Properties

Label 1260.2.c.e.811.7
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.7
Root \(0.309204 - 1.38000i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.e.811.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} -1.00000i q^{5} +(2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +O(q^{10})\) \(q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} -1.00000i q^{5} +(2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +(-1.38000 + 0.309204i) q^{10} -0.987080i q^{11} +4.69157i q^{13} +(-0.709355 - 3.67380i) q^{14} +(2.54341 - 3.08724i) q^{16} -3.93531i q^{17} -0.223896 q^{19} +(0.853401 + 1.80879i) q^{20} +(-1.36217 + 0.305209i) q^{22} +5.88128i q^{23} -1.00000 q^{25} +(6.47436 - 1.45065i) q^{26} +(-4.85050 + 2.11486i) q^{28} +10.2502 q^{29} +2.77439 q^{31} +(-5.04682 - 2.55532i) q^{32} +(-5.43072 + 1.21681i) q^{34} +(0.0785232 - 2.64459i) q^{35} +8.26915 q^{37} +(0.0692296 + 0.308976i) q^{38} +(2.23224 - 1.73698i) q^{40} +7.34910i q^{41} -4.32318i q^{43} +(0.842376 + 1.78542i) q^{44} +(8.11616 - 1.81852i) q^{46} -2.40779 q^{47} +(6.98767 + 0.415323i) q^{49} +(0.309204 + 1.38000i) q^{50} +(-4.00380 - 8.48605i) q^{52} +8.35002 q^{53} -0.987080 q^{55} +(4.41830 + 6.03976i) q^{56} +(-3.16941 - 14.1453i) q^{58} -13.9829 q^{59} +4.93374i q^{61} +(-0.857851 - 3.82865i) q^{62} +(-1.96583 + 7.75471i) q^{64} +4.69157 q^{65} -7.84723i q^{67} +(3.35840 + 7.11814i) q^{68} +(-3.67380 + 0.709355i) q^{70} -8.49881i q^{71} -14.4665i q^{73} +(-2.55685 - 11.4114i) q^{74} +(0.404980 - 0.191073i) q^{76} +(0.0775087 - 2.61042i) q^{77} -11.5183i q^{79} +(-3.08724 - 2.54341i) q^{80} +(10.1417 - 2.27237i) q^{82} +1.67114 q^{83} -3.93531 q^{85} +(-5.96597 + 1.33674i) q^{86} +(2.20340 - 1.71453i) q^{88} -0.493375i q^{89} +(-0.368398 + 12.4073i) q^{91} +(-5.01910 - 10.6380i) q^{92} +(0.744498 + 3.32274i) q^{94} +0.223896i q^{95} -4.31036i q^{97} +(-1.58747 - 9.77138i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309204 1.38000i −0.218640 0.975806i
\(3\) 0 0
\(4\) −1.80879 + 0.853401i −0.904393 + 0.426701i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 2.64459 + 0.0785232i 0.999559 + 0.0296790i
\(8\) 1.73698 + 2.23224i 0.614114 + 0.789218i
\(9\) 0 0
\(10\) −1.38000 + 0.309204i −0.436394 + 0.0977789i
\(11\) 0.987080i 0.297616i −0.988866 0.148808i \(-0.952456\pi\)
0.988866 0.148808i \(-0.0475436\pi\)
\(12\) 0 0
\(13\) 4.69157i 1.30121i 0.759417 + 0.650604i \(0.225484\pi\)
−0.759417 + 0.650604i \(0.774516\pi\)
\(14\) −0.709355 3.67380i −0.189583 0.981865i
\(15\) 0 0
\(16\) 2.54341 3.08724i 0.635853 0.771810i
\(17\) 3.93531i 0.954453i −0.878780 0.477227i \(-0.841642\pi\)
0.878780 0.477227i \(-0.158358\pi\)
\(18\) 0 0
\(19\) −0.223896 −0.0513653 −0.0256826 0.999670i \(-0.508176\pi\)
−0.0256826 + 0.999670i \(0.508176\pi\)
\(20\) 0.853401 + 1.80879i 0.190826 + 0.404457i
\(21\) 0 0
\(22\) −1.36217 + 0.305209i −0.290415 + 0.0650708i
\(23\) 5.88128i 1.22633i 0.789954 + 0.613166i \(0.210104\pi\)
−0.789954 + 0.613166i \(0.789896\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 6.47436 1.45065i 1.26973 0.284497i
\(27\) 0 0
\(28\) −4.85050 + 2.11486i −0.916659 + 0.399671i
\(29\) 10.2502 1.90342 0.951710 0.307000i \(-0.0993252\pi\)
0.951710 + 0.307000i \(0.0993252\pi\)
\(30\) 0 0
\(31\) 2.77439 0.498295 0.249147 0.968466i \(-0.419850\pi\)
0.249147 + 0.968466i \(0.419850\pi\)
\(32\) −5.04682 2.55532i −0.892160 0.451720i
\(33\) 0 0
\(34\) −5.43072 + 1.21681i −0.931361 + 0.208682i
\(35\) 0.0785232 2.64459i 0.0132728 0.447017i
\(36\) 0 0
\(37\) 8.26915 1.35944 0.679720 0.733472i \(-0.262101\pi\)
0.679720 + 0.733472i \(0.262101\pi\)
\(38\) 0.0692296 + 0.308976i 0.0112305 + 0.0501225i
\(39\) 0 0
\(40\) 2.23224 1.73698i 0.352949 0.274640i
\(41\) 7.34910i 1.14774i 0.818948 + 0.573868i \(0.194558\pi\)
−0.818948 + 0.573868i \(0.805442\pi\)
\(42\) 0 0
\(43\) 4.32318i 0.659278i −0.944107 0.329639i \(-0.893073\pi\)
0.944107 0.329639i \(-0.106927\pi\)
\(44\) 0.842376 + 1.78542i 0.126993 + 0.269162i
\(45\) 0 0
\(46\) 8.11616 1.81852i 1.19666 0.268126i
\(47\) −2.40779 −0.351212 −0.175606 0.984461i \(-0.556188\pi\)
−0.175606 + 0.984461i \(0.556188\pi\)
\(48\) 0 0
\(49\) 6.98767 + 0.415323i 0.998238 + 0.0593318i
\(50\) 0.309204 + 1.38000i 0.0437280 + 0.195161i
\(51\) 0 0
\(52\) −4.00380 8.48605i −0.555227 1.17680i
\(53\) 8.35002 1.14696 0.573482 0.819218i \(-0.305592\pi\)
0.573482 + 0.819218i \(0.305592\pi\)
\(54\) 0 0
\(55\) −0.987080 −0.133098
\(56\) 4.41830 + 6.03976i 0.590420 + 0.807096i
\(57\) 0 0
\(58\) −3.16941 14.1453i −0.416164 1.85737i
\(59\) −13.9829 −1.82042 −0.910210 0.414147i \(-0.864080\pi\)
−0.910210 + 0.414147i \(0.864080\pi\)
\(60\) 0 0
\(61\) 4.93374i 0.631700i 0.948809 + 0.315850i \(0.102290\pi\)
−0.948809 + 0.315850i \(0.897710\pi\)
\(62\) −0.857851 3.82865i −0.108947 0.486239i
\(63\) 0 0
\(64\) −1.96583 + 7.75471i −0.245729 + 0.969339i
\(65\) 4.69157 0.581918
\(66\) 0 0
\(67\) 7.84723i 0.958692i −0.877626 0.479346i \(-0.840874\pi\)
0.877626 0.479346i \(-0.159126\pi\)
\(68\) 3.35840 + 7.11814i 0.407266 + 0.863201i
\(69\) 0 0
\(70\) −3.67380 + 0.709355i −0.439103 + 0.0847841i
\(71\) 8.49881i 1.00862i −0.863522 0.504311i \(-0.831746\pi\)
0.863522 0.504311i \(-0.168254\pi\)
\(72\) 0 0
\(73\) 14.4665i 1.69318i −0.532244 0.846591i \(-0.678651\pi\)
0.532244 0.846591i \(-0.321349\pi\)
\(74\) −2.55685 11.4114i −0.297228 1.32655i
\(75\) 0 0
\(76\) 0.404980 0.191073i 0.0464544 0.0219176i
\(77\) 0.0775087 2.61042i 0.00883294 0.297485i
\(78\) 0 0
\(79\) 11.5183i 1.29591i −0.761678 0.647956i \(-0.775624\pi\)
0.761678 0.647956i \(-0.224376\pi\)
\(80\) −3.08724 2.54341i −0.345164 0.284362i
\(81\) 0 0
\(82\) 10.1417 2.27237i 1.11997 0.250941i
\(83\) 1.67114 0.183431 0.0917156 0.995785i \(-0.470765\pi\)
0.0917156 + 0.995785i \(0.470765\pi\)
\(84\) 0 0
\(85\) −3.93531 −0.426845
\(86\) −5.96597 + 1.33674i −0.643327 + 0.144145i
\(87\) 0 0
\(88\) 2.20340 1.71453i 0.234884 0.182770i
\(89\) 0.493375i 0.0522977i −0.999658 0.0261488i \(-0.991676\pi\)
0.999658 0.0261488i \(-0.00832438\pi\)
\(90\) 0 0
\(91\) −0.368398 + 12.4073i −0.0386186 + 1.30064i
\(92\) −5.01910 10.6380i −0.523277 1.10909i
\(93\) 0 0
\(94\) 0.744498 + 3.32274i 0.0767891 + 0.342715i
\(95\) 0.223896i 0.0229713i
\(96\) 0 0
\(97\) 4.31036i 0.437650i −0.975764 0.218825i \(-0.929778\pi\)
0.975764 0.218825i \(-0.0702224\pi\)
\(98\) −1.58747 9.77138i −0.160359 0.987059i
\(99\) 0 0
\(100\) 1.80879 0.853401i 0.180879 0.0853401i
\(101\) 6.03671i 0.600675i −0.953833 0.300338i \(-0.902901\pi\)
0.953833 0.300338i \(-0.0970994\pi\)
\(102\) 0 0
\(103\) 7.83090 0.771602 0.385801 0.922582i \(-0.373925\pi\)
0.385801 + 0.922582i \(0.373925\pi\)
\(104\) −10.4727 + 8.14915i −1.02694 + 0.799090i
\(105\) 0 0
\(106\) −2.58186 11.5230i −0.250772 1.11921i
\(107\) 13.9860i 1.35208i 0.736866 + 0.676039i \(0.236305\pi\)
−0.736866 + 0.676039i \(0.763695\pi\)
\(108\) 0 0
\(109\) 4.06579 0.389432 0.194716 0.980860i \(-0.437621\pi\)
0.194716 + 0.980860i \(0.437621\pi\)
\(110\) 0.305209 + 1.36217i 0.0291005 + 0.129878i
\(111\) 0 0
\(112\) 6.96869 7.96476i 0.658479 0.752599i
\(113\) 8.66412 0.815052 0.407526 0.913194i \(-0.366392\pi\)
0.407526 + 0.913194i \(0.366392\pi\)
\(114\) 0 0
\(115\) 5.88128 0.548433
\(116\) −18.5405 + 8.74756i −1.72144 + 0.812190i
\(117\) 0 0
\(118\) 4.32357 + 19.2964i 0.398017 + 1.77638i
\(119\) 0.309013 10.4073i 0.0283272 0.954033i
\(120\) 0 0
\(121\) 10.0257 0.911425
\(122\) 6.80855 1.52553i 0.616417 0.138115i
\(123\) 0 0
\(124\) −5.01827 + 2.36767i −0.450654 + 0.212623i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 5.18615i 0.460197i −0.973167 0.230098i \(-0.926095\pi\)
0.973167 0.230098i \(-0.0739048\pi\)
\(128\) 11.3093 + 0.315057i 0.999612 + 0.0278473i
\(129\) 0 0
\(130\) −1.45065 6.47436i −0.127231 0.567839i
\(131\) 11.3617 0.992679 0.496340 0.868128i \(-0.334677\pi\)
0.496340 + 0.868128i \(0.334677\pi\)
\(132\) 0 0
\(133\) −0.592112 0.0175810i −0.0513427 0.00152447i
\(134\) −10.8292 + 2.42640i −0.935497 + 0.209609i
\(135\) 0 0
\(136\) 8.78458 6.83554i 0.753272 0.586143i
\(137\) 5.85931 0.500595 0.250297 0.968169i \(-0.419472\pi\)
0.250297 + 0.968169i \(0.419472\pi\)
\(138\) 0 0
\(139\) −18.1460 −1.53912 −0.769562 0.638572i \(-0.779525\pi\)
−0.769562 + 0.638572i \(0.779525\pi\)
\(140\) 2.11486 + 4.85050i 0.178738 + 0.409942i
\(141\) 0 0
\(142\) −11.7283 + 2.62786i −0.984220 + 0.220525i
\(143\) 4.63096 0.387260
\(144\) 0 0
\(145\) 10.2502i 0.851235i
\(146\) −19.9638 + 4.47311i −1.65222 + 0.370198i
\(147\) 0 0
\(148\) −14.9571 + 7.05690i −1.22947 + 0.580074i
\(149\) −15.4737 −1.26766 −0.633829 0.773473i \(-0.718518\pi\)
−0.633829 + 0.773473i \(0.718518\pi\)
\(150\) 0 0
\(151\) 11.5322i 0.938474i 0.883072 + 0.469237i \(0.155471\pi\)
−0.883072 + 0.469237i \(0.844529\pi\)
\(152\) −0.388902 0.499791i −0.0315441 0.0405384i
\(153\) 0 0
\(154\) −3.62634 + 0.700190i −0.292219 + 0.0564229i
\(155\) 2.77439i 0.222844i
\(156\) 0 0
\(157\) 0.806743i 0.0643851i −0.999482 0.0321926i \(-0.989751\pi\)
0.999482 0.0321926i \(-0.0102490\pi\)
\(158\) −15.8952 + 3.56151i −1.26456 + 0.283338i
\(159\) 0 0
\(160\) −2.55532 + 5.04682i −0.202015 + 0.398986i
\(161\) −0.461817 + 15.5536i −0.0363963 + 1.22579i
\(162\) 0 0
\(163\) 6.48272i 0.507766i 0.967235 + 0.253883i \(0.0817077\pi\)
−0.967235 + 0.253883i \(0.918292\pi\)
\(164\) −6.27173 13.2929i −0.489740 1.03800i
\(165\) 0 0
\(166\) −0.516722 2.30616i −0.0401054 0.178993i
\(167\) 7.65678 0.592499 0.296250 0.955111i \(-0.404264\pi\)
0.296250 + 0.955111i \(0.404264\pi\)
\(168\) 0 0
\(169\) −9.01087 −0.693144
\(170\) 1.21681 + 5.43072i 0.0933254 + 0.416517i
\(171\) 0 0
\(172\) 3.68941 + 7.81970i 0.281315 + 0.596247i
\(173\) 7.12007i 0.541329i 0.962674 + 0.270665i \(0.0872434\pi\)
−0.962674 + 0.270665i \(0.912757\pi\)
\(174\) 0 0
\(175\) −2.64459 0.0785232i −0.199912 0.00593580i
\(176\) −3.04735 2.51055i −0.229703 0.189240i
\(177\) 0 0
\(178\) −0.680856 + 0.152554i −0.0510323 + 0.0114344i
\(179\) 20.8439i 1.55794i 0.627059 + 0.778972i \(0.284258\pi\)
−0.627059 + 0.778972i \(0.715742\pi\)
\(180\) 0 0
\(181\) 24.4428i 1.81682i 0.418079 + 0.908411i \(0.362703\pi\)
−0.418079 + 0.908411i \(0.637297\pi\)
\(182\) 17.2359 3.32799i 1.27761 0.246687i
\(183\) 0 0
\(184\) −13.1285 + 10.2156i −0.967843 + 0.753107i
\(185\) 8.26915i 0.607960i
\(186\) 0 0
\(187\) −3.88447 −0.284061
\(188\) 4.35517 2.05481i 0.317634 0.149862i
\(189\) 0 0
\(190\) 0.308976 0.0692296i 0.0224155 0.00502244i
\(191\) 19.3047i 1.39684i −0.715689 0.698419i \(-0.753887\pi\)
0.715689 0.698419i \(-0.246113\pi\)
\(192\) 0 0
\(193\) −15.2505 −1.09776 −0.548879 0.835902i \(-0.684945\pi\)
−0.548879 + 0.835902i \(0.684945\pi\)
\(194\) −5.94828 + 1.33278i −0.427062 + 0.0956880i
\(195\) 0 0
\(196\) −12.9936 + 5.21206i −0.928117 + 0.372290i
\(197\) −3.00729 −0.214260 −0.107130 0.994245i \(-0.534166\pi\)
−0.107130 + 0.994245i \(0.534166\pi\)
\(198\) 0 0
\(199\) −22.1587 −1.57079 −0.785395 0.618995i \(-0.787540\pi\)
−0.785395 + 0.618995i \(0.787540\pi\)
\(200\) −1.73698 2.23224i −0.122823 0.157844i
\(201\) 0 0
\(202\) −8.33065 + 1.86658i −0.586142 + 0.131332i
\(203\) 27.1076 + 0.804881i 1.90258 + 0.0564916i
\(204\) 0 0
\(205\) 7.34910 0.513283
\(206\) −2.42135 10.8066i −0.168703 0.752933i
\(207\) 0 0
\(208\) 14.4840 + 11.9326i 1.00429 + 0.827377i
\(209\) 0.221003i 0.0152871i
\(210\) 0 0
\(211\) 12.6769i 0.872714i 0.899774 + 0.436357i \(0.143731\pi\)
−0.899774 + 0.436357i \(0.856269\pi\)
\(212\) −15.1034 + 7.12592i −1.03731 + 0.489410i
\(213\) 0 0
\(214\) 19.3006 4.32453i 1.31936 0.295618i
\(215\) −4.32318 −0.294838
\(216\) 0 0
\(217\) 7.33710 + 0.217854i 0.498075 + 0.0147889i
\(218\) −1.25716 5.61078i −0.0851455 0.380010i
\(219\) 0 0
\(220\) 1.78542 0.842376i 0.120373 0.0567930i
\(221\) 18.4628 1.24194
\(222\) 0 0
\(223\) −6.45632 −0.432347 −0.216173 0.976355i \(-0.569358\pi\)
−0.216173 + 0.976355i \(0.569358\pi\)
\(224\) −13.1461 7.15404i −0.878360 0.478000i
\(225\) 0 0
\(226\) −2.67898 11.9565i −0.178203 0.795332i
\(227\) 14.0882 0.935066 0.467533 0.883976i \(-0.345143\pi\)
0.467533 + 0.883976i \(0.345143\pi\)
\(228\) 0 0
\(229\) 9.74932i 0.644253i 0.946697 + 0.322126i \(0.104398\pi\)
−0.946697 + 0.322126i \(0.895602\pi\)
\(230\) −1.81852 8.11616i −0.119909 0.535164i
\(231\) 0 0
\(232\) 17.8044 + 22.8810i 1.16892 + 1.50221i
\(233\) −1.64231 −0.107591 −0.0537955 0.998552i \(-0.517132\pi\)
−0.0537955 + 0.998552i \(0.517132\pi\)
\(234\) 0 0
\(235\) 2.40779i 0.157067i
\(236\) 25.2921 11.9330i 1.64637 0.776774i
\(237\) 0 0
\(238\) −14.4576 + 2.79153i −0.937144 + 0.180948i
\(239\) 9.77724i 0.632437i 0.948686 + 0.316219i \(0.102413\pi\)
−0.948686 + 0.316219i \(0.897587\pi\)
\(240\) 0 0
\(241\) 6.84106i 0.440671i 0.975424 + 0.220336i \(0.0707152\pi\)
−0.975424 + 0.220336i \(0.929285\pi\)
\(242\) −3.09998 13.8354i −0.199274 0.889373i
\(243\) 0 0
\(244\) −4.21046 8.92408i −0.269547 0.571305i
\(245\) 0.415323 6.98767i 0.0265340 0.446426i
\(246\) 0 0
\(247\) 1.05043i 0.0668370i
\(248\) 4.81904 + 6.19311i 0.306009 + 0.393263i
\(249\) 0 0
\(250\) 1.38000 0.309204i 0.0872787 0.0195558i
\(251\) 2.34972 0.148313 0.0741564 0.997247i \(-0.476374\pi\)
0.0741564 + 0.997247i \(0.476374\pi\)
\(252\) 0 0
\(253\) 5.80530 0.364976
\(254\) −7.15688 + 1.60358i −0.449063 + 0.100618i
\(255\) 0 0
\(256\) −3.06211 15.7043i −0.191382 0.981516i
\(257\) 6.47150i 0.403681i 0.979418 + 0.201840i \(0.0646922\pi\)
−0.979418 + 0.201840i \(0.935308\pi\)
\(258\) 0 0
\(259\) 21.8685 + 0.649320i 1.35884 + 0.0403468i
\(260\) −8.48605 + 4.00380i −0.526283 + 0.248305i
\(261\) 0 0
\(262\) −3.51309 15.6792i −0.217040 0.968662i
\(263\) 2.38076i 0.146804i 0.997302 + 0.0734018i \(0.0233856\pi\)
−0.997302 + 0.0734018i \(0.976614\pi\)
\(264\) 0 0
\(265\) 8.35002i 0.512938i
\(266\) 0.158822 + 0.822550i 0.00973799 + 0.0504338i
\(267\) 0 0
\(268\) 6.69684 + 14.1940i 0.409075 + 0.867034i
\(269\) 9.44894i 0.576112i −0.957614 0.288056i \(-0.906991\pi\)
0.957614 0.288056i \(-0.0930089\pi\)
\(270\) 0 0
\(271\) −22.1827 −1.34750 −0.673752 0.738958i \(-0.735318\pi\)
−0.673752 + 0.738958i \(0.735318\pi\)
\(272\) −12.1493 10.0091i −0.736657 0.606892i
\(273\) 0 0
\(274\) −1.81172 8.08583i −0.109450 0.488483i
\(275\) 0.987080i 0.0595232i
\(276\) 0 0
\(277\) −26.7718 −1.60856 −0.804281 0.594249i \(-0.797449\pi\)
−0.804281 + 0.594249i \(0.797449\pi\)
\(278\) 5.61082 + 25.0414i 0.336514 + 1.50189i
\(279\) 0 0
\(280\) 6.03976 4.41830i 0.360944 0.264044i
\(281\) 8.64183 0.515529 0.257764 0.966208i \(-0.417014\pi\)
0.257764 + 0.966208i \(0.417014\pi\)
\(282\) 0 0
\(283\) 5.92047 0.351935 0.175968 0.984396i \(-0.443695\pi\)
0.175968 + 0.984396i \(0.443695\pi\)
\(284\) 7.25289 + 15.3725i 0.430380 + 0.912191i
\(285\) 0 0
\(286\) −1.43191 6.39071i −0.0846707 0.377891i
\(287\) −0.577075 + 19.4353i −0.0340637 + 1.14723i
\(288\) 0 0
\(289\) 1.51332 0.0890186
\(290\) −14.1453 + 3.16941i −0.830640 + 0.186114i
\(291\) 0 0
\(292\) 12.3458 + 26.1669i 0.722482 + 1.53130i
\(293\) 26.2654i 1.53444i −0.641382 0.767221i \(-0.721639\pi\)
0.641382 0.767221i \(-0.278361\pi\)
\(294\) 0 0
\(295\) 13.9829i 0.814116i
\(296\) 14.3633 + 18.4588i 0.834850 + 1.07289i
\(297\) 0 0
\(298\) 4.78454 + 21.3537i 0.277161 + 1.23699i
\(299\) −27.5925 −1.59571
\(300\) 0 0
\(301\) 0.339470 11.4330i 0.0195667 0.658988i
\(302\) 15.9144 3.56579i 0.915768 0.205188i
\(303\) 0 0
\(304\) −0.569460 + 0.691221i −0.0326608 + 0.0396443i
\(305\) 4.93374 0.282505
\(306\) 0 0
\(307\) 18.5432 1.05832 0.529158 0.848524i \(-0.322508\pi\)
0.529158 + 0.848524i \(0.322508\pi\)
\(308\) 2.08754 + 4.78783i 0.118949 + 0.272812i
\(309\) 0 0
\(310\) −3.82865 + 0.857851i −0.217453 + 0.0487227i
\(311\) −30.8370 −1.74861 −0.874304 0.485379i \(-0.838682\pi\)
−0.874304 + 0.485379i \(0.838682\pi\)
\(312\) 0 0
\(313\) 20.8250i 1.17710i −0.808461 0.588550i \(-0.799699\pi\)
0.808461 0.588550i \(-0.200301\pi\)
\(314\) −1.11330 + 0.249448i −0.0628274 + 0.0140772i
\(315\) 0 0
\(316\) 9.82975 + 20.8342i 0.552967 + 1.17201i
\(317\) −5.41152 −0.303941 −0.151971 0.988385i \(-0.548562\pi\)
−0.151971 + 0.988385i \(0.548562\pi\)
\(318\) 0 0
\(319\) 10.1178i 0.566488i
\(320\) 7.75471 + 1.96583i 0.433501 + 0.109893i
\(321\) 0 0
\(322\) 21.6067 4.17192i 1.20409 0.232492i
\(323\) 0.881101i 0.0490258i
\(324\) 0 0
\(325\) 4.69157i 0.260242i
\(326\) 8.94613 2.00448i 0.495480 0.111018i
\(327\) 0 0
\(328\) −16.4050 + 12.7652i −0.905814 + 0.704841i
\(329\) −6.36760 0.189067i −0.351057 0.0104236i
\(330\) 0 0
\(331\) 1.77494i 0.0975597i −0.998810 0.0487799i \(-0.984467\pi\)
0.998810 0.0487799i \(-0.0155333\pi\)
\(332\) −3.02273 + 1.42615i −0.165894 + 0.0782702i
\(333\) 0 0
\(334\) −2.36751 10.5663i −0.129544 0.578164i
\(335\) −7.84723 −0.428740
\(336\) 0 0
\(337\) 22.3668 1.21839 0.609197 0.793019i \(-0.291492\pi\)
0.609197 + 0.793019i \(0.291492\pi\)
\(338\) 2.78620 + 12.4350i 0.151549 + 0.676374i
\(339\) 0 0
\(340\) 7.11814 3.35840i 0.386035 0.182135i
\(341\) 2.73854i 0.148300i
\(342\) 0 0
\(343\) 18.4469 + 1.64705i 0.996038 + 0.0889324i
\(344\) 9.65039 7.50925i 0.520314 0.404872i
\(345\) 0 0
\(346\) 9.82569 2.20156i 0.528232 0.118356i
\(347\) 0.606084i 0.0325363i −0.999868 0.0162681i \(-0.994821\pi\)
0.999868 0.0162681i \(-0.00517854\pi\)
\(348\) 0 0
\(349\) 31.6682i 1.69516i 0.530668 + 0.847580i \(0.321941\pi\)
−0.530668 + 0.847580i \(0.678059\pi\)
\(350\) 0.709355 + 3.67380i 0.0379166 + 0.196373i
\(351\) 0 0
\(352\) −2.52230 + 4.98161i −0.134439 + 0.265521i
\(353\) 4.06901i 0.216572i 0.994120 + 0.108286i \(0.0345362\pi\)
−0.994120 + 0.108286i \(0.965464\pi\)
\(354\) 0 0
\(355\) −8.49881 −0.451070
\(356\) 0.421047 + 0.892410i 0.0223154 + 0.0472976i
\(357\) 0 0
\(358\) 28.7645 6.44500i 1.52025 0.340629i
\(359\) 11.0427i 0.582809i 0.956600 + 0.291405i \(0.0941226\pi\)
−0.956600 + 0.291405i \(0.905877\pi\)
\(360\) 0 0
\(361\) −18.9499 −0.997362
\(362\) 33.7310 7.55782i 1.77286 0.397230i
\(363\) 0 0
\(364\) −9.92203 22.7565i −0.520056 1.19276i
\(365\) −14.4665 −0.757214
\(366\) 0 0
\(367\) −0.0725720 −0.00378823 −0.00189411 0.999998i \(-0.500603\pi\)
−0.00189411 + 0.999998i \(0.500603\pi\)
\(368\) 18.1569 + 14.9585i 0.946496 + 0.779767i
\(369\) 0 0
\(370\) −11.4114 + 2.55685i −0.593251 + 0.132924i
\(371\) 22.0824 + 0.655671i 1.14646 + 0.0340407i
\(372\) 0 0
\(373\) 22.4132 1.16051 0.580257 0.814433i \(-0.302952\pi\)
0.580257 + 0.814433i \(0.302952\pi\)
\(374\) 1.20109 + 5.36056i 0.0621071 + 0.277188i
\(375\) 0 0
\(376\) −4.18227 5.37477i −0.215684 0.277183i
\(377\) 48.0897i 2.47675i
\(378\) 0 0
\(379\) 26.9969i 1.38674i 0.720584 + 0.693368i \(0.243874\pi\)
−0.720584 + 0.693368i \(0.756126\pi\)
\(380\) −0.191073 0.404980i −0.00980185 0.0207750i
\(381\) 0 0
\(382\) −26.6404 + 5.96909i −1.36304 + 0.305405i
\(383\) −19.7866 −1.01105 −0.505523 0.862813i \(-0.668701\pi\)
−0.505523 + 0.862813i \(0.668701\pi\)
\(384\) 0 0
\(385\) −2.61042 0.0775087i −0.133039 0.00395021i
\(386\) 4.71553 + 21.0457i 0.240014 + 1.07120i
\(387\) 0 0
\(388\) 3.67846 + 7.79651i 0.186746 + 0.395808i
\(389\) 29.6119 1.50138 0.750690 0.660654i \(-0.229721\pi\)
0.750690 + 0.660654i \(0.229721\pi\)
\(390\) 0 0
\(391\) 23.1447 1.17048
\(392\) 11.2103 + 16.3196i 0.566206 + 0.824264i
\(393\) 0 0
\(394\) 0.929865 + 4.15005i 0.0468459 + 0.209076i
\(395\) −11.5183 −0.579549
\(396\) 0 0
\(397\) 21.2555i 1.06678i 0.845868 + 0.533392i \(0.179083\pi\)
−0.845868 + 0.533392i \(0.820917\pi\)
\(398\) 6.85156 + 30.5790i 0.343438 + 1.53279i
\(399\) 0 0
\(400\) −2.54341 + 3.08724i −0.127171 + 0.154362i
\(401\) −24.5750 −1.22722 −0.613608 0.789610i \(-0.710283\pi\)
−0.613608 + 0.789610i \(0.710283\pi\)
\(402\) 0 0
\(403\) 13.0162i 0.648385i
\(404\) 5.15174 + 10.9191i 0.256309 + 0.543246i
\(405\) 0 0
\(406\) −7.27104 37.6573i −0.360856 1.86890i
\(407\) 8.16231i 0.404591i
\(408\) 0 0
\(409\) 34.9158i 1.72648i −0.504797 0.863238i \(-0.668433\pi\)
0.504797 0.863238i \(-0.331567\pi\)
\(410\) −2.27237 10.1417i −0.112224 0.500865i
\(411\) 0 0
\(412\) −14.1644 + 6.68290i −0.697831 + 0.329243i
\(413\) −36.9790 1.09798i −1.81962 0.0540282i
\(414\) 0 0
\(415\) 1.67114i 0.0820329i
\(416\) 11.9885 23.6775i 0.587782 1.16089i
\(417\) 0 0
\(418\) 0.304984 0.0683351i 0.0149173 0.00334238i
\(419\) −2.32360 −0.113515 −0.0567577 0.998388i \(-0.518076\pi\)
−0.0567577 + 0.998388i \(0.518076\pi\)
\(420\) 0 0
\(421\) −22.9539 −1.11870 −0.559352 0.828930i \(-0.688950\pi\)
−0.559352 + 0.828930i \(0.688950\pi\)
\(422\) 17.4941 3.91975i 0.851599 0.190810i
\(423\) 0 0
\(424\) 14.5038 + 18.6393i 0.704366 + 0.905204i
\(425\) 3.93531i 0.190891i
\(426\) 0 0
\(427\) −0.387413 + 13.0477i −0.0187482 + 0.631422i
\(428\) −11.9357 25.2977i −0.576932 1.22281i
\(429\) 0 0
\(430\) 1.33674 + 5.96597i 0.0644635 + 0.287705i
\(431\) 0.0761033i 0.00366577i 0.999998 + 0.00183288i \(0.000583425\pi\)
−0.999998 + 0.00183288i \(0.999417\pi\)
\(432\) 0 0
\(433\) 9.43899i 0.453609i 0.973940 + 0.226805i \(0.0728278\pi\)
−0.973940 + 0.226805i \(0.927172\pi\)
\(434\) −1.96802 10.1925i −0.0944682 0.489258i
\(435\) 0 0
\(436\) −7.35414 + 3.46975i −0.352199 + 0.166171i
\(437\) 1.31680i 0.0629909i
\(438\) 0 0
\(439\) −4.35512 −0.207858 −0.103929 0.994585i \(-0.533142\pi\)
−0.103929 + 0.994585i \(0.533142\pi\)
\(440\) −1.71453 2.20340i −0.0817372 0.105043i
\(441\) 0 0
\(442\) −5.70878 25.4786i −0.271539 1.21190i
\(443\) 35.6619i 1.69435i −0.531315 0.847174i \(-0.678302\pi\)
0.531315 0.847174i \(-0.321698\pi\)
\(444\) 0 0
\(445\) −0.493375 −0.0233882
\(446\) 1.99632 + 8.90970i 0.0945284 + 0.421886i
\(447\) 0 0
\(448\) −5.80774 + 20.3536i −0.274390 + 0.961619i
\(449\) −15.1046 −0.712832 −0.356416 0.934327i \(-0.616001\pi\)
−0.356416 + 0.934327i \(0.616001\pi\)
\(450\) 0 0
\(451\) 7.25415 0.341585
\(452\) −15.6715 + 7.39397i −0.737127 + 0.347783i
\(453\) 0 0
\(454\) −4.35613 19.4417i −0.204443 0.912443i
\(455\) 12.4073 + 0.368398i 0.581662 + 0.0172707i
\(456\) 0 0
\(457\) −23.3917 −1.09422 −0.547109 0.837061i \(-0.684272\pi\)
−0.547109 + 0.837061i \(0.684272\pi\)
\(458\) 13.4540 3.01453i 0.628666 0.140860i
\(459\) 0 0
\(460\) −10.6380 + 5.01910i −0.495999 + 0.234017i
\(461\) 22.6568i 1.05523i 0.849482 + 0.527617i \(0.176914\pi\)
−0.849482 + 0.527617i \(0.823086\pi\)
\(462\) 0 0
\(463\) 31.9975i 1.48705i −0.668707 0.743526i \(-0.733152\pi\)
0.668707 0.743526i \(-0.266848\pi\)
\(464\) 26.0705 31.6449i 1.21029 1.46908i
\(465\) 0 0
\(466\) 0.507807 + 2.26638i 0.0235237 + 0.104988i
\(467\) −42.6816 −1.97507 −0.987533 0.157409i \(-0.949686\pi\)
−0.987533 + 0.157409i \(0.949686\pi\)
\(468\) 0 0
\(469\) 0.616190 20.7527i 0.0284530 0.958270i
\(470\) 3.32274 0.744498i 0.153267 0.0343411i
\(471\) 0 0
\(472\) −24.2880 31.2133i −1.11794 1.43671i
\(473\) −4.26732 −0.196212
\(474\) 0 0
\(475\) 0.223896 0.0102731
\(476\) 8.32264 + 19.0882i 0.381468 + 0.874908i
\(477\) 0 0
\(478\) 13.4926 3.02316i 0.617136 0.138276i
\(479\) 0.259729 0.0118673 0.00593366 0.999982i \(-0.498111\pi\)
0.00593366 + 0.999982i \(0.498111\pi\)
\(480\) 0 0
\(481\) 38.7953i 1.76891i
\(482\) 9.44064 2.11528i 0.430009 0.0963484i
\(483\) 0 0
\(484\) −18.1343 + 8.55592i −0.824286 + 0.388906i
\(485\) −4.31036 −0.195723
\(486\) 0 0
\(487\) 29.8196i 1.35126i −0.737242 0.675628i \(-0.763872\pi\)
0.737242 0.675628i \(-0.236128\pi\)
\(488\) −11.0133 + 8.56978i −0.498549 + 0.387936i
\(489\) 0 0
\(490\) −9.77138 + 1.58747i −0.441426 + 0.0717146i
\(491\) 25.9448i 1.17087i 0.810718 + 0.585437i \(0.199077\pi\)
−0.810718 + 0.585437i \(0.800923\pi\)
\(492\) 0 0
\(493\) 40.3378i 1.81672i
\(494\) −1.44958 + 0.324796i −0.0652199 + 0.0146132i
\(495\) 0 0
\(496\) 7.05641 8.56520i 0.316842 0.384589i
\(497\) 0.667354 22.4758i 0.0299349 1.00818i
\(498\) 0 0
\(499\) 22.9135i 1.02575i 0.858464 + 0.512874i \(0.171419\pi\)
−0.858464 + 0.512874i \(0.828581\pi\)
\(500\) −0.853401 1.80879i −0.0381653 0.0808914i
\(501\) 0 0
\(502\) −0.726541 3.24260i −0.0324271 0.144724i
\(503\) 29.7060 1.32453 0.662263 0.749271i \(-0.269596\pi\)
0.662263 + 0.749271i \(0.269596\pi\)
\(504\) 0 0
\(505\) −6.03671 −0.268630
\(506\) −1.79502 8.01130i −0.0797984 0.356146i
\(507\) 0 0
\(508\) 4.42587 + 9.38064i 0.196366 + 0.416199i
\(509\) 15.8710i 0.703470i −0.936100 0.351735i \(-0.885592\pi\)
0.936100 0.351735i \(-0.114408\pi\)
\(510\) 0 0
\(511\) 1.13596 38.2580i 0.0502519 1.69244i
\(512\) −20.7250 + 9.08152i −0.915925 + 0.401350i
\(513\) 0 0
\(514\) 8.93065 2.00101i 0.393914 0.0882609i
\(515\) 7.83090i 0.345071i
\(516\) 0 0
\(517\) 2.37668i 0.104526i
\(518\) −5.86576 30.3792i −0.257727 1.33479i
\(519\) 0 0
\(520\) 8.14915 + 10.4727i 0.357364 + 0.459260i
\(521\) 10.0748i 0.441387i −0.975343 0.220693i \(-0.929168\pi\)
0.975343 0.220693i \(-0.0708320\pi\)
\(522\) 0 0
\(523\) 15.4083 0.673759 0.336880 0.941548i \(-0.390628\pi\)
0.336880 + 0.941548i \(0.390628\pi\)
\(524\) −20.5509 + 9.69612i −0.897772 + 0.423577i
\(525\) 0 0
\(526\) 3.28544 0.736139i 0.143252 0.0320972i
\(527\) 10.9181i 0.475599i
\(528\) 0 0
\(529\) −11.5895 −0.503891
\(530\) −11.5230 + 2.58186i −0.500528 + 0.112149i
\(531\) 0 0
\(532\) 1.08601 0.473509i 0.0470844 0.0205292i
\(533\) −34.4788 −1.49344
\(534\) 0 0
\(535\) 13.9860 0.604667
\(536\) 17.5169 13.6305i 0.756617 0.588746i
\(537\) 0 0
\(538\) −13.0395 + 2.92165i −0.562173 + 0.125961i
\(539\) 0.409957 6.89739i 0.0176581 0.297092i
\(540\) 0 0
\(541\) −11.4549 −0.492486 −0.246243 0.969208i \(-0.579196\pi\)
−0.246243 + 0.969208i \(0.579196\pi\)
\(542\) 6.85898 + 30.6121i 0.294619 + 1.31490i
\(543\) 0 0
\(544\) −10.0560 + 19.8608i −0.431146 + 0.851525i
\(545\) 4.06579i 0.174159i
\(546\) 0 0
\(547\) 25.1553i 1.07556i −0.843085 0.537781i \(-0.819263\pi\)
0.843085 0.537781i \(-0.180737\pi\)
\(548\) −10.5982 + 5.00034i −0.452734 + 0.213604i
\(549\) 0 0
\(550\) 1.36217 0.305209i 0.0580830 0.0130142i
\(551\) −2.29499 −0.0977697
\(552\) 0 0
\(553\) 0.904455 30.4612i 0.0384614 1.29534i
\(554\) 8.27795 + 36.9450i 0.351696 + 1.56964i
\(555\) 0 0
\(556\) 32.8222 15.4858i 1.39197 0.656745i
\(557\) −26.6942 −1.13107 −0.565534 0.824725i \(-0.691330\pi\)
−0.565534 + 0.824725i \(0.691330\pi\)
\(558\) 0 0
\(559\) 20.2825 0.857859
\(560\) −7.96476 6.96869i −0.336572 0.294481i
\(561\) 0 0
\(562\) −2.67209 11.9257i −0.112715 0.503056i
\(563\) 10.8180 0.455923 0.227962 0.973670i \(-0.426794\pi\)
0.227962 + 0.973670i \(0.426794\pi\)
\(564\) 0 0
\(565\) 8.66412i 0.364502i
\(566\) −1.83063 8.17023i −0.0769472 0.343420i
\(567\) 0 0
\(568\) 18.9714 14.7622i 0.796023 0.619409i
\(569\) −15.0833 −0.632323 −0.316162 0.948705i \(-0.602394\pi\)
−0.316162 + 0.948705i \(0.602394\pi\)
\(570\) 0 0
\(571\) 11.4509i 0.479206i 0.970871 + 0.239603i \(0.0770174\pi\)
−0.970871 + 0.239603i \(0.922983\pi\)
\(572\) −8.37642 + 3.95207i −0.350236 + 0.165244i
\(573\) 0 0
\(574\) 26.9991 5.21312i 1.12692 0.217591i
\(575\) 5.88128i 0.245267i
\(576\) 0 0
\(577\) 27.7622i 1.15576i 0.816123 + 0.577878i \(0.196119\pi\)
−0.816123 + 0.577878i \(0.803881\pi\)
\(578\) −0.467923 2.08837i −0.0194630 0.0868648i
\(579\) 0 0
\(580\) 8.74756 + 18.5405i 0.363223 + 0.769851i
\(581\) 4.41946 + 0.131223i 0.183350 + 0.00544405i
\(582\) 0 0
\(583\) 8.24214i 0.341355i
\(584\) 32.2929 25.1280i 1.33629 1.03981i
\(585\) 0 0
\(586\) −36.2462 + 8.12137i −1.49732 + 0.335491i
\(587\) 4.20086 0.173388 0.0866941 0.996235i \(-0.472370\pi\)
0.0866941 + 0.996235i \(0.472370\pi\)
\(588\) 0 0
\(589\) −0.621174 −0.0255950
\(590\) 19.2964 4.32357i 0.794419 0.177999i
\(591\) 0 0
\(592\) 21.0319 25.5289i 0.864404 1.04923i
\(593\) 12.2323i 0.502321i −0.967945 0.251161i \(-0.919188\pi\)
0.967945 0.251161i \(-0.0808123\pi\)
\(594\) 0 0
\(595\) −10.4073 0.309013i −0.426657 0.0126683i
\(596\) 27.9887 13.2053i 1.14646 0.540911i
\(597\) 0 0
\(598\) 8.53171 + 38.0776i 0.348887 + 1.55711i
\(599\) 43.8944i 1.79348i −0.442562 0.896738i \(-0.645930\pi\)
0.442562 0.896738i \(-0.354070\pi\)
\(600\) 0 0
\(601\) 5.44570i 0.222135i 0.993813 + 0.111067i \(0.0354269\pi\)
−0.993813 + 0.111067i \(0.964573\pi\)
\(602\) −15.8825 + 3.06667i −0.647322 + 0.124988i
\(603\) 0 0
\(604\) −9.84156 20.8592i −0.400447 0.848749i
\(605\) 10.0257i 0.407602i
\(606\) 0 0
\(607\) −29.7406 −1.20713 −0.603567 0.797312i \(-0.706255\pi\)
−0.603567 + 0.797312i \(0.706255\pi\)
\(608\) 1.12996 + 0.572125i 0.0458260 + 0.0232027i
\(609\) 0 0
\(610\) −1.52553 6.80855i −0.0617670 0.275670i
\(611\) 11.2963i 0.457000i
\(612\) 0 0
\(613\) 26.7046 1.07859 0.539295 0.842117i \(-0.318691\pi\)
0.539295 + 0.842117i \(0.318691\pi\)
\(614\) −5.73363 25.5895i −0.231390 1.03271i
\(615\) 0 0
\(616\) 5.96172 4.36121i 0.240205 0.175718i
\(617\) 18.7712 0.755701 0.377851 0.925867i \(-0.376663\pi\)
0.377851 + 0.925867i \(0.376663\pi\)
\(618\) 0 0
\(619\) −6.00143 −0.241218 −0.120609 0.992700i \(-0.538485\pi\)
−0.120609 + 0.992700i \(0.538485\pi\)
\(620\) 2.36767 + 5.01827i 0.0950877 + 0.201539i
\(621\) 0 0
\(622\) 9.53493 + 42.5550i 0.382316 + 1.70630i
\(623\) 0.0387414 1.30477i 0.00155214 0.0522746i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −28.7385 + 6.43918i −1.14862 + 0.257361i
\(627\) 0 0
\(628\) 0.688476 + 1.45923i 0.0274732 + 0.0582294i
\(629\) 32.5417i 1.29752i
\(630\) 0 0
\(631\) 42.7851i 1.70325i −0.524154 0.851623i \(-0.675619\pi\)
0.524154 0.851623i \(-0.324381\pi\)
\(632\) 25.7117 20.0070i 1.02276 0.795837i
\(633\) 0 0
\(634\) 1.67326 + 7.46788i 0.0664538 + 0.296587i
\(635\) −5.18615 −0.205806
\(636\) 0 0
\(637\) −1.94852 + 32.7832i −0.0772031 + 1.29892i
\(638\) −13.9625 + 3.12846i −0.552782 + 0.123857i
\(639\) 0 0
\(640\) 0.315057 11.3093i 0.0124537 0.447040i
\(641\) −32.5398 −1.28525 −0.642623 0.766182i \(-0.722154\pi\)
−0.642623 + 0.766182i \(0.722154\pi\)
\(642\) 0 0
\(643\) 10.1954 0.402068 0.201034 0.979584i \(-0.435570\pi\)
0.201034 + 0.979584i \(0.435570\pi\)
\(644\) −12.4381 28.5272i −0.490130 1.12413i
\(645\) 0 0
\(646\) 1.21592 0.272440i 0.0478396 0.0107190i
\(647\) 32.1295 1.26314 0.631571 0.775318i \(-0.282410\pi\)
0.631571 + 0.775318i \(0.282410\pi\)
\(648\) 0 0
\(649\) 13.8023i 0.541786i
\(650\) −6.47436 + 1.45065i −0.253945 + 0.0568993i
\(651\) 0 0
\(652\) −5.53236 11.7258i −0.216664 0.459220i
\(653\) 25.0805 0.981476 0.490738 0.871307i \(-0.336727\pi\)
0.490738 + 0.871307i \(0.336727\pi\)
\(654\) 0 0
\(655\) 11.3617i 0.443940i
\(656\) 22.6884 + 18.6918i 0.885835 + 0.729792i
\(657\) 0 0
\(658\) 1.70798 + 8.84574i 0.0665838 + 0.344843i
\(659\) 8.80669i 0.343060i −0.985179 0.171530i \(-0.945129\pi\)
0.985179 0.171530i \(-0.0548710\pi\)
\(660\) 0 0
\(661\) 43.1173i 1.67707i 0.544849 + 0.838534i \(0.316587\pi\)
−0.544849 + 0.838534i \(0.683413\pi\)
\(662\) −2.44942 + 0.548820i −0.0951993 + 0.0213305i
\(663\) 0 0
\(664\) 2.90272 + 3.73039i 0.112648 + 0.144767i
\(665\) −0.0175810 + 0.592112i −0.000681764 + 0.0229611i
\(666\) 0 0
\(667\) 60.2845i 2.33422i
\(668\) −13.8495 + 6.53430i −0.535852 + 0.252820i
\(669\) 0 0
\(670\) 2.42640 + 10.8292i 0.0937399 + 0.418367i
\(671\) 4.87000 0.188004
\(672\) 0 0
\(673\) −12.2583 −0.472524 −0.236262 0.971689i \(-0.575922\pi\)
−0.236262 + 0.971689i \(0.575922\pi\)
\(674\) −6.91589 30.8661i −0.266390 1.18892i
\(675\) 0 0
\(676\) 16.2987 7.68989i 0.626875 0.295765i
\(677\) 29.7024i 1.14155i −0.821105 0.570777i \(-0.806642\pi\)
0.821105 0.570777i \(-0.193358\pi\)
\(678\) 0 0
\(679\) 0.338463 11.3991i 0.0129890 0.437458i
\(680\) −6.83554 8.78458i −0.262131 0.336873i
\(681\) 0 0
\(682\) −3.77918 + 0.846768i −0.144712 + 0.0324244i
\(683\) 35.1749i 1.34593i 0.739674 + 0.672965i \(0.234980\pi\)
−0.739674 + 0.672965i \(0.765020\pi\)
\(684\) 0 0
\(685\) 5.85931i 0.223873i
\(686\) −3.43092 25.9659i −0.130993 0.991383i
\(687\) 0 0
\(688\) −13.3467 10.9956i −0.508838 0.419204i
\(689\) 39.1748i 1.49244i
\(690\) 0 0
\(691\) −42.9454 −1.63372 −0.816860 0.576836i \(-0.804287\pi\)
−0.816860 + 0.576836i \(0.804287\pi\)
\(692\) −6.07628 12.8787i −0.230986 0.489574i
\(693\) 0 0
\(694\) −0.836394 + 0.187403i −0.0317491 + 0.00711374i
\(695\) 18.1460i 0.688317i
\(696\) 0 0
\(697\) 28.9210 1.09546
\(698\) 43.7020 9.79193i 1.65415 0.370630i
\(699\) 0 0
\(700\) 4.85050 2.11486i 0.183332 0.0799343i
\(701\) 9.37675 0.354155 0.177077 0.984197i \(-0.443336\pi\)
0.177077 + 0.984197i \(0.443336\pi\)
\(702\) 0 0
\(703\) −1.85143 −0.0698280
\(704\) 7.65452 + 1.94043i 0.288491 + 0.0731329i
\(705\) 0 0
\(706\) 5.61523 1.25815i 0.211332 0.0473513i
\(707\) 0.474022 15.9646i 0.0178274 0.600411i
\(708\) 0 0
\(709\) −27.6729 −1.03928 −0.519638 0.854386i \(-0.673933\pi\)
−0.519638 + 0.854386i \(0.673933\pi\)
\(710\) 2.62786 + 11.7283i 0.0986220 + 0.440156i
\(711\) 0 0
\(712\) 1.10133 0.856980i 0.0412742 0.0321167i
\(713\) 16.3170i 0.611075i
\(714\) 0 0
\(715\) 4.63096i 0.173188i
\(716\) −17.7882 37.7021i −0.664776 1.40899i
\(717\) 0 0
\(718\) 15.2388 3.41443i 0.568708 0.127426i
\(719\) −9.24786 −0.344887 −0.172444 0.985019i \(-0.555166\pi\)
−0.172444 + 0.985019i \(0.555166\pi\)
\(720\) 0 0
\(721\) 20.7095 + 0.614908i 0.771262 + 0.0229004i
\(722\) 5.85938 + 26.1508i 0.218063 + 0.973231i
\(723\) 0 0
\(724\) −20.8595 44.2118i −0.775239 1.64312i
\(725\) −10.2502 −0.380684
\(726\) 0 0
\(727\) −34.7371 −1.28833 −0.644163 0.764888i \(-0.722794\pi\)
−0.644163 + 0.764888i \(0.722794\pi\)
\(728\) −28.3360 + 20.7288i −1.05020 + 0.768259i
\(729\) 0 0
\(730\) 4.47311 + 19.9638i 0.165557 + 0.738893i
\(731\) −17.0131 −0.629250
\(732\) 0 0
\(733\) 38.6871i 1.42894i −0.699666 0.714470i \(-0.746668\pi\)
0.699666 0.714470i \(-0.253332\pi\)
\(734\) 0.0224396 + 0.100149i 0.000828259 + 0.00369657i
\(735\) 0 0
\(736\) 15.0285 29.6818i 0.553959 1.09408i
\(737\) −7.74585 −0.285322
\(738\) 0 0
\(739\) 40.4228i 1.48698i −0.668748 0.743489i \(-0.733170\pi\)
0.668748 0.743489i \(-0.266830\pi\)
\(740\) 7.05690 + 14.9571i 0.259417 + 0.549835i
\(741\) 0 0
\(742\) −5.92313 30.6763i −0.217445 1.12616i
\(743\) 25.5119i 0.935941i −0.883744 0.467970i \(-0.844985\pi\)
0.883744 0.467970i \(-0.155015\pi\)
\(744\) 0 0
\(745\) 15.4737i 0.566914i
\(746\) −6.93026 30.9302i −0.253735 1.13244i
\(747\) 0 0
\(748\) 7.02617 3.31501i 0.256902 0.121209i
\(749\) −1.09823 + 36.9872i −0.0401283 + 1.35148i
\(750\) 0 0
\(751\) 31.4000i 1.14580i −0.819625 0.572901i \(-0.805818\pi\)
0.819625 0.572901i \(-0.194182\pi\)
\(752\) −6.12400 + 7.43342i −0.223319 + 0.271069i
\(753\) 0 0
\(754\) 66.3637 14.8695i 2.41682 0.541516i
\(755\) 11.5322 0.419698
\(756\) 0 0
\(757\) −32.9674 −1.19822 −0.599111 0.800666i \(-0.704479\pi\)
−0.599111 + 0.800666i \(0.704479\pi\)
\(758\) 37.2556 8.34754i 1.35318 0.303196i
\(759\) 0 0
\(760\) −0.499791 + 0.388902i −0.0181293 + 0.0141070i
\(761\) 45.0372i 1.63260i 0.577631 + 0.816298i \(0.303977\pi\)
−0.577631 + 0.816298i \(0.696023\pi\)
\(762\) 0 0
\(763\) 10.7523 + 0.319259i 0.389260 + 0.0115579i
\(764\) 16.4747 + 34.9181i 0.596032 + 1.26329i
\(765\) 0 0
\(766\) 6.11809 + 27.3054i 0.221056 + 0.986585i
\(767\) 65.6019i 2.36875i
\(768\) 0 0
\(769\) 16.6023i 0.598694i 0.954144 + 0.299347i \(0.0967688\pi\)
−0.954144 + 0.299347i \(0.903231\pi\)
\(770\) 0.700190 + 3.62634i 0.0252331 + 0.130684i
\(771\) 0 0
\(772\) 27.5850 13.0148i 0.992804 0.468414i
\(773\) 23.1862i 0.833951i −0.908918 0.416975i \(-0.863090\pi\)
0.908918 0.416975i \(-0.136910\pi\)
\(774\) 0 0
\(775\) −2.77439 −0.0996589
\(776\) 9.62177 7.48698i 0.345401 0.268767i
\(777\) 0 0
\(778\) −9.15610 40.8643i −0.328262 1.46506i
\(779\) 1.64543i 0.0589538i
\(780\) 0 0
\(781\) −8.38900 −0.300182
\(782\) −7.15643 31.9396i −0.255913 1.14216i
\(783\) 0 0
\(784\) 19.0547 20.5163i 0.680526 0.732724i
\(785\) −0.806743 −0.0287939
\(786\) 0 0
\(787\) −45.5418 −1.62339 −0.811695 0.584081i \(-0.801455\pi\)
−0.811695 + 0.584081i \(0.801455\pi\)
\(788\) 5.43954 2.56642i 0.193775 0.0914250i
\(789\) 0 0
\(790\) 3.56151 + 15.8952i 0.126713 + 0.565528i
\(791\) 22.9130 + 0.680334i 0.814692 + 0.0241899i
\(792\)