Properties

Label 300.2.j.d.7.3
Level $300$
Weight $2$
Character 300.7
Analytic conductor $2.396$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.426337261060096.1
Defining polynomial: \(x^{12} - 4 x^{9} - 3 x^{8} + 4 x^{7} + 8 x^{6} + 8 x^{5} - 12 x^{4} - 32 x^{3} + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.3
Root \(-0.394157 - 1.35818i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.d.43.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.394157 - 1.35818i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.68928 + 1.07067i) q^{4} +(-0.681664 + 1.23909i) q^{6} +(-2.47817 + 2.47817i) q^{7} +(2.12000 + 1.87233i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.394157 - 1.35818i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.68928 + 1.07067i) q^{4} +(-0.681664 + 1.23909i) q^{6} +(-2.47817 + 2.47817i) q^{7} +(2.12000 + 1.87233i) q^{8} +1.00000i q^{9} +3.02831i q^{11} +(1.95158 + 0.437425i) q^{12} +(-0.363328 + 0.363328i) q^{13} +(4.34258 + 2.38900i) q^{14} +(1.70734 - 3.61732i) q^{16} +(2.36333 + 2.36333i) q^{17} +(1.35818 - 0.394157i) q^{18} -4.95634 q^{19} +3.50466 q^{21} +(4.11297 - 1.19363i) q^{22} +(0.900390 + 0.900390i) q^{23} +(-0.175128 - 2.82300i) q^{24} +(0.636672 + 0.350255i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.53303 - 6.83963i) q^{28} +3.50466i q^{29} +3.85607i q^{31} +(-5.58591 - 0.893077i) q^{32} +(2.14134 - 2.14134i) q^{33} +(2.27829 - 4.14134i) q^{34} +(-1.07067 - 1.68928i) q^{36} +(0.363328 + 0.363328i) q^{37} +(1.95358 + 6.73158i) q^{38} +0.513824 q^{39} +2.72666 q^{41} +(-1.38139 - 4.75995i) q^{42} +(-3.92870 - 3.92870i) q^{43} +(-3.24231 - 5.11566i) q^{44} +(0.867993 - 1.57778i) q^{46} +(-5.85673 + 5.85673i) q^{47} +(-3.76510 + 1.35056i) q^{48} -5.28267i q^{49} -3.34225i q^{51} +(0.224760 - 1.00277i) q^{52} +(-3.14134 + 3.14134i) q^{53} +(-1.23909 - 0.681664i) q^{54} +(-9.89367 + 0.613763i) q^{56} +(3.50466 + 3.50466i) q^{57} +(4.75995 - 1.38139i) q^{58} +8.68516 q^{59} -15.2920 q^{61} +(5.23723 - 1.51990i) q^{62} +(-2.47817 - 2.47817i) q^{63} +(0.988770 + 7.93866i) q^{64} +(-3.75233 - 2.06429i) q^{66} +(3.92870 - 3.92870i) q^{67} +(-6.52267 - 1.46199i) q^{68} -1.27334i q^{69} -4.25583i q^{71} +(-1.87233 + 2.12000i) q^{72} +(-9.28267 + 9.28267i) q^{73} +(0.350255 - 0.636672i) q^{74} +(8.37266 - 5.30660i) q^{76} +(-7.50466 - 7.50466i) q^{77} +(-0.202527 - 0.697863i) q^{78} +0.399759 q^{79} -1.00000 q^{81} +(-1.07473 - 3.70328i) q^{82} +(0.199879 + 0.199879i) q^{83} +(-5.92036 + 3.75233i) q^{84} +(-3.78734 + 6.88438i) q^{86} +(2.47817 - 2.47817i) q^{87} +(-5.66999 + 6.42000i) q^{88} +4.28267i q^{89} -1.80078i q^{91} +(-2.48503 - 0.556993i) q^{92} +(2.72666 - 2.72666i) q^{93} +(10.2629 + 5.64600i) q^{94} +(3.31834 + 4.58134i) q^{96} +(-6.73599 - 6.73599i) q^{97} +(-7.17480 + 2.08220i) q^{98} -3.02831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{6} + 12q^{8} + O(q^{10}) \) \( 12q - 4q^{6} + 12q^{8} + 8q^{12} + 4q^{13} + 12q^{16} + 20q^{17} - 12q^{22} + 16q^{26} + 4q^{28} - 20q^{32} - 8q^{33} + 4q^{36} - 4q^{37} - 16q^{38} + 16q^{41} - 20q^{42} - 40q^{46} - 16q^{48} + 8q^{52} - 4q^{53} - 64q^{56} + 20q^{58} - 32q^{61} + 56q^{62} - 24q^{66} + 16q^{68} + 12q^{72} - 44q^{73} + 8q^{76} - 48q^{77} + 24q^{78} - 12q^{81} - 16q^{82} + 64q^{86} - 60q^{88} - 56q^{92} + 16q^{93} + 44q^{96} + 20q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.394157 1.35818i −0.278711 0.960375i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.68928 + 1.07067i −0.844640 + 0.535334i
\(5\) 0 0
\(6\) −0.681664 + 1.23909i −0.278288 + 0.505855i
\(7\) −2.47817 + 2.47817i −0.936661 + 0.936661i −0.998110 0.0614493i \(-0.980428\pi\)
0.0614493 + 0.998110i \(0.480428\pi\)
\(8\) 2.12000 + 1.87233i 0.749532 + 0.661968i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 3.02831i 0.913069i 0.889706 + 0.456534i \(0.150909\pi\)
−0.889706 + 0.456534i \(0.849091\pi\)
\(12\) 1.95158 + 0.437425i 0.563372 + 0.126274i
\(13\) −0.363328 + 0.363328i −0.100769 + 0.100769i −0.755694 0.654925i \(-0.772700\pi\)
0.654925 + 0.755694i \(0.272700\pi\)
\(14\) 4.34258 + 2.38900i 1.16060 + 0.638488i
\(15\) 0 0
\(16\) 1.70734 3.61732i 0.426835 0.904330i
\(17\) 2.36333 + 2.36333i 0.573191 + 0.573191i 0.933019 0.359828i \(-0.117164\pi\)
−0.359828 + 0.933019i \(0.617164\pi\)
\(18\) 1.35818 0.394157i 0.320125 0.0929036i
\(19\) −4.95634 −1.13706 −0.568532 0.822661i \(-0.692488\pi\)
−0.568532 + 0.822661i \(0.692488\pi\)
\(20\) 0 0
\(21\) 3.50466 0.764780
\(22\) 4.11297 1.19363i 0.876888 0.254482i
\(23\) 0.900390 + 0.900390i 0.187744 + 0.187744i 0.794720 0.606976i \(-0.207618\pi\)
−0.606976 + 0.794720i \(0.707618\pi\)
\(24\) −0.175128 2.82300i −0.0357478 0.576243i
\(25\) 0 0
\(26\) 0.636672 + 0.350255i 0.124862 + 0.0686907i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 1.53303 6.83963i 0.289715 1.29257i
\(29\) 3.50466i 0.650800i 0.945576 + 0.325400i \(0.105499\pi\)
−0.945576 + 0.325400i \(0.894501\pi\)
\(30\) 0 0
\(31\) 3.85607i 0.692571i 0.938129 + 0.346286i \(0.112557\pi\)
−0.938129 + 0.346286i \(0.887443\pi\)
\(32\) −5.58591 0.893077i −0.987459 0.157875i
\(33\) 2.14134 2.14134i 0.372759 0.372759i
\(34\) 2.27829 4.14134i 0.390724 0.710233i
\(35\) 0 0
\(36\) −1.07067 1.68928i −0.178445 0.281547i
\(37\) 0.363328 + 0.363328i 0.0597308 + 0.0597308i 0.736341 0.676610i \(-0.236552\pi\)
−0.676610 + 0.736341i \(0.736552\pi\)
\(38\) 1.95358 + 6.73158i 0.316912 + 1.09201i
\(39\) 0.513824 0.0822776
\(40\) 0 0
\(41\) 2.72666 0.425832 0.212916 0.977070i \(-0.431704\pi\)
0.212916 + 0.977070i \(0.431704\pi\)
\(42\) −1.38139 4.75995i −0.213153 0.734476i
\(43\) −3.92870 3.92870i −0.599121 0.599121i 0.340958 0.940079i \(-0.389249\pi\)
−0.940079 + 0.340958i \(0.889249\pi\)
\(44\) −3.24231 5.11566i −0.488797 0.771215i
\(45\) 0 0
\(46\) 0.867993 1.57778i 0.127979 0.232631i
\(47\) −5.85673 + 5.85673i −0.854292 + 0.854292i −0.990659 0.136366i \(-0.956458\pi\)
0.136366 + 0.990659i \(0.456458\pi\)
\(48\) −3.76510 + 1.35056i −0.543446 + 0.194936i
\(49\) 5.28267i 0.754667i
\(50\) 0 0
\(51\) 3.34225i 0.468009i
\(52\) 0.224760 1.00277i 0.0311685 0.139059i
\(53\) −3.14134 + 3.14134i −0.431496 + 0.431496i −0.889137 0.457641i \(-0.848694\pi\)
0.457641 + 0.889137i \(0.348694\pi\)
\(54\) −1.23909 0.681664i −0.168618 0.0927627i
\(55\) 0 0
\(56\) −9.89367 + 0.613763i −1.32210 + 0.0820176i
\(57\) 3.50466 + 3.50466i 0.464204 + 0.464204i
\(58\) 4.75995 1.38139i 0.625012 0.181385i
\(59\) 8.68516 1.13071 0.565356 0.824847i \(-0.308739\pi\)
0.565356 + 0.824847i \(0.308739\pi\)
\(60\) 0 0
\(61\) −15.2920 −1.95794 −0.978970 0.204004i \(-0.934604\pi\)
−0.978970 + 0.204004i \(0.934604\pi\)
\(62\) 5.23723 1.51990i 0.665128 0.193027i
\(63\) −2.47817 2.47817i −0.312220 0.312220i
\(64\) 0.988770 + 7.93866i 0.123596 + 0.992333i
\(65\) 0 0
\(66\) −3.75233 2.06429i −0.461880 0.254096i
\(67\) 3.92870 3.92870i 0.479967 0.479967i −0.425154 0.905121i \(-0.639780\pi\)
0.905121 + 0.425154i \(0.139780\pi\)
\(68\) −6.52267 1.46199i −0.790989 0.177292i
\(69\) 1.27334i 0.153293i
\(70\) 0 0
\(71\) 4.25583i 0.505075i −0.967587 0.252537i \(-0.918735\pi\)
0.967587 0.252537i \(-0.0812650\pi\)
\(72\) −1.87233 + 2.12000i −0.220656 + 0.249844i
\(73\) −9.28267 + 9.28267i −1.08645 + 1.08645i −0.0905640 + 0.995891i \(0.528867\pi\)
−0.995891 + 0.0905640i \(0.971133\pi\)
\(74\) 0.350255 0.636672i 0.0407163 0.0740116i
\(75\) 0 0
\(76\) 8.37266 5.30660i 0.960410 0.608709i
\(77\) −7.50466 7.50466i −0.855236 0.855236i
\(78\) −0.202527 0.697863i −0.0229317 0.0790174i
\(79\) 0.399759 0.0449764 0.0224882 0.999747i \(-0.492841\pi\)
0.0224882 + 0.999747i \(0.492841\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −1.07473 3.70328i −0.118684 0.408959i
\(83\) 0.199879 + 0.199879i 0.0219396 + 0.0219396i 0.717991 0.696052i \(-0.245062\pi\)
−0.696052 + 0.717991i \(0.745062\pi\)
\(84\) −5.92036 + 3.75233i −0.645965 + 0.409413i
\(85\) 0 0
\(86\) −3.78734 + 6.88438i −0.408399 + 0.742362i
\(87\) 2.47817 2.47817i 0.265688 0.265688i
\(88\) −5.66999 + 6.42000i −0.604422 + 0.684374i
\(89\) 4.28267i 0.453962i 0.973899 + 0.226981i \(0.0728856\pi\)
−0.973899 + 0.226981i \(0.927114\pi\)
\(90\) 0 0
\(91\) 1.80078i 0.188773i
\(92\) −2.48503 0.556993i −0.259082 0.0580705i
\(93\) 2.72666 2.72666i 0.282741 0.282741i
\(94\) 10.2629 + 5.64600i 1.05854 + 0.582340i
\(95\) 0 0
\(96\) 3.31834 + 4.58134i 0.338676 + 0.467581i
\(97\) −6.73599 6.73599i −0.683936 0.683936i 0.276949 0.960885i \(-0.410677\pi\)
−0.960885 + 0.276949i \(0.910677\pi\)
\(98\) −7.17480 + 2.08220i −0.724764 + 0.210334i
\(99\) −3.02831 −0.304356
\(100\) 0 0
\(101\) 5.78734 0.575862 0.287931 0.957651i \(-0.407033\pi\)
0.287931 + 0.957651i \(0.407033\pi\)
\(102\) −4.53936 + 1.31737i −0.449464 + 0.130439i
\(103\) 13.0914 + 13.0914i 1.28993 + 1.28993i 0.934827 + 0.355104i \(0.115555\pi\)
0.355104 + 0.934827i \(0.384445\pi\)
\(104\) −1.45052 + 0.0899847i −0.142236 + 0.00882373i
\(105\) 0 0
\(106\) 5.50466 + 3.02831i 0.534660 + 0.294135i
\(107\) 9.71281 9.71281i 0.938973 0.938973i −0.0592694 0.998242i \(-0.518877\pi\)
0.998242 + 0.0592694i \(0.0188771\pi\)
\(108\) −0.437425 + 1.95158i −0.0420913 + 0.187791i
\(109\) 10.4626i 1.00214i −0.865407 0.501070i \(-0.832940\pi\)
0.865407 0.501070i \(-0.167060\pi\)
\(110\) 0 0
\(111\) 0.513824i 0.0487700i
\(112\) 4.73325 + 13.1954i 0.447251 + 1.24685i
\(113\) 10.6460 10.6460i 1.00149 1.00149i 0.00149259 0.999999i \(-0.499525\pi\)
0.999999 0.00149259i \(-0.000475108\pi\)
\(114\) 3.37856 6.14134i 0.316431 0.575189i
\(115\) 0 0
\(116\) −3.75233 5.92036i −0.348395 0.549692i
\(117\) −0.363328 0.363328i −0.0335897 0.0335897i
\(118\) −3.42331 11.7960i −0.315142 1.08591i
\(119\) −11.7135 −1.07377
\(120\) 0 0
\(121\) 1.82936 0.166305
\(122\) 6.02745 + 20.7692i 0.545699 + 1.88036i
\(123\) −1.92804 1.92804i −0.173845 0.173845i
\(124\) −4.12858 6.51399i −0.370757 0.584974i
\(125\) 0 0
\(126\) −2.38900 + 4.34258i −0.212829 + 0.386868i
\(127\) 1.77766 1.77766i 0.157742 0.157742i −0.623823 0.781565i \(-0.714422\pi\)
0.781565 + 0.623823i \(0.214422\pi\)
\(128\) 10.3924 4.47200i 0.918564 0.395273i
\(129\) 5.55602i 0.489180i
\(130\) 0 0
\(131\) 18.1981i 1.58997i −0.606626 0.794987i \(-0.707477\pi\)
0.606626 0.794987i \(-0.292523\pi\)
\(132\) −1.32466 + 5.90998i −0.115297 + 0.514398i
\(133\) 12.2827 12.2827i 1.06504 1.06504i
\(134\) −6.88438 3.78734i −0.594720 0.327176i
\(135\) 0 0
\(136\) 0.585320 + 9.43517i 0.0501908 + 0.809060i
\(137\) 5.91934 + 5.91934i 0.505724 + 0.505724i 0.913211 0.407487i \(-0.133595\pi\)
−0.407487 + 0.913211i \(0.633595\pi\)
\(138\) −1.72942 + 0.501897i −0.147218 + 0.0427243i
\(139\) 12.4140 1.05294 0.526470 0.850194i \(-0.323515\pi\)
0.526470 + 0.850194i \(0.323515\pi\)
\(140\) 0 0
\(141\) 8.28267 0.697527
\(142\) −5.78017 + 1.67747i −0.485061 + 0.140770i
\(143\) −1.10027 1.10027i −0.0920091 0.0920091i
\(144\) 3.61732 + 1.70734i 0.301443 + 0.142278i
\(145\) 0 0
\(146\) 16.2663 + 8.94867i 1.34621 + 0.740597i
\(147\) −3.73541 + 3.73541i −0.308092 + 0.308092i
\(148\) −1.00277 0.224760i −0.0824270 0.0184751i
\(149\) 5.78734i 0.474117i −0.971495 0.237059i \(-0.923817\pi\)
0.971495 0.237059i \(-0.0761833\pi\)
\(150\) 0 0
\(151\) 18.0708i 1.47058i 0.677751 + 0.735292i \(0.262955\pi\)
−0.677751 + 0.735292i \(0.737045\pi\)
\(152\) −10.5074 9.27990i −0.852265 0.752700i
\(153\) −2.36333 + 2.36333i −0.191064 + 0.191064i
\(154\) −7.23464 + 13.1507i −0.582984 + 1.05971i
\(155\) 0 0
\(156\) −0.867993 + 0.550135i −0.0694950 + 0.0440460i
\(157\) 3.91934 + 3.91934i 0.312798 + 0.312798i 0.845992 0.533195i \(-0.179009\pi\)
−0.533195 + 0.845992i \(0.679009\pi\)
\(158\) −0.157568 0.542943i −0.0125354 0.0431942i
\(159\) 4.44252 0.352315
\(160\) 0 0
\(161\) −4.46264 −0.351705
\(162\) 0.394157 + 1.35818i 0.0309679 + 0.106708i
\(163\) 3.22819 + 3.22819i 0.252851 + 0.252851i 0.822139 0.569287i \(-0.192781\pi\)
−0.569287 + 0.822139i \(0.692781\pi\)
\(164\) −4.60609 + 2.91934i −0.359675 + 0.227962i
\(165\) 0 0
\(166\) 0.192688 0.350255i 0.0149555 0.0271851i
\(167\) 6.95700 6.95700i 0.538349 0.538349i −0.384695 0.923044i \(-0.625693\pi\)
0.923044 + 0.384695i \(0.125693\pi\)
\(168\) 7.42988 + 6.56188i 0.573227 + 0.506260i
\(169\) 12.7360i 0.979691i
\(170\) 0 0
\(171\) 4.95634i 0.379021i
\(172\) 10.8430 + 2.43034i 0.826771 + 0.185312i
\(173\) −0.627343 + 0.627343i −0.0476960 + 0.0476960i −0.730553 0.682857i \(-0.760737\pi\)
0.682857 + 0.730553i \(0.260737\pi\)
\(174\) −4.34258 2.38900i −0.329210 0.181110i
\(175\) 0 0
\(176\) 10.9543 + 5.17035i 0.825715 + 0.389730i
\(177\) −6.14134 6.14134i −0.461611 0.461611i
\(178\) 5.81662 1.68804i 0.435974 0.126524i
\(179\) 8.93968 0.668183 0.334091 0.942541i \(-0.391571\pi\)
0.334091 + 0.942541i \(0.391571\pi\)
\(180\) 0 0
\(181\) −1.00933 −0.0750228 −0.0375114 0.999296i \(-0.511943\pi\)
−0.0375114 + 0.999296i \(0.511943\pi\)
\(182\) −2.44577 + 0.709789i −0.181293 + 0.0526131i
\(183\) 10.8131 + 10.8131i 0.799326 + 0.799326i
\(184\) 0.222998 + 3.59465i 0.0164396 + 0.265001i
\(185\) 0 0
\(186\) −4.77801 2.62855i −0.350341 0.192734i
\(187\) −7.15688 + 7.15688i −0.523363 + 0.523363i
\(188\) 3.62305 16.1643i 0.264238 1.17890i
\(189\) 3.50466i 0.254927i
\(190\) 0 0
\(191\) 21.6262i 1.56481i 0.622768 + 0.782407i \(0.286008\pi\)
−0.622768 + 0.782407i \(0.713992\pi\)
\(192\) 4.91431 6.31265i 0.354660 0.455576i
\(193\) −11.5653 + 11.5653i −0.832492 + 0.832492i −0.987857 0.155365i \(-0.950345\pi\)
0.155365 + 0.987857i \(0.450345\pi\)
\(194\) −6.49362 + 11.8037i −0.466214 + 0.847455i
\(195\) 0 0
\(196\) 5.65599 + 8.92392i 0.403999 + 0.637423i
\(197\) 9.42401 + 9.42401i 0.671433 + 0.671433i 0.958046 0.286614i \(-0.0925296\pi\)
−0.286614 + 0.958046i \(0.592530\pi\)
\(198\) 1.19363 + 4.11297i 0.0848274 + 0.292296i
\(199\) −11.0130 −0.780688 −0.390344 0.920669i \(-0.627644\pi\)
−0.390344 + 0.920669i \(0.627644\pi\)
\(200\) 0 0
\(201\) −5.55602 −0.391891
\(202\) −2.28112 7.86022i −0.160499 0.553043i
\(203\) −8.68516 8.68516i −0.609579 0.609579i
\(204\) 3.57844 + 5.64600i 0.250541 + 0.395299i
\(205\) 0 0
\(206\) 12.6203 22.9404i 0.879300 1.59834i
\(207\) −0.900390 + 0.900390i −0.0625814 + 0.0625814i
\(208\) 0.693949 + 1.93460i 0.0481167 + 0.134140i
\(209\) 15.0093i 1.03822i
\(210\) 0 0
\(211\) 27.9835i 1.92646i −0.268669 0.963232i \(-0.586584\pi\)
0.268669 0.963232i \(-0.413416\pi\)
\(212\) 1.94327 8.66993i 0.133464 0.595453i
\(213\) −3.00933 + 3.00933i −0.206196 + 0.206196i
\(214\) −17.0201 9.36333i −1.16347 0.640064i
\(215\) 0 0
\(216\) 2.82300 0.175128i 0.192081 0.0119159i
\(217\) −9.55602 9.55602i −0.648705 0.648705i
\(218\) −14.2101 + 4.12392i −0.962430 + 0.279307i
\(219\) 13.1277 0.887086
\(220\) 0 0
\(221\) −1.71733 −0.115520
\(222\) −0.697863 + 0.202527i −0.0468375 + 0.0135927i
\(223\) −8.53479 8.53479i −0.571531 0.571531i 0.361025 0.932556i \(-0.382427\pi\)
−0.932556 + 0.361025i \(0.882427\pi\)
\(224\) 16.0560 11.6297i 1.07279 0.777039i
\(225\) 0 0
\(226\) −18.6553 10.2629i −1.24093 0.682681i
\(227\) −1.02765 + 1.02765i −0.0682074 + 0.0682074i −0.740388 0.672180i \(-0.765358\pi\)
0.672180 + 0.740388i \(0.265358\pi\)
\(228\) −9.67269 2.16803i −0.640590 0.143581i
\(229\) 8.84802i 0.584693i 0.956312 + 0.292347i \(0.0944361\pi\)
−0.956312 + 0.292347i \(0.905564\pi\)
\(230\) 0 0
\(231\) 10.6132i 0.698297i
\(232\) −6.56188 + 7.42988i −0.430809 + 0.487795i
\(233\) 4.91002 4.91002i 0.321666 0.321666i −0.527740 0.849406i \(-0.676960\pi\)
0.849406 + 0.527740i \(0.176960\pi\)
\(234\) −0.350255 + 0.636672i −0.0228969 + 0.0416205i
\(235\) 0 0
\(236\) −14.6717 + 9.29892i −0.955045 + 0.605308i
\(237\) −0.282672 0.282672i −0.0183615 0.0183615i
\(238\) 4.61694 + 15.9089i 0.299272 + 1.03122i
\(239\) −19.0259 −1.23068 −0.615340 0.788262i \(-0.710981\pi\)
−0.615340 + 0.788262i \(0.710981\pi\)
\(240\) 0 0
\(241\) 2.90663 0.187232 0.0936161 0.995608i \(-0.470157\pi\)
0.0936161 + 0.995608i \(0.470157\pi\)
\(242\) −0.721054 2.48459i −0.0463511 0.159716i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 25.8325 16.3727i 1.65376 1.04815i
\(245\) 0 0
\(246\) −1.85866 + 3.37856i −0.118504 + 0.215409i
\(247\) 1.80078 1.80078i 0.114581 0.114581i
\(248\) −7.21984 + 8.17486i −0.458460 + 0.519104i
\(249\) 0.282672i 0.0179136i
\(250\) 0 0
\(251\) 2.77379i 0.175080i −0.996161 0.0875401i \(-0.972099\pi\)
0.996161 0.0875401i \(-0.0279006\pi\)
\(252\) 6.83963 + 1.53303i 0.430856 + 0.0965717i
\(253\) −2.72666 + 2.72666i −0.171423 + 0.171423i
\(254\) −3.11505 1.71370i −0.195456 0.107527i
\(255\) 0 0
\(256\) −10.1700 12.3520i −0.635624 0.771999i
\(257\) 2.08066 + 2.08066i 0.129788 + 0.129788i 0.769017 0.639229i \(-0.220746\pi\)
−0.639229 + 0.769017i \(0.720746\pi\)
\(258\) 7.54604 2.18994i 0.469796 0.136340i
\(259\) −1.80078 −0.111895
\(260\) 0 0
\(261\) −3.50466 −0.216933
\(262\) −24.7162 + 7.17290i −1.52697 + 0.443143i
\(263\) 4.75646 + 4.75646i 0.293296 + 0.293296i 0.838381 0.545085i \(-0.183503\pi\)
−0.545085 + 0.838381i \(0.683503\pi\)
\(264\) 8.54891 0.530340i 0.526149 0.0326402i
\(265\) 0 0
\(266\) −21.5233 11.8407i −1.31968 0.726001i
\(267\) 3.02831 3.02831i 0.185329 0.185329i
\(268\) −2.43034 + 10.8430i −0.148457 + 0.662342i
\(269\) 21.6846i 1.32214i 0.750326 + 0.661068i \(0.229896\pi\)
−0.750326 + 0.661068i \(0.770104\pi\)
\(270\) 0 0
\(271\) 3.15556i 0.191687i −0.995396 0.0958434i \(-0.969445\pi\)
0.995396 0.0958434i \(-0.0305548\pi\)
\(272\) 12.5839 4.51391i 0.763012 0.273696i
\(273\) −1.27334 + 1.27334i −0.0770663 + 0.0770663i
\(274\) 5.70636 10.3727i 0.344734 0.626635i
\(275\) 0 0
\(276\) 1.36333 + 2.15103i 0.0820627 + 0.129477i
\(277\) 3.53397 + 3.53397i 0.212336 + 0.212336i 0.805259 0.592923i \(-0.202026\pi\)
−0.592923 + 0.805259i \(0.702026\pi\)
\(278\) −4.89305 16.8604i −0.293466 1.01122i
\(279\) −3.85607 −0.230857
\(280\) 0 0
\(281\) 0.179969 0.0107361 0.00536804 0.999986i \(-0.498291\pi\)
0.00536804 + 0.999986i \(0.498291\pi\)
\(282\) −3.26467 11.2493i −0.194408 0.669887i
\(283\) −9.84007 9.84007i −0.584931 0.584931i 0.351323 0.936254i \(-0.385732\pi\)
−0.936254 + 0.351323i \(0.885732\pi\)
\(284\) 4.55658 + 7.18930i 0.270384 + 0.426606i
\(285\) 0 0
\(286\) −1.06068 + 1.92804i −0.0627193 + 0.114007i
\(287\) −6.75712 + 6.75712i −0.398860 + 0.398860i
\(288\) 0.893077 5.58591i 0.0526250 0.329153i
\(289\) 5.82936i 0.342903i
\(290\) 0 0
\(291\) 9.52612i 0.558431i
\(292\) 5.74238 25.6197i 0.336047 1.49928i
\(293\) −15.8680 + 15.8680i −0.927018 + 0.927018i −0.997512 0.0704942i \(-0.977542\pi\)
0.0704942 + 0.997512i \(0.477542\pi\)
\(294\) 6.54569 + 3.60101i 0.381752 + 0.210015i
\(295\) 0 0
\(296\) 0.0899847 + 1.45052i 0.00523026 + 0.0843100i
\(297\) 2.14134 + 2.14134i 0.124253 + 0.124253i
\(298\) −7.86022 + 2.28112i −0.455330 + 0.132142i
\(299\) −0.654274 −0.0378376
\(300\) 0 0
\(301\) 19.4720 1.12235
\(302\) 24.5434 7.12274i 1.41231 0.409868i
\(303\) −4.09226 4.09226i −0.235094 0.235094i
\(304\) −8.46216 + 17.9287i −0.485338 + 1.02828i
\(305\) 0 0
\(306\) 4.14134 + 2.27829i 0.236744 + 0.130241i
\(307\) −7.78477 + 7.78477i −0.444300 + 0.444300i −0.893454 0.449154i \(-0.851725\pi\)
0.449154 + 0.893454i \(0.351725\pi\)
\(308\) 20.7125 + 4.64248i 1.18020 + 0.264530i
\(309\) 18.5140i 1.05322i
\(310\) 0 0
\(311\) 7.05788i 0.400215i 0.979774 + 0.200108i \(0.0641292\pi\)
−0.979774 + 0.200108i \(0.935871\pi\)
\(312\) 1.08930 + 0.962047i 0.0616697 + 0.0544652i
\(313\) 11.3013 11.3013i 0.638789 0.638789i −0.311468 0.950257i \(-0.600821\pi\)
0.950257 + 0.311468i \(0.100821\pi\)
\(314\) 3.77832 6.86799i 0.213223 0.387583i
\(315\) 0 0
\(316\) −0.675305 + 0.428009i −0.0379889 + 0.0240774i
\(317\) −19.4754 19.4754i −1.09385 1.09385i −0.995114 0.0987310i \(-0.968522\pi\)
−0.0987310 0.995114i \(-0.531478\pi\)
\(318\) −1.75105 6.03372i −0.0981940 0.338354i
\(319\) −10.6132 −0.594225
\(320\) 0 0
\(321\) −13.7360 −0.766668
\(322\) 1.75898 + 6.06105i 0.0980241 + 0.337769i
\(323\) −11.7135 11.7135i −0.651755 0.651755i
\(324\) 1.68928 1.07067i 0.0938489 0.0594816i
\(325\) 0 0
\(326\) 3.11203 5.65685i 0.172359 0.313304i
\(327\) −7.39820 + 7.39820i −0.409122 + 0.409122i
\(328\) 5.78050 + 5.10520i 0.319175 + 0.281887i
\(329\) 29.0280i 1.60036i
\(330\) 0 0
\(331\) 15.0143i 0.825259i 0.910899 + 0.412630i \(0.135390\pi\)
−0.910899 + 0.412630i \(0.864610\pi\)
\(332\) −0.551657 0.123648i −0.0302761 0.00678607i
\(333\) −0.363328 + 0.363328i −0.0199103 + 0.0199103i
\(334\) −12.1910 6.70668i −0.667061 0.366973i
\(335\) 0 0
\(336\) 5.98365 12.6775i 0.326435 0.691614i
\(337\) 21.5840 + 21.5840i 1.17576 + 1.17576i 0.980815 + 0.194940i \(0.0624513\pi\)
0.194940 + 0.980815i \(0.437549\pi\)
\(338\) 17.2977 5.01997i 0.940871 0.273051i
\(339\) −15.0557 −0.817714
\(340\) 0 0
\(341\) −11.6774 −0.632365
\(342\) −6.73158 + 1.95358i −0.364002 + 0.105637i
\(343\) −4.25583 4.25583i −0.229793 0.229793i
\(344\) −0.973012 15.6846i −0.0524613 0.845659i
\(345\) 0 0
\(346\) 1.09931 + 0.604770i 0.0590995 + 0.0325127i
\(347\) −16.9969 + 16.9969i −0.912444 + 0.912444i −0.996464 0.0840201i \(-0.973224\pi\)
0.0840201 + 0.996464i \(0.473224\pi\)
\(348\) −1.53303 + 6.83963i −0.0821790 + 0.366643i
\(349\) 4.38538i 0.234744i −0.993088 0.117372i \(-0.962553\pi\)
0.993088 0.117372i \(-0.0374469\pi\)
\(350\) 0 0
\(351\) 0.513824i 0.0274259i
\(352\) 2.70451 16.9159i 0.144151 0.901618i
\(353\) 2.62734 2.62734i 0.139839 0.139839i −0.633722 0.773561i \(-0.718474\pi\)
0.773561 + 0.633722i \(0.218474\pi\)
\(354\) −5.92036 + 10.7617i −0.314664 + 0.571976i
\(355\) 0 0
\(356\) −4.58532 7.23464i −0.243021 0.383435i
\(357\) 8.28267 + 8.28267i 0.438366 + 0.438366i
\(358\) −3.52363 12.1416i −0.186230 0.641706i
\(359\) 34.9952 1.84697 0.923487 0.383630i \(-0.125326\pi\)
0.923487 + 0.383630i \(0.125326\pi\)
\(360\) 0 0
\(361\) 5.56534 0.292913
\(362\) 0.397834 + 1.37085i 0.0209097 + 0.0720500i
\(363\) −1.29355 1.29355i −0.0678939 0.0678939i
\(364\) 1.92804 + 3.04202i 0.101057 + 0.159445i
\(365\) 0 0
\(366\) 10.4240 18.9481i 0.544872 0.990433i
\(367\) −9.93581 + 9.93581i −0.518645 + 0.518645i −0.917161 0.398516i \(-0.869525\pi\)
0.398516 + 0.917161i \(0.369525\pi\)
\(368\) 4.79427 1.71973i 0.249918 0.0896469i
\(369\) 2.72666i 0.141944i
\(370\) 0 0
\(371\) 15.5695i 0.808330i
\(372\) −1.68674 + 7.52543i −0.0874536 + 0.390176i
\(373\) 7.08998 7.08998i 0.367105 0.367105i −0.499315 0.866421i \(-0.666415\pi\)
0.866421 + 0.499315i \(0.166415\pi\)
\(374\) 12.5412 + 6.89937i 0.648492 + 0.356758i
\(375\) 0 0
\(376\) −23.3820 + 1.45052i −1.20583 + 0.0748051i
\(377\) −1.27334 1.27334i −0.0655805 0.0655805i
\(378\) 4.75995 1.38139i 0.244825 0.0710509i
\(379\) 30.0388 1.54299 0.771495 0.636235i \(-0.219509\pi\)
0.771495 + 0.636235i \(0.219509\pi\)
\(380\) 0 0
\(381\) −2.51399 −0.128796
\(382\) 29.3721 8.52410i 1.50281 0.436131i
\(383\) 11.9133 + 11.9133i 0.608744 + 0.608744i 0.942618 0.333874i \(-0.108356\pi\)
−0.333874 + 0.942618i \(0.608356\pi\)
\(384\) −10.5107 4.18633i −0.536372 0.213633i
\(385\) 0 0
\(386\) 20.2663 + 11.1492i 1.03153 + 0.567480i
\(387\) 3.92870 3.92870i 0.199707 0.199707i
\(388\) 18.5910 + 4.16697i 0.943814 + 0.211546i
\(389\) 16.3340i 0.828168i 0.910239 + 0.414084i \(0.135898\pi\)
−0.910239 + 0.414084i \(0.864102\pi\)
\(390\) 0 0
\(391\) 4.25583i 0.215227i
\(392\) 9.89090 11.1992i 0.499566 0.565647i
\(393\) −12.8680 + 12.8680i −0.649104 + 0.649104i
\(394\) 9.08492 16.5140i 0.457692 0.831963i
\(395\) 0 0
\(396\) 5.11566 3.24231i 0.257072 0.162932i
\(397\) 19.1927 + 19.1927i 0.963253 + 0.963253i 0.999348 0.0360950i \(-0.0114919\pi\)
−0.0360950 + 0.999348i \(0.511492\pi\)
\(398\) 4.34083 + 14.9575i 0.217586 + 0.749753i
\(399\) −17.3703 −0.869604
\(400\) 0 0
\(401\) 26.5653 1.32661 0.663305 0.748349i \(-0.269153\pi\)
0.663305 + 0.748349i \(0.269153\pi\)
\(402\) 2.18994 + 7.54604i 0.109224 + 0.376362i
\(403\) −1.40102 1.40102i −0.0697898 0.0697898i
\(404\) −9.77644 + 6.19632i −0.486396 + 0.308278i
\(405\) 0 0
\(406\) −8.37266 + 15.2193i −0.415528 + 0.755321i
\(407\) −1.10027 + 1.10027i −0.0545383 + 0.0545383i
\(408\) 6.25779 7.08556i 0.309807 0.350787i
\(409\) 25.3947i 1.25569i 0.778339 + 0.627844i \(0.216062\pi\)
−0.778339 + 0.627844i \(0.783938\pi\)
\(410\) 0 0
\(411\) 8.37122i 0.412922i
\(412\) −36.1315 8.09849i −1.78007 0.398984i
\(413\) −21.5233 + 21.5233i −1.05909 + 1.05909i
\(414\) 1.57778 + 0.867993i 0.0775438 + 0.0426595i
\(415\) 0 0
\(416\) 2.35400 1.70504i 0.115414 0.0835964i
\(417\) −8.77801 8.77801i −0.429861 0.429861i
\(418\) −20.3853 + 5.91603i −0.997078 + 0.289362i
\(419\) −40.0788 −1.95798 −0.978988 0.203919i \(-0.934632\pi\)
−0.978988 + 0.203919i \(0.934632\pi\)
\(420\) 0 0
\(421\) 19.3947 0.945240 0.472620 0.881266i \(-0.343308\pi\)
0.472620 + 0.881266i \(0.343308\pi\)
\(422\) −38.0065 + 11.0299i −1.85013 + 0.536927i
\(423\) −5.85673 5.85673i −0.284764 0.284764i
\(424\) −12.5412 + 0.778008i −0.609056 + 0.0377834i
\(425\) 0 0
\(426\) 5.27334 + 2.90105i 0.255494 + 0.140556i
\(427\) 37.8962 37.8962i 1.83393 1.83393i
\(428\) −6.00847 + 26.8069i −0.290430 + 1.29576i
\(429\) 1.55602i 0.0751251i
\(430\) 0 0
\(431\) 15.8241i 0.762218i 0.924530 + 0.381109i \(0.124458\pi\)
−0.924530 + 0.381109i \(0.875542\pi\)
\(432\) −1.35056 3.76510i −0.0649788 0.181149i
\(433\) 21.1214 21.1214i 1.01503 1.01503i 0.0151424 0.999885i \(-0.495180\pi\)
0.999885 0.0151424i \(-0.00482018\pi\)
\(434\) −9.21218 + 16.7453i −0.442199 + 0.803801i
\(435\) 0 0
\(436\) 11.2020 + 17.6743i 0.536479 + 0.846447i
\(437\) −4.46264 4.46264i −0.213477 0.213477i
\(438\) −5.17436 17.8297i −0.247241 0.851936i
\(439\) 6.61188 0.315568 0.157784 0.987474i \(-0.449565\pi\)
0.157784 + 0.987474i \(0.449565\pi\)
\(440\) 0 0
\(441\) 5.28267 0.251556
\(442\) 0.676896 + 2.33243i 0.0321967 + 0.110942i
\(443\) 14.5419 + 14.5419i 0.690906 + 0.690906i 0.962431 0.271525i \(-0.0875280\pi\)
−0.271525 + 0.962431i \(0.587528\pi\)
\(444\) 0.550135 + 0.867993i 0.0261082 + 0.0411931i
\(445\) 0 0
\(446\) −8.22769 + 14.9558i −0.389593 + 0.708177i
\(447\) −4.09226 + 4.09226i −0.193557 + 0.193557i
\(448\) −22.1237 17.2230i −1.04525 0.813711i
\(449\) 33.6120i 1.58625i 0.609060 + 0.793124i \(0.291547\pi\)
−0.609060 + 0.793124i \(0.708453\pi\)
\(450\) 0 0
\(451\) 8.25715i 0.388814i
\(452\) −6.58575 + 29.3824i −0.309768 + 1.38203i
\(453\) 12.7780 12.7780i 0.600363 0.600363i
\(454\) 1.80078 + 0.990671i 0.0845148 + 0.0464945i
\(455\) 0 0
\(456\) 0.867993 + 13.9918i 0.0406475 + 0.655224i
\(457\) −15.5653 15.5653i −0.728116 0.728116i 0.242128 0.970244i \(-0.422155\pi\)
−0.970244 + 0.242128i \(0.922155\pi\)
\(458\) 12.0172 3.48751i 0.561525 0.162960i
\(459\) 3.34225 0.156003
\(460\) 0 0
\(461\) −26.1473 −1.21780 −0.608900 0.793247i \(-0.708389\pi\)
−0.608900 + 0.793247i \(0.708389\pi\)
\(462\) 14.4146 4.18326i 0.670627 0.194623i
\(463\) 5.77898 + 5.77898i 0.268572 + 0.268572i 0.828525 0.559953i \(-0.189181\pi\)
−0.559953 + 0.828525i \(0.689181\pi\)
\(464\) 12.6775 + 5.98365i 0.588538 + 0.277784i
\(465\) 0 0
\(466\) −8.60398 4.73335i −0.398572 0.219268i
\(467\) 2.25517 2.25517i 0.104357 0.104357i −0.653000 0.757357i \(-0.726490\pi\)
0.757357 + 0.653000i \(0.226490\pi\)
\(468\) 1.00277 + 0.224760i 0.0463529 + 0.0103895i
\(469\) 19.4720i 0.899132i
\(470\) 0 0
\(471\) 5.54279i 0.255398i
\(472\) 18.4125 + 16.2615i 0.847505 + 0.748495i
\(473\) 11.8973 11.8973i 0.547038 0.547038i
\(474\) −0.272501 + 0.495336i −0.0125164 + 0.0227515i
\(475\) 0 0
\(476\) 19.7873 12.5412i 0.906951 0.574827i
\(477\) −3.14134 3.14134i −0.143832 0.143832i
\(478\) 7.49917 + 25.8405i 0.343004 + 1.18191i
\(479\) −1.40102 −0.0640143 −0.0320071 0.999488i \(-0.510190\pi\)
−0.0320071 + 0.999488i \(0.510190\pi\)
\(480\) 0 0
\(481\) −0.264015 −0.0120380
\(482\) −1.14567 3.94771i −0.0521837 0.179813i
\(483\) 3.15556 + 3.15556i 0.143583 + 0.143583i
\(484\) −3.09030 + 1.95864i −0.140468 + 0.0890289i
\(485\) 0 0
\(486\) 0.681664 1.23909i 0.0309209 0.0562061i
\(487\) 0.978144 0.978144i 0.0443239 0.0443239i −0.684597 0.728921i \(-0.740022\pi\)
0.728921 + 0.684597i \(0.240022\pi\)
\(488\) −32.4190 28.6317i −1.46754 1.29609i
\(489\) 4.56534i 0.206452i
\(490\) 0 0
\(491\) 36.1134i 1.62978i 0.579619 + 0.814888i \(0.303201\pi\)
−0.579619 + 0.814888i \(0.696799\pi\)
\(492\) 5.32128 + 1.19271i 0.239902 + 0.0537715i
\(493\) −8.28267 + 8.28267i −0.373033 + 0.373033i
\(494\) −3.15556 1.73599i −0.141976 0.0781057i
\(495\) 0 0
\(496\) 13.9486 + 6.58363i 0.626313 + 0.295614i
\(497\) 10.5467 + 10.5467i 0.473084 + 0.473084i
\(498\) −0.383918 + 0.111417i −0.0172038 + 0.00499272i
\(499\) −6.35736 −0.284595 −0.142297 0.989824i \(-0.545449\pi\)
−0.142297 + 0.989824i \(0.545449\pi\)
\(500\) 0 0
\(501\) −9.83869 −0.439560
\(502\) −3.76730 + 1.09331i −0.168143 + 0.0487968i
\(503\) 17.1704 + 17.1704i 0.765592 + 0.765592i 0.977327 0.211735i \(-0.0679114\pi\)
−0.211735 + 0.977327i \(0.567911\pi\)
\(504\) −0.613763 9.89367i −0.0273392 0.440699i
\(505\) 0 0
\(506\) 4.77801 + 2.62855i 0.212408 + 0.116853i
\(507\) 9.00570 9.00570i 0.399957 0.399957i
\(508\) −1.09968 + 4.90626i −0.0487906 + 0.217680i
\(509\) 18.8739i 0.836572i −0.908315 0.418286i \(-0.862631\pi\)
0.908315 0.418286i \(-0.137369\pi\)
\(510\) 0 0
\(511\) 46.0081i 2.03528i
\(512\) −12.7676 + 18.6812i −0.564253 + 0.825602i
\(513\) −3.50466 + 3.50466i −0.154735 + 0.154735i
\(514\) 2.00579 3.64600i 0.0884717 0.160818i
\(515\) 0 0
\(516\) −5.94865 9.38567i −0.261875 0.413181i
\(517\) −17.7360 17.7360i −0.780028 0.780028i
\(518\) 0.709789 + 2.44577i 0.0311864 + 0.107461i
\(519\) 0.887197 0.0389436
\(520\) 0 0
\(521\) −33.9346 −1.48670 −0.743351 0.668901i \(-0.766765\pi\)
−0.743351 + 0.668901i \(0.766765\pi\)
\(522\) 1.38139 + 4.75995i 0.0604617 + 0.208337i
\(523\) 3.78345 + 3.78345i 0.165439 + 0.165439i 0.784971 0.619532i \(-0.212678\pi\)
−0.619532 + 0.784971i \(0.712678\pi\)
\(524\) 19.4841 + 30.7417i 0.851167 + 1.34296i
\(525\) 0 0
\(526\) 4.58532 8.33491i 0.199929 0.363419i
\(527\) −9.11317 + 9.11317i −0.396976 + 0.396976i
\(528\) −4.08991 11.4019i −0.177990 0.496203i
\(529\) 21.3786i 0.929504i
\(530\) 0 0
\(531\) 8.68516i 0.376904i
\(532\) −7.59822 + 33.8995i −0.329425 + 1.46973i
\(533\) −0.990671 + 0.990671i −0.0429107 + 0.0429107i
\(534\) −5.30660 2.91934i −0.229639 0.126332i
\(535\) 0 0
\(536\) 15.6846 0.973012i 0.677473 0.0420277i
\(537\) −6.32131 6.32131i −0.272784 0.272784i
\(538\) 29.4515 8.54715i 1.26975 0.368494i
\(539\) 15.9976 0.689063
\(540\) 0 0
\(541\) 28.4813 1.22451 0.612253 0.790662i \(-0.290263\pi\)
0.612253 + 0.790662i \(0.290263\pi\)
\(542\) −4.28581 + 1.24379i −0.184091 + 0.0534252i
\(543\) 0.713703 + 0.713703i 0.0306279 + 0.0306279i
\(544\) −11.0907 15.3120i −0.475510 0.656496i
\(545\) 0 0
\(546\) 2.23132 + 1.22753i 0.0954917 + 0.0525333i
\(547\) 0.726896 0.726896i 0.0310798 0.0310798i −0.691396 0.722476i \(-0.743004\pi\)
0.722476 + 0.691396i \(0.243004\pi\)
\(548\) −16.3371 3.66178i −0.697886 0.156424i
\(549\) 15.2920i 0.652647i
\(550\) 0 0
\(551\) 17.3703i 0.740001i
\(552\) 2.38412 2.69948i 0.101475 0.114898i
\(553\) −0.990671 + 0.990671i −0.0421276 + 0.0421276i
\(554\) 3.40681 6.19269i 0.144742 0.263102i
\(555\) 0 0
\(556\) −20.9707 + 13.2912i −0.889356 + 0.563675i
\(557\) 11.4427 + 11.4427i 0.484841 + 0.484841i 0.906674 0.421832i \(-0.138613\pi\)
−0.421832 + 0.906674i \(0.638613\pi\)
\(558\) 1.51990 + 5.23723i 0.0643424 + 0.221709i
\(559\) 2.85481 0.120746
\(560\) 0 0
\(561\) 10.1214 0.427324
\(562\) −0.0709362 0.244430i −0.00299226 0.0103107i
\(563\) −7.08426 7.08426i −0.298566 0.298566i 0.541886 0.840452i \(-0.317710\pi\)
−0.840452 + 0.541886i \(0.817710\pi\)
\(564\) −13.9918 + 8.86799i −0.589159 + 0.373410i
\(565\) 0 0
\(566\) −9.48601 + 17.2431i −0.398727 + 0.724780i
\(567\) 2.47817 2.47817i 0.104073 0.104073i
\(568\) 7.96832 9.02235i 0.334343 0.378569i
\(569\) 46.2427i 1.93860i −0.245890 0.969298i \(-0.579080\pi\)
0.245890 0.969298i \(-0.420920\pi\)
\(570\) 0 0
\(571\) 31.2381i 1.30727i −0.756808 0.653637i \(-0.773242\pi\)
0.756808 0.653637i \(-0.226758\pi\)
\(572\) 3.03669 + 0.680641i 0.126970 + 0.0284590i
\(573\) 15.2920 15.2920i 0.638833 0.638833i
\(574\) 11.8407 + 6.51399i 0.494222 + 0.271889i
\(575\) 0 0
\(576\) −7.93866 + 0.988770i −0.330778 + 0.0411988i
\(577\) −1.16131 1.16131i −0.0483461 0.0483461i 0.682520 0.730866i \(-0.260884\pi\)
−0.730866 + 0.682520i \(0.760884\pi\)
\(578\) −7.91729 + 2.29768i −0.329316 + 0.0955709i
\(579\) 16.3559 0.679727
\(580\) 0 0
\(581\) −0.990671 −0.0411000
\(582\) 12.9381 3.75479i 0.536303 0.155641i
\(583\) −9.51293 9.51293i −0.393985 0.393985i
\(584\) −37.0594 + 2.29902i −1.53353 + 0.0951341i
\(585\) 0 0
\(586\) 27.8060 + 15.2970i 1.14866 + 0.631915i
\(587\) 23.6268 23.6268i 0.975183 0.975183i −0.0245164 0.999699i \(-0.507805\pi\)
0.999699 + 0.0245164i \(0.00780461\pi\)
\(588\) 2.31077 10.3096i 0.0952947 0.425159i
\(589\) 19.1120i 0.787498i
\(590\) 0 0
\(591\) 13.3276i 0.548223i
\(592\) 1.93460 0.693949i 0.0795115 0.0285211i
\(593\) 0.260625 0.260625i 0.0107026 0.0107026i −0.701735 0.712438i \(-0.747591\pi\)
0.712438 + 0.701735i \(0.247591\pi\)
\(594\) 2.06429 3.75233i 0.0846988 0.153960i
\(595\) 0 0
\(596\) 6.19632 + 9.77644i 0.253811 + 0.400458i
\(597\) 7.78734 + 7.78734i 0.318714 + 0.318714i
\(598\) 0.257887 + 0.888619i 0.0105458 + 0.0363383i
\(599\) 33.0851 1.35182 0.675910 0.736984i \(-0.263751\pi\)
0.675910 + 0.736984i \(0.263751\pi\)
\(600\) 0 0
\(601\) −24.3200 −0.992033 −0.496016 0.868313i \(-0.665204\pi\)
−0.496016 + 0.868313i \(0.665204\pi\)
\(602\) −7.67501 26.4464i −0.312810 1.07787i
\(603\) 3.92870 + 3.92870i 0.159989 + 0.159989i
\(604\) −19.3479 30.5267i −0.787253 1.24211i
\(605\) 0 0
\(606\) −3.94502 + 7.17101i −0.160255 + 0.291302i
\(607\) −4.53347 + 4.53347i −0.184008 + 0.184008i −0.793100 0.609092i \(-0.791534\pi\)
0.609092 + 0.793100i \(0.291534\pi\)
\(608\) 27.6857 + 4.42639i 1.12280 + 0.179514i
\(609\) 12.2827i 0.497719i
\(610\) 0 0
\(611\) 4.25583i 0.172173i
\(612\) 1.46199 6.52267i 0.0590972 0.263663i
\(613\) 20.2793 20.2793i 0.819073 0.819073i −0.166901 0.985974i \(-0.553376\pi\)
0.985974 + 0.166901i \(0.0533761\pi\)
\(614\) 13.6415 + 7.50466i 0.550526 + 0.302864i
\(615\) 0 0
\(616\) −1.85866 29.9611i −0.0748877 1.20717i
\(617\) −17.1086 17.1086i −0.688768 0.688768i 0.273192 0.961960i \(-0.411921\pi\)
−0.961960 + 0.273192i \(0.911921\pi\)
\(618\) −25.1453 + 7.29742i −1.01149 + 0.293545i
\(619\) −29.4373 −1.18319 −0.591593 0.806237i \(-0.701501\pi\)
−0.591593 + 0.806237i \(0.701501\pi\)
\(620\) 0 0
\(621\) 1.27334 0.0510975
\(622\) 9.58583 2.78191i 0.384357 0.111544i
\(623\) −10.6132 10.6132i −0.425209 0.425209i
\(624\) 0.877272 1.85866i 0.0351190 0.0744061i
\(625\) 0 0
\(626\) −19.8037 10.8947i −0.791514 0.435439i
\(627\) −10.6132 + 10.6132i −0.423850 + 0.423850i
\(628\) −10.8172 2.42456i −0.431653 0.0967503i
\(629\) 1.71733i 0.0684743i
\(630\) 0 0
\(631\) 5.25710i 0.209282i 0.994510 + 0.104641i \(0.0333693\pi\)
−0.994510 + 0.104641i \(0.966631\pi\)
\(632\) 0.847487 + 0.748480i 0.0337112 + 0.0297729i
\(633\) −19.7873 + 19.7873i −0.786476 + 0.786476i
\(634\) −18.7746 + 34.1273i −0.745635 + 1.35537i
\(635\) 0 0
\(636\) −7.50466 + 4.75646i −0.297579 + 0.188606i
\(637\) 1.91934 + 1.91934i 0.0760472 + 0.0760472i
\(638\) 4.18326 + 14.4146i 0.165617 + 0.570679i
\(639\) 4.25583 0.168358
\(640\) 0 0
\(641\) 20.0773 0.793004 0.396502 0.918034i \(-0.370224\pi\)
0.396502 + 0.918034i \(0.370224\pi\)
\(642\) 5.41413 + 18.6559i 0.213679 + 0.736289i
\(643\) −9.28480 9.28480i −0.366157 0.366157i 0.499917 0.866073i \(-0.333364\pi\)
−0.866073 + 0.499917i \(0.833364\pi\)
\(644\) 7.53866 4.77801i 0.297065 0.188280i
\(645\) 0 0
\(646\) −11.2920 + 20.5259i −0.444278 + 0.807580i
\(647\) 28.7387 28.7387i 1.12983 1.12983i 0.139630 0.990204i \(-0.455409\pi\)
0.990204 0.139630i \(-0.0445912\pi\)
\(648\) −2.12000 1.87233i −0.0832813 0.0735520i
\(649\) 26.3013i 1.03242i
\(650\) 0 0
\(651\) 13.5142i 0.529665i
\(652\) −8.90963 1.99700i −0.348928 0.0782084i
\(653\) 11.9380 11.9380i 0.467170 0.467170i −0.433826 0.900996i \(-0.642837\pi\)
0.900996 + 0.433826i \(0.142837\pi\)
\(654\) 12.9641 + 7.13201i 0.506937 + 0.278884i
\(655\) 0 0
\(656\) 4.65533 9.86318i 0.181760 0.385093i
\(657\) −9.28267 9.28267i −0.362152 0.362152i
\(658\) −39.4251 + 11.4416i −1.53695 + 0.446039i
\(659\) 17.9963 0.701038 0.350519 0.936556i \(-0.386005\pi\)
0.350519 + 0.936556i \(0.386005\pi\)
\(660\) 0 0
\(661\) −9.06794 −0.352702 −0.176351 0.984327i \(-0.556429\pi\)
−0.176351 + 0.984327i \(0.556429\pi\)
\(662\) 20.3920 5.91798i 0.792558 0.230009i
\(663\) 1.21433 + 1.21433i 0.0471608 + 0.0471608i
\(664\) 0.0495037 + 0.797984i 0.00192112 + 0.0309678i
\(665\) 0 0
\(666\) 0.636672 + 0.350255i 0.0246705 + 0.0135721i
\(667\) −3.15556 + 3.15556i −0.122184 + 0.122184i
\(668\) −4.30369 + 19.2010i −0.166515 + 0.742908i
\(669\) 12.0700i 0.466654i
\(670\) 0 0
\(671\) 46.3089i 1.78773i
\(672\) −19.5767 3.12993i −0.755189 0.120740i
\(673\) −35.7640 + 35.7640i −1.37860 + 1.37860i −0.531611 + 0.846988i \(0.678413\pi\)
−0.846988 + 0.531611i \(0.821587\pi\)
\(674\) 20.8074 37.8223i 0.801470 1.45686i
\(675\) 0 0
\(676\) −13.6360 21.5147i −0.524462 0.827487i
\(677\) −16.2020 16.2020i −0.622694 0.622694i 0.323525 0.946219i \(-0.395132\pi\)
−0.946219 + 0.323525i \(0.895132\pi\)
\(678\) 5.93431 + 20.4483i 0.227906 + 0.785312i
\(679\) 33.3859 1.28123
\(680\) 0 0
\(681\) 1.45331 0.0556911
\(682\) 4.60272 + 15.8599i 0.176247 + 0.607308i
\(683\) 33.3943 + 33.3943i 1.27780 + 1.27780i 0.941899 + 0.335897i \(0.109039\pi\)
0.335897 + 0.941899i \(0.390961\pi\)
\(684\) 5.30660 + 8.37266i 0.202903 + 0.320137i
\(685\) 0 0
\(686\) −4.10270 + 7.45763i −0.156642 + 0.284734i
\(687\) 6.25649 6.25649i 0.238700 0.238700i
\(688\) −20.9190 + 7.50373i −0.797528 + 0.286077i
\(689\) 2.28267i 0.0869629i
\(690\) 0 0
\(691\) 24.6365i 0.937216i 0.883406 + 0.468608i \(0.155244\pi\)
−0.883406 + 0.468608i \(0.844756\pi\)
\(692\) 0.388082 1.73143i 0.0147527 0.0658193i
\(693\) 7.50466 7.50466i 0.285079 0.285079i
\(694\) 29.7843 + 16.3854i 1.13060 + 0.621980i
\(695\) 0 0
\(696\) 9.89367 0.613763i 0.375019 0.0232646i
\(697\) 6.44398 + 6.44398i 0.244083 + 0.244083i
\(698\) −5.95611 + 1.72853i −0.225442 + 0.0654256i
\(699\) −6.94381 −0.262639
\(700\) 0 0
\(701\) −23.0420 −0.870285 −0.435143 0.900362i \(-0.643302\pi\)
−0.435143 + 0.900362i \(0.643302\pi\)
\(702\) 0.697863 0.202527i 0.0263391 0.00764389i
\(703\) −1.80078 1.80078i −0.0679177 0.0679177i
\(704\) −24.0407 + 2.99430i −0.906068 + 0.112852i
\(705\) 0 0
\(706\) −4.60398 2.53281i −0.173273 0.0953235i
\(707\) −14.3420 + 14.3420i −0.539387 + 0.539387i
\(708\) 16.9498 + 3.79911i 0.637012 + 0.142779i
\(709\) 37.7360i 1.41720i −0.705608 0.708602i \(-0.749326\pi\)
0.705608 0.708602i \(-0.250674\pi\)
\(710\) 0 0
\(711\) 0.399759i 0.0149921i
\(712\) −8.01857 + 9.07925i −0.300509 + 0.340259i
\(713\) −3.47197 + 3.47197i −0.130026 + 0.130026i
\(714\) 7.98465 14.5140i 0.298818 0.543173i
\(715\) 0 0
\(716\) −15.1016 + 9.57143i −0.564374 + 0.357701i
\(717\) 13.4533 + 13.4533i 0.502423 + 0.502423i
\(718\) −13.7936 47.5296i −0.514772 1.77379i
\(719\) −41.3423 −1.54181 −0.770903 0.636953i \(-0.780195\pi\)
−0.770903 + 0.636953i \(0.780195\pi\)
\(720\) 0 0
\(721\) −64.8853 −2.41646
\(722\) −2.19362 7.55871i −0.0816380 0.281306i
\(723\) −2.05529 2.05529i −0.0764372 0.0764372i
\(724\) 1.70504 1.08066i 0.0633673 0.0401623i
\(725\) 0 0
\(726\) −1.24701 + 2.26673i −0.0462808 + 0.0841264i
\(727\) 9.48981 9.48981i 0.351958 0.351958i −0.508880 0.860838i \(-0.669940\pi\)
0.860838 + 0.508880i \(0.169940\pi\)
\(728\) 3.37165 3.81765i 0.124962 0.141491i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 18.5696i 0.686821i
\(732\) −29.8435 6.68911i −1.10305 0.247237i
\(733\) −3.21134 + 3.21134i −0.118614 + 0.118614i −0.763922 0.645308i \(-0.776729\pi\)
0.645308 + 0.763922i \(0.276729\pi\)
\(734\) 17.4108 + 9.57830i 0.642646 + 0.353542i
\(735\) 0 0
\(736\) −4.22538 5.83362i −0.155750 0.215030i
\(737\) 11.8973 + 11.8973i 0.438243 + 0.438243i
\(738\) 3.70328 1.07473i 0.136320 0.0395614i
\(739\) −25.3832 −0.933737 −0.466868 0.884327i \(-0.654618\pi\)
−0.466868 + 0.884327i \(0.654618\pi\)
\(740\) 0 0
\(741\) −2.54669 −0.0935549
\(742\) −21.1462 + 6.13684i −0.776300 + 0.225290i
\(743\) −32.7400 32.7400i −1.20111 1.20111i −0.973828 0.227285i \(-0.927015\pi\)
−0.227285 0.973828i \(-0.572985\pi\)
\(744\) 10.8857 0.675305i 0.399089 0.0247579i
\(745\) 0 0
\(746\) −12.4240 6.83488i −0.454875 0.250243i
\(747\) −0.199879 + 0.199879i −0.00731321 + 0.00731321i
\(748\) 4.42734 19.7526i 0.161880 0.722228i
\(749\) 48.1400i 1.75900i
\(750\) 0 0
\(751\) 24.4810i 0.893323i 0.894703 + 0.446662i \(0.147387\pi\)
−0.894703 + 0.446662i \(0.852613\pi\)
\(752\) 11.1862 + 31.1851i 0.407920 + 1.13720i
\(753\) −1.96137 + 1.96137i −0.0714762 + 0.0714762i
\(754\) −1.22753 + 2.23132i −0.0447039 + 0.0812599i
\(755\) 0 0
\(756\) −3.75233 5.92036i −0.136471 0.215322i
\(757\) −22.9473 22.9473i −0.834035 0.834035i 0.154031 0.988066i \(-0.450774\pi\)
−0.988066 + 0.154031i \(0.950774\pi\)
\(758\) −11.8400 40.7980i −0.430048 1.48185i
\(759\) 3.85607 0.139967
\(760\) 0 0
\(761\) 37.0466 1.34294 0.671470 0.741032i \(-0.265663\pi\)
0.671470 + 0.741032i \(0.265663\pi\)
\(762\) 0.990907 + 3.41444i 0.0358968 + 0.123692i
\(763\) 25.9282 + 25.9282i 0.938665 + 0.938665i
\(764\) −23.1544 36.5327i −0.837698 1.32170i
\(765\) 0 0
\(766\) 11.4847 20.8761i 0.414959 0.754286i
\(767\) −3.15556 + 3.15556i −0.113941 + 0.113941i
\(768\) −1.54291 + 15.9254i −0.0556749 + 0.574660i
\(769\) 6.62395i 0.238866i 0.992842 + 0.119433i \(0.0381077\pi\)
−0.992842 + 0.119433i \(0.961892\pi\)
\(770\) 0 0
\(771\) 2.94249i 0.105971i
\(772\) 7.15447 31.9198i 0.257495 1.14882i
\(773\) −16.2606 + 16.2606i −0.584854 + 0.584854i −0.936233 0.351379i \(-0.885713\pi\)
0.351379 + 0.936233i \(0.385713\pi\)
\(774\) −6.88438 3.78734i −0.247454 0.136133i
\(775\) 0 0
\(776\) −1.66829 26.8922i −0.0598880 0.965375i
\(777\) 1.27334 + 1.27334i 0.0456809 + 0.0456809i
\(778\) 22.1845 6.43817i 0.795352 0.230819i
\(779\) −13.5142 −0.484198
\(780\) 0 0
\(781\) 12.8880 0.461168
\(782\) 5.78017 1.67747i 0.206698 0.0599860i
\(783\) 2.47817 + 2.47817i 0.0885626 + 0.0885626i
\(784\) −19.1091 9.01932i −0.682468 0.322118i