053
\(562\) 0 0
\(563\) −0.987331 1.71011i −0.0416110 0.0720724i 0.844470 0.535603i \(-0.179916\pi\)
−0.886081 + 0.463531i \(0.846582\pi\)
\(564\) 0 0
\(565\) −6.07709 + 10.5258i −0.255665 + 0.442825i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.86403 10.1568i 0.245833 0.425795i −0.716532 0.697554i \(-0.754272\pi\)
0.962365 + 0.271758i \(0.0876052\pi\)
\(570\) 0 0
\(571\) −2.84987 4.93612i −0.119263 0.206570i 0.800213 0.599716i \(-0.204720\pi\)
−0.919476 + 0.393146i \(0.871387\pi\)
\(572\) 0 0
\(573\) 55.8052 2.33130
\(574\) 0 0
\(575\) 2.62814 0.109601
\(576\) 0 0
\(577\) 11.6671 + 20.2081i 0.485709 + 0.841272i 0.999865 0.0164241i \(-0.00522820\pi\)
−0.514156 + 0.857697i \(0.671895\pi\)
\(578\) 0 0
\(579\) 23.0305 39.8899i 0.957114 1.65777i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 7.39028 12.8003i 0.306074 0.530136i
\(584\) 0 0
\(585\) −5.18398 8.97892i −0.214331 0.371232i
\(586\) 0 0
\(587\) 22.8470 0.942997 0.471498 0.881867i \(-0.343713\pi\)
0.471498 + 0.881867i \(0.343713\pi\)
\(588\) 0 0
\(589\) −29.8454 −1.22976
\(590\) 0 0
\(591\) 17.9766 + 31.1364i 0.739458 + 1.28078i
\(592\) 0 0
\(593\) −7.24051 + 12.5409i −0.297332 + 0.514994i −0.975525 0.219890i \(-0.929430\pi\)
0.678193 + 0.734884i \(0.262763\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 28.3282 49.0659i 1.15940 2.00814i
\(598\) 0 0
\(599\) 1.56762 + 2.71520i 0.0640512 + 0.110940i 0.896273 0.443503i \(-0.146265\pi\)
−0.832222 + 0.554443i \(0.812931\pi\)
\(600\) 0 0
\(601\) −32.2118 −1.31395 −0.656973 0.753914i \(-0.728164\pi\)
−0.656973 + 0.753914i \(0.728164\pi\)
\(602\) 0 0
\(603\) 6.01131 0.244799
\(604\) 0 0
\(605\) 0.973496 + 1.68614i 0.0395782 + 0.0685515i
\(606\) 0 0
\(607\) 5.57929 9.66362i 0.226456 0.392234i −0.730299 0.683128i \(-0.760619\pi\)
0.956755 + 0.290894i \(0.0939526\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.79234 + 11.7647i −0.274789 + 0.475948i
\(612\) 0 0
\(613\) −3.76852 6.52727i −0.152209 0.263634i 0.779830 0.625991i \(-0.215305\pi\)
−0.932039 + 0.362357i \(0.881972\pi\)
\(614\) 0 0
\(615\) −15.7759 −0.636147
\(616\) 0 0
\(617\) −22.7728 −0.916797 −0.458399 0.888747i \(-0.651577\pi\)
−0.458399 + 0.888747i \(0.651577\pi\)
\(618\) 0 0
\(619\) −0.482383 0.835512i −0.0193886 0.0335821i 0.856168 0.516697i \(-0.172839\pi\)
−0.875557 + 0.483115i \(0.839505\pi\)
\(620\) 0 0
\(621\) −3.53066 + 6.11528i −0.141680 + 0.245398i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −17.6925 30.6442i −0.706569 1.22381i
\(628\) 0 0
\(629\) −37.6395 −1.50079
\(630\) 0 0
\(631\) 6.90059 0.274708 0.137354 0.990522i \(-0.456140\pi\)
0.137354 + 0.990522i \(0.456140\pi\)
\(632\) 0 0
\(633\) 9.66277 + 16.7364i 0.384060 + 0.665212i
\(634\) 0 0
\(635\) −4.91227 + 8.50829i −0.194937 + 0.337641i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −14.7974 + 25.6298i −0.585375 + 1.01390i
\(640\) 0 0
\(641\) 1.07217 + 1.85705i 0.0423481 + 0.0733490i 0.886423 0.462877i \(-0.153183\pi\)
−0.844074 + 0.536226i \(0.819849\pi\)
\(642\) 0 0
\(643\) 27.4980 1.08441 0.542207 0.840245i \(-0.317589\pi\)
0.542207 + 0.840245i \(0.317589\pi\)
\(644\) 0 0
\(645\) −11.6817 −0.459965
\(646\) 0 0
\(647\) 15.4741 + 26.8020i 0.608350 + 1.05369i 0.991512 + 0.130013i \(0.0415018\pi\)
−0.383162 + 0.923681i \(0.625165\pi\)
\(648\) 0 0
\(649\) −9.12334 + 15.8021i −0.358122 + 0.620286i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.7224 34.1602i 0.771798 1.33679i −0.164779 0.986330i \(-0.552691\pi\)
0.936577 0.350462i \(-0.113975\pi\)
\(654\) 0 0
\(655\) −2.47687 4.29007i −0.0967794 0.167627i
\(656\) 0 0
\(657\) −26.0481 −1.01623
\(658\) 0 0
\(659\) 8.80237 0.342892 0.171446 0.985194i \(-0.445156\pi\)
0.171446 + 0.985194i \(0.445156\pi\)
\(660\) 0 0
\(661\) 14.0548 + 24.3436i 0.546667 + 0.946855i 0.998500 + 0.0547525i \(0.0174370\pi\)
−0.451833 + 0.892103i \(0.649230\pi\)
\(662\) 0 0
\(663\) −40.6945 + 70.4849i −1.58044 + 2.73741i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.70523 + 4.68560i −0.104747 + 0.181427i
\(668\) 0 0
\(669\) −4.43393 7.67980i −0.171426 0.296918i
\(670\) 0 0
\(671\) 26.5317 1.02424
\(672\) 0 0
\(673\) −14.7933 −0.570241 −0.285121 0.958492i \(-0.592034\pi\)
−0.285121 + 0.958492i \(0.592034\pi\)
\(674\) 0 0
\(675\) −1.34340 2.32684i −0.0517076 0.0895602i
\(676\) 0 0
\(677\) −1.35581 + 2.34833i −0.0521080 + 0.0902537i −0.890903 0.454194i \(-0.849927\pi\)
0.838795 + 0.544448i \(0.183261\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13.0609 22.6221i 0.500495 0.866882i
\(682\) 0 0
\(683\) 0.813164 + 1.40844i 0.0311149 + 0.0538925i 0.881164 0.472812i \(-0.156761\pi\)
−0.850049 + 0.526704i \(0.823428\pi\)
\(684\) 0 0
\(685\) 11.3137 0.432275
\(686\) 0 0
\(687\) 24.6880 0.941908
\(688\) 0 0
\(689\) −12.0324 20.8408i −0.458400 0.793971i
\(690\) 0 0
\(691\) 25.4410 44.0652i 0.967823 1.67632i 0.265992 0.963975i \(-0.414301\pi\)
0.701831 0.712343i \(-0.252366\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.35155 + 7.53711i −0.165064 + 0.285899i
\(696\) 0 0
\(697\) 22.9750 + 39.7939i 0.870241 + 1.50730i
\(698\) 0 0
\(699\) −46.5317 −1.75999
\(700\) 0 0
\(701\) 7.93106 0.299552 0.149776 0.988720i \(-0.452145\pi\)
0.149776 + 0.988720i \(0.452145\pi\)
\(702\) 0 0
\(703\) −13.3217 23.0739i −0.502438 0.870247i
\(704\) 0 0
\(705\) 2.53216 4.38583i 0.0953666 0.165180i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −8.74609 + 15.1487i −0.328466 + 0.568920i −0.982208 0.187798i \(-0.939865\pi\)
0.653741 + 0.756718i \(0.273198\pi\)
\(710\) 0 0
\(711\) 2.88034 + 4.98889i 0.108021 + 0.187098i
\(712\) 0 0
\(713\) 17.4197 0.652374
\(714\) 0 0
\(715\) 21.0796 0.788332
\(716\) 0 0
\(717\) −24.6092 42.6245i −0.919049 1.59184i
\(718\) 0 0
\(719\) 9.06468 15.7005i 0.338055 0.585529i −0.646011 0.763328i \(-0.723564\pi\)
0.984067 + 0.177798i \(0.0568975\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 14.0296 24.3000i 0.521766 0.903725i
\(724\) 0 0
\(725\) −1.02933 1.78285i −0.0382284 0.0662135i
\(726\) 0 0
\(727\) −2.42538 −0.0899523 −0.0449761 0.998988i \(-0.514321\pi\)
−0.0449761 + 0.998988i \(0.514321\pi\)
\(728\) 0 0
\(729\) −2.17729 −0.0806402
\(730\) 0 0
\(731\) 17.0124 + 29.4664i 0.629227 + 1.08985i
\(732\) 0 0
\(733\) −9.88293 + 17.1177i −0.365035 + 0.632258i −0.988782 0.149368i \(-0.952276\pi\)
0.623747 + 0.781626i \(0.285609\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.11093 + 10.5844i −0.225099 + 0.389883i
\(738\) 0 0
\(739\) −19.9533 34.5601i −0.733993 1.27131i −0.955164 0.296078i \(-0.904321\pi\)
0.221171 0.975235i \(-0.429012\pi\)
\(740\) 0 0
\(741\) −57.6118 −2.11642
\(742\) 0 0
\(743\) 33.0921 1.21403 0.607016 0.794689i \(-0.292366\pi\)
0.607016 + 0.794689i \(0.292366\pi\)
\(744\) 0 0
\(745\) −3.22634 5.58818i −0.118204 0.204735i
\(746\) 0 0
\(747\) 9.46255 16.3896i 0.346217 0.599665i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 3.49266 6.04946i 0.127449 0.220748i −0.795239 0.606296i \(-0.792654\pi\)
0.922688 + 0.385549i \(0.125988\pi\)
\(752\) 0 0
\(753\) −25.9195 44.8939i −0.944560 1.63603i
\(754\) 0 0
\(755\) 4.02606 0.146523
\(756\) 0 0
\(757\) −24.4796 −0.889725 −0.444863 0.895599i \(-0.646747\pi\)
−0.444863 + 0.895599i \(0.646747\pi\)
\(758\) 0 0
\(759\) 10.3265 + 17.8860i 0.374827 + 0.649220i
\(760\) 0 0
\(761\) 4.69756 8.13641i 0.170286 0.294945i −0.768234 0.640170i \(-0.778864\pi\)
0.938520 + 0.345225i \(0.112197\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 5.62892 9.74958i 0.203514 0.352497i
\(766\) 0 0
\(767\) 14.8541 + 25.7281i 0.536351 + 0.928987i
\(768\) 0 0
\(769\) −29.7183 −1.07167 −0.535835 0.844323i \(-0.680003\pi\)
−0.535835 + 0.844323i \(0.680003\pi\)
\(770\) 0 0
\(771\) 28.8590 1.03933
\(772\) 0 0
\(773\) −19.1054 33.0915i −0.687173 1.19022i −0.972749 0.231862i \(-0.925518\pi\)
0.285576 0.958356i \(-0.407815\pi\)
\(774\) 0 0
\(775\) −3.31407 + 5.74014i −0.119045 + 0.206192i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16.2630 + 28.1684i −0.582684 + 1.00924i
\(780\) 0 0
\(781\) −30.0852 52.1091i −1.07653 1.86461i
\(782\) 0 0
\(783\) 5.53122 0.197670
\(784\) 0 0
\(785\) 15.5260 0.554148
\(786\) 0 0
\(787\) 12.4057 + 21.4873i 0.442215 + 0.765940i 0.997854 0.0654847i \(-0.0208594\pi\)
−0.555638 + 0.831424i \(0.687526\pi\)
\(788\) 0 0
\(789\) −31.5074 + 54.5725i −1.12169 + 1.94283i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 21.5987 37.4101i 0.766993 1.32847i
\(794\) 0 0
\(795\) 4.48565 + 7.76937i 0.159089 + 0.275551i
\(796\) 0 0
\(797\) 22.9296 0.812210 0.406105 0.913826i \(-0.366887\pi\)
0.406105 + 0.913826i \(0.366887\pi\)
\(798\) 0 0
\(799\) −14.7507 −0.521841
\(800\) 0 0