Properties

Label 1960.2.q.y.361.3
Level $1960$
Weight $2$
Character 1960.361
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 361.3
Root \(1.09199 - 1.89138i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.y.961.3

$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 −0.356997 0.934105i \(-0.616199\pi\)
0.987458 0.157884i \(-0.0504673\pi\)
\(4\) 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 0.456315 + 0.889818i \(0.349169\pi\)
−0.998763 + 0.0497290i \(0.984164\pi\)
\(12\) 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 0.165381 + 0.986230i \(0.447115\pi\)
−0.936791 + 0.349891i \(0.886219\pi\)
\(18\) 0 0
\(19\) 2.25141 + 3.89956i 0.516510 + 0.894621i 0.999816 + 0.0191698i \(0.00610231\pi\)
−0.483307 + 0.875451i \(0.660564\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.31407 2.27604i −0.274003 0.474587i 0.695880 0.718158i \(-0.255015\pi\)
−0.969883 + 0.243571i \(0.921681\pi\)
\(24\) 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 0.398290 + 0.917259i \(0.369604\pi\)
−0.993515 + 0.113700i \(0.963730\pi\)
\(32\) 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 0.999877 0.0156589i \(-0.00498458\pi\)
−0.513500 + 0.858090i \(0.671651\pi\)
\(38\) 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 0.938110 0.346336i \(-0.112574\pi\)
−0.768991 + 0.639259i \(0.779241\pi\)
\(48\) 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 −0.689784 0.724015i \(-0.742295\pi\)
0.971907 + 0.235363i \(0.0756280\pi\)
\(54\) 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 −0.982531 0.186100i \(-0.940415\pi\)
0.652432 + 0.757847i \(0.273749\pi\)
\(60\) 0 0
\(61\) −3.68681 6.38574i −0.472047 0.817610i 0.527441 0.849591i \(-0.323151\pi\)
−0.999488 + 0.0319818i \(0.989818\pi\)
\(62\) 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 −0.950921 0.309432i \(-0.899861\pi\)
0.743437 + 0.668806i \(0.233194\pi\)
\(68\) 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 −0.00932043 0.999957i \(-0.502967\pi\)
0.870648 0.491907i \(-0.163700\pi\)
\(74\) 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 0.942938 0.332968i \(-0.108050\pi\)
−0.759828 + 0.650125i \(0.774717\pi\)
\(80\) 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 0.994076 + 0.108685i \(0.0346641\pi\)
−0.402914 + 0.915238i \(0.632003\pi\)
\(90\) 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 −0.767632 0.640891i \(-0.778565\pi\)
0.938844 + 0.344344i \(0.111899\pi\)
\(102\) 0 0
\(103\) −5.98785 10.3713i −0.590000 1.02191i −0.994232 0.107254i \(-0.965794\pi\)
0.404231 0.914657i \(-0.367539\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.33801 + 9.24570i 0.516045 + 0.893815i 0.999827 + 0.0186269i \(0.00592946\pi\)
−0.483782 + 0.875189i \(0.660737\pi\)
\(108\) 0 0
\(109\) 4.16706 7.21755i 0.399131 0.691316i −0.594487 0.804105i \(-0.702645\pi\)
0.993619 + 0.112789i \(0.0359784\pi\)
\(110\) 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 0.953706 0.300739i \(-0.0972334\pi\)
−0.737301 + 0.675564i \(0.763900\pi\)
\(132\) 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 −0.516518 0.856276i \(-0.672772\pi\)
0.999816 + 0.0191800i \(0.00610555\pi\)
\(138\) 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 0.967383 0.253318i \(-0.0815218\pi\)
−0.703071 + 0.711119i \(0.748189\pi\)
\(150\) 0 0
\(151\) 2.01303 3.48667i 0.163818 0.283741i −0.772417 0.635116i \(-0.780952\pi\)
0.936235 + 0.351375i \(0.114286\pi\)
\(152\) 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 −0.370011 0.929027i \(-0.620646\pi\)
0.989567 0.144075i \(-0.0460206\pi\)
\(158\) 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 0.671254 + 0.741227i \(0.265756\pi\)
0.306294 + 0.951937i \(0.400911\pi\)
\(164\) 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 0.865348 0.501172i \(-0.167098\pi\)
−0.866701 + 0.498827i \(0.833764\pi\)
\(174\) 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 −0.770749 0.637139i \(-0.780118\pi\)
0.937153 + 0.348918i \(0.113451\pi\)
\(180\) 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 0.792456 + 0.609929i \(0.208802\pi\)
0.131985 + 0.991252i \(0.457865\pi\)
\(192\) 0 0
\(193\) −10.5452 + 18.2648i −0.759059 + 1.31473i 0.184272 + 0.982875i \(0.441007\pi\)
−0.943331 + 0.331854i \(0.892326\pi\)
\(194\) 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 −0.119285 + 0.992860i \(0.538060\pi\)
−0.800199 + 0.599734i \(0.795273\pi\)
\(200\) 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 −0.993345 0.115175i \(-0.963257\pi\)
0.596417 + 0.802674i \(0.296590\pi\)
\(228\) 0 0
\(229\) 5.65208 + 9.78969i 0.373500 + 0.646921i 0.990101 0.140355i \(-0.0448243\pi\)
−0.616601 + 0.787276i \(0.711491\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.6530 18.4515i −0.697898 1.20880i −0.969194 0.246299i \(-0.920785\pi\)
0.271295 0.962496i \(-0.412548\pi\)
\(234\) 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 −0.995301 0.0968253i \(-0.969131\pi\)
0.581504 + 0.813544i \(0.302465\pi\)
\(242\) 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 0.995123 0.0986462i \(-0.0314512\pi\)
−0.582991 + 0.812478i \(0.698118\pi\)
\(258\) 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 0.0492151 0.998788i \(-0.484328\pi\)
0.840368 0.542016i \(-0.182339\pi\)
\(264\) 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 −0.824177 0.566333i \(-0.808362\pi\)
0.902547 + 0.430592i \(0.141695\pi\)
\(270\) 0 0
\(271\) 3.37361 + 5.84327i 0.204932 + 0.354953i 0.950111 0.311911i \(-0.100969\pi\)
−0.745179 + 0.666865i \(0.767636\pi\)
\(272\) 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 −0.812990 0.582278i \(-0.802161\pi\)
0.910763 + 0.412931i \(0.135495\pi\)
\(278\) 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 −0.989862 0.142031i \(-0.954637\pi\)
0.617933 + 0.786230i \(0.287970\pi\)
\(284\) 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 −0.720027 0.693946i \(-0.755871\pi\)
0.960988 + 0.276589i \(0.0892041\pi\)
\(312\) 0 0
\(313\) −0.878058 1.52084i −0.0496308 0.0859631i 0.840143 0.542365i \(-0.182471\pi\)
−0.889774 + 0.456402i \(0.849138\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.98245 5.16576i −0.167511 0.290138i 0.770033 0.638004i \(-0.220240\pi\)
−0.937544 + 0.347866i \(0.886906\pi\)
\(318\) 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 0.992127 0.125234i \(-0.0399681\pi\)
−0.604519 + 0.796590i \(0.706635\pi\)
\(332\) 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 −0.351478 0.936196i \(-0.614321\pi\)
0.986509 0.163709i \(-0.0523458\pi\)
\(348\) 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 −0.433872 0.900974i \(-0.642853\pi\)
0.997203 0.0747430i \(-0.0238136\pi\)
\(354\) 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 −0.728528 0.685016i \(-0.759795\pi\)
−0.228977 0.973432i \(-0.573538\pi\)
\(360\) 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 0.0973579 + 0.995249i \(0.468961\pi\)
−0.910590 + 0.413310i \(0.864372\pi\)
\(368\) 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 0.939381 0.342875i \(-0.111401\pi\)
−0.766629 + 0.642090i \(0.778067\pi\)
\(374\) 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 0.908713 0.417422i \(-0.137066\pi\)
−0.815855 + 0.578257i \(0.803733\pi\)
\(384\) 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 0.442832 + 0.896604i \(0.353974\pi\)
−0.997898 + 0.0647981i \(0.979360\pi\)
\(390\) 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 0.547367 0.836893i \(-0.315630\pi\)
−0.998454 + 0.0555869i \(0.982297\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.8172 23.9320i −0.689996 1.19511i −0.971839 0.235647i \(-0.924279\pi\)
0.281843 0.959461i \(-0.409054\pi\)
\(402\) 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 −0.354944 + 0.934887i \(0.615500\pi\)
−0.632164 + 0.774834i \(0.717833\pi\)
\(410\) 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 −0.869982 0.493083i \(-0.835870\pi\)
0.862013 + 0.506885i \(0.169203\pi\)
\(432\) 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 −0.981479 0.191571i \(-0.938642\pi\)
0.324834 0.945771i \(-0.394692\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.85838 + 17.0752i 0.468386 + 0.811268i 0.999347 0.0361281i \(-0.0115024\pi\)
−0.530961 + 0.847396i \(0.678169\pi\)
\(444\) 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 0.818818 0.574053i \(-0.194630\pi\)
−0.906553 + 0.422091i \(0.861296\pi\)
\(458\) 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 0.999966 + 0.00829277i \(0.00263970\pi\)
−0.492801 + 0.870142i \(0.664027\pi\)
\(468\) 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 −0.802027 0.597287i \(-0.796245\pi\)
0.918280 + 0.395932i \(0.129579\pi\)
\(480\) 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 −0.942697 0.333651i \(-0.891719\pi\)
0.760299 + 0.649574i \(0.225053\pi\)
\(488\) 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 0.985751 + 0.168213i \(0.0537997\pi\)
−0.347198 + 0.937792i \(0.612867\pi\)
\(500\) 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 0.999145 + 0.0413458i \(0.0131645\pi\)
−0.463766 + 0.885958i \(0.653502\pi\)
\(510\) 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 −0.541789 0.840514i \(-0.682253\pi\)
0.998801 + 0.0489461i \(0.0155863\pi\)
\(522\) 0 0
\(523\) −6.43539 11.1464i −0.281400 0.487399i 0.690330 0.723495i \(-0.257465\pi\)
−0.971730 + 0.236096i \(0.924132\pi\)
\(524\) 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 0.999488 + 0.0319870i \(0.0101835\pi\)
−0.472043 + 0.881576i \(0.656483\pi\)
\(542\) 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 −0.787571 0.616224i \(-0.788661\pi\)
0.927451 + 0.373944i \(0.121995\pi\)
\(558\) 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 −0.886081 0.463531i \(-0.846582\pi\)
0.844470 + 0.535603i \(0.179916\pi\)
\(564\) 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 0.962365 0.271758i \(-0.0876052\pi\)
−0.716532 + 0.697554i \(0.754272\pi\)
\(570\) 0 0
\(571\) −2.84987 + 4.93612i −0.119263 + 0.206570i −0.919476 0.393146i \(-0.871387\pi\)
0.800213 + 0.599716i \(0.204720\pi\)
\(572\) 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 −0.514156 0.857697i \(-0.671895\pi\)
0.999865 + 0.0164241i \(0.00522820\pi\)
\(578\) 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 0.678193 0.734884i \(-0.262763\pi\)
−0.975525 + 0.219890i \(0.929430\pi\)
\(594\) 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 −0.832222 0.554443i \(-0.812931\pi\)
0.896273 + 0.443503i \(0.146265\pi\)
\(600\) 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 0.956755 0.290894i \(-0.0939526\pi\)
−0.730299 + 0.683128i \(0.760619\pi\)
\(608\) 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 −0.932039 0.362357i \(-0.881972\pi\)
0.779830 + 0.625991i \(0.215305\pi\)
\(614\) 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 −0.875557 0.483115i \(-0.839505\pi\)
0.856168 + 0.516697i \(0.172839\pi\)
\(620\) 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 −0.844074 0.536226i \(-0.819849\pi\)
0.886423 + 0.462877i \(0.153183\pi\)
\(642\) 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 −0.383162 0.923681i \(-0.625165\pi\)
0.991512 0.130013i \(-0.0415018\pi\)
\(648\) 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 0.936577 + 0.350462i \(0.113975\pi\)
−0.164779 + 0.986330i \(0.552691\pi\)
\(654\) 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 −0.451833 0.892103i \(-0.649230\pi\)
0.998500 0.0547525i \(-0.0174370\pi\)
\(662\) 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 0.838795 0.544448i \(-0.183261\pi\)
−0.890903 + 0.454194i \(0.849927\pi\)
\(678\) 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 −0.850049 0.526704i \(-0.823428\pi\)
0.881164 + 0.472812i \(0.156761\pi\)
\(684\) 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 0.701831 + 0.712343i \(0.252366\pi\)
0.265992 + 0.963975i \(0.414301\pi\)
\(692\) 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 0.653741 0.756718i \(-0.273198\pi\)
−0.982208 + 0.187798i \(0.939865\pi\)
\(710\) 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 0.984067 0.177798i \(-0.0568975\pi\)
−0.646011 + 0.763328i \(0.723564\pi\)
\(720\) 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 0.623747 0.781626i \(-0.285609\pi\)
−0.988782 + 0.149368i \(0.952276\pi\)
\(734\) 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 0.221171 + 0.975235i \(0.429012\pi\)
−0.955164 + 0.296078i \(0.904321\pi\)
\(740\) 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 0.922688 0.385549i \(-0.125988\pi\)
−0.795239 + 0.606296i \(0.792654\pi\)
\(752\) 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 0.938520 0.345225i \(-0.112197\pi\)
−0.768234 + 0.640170i \(0.778864\pi\)
\(762\) 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 0.285576 + 0.958356i \(0.407815\pi\)
−0.972749 + 0.231862i \(0.925518\pi\)
\(774\) 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 −0.555638 0.831424i \(-0.687526\pi\)
0.997854 + 0.0654847i \(0.0208594\pi\)
\(788\) 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