Properties

Label 690.3.k.a.277.14
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
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: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.14
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.99686 - 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 - 4.63984i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.99686 - 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 - 4.63984i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.17412 + 4.81959i) q^{10} +2.27620 q^{11} +(2.44949 + 2.44949i) q^{12} +(6.59512 - 6.59512i) q^{13} -9.27967i q^{14} +(5.90277 - 6.33698i) q^{15} -4.00000 q^{16} +(16.0847 + 16.0847i) q^{17} +(3.00000 - 3.00000i) q^{18} -33.4152i q^{19} +(0.354533 + 9.99371i) q^{20} -11.3652 q^{21} +(2.27620 + 2.27620i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(24.9372 - 1.77155i) q^{25} +13.1902 q^{26} +(-3.67423 - 3.67423i) q^{27} +(9.27967 - 9.27967i) q^{28} +8.75349i q^{29} +(12.2397 - 0.434212i) q^{30} +26.0099 q^{31} +(-4.00000 - 4.00000i) q^{32} +(2.78777 - 2.78777i) q^{33} +32.1694i q^{34} +(-24.0071 - 22.3621i) q^{35} +6.00000 q^{36} +(18.6213 + 18.6213i) q^{37} +(33.4152 - 33.4152i) q^{38} -16.1547i q^{39} +(-9.63918 + 10.3482i) q^{40} +4.34271 q^{41} +(-11.3652 - 11.3652i) q^{42} +(33.4812 - 33.4812i) q^{43} +4.55240i q^{44} +(-0.531799 - 14.9906i) q^{45} +6.78233 q^{46} +(-28.7769 - 28.7769i) q^{47} +(-4.89898 + 4.89898i) q^{48} -5.94385i q^{49} +(26.7087 + 23.1656i) q^{50} +39.3992 q^{51} +(13.1902 + 13.1902i) q^{52} +(-34.3298 + 34.3298i) q^{53} -7.34847i q^{54} +(11.3739 - 0.403494i) q^{55} +18.5593 q^{56} +(-40.9250 - 40.9250i) q^{57} +(-8.75349 + 8.75349i) q^{58} +71.9203i q^{59} +(12.6740 + 11.8055i) q^{60} -71.6157 q^{61} +(26.0099 + 26.0099i) q^{62} +(-13.9195 + 13.9195i) q^{63} -8.00000i q^{64} +(31.7858 - 34.1240i) q^{65} +5.57553 q^{66} +(-80.0034 - 80.0034i) q^{67} +(-32.1694 + 32.1694i) q^{68} -8.30662i q^{69} +(-1.64497 - 46.3692i) q^{70} +103.758 q^{71} +(6.00000 + 6.00000i) q^{72} +(1.17476 - 1.17476i) q^{73} +37.2426i q^{74} +(28.3720 - 32.7113i) q^{75} +66.8303 q^{76} +(-10.5612 - 10.5612i) q^{77} +(16.1547 - 16.1547i) q^{78} +134.376i q^{79} +(-19.9874 + 0.709066i) q^{80} -9.00000 q^{81} +(4.34271 + 4.34271i) q^{82} +(-11.8656 + 11.8656i) q^{83} -22.7305i q^{84} +(83.2241 + 77.5215i) q^{85} +66.9623 q^{86} +(10.7208 + 10.7208i) q^{87} +(-4.55240 + 4.55240i) q^{88} +40.9315i q^{89} +(14.4588 - 15.5224i) q^{90} -61.2005 q^{91} +(6.78233 + 6.78233i) q^{92} +(31.8555 - 31.8555i) q^{93} -57.5539i q^{94} +(-5.92339 - 166.971i) q^{95} -9.79796 q^{96} +(31.1861 + 31.1861i) q^{97} +(5.94385 - 5.94385i) q^{98} -6.82860i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

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
\(5\) 4.99686 0.177266i 0.999371 0.0354533i
\(6\) 2.44949 0.408248
\(7\) −4.63984 4.63984i −0.662834 0.662834i 0.293213 0.956047i \(-0.405275\pi\)
−0.956047 + 0.293213i \(0.905275\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 5.17412 + 4.81959i 0.517412 + 0.481959i
\(11\) 2.27620 0.206927 0.103464 0.994633i \(-0.467007\pi\)
0.103464 + 0.994633i \(0.467007\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 6.59512 6.59512i 0.507317 0.507317i −0.406385 0.913702i \(-0.633211\pi\)
0.913702 + 0.406385i \(0.133211\pi\)
\(14\) 9.27967i 0.662834i
\(15\) 5.90277 6.33698i 0.393518 0.422465i
\(16\) −4.00000 −0.250000
\(17\) 16.0847 + 16.0847i 0.946157 + 0.946157i 0.998623 0.0524654i \(-0.0167079\pi\)
−0.0524654 + 0.998623i \(0.516708\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 33.4152i 1.75869i −0.476183 0.879346i \(-0.657980\pi\)
0.476183 0.879346i \(-0.342020\pi\)
\(20\) 0.354533 + 9.99371i 0.0177266 + 0.499686i
\(21\) −11.3652 −0.541201
\(22\) 2.27620 + 2.27620i 0.103464 + 0.103464i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 24.9372 1.77155i 0.997486 0.0708620i
\(26\) 13.1902 0.507317
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 9.27967 9.27967i 0.331417 0.331417i
\(29\) 8.75349i 0.301844i 0.988546 + 0.150922i \(0.0482243\pi\)
−0.988546 + 0.150922i \(0.951776\pi\)
\(30\) 12.2397 0.434212i 0.407992 0.0144737i
\(31\) 26.0099 0.839028 0.419514 0.907749i \(-0.362200\pi\)
0.419514 + 0.907749i \(0.362200\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 2.78777 2.78777i 0.0844778 0.0844778i
\(34\) 32.1694i 0.946157i
\(35\) −24.0071 22.3621i −0.685917 0.638917i
\(36\) 6.00000 0.166667
\(37\) 18.6213 + 18.6213i 0.503278 + 0.503278i 0.912455 0.409177i \(-0.134184\pi\)
−0.409177 + 0.912455i \(0.634184\pi\)
\(38\) 33.4152 33.4152i 0.879346 0.879346i
\(39\) 16.1547i 0.414222i
\(40\) −9.63918 + 10.3482i −0.240980 + 0.258706i
\(41\) 4.34271 0.105920 0.0529599 0.998597i \(-0.483134\pi\)
0.0529599 + 0.998597i \(0.483134\pi\)
\(42\) −11.3652 11.3652i −0.270601 0.270601i
\(43\) 33.4812 33.4812i 0.778631 0.778631i −0.200967 0.979598i \(-0.564408\pi\)
0.979598 + 0.200967i \(0.0644083\pi\)
\(44\) 4.55240i 0.103464i
\(45\) −0.531799 14.9906i −0.0118178 0.333124i
\(46\) 6.78233 0.147442
\(47\) −28.7769 28.7769i −0.612275 0.612275i 0.331263 0.943538i \(-0.392525\pi\)
−0.943538 + 0.331263i \(0.892525\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 5.94385i 0.121303i
\(50\) 26.7087 + 23.1656i 0.534174 + 0.463312i
\(51\) 39.3992 0.772534
\(52\) 13.1902 + 13.1902i 0.253658 + 0.253658i
\(53\) −34.3298 + 34.3298i −0.647732 + 0.647732i −0.952444 0.304712i \(-0.901440\pi\)
0.304712 + 0.952444i \(0.401440\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 11.3739 0.403494i 0.206797 0.00733626i
\(56\) 18.5593 0.331417
\(57\) −40.9250 40.9250i −0.717983 0.717983i
\(58\) −8.75349 + 8.75349i −0.150922 + 0.150922i
\(59\) 71.9203i 1.21899i 0.792791 + 0.609494i \(0.208627\pi\)
−0.792791 + 0.609494i \(0.791373\pi\)
\(60\) 12.6740 + 11.8055i 0.211233 + 0.196759i
\(61\) −71.6157 −1.17403 −0.587014 0.809577i \(-0.699697\pi\)
−0.587014 + 0.809577i \(0.699697\pi\)
\(62\) 26.0099 + 26.0099i 0.419514 + 0.419514i
\(63\) −13.9195 + 13.9195i −0.220945 + 0.220945i
\(64\) 8.00000i 0.125000i
\(65\) 31.7858 34.1240i 0.489012 0.524984i
\(66\) 5.57553 0.0844778
\(67\) −80.0034 80.0034i −1.19408 1.19408i −0.975911 0.218169i \(-0.929991\pi\)
−0.218169 0.975911i \(-0.570009\pi\)
\(68\) −32.1694 + 32.1694i −0.473079 + 0.473079i
\(69\) 8.30662i 0.120386i
\(70\) −1.64497 46.3692i −0.0234996 0.662417i
\(71\) 103.758 1.46139 0.730694 0.682706i \(-0.239197\pi\)
0.730694 + 0.682706i \(0.239197\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 1.17476 1.17476i 0.0160926 0.0160926i −0.699015 0.715107i \(-0.746378\pi\)
0.715107 + 0.699015i \(0.246378\pi\)
\(74\) 37.2426i 0.503278i
\(75\) 28.3720 32.7113i 0.378293 0.436151i
\(76\) 66.8303 0.879346
\(77\) −10.5612 10.5612i −0.137158 0.137158i
\(78\) 16.1547 16.1547i 0.207111 0.207111i
\(79\) 134.376i 1.70096i 0.526008 + 0.850479i \(0.323688\pi\)
−0.526008 + 0.850479i \(0.676312\pi\)
\(80\) −19.9874 + 0.709066i −0.249843 + 0.00886332i
\(81\) −9.00000 −0.111111
\(82\) 4.34271 + 4.34271i 0.0529599 + 0.0529599i
\(83\) −11.8656 + 11.8656i −0.142959 + 0.142959i −0.774964 0.632005i \(-0.782232\pi\)
0.632005 + 0.774964i \(0.282232\pi\)
\(84\) 22.7305i 0.270601i
\(85\) 83.2241 + 77.5215i 0.979107 + 0.912018i
\(86\) 66.9623 0.778631
\(87\) 10.7208 + 10.7208i 0.123227 + 0.123227i
\(88\) −4.55240 + 4.55240i −0.0517319 + 0.0517319i
\(89\) 40.9315i 0.459905i 0.973202 + 0.229952i \(0.0738570\pi\)
−0.973202 + 0.229952i \(0.926143\pi\)
\(90\) 14.4588 15.5224i 0.160653 0.172471i
\(91\) −61.2005 −0.672533
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 31.8555 31.8555i 0.342532 0.342532i
\(94\) 57.5539i 0.612275i
\(95\) −5.92339 166.971i −0.0623514 1.75759i
\(96\) −9.79796 −0.102062
\(97\) 31.1861 + 31.1861i 0.321506 + 0.321506i 0.849345 0.527839i \(-0.176997\pi\)
−0.527839 + 0.849345i \(0.676997\pi\)
\(98\) 5.94385 5.94385i 0.0606515 0.0606515i
\(99\) 6.82860i 0.0689758i
\(100\) 3.54310 + 49.8743i 0.0354310 + 0.498743i
\(101\) 44.4799 0.440395 0.220197 0.975455i \(-0.429330\pi\)
0.220197 + 0.975455i \(0.429330\pi\)
\(102\) 39.3992 + 39.3992i 0.386267 + 0.386267i
\(103\) 87.3328 87.3328i 0.847891 0.847891i −0.141979 0.989870i \(-0.545346\pi\)
0.989870 + 0.141979i \(0.0453465\pi\)
\(104\) 26.3805i 0.253658i
\(105\) −56.7904 + 2.01467i −0.540861 + 0.0191874i
\(106\) −68.6596 −0.647732
\(107\) 15.9149 + 15.9149i 0.148737 + 0.148737i 0.777554 0.628817i \(-0.216460\pi\)
−0.628817 + 0.777554i \(0.716460\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 40.4073i 0.370709i 0.982672 + 0.185355i \(0.0593434\pi\)
−0.982672 + 0.185355i \(0.940657\pi\)
\(110\) 11.7773 + 10.9704i 0.107067 + 0.0997305i
\(111\) 45.6127 0.410925
\(112\) 18.5593 + 18.5593i 0.165708 + 0.165708i
\(113\) −44.9394 + 44.9394i −0.397694 + 0.397694i −0.877419 0.479725i \(-0.840736\pi\)
0.479725 + 0.877419i \(0.340736\pi\)
\(114\) 81.8501i 0.717983i
\(115\) 16.3440 17.5463i 0.142122 0.152577i
\(116\) −17.5070 −0.150922
\(117\) −19.7854 19.7854i −0.169106 0.169106i
\(118\) −71.9203 + 71.9203i −0.609494 + 0.609494i
\(119\) 149.260i 1.25429i
\(120\) 0.868424 + 24.4795i 0.00723687 + 0.203996i
\(121\) −115.819 −0.957181
\(122\) −71.6157 71.6157i −0.587014 0.587014i
\(123\) 5.31871 5.31871i 0.0432416 0.0432416i
\(124\) 52.0197i 0.419514i
\(125\) 124.293 13.2727i 0.994347 0.106182i
\(126\) −27.8390 −0.220945
\(127\) 84.8776 + 84.8776i 0.668328 + 0.668328i 0.957329 0.289001i \(-0.0933231\pi\)
−0.289001 + 0.957329i \(0.593323\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 82.0117i 0.635750i
\(130\) 65.9097 2.33819i 0.506998 0.0179860i
\(131\) −29.0659 −0.221877 −0.110939 0.993827i \(-0.535386\pi\)
−0.110939 + 0.993827i \(0.535386\pi\)
\(132\) 5.57553 + 5.57553i 0.0422389 + 0.0422389i
\(133\) −155.041 + 155.041i −1.16572 + 1.16572i
\(134\) 160.007i 1.19408i
\(135\) −19.0109 17.7083i −0.140822 0.131173i
\(136\) −64.3387 −0.473079
\(137\) 50.3452 + 50.3452i 0.367483 + 0.367483i 0.866558 0.499076i \(-0.166327\pi\)
−0.499076 + 0.866558i \(0.666327\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 83.2681i 0.599051i 0.954088 + 0.299525i \(0.0968283\pi\)
−0.954088 + 0.299525i \(0.903172\pi\)
\(140\) 44.7242 48.0142i 0.319459 0.342958i
\(141\) −70.4888 −0.499921
\(142\) 103.758 + 103.758i 0.730694 + 0.730694i
\(143\) 15.0118 15.0118i 0.104978 0.104978i
\(144\) 12.0000i 0.0833333i
\(145\) 1.55170 + 43.7399i 0.0107014 + 0.301655i
\(146\) 2.34952 0.0160926
\(147\) −7.27970 7.27970i −0.0495218 0.0495218i
\(148\) −37.2426 + 37.2426i −0.251639 + 0.251639i
\(149\) 35.8235i 0.240426i −0.992748 0.120213i \(-0.961642\pi\)
0.992748 0.120213i \(-0.0383578\pi\)
\(150\) 61.0833 4.33939i 0.407222 0.0289293i
\(151\) −296.868 −1.96602 −0.983008 0.183562i \(-0.941237\pi\)
−0.983008 + 0.183562i \(0.941237\pi\)
\(152\) 66.8303 + 66.8303i 0.439673 + 0.439673i
\(153\) 48.2540 48.2540i 0.315386 0.315386i
\(154\) 21.1224i 0.137158i
\(155\) 129.968 4.61068i 0.838501 0.0297463i
\(156\) 32.3094 0.207111
\(157\) −171.782 171.782i −1.09415 1.09415i −0.995080 0.0990741i \(-0.968412\pi\)
−0.0990741 0.995080i \(-0.531588\pi\)
\(158\) −134.376 + 134.376i −0.850479 + 0.850479i
\(159\) 84.0905i 0.528871i
\(160\) −20.6965 19.2784i −0.129353 0.120490i
\(161\) −31.4689 −0.195459
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −153.218 + 153.218i −0.939991 + 0.939991i −0.998299 0.0583080i \(-0.981429\pi\)
0.0583080 + 0.998299i \(0.481429\pi\)
\(164\) 8.68542i 0.0529599i
\(165\) 13.4359 14.4242i 0.0814296 0.0874197i
\(166\) −23.7312 −0.142959
\(167\) −125.613 125.613i −0.752174 0.752174i 0.222711 0.974885i \(-0.428510\pi\)
−0.974885 + 0.222711i \(0.928510\pi\)
\(168\) 22.7305 22.7305i 0.135300 0.135300i
\(169\) 82.0088i 0.485259i
\(170\) 5.70254 + 160.746i 0.0335444 + 0.945563i
\(171\) −100.245 −0.586231
\(172\) 66.9623 + 66.9623i 0.389316 + 0.389316i
\(173\) −125.643 + 125.643i −0.726262 + 0.726262i −0.969873 0.243611i \(-0.921668\pi\)
0.243611 + 0.969873i \(0.421668\pi\)
\(174\) 21.4416i 0.123227i
\(175\) −123.924 107.485i −0.708137 0.614198i
\(176\) −9.10481 −0.0517319
\(177\) 88.0840 + 88.0840i 0.497650 + 0.497650i
\(178\) −40.9315 + 40.9315i −0.229952 + 0.229952i
\(179\) 92.2918i 0.515596i 0.966199 + 0.257798i \(0.0829970\pi\)
−0.966199 + 0.257798i \(0.917003\pi\)
\(180\) 29.9811 1.06360i 0.166562 0.00590888i
\(181\) −111.846 −0.617932 −0.308966 0.951073i \(-0.599983\pi\)
−0.308966 + 0.951073i \(0.599983\pi\)
\(182\) −61.2005 61.2005i −0.336267 0.336267i
\(183\) −87.7110 + 87.7110i −0.479295 + 0.479295i
\(184\) 13.5647i 0.0737210i
\(185\) 96.3489 + 89.7470i 0.520805 + 0.485119i
\(186\) 63.7109 0.342532
\(187\) 36.6120 + 36.6120i 0.195786 + 0.195786i
\(188\) 57.5539 57.5539i 0.306138 0.306138i
\(189\) 34.0957i 0.180400i
\(190\) 161.047 172.894i 0.847618 0.909969i
\(191\) −93.7491 −0.490833 −0.245416 0.969418i \(-0.578925\pi\)
−0.245416 + 0.969418i \(0.578925\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −100.013 + 100.013i −0.518201 + 0.518201i −0.917027 0.398826i \(-0.869418\pi\)
0.398826 + 0.917027i \(0.369418\pi\)
\(194\) 62.3722i 0.321506i
\(195\) −2.86368 80.7226i −0.0146855 0.413962i
\(196\) 11.8877 0.0606515
\(197\) 112.363 + 112.363i 0.570371 + 0.570371i 0.932232 0.361861i \(-0.117859\pi\)
−0.361861 + 0.932232i \(0.617859\pi\)
\(198\) 6.82860 6.82860i 0.0344879 0.0344879i
\(199\) 60.0337i 0.301677i −0.988558 0.150838i \(-0.951803\pi\)
0.988558 0.150838i \(-0.0481973\pi\)
\(200\) −46.3312 + 53.4174i −0.231656 + 0.267087i
\(201\) −195.967 −0.974963
\(202\) 44.4799 + 44.4799i 0.220197 + 0.220197i
\(203\) 40.6147 40.6147i 0.200073 0.200073i
\(204\) 78.7985i 0.386267i
\(205\) 21.6999 0.769817i 0.105853 0.00375520i
\(206\) 174.666 0.847891
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −26.3805 + 26.3805i −0.126829 + 0.126829i
\(209\) 76.0596i 0.363922i
\(210\) −58.8051 54.7758i −0.280024 0.260837i
\(211\) −72.4262 −0.343252 −0.171626 0.985162i \(-0.554902\pi\)
−0.171626 + 0.985162i \(0.554902\pi\)
\(212\) −68.6596 68.6596i −0.323866 0.323866i
\(213\) 127.078 127.078i 0.596609 0.596609i
\(214\) 31.8298i 0.148737i
\(215\) 161.365 173.236i 0.750537 0.805747i
\(216\) 14.6969 0.0680414
\(217\) −120.682 120.682i −0.556136 0.556136i
\(218\) −40.4073 + 40.4073i −0.185355 + 0.185355i
\(219\) 2.87757i 0.0131396i
\(220\) 0.806988 + 22.7477i 0.00366813 + 0.103399i
\(221\) 212.161 0.960003
\(222\) 45.6127 + 45.6127i 0.205463 + 0.205463i
\(223\) 161.871 161.871i 0.725879 0.725879i −0.243917 0.969796i \(-0.578432\pi\)
0.969796 + 0.243917i \(0.0784324\pi\)
\(224\) 37.1187i 0.165708i
\(225\) −5.31465 74.8115i −0.0236207 0.332495i
\(226\) −89.8788 −0.397694
\(227\) −258.326 258.326i −1.13800 1.13800i −0.988808 0.149193i \(-0.952332\pi\)
−0.149193 0.988808i \(-0.547668\pi\)
\(228\) 81.8501 81.8501i 0.358992 0.358992i
\(229\) 210.083i 0.917395i 0.888593 + 0.458697i \(0.151684\pi\)
−0.888593 + 0.458697i \(0.848316\pi\)
\(230\) 33.8903 1.20228i 0.147349 0.00522730i
\(231\) −25.8696 −0.111989
\(232\) −17.5070 17.5070i −0.0754611 0.0754611i
\(233\) 244.089 244.089i 1.04759 1.04759i 0.0487828 0.998809i \(-0.484466\pi\)
0.998809 0.0487828i \(-0.0155342\pi\)
\(234\) 39.5707i 0.169106i
\(235\) −148.895 138.693i −0.633598 0.590183i
\(236\) −143.841 −0.609494
\(237\) 164.576 + 164.576i 0.694414 + 0.694414i
\(238\) 149.260 149.260i 0.627145 0.627145i
\(239\) 314.702i 1.31675i 0.752692 + 0.658373i \(0.228755\pi\)
−0.752692 + 0.658373i \(0.771245\pi\)
\(240\) −23.6111 + 25.3479i −0.0983795 + 0.105616i
\(241\) −178.804 −0.741927 −0.370964 0.928647i \(-0.620973\pi\)
−0.370964 + 0.928647i \(0.620973\pi\)
\(242\) −115.819 115.819i −0.478591 0.478591i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 143.231i 0.587014i
\(245\) −1.05364 29.7006i −0.00430059 0.121227i
\(246\) 10.6374 0.0432416
\(247\) −220.377 220.377i −0.892215 0.892215i
\(248\) −52.0197 + 52.0197i −0.209757 + 0.209757i
\(249\) 29.0646i 0.116725i
\(250\) 137.566 + 111.021i 0.550264 + 0.444083i
\(251\) 183.648 0.731664 0.365832 0.930681i \(-0.380784\pi\)
0.365832 + 0.930681i \(0.380784\pi\)
\(252\) −27.8390 27.8390i −0.110472 0.110472i
\(253\) 7.71898 7.71898i 0.0305098 0.0305098i
\(254\) 169.755i 0.668328i
\(255\) 196.872 6.98416i 0.772049 0.0273889i
\(256\) 16.0000 0.0625000
\(257\) −258.659 258.659i −1.00646 1.00646i −0.999979 0.00647714i \(-0.997938\pi\)
−0.00647714 0.999979i \(-0.502062\pi\)
\(258\) 82.0117 82.0117i 0.317875 0.317875i
\(259\) 172.800i 0.667180i
\(260\) 68.2479 + 63.5715i 0.262492 + 0.244506i
\(261\) 26.2605 0.100615
\(262\) −29.0659 29.0659i −0.110939 0.110939i
\(263\) −6.73066 + 6.73066i −0.0255919 + 0.0255919i −0.719787 0.694195i \(-0.755761\pi\)
0.694195 + 0.719787i \(0.255761\pi\)
\(264\) 11.1511i 0.0422389i
\(265\) −165.456 + 177.627i −0.624361 + 0.670289i
\(266\) −310.082 −1.16572
\(267\) 50.1307 + 50.1307i 0.187755 + 0.187755i
\(268\) 160.007 160.007i 0.597040 0.597040i
\(269\) 195.237i 0.725787i −0.931831 0.362893i \(-0.881789\pi\)
0.931831 0.362893i \(-0.118211\pi\)
\(270\) −1.30264 36.7192i −0.00482458 0.135997i
\(271\) −190.383 −0.702522 −0.351261 0.936278i \(-0.614247\pi\)
−0.351261 + 0.936278i \(0.614247\pi\)
\(272\) −64.3387 64.3387i −0.236539 0.236539i
\(273\) −74.9550 + 74.9550i −0.274561 + 0.274561i
\(274\) 100.690i 0.367483i
\(275\) 56.7620 4.03240i 0.206407 0.0146633i
\(276\) 16.6132 0.0601929
\(277\) 361.616 + 361.616i 1.30547 + 1.30547i 0.924647 + 0.380824i \(0.124360\pi\)
0.380824 + 0.924647i \(0.375640\pi\)
\(278\) −83.2681 + 83.2681i −0.299525 + 0.299525i
\(279\) 78.0296i 0.279676i
\(280\) 92.7384 3.28995i 0.331208 0.0117498i
\(281\) −259.206 −0.922440 −0.461220 0.887286i \(-0.652588\pi\)
−0.461220 + 0.887286i \(0.652588\pi\)
\(282\) −70.4888 70.4888i −0.249960 0.249960i
\(283\) −283.592 + 283.592i −1.00209 + 1.00209i −0.00209570 + 0.999998i \(0.500667\pi\)
−0.999998 + 0.00209570i \(0.999333\pi\)
\(284\) 207.517i 0.730694i
\(285\) −211.751 197.242i −0.742987 0.692077i
\(286\) 30.0236 0.104978
\(287\) −20.1495 20.1495i −0.0702072 0.0702072i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 228.434i 0.790428i
\(290\) −42.1882 + 45.2916i −0.145477 + 0.156178i
\(291\) 76.3900 0.262509
\(292\) 2.34952 + 2.34952i 0.00804632 + 0.00804632i
\(293\) 104.580 104.580i 0.356927 0.356927i −0.505752 0.862679i \(-0.668785\pi\)
0.862679 + 0.505752i \(0.168785\pi\)
\(294\) 14.5594i 0.0495218i
\(295\) 12.7490 + 359.375i 0.0432171 + 1.21822i
\(296\) −74.4852 −0.251639
\(297\) −8.36330 8.36330i −0.0281593 0.0281593i
\(298\) 35.8235 35.8235i 0.120213 0.120213i
\(299\) 44.7303i 0.149600i
\(300\) 65.4227 + 56.7439i 0.218076 + 0.189146i
\(301\) −310.694 −1.03221
\(302\) −296.868 296.868i −0.983008 0.983008i
\(303\) 54.4765 54.4765i 0.179790 0.179790i
\(304\) 133.661i 0.439673i
\(305\) −357.853 + 12.6951i −1.17329 + 0.0416231i
\(306\) 96.5081 0.315386
\(307\) 212.425 + 212.425i 0.691938 + 0.691938i 0.962658 0.270720i \(-0.0872618\pi\)
−0.270720 + 0.962658i \(0.587262\pi\)
\(308\) 21.1224 21.1224i 0.0685792 0.0685792i
\(309\) 213.921i 0.692300i
\(310\) 134.578 + 125.357i 0.434124 + 0.404377i
\(311\) −206.221 −0.663089 −0.331545 0.943440i \(-0.607570\pi\)
−0.331545 + 0.943440i \(0.607570\pi\)
\(312\) 32.3094 + 32.3094i 0.103556 + 0.103556i
\(313\) 203.838 203.838i 0.651240 0.651240i −0.302052 0.953292i \(-0.597672\pi\)
0.953292 + 0.302052i \(0.0976716\pi\)
\(314\) 343.564i 1.09415i
\(315\) −67.0863 + 72.0212i −0.212972 + 0.228639i
\(316\) −268.751 −0.850479
\(317\) 71.5639 + 71.5639i 0.225754 + 0.225754i 0.810916 0.585162i \(-0.198969\pi\)
−0.585162 + 0.810916i \(0.698969\pi\)
\(318\) −84.0905 + 84.0905i −0.264436 + 0.264436i
\(319\) 19.9247i 0.0624599i
\(320\) −1.41813 39.9749i −0.00443166 0.124921i
\(321\) 38.9833 0.121443
\(322\) −31.4689 31.4689i −0.0977295 0.0977295i
\(323\) 537.472 537.472i 1.66400 1.66400i
\(324\) 18.0000i 0.0555556i
\(325\) 152.780 176.147i 0.470092 0.541991i
\(326\) −306.437 −0.939991
\(327\) 49.4887 + 49.4887i 0.151341 + 0.151341i
\(328\) −8.68542 + 8.68542i −0.0264799 + 0.0264799i
\(329\) 267.041i 0.811673i
\(330\) 27.8601 0.988355i 0.0844247 0.00299501i
\(331\) 480.713 1.45230 0.726152 0.687534i \(-0.241307\pi\)
0.726152 + 0.687534i \(0.241307\pi\)
\(332\) −23.7312 23.7312i −0.0714794 0.0714794i
\(333\) 55.8639 55.8639i 0.167759 0.167759i
\(334\) 251.226i 0.752174i
\(335\) −413.947 385.584i −1.23566 1.15100i
\(336\) 45.4609 0.135300
\(337\) −220.766 220.766i −0.655093 0.655093i 0.299122 0.954215i \(-0.403306\pi\)
−0.954215 + 0.299122i \(0.903306\pi\)
\(338\) −82.0088 + 82.0088i −0.242630 + 0.242630i
\(339\) 110.079i 0.324716i
\(340\) −155.043 + 166.448i −0.456009 + 0.489553i
\(341\) 59.2037 0.173618
\(342\) −100.245 100.245i −0.293115 0.293115i
\(343\) −254.930 + 254.930i −0.743237 + 0.743237i
\(344\) 133.925i 0.389316i
\(345\) −1.47249 41.5070i −0.00426807 0.120310i
\(346\) −251.287 −0.726262
\(347\) 229.061 + 229.061i 0.660118 + 0.660118i 0.955408 0.295290i \(-0.0954163\pi\)
−0.295290 + 0.955408i \(0.595416\pi\)
\(348\) −21.4416 + 21.4416i −0.0616137 + 0.0616137i
\(349\) 498.993i 1.42978i 0.699237 + 0.714890i \(0.253523\pi\)
−0.699237 + 0.714890i \(0.746477\pi\)
\(350\) −16.4394 231.409i −0.0469697 0.661167i
\(351\) −48.4640 −0.138074
\(352\) −9.10481 9.10481i −0.0258659 0.0258659i
\(353\) 99.5617 99.5617i 0.282044 0.282044i −0.551879 0.833924i \(-0.686089\pi\)
0.833924 + 0.551879i \(0.186089\pi\)
\(354\) 176.168i 0.497650i
\(355\) 518.466 18.3929i 1.46047 0.0518110i
\(356\) −81.8630 −0.229952
\(357\) −182.806 182.806i −0.512062 0.512062i
\(358\) −92.2918 + 92.2918i −0.257798 + 0.257798i
\(359\) 320.098i 0.891639i 0.895123 + 0.445819i \(0.147088\pi\)
−0.895123 + 0.445819i \(0.852912\pi\)
\(360\) 31.0447 + 28.9175i 0.0862354 + 0.0803265i
\(361\) −755.573 −2.09300
\(362\) −111.846 111.846i −0.308966 0.308966i
\(363\) −141.849 + 141.849i −0.390768 + 0.390768i
\(364\) 122.401i 0.336267i
\(365\) 5.66187 6.07836i 0.0155120 0.0166531i
\(366\) −175.422 −0.479295
\(367\) 114.617 + 114.617i 0.312308 + 0.312308i 0.845803 0.533495i \(-0.179122\pi\)
−0.533495 + 0.845803i \(0.679122\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 13.0281i 0.0353066i
\(370\) 6.60186 + 186.096i 0.0178429 + 0.502962i
\(371\) 318.569 0.858677
\(372\) 63.7109 + 63.7109i 0.171266 + 0.171266i
\(373\) 444.902 444.902i 1.19277 1.19277i 0.216480 0.976287i \(-0.430542\pi\)
0.976287 0.216480i \(-0.0694576\pi\)
\(374\) 73.2239i 0.195786i
\(375\) 135.972 168.483i 0.362592 0.449289i
\(376\) 115.108 0.306138
\(377\) 57.7303 + 57.7303i 0.153131 + 0.153131i
\(378\) −34.0957 + 34.0957i −0.0902002 + 0.0902002i
\(379\) 255.776i 0.674870i 0.941349 + 0.337435i \(0.109559\pi\)
−0.941349 + 0.337435i \(0.890441\pi\)
\(380\) 333.942 11.8468i 0.878794 0.0311757i
\(381\) 207.907 0.545687
\(382\) −93.7491 93.7491i −0.245416 0.245416i
\(383\) 336.758 336.758i 0.879265 0.879265i −0.114194 0.993458i \(-0.536428\pi\)
0.993458 + 0.114194i \(0.0364285\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −54.6450 50.9007i −0.141935 0.132210i
\(386\) −200.026 −0.518201
\(387\) −100.443 100.443i −0.259544 0.259544i
\(388\) −62.3722 + 62.3722i −0.160753 + 0.160753i
\(389\) 459.806i 1.18202i 0.806664 + 0.591011i \(0.201271\pi\)
−0.806664 + 0.591011i \(0.798729\pi\)
\(390\) 77.8589 83.5863i 0.199638 0.214324i
\(391\) 109.092 0.279007
\(392\) 11.8877 + 11.8877i 0.0303258 + 0.0303258i
\(393\) −35.5984 + 35.5984i −0.0905811 + 0.0905811i
\(394\) 224.726i 0.570371i
\(395\) 23.8203 + 671.456i 0.0603046 + 1.69989i
\(396\) 13.6572 0.0344879
\(397\) 76.9931 + 76.9931i 0.193937 + 0.193937i 0.797395 0.603458i \(-0.206211\pi\)
−0.603458 + 0.797395i \(0.706211\pi\)
\(398\) 60.0337 60.0337i 0.150838 0.150838i
\(399\) 379.771i 0.951807i
\(400\) −99.7486 + 7.08620i −0.249372 + 0.0177155i
\(401\) 50.6120 0.126215 0.0631073 0.998007i \(-0.479899\pi\)
0.0631073 + 0.998007i \(0.479899\pi\)
\(402\) −195.967 195.967i −0.487481 0.487481i
\(403\) 171.538 171.538i 0.425653 0.425653i
\(404\) 88.9598i 0.220197i
\(405\) −44.9717 + 1.59540i −0.111041 + 0.00393925i
\(406\) 81.2295 0.200073
\(407\) 42.3858 + 42.3858i 0.104142 + 0.104142i
\(408\) −78.7985 + 78.7985i −0.193134 + 0.193134i
\(409\) 570.317i 1.39442i 0.716867 + 0.697210i \(0.245575\pi\)
−0.716867 + 0.697210i \(0.754425\pi\)
\(410\) 22.4697 + 20.9301i 0.0548042 + 0.0510490i
\(411\) 123.320 0.300049
\(412\) 174.666 + 174.666i 0.423945 + 0.423945i
\(413\) 333.698 333.698i 0.807986 0.807986i
\(414\) 20.3470i 0.0491473i
\(415\) −57.1873 + 61.3940i −0.137801 + 0.147937i
\(416\) −52.7610 −0.126829
\(417\) 101.982 + 101.982i 0.244561 + 0.244561i
\(418\) 76.0596 76.0596i 0.181961 0.181961i
\(419\) 230.287i 0.549610i 0.961500 + 0.274805i \(0.0886133\pi\)
−0.961500 + 0.274805i \(0.911387\pi\)
\(420\) −4.02935 113.581i −0.00959368 0.270431i
\(421\) 506.694 1.20355 0.601774 0.798666i \(-0.294461\pi\)
0.601774 + 0.798666i \(0.294461\pi\)
\(422\) −72.4262 72.4262i −0.171626 0.171626i
\(423\) −86.3308 + 86.3308i −0.204092 + 0.204092i
\(424\) 137.319i 0.323866i
\(425\) 429.601 + 372.611i 1.01083 + 0.876732i
\(426\) 254.155 0.596609
\(427\) 332.285 + 332.285i 0.778185 + 0.778185i
\(428\) −31.8298 + 31.8298i −0.0743686 + 0.0743686i
\(429\) 36.7713i 0.0857140i
\(430\) 334.601 11.8702i 0.778142 0.0276050i
\(431\) 693.838 1.60983 0.804916 0.593389i \(-0.202210\pi\)
0.804916 + 0.593389i \(0.202210\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 203.719 203.719i 0.470482 0.470482i −0.431589 0.902070i \(-0.642047\pi\)
0.902070 + 0.431589i \(0.142047\pi\)
\(434\) 241.363i 0.556136i
\(435\) 55.4707 + 51.6698i 0.127519 + 0.118781i
\(436\) −80.8147 −0.185355
\(437\) −113.316 113.316i −0.259305 0.259305i
\(438\) 2.87757 2.87757i 0.00656979 0.00656979i
\(439\) 719.749i 1.63952i −0.572708 0.819759i \(-0.694107\pi\)
0.572708 0.819759i \(-0.305893\pi\)
\(440\) −21.9407 + 23.5547i −0.0498653 + 0.0535334i
\(441\) −17.8316 −0.0404344
\(442\) 212.161 + 212.161i 0.480002 + 0.480002i
\(443\) 257.483 257.483i 0.581225 0.581225i −0.354015 0.935240i \(-0.615184\pi\)
0.935240 + 0.354015i \(0.115184\pi\)
\(444\) 91.2254i 0.205463i
\(445\) 7.25578 + 204.529i 0.0163051 + 0.459615i
\(446\) 323.742 0.725879
\(447\) −43.8746 43.8746i −0.0981535 0.0981535i
\(448\) −37.1187 + 37.1187i −0.0828542 + 0.0828542i
\(449\) 520.870i 1.16007i 0.814593 + 0.580033i \(0.196960\pi\)
−0.814593 + 0.580033i \(0.803040\pi\)
\(450\) 69.4968 80.1261i 0.154437 0.178058i
\(451\) 9.88489 0.0219177
\(452\) −89.8788 89.8788i −0.198847 0.198847i
\(453\) −363.588 + 363.588i −0.802623 + 0.802623i
\(454\) 516.653i 1.13800i
\(455\) −305.810 + 10.8488i −0.672111 + 0.0238435i
\(456\) 163.700 0.358992
\(457\) −274.247 274.247i −0.600103 0.600103i 0.340237 0.940340i \(-0.389493\pi\)
−0.940340 + 0.340237i \(0.889493\pi\)
\(458\) −210.083 + 210.083i −0.458697 + 0.458697i
\(459\) 118.198i 0.257511i
\(460\) 35.0926 + 32.6881i 0.0762883 + 0.0710610i
\(461\) −72.7050 −0.157712 −0.0788558 0.996886i \(-0.525127\pi\)
−0.0788558 + 0.996886i \(0.525127\pi\)
\(462\) −25.8696 25.8696i −0.0559947 0.0559947i
\(463\) 455.202 455.202i 0.983158 0.983158i −0.0167027 0.999861i \(-0.505317\pi\)
0.999861 + 0.0167027i \(0.00531687\pi\)
\(464\) 35.0139i 0.0754611i
\(465\) 153.530 164.824i 0.330173 0.354460i
\(466\) 488.178 1.04759
\(467\) −569.865 569.865i −1.22027 1.22027i −0.967536 0.252733i \(-0.918671\pi\)
−0.252733 0.967536i \(-0.581329\pi\)
\(468\) 39.5707 39.5707i 0.0845528 0.0845528i
\(469\) 742.405i 1.58295i
\(470\) −10.2024 287.588i −0.0217072 0.611890i
\(471\) −420.779 −0.893373
\(472\) −143.841 143.841i −0.304747 0.304747i
\(473\) 76.2099 76.2099i 0.161120 0.161120i
\(474\) 329.152i 0.694414i
\(475\) −59.1966 833.279i −0.124624 1.75427i
\(476\) 298.521 0.627145
\(477\) 102.989 + 102.989i 0.215911 + 0.215911i
\(478\) −314.702 + 314.702i −0.658373 + 0.658373i
\(479\) 681.451i 1.42265i −0.702861 0.711327i \(-0.748095\pi\)
0.702861 0.711327i \(-0.251905\pi\)
\(480\) −48.9590 + 1.73685i −0.101998 + 0.00361844i
\(481\) 245.619 0.510643
\(482\) −178.804 178.804i −0.370964 0.370964i
\(483\) −38.5414 + 38.5414i −0.0797958 + 0.0797958i
\(484\) 231.638i 0.478591i
\(485\) 161.361 + 150.304i 0.332703 + 0.309906i
\(486\) −22.0454 −0.0453609
\(487\) 457.067 + 457.067i 0.938535 + 0.938535i 0.998217 0.0596820i \(-0.0190087\pi\)
−0.0596820 + 0.998217i \(0.519009\pi\)
\(488\) 143.231 143.231i 0.293507 0.293507i
\(489\) 375.307i 0.767499i
\(490\) 28.6469 30.7542i 0.0584631 0.0627637i
\(491\) −2.82990 −0.00576355 −0.00288178 0.999996i \(-0.500917\pi\)
−0.00288178 + 0.999996i \(0.500917\pi\)
\(492\) 10.6374 + 10.6374i 0.0216208 + 0.0216208i
\(493\) −140.797 + 140.797i −0.285592 + 0.285592i
\(494\) 440.754i 0.892215i
\(495\) −1.21048 34.1216i −0.00244542 0.0689324i
\(496\) −104.039 −0.209757
\(497\) −481.422 481.422i −0.968657 0.968657i
\(498\) −29.0646 + 29.0646i −0.0583627 + 0.0583627i
\(499\) 562.240i 1.12673i 0.826207 + 0.563367i \(0.190494\pi\)
−0.826207 + 0.563367i \(0.809506\pi\)
\(500\) 26.5454 + 248.587i 0.0530908 + 0.497173i
\(501\) −307.688 −0.614147
\(502\) 183.648 + 183.648i 0.365832 + 0.365832i
\(503\) −516.973 + 516.973i −1.02778 + 1.02778i −0.0281756 + 0.999603i \(0.508970\pi\)
−0.999603 + 0.0281756i \(0.991030\pi\)
\(504\) 55.6780i 0.110472i
\(505\) 222.260 7.88479i 0.440118 0.0156134i
\(506\) 15.4380 0.0305098
\(507\) 100.440 + 100.440i 0.198106 + 0.198106i
\(508\) −169.755 + 169.755i −0.334164 + 0.334164i
\(509\) 347.014i 0.681756i 0.940108 + 0.340878i \(0.110724\pi\)
−0.940108 + 0.340878i \(0.889276\pi\)
\(510\) 203.857 + 189.888i 0.399719 + 0.372330i
\(511\) −10.9014 −0.0213335
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −122.775 + 122.775i −0.239328 + 0.239328i
\(514\) 517.318i 1.00646i
\(515\) 420.908 451.871i 0.817297 0.877418i
\(516\) 164.023 0.317875
\(517\) −65.5021 65.5021i −0.126697 0.126697i
\(518\) 172.800 172.800i 0.333590 0.333590i
\(519\) 307.762i 0.592990i
\(520\) 4.67637 + 131.819i 0.00899302 + 0.253499i
\(521\) 910.660 1.74791 0.873954 0.486010i \(-0.161548\pi\)
0.873954 + 0.486010i \(0.161548\pi\)
\(522\) 26.2605 + 26.2605i 0.0503074 + 0.0503074i
\(523\) 595.957 595.957i 1.13950 1.13950i 0.150957 0.988540i \(-0.451765\pi\)
0.988540 0.150957i \(-0.0482355\pi\)
\(524\) 58.1319i 0.110939i
\(525\) −283.416 + 20.1341i −0.539841 + 0.0383506i
\(526\) −13.4613 −0.0255919
\(527\) 418.360 + 418.360i 0.793853 + 0.793853i
\(528\) −11.1511 + 11.1511i −0.0211194 + 0.0211194i
\(529\) 23.0000i 0.0434783i
\(530\) −343.082 + 12.1710i −0.647325 + 0.0229642i
\(531\) 215.761 0.406329
\(532\) −310.082 310.082i −0.582860 0.582860i
\(533\) 28.6407 28.6407i 0.0537349 0.0537349i
\(534\) 100.261i 0.187755i
\(535\) 82.3456 + 76.7032i 0.153917 + 0.143370i
\(536\) 320.014 0.597040
\(537\) 113.034 + 113.034i 0.210491 + 0.210491i
\(538\) 195.237 195.237i 0.362893 0.362893i
\(539\) 13.5294i 0.0251009i
\(540\) 35.4166 38.0219i 0.0655863 0.0704109i
\(541\) −876.710 −1.62054 −0.810268 0.586059i \(-0.800679\pi\)
−0.810268 + 0.586059i \(0.800679\pi\)
\(542\) −190.383 190.383i −0.351261 0.351261i
\(543\) −136.983 + 136.983i −0.252270 + 0.252270i
\(544\) 128.677i 0.236539i
\(545\) 7.16286 + 201.910i 0.0131429 + 0.370476i
\(546\) −149.910 −0.274561
\(547\) −628.878 628.878i −1.14969 1.14969i −0.986614 0.163071i \(-0.947860\pi\)
−0.163071 0.986614i \(-0.552140\pi\)
\(548\) −100.690 + 100.690i −0.183741 + 0.183741i
\(549\) 214.847i 0.391343i
\(550\) 60.7944 + 52.7296i 0.110535 + 0.0958720i
\(551\) 292.499 0.530852
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 623.481 623.481i 1.12745 1.12745i
\(554\) 723.231i 1.30547i
\(555\) 227.920 8.08560i 0.410667 0.0145686i
\(556\) −166.536 −0.299525
\(557\) 628.139 + 628.139i 1.12772 + 1.12772i 0.990547 + 0.137170i \(0.0438008\pi\)
0.137170 + 0.990547i \(0.456199\pi\)
\(558\) 78.0296 78.0296i 0.139838 0.139838i
\(559\) 441.624i 0.790026i
\(560\) 96.0283 + 89.4484i 0.171479 + 0.159729i
\(561\) 89.6806 0.159859
\(562\) −259.206 259.206i −0.461220 0.461220i
\(563\) 318.946 318.946i 0.566511 0.566511i −0.364638 0.931149i \(-0.618807\pi\)
0.931149 + 0.364638i \(0.118807\pi\)
\(564\) 140.978i 0.249960i
\(565\) −216.590 + 232.522i −0.383344 + 0.411543i
\(566\) −567.185 −1.00209
\(567\) 41.7585 + 41.7585i 0.0736482 + 0.0736482i
\(568\) −207.517 + 207.517i −0.365347 + 0.365347i
\(569\) 496.154i 0.871976i 0.899952 + 0.435988i \(0.143601\pi\)
−0.899952 + 0.435988i \(0.856399\pi\)
\(570\) −14.5093 408.993i −0.0254549 0.717532i
\(571\) −623.806 −1.09248 −0.546240 0.837629i \(-0.683941\pi\)
−0.546240 + 0.837629i \(0.683941\pi\)
\(572\) 30.0236 + 30.0236i 0.0524889 + 0.0524889i
\(573\) −114.819 + 114.819i −0.200382 + 0.200382i
\(574\) 40.2989i 0.0702072i
\(575\) 78.5584 90.5736i 0.136623 0.157519i
\(576\) −24.0000 −0.0416667
\(577\) 299.545 + 299.545i 0.519143 + 0.519143i 0.917312 0.398169i \(-0.130354\pi\)
−0.398169 + 0.917312i \(0.630354\pi\)
\(578\) −228.434 + 228.434i −0.395214 + 0.395214i
\(579\) 244.980i 0.423109i
\(580\) −87.4798 + 3.10340i −0.150827 + 0.00535069i
\(581\) 110.109 0.189516
\(582\) 76.3900 + 76.3900i 0.131254 + 0.131254i
\(583\) −78.1416 + 78.1416i −0.134034 + 0.134034i
\(584\) 4.69905i 0.00804632i
\(585\) −102.372 95.3573i −0.174995 0.163004i
\(586\) 209.159 0.356927
\(587\) −76.2399 76.2399i −0.129881 0.129881i 0.639178 0.769059i \(-0.279275\pi\)
−0.769059 + 0.639178i \(0.779275\pi\)
\(588\) 14.5594 14.5594i 0.0247609 0.0247609i
\(589\) 869.124i 1.47559i
\(590\) −346.626 + 372.124i −0.587502 + 0.630719i
\(591\) 275.232 0.465706
\(592\) −74.4852 74.4852i −0.125820 0.125820i
\(593\) 312.744 312.744i 0.527393 0.527393i −0.392401 0.919794i \(-0.628356\pi\)
0.919794 + 0.392401i \(0.128356\pi\)
\(594\) 16.7266i 0.0281593i
\(595\) −26.4589 745.833i −0.0444687 1.25350i
\(596\) 71.6470 0.120213
\(597\) −73.5259 73.5259i −0.123159 0.123159i
\(598\) 44.7303 44.7303i 0.0747998 0.0747998i
\(599\) 822.073i 1.37241i −0.727408 0.686205i \(-0.759275\pi\)
0.727408 0.686205i \(-0.240725\pi\)
\(600\) 8.67879 + 122.167i 0.0144646 + 0.203611i
\(601\) −70.4421 −0.117208 −0.0586040 0.998281i \(-0.518665\pi\)
−0.0586040 + 0.998281i \(0.518665\pi\)
\(602\) −310.694 310.694i −0.516103 0.516103i
\(603\) −240.010 + 240.010i −0.398027 + 0.398027i
\(604\) 593.737i 0.983008i
\(605\) −578.730 + 20.5308i −0.956579 + 0.0339352i
\(606\) 108.953 0.179790
\(607\) 66.6471 + 66.6471i 0.109797 + 0.109797i 0.759871 0.650074i \(-0.225262\pi\)
−0.650074 + 0.759871i \(0.725262\pi\)
\(608\) −133.661 + 133.661i −0.219837 + 0.219837i
\(609\) 99.4854i 0.163359i
\(610\) −370.549 345.158i −0.607457 0.565833i
\(611\) −379.575 −0.621235
\(612\) 96.5081 + 96.5081i 0.157693 + 0.157693i
\(613\) 182.027 182.027i 0.296945 0.296945i −0.542871 0.839816i \(-0.682663\pi\)
0.839816 + 0.542871i \(0.182663\pi\)
\(614\) 424.850i 0.691938i
\(615\) 25.6340 27.5197i 0.0416813 0.0447474i
\(616\) 42.2448 0.0685792
\(617\) −312.757 312.757i −0.506900 0.506900i 0.406674 0.913573i \(-0.366689\pi\)
−0.913573 + 0.406674i \(0.866689\pi\)
\(618\) 213.921 213.921i 0.346150 0.346150i
\(619\) 779.683i 1.25958i −0.776764 0.629792i \(-0.783140\pi\)
0.776764 0.629792i \(-0.216860\pi\)
\(620\) 9.22135 + 259.935i 0.0148732 + 0.419250i
\(621\) −24.9199 −0.0401286
\(622\) −206.221 206.221i −0.331545 0.331545i
\(623\) 189.915 189.915i 0.304840 0.304840i
\(624\) 64.6187i 0.103556i
\(625\) 618.723 88.3548i 0.989957 0.141368i
\(626\) 407.676 0.651240
\(627\) −93.1537 93.1537i −0.148570 0.148570i
\(628\) 343.564 343.564i 0.547077 0.547077i
\(629\) 599.035i 0.952361i
\(630\) −139.108 + 4.93492i −0.220806 + 0.00783321i
\(631\) 286.619 0.454230 0.227115 0.973868i \(-0.427071\pi\)
0.227115 + 0.973868i \(0.427071\pi\)
\(632\) −268.751 268.751i −0.425240 0.425240i
\(633\) −88.7037 + 88.7037i −0.140132 + 0.140132i
\(634\) 143.128i 0.225754i
\(635\) 439.167 + 409.075i 0.691602 + 0.644213i
\(636\) −168.181 −0.264436
\(637\) −39.2004 39.2004i −0.0615391 0.0615391i
\(638\) −19.9247 + 19.9247i −0.0312299 + 0.0312299i
\(639\) 311.275i 0.487129i
\(640\) 38.5567 41.3930i 0.0602449 0.0646765i
\(641\) 328.082 0.511829 0.255914 0.966699i \(-0.417623\pi\)
0.255914 + 0.966699i \(0.417623\pi\)
\(642\) 38.9833 + 38.9833i 0.0607217 + 0.0607217i
\(643\) 159.578 159.578i 0.248177 0.248177i −0.572045 0.820222i \(-0.693850\pi\)
0.820222 + 0.572045i \(0.193850\pi\)
\(644\) 62.9378i 0.0977295i
\(645\) −14.5379 409.801i −0.0225394 0.635350i
\(646\) 1074.94 1.66400
\(647\) 127.452 + 127.452i 0.196989 + 0.196989i 0.798708 0.601719i \(-0.205517\pi\)
−0.601719 + 0.798708i \(0.705517\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 163.705i 0.252242i
\(650\) 328.927 23.3672i 0.506042 0.0359495i
\(651\) −295.608 −0.454083
\(652\) −306.437 306.437i −0.469995 0.469995i
\(653\) −902.017 + 902.017i −1.38134 + 1.38134i −0.539105 + 0.842238i \(0.681238\pi\)
−0.842238 + 0.539105i \(0.818762\pi\)
\(654\) 98.9773i 0.151341i
\(655\) −145.238 + 5.15241i −0.221738 + 0.00786628i
\(656\) −17.3708 −0.0264799
\(657\) −3.52429 3.52429i −0.00536421 0.00536421i
\(658\) −267.041 + 267.041i −0.405837 + 0.405837i
\(659\) 723.945i 1.09855i −0.835641 0.549276i \(-0.814904\pi\)
0.835641 0.549276i \(-0.185096\pi\)
\(660\) 28.8485 + 26.8718i 0.0437098 + 0.0407148i
\(661\) 38.6236 0.0584321 0.0292160 0.999573i \(-0.490699\pi\)
0.0292160 + 0.999573i \(0.490699\pi\)
\(662\) 480.713 + 480.713i 0.726152 + 0.726152i
\(663\) 259.843 259.843i 0.391920 0.391920i
\(664\) 47.4623i 0.0714794i
\(665\) −747.233 + 802.201i −1.12366 + 1.20632i
\(666\) 111.728 0.167759
\(667\) 29.6845 + 29.6845i 0.0445045 + 0.0445045i
\(668\) 251.226 251.226i 0.376087 0.376087i
\(669\) 396.502i 0.592678i
\(670\) −28.3638 799.531i −0.0423341 1.19333i
\(671\) −163.012 −0.242939
\(672\) 45.4609 + 45.4609i 0.0676502 + 0.0676502i
\(673\) −691.238 + 691.238i −1.02710 + 1.02710i −0.0274776 + 0.999622i \(0.508747\pi\)
−0.999622 + 0.0274776i \(0.991253\pi\)
\(674\) 441.533i 0.655093i
\(675\) −98.1340 85.1159i −0.145384 0.126098i
\(676\) −164.018 −0.242630
\(677\) 242.001 + 242.001i 0.357460 + 0.357460i 0.862876 0.505416i \(-0.168661\pi\)
−0.505416 + 0.862876i \(0.668661\pi\)
\(678\) −110.079 + 110.079i −0.162358 + 0.162358i
\(679\) 289.397i 0.426210i
\(680\) −321.491 + 11.4051i −0.472781 + 0.0167722i
\(681\) −632.768 −0.929174
\(682\) 59.2037 + 59.2037i 0.0868090 + 0.0868090i
\(683\) −166.819 + 166.819i −0.244245 + 0.244245i −0.818604 0.574359i \(-0.805251\pi\)
0.574359 + 0.818604i \(0.305251\pi\)
\(684\) 200.491i 0.293115i
\(685\) 260.492 + 242.643i 0.380280 + 0.354223i
\(686\) −509.861 −0.743237
\(687\) 257.299 + 257.299i 0.374525 + 0.374525i
\(688\) −133.925 + 133.925i −0.194658 + 0.194658i
\(689\) 452.818i 0.657211i
\(690\) 40.0345 42.9795i 0.0580210 0.0622891i
\(691\) 230.554 0.333653 0.166827 0.985986i \(-0.446648\pi\)
0.166827 + 0.985986i \(0.446648\pi\)
\(692\) −251.287 251.287i −0.363131 0.363131i
\(693\) −31.6836 + 31.6836i −0.0457195 + 0.0457195i
\(694\) 458.122i 0.660118i
\(695\) 14.7606 + 416.079i 0.0212383 + 0.598674i
\(696\) −42.8832 −0.0616137
\(697\) 69.8511 + 69.8511i 0.100217 + 0.100217i
\(698\) −498.993 + 498.993i −0.714890 + 0.714890i
\(699\) 597.893i 0.855355i
\(700\) 214.969 247.848i 0.307099 0.354069i
\(701\) −569.921 −0.813012 −0.406506 0.913648i \(-0.633253\pi\)
−0.406506 + 0.913648i \(0.633253\pi\)
\(702\) −48.4640 48.4640i −0.0690371 0.0690371i
\(703\) 622.234 622.234i 0.885112 0.885112i
\(704\) 18.2096i 0.0258659i
\(705\) −352.222 + 12.4953i −0.499606 + 0.0177238i
\(706\) 199.123 0.282044
\(707\) −206.379 206.379i −0.291909 0.291909i
\(708\) −176.168 + 176.168i −0.248825 + 0.248825i
\(709\) 1007.05i 1.42039i 0.704008 + 0.710193i \(0.251392\pi\)
−0.704008 + 0.710193i \(0.748608\pi\)
\(710\) 536.859 + 500.073i 0.756140 + 0.704329i
\(711\) 403.127 0.566986
\(712\) −81.8630 81.8630i −0.114976 0.114976i
\(713\) 88.2038 88.2038i 0.123708 0.123708i
\(714\) 365.612i 0.512062i
\(715\) 72.3508 77.6730i 0.101190 0.108634i
\(716\) −184.584 −0.257798
\(717\) 385.430 + 385.430i 0.537559 + 0.537559i
\(718\) −320.098 + 320.098i −0.445819 + 0.445819i
\(719\) 1131.87i 1.57423i 0.616806 + 0.787115i \(0.288426\pi\)
−0.616806 + 0.787115i \(0.711574\pi\)
\(720\) 2.12720 + 59.9623i 0.00295444 + 0.0832809i
\(721\) −810.419 −1.12402
\(722\) −755.573 755.573i −1.04650 1.04650i
\(723\) −218.990 + 218.990i −0.302891 + 0.302891i
\(724\) 223.692i 0.308966i
\(725\) 15.5072 + 218.287i 0.0213893 + 0.301086i
\(726\) −283.697 −0.390768
\(727\) 745.476 + 745.476i 1.02541 + 1.02541i 0.999669 + 0.0257448i \(0.00819574\pi\)
0.0257448 + 0.999669i \(0.491804\pi\)
\(728\) 122.401 122.401i 0.168133 0.168133i
\(729\) 27.0000i 0.0370370i
\(730\) 11.7402 0.416492i 0.0160825 0.000570537i
\(731\) 1077.07 1.47342
\(732\) −175.422 175.422i −0.239647 0.239647i
\(733\) 917.155 917.155i 1.25123 1.25123i 0.296067 0.955167i \(-0.404325\pi\)
0.955167 0.296067i \(-0.0956753\pi\)
\(734\) 229.234i 0.312308i
\(735\) −37.6661 35.0852i −0.0512463 0.0477349i
\(736\) −27.1293 −0.0368605
\(737\) −182.104 182.104i −0.247088 0.247088i
\(738\) 13.0281 13.0281i 0.0176533 0.0176533i
\(739\) 413.291i 0.559257i 0.960108 + 0.279629i \(0.0902114\pi\)
−0.960108 + 0.279629i \(0.909789\pi\)
\(740\) −179.494 + 192.698i −0.242560 + 0.260402i
\(741\) −539.811 −0.728490
\(742\) 318.569 + 318.569i 0.429339 + 0.429339i
\(743\) 674.486 674.486i 0.907788 0.907788i −0.0883055 0.996093i \(-0.528145\pi\)
0.996093 + 0.0883055i \(0.0281452\pi\)
\(744\) 127.422i 0.171266i
\(745\) −6.35030 179.005i −0.00852389 0.240275i
\(746\) 889.804 1.19277
\(747\) 35.5968 + 35.5968i 0.0476529 + 0.0476529i
\(748\) −73.2239 + 73.2239i −0.0978930 + 0.0978930i
\(749\) 147.685i 0.197176i
\(750\) 304.455 32.5113i 0.405940 0.0433485i
\(751\) 233.606 0.311060 0.155530 0.987831i \(-0.450291\pi\)
0.155530 + 0.987831i \(0.450291\pi\)
\(752\) 115.108 + 115.108i 0.153069 + 0.153069i
\(753\) 224.922 224.922i 0.298701 0.298701i
\(754\) 115.461i 0.153131i
\(755\) −1483.41 + 52.6248i −1.96478 + 0.0697017i
\(756\) −68.1914 −0.0902002
\(757\) 0.636656 + 0.636656i 0.000841026 + 0.000841026i 0.707527 0.706686i \(-0.249811\pi\)
−0.706686 + 0.707527i \(0.749811\pi\)
\(758\) −255.776 + 255.776i −0.337435 + 0.337435i
\(759\) 18.9076i 0.0249111i
\(760\) 345.788 + 322.095i 0.454985 + 0.423809i
\(761\) −400.232 −0.525929 −0.262964 0.964806i \(-0.584700\pi\)
−0.262964 + 0.964806i \(0.584700\pi\)
\(762\) 207.907 + 207.907i 0.272844 + 0.272844i
\(763\) 187.483 187.483i 0.245719 0.245719i
\(764\) 187.498i 0.245416i
\(765\) 232.565 249.672i 0.304006 0.326369i
\(766\) 673.517 0.879265
\(767\) 474.323 + 474.323i 0.618413 + 0.618413i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 818.791i 1.06475i −0.846509 0.532374i \(-0.821300\pi\)
0.846509 0.532374i \(-0.178700\pi\)
\(770\) −3.74429 105.546i −0.00486272 0.137072i
\(771\) −633.583 −0.821768
\(772\) −200.026 200.026i −0.259100 0.259100i
\(773\) −836.271 + 836.271i −1.08185 + 1.08185i −0.0855136 + 0.996337i \(0.527253\pi\)
−0.996337 + 0.0855136i \(0.972747\pi\)
\(774\) 200.887i 0.259544i
\(775\) 648.612 46.0778i 0.836919 0.0594552i
\(776\) −124.744 −0.160753
\(777\) −211.635 211.635i −0.272375 0.272375i
\(778\) −459.806 + 459.806i −0.591011 + 0.591011i
\(779\) 145.112i