Properties

Label 252.2.x.a.209.3
Level $252$
Weight $2$
Character 252.209
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 3 x^{14} - 9 x^{12} - 9 x^{10} + 225 x^{8} - 81 x^{6} - 729 x^{4} - 2187 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 209.3
Root \(-0.604587 + 1.62311i\) of defining polynomial
Character \(\chi\) \(=\) 252.209
Dual form 252.2.x.a.41.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.10336 - 1.33514i) q^{3} +(-0.266780 - 0.462077i) q^{5} +(-1.89325 - 1.84814i) q^{7} +(-0.565203 + 2.94628i) q^{9} +O(q^{10})\) \(q+(-1.10336 - 1.33514i) q^{3} +(-0.266780 - 0.462077i) q^{5} +(-1.89325 - 1.84814i) q^{7} +(-0.565203 + 2.94628i) q^{9} +(-3.39936 - 1.96262i) q^{11} +(0.116911 - 0.0674987i) q^{13} +(-0.322584 + 0.866025i) q^{15} -4.32533 q^{17} -2.22935i q^{19} +(-0.378597 + 4.56691i) q^{21} +(-1.70375 + 0.983658i) q^{23} +(2.35766 - 4.08358i) q^{25} +(4.55732 - 2.49617i) q^{27} +(-5.16548 - 2.98229i) q^{29} +(0.800341 - 0.462077i) q^{31} +(1.13033 + 6.70409i) q^{33} +(-0.348901 + 1.36787i) q^{35} +7.79871 q^{37} +(-0.219115 - 0.0816177i) q^{39} +(4.59027 + 7.95059i) q^{41} +(3.24544 - 5.62127i) q^{43} +(1.51219 - 0.524841i) q^{45} +(3.04329 - 5.27114i) q^{47} +(0.168767 + 6.99797i) q^{49} +(4.77238 + 5.77492i) q^{51} -11.0167i q^{53} +2.09435i q^{55} +(-2.97650 + 2.45977i) q^{57} +(1.89588 + 3.28377i) q^{59} +(9.35116 + 5.39889i) q^{61} +(6.51520 - 4.53345i) q^{63} +(-0.0623791 - 0.0360146i) q^{65} +(-5.75701 - 9.97144i) q^{67} +(3.19316 + 1.18941i) q^{69} +3.22884i q^{71} -0.381041i q^{73} +(-8.05350 + 1.35785i) q^{75} +(2.80863 + 9.99820i) q^{77} +(-4.60310 + 7.97280i) q^{79} +(-8.36109 - 3.33049i) q^{81} +(1.28020 - 2.21737i) q^{83} +(1.15391 + 1.99863i) q^{85} +(1.71759 + 10.1872i) q^{87} -17.1334 q^{89} +(-0.346088 - 0.0882763i) q^{91} +(-1.50000 - 0.558732i) q^{93} +(-1.03013 + 0.594746i) q^{95} +(-13.6747 - 7.89507i) q^{97} +(7.70375 - 8.90616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + O(q^{10}) \) \( 16q - q^{7} + 6q^{11} - 12q^{15} + 9q^{21} + 6q^{23} - 8q^{25} - 12q^{29} + 4q^{37} + 18q^{39} + 4q^{43} - 5q^{49} - 18q^{51} - 42q^{57} - 27q^{63} - 24q^{65} + 14q^{67} - 21q^{77} + 20q^{79} - 36q^{81} + 6q^{85} - 18q^{91} - 24q^{93} - 60q^{95} + 90q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\)

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
\(3\) −1.10336 1.33514i −0.637024 0.770844i
\(4\) 0 0
\(5\) −0.266780 0.462077i −0.119308 0.206647i 0.800186 0.599752i \(-0.204734\pi\)
−0.919494 + 0.393105i \(0.871401\pi\)
\(6\) 0 0
\(7\) −1.89325 1.84814i −0.715580 0.698531i
\(8\) 0 0
\(9\) −0.565203 + 2.94628i −0.188401 + 0.982092i
\(10\) 0 0
\(11\) −3.39936 1.96262i −1.02494 0.591752i −0.109412 0.993996i \(-0.534897\pi\)
−0.915532 + 0.402245i \(0.868230\pi\)
\(12\) 0 0
\(13\) 0.116911 0.0674987i 0.0324253 0.0187208i −0.483700 0.875234i \(-0.660707\pi\)
0.516125 + 0.856513i \(0.327374\pi\)
\(14\) 0 0
\(15\) −0.322584 + 0.866025i −0.0832908 + 0.223607i
\(16\) 0 0
\(17\) −4.32533 −1.04905 −0.524523 0.851396i \(-0.675756\pi\)
−0.524523 + 0.851396i \(0.675756\pi\)
\(18\) 0 0
\(19\) 2.22935i 0.511448i −0.966750 0.255724i \(-0.917686\pi\)
0.966750 0.255724i \(-0.0823138\pi\)
\(20\) 0 0
\(21\) −0.378597 + 4.56691i −0.0826167 + 0.996581i
\(22\) 0 0
\(23\) −1.70375 + 0.983658i −0.355255 + 0.205107i −0.666998 0.745060i \(-0.732421\pi\)
0.311742 + 0.950167i \(0.399088\pi\)
\(24\) 0 0
\(25\) 2.35766 4.08358i 0.471531 0.816716i
\(26\) 0 0
\(27\) 4.55732 2.49617i 0.877056 0.480388i
\(28\) 0 0
\(29\) −5.16548 2.98229i −0.959205 0.553798i −0.0632771 0.997996i \(-0.520155\pi\)
−0.895928 + 0.444198i \(0.853489\pi\)
\(30\) 0 0
\(31\) 0.800341 0.462077i 0.143745 0.0829915i −0.426402 0.904534i \(-0.640219\pi\)
0.570148 + 0.821542i \(0.306886\pi\)
\(32\) 0 0
\(33\) 1.13033 + 6.70409i 0.196766 + 1.16703i
\(34\) 0 0
\(35\) −0.348901 + 1.36787i −0.0589751 + 0.231213i
\(36\) 0 0
\(37\) 7.79871 1.28210 0.641050 0.767499i \(-0.278499\pi\)
0.641050 + 0.767499i \(0.278499\pi\)
\(38\) 0 0
\(39\) −0.219115 0.0816177i −0.0350865 0.0130693i
\(40\) 0 0
\(41\) 4.59027 + 7.95059i 0.716880 + 1.24167i 0.962230 + 0.272239i \(0.0877640\pi\)
−0.245349 + 0.969435i \(0.578903\pi\)
\(42\) 0 0
\(43\) 3.24544 5.62127i 0.494926 0.857236i −0.505057 0.863086i \(-0.668529\pi\)
0.999983 + 0.00584958i \(0.00186199\pi\)
\(44\) 0 0
\(45\) 1.51219 0.524841i 0.225424 0.0782387i
\(46\) 0 0
\(47\) 3.04329 5.27114i 0.443910 0.768874i −0.554066 0.832473i \(-0.686924\pi\)
0.997976 + 0.0635985i \(0.0202577\pi\)
\(48\) 0 0
\(49\) 0.168767 + 6.99797i 0.0241096 + 0.999709i
\(50\) 0 0
\(51\) 4.77238 + 5.77492i 0.668267 + 0.808651i
\(52\) 0 0
\(53\) 11.0167i 1.51326i −0.653845 0.756628i \(-0.726845\pi\)
0.653845 0.756628i \(-0.273155\pi\)
\(54\) 0 0
\(55\) 2.09435i 0.282402i
\(56\) 0 0
\(57\) −2.97650 + 2.45977i −0.394246 + 0.325804i
\(58\) 0 0
\(59\) 1.89588 + 3.28377i 0.246823 + 0.427510i 0.962643 0.270775i \(-0.0872801\pi\)
−0.715820 + 0.698285i \(0.753947\pi\)
\(60\) 0 0
\(61\) 9.35116 + 5.39889i 1.19729 + 0.691258i 0.959951 0.280168i \(-0.0903903\pi\)
0.237342 + 0.971426i \(0.423724\pi\)
\(62\) 0 0
\(63\) 6.51520 4.53345i 0.820838 0.571162i
\(64\) 0 0
\(65\) −0.0623791 0.0360146i −0.00773718 0.00446706i
\(66\) 0 0
\(67\) −5.75701 9.97144i −0.703331 1.21820i −0.967291 0.253671i \(-0.918362\pi\)
0.263960 0.964534i \(-0.414971\pi\)
\(68\) 0 0
\(69\) 3.19316 + 1.18941i 0.384412 + 0.143189i
\(70\) 0 0
\(71\) 3.22884i 0.383192i 0.981474 + 0.191596i \(0.0613664\pi\)
−0.981474 + 0.191596i \(0.938634\pi\)
\(72\) 0 0
\(73\) 0.381041i 0.0445975i −0.999751 0.0222988i \(-0.992901\pi\)
0.999751 0.0222988i \(-0.00709850\pi\)
\(74\) 0 0
\(75\) −8.05350 + 1.35785i −0.929938 + 0.156791i
\(76\) 0 0
\(77\) 2.80863 + 9.99820i 0.320073 + 1.13940i
\(78\) 0 0
\(79\) −4.60310 + 7.97280i −0.517889 + 0.897011i 0.481895 + 0.876229i \(0.339949\pi\)
−0.999784 + 0.0207814i \(0.993385\pi\)
\(80\) 0 0
\(81\) −8.36109 3.33049i −0.929010 0.370055i
\(82\) 0 0
\(83\) 1.28020 2.21737i 0.140520 0.243388i −0.787172 0.616733i \(-0.788456\pi\)
0.927693 + 0.373345i \(0.121789\pi\)
\(84\) 0 0
\(85\) 1.15391 + 1.99863i 0.125159 + 0.216782i
\(86\) 0 0
\(87\) 1.71759 + 10.1872i 0.184145 + 1.09218i
\(88\) 0 0
\(89\) −17.1334 −1.81614 −0.908068 0.418822i \(-0.862443\pi\)
−0.908068 + 0.418822i \(0.862443\pi\)
\(90\) 0 0
\(91\) −0.346088 0.0882763i −0.0362799 0.00925387i
\(92\) 0 0
\(93\) −1.50000 0.558732i −0.155543 0.0579378i
\(94\) 0 0
\(95\) −1.03013 + 0.594746i −0.105689 + 0.0610197i
\(96\) 0 0
\(97\) −13.6747 7.89507i −1.38845 0.801622i −0.395310 0.918548i \(-0.629363\pi\)
−0.993141 + 0.116925i \(0.962696\pi\)
\(98\) 0 0
\(99\) 7.70375 8.90616i 0.774256 0.895103i
\(100\) 0 0
\(101\) 7.36862 12.7628i 0.733205 1.26995i −0.222301 0.974978i \(-0.571357\pi\)
0.955506 0.294970i \(-0.0953098\pi\)
\(102\) 0 0
\(103\) 11.1442 6.43410i 1.09807 0.633970i 0.162356 0.986732i \(-0.448091\pi\)
0.935713 + 0.352762i \(0.114757\pi\)
\(104\) 0 0
\(105\) 2.21127 1.04342i 0.215797 0.101827i
\(106\) 0 0
\(107\) 15.7824i 1.52574i 0.646552 + 0.762870i \(0.276210\pi\)
−0.646552 + 0.762870i \(0.723790\pi\)
\(108\) 0 0
\(109\) −3.08340 −0.295336 −0.147668 0.989037i \(-0.547177\pi\)
−0.147668 + 0.989037i \(0.547177\pi\)
\(110\) 0 0
\(111\) −8.60477 10.4124i −0.816728 0.988299i
\(112\) 0 0
\(113\) 7.96173 4.59671i 0.748977 0.432422i −0.0763472 0.997081i \(-0.524326\pi\)
0.825324 + 0.564659i \(0.190992\pi\)
\(114\) 0 0
\(115\) 0.909051 + 0.524841i 0.0847694 + 0.0489417i
\(116\) 0 0
\(117\) 0.132791 + 0.382603i 0.0122765 + 0.0353717i
\(118\) 0 0
\(119\) 8.18891 + 7.99380i 0.750676 + 0.732791i
\(120\) 0 0
\(121\) 2.20375 + 3.81700i 0.200340 + 0.347000i
\(122\) 0 0
\(123\) 5.55044 14.9010i 0.500467 1.34358i
\(124\) 0 0
\(125\) −5.18371 −0.463645
\(126\) 0 0
\(127\) −10.1065 −0.896810 −0.448405 0.893831i \(-0.648008\pi\)
−0.448405 + 0.893831i \(0.648008\pi\)
\(128\) 0 0
\(129\) −11.0861 + 1.86915i −0.976075 + 0.164570i
\(130\) 0 0
\(131\) −7.81823 13.5416i −0.683082 1.18313i −0.974036 0.226395i \(-0.927306\pi\)
0.290954 0.956737i \(-0.406027\pi\)
\(132\) 0 0
\(133\) −4.12015 + 4.22071i −0.357262 + 0.365982i
\(134\) 0 0
\(135\) −2.36922 1.43990i −0.203910 0.123927i
\(136\) 0 0
\(137\) 2.13891 + 1.23490i 0.182739 + 0.105505i 0.588579 0.808440i \(-0.299688\pi\)
−0.405840 + 0.913944i \(0.633021\pi\)
\(138\) 0 0
\(139\) −16.8526 + 9.72984i −1.42942 + 0.825274i −0.997074 0.0764359i \(-0.975646\pi\)
−0.432342 + 0.901710i \(0.642313\pi\)
\(140\) 0 0
\(141\) −10.3956 + 1.75273i −0.875464 + 0.147606i
\(142\) 0 0
\(143\) −0.529897 −0.0443122
\(144\) 0 0
\(145\) 3.18247i 0.264289i
\(146\) 0 0
\(147\) 9.15706 7.94659i 0.755262 0.655423i
\(148\) 0 0
\(149\) 13.7303 7.92720i 1.12483 0.649422i 0.182201 0.983261i \(-0.441678\pi\)
0.942630 + 0.333840i \(0.108344\pi\)
\(150\) 0 0
\(151\) −4.16548 + 7.21482i −0.338982 + 0.587134i −0.984242 0.176829i \(-0.943416\pi\)
0.645260 + 0.763963i \(0.276749\pi\)
\(152\) 0 0
\(153\) 2.44469 12.7436i 0.197641 1.03026i
\(154\) 0 0
\(155\) −0.427030 0.246546i −0.0342999 0.0198031i
\(156\) 0 0
\(157\) 7.73794 4.46750i 0.617555 0.356545i −0.158362 0.987381i \(-0.550621\pi\)
0.775916 + 0.630836i \(0.217288\pi\)
\(158\) 0 0
\(159\) −14.7088 + 12.1553i −1.16649 + 0.963981i
\(160\) 0 0
\(161\) 5.04355 + 1.28645i 0.397487 + 0.101386i
\(162\) 0 0
\(163\) −14.2062 −1.11272 −0.556358 0.830943i \(-0.687802\pi\)
−0.556358 + 0.830943i \(0.687802\pi\)
\(164\) 0 0
\(165\) 2.79625 2.31082i 0.217688 0.179897i
\(166\) 0 0
\(167\) 6.27308 + 10.8653i 0.485425 + 0.840781i 0.999860 0.0167485i \(-0.00533145\pi\)
−0.514434 + 0.857530i \(0.671998\pi\)
\(168\) 0 0
\(169\) −6.49089 + 11.2425i −0.499299 + 0.864811i
\(170\) 0 0
\(171\) 6.56828 + 1.26004i 0.502289 + 0.0963573i
\(172\) 0 0
\(173\) 10.6787 18.4960i 0.811886 1.40623i −0.0996566 0.995022i \(-0.531774\pi\)
0.911543 0.411206i \(-0.134892\pi\)
\(174\) 0 0
\(175\) −12.0106 + 3.37395i −0.907920 + 0.255047i
\(176\) 0 0
\(177\) 2.29245 6.15444i 0.172311 0.462596i
\(178\) 0 0
\(179\) 5.81113i 0.434344i 0.976133 + 0.217172i \(0.0696833\pi\)
−0.976133 + 0.217172i \(0.930317\pi\)
\(180\) 0 0
\(181\) 7.38877i 0.549203i −0.961558 0.274602i \(-0.911454\pi\)
0.961558 0.274602i \(-0.0885460\pi\)
\(182\) 0 0
\(183\) −3.10939 18.4420i −0.229853 1.36327i
\(184\) 0 0
\(185\) −2.08054 3.60360i −0.152964 0.264942i
\(186\) 0 0
\(187\) 14.7033 + 8.48897i 1.07521 + 0.620775i
\(188\) 0 0
\(189\) −13.2414 3.69669i −0.963170 0.268894i
\(190\) 0 0
\(191\) 6.86109 + 3.96125i 0.496451 + 0.286626i 0.727247 0.686376i \(-0.240800\pi\)
−0.230796 + 0.973002i \(0.574133\pi\)
\(192\) 0 0
\(193\) 3.16548 + 5.48277i 0.227856 + 0.394659i 0.957173 0.289518i \(-0.0934951\pi\)
−0.729316 + 0.684177i \(0.760162\pi\)
\(194\) 0 0
\(195\) 0.0207419 + 0.123022i 0.00148536 + 0.00880979i
\(196\) 0 0
\(197\) 15.1580i 1.07996i 0.841677 + 0.539981i \(0.181569\pi\)
−0.841677 + 0.539981i \(0.818431\pi\)
\(198\) 0 0
\(199\) 8.55084i 0.606153i 0.952966 + 0.303076i \(0.0980137\pi\)
−0.952966 + 0.303076i \(0.901986\pi\)
\(200\) 0 0
\(201\) −6.96123 + 18.6885i −0.491007 + 1.31818i
\(202\) 0 0
\(203\) 4.26784 + 15.1927i 0.299544 + 1.06632i
\(204\) 0 0
\(205\) 2.44919 4.24212i 0.171059 0.296282i
\(206\) 0 0
\(207\) −1.93516 5.57567i −0.134503 0.387536i
\(208\) 0 0
\(209\) −4.37536 + 7.57835i −0.302650 + 0.524205i
\(210\) 0 0
\(211\) −2.80782 4.86329i −0.193299 0.334803i 0.753043 0.657971i \(-0.228585\pi\)
−0.946341 + 0.323169i \(0.895252\pi\)
\(212\) 0 0
\(213\) 4.31095 3.56256i 0.295382 0.244103i
\(214\) 0 0
\(215\) −3.46328 −0.236194
\(216\) 0 0
\(217\) −2.36922 0.604315i −0.160833 0.0410236i
\(218\) 0 0
\(219\) −0.508744 + 0.420425i −0.0343777 + 0.0284097i
\(220\) 0 0
\(221\) −0.505679 + 0.291954i −0.0340156 + 0.0196389i
\(222\) 0 0
\(223\) 6.00510 + 3.46705i 0.402131 + 0.232171i 0.687403 0.726276i \(-0.258751\pi\)
−0.285272 + 0.958447i \(0.592084\pi\)
\(224\) 0 0
\(225\) 10.6988 + 9.25436i 0.713254 + 0.616957i
\(226\) 0 0
\(227\) −7.28833 + 12.6238i −0.483743 + 0.837868i −0.999826 0.0186708i \(-0.994057\pi\)
0.516082 + 0.856539i \(0.327390\pi\)
\(228\) 0 0
\(229\) 21.2722 12.2815i 1.40571 0.811586i 0.410738 0.911753i \(-0.365271\pi\)
0.994971 + 0.100167i \(0.0319377\pi\)
\(230\) 0 0
\(231\) 10.2501 14.7815i 0.674406 0.972552i
\(232\) 0 0
\(233\) 10.5142i 0.688808i −0.938822 0.344404i \(-0.888081\pi\)
0.938822 0.344404i \(-0.111919\pi\)
\(234\) 0 0
\(235\) −3.24756 −0.211848
\(236\) 0 0
\(237\) 15.7237 2.65107i 1.02136 0.172205i
\(238\) 0 0
\(239\) 16.9075 9.76154i 1.09365 0.631422i 0.159108 0.987261i \(-0.449138\pi\)
0.934547 + 0.355839i \(0.115805\pi\)
\(240\) 0 0
\(241\) 11.3780 + 6.56909i 0.732922 + 0.423152i 0.819490 0.573093i \(-0.194257\pi\)
−0.0865685 + 0.996246i \(0.527590\pi\)
\(242\) 0 0
\(243\) 4.77860 + 14.8380i 0.306547 + 0.951855i
\(244\) 0 0
\(245\) 3.18857 1.94490i 0.203711 0.124255i
\(246\) 0 0
\(247\) −0.150478 0.260636i −0.00957469 0.0165838i
\(248\) 0 0
\(249\) −4.37303 + 0.737307i −0.277129 + 0.0467249i
\(250\) 0 0
\(251\) 22.6864 1.43195 0.715977 0.698124i \(-0.245981\pi\)
0.715977 + 0.698124i \(0.245981\pi\)
\(252\) 0 0
\(253\) 7.72218 0.485489
\(254\) 0 0
\(255\) 1.39528 3.74584i 0.0873758 0.234574i
\(256\) 0 0
\(257\) −6.80481 11.7863i −0.424472 0.735207i 0.571899 0.820324i \(-0.306207\pi\)
−0.996371 + 0.0851169i \(0.972874\pi\)
\(258\) 0 0
\(259\) −14.7649 14.4131i −0.917445 0.895586i
\(260\) 0 0
\(261\) 11.7062 13.5333i 0.724596 0.837692i
\(262\) 0 0
\(263\) 19.7930 + 11.4275i 1.22049 + 0.704651i 0.965023 0.262167i \(-0.0844371\pi\)
0.255468 + 0.966817i \(0.417770\pi\)
\(264\) 0 0
\(265\) −5.09055 + 2.93903i −0.312710 + 0.180543i
\(266\) 0 0
\(267\) 18.9043 + 22.8755i 1.15692 + 1.39996i
\(268\) 0 0
\(269\) −10.6775 −0.651018 −0.325509 0.945539i \(-0.605536\pi\)
−0.325509 + 0.945539i \(0.605536\pi\)
\(270\) 0 0
\(271\) 4.51473i 0.274251i 0.990554 + 0.137125i \(0.0437863\pi\)
−0.990554 + 0.137125i \(0.956214\pi\)
\(272\) 0 0
\(273\) 0.263998 + 0.559477i 0.0159779 + 0.0338611i
\(274\) 0 0
\(275\) −16.0290 + 9.25436i −0.966587 + 0.558059i
\(276\) 0 0
\(277\) 3.34952 5.80154i 0.201253 0.348581i −0.747679 0.664060i \(-0.768832\pi\)
0.948932 + 0.315479i \(0.102165\pi\)
\(278\) 0 0
\(279\) 0.909051 + 2.61919i 0.0544235 + 0.156807i
\(280\) 0 0
\(281\) −15.1414 8.74187i −0.903258 0.521496i −0.0250023 0.999687i \(-0.507959\pi\)
−0.878256 + 0.478191i \(0.841293\pi\)
\(282\) 0 0
\(283\) 7.42049 4.28422i 0.441102 0.254670i −0.262963 0.964806i \(-0.584700\pi\)
0.704065 + 0.710135i \(0.251366\pi\)
\(284\) 0 0
\(285\) 1.93067 + 0.719152i 0.114363 + 0.0425989i
\(286\) 0 0
\(287\) 6.00327 23.5359i 0.354362 1.38928i
\(288\) 0 0
\(289\) 1.70845 0.100497
\(290\) 0 0
\(291\) 4.54701 + 26.9687i 0.266550 + 1.58093i
\(292\) 0 0
\(293\) 12.1436 + 21.0333i 0.709434 + 1.22878i 0.965067 + 0.262002i \(0.0843826\pi\)
−0.255633 + 0.966774i \(0.582284\pi\)
\(294\) 0 0
\(295\) 1.01157 1.75209i 0.0588958 0.102010i
\(296\) 0 0
\(297\) −20.3910 0.458904i −1.18320 0.0266283i
\(298\) 0 0
\(299\) −0.132791 + 0.230001i −0.00767951 + 0.0133013i
\(300\) 0 0
\(301\) −16.5333 + 4.64443i −0.952965 + 0.267700i
\(302\) 0 0
\(303\) −25.1704 + 4.24381i −1.44600 + 0.243801i
\(304\) 0 0
\(305\) 5.76127i 0.329890i
\(306\) 0 0
\(307\) 12.4777i 0.712139i 0.934460 + 0.356069i \(0.115883\pi\)
−0.934460 + 0.356069i \(0.884117\pi\)
\(308\) 0 0
\(309\) −20.8864 7.77994i −1.18819 0.442586i
\(310\) 0 0
\(311\) −9.07984 15.7267i −0.514871 0.891782i −0.999851 0.0172571i \(-0.994507\pi\)
0.484980 0.874525i \(-0.338827\pi\)
\(312\) 0 0
\(313\) 2.76700 + 1.59753i 0.156400 + 0.0902977i 0.576157 0.817339i \(-0.304551\pi\)
−0.419757 + 0.907636i \(0.637885\pi\)
\(314\) 0 0
\(315\) −3.83293 1.80109i −0.215961 0.101480i
\(316\) 0 0
\(317\) −22.5893 13.0419i −1.26874 0.732508i −0.293991 0.955808i \(-0.594984\pi\)
−0.974750 + 0.223300i \(0.928317\pi\)
\(318\) 0 0
\(319\) 11.7062 + 20.2757i 0.655421 + 1.13522i
\(320\) 0 0
\(321\) 21.0717 17.4136i 1.17611 0.971933i
\(322\) 0 0
\(323\) 9.64266i 0.536532i
\(324\) 0 0
\(325\) 0.636555i 0.0353097i
\(326\) 0 0
\(327\) 3.40209 + 4.11677i 0.188136 + 0.227658i
\(328\) 0 0
\(329\) −15.5035 + 4.35514i −0.854736 + 0.240107i
\(330\) 0 0
\(331\) 8.06484 13.9687i 0.443283 0.767789i −0.554647 0.832085i \(-0.687147\pi\)
0.997931 + 0.0642960i \(0.0204802\pi\)
\(332\) 0 0
\(333\) −4.40786 + 22.9772i −0.241549 + 1.25914i
\(334\) 0 0
\(335\) −3.07171 + 5.32036i −0.167826 + 0.290683i
\(336\) 0 0
\(337\) −4.16548 7.21482i −0.226908 0.393016i 0.729982 0.683466i \(-0.239528\pi\)
−0.956890 + 0.290450i \(0.906195\pi\)
\(338\) 0 0
\(339\) −14.9219 5.55822i −0.810446 0.301881i
\(340\) 0 0
\(341\) −3.62752 −0.196441
\(342\) 0 0
\(343\) 12.6137 13.5608i 0.681075 0.732213i
\(344\) 0 0
\(345\) −0.302272 1.79280i −0.0162738 0.0965210i
\(346\) 0 0
\(347\) −30.1403 + 17.4015i −1.61801 + 0.934161i −0.630581 + 0.776124i \(0.717183\pi\)
−0.987433 + 0.158037i \(0.949483\pi\)
\(348\) 0 0
\(349\) −19.6825 11.3637i −1.05358 0.608283i −0.129929 0.991523i \(-0.541475\pi\)
−0.923649 + 0.383240i \(0.874808\pi\)
\(350\) 0 0
\(351\) 0.364313 0.599443i 0.0194456 0.0319959i
\(352\) 0 0
\(353\) 4.02829 6.97721i 0.214404 0.371359i −0.738684 0.674052i \(-0.764552\pi\)
0.953088 + 0.302693i \(0.0978856\pi\)
\(354\) 0 0
\(355\) 1.49197 0.861390i 0.0791856 0.0457178i
\(356\) 0 0
\(357\) 1.63756 19.7534i 0.0866687 1.04546i
\(358\) 0 0
\(359\) 17.8217i 0.940594i −0.882508 0.470297i \(-0.844147\pi\)
0.882508 0.470297i \(-0.155853\pi\)
\(360\) 0 0
\(361\) 14.0300 0.738421
\(362\) 0 0
\(363\) 2.66471 7.15383i 0.139861 0.375478i
\(364\) 0 0
\(365\) −0.176070 + 0.101654i −0.00921594 + 0.00532083i
\(366\) 0 0
\(367\) −20.5888 11.8870i −1.07473 0.620494i −0.145258 0.989394i \(-0.546401\pi\)
−0.929469 + 0.368900i \(0.879734\pi\)
\(368\) 0 0
\(369\) −26.0191 + 9.03052i −1.35450 + 0.470110i
\(370\) 0 0
\(371\) −20.3603 + 20.8573i −1.05706 + 1.08286i
\(372\) 0 0
\(373\) −5.26858 9.12545i −0.272797 0.472498i 0.696780 0.717285i \(-0.254615\pi\)
−0.969577 + 0.244787i \(0.921282\pi\)
\(374\) 0 0
\(375\) 5.71948 + 6.92098i 0.295353 + 0.357398i
\(376\) 0 0
\(377\) −0.805203 −0.0414700
\(378\) 0 0
\(379\) 24.0049 1.23305 0.616525 0.787336i \(-0.288540\pi\)
0.616525 + 0.787336i \(0.288540\pi\)
\(380\) 0 0
\(381\) 11.1511 + 13.4936i 0.571289 + 0.691301i
\(382\) 0 0
\(383\) −18.0980 31.3466i −0.924764 1.60174i −0.791941 0.610598i \(-0.790929\pi\)
−0.132823 0.991140i \(-0.542404\pi\)
\(384\) 0 0
\(385\) 3.87065 3.96512i 0.197267 0.202081i
\(386\) 0 0
\(387\) 14.7275 + 12.7391i 0.748640 + 0.647567i
\(388\) 0 0
\(389\) 18.6031 + 10.7405i 0.943215 + 0.544565i 0.890967 0.454069i \(-0.150028\pi\)
0.0522481 + 0.998634i \(0.483361\pi\)
\(390\) 0 0
\(391\) 7.36925 4.25464i 0.372679 0.215166i
\(392\) 0 0
\(393\) −9.45360 + 25.3796i −0.476871 + 1.28023i
\(394\) 0 0
\(395\) 4.91207 0.247153
\(396\) 0 0
\(397\) 21.3049i 1.06926i −0.845086 0.534630i \(-0.820451\pi\)
0.845086 0.534630i \(-0.179549\pi\)
\(398\) 0 0
\(399\) 10.1812 + 0.844025i 0.509699 + 0.0422541i
\(400\) 0 0
\(401\) 15.6821 9.05406i 0.783126 0.452138i −0.0544110 0.998519i \(-0.517328\pi\)
0.837537 + 0.546381i \(0.183995\pi\)
\(402\) 0 0
\(403\) 0.0623791 0.108044i 0.00310733 0.00538205i
\(404\) 0 0
\(405\) 0.691630 + 4.75198i 0.0343674 + 0.236128i
\(406\) 0 0
\(407\) −26.5106 15.3059i −1.31408 0.758685i
\(408\) 0 0
\(409\) −17.6807 + 10.2080i −0.874254 + 0.504751i −0.868760 0.495234i \(-0.835082\pi\)
−0.00549461 + 0.999985i \(0.501749\pi\)
\(410\) 0 0
\(411\) −0.711217 4.21828i −0.0350817 0.208073i
\(412\) 0 0
\(413\) 2.47948 9.72083i 0.122007 0.478331i
\(414\) 0 0
\(415\) −1.36613 −0.0670607
\(416\) 0 0
\(417\) 31.5851 + 11.7651i 1.54673 + 0.576138i
\(418\) 0 0
\(419\) −12.6789 21.9606i −0.619407 1.07284i −0.989594 0.143887i \(-0.954040\pi\)
0.370187 0.928957i \(-0.379294\pi\)
\(420\) 0 0
\(421\) −3.21875 + 5.57503i −0.156872 + 0.271710i −0.933739 0.357954i \(-0.883474\pi\)
0.776867 + 0.629665i \(0.216808\pi\)
\(422\) 0 0
\(423\) 13.8102 + 11.9456i 0.671472 + 0.580817i
\(424\) 0 0
\(425\) −10.1976 + 17.6628i −0.494658 + 0.856773i
\(426\) 0 0
\(427\) −7.72615 27.5037i −0.373895 1.33100i
\(428\) 0 0
\(429\) 0.584665 + 0.707487i 0.0282279 + 0.0341578i
\(430\) 0 0
\(431\) 15.1392i 0.729230i −0.931158 0.364615i \(-0.881201\pi\)
0.931158 0.364615i \(-0.118799\pi\)
\(432\) 0 0
\(433\) 8.44792i 0.405981i −0.979181 0.202991i \(-0.934934\pi\)
0.979181 0.202991i \(-0.0650661\pi\)
\(434\) 0 0
\(435\) 4.24904 3.51140i 0.203726 0.168359i
\(436\) 0 0
\(437\) 2.19292 + 3.79824i 0.104901 + 0.181695i
\(438\) 0 0
\(439\) 23.6831 + 13.6734i 1.13033 + 0.652598i 0.944018 0.329893i \(-0.107013\pi\)
0.186314 + 0.982490i \(0.440346\pi\)
\(440\) 0 0
\(441\) −20.7133 3.45804i −0.986349 0.164669i
\(442\) 0 0
\(443\) −14.6520 8.45931i −0.696135 0.401914i 0.109771 0.993957i \(-0.464988\pi\)
−0.805906 + 0.592043i \(0.798322\pi\)
\(444\) 0 0
\(445\) 4.57085 + 7.91695i 0.216679 + 0.375299i
\(446\) 0 0
\(447\) −25.7334 9.58537i −1.21715 0.453372i
\(448\) 0 0
\(449\) 22.5985i 1.06649i 0.845962 + 0.533244i \(0.179027\pi\)
−0.845962 + 0.533244i \(0.820973\pi\)
\(450\) 0 0
\(451\) 36.0358i 1.69686i
\(452\) 0 0
\(453\) 14.2288 2.39903i 0.668528 0.112716i
\(454\) 0 0
\(455\) 0.0515391 + 0.183470i 0.00241619 + 0.00860120i
\(456\) 0 0
\(457\) 17.4018 30.1408i 0.814022 1.40993i −0.0960053 0.995381i \(-0.530607\pi\)
0.910028 0.414547i \(-0.136060\pi\)
\(458\) 0 0
\(459\) −19.7119 + 10.7968i −0.920072 + 0.503949i
\(460\) 0 0
\(461\) −13.8264 + 23.9479i −0.643958 + 1.11537i 0.340584 + 0.940214i \(0.389375\pi\)
−0.984541 + 0.175153i \(0.943958\pi\)
\(462\) 0 0
\(463\) 10.6272 + 18.4069i 0.493889 + 0.855440i 0.999975 0.00704260i \(-0.00224175\pi\)
−0.506087 + 0.862483i \(0.668908\pi\)
\(464\) 0 0
\(465\) 0.141993 + 0.842174i 0.00658478 + 0.0390549i
\(466\) 0 0
\(467\) 8.80757 0.407566 0.203783 0.979016i \(-0.434676\pi\)
0.203783 + 0.979016i \(0.434676\pi\)
\(468\) 0 0
\(469\) −7.52915 + 29.5181i −0.347664 + 1.36302i
\(470\) 0 0
\(471\) −14.5025 5.40199i −0.668238 0.248910i
\(472\) 0 0
\(473\) −22.0648 + 12.7391i −1.01454 + 0.585746i
\(474\) 0 0
\(475\) −9.10373 5.25604i −0.417708 0.241164i
\(476\) 0 0
\(477\) 32.4582 + 6.22666i 1.48616 + 0.285099i
\(478\) 0 0
\(479\) −6.83139 + 11.8323i −0.312134 + 0.540633i −0.978824 0.204703i \(-0.934377\pi\)
0.666690 + 0.745335i \(0.267711\pi\)
\(480\) 0 0
\(481\) 0.911756 0.526403i 0.0415725 0.0240019i
\(482\) 0 0
\(483\) −3.84724 8.15326i −0.175056 0.370986i
\(484\) 0 0
\(485\) 8.42499i 0.382559i
\(486\) 0 0
\(487\) 16.6206 0.753149 0.376575 0.926386i \(-0.377102\pi\)
0.376575 + 0.926386i \(0.377102\pi\)
\(488\) 0 0
\(489\) 15.6745 + 18.9673i 0.708826 + 0.857730i
\(490\) 0 0
\(491\) 17.8129 10.2843i 0.803883 0.464122i −0.0409440 0.999161i \(-0.513037\pi\)
0.844827 + 0.535039i \(0.179703\pi\)
\(492\) 0 0
\(493\) 22.3424 + 12.8994i 1.00625 + 0.580959i
\(494\) 0 0
\(495\) −6.17054 1.18373i −0.277345 0.0532049i
\(496\) 0 0
\(497\) 5.96734 6.11299i 0.267672 0.274205i
\(498\) 0 0
\(499\) 1.34609 + 2.33149i 0.0602592 + 0.104372i 0.894581 0.446905i \(-0.147474\pi\)
−0.834322 + 0.551277i \(0.814141\pi\)
\(500\) 0 0
\(501\) 7.58524 20.3637i 0.338884 0.909785i
\(502\) 0 0
\(503\) 27.3871 1.22113 0.610566 0.791965i \(-0.290942\pi\)
0.610566 + 0.791965i \(0.290942\pi\)
\(504\) 0 0
\(505\) −7.86321 −0.349908
\(506\) 0 0
\(507\) 22.1722 3.73830i 0.984700 0.166024i
\(508\) 0 0
\(509\) 2.96117 + 5.12890i 0.131252 + 0.227334i 0.924159 0.382007i \(-0.124767\pi\)
−0.792908 + 0.609342i \(0.791434\pi\)
\(510\) 0 0
\(511\) −0.704217 + 0.721405i −0.0311527 + 0.0319131i
\(512\) 0 0
\(513\) −5.56484 10.1598i −0.245693 0.448568i
\(514\) 0 0
\(515\) −5.94609 3.43298i −0.262016 0.151275i
\(516\) 0 0
\(517\) −20.6905 + 11.9456i −0.909966 + 0.525369i
\(518\) 0 0
\(519\) −36.4772 + 6.15019i −1.60117 + 0.269963i
\(520\) 0 0
\(521\) 39.1886 1.71688 0.858442 0.512911i \(-0.171433\pi\)
0.858442 + 0.512911i \(0.171433\pi\)
\(522\) 0 0
\(523\) 23.0358i 1.00728i 0.863912 + 0.503642i \(0.168007\pi\)
−0.863912 + 0.503642i \(0.831993\pi\)
\(524\) 0 0
\(525\) 17.7567 + 12.3132i 0.774968 + 0.537394i
\(526\) 0 0
\(527\) −3.46173 + 1.99863i −0.150796 + 0.0870618i
\(528\) 0 0
\(529\) −9.56484 + 16.5668i −0.415862 + 0.720295i
\(530\) 0 0
\(531\) −10.7464 + 3.72980i −0.466356 + 0.161860i
\(532\) 0 0
\(533\) 1.07331 + 0.619675i 0.0464901 + 0.0268411i
\(534\) 0 0
\(535\) 7.29267 4.21043i 0.315290 0.182033i
\(536\) 0 0
\(537\) 7.75868 6.41176i 0.334812 0.276688i
\(538\) 0 0
\(539\) 13.1606 24.1198i 0.566869 1.03891i
\(540\) 0 0
\(541\) −3.32605 −0.142998 −0.0714990 0.997441i \(-0.522778\pi\)
−0.0714990 + 0.997441i \(0.522778\pi\)
\(542\) 0 0
\(543\) −9.86505 + 8.15246i −0.423350 + 0.349856i
\(544\) 0 0
\(545\) 0.822590 + 1.42477i 0.0352359 + 0.0610303i
\(546\) 0 0
\(547\) 13.8937 24.0646i 0.594051 1.02893i −0.399629 0.916677i \(-0.630861\pi\)
0.993680 0.112249i \(-0.0358055\pi\)
\(548\) 0 0
\(549\) −21.1919 + 24.4996i −0.904450 + 1.04562i
\(550\) 0 0
\(551\) −6.64857 + 11.5157i −0.283238 + 0.490583i
\(552\) 0 0
\(553\) 23.4497 6.58732i 0.997181 0.280121i
\(554\) 0 0
\(555\) −2.51574 + 6.75388i −0.106787 + 0.286686i
\(556\) 0 0
\(557\) 3.61667i 0.153243i 0.997060 + 0.0766216i \(0.0244133\pi\)
−0.997060 + 0.0766216i \(0.975587\pi\)
\(558\) 0 0
\(559\) 0.876252i 0.0370615i
\(560\) 0 0
\(561\) −4.88906 28.9974i −0.206416 1.22427i
\(562\) 0 0
\(563\) −4.75452 8.23506i −0.200379 0.347067i 0.748272 0.663393i \(-0.230884\pi\)
−0.948651 + 0.316326i \(0.897551\pi\)
\(564\) 0 0
\(565\) −4.24807 2.45262i −0.178718 0.103183i
\(566\) 0 0
\(567\) 9.67440 + 21.7579i 0.406287 + 0.913746i
\(568\) 0 0
\(569\) 9.09742 + 5.25240i 0.381384 + 0.220192i 0.678420 0.734674i \(-0.262665\pi\)
−0.297036 + 0.954866i \(0.595998\pi\)
\(570\) 0 0
\(571\) −2.24201 3.88328i −0.0938252 0.162510i 0.815292 0.579049i \(-0.196576\pi\)
−0.909118 + 0.416539i \(0.863243\pi\)
\(572\) 0 0
\(573\) −2.28141 13.5312i −0.0953071 0.565274i
\(574\) 0 0
\(575\) 9.27651i 0.386857i
\(576\) 0 0
\(577\) 47.1812i 1.96418i 0.188410 + 0.982090i \(0.439667\pi\)
−0.188410 + 0.982090i \(0.560333\pi\)
\(578\) 0 0
\(579\) 3.82762 10.2758i 0.159070 0.427049i
\(580\) 0 0
\(581\) −6.52175 + 1.83205i −0.270568 + 0.0760061i
\(582\) 0 0
\(583\) −21.6215 + 37.4496i −0.895473 + 1.55100i
\(584\) 0 0
\(585\) 0.141366 0.163431i 0.00584476 0.00675702i
\(586\) 0 0
\(587\) 5.65373 9.79255i 0.233354 0.404182i −0.725439 0.688287i \(-0.758363\pi\)
0.958793 + 0.284105i \(0.0916964\pi\)
\(588\) 0 0
\(589\) −1.03013 1.78424i −0.0424458 0.0735183i
\(590\) 0 0
\(591\) 20.2381 16.7247i 0.832483 0.687962i
\(592\) 0 0
\(593\) 9.44980 0.388057 0.194028 0.980996i \(-0.437845\pi\)
0.194028 + 0.980996i \(0.437845\pi\)
\(594\) 0 0
\(595\) 1.50911 5.91649i 0.0618676 0.242553i
\(596\) 0 0
\(597\) 11.4166 9.43463i 0.467249 0.386134i
\(598\) 0 0
\(599\) 31.6406 18.2677i 1.29280 0.746398i 0.313650 0.949539i \(-0.398448\pi\)
0.979150 + 0.203140i \(0.0651147\pi\)
\(600\) 0 0
\(601\) 1.92247 + 1.10994i 0.0784193 + 0.0452754i 0.538697 0.842500i \(-0.318917\pi\)
−0.460278 + 0.887775i \(0.652250\pi\)
\(602\) 0 0
\(603\) 32.6325 11.3259i 1.32890 0.461225i
\(604\) 0 0
\(605\) 1.17583 2.03660i 0.0478043 0.0827995i
\(606\) 0 0
\(607\) 1.71759 0.991653i 0.0697149 0.0402499i −0.464737 0.885449i \(-0.653851\pi\)
0.534452 + 0.845199i \(0.320518\pi\)
\(608\) 0 0
\(609\) 15.5755 22.4612i 0.631151 0.910173i
\(610\) 0 0
\(611\) 0.821673i 0.0332413i
\(612\) 0 0
\(613\) −23.1365 −0.934476 −0.467238 0.884132i \(-0.654751\pi\)
−0.467238 + 0.884132i \(0.654751\pi\)
\(614\) 0 0
\(615\) −8.36616 + 1.41056i −0.337356 + 0.0568794i
\(616\) 0 0
\(617\) −1.19807 + 0.691704i −0.0482323 + 0.0278470i −0.523922 0.851766i \(-0.675532\pi\)
0.475690 + 0.879613i \(0.342198\pi\)
\(618\) 0 0
\(619\) 5.22550 + 3.01694i 0.210031 + 0.121261i 0.601326 0.799004i \(-0.294639\pi\)
−0.391295 + 0.920265i \(0.627973\pi\)
\(620\) 0 0
\(621\) −5.30913 + 8.73568i −0.213048 + 0.350551i
\(622\) 0 0
\(623\) 32.4378 + 31.6649i 1.29959 + 1.26863i
\(624\) 0 0
\(625\) −10.4054 18.0226i −0.416215 0.720905i
\(626\) 0 0
\(627\) 14.9458 2.51990i 0.596876 0.100635i
\(628\) 0 0
\(629\) −33.7320 −1.34498
\(630\) 0 0
\(631\) −20.4727 −0.815004 −0.407502 0.913204i \(-0.633600\pi\)
−0.407502 + 0.913204i \(0.633600\pi\)
\(632\) 0 0
\(633\) −3.39515 + 9.11479i −0.134945 + 0.362280i
\(634\) 0 0
\(635\) 2.69622 + 4.67000i 0.106996 + 0.185323i
\(636\) 0 0
\(637\) 0.492084 + 0.806748i 0.0194971 + 0.0319645i
\(638\) 0 0
\(639\) −9.51305 1.82495i −0.376330 0.0721939i
\(640\) 0 0
\(641\) 40.2246 + 23.2237i 1.58878 + 0.917281i 0.993509 + 0.113754i \(0.0362877\pi\)
0.595269 + 0.803527i \(0.297046\pi\)
\(642\) 0 0
\(643\) 9.74133 5.62416i 0.384161 0.221795i −0.295466 0.955353i \(-0.595475\pi\)
0.679627 + 0.733558i \(0.262142\pi\)
\(644\) 0 0
\(645\) 3.82124 + 4.62397i 0.150461 + 0.182069i
\(646\) 0 0
\(647\) −4.65015 −0.182816 −0.0914081 0.995814i \(-0.529137\pi\)
−0.0914081 + 0.995814i \(0.529137\pi\)
\(648\) 0 0
\(649\) 14.8836i 0.584232i
\(650\) 0 0
\(651\) 1.80726 + 3.83002i 0.0708320 + 0.150111i
\(652\) 0 0
\(653\) 2.99966 1.73186i 0.117386 0.0677727i −0.440157 0.897921i \(-0.645077\pi\)
0.557543 + 0.830148i \(0.311744\pi\)
\(654\) 0 0
\(655\) −4.17150 + 7.22524i −0.162994 + 0.282314i
\(656\) 0 0
\(657\) 1.12265 + 0.215366i 0.0437989 + 0.00840222i
\(658\) 0 0
\(659\) −1.59819 0.922715i −0.0622566 0.0359439i 0.468549 0.883438i \(-0.344777\pi\)
−0.530805 + 0.847494i \(0.678110\pi\)
\(660\) 0 0
\(661\) 17.5196 10.1149i 0.681433 0.393426i −0.118962 0.992899i \(-0.537957\pi\)
0.800395 + 0.599473i \(0.204623\pi\)
\(662\) 0 0
\(663\) 0.947744 + 0.353023i 0.0368073 + 0.0137103i
\(664\) 0 0
\(665\) 3.04947 + 0.777823i 0.118253 + 0.0301627i
\(666\) 0 0
\(667\) 11.7342 0.454351
\(668\) 0 0
\(669\) −1.99678 11.8430i −0.0771999 0.457879i
\(670\) 0 0
\(671\) −21.1919 36.7055i −0.818106 1.41700i
\(672\) 0 0
\(673\) −7.31596 + 12.6716i −0.282009 + 0.488455i −0.971880 0.235478i \(-0.924334\pi\)
0.689870 + 0.723933i \(0.257668\pi\)
\(674\) 0 0
\(675\) 0.551272 24.4953i 0.0212185 0.942824i
\(676\) 0 0
\(677\) 7.71449 13.3619i 0.296492 0.513539i −0.678839 0.734287i \(-0.737517\pi\)
0.975331 + 0.220748i \(0.0708499\pi\)
\(678\) 0 0
\(679\) 11.2983 + 40.2200i 0.433590 + 1.54350i
\(680\) 0 0
\(681\) 24.8961 4.19757i 0.954022 0.160851i
\(682\) 0 0
\(683\) 15.7197i 0.601499i −0.953703 0.300750i \(-0.902763\pi\)
0.953703 0.300750i \(-0.0972368\pi\)
\(684\) 0 0
\(685\) 1.31779i 0.0503501i
\(686\) 0 0
\(687\) −39.8685 14.8505i −1.52108 0.566582i
\(688\) 0 0
\(689\) −0.743611 1.28797i −0.0283293 0.0490678i
\(690\) 0 0
\(691\) −41.5878 24.0107i −1.58207 0.913411i −0.994556 0.104199i \(-0.966772\pi\)
−0.587517 0.809212i \(-0.699894\pi\)
\(692\) 0 0
\(693\) −31.0449 + 2.62397i −1.17930 + 0.0996766i
\(694\) 0 0
\(695\) 8.99187 + 5.19146i 0.341081 + 0.196923i
\(696\) 0 0
\(697\) −19.8544 34.3889i −0.752040 1.30257i
\(698\) 0 0
\(699\) −14.0379 + 11.6009i −0.530963 + 0.438787i
\(700\) 0 0
\(701\) 24.7005i 0.932923i 0.884541 + 0.466462i \(0.154471\pi\)
−0.884541 + 0.466462i \(0.845529\pi\)
\(702\) 0 0
\(703\) 17.3860i 0.655727i
\(704\) 0 0
\(705\) 3.58322 + 4.33595i 0.134952 + 0.163301i
\(706\) 0 0
\(707\) −37.5381 + 10.5449i −1.41176 + 0.396583i
\(708\) 0 0
\(709\) −17.0432 + 29.5196i −0.640070 + 1.10863i 0.345347 + 0.938475i \(0.387761\pi\)
−0.985417 + 0.170159i \(0.945572\pi\)
\(710\) 0 0
\(711\) −20.8884 18.0683i −0.783376 0.677613i
\(712\) 0 0
\(713\) −0.909051 + 1.57452i −0.0340442 + 0.0589663i
\(714\) 0 0
\(715\) 0.141366 + 0.244853i 0.00528679 + 0.00915698i
\(716\) 0 0
\(717\) −31.6880 11.8034i −1.18341 0.440806i
\(718\) 0 0
\(719\) 18.4758 0.689032 0.344516 0.938780i \(-0.388043\pi\)
0.344516 + 0.938780i \(0.388043\pi\)
\(720\) 0 0
\(721\) −32.9898 8.41466i −1.22860 0.313378i
\(722\) 0 0
\(723\) −3.78334 22.4393i −0.140704 0.834526i
\(724\) 0 0
\(725\) −24.3569 + 14.0624i −0.904591 + 0.522266i
\(726\) 0 0
\(727\) 39.2911 + 22.6847i 1.45723 + 0.841330i 0.998874 0.0474398i \(-0.0151062\pi\)
0.458353 + 0.888770i \(0.348440\pi\)
\(728\) 0 0
\(729\) 14.5383 22.7517i 0.538454 0.842655i
\(730\) 0 0
\(731\) −14.0376 + 24.3138i −0.519200 + 0.899280i
\(732\) 0 0
\(733\) −43.3683 + 25.0387i −1.60184 + 0.924825i −0.610724 + 0.791843i \(0.709122\pi\)
−0.991119 + 0.132981i \(0.957545\pi\)
\(734\) 0 0
\(735\) −6.11486 2.11127i −0.225550 0.0778755i
\(736\) 0 0
\(737\) 45.1953i 1.66479i
\(738\) 0 0
\(739\) −16.9404 −0.623163 −0.311582 0.950219i \(-0.600859\pi\)
−0.311582 + 0.950219i \(0.600859\pi\)
\(740\) 0 0
\(741\) −0.181954 + 0.488484i −0.00668426 + 0.0179449i
\(742\) 0 0
\(743\) 34.4723 19.9026i 1.26467 0.730156i 0.290693 0.956816i \(-0.406114\pi\)
0.973974 + 0.226661i \(0.0727808\pi\)
\(744\) 0 0
\(745\) −7.32595 4.22964i −0.268402 0.154962i
\(746\) 0 0
\(747\) 5.80942 + 5.02509i 0.212556 + 0.183859i
\(748\) 0 0
\(749\) 29.1680 29.8799i 1.06578 1.09179i
\(750\) 0 0
\(751\) 14.7028 + 25.4659i 0.536512 + 0.929265i 0.999089 + 0.0426862i \(0.0135916\pi\)
−0.462577 + 0.886579i \(0.653075\pi\)
\(752\) 0 0
\(753\) −25.0312 30.2896i −0.912189 1.10381i
\(754\) 0 0
\(755\) 4.44507 0.161773
\(756\) 0 0
\(757\) −27.4010 −0.995908 −0.497954 0.867203i \(-0.665915\pi\)
−0.497954 + 0.867203i \(0.665915\pi\)
\(758\) 0 0
\(759\) −8.52033 10.3102i −0.309268 0.374237i
\(760\) 0 0
\(761\) 6.11067 + 10.5840i 0.221511 + 0.383669i 0.955267 0.295744i \(-0.0955676\pi\)
−0.733756 + 0.679413i \(0.762234\pi\)
\(762\) 0 0
\(763\) 5.83763 + 5.69855i 0.211337 + 0.206301i
\(764\) 0 0
\(765\) −6.54072 + 2.27011i −0.236480 + 0.0820759i
\(766\) 0 0
\(767\) 0.443300 + 0.255939i 0.0160066 + 0.00924143i
\(768\) 0 0
\(769\) 29.4039 16.9764i 1.06033 0.612184i 0.134809 0.990872i \(-0.456958\pi\)
0.925524 + 0.378688i \(0.123625\pi\)
\(770\) 0 0
\(771\) −8.22820 + 22.0898i −0.296331 + 0.795546i
\(772\) 0 0
\(773\) −30.2094 −1.08656 −0.543279 0.839552i \(-0.682817\pi\)
−0.543279 + 0.839552i \(0.682817\pi\)
\(774\) 0 0
\(775\) 4.35767i 0.156532i
\(776\) 0 0
\(777\) −2.95257 + 35.6160i −0.105923 + 1.27772i
\(778\) 0 0
\(779\) 17.7246 10.2333i 0.635051 0.366647i
\(780\) 0 0
\(781\) 6.33698 10.9760i 0.226755 0.392751i
\(782\) 0 0
\(783\) −30.9850 0.697326i −1.10731 0.0249204i
\(784\) 0 0
\(785\) −4.12866 2.38368i −0.147358 0.0850772i
\(786\) 0 0
\(787\) −33.3310 + 19.2436i −1.18812 + 0.685962i −0.957879 0.287172i \(-0.907285\pi\)
−0.230241 + 0.973134i \(0.573952\pi\)
\(788\) 0 0
\(789\) −6.58145 39.0351i −0.234306 1.38969i
\(790\) 0 0
\(791\) −23.5689 6.01168i −0.838013 0.213751i
\(792\) 0 0
\(793\) 1.45767 0.0517635
\(794\) 0 0
\(795\) 9.54072 + 3.55380i 0.338375 + 0.126040i
\(796\) 0 0