Properties

Label 690.3.k.a.277.2
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 277.2
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.69807 + 4.20956i) q^{5} -2.44949 q^{6} +(-5.61863 - 5.61863i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.69807 + 4.20956i) q^{5} -2.44949 q^{6} +(-5.61863 - 5.61863i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.51149 + 6.90763i) q^{10} -12.8664 q^{11} +(-2.44949 - 2.44949i) q^{12} +(9.49626 - 9.49626i) q^{13} -11.2373i q^{14} +(-8.46009 - 1.85119i) q^{15} -4.00000 q^{16} +(-16.0031 - 16.0031i) q^{17} +(3.00000 - 3.00000i) q^{18} -27.2561i q^{19} +(-8.41912 + 5.39614i) q^{20} +13.7628 q^{21} +(-12.8664 - 12.8664i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-10.4408 + 22.7154i) q^{25} +18.9925 q^{26} +(3.67423 + 3.67423i) q^{27} +(11.2373 - 11.2373i) q^{28} +10.8625i q^{29} +(-6.60890 - 10.3113i) q^{30} +11.1289 q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.7581 - 15.7581i) q^{33} -32.0062i q^{34} +(8.49251 - 38.8114i) q^{35} +6.00000 q^{36} +(23.3287 + 23.3287i) q^{37} +(27.2561 - 27.2561i) q^{38} +23.2610i q^{39} +(-13.8153 - 3.02298i) q^{40} -48.0560 q^{41} +(13.7628 + 13.7628i) q^{42} +(19.0800 - 19.0800i) q^{43} -25.7328i q^{44} +(12.6287 - 8.09421i) q^{45} -6.78233 q^{46} +(-56.5992 - 56.5992i) q^{47} +(4.89898 - 4.89898i) q^{48} +14.1380i q^{49} +(-33.1562 + 12.2746i) q^{50} +39.1994 q^{51} +(18.9925 + 18.9925i) q^{52} +(-40.7367 + 40.7367i) q^{53} +7.34847i q^{54} +(-34.7145 - 54.1620i) q^{55} +22.4745 q^{56} +(33.3817 + 33.3817i) q^{57} +(-10.8625 + 10.8625i) q^{58} -63.6669i q^{59} +(3.70238 - 16.9202i) q^{60} +104.528 q^{61} +(11.1289 + 11.1289i) q^{62} +(-16.8559 + 16.8559i) q^{63} -8.00000i q^{64} +(65.5967 + 14.3535i) q^{65} +31.5162 q^{66} +(-3.47681 - 3.47681i) q^{67} +(32.0062 - 32.0062i) q^{68} -8.30662i q^{69} +(47.3039 - 30.3189i) q^{70} -90.8333 q^{71} +(6.00000 + 6.00000i) q^{72} +(6.81243 - 6.81243i) q^{73} +46.6573i q^{74} +(-15.0332 - 40.6079i) q^{75} +54.5121 q^{76} +(72.2917 + 72.2917i) q^{77} +(-23.2610 + 23.2610i) q^{78} +103.414i q^{79} +(-10.7923 - 16.8382i) q^{80} -9.00000 q^{81} +(-48.0560 - 48.0560i) q^{82} +(87.6868 - 87.6868i) q^{83} +27.5255i q^{84} +(24.1885 - 110.543i) q^{85} +38.1600 q^{86} +(-13.3038 - 13.3038i) q^{87} +(25.7328 - 25.7328i) q^{88} +65.1773i q^{89} +(20.7229 + 4.53448i) q^{90} -106.712 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-13.6301 + 13.6301i) q^{93} -113.198i q^{94} +(114.736 - 73.5388i) q^{95} +9.79796 q^{96} +(-121.933 - 121.933i) q^{97} +(-14.1380 + 14.1380i) q^{98} +38.5993i 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
\(5\) 2.69807 + 4.20956i 0.539614 + 0.841912i
\(6\) −2.44949 −0.408248
\(7\) −5.61863 5.61863i −0.802661 0.802661i 0.180849 0.983511i \(-0.442115\pi\)
−0.983511 + 0.180849i \(0.942115\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −1.51149 + 6.90763i −0.151149 + 0.690763i
\(11\) −12.8664 −1.16967 −0.584837 0.811151i \(-0.698842\pi\)
−0.584837 + 0.811151i \(0.698842\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 9.49626 9.49626i 0.730481 0.730481i −0.240234 0.970715i \(-0.577224\pi\)
0.970715 + 0.240234i \(0.0772241\pi\)
\(14\) 11.2373i 0.802661i
\(15\) −8.46009 1.85119i −0.564006 0.123413i
\(16\) −4.00000 −0.250000
\(17\) −16.0031 16.0031i −0.941358 0.941358i 0.0570149 0.998373i \(-0.481842\pi\)
−0.998373 + 0.0570149i \(0.981842\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 27.2561i 1.43453i −0.696800 0.717265i \(-0.745394\pi\)
0.696800 0.717265i \(-0.254606\pi\)
\(20\) −8.41912 + 5.39614i −0.420956 + 0.269807i
\(21\) 13.7628 0.655370
\(22\) −12.8664 12.8664i −0.584837 0.584837i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −10.4408 + 22.7154i −0.417633 + 0.908616i
\(26\) 18.9925 0.730481
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 11.2373 11.2373i 0.401331 0.401331i
\(29\) 10.8625i 0.374569i 0.982306 + 0.187284i \(0.0599686\pi\)
−0.982306 + 0.187284i \(0.940031\pi\)
\(30\) −6.60890 10.3113i −0.220297 0.343709i
\(31\) 11.1289 0.358997 0.179499 0.983758i \(-0.442552\pi\)
0.179499 + 0.983758i \(0.442552\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 15.7581 15.7581i 0.477518 0.477518i
\(34\) 32.0062i 0.941358i
\(35\) 8.49251 38.8114i 0.242643 1.10890i
\(36\) 6.00000 0.166667
\(37\) 23.3287 + 23.3287i 0.630504 + 0.630504i 0.948195 0.317690i \(-0.102907\pi\)
−0.317690 + 0.948195i \(0.602907\pi\)
\(38\) 27.2561 27.2561i 0.717265 0.717265i
\(39\) 23.2610i 0.596435i
\(40\) −13.8153 3.02298i −0.345382 0.0755746i
\(41\) −48.0560 −1.17210 −0.586049 0.810276i \(-0.699317\pi\)
−0.586049 + 0.810276i \(0.699317\pi\)
\(42\) 13.7628 + 13.7628i 0.327685 + 0.327685i
\(43\) 19.0800 19.0800i 0.443721 0.443721i −0.449540 0.893260i \(-0.648412\pi\)
0.893260 + 0.449540i \(0.148412\pi\)
\(44\) 25.7328i 0.584837i
\(45\) 12.6287 8.09421i 0.280637 0.179871i
\(46\) −6.78233 −0.147442
\(47\) −56.5992 56.5992i −1.20424 1.20424i −0.972865 0.231374i \(-0.925678\pi\)
−0.231374 0.972865i \(-0.574322\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 14.1380i 0.288530i
\(50\) −33.1562 + 12.2746i −0.663124 + 0.245491i
\(51\) 39.1994 0.768616
\(52\) 18.9925 + 18.9925i 0.365241 + 0.365241i
\(53\) −40.7367 + 40.7367i −0.768617 + 0.768617i −0.977863 0.209246i \(-0.932899\pi\)
0.209246 + 0.977863i \(0.432899\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −34.7145 54.1620i −0.631173 0.984764i
\(56\) 22.4745 0.401331
\(57\) 33.3817 + 33.3817i 0.585644 + 0.585644i
\(58\) −10.8625 + 10.8625i −0.187284 + 0.187284i
\(59\) 63.6669i 1.07910i −0.841954 0.539550i \(-0.818594\pi\)
0.841954 0.539550i \(-0.181406\pi\)
\(60\) 3.70238 16.9202i 0.0617064 0.282003i
\(61\) 104.528 1.71358 0.856788 0.515670i \(-0.172457\pi\)
0.856788 + 0.515670i \(0.172457\pi\)
\(62\) 11.1289 + 11.1289i 0.179499 + 0.179499i
\(63\) −16.8559 + 16.8559i −0.267554 + 0.267554i
\(64\) 8.00000i 0.125000i
\(65\) 65.5967 + 14.3535i 1.00918 + 0.220823i
\(66\) 31.5162 0.477518
\(67\) −3.47681 3.47681i −0.0518926 0.0518926i 0.680684 0.732577i \(-0.261683\pi\)
−0.732577 + 0.680684i \(0.761683\pi\)
\(68\) 32.0062 32.0062i 0.470679 0.470679i
\(69\) 8.30662i 0.120386i
\(70\) 47.3039 30.3189i 0.675771 0.433127i
\(71\) −90.8333 −1.27934 −0.639671 0.768649i \(-0.720930\pi\)
−0.639671 + 0.768649i \(0.720930\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 6.81243 6.81243i 0.0933210 0.0933210i −0.658905 0.752226i \(-0.728980\pi\)
0.752226 + 0.658905i \(0.228980\pi\)
\(74\) 46.6573i 0.630504i
\(75\) −15.0332 40.6079i −0.200443 0.541439i
\(76\) 54.5121 0.717265
\(77\) 72.2917 + 72.2917i 0.938853 + 0.938853i
\(78\) −23.2610 + 23.2610i −0.298218 + 0.298218i
\(79\) 103.414i 1.30904i 0.756045 + 0.654520i \(0.227129\pi\)
−0.756045 + 0.654520i \(0.772871\pi\)
\(80\) −10.7923 16.8382i −0.134904 0.210478i
\(81\) −9.00000 −0.111111
\(82\) −48.0560 48.0560i −0.586049 0.586049i
\(83\) 87.6868 87.6868i 1.05647 1.05647i 0.0581608 0.998307i \(-0.481476\pi\)
0.998307 0.0581608i \(-0.0185236\pi\)
\(84\) 27.5255i 0.327685i
\(85\) 24.1885 110.543i 0.284571 1.30051i
\(86\) 38.1600 0.443721
\(87\) −13.3038 13.3038i −0.152917 0.152917i
\(88\) 25.7328 25.7328i 0.292419 0.292419i
\(89\) 65.1773i 0.732329i 0.930550 + 0.366165i \(0.119329\pi\)
−0.930550 + 0.366165i \(0.880671\pi\)
\(90\) 20.7229 + 4.53448i 0.230254 + 0.0503831i
\(91\) −106.712 −1.17266
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) −13.6301 + 13.6301i −0.146560 + 0.146560i
\(94\) 113.198i 1.20424i
\(95\) 114.736 73.5388i 1.20775 0.774093i
\(96\) 9.79796 0.102062
\(97\) −121.933 121.933i −1.25704 1.25704i −0.952497 0.304547i \(-0.901495\pi\)
−0.304547 0.952497i \(-0.598505\pi\)
\(98\) −14.1380 + 14.1380i −0.144265 + 0.144265i
\(99\) 38.5993i 0.389892i
\(100\) −45.4308 20.8817i −0.454308 0.208817i
\(101\) −129.221 −1.27941 −0.639705 0.768620i \(-0.720944\pi\)
−0.639705 + 0.768620i \(0.720944\pi\)
\(102\) 39.1994 + 39.1994i 0.384308 + 0.384308i
\(103\) −4.11421 + 4.11421i −0.0399438 + 0.0399438i −0.726797 0.686853i \(-0.758992\pi\)
0.686853 + 0.726797i \(0.258992\pi\)
\(104\) 37.9850i 0.365241i
\(105\) 37.1329 + 57.9353i 0.353647 + 0.551764i
\(106\) −81.4734 −0.768617
\(107\) 24.7912 + 24.7912i 0.231693 + 0.231693i 0.813399 0.581706i \(-0.197615\pi\)
−0.581706 + 0.813399i \(0.697615\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 0.116226i 0.00106629i 1.00000 0.000533145i \(0.000169705\pi\)
−1.00000 0.000533145i \(0.999830\pi\)
\(110\) 19.4475 88.8765i 0.176795 0.807968i
\(111\) −57.1433 −0.514805
\(112\) 22.4745 + 22.4745i 0.200665 + 0.200665i
\(113\) 150.629 150.629i 1.33300 1.33300i 0.430335 0.902669i \(-0.358396\pi\)
0.902669 0.430335i \(-0.141604\pi\)
\(114\) 66.7635i 0.585644i
\(115\) −23.4249 5.12572i −0.203695 0.0445715i
\(116\) −21.7250 −0.187284
\(117\) −28.4888 28.4888i −0.243494 0.243494i
\(118\) 63.6669 63.6669i 0.539550 0.539550i
\(119\) 179.831i 1.51118i
\(120\) 20.6226 13.2178i 0.171855 0.110148i
\(121\) 44.5449 0.368139
\(122\) 104.528 + 104.528i 0.856788 + 0.856788i
\(123\) 58.8564 58.8564i 0.478507 0.478507i
\(124\) 22.2578i 0.179499i
\(125\) −123.792 + 17.3364i −0.990336 + 0.138691i
\(126\) −33.7118 −0.267554
\(127\) −153.452 153.452i −1.20829 1.20829i −0.971582 0.236705i \(-0.923932\pi\)
−0.236705 0.971582i \(-0.576068\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 46.7362i 0.362296i
\(130\) 51.2431 + 79.9502i 0.394178 + 0.615001i
\(131\) −233.897 −1.78548 −0.892738 0.450576i \(-0.851219\pi\)
−0.892738 + 0.450576i \(0.851219\pi\)
\(132\) 31.5162 + 31.5162i 0.238759 + 0.238759i
\(133\) −153.142 + 153.142i −1.15144 + 1.15144i
\(134\) 6.95361i 0.0518926i
\(135\) −5.55358 + 25.3803i −0.0411376 + 0.188002i
\(136\) 64.0124 0.470679
\(137\) 40.9626 + 40.9626i 0.298997 + 0.298997i 0.840621 0.541624i \(-0.182190\pi\)
−0.541624 + 0.840621i \(0.682190\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 148.538i 1.06862i −0.845290 0.534308i \(-0.820572\pi\)
0.845290 0.534308i \(-0.179428\pi\)
\(140\) 77.6229 + 16.9850i 0.554449 + 0.121322i
\(141\) 138.639 0.983257
\(142\) −90.8333 90.8333i −0.639671 0.639671i
\(143\) −122.183 + 122.183i −0.854426 + 0.854426i
\(144\) 12.0000i 0.0833333i
\(145\) −45.7264 + 29.3078i −0.315354 + 0.202123i
\(146\) 13.6249 0.0933210
\(147\) −17.3154 17.3154i −0.117792 0.117792i
\(148\) −46.6573 + 46.6573i −0.315252 + 0.315252i
\(149\) 10.9701i 0.0736249i 0.999322 + 0.0368125i \(0.0117204\pi\)
−0.999322 + 0.0368125i \(0.988280\pi\)
\(150\) 25.5747 55.6411i 0.170498 0.370941i
\(151\) −109.516 −0.725269 −0.362635 0.931931i \(-0.618123\pi\)
−0.362635 + 0.931931i \(0.618123\pi\)
\(152\) 54.5121 + 54.5121i 0.358633 + 0.358633i
\(153\) −48.0093 + 48.0093i −0.313786 + 0.313786i
\(154\) 144.583i 0.938853i
\(155\) 30.0266 + 46.8479i 0.193720 + 0.302244i
\(156\) −46.5220 −0.298218
\(157\) 91.3919 + 91.3919i 0.582114 + 0.582114i 0.935484 0.353370i \(-0.114964\pi\)
−0.353370 + 0.935484i \(0.614964\pi\)
\(158\) −103.414 + 103.414i −0.654520 + 0.654520i
\(159\) 99.7841i 0.627573i
\(160\) 6.04597 27.6305i 0.0377873 0.172691i
\(161\) 38.1074 0.236692
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 48.2405 48.2405i 0.295954 0.295954i −0.543473 0.839427i \(-0.682891\pi\)
0.839427 + 0.543473i \(0.182891\pi\)
\(164\) 96.1120i 0.586049i
\(165\) 108.851 + 23.8182i 0.659704 + 0.144353i
\(166\) 175.374 1.05647
\(167\) 194.552 + 194.552i 1.16498 + 1.16498i 0.983371 + 0.181609i \(0.0581305\pi\)
0.181609 + 0.983371i \(0.441869\pi\)
\(168\) −27.5255 + 27.5255i −0.163843 + 0.163843i
\(169\) 11.3578i 0.0672057i
\(170\) 134.732 86.3549i 0.792541 0.507970i
\(171\) −81.7682 −0.478177
\(172\) 38.1600 + 38.1600i 0.221860 + 0.221860i
\(173\) −126.996 + 126.996i −0.734081 + 0.734081i −0.971426 0.237344i \(-0.923723\pi\)
0.237344 + 0.971426i \(0.423723\pi\)
\(174\) 26.6076i 0.152917i
\(175\) 186.293 68.9662i 1.06453 0.394093i
\(176\) 51.4657 0.292419
\(177\) 77.9757 + 77.9757i 0.440541 + 0.440541i
\(178\) −65.1773 + 65.1773i −0.366165 + 0.366165i
\(179\) 281.606i 1.57322i 0.617453 + 0.786608i \(0.288165\pi\)
−0.617453 + 0.786608i \(0.711835\pi\)
\(180\) 16.1884 + 25.2574i 0.0899357 + 0.140319i
\(181\) −153.271 −0.846803 −0.423402 0.905942i \(-0.639164\pi\)
−0.423402 + 0.905942i \(0.639164\pi\)
\(182\) −106.712 106.712i −0.586329 0.586329i
\(183\) −128.020 + 128.020i −0.699564 + 0.699564i
\(184\) 13.5647i 0.0737210i
\(185\) −35.2611 + 161.146i −0.190600 + 0.871059i
\(186\) −27.2602 −0.146560
\(187\) 205.903 + 205.903i 1.10108 + 1.10108i
\(188\) 113.198 113.198i 0.602119 0.602119i
\(189\) 41.2883i 0.218457i
\(190\) 188.275 + 41.1973i 0.990921 + 0.216828i
\(191\) −326.257 −1.70815 −0.854076 0.520148i \(-0.825877\pi\)
−0.854076 + 0.520148i \(0.825877\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 113.315 113.315i 0.587123 0.587123i −0.349728 0.936851i \(-0.613726\pi\)
0.936851 + 0.349728i \(0.113726\pi\)
\(194\) 243.867i 1.25704i
\(195\) −97.9186 + 62.7598i −0.502146 + 0.321845i
\(196\) −28.2760 −0.144265
\(197\) 62.0545 + 62.0545i 0.314997 + 0.314997i 0.846842 0.531845i \(-0.178501\pi\)
−0.531845 + 0.846842i \(0.678501\pi\)
\(198\) −38.5993 + 38.5993i −0.194946 + 0.194946i
\(199\) 132.815i 0.667412i 0.942677 + 0.333706i \(0.108299\pi\)
−0.942677 + 0.333706i \(0.891701\pi\)
\(200\) −24.5491 66.3124i −0.122746 0.331562i
\(201\) 8.51640 0.0423702
\(202\) −129.221 129.221i −0.639705 0.639705i
\(203\) 61.0324 61.0324i 0.300652 0.300652i
\(204\) 78.3988i 0.384308i
\(205\) −129.659 202.295i −0.632481 0.986804i
\(206\) −8.22842 −0.0399438
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −37.9850 + 37.9850i −0.182620 + 0.182620i
\(209\) 350.688i 1.67793i
\(210\) −20.8023 + 95.0682i −0.0990587 + 0.452706i
\(211\) −202.742 −0.960861 −0.480430 0.877033i \(-0.659520\pi\)
−0.480430 + 0.877033i \(0.659520\pi\)
\(212\) −81.4734 81.4734i −0.384308 0.384308i
\(213\) 111.248 111.248i 0.522289 0.522289i
\(214\) 49.5823i 0.231693i
\(215\) 131.798 + 28.8392i 0.613012 + 0.134136i
\(216\) −14.6969 −0.0680414
\(217\) −62.5293 62.5293i −0.288153 0.288153i
\(218\) −0.116226 + 0.116226i −0.000533145 + 0.000533145i
\(219\) 16.6870i 0.0761962i
\(220\) 108.324 69.4290i 0.492382 0.315587i
\(221\) −303.939 −1.37529
\(222\) −57.1433 57.1433i −0.257402 0.257402i
\(223\) −11.5319 + 11.5319i −0.0517127 + 0.0517127i −0.732490 0.680778i \(-0.761642\pi\)
0.680778 + 0.732490i \(0.261642\pi\)
\(224\) 44.9490i 0.200665i
\(225\) 68.1462 + 31.3225i 0.302872 + 0.139211i
\(226\) 301.259 1.33300
\(227\) 163.407 + 163.407i 0.719853 + 0.719853i 0.968575 0.248722i \(-0.0800105\pi\)
−0.248722 + 0.968575i \(0.580011\pi\)
\(228\) −66.7635 + 66.7635i −0.292822 + 0.292822i
\(229\) 154.404i 0.674251i 0.941460 + 0.337126i \(0.109455\pi\)
−0.941460 + 0.337126i \(0.890545\pi\)
\(230\) −18.2992 28.5506i −0.0795618 0.124133i
\(231\) −177.078 −0.766570
\(232\) −21.7250 21.7250i −0.0936422 0.0936422i
\(233\) −259.278 + 259.278i −1.11278 + 1.11278i −0.120009 + 0.992773i \(0.538292\pi\)
−0.992773 + 0.120009i \(0.961708\pi\)
\(234\) 56.9775i 0.243494i
\(235\) 85.5493 390.967i 0.364039 1.66369i
\(236\) 127.334 0.539550
\(237\) −126.656 126.656i −0.534413 0.534413i
\(238\) −179.831 + 179.831i −0.755592 + 0.755592i
\(239\) 89.5241i 0.374578i −0.982305 0.187289i \(-0.940030\pi\)
0.982305 0.187289i \(-0.0599701\pi\)
\(240\) 33.8404 + 7.40477i 0.141001 + 0.0308532i
\(241\) −153.366 −0.636373 −0.318187 0.948028i \(-0.603074\pi\)
−0.318187 + 0.948028i \(0.603074\pi\)
\(242\) 44.5449 + 44.5449i 0.184070 + 0.184070i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 209.056i 0.856788i
\(245\) −59.5148 + 38.1453i −0.242917 + 0.155695i
\(246\) 117.713 0.478507
\(247\) −258.831 258.831i −1.04790 1.04790i
\(248\) −22.2578 + 22.2578i −0.0897493 + 0.0897493i
\(249\) 214.788i 0.862603i
\(250\) −141.128 106.456i −0.564513 0.425822i
\(251\) −190.513 −0.759016 −0.379508 0.925188i \(-0.623907\pi\)
−0.379508 + 0.925188i \(0.623907\pi\)
\(252\) −33.7118 33.7118i −0.133777 0.133777i
\(253\) 43.6322 43.6322i 0.172459 0.172459i
\(254\) 306.905i 1.20829i
\(255\) 105.763 + 165.012i 0.414756 + 0.647107i
\(256\) 16.0000 0.0625000
\(257\) −116.546 116.546i −0.453486 0.453486i 0.443024 0.896510i \(-0.353906\pi\)
−0.896510 + 0.443024i \(0.853906\pi\)
\(258\) −46.7362 + 46.7362i −0.181148 + 0.181148i
\(259\) 262.150i 1.01216i
\(260\) −28.7070 + 131.193i −0.110412 + 0.504590i
\(261\) 32.5875 0.124856
\(262\) −233.897 233.897i −0.892738 0.892738i
\(263\) 267.847 267.847i 1.01843 1.01843i 0.0186010 0.999827i \(-0.494079\pi\)
0.999827 0.0186010i \(-0.00592123\pi\)
\(264\) 63.0323i 0.238759i
\(265\) −281.394 61.5732i −1.06186 0.232352i
\(266\) −306.284 −1.15144
\(267\) −79.8256 79.8256i −0.298972 0.298972i
\(268\) 6.95361 6.95361i 0.0259463 0.0259463i
\(269\) 161.335i 0.599757i −0.953977 0.299879i \(-0.903054\pi\)
0.953977 0.299879i \(-0.0969462\pi\)
\(270\) −30.9338 + 19.8267i −0.114570 + 0.0734322i
\(271\) 182.280 0.672620 0.336310 0.941751i \(-0.390821\pi\)
0.336310 + 0.941751i \(0.390821\pi\)
\(272\) 64.0124 + 64.0124i 0.235340 + 0.235340i
\(273\) 130.695 130.695i 0.478736 0.478736i
\(274\) 81.9252i 0.298997i
\(275\) 134.336 292.266i 0.488495 1.06278i
\(276\) 16.6132 0.0601929
\(277\) 211.687 + 211.687i 0.764215 + 0.764215i 0.977081 0.212867i \(-0.0682800\pi\)
−0.212867 + 0.977081i \(0.568280\pi\)
\(278\) 148.538 148.538i 0.534308 0.534308i
\(279\) 33.3868i 0.119666i
\(280\) 60.6378 + 94.6079i 0.216564 + 0.337885i
\(281\) 195.698 0.696433 0.348216 0.937414i \(-0.386787\pi\)
0.348216 + 0.937414i \(0.386787\pi\)
\(282\) 138.639 + 138.639i 0.491628 + 0.491628i
\(283\) 282.722 282.722i 0.999016 0.999016i −0.000983541 1.00000i \(-0.500313\pi\)
1.00000 0.000983541i \(0.000313071\pi\)
\(284\) 181.667i 0.639671i
\(285\) −50.4562 + 230.589i −0.177039 + 0.809083i
\(286\) −244.366 −0.854426
\(287\) 270.009 + 270.009i 0.940798 + 0.940798i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 223.198i 0.772311i
\(290\) −75.0342 16.4186i −0.258738 0.0566158i
\(291\) 298.674 1.02637
\(292\) 13.6249 + 13.6249i 0.0466605 + 0.0466605i
\(293\) 303.769 303.769i 1.03676 1.03676i 0.0374575 0.999298i \(-0.488074\pi\)
0.999298 0.0374575i \(-0.0119259\pi\)
\(294\) 34.6309i 0.117792i
\(295\) 268.010 171.778i 0.908508 0.582298i
\(296\) −93.3147 −0.315252
\(297\) −47.2743 47.2743i −0.159173 0.159173i
\(298\) −10.9701 + 10.9701i −0.0368125 + 0.0368125i
\(299\) 64.4067i 0.215407i
\(300\) 81.2158 30.0664i 0.270719 0.100221i
\(301\) −214.407 −0.712315
\(302\) −109.516 109.516i −0.362635 0.362635i
\(303\) 158.262 158.262i 0.522317 0.522317i
\(304\) 109.024i 0.358633i
\(305\) 282.024 + 440.017i 0.924669 + 1.44268i
\(306\) −96.0186 −0.313786
\(307\) −381.391 381.391i −1.24231 1.24231i −0.959038 0.283276i \(-0.908579\pi\)
−0.283276 0.959038i \(-0.591421\pi\)
\(308\) −144.583 + 144.583i −0.469426 + 0.469426i
\(309\) 10.0777i 0.0326139i
\(310\) −16.8213 + 76.8745i −0.0542622 + 0.247982i
\(311\) 34.0026 0.109333 0.0546666 0.998505i \(-0.482590\pi\)
0.0546666 + 0.998505i \(0.482590\pi\)
\(312\) −46.5220 46.5220i −0.149109 0.149109i
\(313\) −62.9469 + 62.9469i −0.201108 + 0.201108i −0.800475 0.599366i \(-0.795419\pi\)
0.599366 + 0.800475i \(0.295419\pi\)
\(314\) 182.784i 0.582114i
\(315\) −116.434 25.4775i −0.369633 0.0808811i
\(316\) −206.828 −0.654520
\(317\) −144.059 144.059i −0.454444 0.454444i 0.442383 0.896826i \(-0.354133\pi\)
−0.896826 + 0.442383i \(0.854133\pi\)
\(318\) 99.7841 99.7841i 0.313786 0.313786i
\(319\) 139.762i 0.438124i
\(320\) 33.6765 21.5846i 0.105239 0.0674518i
\(321\) −60.7257 −0.189177
\(322\) 38.1074 + 38.1074i 0.118346 + 0.118346i
\(323\) −436.181 + 436.181i −1.35041 + 1.35041i
\(324\) 18.0000i 0.0555556i
\(325\) 116.562 + 314.860i 0.358653 + 0.968800i
\(326\) 96.4810 0.295954
\(327\) −0.142347 0.142347i −0.000435311 0.000435311i
\(328\) 96.1120 96.1120i 0.293025 0.293025i
\(329\) 636.020i 1.93319i
\(330\) 85.0329 + 132.669i 0.257675 + 0.402028i
\(331\) 133.019 0.401871 0.200936 0.979604i \(-0.435602\pi\)
0.200936 + 0.979604i \(0.435602\pi\)
\(332\) 175.374 + 175.374i 0.528234 + 0.528234i
\(333\) 69.9860 69.9860i 0.210168 0.210168i
\(334\) 389.103i 1.16498i
\(335\) 5.25517 24.0165i 0.0156871 0.0716911i
\(336\) −55.0511 −0.163843
\(337\) 221.295 + 221.295i 0.656662 + 0.656662i 0.954589 0.297926i \(-0.0962950\pi\)
−0.297926 + 0.954589i \(0.596295\pi\)
\(338\) 11.3578 11.3578i 0.0336028 0.0336028i
\(339\) 368.965i 1.08839i
\(340\) 221.087 + 48.3771i 0.650256 + 0.142286i
\(341\) −143.189 −0.419910
\(342\) −81.7682 81.7682i −0.239088 0.239088i
\(343\) −195.877 + 195.877i −0.571069 + 0.571069i
\(344\) 76.3199i 0.221860i
\(345\) 34.9673 22.4119i 0.101354 0.0649619i
\(346\) −253.992 −0.734081
\(347\) 5.64579 + 5.64579i 0.0162703 + 0.0162703i 0.715195 0.698925i \(-0.246338\pi\)
−0.698925 + 0.715195i \(0.746338\pi\)
\(348\) 26.6076 26.6076i 0.0764586 0.0764586i
\(349\) 356.420i 1.02126i −0.859800 0.510631i \(-0.829412\pi\)
0.859800 0.510631i \(-0.170588\pi\)
\(350\) 255.259 + 117.326i 0.729311 + 0.335218i
\(351\) 69.7829 0.198812
\(352\) 51.4657 + 51.4657i 0.146209 + 0.146209i
\(353\) 220.393 220.393i 0.624341 0.624341i −0.322297 0.946639i \(-0.604455\pi\)
0.946639 + 0.322297i \(0.104455\pi\)
\(354\) 155.951i 0.440541i
\(355\) −245.075 382.369i −0.690351 1.07709i
\(356\) −130.355 −0.366165
\(357\) −220.247 220.247i −0.616938 0.616938i
\(358\) −281.606 + 281.606i −0.786608 + 0.786608i
\(359\) 339.199i 0.944844i 0.881373 + 0.472422i \(0.156620\pi\)
−0.881373 + 0.472422i \(0.843380\pi\)
\(360\) −9.06895 + 41.4458i −0.0251915 + 0.115127i
\(361\) −381.893 −1.05788
\(362\) −153.271 153.271i −0.423402 0.423402i
\(363\) −54.5561 + 54.5561i −0.150292 + 0.150292i
\(364\) 213.424i 0.586329i
\(365\) 47.0578 + 10.2969i 0.128925 + 0.0282108i
\(366\) −256.040 −0.699564
\(367\) 34.4028 + 34.4028i 0.0937407 + 0.0937407i 0.752422 0.658681i \(-0.228885\pi\)
−0.658681 + 0.752422i \(0.728885\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 144.168i 0.390699i
\(370\) −196.407 + 125.885i −0.530830 + 0.340229i
\(371\) 457.769 1.23388
\(372\) −27.2602 27.2602i −0.0732800 0.0732800i
\(373\) 76.1551 76.1551i 0.204169 0.204169i −0.597614 0.801784i \(-0.703885\pi\)
0.801784 + 0.597614i \(0.203885\pi\)
\(374\) 411.805i 1.10108i
\(375\) 130.381 172.846i 0.347682 0.460923i
\(376\) 226.397 0.602119
\(377\) 103.153 + 103.153i 0.273616 + 0.273616i
\(378\) 41.2883 41.2883i 0.109228 0.109228i
\(379\) 101.960i 0.269024i −0.990912 0.134512i \(-0.957053\pi\)
0.990912 0.134512i \(-0.0429468\pi\)
\(380\) 147.078 + 229.472i 0.387046 + 0.603874i
\(381\) 375.880 0.986562
\(382\) −326.257 326.257i −0.854076 0.854076i
\(383\) 523.069 523.069i 1.36572 1.36572i 0.499267 0.866448i \(-0.333603\pi\)
0.866448 0.499267i \(-0.166397\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −109.268 + 499.364i −0.283814 + 1.29705i
\(386\) 226.630 0.587123
\(387\) −57.2400 57.2400i −0.147907 0.147907i
\(388\) 243.867 243.867i 0.628522 0.628522i
\(389\) 8.10447i 0.0208341i 0.999946 + 0.0104171i \(0.00331591\pi\)
−0.999946 + 0.0104171i \(0.996684\pi\)
\(390\) −160.678 35.1588i −0.411996 0.0901507i
\(391\) 108.538 0.277591
\(392\) −28.2760 28.2760i −0.0721326 0.0721326i
\(393\) 286.465 286.465i 0.728917 0.728917i
\(394\) 124.109i 0.314997i
\(395\) −435.328 + 279.019i −1.10210 + 0.706376i
\(396\) −77.1985 −0.194946
\(397\) −46.7570 46.7570i −0.117776 0.117776i 0.645763 0.763538i \(-0.276540\pi\)
−0.763538 + 0.645763i \(0.776540\pi\)
\(398\) −132.815 + 132.815i −0.333706 + 0.333706i
\(399\) 375.119i 0.940148i
\(400\) 41.7633 90.8616i 0.104408 0.227154i
\(401\) 212.655 0.530311 0.265156 0.964206i \(-0.414577\pi\)
0.265156 + 0.964206i \(0.414577\pi\)
\(402\) 8.51640 + 8.51640i 0.0211851 + 0.0211851i
\(403\) 105.683 105.683i 0.262241 0.262241i
\(404\) 258.441i 0.639705i
\(405\) −24.2826 37.8861i −0.0599571 0.0935458i
\(406\) 122.065 0.300652
\(407\) −300.156 300.156i −0.737485 0.737485i
\(408\) −78.3988 + 78.3988i −0.192154 + 0.192154i
\(409\) 201.150i 0.491810i 0.969294 + 0.245905i \(0.0790852\pi\)
−0.969294 + 0.245905i \(0.920915\pi\)
\(410\) 72.6363 331.953i 0.177162 0.809642i
\(411\) −100.337 −0.244130
\(412\) −8.22842 8.22842i −0.0199719 0.0199719i
\(413\) −357.721 + 357.721i −0.866152 + 0.866152i
\(414\) 20.3470i 0.0491473i
\(415\) 605.709 + 132.538i 1.45954 + 0.319369i
\(416\) −75.9700 −0.182620
\(417\) 181.921 + 181.921i 0.436260 + 0.436260i
\(418\) −350.688 + 350.688i −0.838967 + 0.838967i
\(419\) 284.817i 0.679753i −0.940470 0.339877i \(-0.889615\pi\)
0.940470 0.339877i \(-0.110385\pi\)
\(420\) −115.871 + 74.2659i −0.275882 + 0.176824i
\(421\) −162.868 −0.386860 −0.193430 0.981114i \(-0.561961\pi\)
−0.193430 + 0.981114i \(0.561961\pi\)
\(422\) −202.742 202.742i −0.480430 0.480430i
\(423\) −169.798 + 169.798i −0.401413 + 0.401413i
\(424\) 162.947i 0.384308i
\(425\) 530.602 196.431i 1.24848 0.462190i
\(426\) 222.495 0.522289
\(427\) −587.305 587.305i −1.37542 1.37542i
\(428\) −49.5823 + 49.5823i −0.115847 + 0.115847i
\(429\) 299.286i 0.697636i
\(430\) 102.958 + 160.637i 0.239438 + 0.373574i
\(431\) 740.079 1.71712 0.858561 0.512712i \(-0.171359\pi\)
0.858561 + 0.512712i \(0.171359\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 542.660 542.660i 1.25326 1.25326i 0.299003 0.954252i \(-0.403346\pi\)
0.954252 0.299003i \(-0.0966541\pi\)
\(434\) 125.059i 0.288153i
\(435\) 20.1086 91.8977i 0.0462266 0.211259i
\(436\) −0.232451 −0.000533145
\(437\) 92.4298 + 92.4298i 0.211510 + 0.211510i
\(438\) −16.6870 + 16.6870i −0.0380981 + 0.0380981i
\(439\) 484.445i 1.10352i 0.834003 + 0.551760i \(0.186043\pi\)
−0.834003 + 0.551760i \(0.813957\pi\)
\(440\) 177.753 + 38.8950i 0.403984 + 0.0883977i
\(441\) 42.4140 0.0961768
\(442\) −303.939 303.939i −0.687645 0.687645i
\(443\) 526.218 526.218i 1.18785 1.18785i 0.210190 0.977661i \(-0.432592\pi\)
0.977661 0.210190i \(-0.0674082\pi\)
\(444\) 114.287i 0.257402i
\(445\) −274.368 + 175.853i −0.616557 + 0.395175i
\(446\) −23.0638 −0.0517127
\(447\) −13.4356 13.4356i −0.0300572 0.0300572i
\(448\) −44.9490 + 44.9490i −0.100333 + 0.100333i
\(449\) 620.540i 1.38205i −0.722831 0.691025i \(-0.757160\pi\)
0.722831 0.691025i \(-0.242840\pi\)
\(450\) 36.8237 + 99.4687i 0.0818304 + 0.221041i
\(451\) 618.309 1.37097
\(452\) 301.259 + 301.259i 0.666502 + 0.666502i
\(453\) 134.129 134.129i 0.296090 0.296090i
\(454\) 326.813i 0.719853i
\(455\) −287.916 449.210i −0.632783 0.987275i
\(456\) −133.527 −0.292822
\(457\) −2.93906 2.93906i −0.00643119 0.00643119i 0.703884 0.710315i \(-0.251448\pi\)
−0.710315 + 0.703884i \(0.751448\pi\)
\(458\) −154.404 + 154.404i −0.337126 + 0.337126i
\(459\) 117.598i 0.256205i
\(460\) 10.2514 46.8498i 0.0222857 0.101847i
\(461\) 336.573 0.730093 0.365046 0.930989i \(-0.381053\pi\)
0.365046 + 0.930989i \(0.381053\pi\)
\(462\) −177.078 177.078i −0.383285 0.383285i
\(463\) −592.717 + 592.717i −1.28017 + 1.28017i −0.339595 + 0.940572i \(0.610290\pi\)
−0.940572 + 0.339595i \(0.889710\pi\)
\(464\) 43.4500i 0.0936422i
\(465\) −94.1516 20.6018i −0.202477 0.0443049i
\(466\) −518.556 −1.11278
\(467\) −352.885 352.885i −0.755642 0.755642i 0.219884 0.975526i \(-0.429432\pi\)
−0.975526 + 0.219884i \(0.929432\pi\)
\(468\) 56.9775 56.9775i 0.121747 0.121747i
\(469\) 39.0698i 0.0833044i
\(470\) 476.516 305.417i 1.01386 0.649824i
\(471\) −223.864 −0.475294
\(472\) 127.334 + 127.334i 0.269775 + 0.269775i
\(473\) −245.491 + 245.491i −0.519009 + 0.519009i
\(474\) 253.312i 0.534413i
\(475\) 619.132 + 284.576i 1.30344 + 0.599107i
\(476\) −359.662 −0.755592
\(477\) 122.210 + 122.210i 0.256206 + 0.256206i
\(478\) 89.5241 89.5241i 0.187289 0.187289i
\(479\) 160.749i 0.335593i 0.985822 + 0.167797i \(0.0536652\pi\)
−0.985822 + 0.167797i \(0.946335\pi\)
\(480\) 26.4356 + 41.2451i 0.0550741 + 0.0859273i
\(481\) 443.070 0.921143
\(482\) −153.366 153.366i −0.318187 0.318187i
\(483\) −46.6718 + 46.6718i −0.0966291 + 0.0966291i
\(484\) 89.0897i 0.184070i
\(485\) 184.301 842.270i 0.380002 1.73664i
\(486\) 22.0454 0.0453609
\(487\) −212.553 212.553i −0.436454 0.436454i 0.454363 0.890817i \(-0.349867\pi\)
−0.890817 + 0.454363i \(0.849867\pi\)
\(488\) −209.056 + 209.056i −0.428394 + 0.428394i
\(489\) 118.165i 0.241645i
\(490\) −97.6601 21.3695i −0.199306 0.0436111i
\(491\) −399.924 −0.814510 −0.407255 0.913314i \(-0.633514\pi\)
−0.407255 + 0.913314i \(0.633514\pi\)
\(492\) 117.713 + 117.713i 0.239254 + 0.239254i
\(493\) 173.834 173.834i 0.352604 0.352604i
\(494\) 517.661i 1.04790i
\(495\) −162.486 + 104.144i −0.328255 + 0.210391i
\(496\) −44.5157 −0.0897493
\(497\) 510.359 + 510.359i 1.02688 + 1.02688i
\(498\) −214.788 + 214.788i −0.431301 + 0.431301i
\(499\) 284.551i 0.570242i 0.958492 + 0.285121i \(0.0920338\pi\)
−0.958492 + 0.285121i \(0.907966\pi\)
\(500\) −34.6728 247.584i −0.0693456 0.495168i
\(501\) −476.552 −0.951202
\(502\) −190.513 190.513i −0.379508 0.379508i
\(503\) −123.416 + 123.416i −0.245359 + 0.245359i −0.819063 0.573704i \(-0.805506\pi\)
0.573704 + 0.819063i \(0.305506\pi\)
\(504\) 67.4236i 0.133777i
\(505\) −348.646 543.962i −0.690388 1.07715i
\(506\) 87.2643 0.172459
\(507\) 13.9104 + 13.9104i 0.0274366 + 0.0274366i
\(508\) 306.905 306.905i 0.604143 0.604143i
\(509\) 501.577i 0.985416i 0.870195 + 0.492708i \(0.163993\pi\)
−0.870195 + 0.492708i \(0.836007\pi\)
\(510\) −59.2496 + 270.775i −0.116176 + 0.530932i
\(511\) −76.5530 −0.149810
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 100.145 100.145i 0.195215 0.195215i
\(514\) 233.092i 0.453486i
\(515\) −28.4194 6.21859i −0.0551834 0.0120749i
\(516\) −93.4724 −0.181148
\(517\) 728.230 + 728.230i 1.40857 + 1.40857i
\(518\) 262.150 262.150i 0.506082 0.506082i
\(519\) 311.076i 0.599375i
\(520\) −159.900 + 102.486i −0.307501 + 0.197089i
\(521\) −622.530 −1.19488 −0.597438 0.801915i \(-0.703814\pi\)
−0.597438 + 0.801915i \(0.703814\pi\)
\(522\) 32.5875 + 32.5875i 0.0624282 + 0.0624282i
\(523\) −271.805 + 271.805i −0.519703 + 0.519703i −0.917481 0.397779i \(-0.869781\pi\)
0.397779 + 0.917481i \(0.369781\pi\)
\(524\) 467.795i 0.892738i
\(525\) −143.695 + 312.627i −0.273704 + 0.595480i
\(526\) 535.693 1.01843
\(527\) −178.097 178.097i −0.337945 0.337945i
\(528\) −63.0323 + 63.0323i −0.119379 + 0.119379i
\(529\) 23.0000i 0.0434783i
\(530\) −219.821 342.967i −0.414756 0.647108i
\(531\) −191.001 −0.359700
\(532\) −306.284 306.284i −0.575721 0.575721i
\(533\) −456.352 + 456.352i −0.856196 + 0.856196i
\(534\) 159.651i 0.298972i
\(535\) −37.4716 + 171.248i −0.0700404 + 0.320090i
\(536\) 13.9072 0.0259463
\(537\) −344.895 344.895i −0.642263 0.642263i
\(538\) 161.335 161.335i 0.299879 0.299879i
\(539\) 181.905i 0.337487i
\(540\) −50.7605 11.1072i −0.0940010 0.0205688i
\(541\) 1017.17 1.88017 0.940085 0.340940i \(-0.110745\pi\)
0.940085 + 0.340940i \(0.110745\pi\)
\(542\) 182.280 + 182.280i 0.336310 + 0.336310i
\(543\) 187.718 187.718i 0.345706 0.345706i
\(544\) 128.025i 0.235340i
\(545\) −0.489259 + 0.313585i −0.000897722 + 0.000575385i
\(546\) 261.390 0.478736
\(547\) −533.088 533.088i −0.974567 0.974567i 0.0251176 0.999685i \(-0.492004\pi\)
−0.999685 + 0.0251176i \(0.992004\pi\)
\(548\) −81.9252 + 81.9252i −0.149498 + 0.149498i
\(549\) 313.584i 0.571192i
\(550\) 426.602 157.930i 0.775640 0.287145i
\(551\) 296.069 0.537330
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 581.046 581.046i 1.05072 1.05072i
\(554\) 423.375i 0.764215i
\(555\) −154.177 240.548i −0.277796 0.433421i
\(556\) 297.075 0.534308
\(557\) −359.466 359.466i −0.645361 0.645361i 0.306507 0.951868i \(-0.400840\pi\)
−0.951868 + 0.306507i \(0.900840\pi\)
\(558\) 33.3868 33.3868i 0.0598329 0.0598329i
\(559\) 362.377i 0.648259i
\(560\) −33.9701 + 155.246i −0.0606608 + 0.277224i
\(561\) −504.356 −0.899031
\(562\) 195.698 + 195.698i 0.348216 + 0.348216i
\(563\) −342.658 + 342.658i −0.608628 + 0.608628i −0.942587 0.333959i \(-0.891615\pi\)
0.333959 + 0.942587i \(0.391615\pi\)
\(564\) 277.278i 0.491628i
\(565\) 1040.49 + 227.675i 1.84158 + 0.402965i
\(566\) 565.443 0.999016
\(567\) 50.5677 + 50.5677i 0.0891846 + 0.0891846i
\(568\) 181.667 181.667i 0.319836 0.319836i
\(569\) 236.879i 0.416307i 0.978096 + 0.208154i \(0.0667454\pi\)
−0.978096 + 0.208154i \(0.933255\pi\)
\(570\) −281.045 + 180.133i −0.493061 + 0.316022i
\(571\) 402.396 0.704722 0.352361 0.935864i \(-0.385379\pi\)
0.352361 + 0.935864i \(0.385379\pi\)
\(572\) −244.366 244.366i −0.427213 0.427213i
\(573\) 399.582 399.582i 0.697350 0.697350i
\(574\) 540.018i 0.940798i
\(575\) −41.6251 112.438i −0.0723914 0.195545i
\(576\) −24.0000 −0.0416667
\(577\) 255.514 + 255.514i 0.442832 + 0.442832i 0.892963 0.450131i \(-0.148623\pi\)
−0.450131 + 0.892963i \(0.648623\pi\)
\(578\) −223.198 + 223.198i −0.386156 + 0.386156i
\(579\) 277.564i 0.479384i
\(580\) −58.6156 91.4527i −0.101061 0.157677i
\(581\) −985.360 −1.69597
\(582\) 298.674 + 298.674i 0.513186 + 0.513186i
\(583\) 524.135 524.135i 0.899032 0.899032i
\(584\) 27.2497i 0.0466605i
\(585\) 43.0605 196.790i 0.0736078 0.336393i
\(586\) 607.539 1.03676
\(587\) 533.089 + 533.089i 0.908158 + 0.908158i 0.996124 0.0879655i \(-0.0280365\pi\)
−0.0879655 + 0.996124i \(0.528037\pi\)
\(588\) 34.6309 34.6309i 0.0588960 0.0588960i
\(589\) 303.331i 0.514992i
\(590\) 439.788 + 96.2320i 0.745403 + 0.163105i
\(591\) −152.002 −0.257194
\(592\) −93.3147 93.3147i −0.157626 0.157626i
\(593\) 433.233 433.233i 0.730579 0.730579i −0.240156 0.970734i \(-0.577199\pi\)
0.970734 + 0.240156i \(0.0771985\pi\)
\(594\) 94.5485i 0.159173i
\(595\) −757.009 + 485.196i −1.27228 + 0.815456i
\(596\) −21.9402 −0.0368125
\(597\) −162.664 162.664i −0.272470 0.272470i
\(598\) −64.4067 + 64.4067i −0.107704 + 0.107704i
\(599\) 111.533i 0.186198i 0.995657 + 0.0930989i \(0.0296773\pi\)
−0.995657 + 0.0930989i \(0.970323\pi\)
\(600\) 111.282 + 51.1494i 0.185470 + 0.0852490i
\(601\) 523.677 0.871343 0.435671 0.900106i \(-0.356511\pi\)
0.435671 + 0.900106i \(0.356511\pi\)
\(602\) −214.407 214.407i −0.356157 0.356157i
\(603\) −10.4304 + 10.4304i −0.0172975 + 0.0172975i
\(604\) 219.031i 0.362635i
\(605\) 120.185 + 187.514i 0.198653 + 0.309941i
\(606\) 316.524 0.522317
\(607\) 3.99156 + 3.99156i 0.00657588 + 0.00657588i 0.710387 0.703811i \(-0.248520\pi\)
−0.703811 + 0.710387i \(0.748520\pi\)
\(608\) −109.024 + 109.024i −0.179316 + 0.179316i
\(609\) 149.498i 0.245481i
\(610\) −157.993 + 722.042i −0.259005 + 1.18367i
\(611\) −1074.96 −1.75935
\(612\) −96.0186 96.0186i −0.156893 0.156893i
\(613\) 87.2893 87.2893i 0.142397 0.142397i −0.632315 0.774712i \(-0.717895\pi\)
0.774712 + 0.632315i \(0.217895\pi\)
\(614\) 762.781i 1.24231i
\(615\) 406.558 + 88.9609i 0.661070 + 0.144652i
\(616\) −289.167 −0.469426
\(617\) −416.059 416.059i −0.674325 0.674325i 0.284385 0.958710i \(-0.408211\pi\)
−0.958710 + 0.284385i \(0.908211\pi\)
\(618\) 10.0777 10.0777i 0.0163070 0.0163070i
\(619\) 248.948i 0.402178i −0.979573 0.201089i \(-0.935552\pi\)
0.979573 0.201089i \(-0.0644480\pi\)
\(620\) −93.6957 + 60.0532i −0.151122 + 0.0968600i
\(621\) −24.9199 −0.0401286
\(622\) 34.0026 + 34.0026i 0.0546666 + 0.0546666i
\(623\) 366.207 366.207i 0.587812 0.587812i
\(624\) 93.0439i 0.149109i
\(625\) −406.978 474.335i −0.651165 0.758936i
\(626\) −125.894 −0.201108
\(627\) −429.504 429.504i −0.685014 0.685014i
\(628\) −182.784 + 182.784i −0.291057 + 0.291057i
\(629\) 746.662i 1.18706i
\(630\) −90.9567 141.912i −0.144376 0.225257i
\(631\) 470.788 0.746098 0.373049 0.927812i \(-0.378312\pi\)
0.373049 + 0.927812i \(0.378312\pi\)
\(632\) −206.828 206.828i −0.327260 0.327260i
\(633\) 248.307 248.307i 0.392270 0.392270i
\(634\) 288.117i 0.454444i
\(635\) 231.942 1059.99i 0.365263 1.66928i
\(636\) 199.568 0.313786
\(637\) 134.258 + 134.258i 0.210766 + 0.210766i
\(638\) 139.762 139.762i 0.219062 0.219062i
\(639\) 272.500i 0.426448i
\(640\) 55.2611 + 12.0919i 0.0863454 + 0.0188936i
\(641\) 1011.49 1.57799 0.788995 0.614400i \(-0.210602\pi\)
0.788995 + 0.614400i \(0.210602\pi\)
\(642\) −60.7257 60.7257i −0.0945883 0.0945883i
\(643\) −422.128 + 422.128i −0.656498 + 0.656498i −0.954550 0.298052i \(-0.903663\pi\)
0.298052 + 0.954550i \(0.403663\pi\)
\(644\) 76.2148i 0.118346i
\(645\) −196.739 + 126.098i −0.305022 + 0.195500i
\(646\) −872.363 −1.35041
\(647\) 482.452 + 482.452i 0.745675 + 0.745675i 0.973664 0.227989i \(-0.0732149\pi\)
−0.227989 + 0.973664i \(0.573215\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 819.165i 1.26220i
\(650\) −198.298 + 431.422i −0.305073 + 0.663727i
\(651\) 153.165 0.235276
\(652\) 96.4810 + 96.4810i 0.147977 + 0.147977i
\(653\) 455.524 455.524i 0.697586 0.697586i −0.266303 0.963889i \(-0.585802\pi\)
0.963889 + 0.266303i \(0.0858022\pi\)
\(654\) 0.284693i 0.000435311i
\(655\) −631.071 984.605i −0.963468 1.50321i
\(656\) 192.224 0.293025
\(657\) −20.4373 20.4373i −0.0311070 0.0311070i
\(658\) −636.020 + 636.020i −0.966596 + 0.966596i
\(659\) 81.7349i 0.124029i 0.998075 + 0.0620143i \(0.0197525\pi\)
−0.998075 + 0.0620143i \(0.980248\pi\)
\(660\) −47.6364 + 217.702i −0.0721764 + 0.329852i
\(661\) −137.438 −0.207925 −0.103962 0.994581i \(-0.533152\pi\)
−0.103962 + 0.994581i \(0.533152\pi\)
\(662\) 133.019 + 133.019i 0.200936 + 0.200936i
\(663\) 372.248 372.248i 0.561459 0.561459i
\(664\) 350.747i 0.528234i
\(665\) −1057.85 231.473i −1.59075 0.348079i
\(666\) 139.972 0.210168
\(667\) −36.8365 36.8365i −0.0552272 0.0552272i
\(668\) −389.103 + 389.103i −0.582490 + 0.582490i
\(669\) 28.2473i 0.0422232i
\(670\) 29.2717 18.7613i 0.0436891 0.0280020i
\(671\) −1344.90 −2.00433
\(672\) −55.0511 55.0511i −0.0819213 0.0819213i
\(673\) −363.220 + 363.220i −0.539702 + 0.539702i −0.923441 0.383739i \(-0.874636\pi\)
0.383739 + 0.923441i \(0.374636\pi\)
\(674\) 442.591i 0.656662i
\(675\) −121.824 + 45.0996i −0.180480 + 0.0668142i
\(676\) 22.7155 0.0336028
\(677\) 202.715 + 202.715i 0.299431 + 0.299431i 0.840791 0.541360i \(-0.182090\pi\)
−0.541360 + 0.840791i \(0.682090\pi\)
\(678\) −368.965 + 368.965i −0.544197 + 0.544197i
\(679\) 1370.20i 2.01796i
\(680\) 172.710 + 269.464i 0.253985 + 0.396271i
\(681\) −400.263 −0.587758
\(682\) −143.189 143.189i −0.209955 0.209955i
\(683\) −496.960 + 496.960i −0.727614 + 0.727614i −0.970144 0.242530i \(-0.922023\pi\)
0.242530 + 0.970144i \(0.422023\pi\)
\(684\) 163.536i 0.239088i
\(685\) −61.9146 + 282.954i −0.0903863 + 0.413072i
\(686\) −391.753 −0.571069
\(687\) −189.105 189.105i −0.275262 0.275262i
\(688\) −76.3199 + 76.3199i −0.110930 + 0.110930i
\(689\) 773.692i 1.12292i
\(690\) 57.3791 + 12.5554i 0.0831581 + 0.0181962i
\(691\) 708.102 1.02475 0.512375 0.858762i \(-0.328766\pi\)
0.512375 + 0.858762i \(0.328766\pi\)
\(692\) −253.992 253.992i −0.367041 0.367041i
\(693\) 216.875 216.875i 0.312951 0.312951i
\(694\) 11.2916i 0.0162703i
\(695\) 625.278 400.765i 0.899681 0.576640i
\(696\) 53.2152 0.0764586
\(697\) 769.045 + 769.045i 1.10336 + 1.10336i
\(698\) 356.420 356.420i 0.510631 0.510631i
\(699\) 635.099i 0.908583i
\(700\) 137.932 + 372.585i 0.197046 + 0.532264i
\(701\) −282.940 −0.403624 −0.201812 0.979424i \(-0.564683\pi\)
−0.201812 + 0.979424i \(0.564683\pi\)
\(702\) 69.7829 + 69.7829i 0.0994059 + 0.0994059i
\(703\) 635.848 635.848i 0.904478 0.904478i
\(704\) 102.931i 0.146209i
\(705\) 374.058 + 583.610i 0.530579 + 0.827816i
\(706\) 440.785 0.624341
\(707\) 726.042 + 726.042i 1.02693 + 1.02693i
\(708\) −155.951 + 155.951i −0.220270 + 0.220270i
\(709\) 348.639i 0.491733i 0.969304 + 0.245867i \(0.0790725\pi\)
−0.969304 + 0.245867i \(0.920927\pi\)
\(710\) 137.294 627.443i 0.193372 0.883723i
\(711\) 310.242 0.436347
\(712\) −130.355 130.355i −0.183082 0.183082i
\(713\) −37.7400 + 37.7400i −0.0529313 + 0.0529313i
\(714\) 440.494i 0.616938i
\(715\) −843.994 184.678i −1.18041 0.258291i
\(716\) −563.211 −0.786608
\(717\) 109.644 + 109.644i 0.152921 + 0.152921i
\(718\) −339.199 + 339.199i −0.472422 + 0.472422i
\(719\) 692.400i 0.963003i −0.876445 0.481502i \(-0.840092\pi\)
0.876445 0.481502i \(-0.159908\pi\)
\(720\) −50.5147 + 32.3768i −0.0701594 + 0.0449678i
\(721\) 46.2324 0.0641226
\(722\) −381.893 381.893i −0.528938 0.528938i
\(723\) 187.834 187.834i 0.259798 0.259798i
\(724\) 306.543i 0.423402i
\(725\) −246.746 113.414i −0.340339 0.156432i
\(726\) −109.112 −0.150292
\(727\) 564.236 + 564.236i 0.776116 + 0.776116i 0.979168 0.203052i \(-0.0650861\pi\)
−0.203052 + 0.979168i \(0.565086\pi\)
\(728\) 213.424 213.424i 0.293165 0.293165i
\(729\) 27.0000i 0.0370370i
\(730\) 36.7608 + 57.3547i 0.0503573 + 0.0785681i
\(731\) −610.677 −0.835400
\(732\) −256.040 256.040i −0.349782 0.349782i
\(733\) −591.205 + 591.205i −0.806555 + 0.806555i −0.984111 0.177556i \(-0.943181\pi\)
0.177556 + 0.984111i \(0.443181\pi\)
\(734\) 68.8057i 0.0937407i
\(735\) 26.1721 119.609i 0.0356083 0.162733i
\(736\) 27.1293 0.0368605
\(737\) 44.7341 + 44.7341i 0.0606975 + 0.0606975i
\(738\) −144.168 + 144.168i −0.195350 + 0.195350i
\(739\) 258.804i 0.350208i 0.984550 + 0.175104i \(0.0560262\pi\)
−0.984550 + 0.175104i \(0.943974\pi\)
\(740\) −322.292 70.5222i −0.435529 0.0953002i
\(741\) 634.003 0.855605
\(742\) 457.769 + 457.769i 0.616939 + 0.616939i
\(743\) 49.1328 49.1328i 0.0661276 0.0661276i −0.673270 0.739397i \(-0.735111\pi\)
0.739397 + 0.673270i \(0.235111\pi\)
\(744\) 54.5203i 0.0732800i
\(745\) −46.1794 + 29.5981i −0.0619857 + 0.0397290i
\(746\) 152.310 0.204169
\(747\) −263.061 263.061i −0.352156 0.352156i
\(748\) −411.805 + 411.805i −0.550542 + 0.550542i
\(749\) 278.585i 0.371942i
\(750\) 303.227 42.4653i 0.404303 0.0566204i
\(751\) −1118.26 −1.48903 −0.744517 0.667604i \(-0.767320\pi\)
−0.744517 + 0.667604i \(0.767320\pi\)
\(752\) 226.397 + 226.397i 0.301060 + 0.301060i
\(753\) 233.330 233.330i 0.309867 0.309867i
\(754\) 206.306i 0.273616i
\(755\) −295.481 461.013i −0.391365 0.610613i
\(756\) 82.5766 0.109228
\(757\) −814.033 814.033i −1.07534 1.07534i −0.996920 0.0784198i \(-0.975013\pi\)
−0.0784198 0.996920i \(-0.524987\pi\)
\(758\) 101.960 101.960i 0.134512 0.134512i
\(759\) 106.877i 0.140812i
\(760\) −82.3947 + 376.550i −0.108414 + 0.495460i
\(761\) −470.046 −0.617669 −0.308835 0.951116i \(-0.599939\pi\)
−0.308835 + 0.951116i \(0.599939\pi\)
\(762\) 375.880 + 375.880i 0.493281 + 0.493281i
\(763\) 0.653028 0.653028i 0.000855869 0.000855869i
\(764\) 652.514i 0.854076i
\(765\) −331.630 72.5656i −0.433504 0.0948570i
\(766\) 1046.14 1.36572
\(767\) −604.597 604.597i −0.788262 0.788262i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 694.030i 0.902510i 0.892395 + 0.451255i \(0.149023\pi\)
−0.892395 + 0.451255i \(0.850977\pi\)
\(770\) −608.633 + 390.096i −0.790432 + 0.506618i
\(771\) 285.478 0.370270
\(772\) 226.630 + 226.630i 0.293562 + 0.293562i
\(773\) −472.817 + 472.817i −0.611665 + 0.611665i −0.943380 0.331714i \(-0.892373\pi\)
0.331714 + 0.943380i \(0.392373\pi\)
\(774\) 114.480i 0.147907i
\(775\) −116.195 + 252.798i −0.149929 + 0.326191i
\(776\) 487.733 0.628522
\(777\) 321.067 + 321.067i 0.413214 + 0.413214i
\(778\) −8.10447 + 8.10447i −0.0104171 + 0.0104171i
\(779\) 1309.82i