Properties

Label 690.3.k.b.277.15
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.15
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.15

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.84935 + 1.21811i) q^{5} -2.44949 q^{6} +(-0.117427 - 0.117427i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.84935 + 1.21811i) q^{5} -2.44949 q^{6} +(-0.117427 - 0.117427i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.06746 + 3.63124i) q^{10} +6.14155 q^{11} +(2.44949 + 2.44949i) q^{12} +(1.79785 - 1.79785i) q^{13} +0.234854i q^{14} +(-4.44734 + 7.43109i) q^{15} -4.00000 q^{16} +(5.21460 + 5.21460i) q^{17} +(-3.00000 + 3.00000i) q^{18} -28.4319i q^{19} +(-2.43622 - 9.69870i) q^{20} -0.287636 q^{21} +(-6.14155 - 6.14155i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(22.0324 - 11.8141i) q^{25} -3.59570 q^{26} +(-3.67423 - 3.67423i) q^{27} +(0.234854 - 0.234854i) q^{28} +34.1603i q^{29} +(11.8784 - 2.98375i) q^{30} -24.7380 q^{31} +(4.00000 + 4.00000i) q^{32} +(7.52183 - 7.52183i) q^{33} -10.4292i q^{34} +(0.712483 + 0.426406i) q^{35} +6.00000 q^{36} +(-48.0222 - 48.0222i) q^{37} +(-28.4319 + 28.4319i) q^{38} -4.40382i q^{39} +(-7.26248 + 12.1349i) q^{40} -62.5499 q^{41} +(0.287636 + 0.287636i) q^{42} +(-26.2996 + 26.2996i) q^{43} +12.2831i q^{44} +(3.65433 + 14.5481i) q^{45} +6.78233 q^{46} +(-46.4294 - 46.4294i) q^{47} +(-4.89898 + 4.89898i) q^{48} -48.9724i q^{49} +(-33.8465 - 10.2183i) q^{50} +12.7731 q^{51} +(3.59570 + 3.59570i) q^{52} +(-4.24683 + 4.24683i) q^{53} +7.34847i q^{54} +(-29.7825 + 7.48108i) q^{55} -0.469708 q^{56} +(-34.8218 - 34.8218i) q^{57} +(34.1603 - 34.1603i) q^{58} -11.1749i q^{59} +(-14.8622 - 8.89469i) q^{60} +80.2086 q^{61} +(24.7380 + 24.7380i) q^{62} +(-0.352281 + 0.352281i) q^{63} -8.00000i q^{64} +(-6.52843 + 10.9084i) q^{65} -15.0437 q^{66} +(-74.7155 - 74.7155i) q^{67} +(-10.4292 + 10.4292i) q^{68} +8.30662i q^{69} +(-0.286078 - 1.13889i) q^{70} +5.49076 q^{71} +(-6.00000 - 6.00000i) q^{72} +(14.2498 - 14.2498i) q^{73} +96.0445i q^{74} +(12.5148 - 41.4533i) q^{75} +56.8637 q^{76} +(-0.721183 - 0.721183i) q^{77} +(-4.40382 + 4.40382i) q^{78} +66.3129i q^{79} +(19.3974 - 4.87244i) q^{80} -9.00000 q^{81} +(62.5499 + 62.5499i) q^{82} +(-113.788 + 113.788i) q^{83} -0.575272i q^{84} +(-31.6394 - 18.9355i) q^{85} +52.5993 q^{86} +(41.8376 + 41.8376i) q^{87} +(12.2831 - 12.2831i) q^{88} -35.8168i q^{89} +(10.8937 - 18.2024i) q^{90} -0.422232 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-30.2978 + 30.2978i) q^{93} +92.8588i q^{94} +(34.6331 + 137.876i) q^{95} +9.79796 q^{96} +(-93.7132 - 93.7132i) q^{97} +(-48.9724 + 48.9724i) q^{98} -18.4246i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.84935 + 1.21811i −0.969870 + 0.243622i
\(6\) −2.44949 −0.408248
\(7\) −0.117427 0.117427i −0.0167753 0.0167753i 0.698669 0.715445i \(-0.253776\pi\)
−0.715445 + 0.698669i \(0.753776\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.06746 + 3.63124i 0.606746 + 0.363124i
\(11\) 6.14155 0.558322 0.279161 0.960244i \(-0.409944\pi\)
0.279161 + 0.960244i \(0.409944\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 1.79785 1.79785i 0.138296 0.138296i −0.634570 0.772866i \(-0.718823\pi\)
0.772866 + 0.634570i \(0.218823\pi\)
\(14\) 0.234854i 0.0167753i
\(15\) −4.44734 + 7.43109i −0.296490 + 0.495406i
\(16\) −4.00000 −0.250000
\(17\) 5.21460 + 5.21460i 0.306741 + 0.306741i 0.843644 0.536903i \(-0.180406\pi\)
−0.536903 + 0.843644i \(0.680406\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 28.4319i 1.49641i −0.663466 0.748207i \(-0.730915\pi\)
0.663466 0.748207i \(-0.269085\pi\)
\(20\) −2.43622 9.69870i −0.121811 0.484935i
\(21\) −0.287636 −0.0136970
\(22\) −6.14155 6.14155i −0.279161 0.279161i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 22.0324 11.8141i 0.881297 0.472563i
\(26\) −3.59570 −0.138296
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 0.234854 0.234854i 0.00838764 0.00838764i
\(29\) 34.1603i 1.17794i 0.808154 + 0.588971i \(0.200467\pi\)
−0.808154 + 0.588971i \(0.799533\pi\)
\(30\) 11.8784 2.98375i 0.395948 0.0994583i
\(31\) −24.7380 −0.798001 −0.399000 0.916951i \(-0.630643\pi\)
−0.399000 + 0.916951i \(0.630643\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 7.52183 7.52183i 0.227934 0.227934i
\(34\) 10.4292i 0.306741i
\(35\) 0.712483 + 0.426406i 0.0203567 + 0.0121830i
\(36\) 6.00000 0.166667
\(37\) −48.0222 48.0222i −1.29790 1.29790i −0.929778 0.368121i \(-0.880001\pi\)
−0.368121 0.929778i \(-0.619999\pi\)
\(38\) −28.4319 + 28.4319i −0.748207 + 0.748207i
\(39\) 4.40382i 0.112918i
\(40\) −7.26248 + 12.1349i −0.181562 + 0.303373i
\(41\) −62.5499 −1.52561 −0.762804 0.646630i \(-0.776178\pi\)
−0.762804 + 0.646630i \(0.776178\pi\)
\(42\) 0.287636 + 0.287636i 0.00684848 + 0.00684848i
\(43\) −26.2996 + 26.2996i −0.611619 + 0.611619i −0.943368 0.331748i \(-0.892361\pi\)
0.331748 + 0.943368i \(0.392361\pi\)
\(44\) 12.2831i 0.279161i
\(45\) 3.65433 + 14.5481i 0.0812073 + 0.323290i
\(46\) 6.78233 0.147442
\(47\) −46.4294 46.4294i −0.987859 0.987859i 0.0120681 0.999927i \(-0.496159\pi\)
−0.999927 + 0.0120681i \(0.996159\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 48.9724i 0.999437i
\(50\) −33.8465 10.2183i −0.676930 0.204367i
\(51\) 12.7731 0.250453
\(52\) 3.59570 + 3.59570i 0.0691481 + 0.0691481i
\(53\) −4.24683 + 4.24683i −0.0801289 + 0.0801289i −0.746035 0.665906i \(-0.768045\pi\)
0.665906 + 0.746035i \(0.268045\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −29.7825 + 7.48108i −0.541500 + 0.136020i
\(56\) −0.469708 −0.00838764
\(57\) −34.8218 34.8218i −0.610908 0.610908i
\(58\) 34.1603 34.1603i 0.588971 0.588971i
\(59\) 11.1749i 0.189405i −0.995506 0.0947023i \(-0.969810\pi\)
0.995506 0.0947023i \(-0.0301899\pi\)
\(60\) −14.8622 8.89469i −0.247703 0.148245i
\(61\) 80.2086 1.31489 0.657447 0.753501i \(-0.271636\pi\)
0.657447 + 0.753501i \(0.271636\pi\)
\(62\) 24.7380 + 24.7380i 0.399000 + 0.399000i
\(63\) −0.352281 + 0.352281i −0.00559176 + 0.00559176i
\(64\) 8.00000i 0.125000i
\(65\) −6.52843 + 10.9084i −0.100437 + 0.167821i
\(66\) −15.0437 −0.227934
\(67\) −74.7155 74.7155i −1.11516 1.11516i −0.992442 0.122714i \(-0.960840\pi\)
−0.122714 0.992442i \(-0.539160\pi\)
\(68\) −10.4292 + 10.4292i −0.153371 + 0.153371i
\(69\) 8.30662i 0.120386i
\(70\) −0.286078 1.13889i −0.00408683 0.0162698i
\(71\) 5.49076 0.0773346 0.0386673 0.999252i \(-0.487689\pi\)
0.0386673 + 0.999252i \(0.487689\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 14.2498 14.2498i 0.195203 0.195203i −0.602737 0.797940i \(-0.705923\pi\)
0.797940 + 0.602737i \(0.205923\pi\)
\(74\) 96.0445i 1.29790i
\(75\) 12.5148 41.4533i 0.166865 0.552711i
\(76\) 56.8637 0.748207
\(77\) −0.721183 0.721183i −0.00936601 0.00936601i
\(78\) −4.40382 + 4.40382i −0.0564592 + 0.0564592i
\(79\) 66.3129i 0.839404i 0.907662 + 0.419702i \(0.137865\pi\)
−0.907662 + 0.419702i \(0.862135\pi\)
\(80\) 19.3974 4.87244i 0.242468 0.0609055i
\(81\) −9.00000 −0.111111
\(82\) 62.5499 + 62.5499i 0.762804 + 0.762804i
\(83\) −113.788 + 113.788i −1.37094 + 1.37094i −0.511886 + 0.859053i \(0.671053\pi\)
−0.859053 + 0.511886i \(0.828947\pi\)
\(84\) 0.575272i 0.00684848i
\(85\) −31.6394 18.9355i −0.372228 0.222770i
\(86\) 52.5993 0.611619
\(87\) 41.8376 + 41.8376i 0.480892 + 0.480892i
\(88\) 12.2831 12.2831i 0.139581 0.139581i
\(89\) 35.8168i 0.402436i −0.979547 0.201218i \(-0.935510\pi\)
0.979547 0.201218i \(-0.0644899\pi\)
\(90\) 10.8937 18.2024i 0.121041 0.202249i
\(91\) −0.422232 −0.00463991
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) −30.2978 + 30.2978i −0.325783 + 0.325783i
\(94\) 92.8588i 0.987859i
\(95\) 34.6331 + 137.876i 0.364559 + 1.45133i
\(96\) 9.79796 0.102062
\(97\) −93.7132 93.7132i −0.966115 0.966115i 0.0333292 0.999444i \(-0.489389\pi\)
−0.999444 + 0.0333292i \(0.989389\pi\)
\(98\) −48.9724 + 48.9724i −0.499719 + 0.499719i
\(99\) 18.4246i 0.186107i
\(100\) 23.6282 + 44.0648i 0.236282 + 0.440648i
\(101\) 46.9695 0.465044 0.232522 0.972591i \(-0.425302\pi\)
0.232522 + 0.972591i \(0.425302\pi\)
\(102\) −12.7731 12.7731i −0.125227 0.125227i
\(103\) 16.5301 16.5301i 0.160487 0.160487i −0.622296 0.782782i \(-0.713800\pi\)
0.782782 + 0.622296i \(0.213800\pi\)
\(104\) 7.19140i 0.0691481i
\(105\) 1.39485 0.350372i 0.0132843 0.00333688i
\(106\) 8.49366 0.0801289
\(107\) −89.6601 89.6601i −0.837945 0.837945i 0.150643 0.988588i \(-0.451866\pi\)
−0.988588 + 0.150643i \(0.951866\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 20.9512i 0.192213i 0.995371 + 0.0961064i \(0.0306389\pi\)
−0.995371 + 0.0961064i \(0.969361\pi\)
\(110\) 37.2636 + 22.3014i 0.338760 + 0.202740i
\(111\) −117.630 −1.05973
\(112\) 0.469708 + 0.469708i 0.00419382 + 0.00419382i
\(113\) 134.864 134.864i 1.19349 1.19349i 0.217404 0.976082i \(-0.430241\pi\)
0.976082 0.217404i \(-0.0697590\pi\)
\(114\) 69.6435i 0.610908i
\(115\) 12.3141 20.5758i 0.107079 0.178920i
\(116\) −68.3206 −0.588971
\(117\) −5.39355 5.39355i −0.0460987 0.0460987i
\(118\) −11.1749 + 11.1749i −0.0947023 + 0.0947023i
\(119\) 1.22467i 0.0102913i
\(120\) 5.96750 + 23.7569i 0.0497291 + 0.197974i
\(121\) −83.2814 −0.688276
\(122\) −80.2086 80.2086i −0.657447 0.657447i
\(123\) −76.6077 + 76.6077i −0.622826 + 0.622826i
\(124\) 49.4761i 0.399000i
\(125\) −92.4521 + 84.1286i −0.739617 + 0.673028i
\(126\) 0.704562 0.00559176
\(127\) 14.6980 + 14.6980i 0.115733 + 0.115733i 0.762601 0.646869i \(-0.223922\pi\)
−0.646869 + 0.762601i \(0.723922\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 64.4207i 0.499385i
\(130\) 17.4368 4.37996i 0.134129 0.0336920i
\(131\) −68.9070 −0.526007 −0.263004 0.964795i \(-0.584713\pi\)
−0.263004 + 0.964795i \(0.584713\pi\)
\(132\) 15.0437 + 15.0437i 0.113967 + 0.113967i
\(133\) −3.33867 + 3.33867i −0.0251028 + 0.0251028i
\(134\) 149.431i 1.11516i
\(135\) 22.2933 + 13.3420i 0.165135 + 0.0988299i
\(136\) 20.8584 0.153371
\(137\) 148.355 + 148.355i 1.08288 + 1.08288i 0.996239 + 0.0866447i \(0.0276145\pi\)
0.0866447 + 0.996239i \(0.472386\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 170.164i 1.22420i −0.790781 0.612099i \(-0.790325\pi\)
0.790781 0.612099i \(-0.209675\pi\)
\(140\) −0.852811 + 1.42497i −0.00609151 + 0.0101783i
\(141\) −113.728 −0.806584
\(142\) −5.49076 5.49076i −0.0386673 0.0386673i
\(143\) 11.0416 11.0416i 0.0772138 0.0772138i
\(144\) 12.0000i 0.0833333i
\(145\) −41.6110 165.655i −0.286972 1.14245i
\(146\) −28.4997 −0.195203
\(147\) −59.9787 59.9787i −0.408019 0.408019i
\(148\) 96.0445 96.0445i 0.648949 0.648949i
\(149\) 209.754i 1.40774i 0.710328 + 0.703871i \(0.248547\pi\)
−0.710328 + 0.703871i \(0.751453\pi\)
\(150\) −53.9682 + 28.9385i −0.359788 + 0.192923i
\(151\) 5.19070 0.0343755 0.0171878 0.999852i \(-0.494529\pi\)
0.0171878 + 0.999852i \(0.494529\pi\)
\(152\) −56.8637 56.8637i −0.374103 0.374103i
\(153\) 15.6438 15.6438i 0.102247 0.102247i
\(154\) 1.44237i 0.00936601i
\(155\) 119.963 30.1336i 0.773957 0.194411i
\(156\) 8.80763 0.0564592
\(157\) −2.34153 2.34153i −0.0149142 0.0149142i 0.699610 0.714525i \(-0.253357\pi\)
−0.714525 + 0.699610i \(0.753357\pi\)
\(158\) 66.3129 66.3129i 0.419702 0.419702i
\(159\) 10.4026i 0.0654249i
\(160\) −24.2698 14.5250i −0.151687 0.0907810i
\(161\) 0.796428 0.00494676
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 80.0854 80.0854i 0.491321 0.491321i −0.417401 0.908722i \(-0.637059\pi\)
0.908722 + 0.417401i \(0.137059\pi\)
\(164\) 125.100i 0.762804i
\(165\) −27.3136 + 45.6384i −0.165537 + 0.276596i
\(166\) 227.576 1.37094
\(167\) −212.730 212.730i −1.27383 1.27383i −0.944060 0.329773i \(-0.893028\pi\)
−0.329773 0.944060i \(-0.606972\pi\)
\(168\) −0.575272 + 0.575272i −0.00342424 + 0.00342424i
\(169\) 162.535i 0.961748i
\(170\) 12.7039 + 50.5749i 0.0747289 + 0.297499i
\(171\) −85.2956 −0.498805
\(172\) −52.5993 52.5993i −0.305810 0.305810i
\(173\) −153.930 + 153.930i −0.889769 + 0.889769i −0.994501 0.104731i \(-0.966602\pi\)
0.104731 + 0.994501i \(0.466602\pi\)
\(174\) 83.6753i 0.480892i
\(175\) −3.97449 1.19991i −0.0227114 0.00685661i
\(176\) −24.5662 −0.139581
\(177\) −13.6864 13.6864i −0.0773241 0.0773241i
\(178\) −35.8168 + 35.8168i −0.201218 + 0.201218i
\(179\) 119.472i 0.667440i −0.942672 0.333720i \(-0.891696\pi\)
0.942672 0.333720i \(-0.108304\pi\)
\(180\) −29.0961 + 7.30866i −0.161645 + 0.0406037i
\(181\) 104.780 0.578895 0.289447 0.957194i \(-0.406528\pi\)
0.289447 + 0.957194i \(0.406528\pi\)
\(182\) 0.422232 + 0.422232i 0.00231996 + 0.00231996i
\(183\) 98.2350 98.2350i 0.536803 0.536803i
\(184\) 13.5647i 0.0737210i
\(185\) 291.373 + 174.380i 1.57499 + 0.942597i
\(186\) 60.5955 0.325783
\(187\) 32.0257 + 32.0257i 0.171261 + 0.171261i
\(188\) 92.8588 92.8588i 0.493930 0.493930i
\(189\) 0.862908i 0.00456565i
\(190\) 103.243 172.509i 0.543384 0.907943i
\(191\) 243.162 1.27310 0.636549 0.771237i \(-0.280361\pi\)
0.636549 + 0.771237i \(0.280361\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 127.755 127.755i 0.661940 0.661940i −0.293897 0.955837i \(-0.594952\pi\)
0.955837 + 0.293897i \(0.0949522\pi\)
\(194\) 187.426i 0.966115i
\(195\) 5.36433 + 21.3556i 0.0275094 + 0.109516i
\(196\) 97.9448 0.499719
\(197\) −158.665 158.665i −0.805407 0.805407i 0.178528 0.983935i \(-0.442866\pi\)
−0.983935 + 0.178528i \(0.942866\pi\)
\(198\) −18.4246 + 18.4246i −0.0930537 + 0.0930537i
\(199\) 185.886i 0.934098i 0.884231 + 0.467049i \(0.154683\pi\)
−0.884231 + 0.467049i \(0.845317\pi\)
\(200\) 20.4367 67.6930i 0.102183 0.338465i
\(201\) −183.015 −0.910521
\(202\) −46.9695 46.9695i −0.232522 0.232522i
\(203\) 4.01134 4.01134i 0.0197603 0.0197603i
\(204\) 25.5462i 0.125227i
\(205\) 303.326 76.1926i 1.47964 0.371671i
\(206\) −33.0602 −0.160487
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −7.19140 + 7.19140i −0.0345740 + 0.0345740i
\(209\) 174.616i 0.835481i
\(210\) −1.74522 1.04448i −0.00831058 0.00497370i
\(211\) −19.0575 −0.0903197 −0.0451599 0.998980i \(-0.514380\pi\)
−0.0451599 + 0.998980i \(0.514380\pi\)
\(212\) −8.49366 8.49366i −0.0400644 0.0400644i
\(213\) 6.72477 6.72477i 0.0315717 0.0315717i
\(214\) 179.320i 0.837945i
\(215\) 95.5003 159.572i 0.444188 0.742195i
\(216\) −14.6969 −0.0680414
\(217\) 2.90491 + 2.90491i 0.0133867 + 0.0133867i
\(218\) 20.9512 20.9512i 0.0961064 0.0961064i
\(219\) 34.9049i 0.159383i
\(220\) −14.9622 59.5650i −0.0680098 0.270750i
\(221\) 18.7501 0.0848423
\(222\) 117.630 + 117.630i 0.529865 + 0.529865i
\(223\) 159.166 159.166i 0.713748 0.713748i −0.253569 0.967317i \(-0.581605\pi\)
0.967317 + 0.253569i \(0.0816046\pi\)
\(224\) 0.939416i 0.00419382i
\(225\) −35.4423 66.0972i −0.157521 0.293766i
\(226\) −269.728 −1.19349
\(227\) 2.50235 + 2.50235i 0.0110235 + 0.0110235i 0.712597 0.701574i \(-0.247519\pi\)
−0.701574 + 0.712597i \(0.747519\pi\)
\(228\) 69.6435 69.6435i 0.305454 0.305454i
\(229\) 108.398i 0.473354i −0.971588 0.236677i \(-0.923942\pi\)
0.971588 0.236677i \(-0.0760583\pi\)
\(230\) −32.8899 + 8.26162i −0.143000 + 0.0359201i
\(231\) −1.76653 −0.00764732
\(232\) 68.3206 + 68.3206i 0.294485 + 0.294485i
\(233\) 24.7659 24.7659i 0.106292 0.106292i −0.651961 0.758253i \(-0.726053\pi\)
0.758253 + 0.651961i \(0.226053\pi\)
\(234\) 10.7871i 0.0460987i
\(235\) 281.708 + 168.596i 1.19876 + 0.717431i
\(236\) 22.3497 0.0947023
\(237\) 81.2164 + 81.2164i 0.342685 + 0.342685i
\(238\) −1.22467 + 1.22467i −0.00514567 + 0.00514567i
\(239\) 264.476i 1.10659i 0.832985 + 0.553296i \(0.186630\pi\)
−0.832985 + 0.553296i \(0.813370\pi\)
\(240\) 17.7894 29.7244i 0.0741224 0.123852i
\(241\) 467.027 1.93787 0.968936 0.247311i \(-0.0795469\pi\)
0.968936 + 0.247311i \(0.0795469\pi\)
\(242\) 83.2814 + 83.2814i 0.344138 + 0.344138i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 160.417i 0.657447i
\(245\) 59.6538 + 237.484i 0.243485 + 0.969324i
\(246\) 153.215 0.622826
\(247\) −51.1162 51.1162i −0.206948 0.206948i
\(248\) −49.4761 + 49.4761i −0.199500 + 0.199500i
\(249\) 278.722i 1.11937i
\(250\) 176.581 + 8.32351i 0.706323 + 0.0332940i
\(251\) 204.851 0.816141 0.408070 0.912950i \(-0.366202\pi\)
0.408070 + 0.912950i \(0.366202\pi\)
\(252\) −0.704562 0.704562i −0.00279588 0.00279588i
\(253\) −20.8270 + 20.8270i −0.0823201 + 0.0823201i
\(254\) 29.3961i 0.115733i
\(255\) −61.9413 + 15.5591i −0.242907 + 0.0610159i
\(256\) 16.0000 0.0625000
\(257\) −142.969 142.969i −0.556301 0.556301i 0.371952 0.928252i \(-0.378689\pi\)
−0.928252 + 0.371952i \(0.878689\pi\)
\(258\) 64.4207 64.4207i 0.249693 0.249693i
\(259\) 11.2782i 0.0435452i
\(260\) −21.8168 13.0569i −0.0839107 0.0502187i
\(261\) 102.481 0.392647
\(262\) 68.9070 + 68.9070i 0.263004 + 0.263004i
\(263\) 337.181 337.181i 1.28206 1.28206i 0.342559 0.939496i \(-0.388706\pi\)
0.939496 0.342559i \(-0.111294\pi\)
\(264\) 30.0873i 0.113967i
\(265\) 15.4213 25.7675i 0.0581934 0.0972357i
\(266\) 6.67733 0.0251028
\(267\) −43.8664 43.8664i −0.164294 0.164294i
\(268\) 149.431 149.431i 0.557578 0.557578i
\(269\) 284.631i 1.05811i 0.848588 + 0.529054i \(0.177453\pi\)
−0.848588 + 0.529054i \(0.822547\pi\)
\(270\) −8.95124 35.6353i −0.0331528 0.131983i
\(271\) 19.1966 0.0708361 0.0354180 0.999373i \(-0.488724\pi\)
0.0354180 + 0.999373i \(0.488724\pi\)
\(272\) −20.8584 20.8584i −0.0766853 0.0766853i
\(273\) −0.517127 + 0.517127i −0.00189424 + 0.00189424i
\(274\) 296.710i 1.08288i
\(275\) 135.313 72.5568i 0.492048 0.263843i
\(276\) −16.6132 −0.0601929
\(277\) −38.3293 38.3293i −0.138373 0.138373i 0.634527 0.772900i \(-0.281195\pi\)
−0.772900 + 0.634527i \(0.781195\pi\)
\(278\) −170.164 + 170.164i −0.612099 + 0.612099i
\(279\) 74.2141i 0.266000i
\(280\) 2.27778 0.572156i 0.00813492 0.00204341i
\(281\) −222.591 −0.792138 −0.396069 0.918221i \(-0.629626\pi\)
−0.396069 + 0.918221i \(0.629626\pi\)
\(282\) 113.728 + 113.728i 0.403292 + 0.403292i
\(283\) 339.400 339.400i 1.19929 1.19929i 0.224916 0.974378i \(-0.427789\pi\)
0.974378 0.224916i \(-0.0722107\pi\)
\(284\) 10.9815i 0.0386673i
\(285\) 211.280 + 126.446i 0.741332 + 0.443671i
\(286\) −22.0832 −0.0772138
\(287\) 7.34504 + 7.34504i 0.0255925 + 0.0255925i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 234.616i 0.811819i
\(290\) −124.044 + 207.266i −0.427739 + 0.714711i
\(291\) −229.549 −0.788830
\(292\) 28.4997 + 28.4997i 0.0976017 + 0.0976017i
\(293\) 320.705 320.705i 1.09456 1.09456i 0.0995214 0.995035i \(-0.468269\pi\)
0.995035 0.0995214i \(-0.0317312\pi\)
\(294\) 119.957i 0.408019i
\(295\) 13.6122 + 54.1909i 0.0461431 + 0.183698i
\(296\) −192.089 −0.648949
\(297\) −22.5655 22.5655i −0.0759780 0.0759780i
\(298\) 209.754 209.754i 0.703871 0.703871i
\(299\) 12.1936i 0.0407813i
\(300\) 82.9067 + 25.0297i 0.276356 + 0.0834323i
\(301\) 6.17657 0.0205202
\(302\) −5.19070 5.19070i −0.0171878 0.0171878i
\(303\) 57.5256 57.5256i 0.189854 0.189854i
\(304\) 113.727i 0.374103i
\(305\) −388.959 + 97.7028i −1.27528 + 0.320337i
\(306\) −31.2876 −0.102247
\(307\) 45.3708 + 45.3708i 0.147788 + 0.147788i 0.777129 0.629341i \(-0.216675\pi\)
−0.629341 + 0.777129i \(0.716675\pi\)
\(308\) 1.44237 1.44237i 0.00468301 0.00468301i
\(309\) 40.4904i 0.131037i
\(310\) −150.097 89.8298i −0.484184 0.289773i
\(311\) −197.722 −0.635761 −0.317881 0.948131i \(-0.602971\pi\)
−0.317881 + 0.948131i \(0.602971\pi\)
\(312\) −8.80763 8.80763i −0.0282296 0.0282296i
\(313\) −330.259 + 330.259i −1.05514 + 1.05514i −0.0567518 + 0.998388i \(0.518074\pi\)
−0.998388 + 0.0567518i \(0.981926\pi\)
\(314\) 4.68306i 0.0149142i
\(315\) 1.27922 2.13745i 0.00406101 0.00678556i
\(316\) −132.626 −0.419702
\(317\) −106.236 106.236i −0.335128 0.335128i 0.519402 0.854530i \(-0.326155\pi\)
−0.854530 + 0.519402i \(0.826155\pi\)
\(318\) 10.4026 10.4026i 0.0327125 0.0327125i
\(319\) 209.797i 0.657671i
\(320\) 9.74488 + 38.7948i 0.0304527 + 0.121234i
\(321\) −219.622 −0.684179
\(322\) −0.796428 0.796428i −0.00247338 0.00247338i
\(323\) 148.261 148.261i 0.459012 0.459012i
\(324\) 18.0000i 0.0555556i
\(325\) 18.3710 60.8509i 0.0565262 0.187234i
\(326\) −160.171 −0.491321
\(327\) 25.6599 + 25.6599i 0.0784705 + 0.0784705i
\(328\) −125.100 + 125.100i −0.381402 + 0.381402i
\(329\) 10.9041i 0.0331432i
\(330\) 72.9520 18.3248i 0.221067 0.0555298i
\(331\) −273.823 −0.827259 −0.413630 0.910445i \(-0.635739\pi\)
−0.413630 + 0.910445i \(0.635739\pi\)
\(332\) −227.576 227.576i −0.685470 0.685470i
\(333\) −144.067 + 144.067i −0.432633 + 0.432633i
\(334\) 425.460i 1.27383i
\(335\) 453.333 + 271.310i 1.35323 + 0.809880i
\(336\) 1.15054 0.00342424
\(337\) 136.789 + 136.789i 0.405901 + 0.405901i 0.880306 0.474406i \(-0.157337\pi\)
−0.474406 + 0.880306i \(0.657337\pi\)
\(338\) 162.535 162.535i 0.480874 0.480874i
\(339\) 330.348i 0.974477i
\(340\) 37.8710 63.2788i 0.111385 0.186114i
\(341\) −151.930 −0.445542
\(342\) 85.2956 + 85.2956i 0.249402 + 0.249402i
\(343\) −11.5046 + 11.5046i −0.0335411 + 0.0335411i
\(344\) 105.199i 0.305810i
\(345\) −10.1184 40.2817i −0.0293286 0.116759i
\(346\) 307.860 0.889769
\(347\) 234.167 + 234.167i 0.674832 + 0.674832i 0.958826 0.283994i \(-0.0916597\pi\)
−0.283994 + 0.958826i \(0.591660\pi\)
\(348\) −83.6753 + 83.6753i −0.240446 + 0.240446i
\(349\) 99.7358i 0.285776i −0.989739 0.142888i \(-0.954361\pi\)
0.989739 0.142888i \(-0.0456389\pi\)
\(350\) 2.77458 + 5.17440i 0.00792738 + 0.0147840i
\(351\) −13.2114 −0.0376395
\(352\) 24.5662 + 24.5662i 0.0697903 + 0.0697903i
\(353\) −380.797 + 380.797i −1.07874 + 1.07874i −0.0821221 + 0.996622i \(0.526170\pi\)
−0.996622 + 0.0821221i \(0.973830\pi\)
\(354\) 27.3727i 0.0773241i
\(355\) −26.6266 + 6.68834i −0.0750045 + 0.0188404i
\(356\) 71.6336 0.201218
\(357\) −1.49991 1.49991i −0.00420142 0.00420142i
\(358\) −119.472 + 119.472i −0.333720 + 0.333720i
\(359\) 219.427i 0.611218i −0.952157 0.305609i \(-0.901140\pi\)
0.952157 0.305609i \(-0.0988600\pi\)
\(360\) 36.4048 + 21.7874i 0.101124 + 0.0605207i
\(361\) −447.371 −1.23925
\(362\) −104.780 104.780i −0.289447 0.289447i
\(363\) −101.998 + 101.998i −0.280988 + 0.280988i
\(364\) 0.844464i 0.00231996i
\(365\) −51.7446 + 86.4604i −0.141766 + 0.236878i
\(366\) −196.470 −0.536803
\(367\) 68.5769 + 68.5769i 0.186858 + 0.186858i 0.794336 0.607478i \(-0.207819\pi\)
−0.607478 + 0.794336i \(0.707819\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 187.650i 0.508536i
\(370\) −116.993 465.754i −0.316197 1.25879i
\(371\) 0.997384 0.00268837
\(372\) −60.5955 60.5955i −0.162891 0.162891i
\(373\) −273.348 + 273.348i −0.732835 + 0.732835i −0.971180 0.238345i \(-0.923395\pi\)
0.238345 + 0.971180i \(0.423395\pi\)
\(374\) 64.0514i 0.171261i
\(375\) −10.1942 + 216.266i −0.0271845 + 0.576710i
\(376\) −185.718 −0.493930
\(377\) 61.4151 + 61.4151i 0.162905 + 0.162905i
\(378\) 0.862908 0.862908i 0.00228283 0.00228283i
\(379\) 63.4309i 0.167364i 0.996493 + 0.0836819i \(0.0266680\pi\)
−0.996493 + 0.0836819i \(0.973332\pi\)
\(380\) −275.752 + 69.2663i −0.725664 + 0.182280i
\(381\) 36.0027 0.0944952
\(382\) −243.162 243.162i −0.636549 0.636549i
\(383\) 205.490 205.490i 0.536528 0.536528i −0.385979 0.922507i \(-0.626136\pi\)
0.922507 + 0.385979i \(0.126136\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 4.37575 + 2.61879i 0.0113656 + 0.00680205i
\(386\) −255.509 −0.661940
\(387\) 78.8989 + 78.8989i 0.203873 + 0.203873i
\(388\) 187.426 187.426i 0.483058 0.483058i
\(389\) 223.663i 0.574968i 0.957785 + 0.287484i \(0.0928188\pi\)
−0.957785 + 0.287484i \(0.907181\pi\)
\(390\) 15.9913 26.7200i 0.0410034 0.0685128i
\(391\) −35.3672 −0.0904531
\(392\) −97.9448 97.9448i −0.249859 0.249859i
\(393\) −84.3935 + 84.3935i −0.214742 + 0.214742i
\(394\) 317.330i 0.805407i
\(395\) −80.7764 321.575i −0.204497 0.814113i
\(396\) 36.8493 0.0930537
\(397\) −364.562 364.562i −0.918293 0.918293i 0.0786121 0.996905i \(-0.474951\pi\)
−0.996905 + 0.0786121i \(0.974951\pi\)
\(398\) 185.886 185.886i 0.467049 0.467049i
\(399\) 8.17803i 0.0204963i
\(400\) −88.1297 + 47.2563i −0.220324 + 0.118141i
\(401\) −66.6545 −0.166221 −0.0831103 0.996540i \(-0.526485\pi\)
−0.0831103 + 0.996540i \(0.526485\pi\)
\(402\) 183.015 + 183.015i 0.455261 + 0.455261i
\(403\) −44.4753 + 44.4753i −0.110360 + 0.110360i
\(404\) 93.9389i 0.232522i
\(405\) 43.6442 10.9630i 0.107763 0.0270691i
\(406\) −8.02268 −0.0197603
\(407\) −294.931 294.931i −0.724646 0.724646i
\(408\) 25.5462 25.5462i 0.0626133 0.0626133i
\(409\) 383.884i 0.938592i −0.883041 0.469296i \(-0.844508\pi\)
0.883041 0.469296i \(-0.155492\pi\)
\(410\) −379.519 227.134i −0.925656 0.553985i
\(411\) 363.394 0.884171
\(412\) 33.0602 + 33.0602i 0.0802433 + 0.0802433i
\(413\) −1.31223 + 1.31223i −0.00317731 + 0.00317731i
\(414\) 20.3470i 0.0491473i
\(415\) 413.192 690.404i 0.995642 1.66362i
\(416\) 14.3828 0.0345740
\(417\) −208.407 208.407i −0.499777 0.499777i
\(418\) −174.616 + 174.616i −0.417741 + 0.417741i
\(419\) 557.095i 1.32958i −0.747030 0.664791i \(-0.768521\pi\)
0.747030 0.664791i \(-0.231479\pi\)
\(420\) 0.700745 + 2.78970i 0.00166844 + 0.00664214i
\(421\) −104.927 −0.249233 −0.124617 0.992205i \(-0.539770\pi\)
−0.124617 + 0.992205i \(0.539770\pi\)
\(422\) 19.0575 + 19.0575i 0.0451599 + 0.0451599i
\(423\) −139.288 + 139.288i −0.329286 + 0.329286i
\(424\) 16.9873i 0.0400644i
\(425\) 176.496 + 53.2845i 0.415285 + 0.125375i
\(426\) −13.4495 −0.0315717
\(427\) −9.41865 9.41865i −0.0220577 0.0220577i
\(428\) 179.320 179.320i 0.418972 0.418972i
\(429\) 27.0462i 0.0630448i
\(430\) −255.072 + 64.0717i −0.593192 + 0.149004i
\(431\) 238.158 0.552571 0.276286 0.961076i \(-0.410896\pi\)
0.276286 + 0.961076i \(0.410896\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −495.395 + 495.395i −1.14410 + 1.14410i −0.156407 + 0.987693i \(0.549991\pi\)
−0.987693 + 0.156407i \(0.950009\pi\)
\(434\) 5.80982i 0.0133867i
\(435\) −253.848 151.923i −0.583559 0.349247i
\(436\) −41.9024 −0.0961064
\(437\) 96.4171 + 96.4171i 0.220634 + 0.220634i
\(438\) −34.9049 + 34.9049i −0.0796915 + 0.0796915i
\(439\) 689.182i 1.56989i 0.619564 + 0.784946i \(0.287309\pi\)
−0.619564 + 0.784946i \(0.712691\pi\)
\(440\) −44.6029 + 74.5272i −0.101370 + 0.169380i
\(441\) −146.917 −0.333146
\(442\) −18.7501 18.7501i −0.0424212 0.0424212i
\(443\) 87.5468 87.5468i 0.197623 0.197623i −0.601357 0.798980i \(-0.705373\pi\)
0.798980 + 0.601357i \(0.205373\pi\)
\(444\) 235.260i 0.529865i
\(445\) 43.6288 + 173.688i 0.0980422 + 0.390310i
\(446\) −318.332 −0.713748
\(447\) 256.895 + 256.895i 0.574708 + 0.574708i
\(448\) −0.939416 + 0.939416i −0.00209691 + 0.00209691i
\(449\) 387.507i 0.863045i 0.902102 + 0.431523i \(0.142023\pi\)
−0.902102 + 0.431523i \(0.857977\pi\)
\(450\) −30.6550 + 101.540i −0.0681222 + 0.225643i
\(451\) −384.153 −0.851781
\(452\) 269.728 + 269.728i 0.596743 + 0.596743i
\(453\) 6.35729 6.35729i 0.0140337 0.0140337i
\(454\) 5.00469i 0.0110235i
\(455\) 2.04755 0.514325i 0.00450011 0.00113038i
\(456\) −139.287 −0.305454
\(457\) 277.891 + 277.891i 0.608077 + 0.608077i 0.942443 0.334366i \(-0.108522\pi\)
−0.334366 + 0.942443i \(0.608522\pi\)
\(458\) −108.398 + 108.398i −0.236677 + 0.236677i
\(459\) 38.3193i 0.0834844i
\(460\) 41.1515 + 24.6283i 0.0894598 + 0.0535397i
\(461\) 15.1488 0.0328607 0.0164304 0.999865i \(-0.494770\pi\)
0.0164304 + 0.999865i \(0.494770\pi\)
\(462\) 1.76653 + 1.76653i 0.00382366 + 0.00382366i
\(463\) −384.007 + 384.007i −0.829390 + 0.829390i −0.987432 0.158043i \(-0.949482\pi\)
0.158043 + 0.987432i \(0.449482\pi\)
\(464\) 136.641i 0.294485i
\(465\) 110.019 183.831i 0.236599 0.395335i
\(466\) −49.5319 −0.106292
\(467\) −296.796 296.796i −0.635538 0.635538i 0.313914 0.949452i \(-0.398360\pi\)
−0.949452 + 0.313914i \(0.898360\pi\)
\(468\) 10.7871 10.7871i 0.0230494 0.0230494i
\(469\) 17.5472i 0.0374141i
\(470\) −113.112 450.305i −0.240664 0.958095i
\(471\) −5.73555 −0.0121774
\(472\) −22.3497 22.3497i −0.0473511 0.0473511i
\(473\) −161.520 + 161.520i −0.341481 + 0.341481i
\(474\) 162.433i 0.342685i
\(475\) −335.896 626.423i −0.707150 1.31878i
\(476\) 2.44934 0.00514567
\(477\) 12.7405 + 12.7405i 0.0267096 + 0.0267096i
\(478\) 264.476 264.476i 0.553296 0.553296i
\(479\) 769.722i 1.60694i 0.595348 + 0.803468i \(0.297014\pi\)
−0.595348 + 0.803468i \(0.702986\pi\)
\(480\) −47.5137 + 11.9350i −0.0989870 + 0.0248646i
\(481\) −172.674 −0.358989
\(482\) −467.027 467.027i −0.968936 0.968936i
\(483\) 0.975421 0.975421i 0.00201951 0.00201951i
\(484\) 166.563i 0.344138i
\(485\) 568.601 + 340.295i 1.17237 + 0.701640i
\(486\) 22.0454 0.0453609
\(487\) 302.447 + 302.447i 0.621041 + 0.621041i 0.945798 0.324757i \(-0.105282\pi\)
−0.324757 + 0.945798i \(0.605282\pi\)
\(488\) 160.417 160.417i 0.328724 0.328724i
\(489\) 196.168i 0.401162i
\(490\) 177.831 297.138i 0.362920 0.606405i
\(491\) 317.270 0.646171 0.323086 0.946370i \(-0.395280\pi\)
0.323086 + 0.946370i \(0.395280\pi\)
\(492\) −153.215 153.215i −0.311413 0.311413i
\(493\) −178.132 + 178.132i −0.361323 + 0.361323i
\(494\) 102.232i 0.206948i
\(495\) 22.4432 + 89.3475i 0.0453399 + 0.180500i
\(496\) 98.9521 0.199500
\(497\) −0.644763 0.644763i −0.00129731 0.00129731i
\(498\) 278.722 278.722i 0.559684 0.559684i
\(499\) 524.718i 1.05154i 0.850627 + 0.525769i \(0.176223\pi\)
−0.850627 + 0.525769i \(0.823777\pi\)
\(500\) −168.257 184.904i −0.336514 0.369808i
\(501\) −521.080 −1.04008
\(502\) −204.851 204.851i −0.408070 0.408070i
\(503\) 325.215 325.215i 0.646551 0.646551i −0.305607 0.952158i \(-0.598859\pi\)
0.952158 + 0.305607i \(0.0988594\pi\)
\(504\) 1.40912i 0.00279588i
\(505\) −227.771 + 57.2140i −0.451033 + 0.113295i
\(506\) 41.6540 0.0823201
\(507\) 199.064 + 199.064i 0.392632 + 0.392632i
\(508\) −29.3961 + 29.3961i −0.0578663 + 0.0578663i
\(509\) 104.801i 0.205897i 0.994687 + 0.102948i \(0.0328276\pi\)
−0.994687 + 0.102948i \(0.967172\pi\)
\(510\) 77.5004 + 46.3823i 0.151962 + 0.0909456i
\(511\) −3.34663 −0.00654918
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −104.465 + 104.465i −0.203636 + 0.203636i
\(514\) 285.938i 0.556301i
\(515\) −60.0248 + 100.296i −0.116553 + 0.194749i
\(516\) −128.841 −0.249693
\(517\) −285.148 285.148i −0.551544 0.551544i
\(518\) 11.2782 11.2782i 0.0217726 0.0217726i
\(519\) 377.050i 0.726493i
\(520\) 8.75992 + 34.8736i 0.0168460 + 0.0670647i
\(521\) 678.468 1.30224 0.651121 0.758974i \(-0.274299\pi\)
0.651121 + 0.758974i \(0.274299\pi\)
\(522\) −102.481 102.481i −0.196324 0.196324i
\(523\) −494.733 + 494.733i −0.945952 + 0.945952i −0.998612 0.0526604i \(-0.983230\pi\)
0.0526604 + 0.998612i \(0.483230\pi\)
\(524\) 137.814i 0.263004i
\(525\) −6.33732 + 3.39816i −0.0120711 + 0.00647268i
\(526\) −674.361 −1.28206
\(527\) −128.999 128.999i −0.244780 0.244780i
\(528\) −30.0873 + 30.0873i −0.0569835 + 0.0569835i
\(529\) 23.0000i 0.0434783i
\(530\) −41.1887 + 10.3462i −0.0777146 + 0.0195212i
\(531\) −33.5246 −0.0631348
\(532\) −6.67733 6.67733i −0.0125514 0.0125514i
\(533\) −112.455 + 112.455i −0.210986 + 0.210986i
\(534\) 87.7328i 0.164294i
\(535\) 544.009 + 325.578i 1.01684 + 0.608556i
\(536\) −298.862 −0.557578
\(537\) −146.322 146.322i −0.272481 0.272481i
\(538\) 284.631 284.631i 0.529054 0.529054i
\(539\) 300.766i 0.558008i
\(540\) −26.6841 + 44.5866i −0.0494149 + 0.0825677i
\(541\) −981.574 −1.81437 −0.907185 0.420732i \(-0.861773\pi\)
−0.907185 + 0.420732i \(0.861773\pi\)
\(542\) −19.1966 19.1966i −0.0354180 0.0354180i
\(543\) 128.329 128.329i 0.236333 0.236333i
\(544\) 41.7168i 0.0766853i
\(545\) −25.5209 101.600i −0.0468273 0.186421i
\(546\) 1.03425 0.00189424
\(547\) −420.807 420.807i −0.769300 0.769300i 0.208683 0.977983i \(-0.433082\pi\)
−0.977983 + 0.208683i \(0.933082\pi\)
\(548\) −296.710 + 296.710i −0.541442 + 0.541442i
\(549\) 240.626i 0.438298i
\(550\) −207.870 62.7563i −0.377945 0.114102i
\(551\) 971.241 1.76269
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 7.78692 7.78692i 0.0140812 0.0140812i
\(554\) 76.6586i 0.138373i
\(555\) 570.429 143.286i 1.02780 0.258173i
\(556\) 340.327 0.612099
\(557\) 113.406 + 113.406i 0.203602 + 0.203602i 0.801541 0.597940i \(-0.204014\pi\)
−0.597940 + 0.801541i \(0.704014\pi\)
\(558\) 74.2141 74.2141i 0.133000 0.133000i
\(559\) 94.5656i 0.169169i
\(560\) −2.84993 1.70562i −0.00508917 0.00304575i
\(561\) 78.4467 0.139834
\(562\) 222.591 + 222.591i 0.396069 + 0.396069i
\(563\) 265.151 265.151i 0.470962 0.470962i −0.431264 0.902226i \(-0.641932\pi\)
0.902226 + 0.431264i \(0.141932\pi\)
\(564\) 227.457i 0.403292i
\(565\) −489.723 + 818.282i −0.866767 + 1.44829i
\(566\) −678.800 −1.19929
\(567\) 1.05684 + 1.05684i 0.00186392 + 0.00186392i
\(568\) 10.9815 10.9815i 0.0193336 0.0193336i
\(569\) 262.710i 0.461705i 0.972989 + 0.230852i \(0.0741515\pi\)
−0.972989 + 0.230852i \(0.925849\pi\)
\(570\) −84.8335 337.726i −0.148831 0.592502i
\(571\) 311.028 0.544707 0.272354 0.962197i \(-0.412198\pi\)
0.272354 + 0.962197i \(0.412198\pi\)
\(572\) 22.0832 + 22.0832i 0.0386069 + 0.0386069i
\(573\) 297.811 297.811i 0.519740 0.519740i
\(574\) 14.6901i 0.0255925i
\(575\) −34.6520 + 114.779i −0.0602644 + 0.199616i
\(576\) −24.0000 −0.0416667
\(577\) 639.863 + 639.863i 1.10895 + 1.10895i 0.993289 + 0.115658i \(0.0368978\pi\)
0.115658 + 0.993289i \(0.463102\pi\)
\(578\) −234.616 + 234.616i −0.405910 + 0.405910i
\(579\) 312.933i 0.540472i
\(580\) 331.311 83.2220i 0.571225 0.143486i
\(581\) 26.7235 0.0459958
\(582\) 229.549 + 229.549i 0.394415 + 0.394415i
\(583\) −26.0821 + 26.0821i −0.0447377 + 0.0447377i
\(584\) 56.9994i 0.0976017i
\(585\) 32.7252 + 19.5853i 0.0559404 + 0.0334791i
\(586\) −641.410 −1.09456
\(587\) −210.805 210.805i −0.359124 0.359124i 0.504366 0.863490i \(-0.331726\pi\)
−0.863490 + 0.504366i \(0.831726\pi\)
\(588\) 119.957 119.957i 0.204009 0.204009i
\(589\) 703.348i 1.19414i
\(590\) 40.5786 67.8031i 0.0687774 0.114920i
\(591\) −388.649 −0.657612
\(592\) 192.089 + 192.089i 0.324475 + 0.324475i
\(593\) −20.9100 + 20.9100i −0.0352615 + 0.0352615i −0.724518 0.689256i \(-0.757937\pi\)
0.689256 + 0.724518i \(0.257937\pi\)
\(594\) 45.1310i 0.0759780i
\(595\) 1.49178 + 5.93885i 0.00250720 + 0.00998127i
\(596\) −419.507 −0.703871
\(597\) 227.662 + 227.662i 0.381344 + 0.381344i
\(598\) 12.1936 12.1936i 0.0203907 0.0203907i
\(599\) 290.370i 0.484759i −0.970182 0.242379i \(-0.922072\pi\)
0.970182 0.242379i \(-0.0779278\pi\)
\(600\) −57.8770 107.936i −0.0964616 0.179894i
\(601\) 240.612 0.400353 0.200177 0.979760i \(-0.435848\pi\)
0.200177 + 0.979760i \(0.435848\pi\)
\(602\) −6.17657 6.17657i −0.0102601 0.0102601i
\(603\) −224.146 + 224.146i −0.371719 + 0.371719i
\(604\) 10.3814i 0.0171878i
\(605\) 403.861 101.446i 0.667539 0.167679i
\(606\) −115.051 −0.189854
\(607\) −311.886 311.886i −0.513816 0.513816i 0.401877 0.915693i \(-0.368358\pi\)
−0.915693 + 0.401877i \(0.868358\pi\)
\(608\) 113.727 113.727i 0.187052 0.187052i
\(609\) 9.82573i 0.0161342i
\(610\) 486.662 + 291.257i 0.797807 + 0.477470i
\(611\) −166.946 −0.273234
\(612\) 31.2876 + 31.2876i 0.0511236 + 0.0511236i
\(613\) −815.318 + 815.318i −1.33005 + 1.33005i −0.424722 + 0.905324i \(0.639628\pi\)
−0.905324 + 0.424722i \(0.860372\pi\)
\(614\) 90.7416i 0.147788i
\(615\) 278.181 464.814i 0.452327 0.755795i
\(616\) −2.88473 −0.00468301
\(617\) 169.873 + 169.873i 0.275321 + 0.275321i 0.831238 0.555917i \(-0.187633\pi\)
−0.555917 + 0.831238i \(0.687633\pi\)
\(618\) −40.4904 + 40.4904i −0.0655184 + 0.0655184i
\(619\) 541.211i 0.874331i −0.899381 0.437166i \(-0.855982\pi\)
0.899381 0.437166i \(-0.144018\pi\)
\(620\) 60.2673 + 239.927i 0.0972053 + 0.386979i
\(621\) 24.9199 0.0401286
\(622\) 197.722 + 197.722i 0.317881 + 0.317881i
\(623\) −4.20586 + 4.20586i −0.00675097 + 0.00675097i
\(624\) 17.6153i 0.0282296i
\(625\) 345.855 520.586i 0.553368 0.832937i
\(626\) 660.518 1.05514
\(627\) −213.860 213.860i −0.341084 0.341084i
\(628\) 4.68306 4.68306i 0.00745709 0.00745709i
\(629\) 500.834i 0.796238i
\(630\) −3.41667 + 0.858234i −0.00542328 + 0.00136228i
\(631\) 488.542 0.774235 0.387118 0.922030i \(-0.373471\pi\)
0.387118 + 0.922030i \(0.373471\pi\)
\(632\) 132.626 + 132.626i 0.209851 + 0.209851i
\(633\) −23.3405 + 23.3405i −0.0368729 + 0.0368729i
\(634\) 212.471i 0.335128i
\(635\) −89.1798 53.3721i −0.140441 0.0840506i
\(636\) −20.8051 −0.0327125
\(637\) −88.0451 88.0451i −0.138218 0.138218i
\(638\) 209.797 209.797i 0.328835 0.328835i
\(639\) 16.4723i 0.0257782i
\(640\) 29.0499 48.5397i 0.0453905 0.0758433i
\(641\) −914.915 −1.42732 −0.713662 0.700490i \(-0.752965\pi\)
−0.713662 + 0.700490i \(0.752965\pi\)
\(642\) 219.622 + 219.622i 0.342090 + 0.342090i
\(643\) 762.346 762.346i 1.18561 1.18561i 0.207339 0.978269i \(-0.433520\pi\)
0.978269 0.207339i \(-0.0664804\pi\)
\(644\) 1.59286i 0.00247338i
\(645\) −78.4715 312.399i −0.121661 0.484339i
\(646\) −296.522 −0.459012
\(647\) −54.6116 54.6116i −0.0844074 0.0844074i 0.663643 0.748050i \(-0.269010\pi\)
−0.748050 + 0.663643i \(0.769010\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 68.6310i 0.105749i
\(650\) −79.2220 + 42.4799i −0.121880 + 0.0653537i
\(651\) 7.11555 0.0109302
\(652\) 160.171 + 160.171i 0.245661 + 0.245661i
\(653\) −455.974 + 455.974i −0.698276 + 0.698276i −0.964039 0.265763i \(-0.914376\pi\)
0.265763 + 0.964039i \(0.414376\pi\)
\(654\) 51.3197i 0.0784705i
\(655\) 334.154 83.9363i 0.510159 0.128147i
\(656\) 250.200 0.381402
\(657\) −42.7495 42.7495i −0.0650678 0.0650678i
\(658\) 10.9041 10.9041i 0.0165716 0.0165716i
\(659\) 89.6678i 0.136066i 0.997683 + 0.0680332i \(0.0216724\pi\)
−0.997683 + 0.0680332i \(0.978328\pi\)
\(660\) −91.2768 54.6271i −0.138298 0.0827684i
\(661\) 1014.42 1.53468 0.767338 0.641243i \(-0.221581\pi\)
0.767338 + 0.641243i \(0.221581\pi\)
\(662\) 273.823 + 273.823i 0.413630 + 0.413630i
\(663\) 22.9641 22.9641i 0.0346367 0.0346367i
\(664\) 455.152i 0.685470i
\(665\) 12.1235 20.2572i 0.0182308 0.0304620i
\(666\) 288.133 0.432633
\(667\) −115.843 115.843i −0.173678 0.173678i
\(668\) 425.460 425.460i 0.636917 0.636917i
\(669\) 389.875i 0.582773i
\(670\) −182.023 724.643i −0.271677 1.08156i
\(671\) 492.604 0.734135
\(672\) −1.15054 1.15054i −0.00171212 0.00171212i
\(673\) 150.044 150.044i 0.222949 0.222949i −0.586790 0.809739i \(-0.699609\pi\)
0.809739 + 0.586790i \(0.199609\pi\)
\(674\) 273.577i 0.405901i
\(675\) −124.360 37.5445i −0.184237 0.0556215i
\(676\) −325.071 −0.480874
\(677\) 405.045 + 405.045i 0.598294 + 0.598294i 0.939859 0.341564i \(-0.110957\pi\)
−0.341564 + 0.939859i \(0.610957\pi\)
\(678\) −330.348 + 330.348i −0.487239 + 0.487239i
\(679\) 22.0089i 0.0324137i
\(680\) −101.150 + 25.4078i −0.148750 + 0.0373645i
\(681\) 6.12947 0.00900069
\(682\) 151.930 + 151.930i 0.222771 + 0.222771i
\(683\) 285.685 285.685i 0.418279 0.418279i −0.466331 0.884610i \(-0.654424\pi\)
0.884610 + 0.466331i \(0.154424\pi\)
\(684\) 170.591i 0.249402i
\(685\) −900.139 538.713i −1.31407 0.786443i
\(686\) 23.0092 0.0335411
\(687\) −132.760 132.760i −0.193246 0.193246i
\(688\) 105.199 105.199i 0.152905 0.152905i
\(689\) 15.2703i 0.0221630i
\(690\) −30.1634 + 50.4001i −0.0437150 + 0.0730437i
\(691\) 586.921 0.849380 0.424690 0.905339i \(-0.360383\pi\)
0.424690 + 0.905339i \(0.360383\pi\)
\(692\) −307.860 307.860i −0.444885 0.444885i
\(693\) −2.16355 + 2.16355i −0.00312200 + 0.00312200i
\(694\) 468.333i 0.674832i
\(695\) 207.278 + 825.183i 0.298242 + 1.18731i
\(696\) 167.351 0.240446
\(697\) −326.173 326.173i −0.467967 0.467967i
\(698\) −99.7358 + 99.7358i −0.142888 + 0.142888i
\(699\) 60.6639i 0.0867867i
\(700\) 2.39981 7.94898i 0.00342831 0.0113557i
\(701\) −188.831 −0.269373 −0.134687 0.990888i \(-0.543003\pi\)
−0.134687 + 0.990888i \(0.543003\pi\)
\(702\) 13.2114 + 13.2114i 0.0188197 + 0.0188197i
\(703\) −1365.36 + 1365.36i −1.94219 + 1.94219i
\(704\) 49.1324i 0.0697903i
\(705\) 551.508 138.534i 0.782281 0.196501i
\(706\) 761.594 1.07874
\(707\) −5.51548 5.51548i −0.00780125 0.00780125i
\(708\) 27.3727 27.3727i 0.0386620 0.0386620i
\(709\) 166.680i 0.235092i 0.993067 + 0.117546i \(0.0375027\pi\)
−0.993067 + 0.117546i \(0.962497\pi\)
\(710\) 33.3149 + 19.9383i 0.0469225 + 0.0280821i
\(711\) 198.939 0.279801
\(712\) −71.6336 71.6336i −0.100609 0.100609i
\(713\) 83.8907 83.8907i 0.117659 0.117659i
\(714\) 2.99982i 0.00420142i
\(715\) −40.0946 + 66.9944i −0.0560764 + 0.0936984i
\(716\) 238.944 0.333720
\(717\) 323.915 + 323.915i 0.451764 + 0.451764i
\(718\) −219.427 + 219.427i −0.305609 + 0.305609i
\(719\) 891.573i 1.24002i −0.784594 0.620009i \(-0.787129\pi\)
0.784594 0.620009i \(-0.212871\pi\)
\(720\) −14.6173 58.1922i −0.0203018 0.0808225i
\(721\) −3.88216 −0.00538441
\(722\) 447.371 + 447.371i 0.619627 + 0.619627i
\(723\) 571.989 571.989i 0.791133 0.791133i
\(724\) 209.560i 0.289447i
\(725\) 403.573 + 752.634i 0.556652 + 1.03812i
\(726\) 203.997 0.280988
\(727\) −277.079 277.079i −0.381127 0.381127i 0.490381 0.871508i \(-0.336858\pi\)
−0.871508 + 0.490381i \(0.836858\pi\)
\(728\) −0.844464 + 0.844464i −0.00115998 + 0.00115998i
\(729\) 27.0000i 0.0370370i
\(730\) 138.205 34.7158i 0.189322 0.0475558i
\(731\) −274.284 −0.375218
\(732\) 196.470 + 196.470i 0.268402 + 0.268402i
\(733\) −746.187 + 746.187i −1.01799 + 1.01799i −0.0181547 + 0.999835i \(0.505779\pi\)
−0.999835 + 0.0181547i \(0.994221\pi\)
\(734\) 137.154i 0.186858i
\(735\) 363.919 + 217.797i 0.495127 + 0.296323i
\(736\) −27.1293 −0.0368605
\(737\) −458.868 458.868i −0.622617 0.622617i
\(738\) 187.650 187.650i 0.254268 0.254268i
\(739\) 948.207i 1.28309i −0.767083 0.641547i \(-0.778293\pi\)
0.767083 0.641547i \(-0.221707\pi\)
\(740\) −348.761 + 582.746i −0.471298 + 0.787495i
\(741\) −125.209 −0.168973
\(742\) −0.997384 0.997384i −0.00134418 0.00134418i
\(743\) 442.342 442.342i 0.595346 0.595346i −0.343724 0.939071i \(-0.611689\pi\)
0.939071 + 0.343724i \(0.111689\pi\)
\(744\) 121.191i 0.162891i
\(745\) −255.503 1017.17i −0.342957 1.36533i
\(746\) 546.695 0.732835
\(747\) 341.364 + 341.364i 0.456980 + 0.456980i
\(748\) −64.0514 + 64.0514i −0.0856303 + 0.0856303i
\(749\) 21.0570i 0.0281135i
\(750\) 226.460 206.072i 0.301947 0.274763i
\(751\) 1168.45 1.55586 0.777930 0.628351i \(-0.216270\pi\)
0.777930 + 0.628351i \(0.216270\pi\)
\(752\) 185.718 + 185.718i 0.246965 + 0.246965i
\(753\) 250.891 250.891i 0.333188 0.333188i
\(754\) 122.830i 0.162905i
\(755\) −25.1715 + 6.32285i −0.0333398 + 0.00837463i
\(756\) −1.72582 −0.00228283
\(757\) 121.372 + 121.372i 0.160332 + 0.160332i 0.782714 0.622382i \(-0.213835\pi\)
−0.622382 + 0.782714i \(0.713835\pi\)
\(758\) 63.4309 63.4309i 0.0836819 0.0836819i
\(759\) 51.0155i 0.0672141i
\(760\) 345.018 + 206.486i 0.453972 + 0.271692i
\(761\) −503.571 −0.661723 −0.330862 0.943679i \(-0.607339\pi\)
−0.330862 + 0.943679i \(0.607339\pi\)
\(762\) −36.0027 36.0027i −0.0472476 0.0472476i
\(763\) 2.46023 2.46023i 0.00322442 0.00322442i
\(764\) 486.323i 0.636549i
\(765\) −56.8064 + 94.9182i −0.0742568 + 0.124076i
\(766\) −410.980 −0.536528
\(767\) −20.0907 20.0907i −0.0261939 0.0261939i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 612.600i 0.796619i −0.917251 0.398310i \(-0.869597\pi\)
0.917251 0.398310i \(-0.130403\pi\)
\(770\) −1.75696 6.99454i −0.00228177 0.00908382i
\(771\) −350.202 −0.454217
\(772\) 255.509 + 255.509i 0.330970 + 0.330970i
\(773\) 205.059 205.059i 0.265276 0.265276i −0.561917 0.827194i \(-0.689936\pi\)
0.827194 + 0.561917i \(0.189936\pi\)
\(774\) 157.798i 0.203873i
\(775\) −545.039 + 292.257i −0.703276 + 0.377106i
\(776\) −374.853 −0.483058
\(777\) 13.8129 + 13.8129i 0.0177773 + 0.0177773i
\(778\) 223.663 223.663i 0.287484 0.287484i