Properties

Label 690.3.k.b.277.5
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 277.5
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0428394 - 4.99982i) q^{5} +2.44949 q^{6} +(0.599576 + 0.599576i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0428394 - 4.99982i) q^{5} +2.44949 q^{6} +(0.599576 + 0.599576i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-5.04266 + 4.95698i) q^{10} +2.79269 q^{11} +(-2.44949 - 2.44949i) q^{12} +(10.4226 - 10.4226i) q^{13} -1.19915i q^{14} +(6.07103 + 6.17597i) q^{15} -4.00000 q^{16} +(8.12418 + 8.12418i) q^{17} +(-3.00000 + 3.00000i) q^{18} +19.7629i q^{19} +(9.99963 + 0.0856788i) q^{20} -1.46866 q^{21} +(-2.79269 - 2.79269i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(-24.9963 - 0.428378i) q^{25} -20.8451 q^{26} +(3.67423 + 3.67423i) q^{27} +(-1.19915 + 1.19915i) q^{28} -53.8793i q^{29} +(0.104935 - 12.2470i) q^{30} -24.2777 q^{31} +(4.00000 + 4.00000i) q^{32} +(-3.42033 + 3.42033i) q^{33} -16.2484i q^{34} +(3.02346 - 2.97209i) q^{35} +6.00000 q^{36} +(21.3933 + 21.3933i) q^{37} +(19.7629 - 19.7629i) q^{38} +25.5299i q^{39} +(-9.91395 - 10.0853i) q^{40} +68.1650 q^{41} +(1.46866 + 1.46866i) q^{42} +(-16.0395 + 16.0395i) q^{43} +5.58538i q^{44} +(-14.9994 - 0.128518i) q^{45} +6.78233 q^{46} +(-10.0218 - 10.0218i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.2810i q^{49} +(24.5680 + 25.4247i) q^{50} -19.9001 q^{51} +(20.8451 + 20.8451i) q^{52} +(20.3778 - 20.3778i) q^{53} -7.34847i q^{54} +(0.119637 - 13.9629i) q^{55} +2.39831 q^{56} +(-24.2045 - 24.2045i) q^{57} +(-53.8793 + 53.8793i) q^{58} -113.656i q^{59} +(-12.3519 + 12.1421i) q^{60} -70.3213 q^{61} +(24.2777 + 24.2777i) q^{62} +(1.79873 - 1.79873i) q^{63} -8.00000i q^{64} +(-51.6643 - 52.5573i) q^{65} +6.84066 q^{66} +(-40.1198 - 40.1198i) q^{67} +(-16.2484 + 16.2484i) q^{68} -8.30662i q^{69} +(-5.99554 - 0.0513710i) q^{70} +117.779 q^{71} +(-6.00000 - 6.00000i) q^{72} +(75.3919 - 75.3919i) q^{73} -42.7867i q^{74} +(31.1388 - 30.0895i) q^{75} -39.5257 q^{76} +(1.67443 + 1.67443i) q^{77} +(25.5299 - 25.5299i) q^{78} -84.1235i q^{79} +(-0.171358 + 19.9993i) q^{80} -9.00000 q^{81} +(-68.1650 - 68.1650i) q^{82} +(-78.5983 + 78.5983i) q^{83} -2.93731i q^{84} +(40.9674 - 40.2714i) q^{85} +32.0790 q^{86} +(65.9883 + 65.9883i) q^{87} +(5.58538 - 5.58538i) q^{88} -67.9727i q^{89} +(14.8709 + 15.1280i) q^{90} +12.4982 q^{91} +(-6.78233 - 6.78233i) q^{92} +(29.7340 - 29.7340i) q^{93} +20.0436i q^{94} +(98.8106 + 0.846629i) q^{95} -9.79796 q^{96} +(-74.6956 - 74.6956i) q^{97} +(-48.2810 + 48.2810i) q^{98} -8.37807i 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
\(5\) 0.0428394 4.99982i 0.00856788 0.999963i
\(6\) 2.44949 0.408248
\(7\) 0.599576 + 0.599576i 0.0856538 + 0.0856538i 0.748636 0.662982i \(-0.230709\pi\)
−0.662982 + 0.748636i \(0.730709\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −5.04266 + 4.95698i −0.504266 + 0.495698i
\(11\) 2.79269 0.253881 0.126940 0.991910i \(-0.459484\pi\)
0.126940 + 0.991910i \(0.459484\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 10.4226 10.4226i 0.801735 0.801735i −0.181632 0.983367i \(-0.558138\pi\)
0.983367 + 0.181632i \(0.0581379\pi\)
\(14\) 1.19915i 0.0856538i
\(15\) 6.07103 + 6.17597i 0.404735 + 0.411731i
\(16\) −4.00000 −0.250000
\(17\) 8.12418 + 8.12418i 0.477893 + 0.477893i 0.904457 0.426564i \(-0.140276\pi\)
−0.426564 + 0.904457i \(0.640276\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 19.7629i 1.04015i 0.854121 + 0.520075i \(0.174096\pi\)
−0.854121 + 0.520075i \(0.825904\pi\)
\(20\) 9.99963 + 0.0856788i 0.499982 + 0.00428394i
\(21\) −1.46866 −0.0699360
\(22\) −2.79269 2.79269i −0.126940 0.126940i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −24.9963 0.428378i −0.999853 0.0171351i
\(26\) −20.8451 −0.801735
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −1.19915 + 1.19915i −0.0428269 + 0.0428269i
\(29\) 53.8793i 1.85791i −0.370198 0.928953i \(-0.620710\pi\)
0.370198 0.928953i \(-0.379290\pi\)
\(30\) 0.104935 12.2470i 0.00349782 0.408233i
\(31\) −24.2777 −0.783153 −0.391576 0.920146i \(-0.628070\pi\)
−0.391576 + 0.920146i \(0.628070\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −3.42033 + 3.42033i −0.103646 + 0.103646i
\(34\) 16.2484i 0.477893i
\(35\) 3.02346 2.97209i 0.0863845 0.0849167i
\(36\) 6.00000 0.166667
\(37\) 21.3933 + 21.3933i 0.578198 + 0.578198i 0.934407 0.356208i \(-0.115931\pi\)
−0.356208 + 0.934407i \(0.615931\pi\)
\(38\) 19.7629 19.7629i 0.520075 0.520075i
\(39\) 25.5299i 0.654614i
\(40\) −9.91395 10.0853i −0.247849 0.252133i
\(41\) 68.1650 1.66256 0.831281 0.555853i \(-0.187608\pi\)
0.831281 + 0.555853i \(0.187608\pi\)
\(42\) 1.46866 + 1.46866i 0.0349680 + 0.0349680i
\(43\) −16.0395 + 16.0395i −0.373012 + 0.373012i −0.868573 0.495561i \(-0.834962\pi\)
0.495561 + 0.868573i \(0.334962\pi\)
\(44\) 5.58538i 0.126940i
\(45\) −14.9994 0.128518i −0.333321 0.00285596i
\(46\) 6.78233 0.147442
\(47\) −10.0218 10.0218i −0.213229 0.213229i 0.592408 0.805638i \(-0.298177\pi\)
−0.805638 + 0.592408i \(0.798177\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 48.2810i 0.985327i
\(50\) 24.5680 + 25.4247i 0.491359 + 0.508494i
\(51\) −19.9001 −0.390198
\(52\) 20.8451 + 20.8451i 0.400867 + 0.400867i
\(53\) 20.3778 20.3778i 0.384487 0.384487i −0.488228 0.872716i \(-0.662357\pi\)
0.872716 + 0.488228i \(0.162357\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0.119637 13.9629i 0.00217522 0.253872i
\(56\) 2.39831 0.0428269
\(57\) −24.2045 24.2045i −0.424640 0.424640i
\(58\) −53.8793 + 53.8793i −0.928953 + 0.928953i
\(59\) 113.656i 1.92637i −0.268846 0.963183i \(-0.586642\pi\)
0.268846 0.963183i \(-0.413358\pi\)
\(60\) −12.3519 + 12.1421i −0.205866 + 0.202368i
\(61\) −70.3213 −1.15281 −0.576404 0.817165i \(-0.695545\pi\)
−0.576404 + 0.817165i \(0.695545\pi\)
\(62\) 24.2777 + 24.2777i 0.391576 + 0.391576i
\(63\) 1.79873 1.79873i 0.0285513 0.0285513i
\(64\) 8.00000i 0.125000i
\(65\) −51.6643 52.5573i −0.794836 0.808574i
\(66\) 6.84066 0.103646
\(67\) −40.1198 40.1198i −0.598803 0.598803i 0.341191 0.939994i \(-0.389170\pi\)
−0.939994 + 0.341191i \(0.889170\pi\)
\(68\) −16.2484 + 16.2484i −0.238946 + 0.238946i
\(69\) 8.30662i 0.120386i
\(70\) −5.99554 0.0513710i −0.0856506 0.000733871i
\(71\) 117.779 1.65886 0.829428 0.558614i \(-0.188667\pi\)
0.829428 + 0.558614i \(0.188667\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 75.3919 75.3919i 1.03277 1.03277i 0.0333207 0.999445i \(-0.489392\pi\)
0.999445 0.0333207i \(-0.0106083\pi\)
\(74\) 42.7867i 0.578198i
\(75\) 31.1388 30.0895i 0.415184 0.401193i
\(76\) −39.5257 −0.520075
\(77\) 1.67443 + 1.67443i 0.0217458 + 0.0217458i
\(78\) 25.5299 25.5299i 0.327307 0.327307i
\(79\) 84.1235i 1.06485i −0.846476 0.532427i \(-0.821280\pi\)
0.846476 0.532427i \(-0.178720\pi\)
\(80\) −0.171358 + 19.9993i −0.00214197 + 0.249991i
\(81\) −9.00000 −0.111111
\(82\) −68.1650 68.1650i −0.831281 0.831281i
\(83\) −78.5983 + 78.5983i −0.946967 + 0.946967i −0.998663 0.0516956i \(-0.983537\pi\)
0.0516956 + 0.998663i \(0.483537\pi\)
\(84\) 2.93731i 0.0349680i
\(85\) 40.9674 40.2714i 0.481970 0.473781i
\(86\) 32.0790 0.373012
\(87\) 65.9883 + 65.9883i 0.758487 + 0.758487i
\(88\) 5.58538 5.58538i 0.0634702 0.0634702i
\(89\) 67.9727i 0.763739i −0.924216 0.381869i \(-0.875280\pi\)
0.924216 0.381869i \(-0.124720\pi\)
\(90\) 14.8709 + 15.1280i 0.165233 + 0.168089i
\(91\) 12.4982 0.137343
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 29.7340 29.7340i 0.319721 0.319721i
\(94\) 20.0436i 0.213229i
\(95\) 98.8106 + 0.846629i 1.04011 + 0.00891188i
\(96\) −9.79796 −0.102062
\(97\) −74.6956 74.6956i −0.770057 0.770057i 0.208059 0.978116i \(-0.433285\pi\)
−0.978116 + 0.208059i \(0.933285\pi\)
\(98\) −48.2810 + 48.2810i −0.492663 + 0.492663i
\(99\) 8.37807i 0.0846269i
\(100\) 0.856757 49.9927i 0.00856757 0.499927i
\(101\) −50.8982 −0.503942 −0.251971 0.967735i \(-0.581079\pi\)
−0.251971 + 0.967735i \(0.581079\pi\)
\(102\) 19.9001 + 19.9001i 0.195099 + 0.195099i
\(103\) −15.8762 + 15.8762i −0.154138 + 0.154138i −0.779963 0.625825i \(-0.784762\pi\)
0.625825 + 0.779963i \(0.284762\pi\)
\(104\) 41.6902i 0.400867i
\(105\) −0.0629163 + 7.34301i −0.000599203 + 0.0699334i
\(106\) −40.7557 −0.384487
\(107\) −33.7185 33.7185i −0.315126 0.315126i 0.531766 0.846892i \(-0.321529\pi\)
−0.846892 + 0.531766i \(0.821529\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 136.307i 1.25053i −0.780414 0.625263i \(-0.784992\pi\)
0.780414 0.625263i \(-0.215008\pi\)
\(110\) −14.0826 + 13.8433i −0.128023 + 0.125848i
\(111\) −52.4028 −0.472097
\(112\) −2.39831 2.39831i −0.0214134 0.0214134i
\(113\) 66.5396 66.5396i 0.588846 0.588846i −0.348473 0.937319i \(-0.613300\pi\)
0.937319 + 0.348473i \(0.113300\pi\)
\(114\) 48.4089i 0.424640i
\(115\) 16.8099 + 17.1005i 0.146173 + 0.148700i
\(116\) 107.759 0.928953
\(117\) −31.2677 31.2677i −0.267245 0.267245i
\(118\) −113.656 + 113.656i −0.963183 + 0.963183i
\(119\) 9.74213i 0.0818666i
\(120\) 24.4940 + 0.209869i 0.204117 + 0.00174891i
\(121\) −113.201 −0.935545
\(122\) 70.3213 + 70.3213i 0.576404 + 0.576404i
\(123\) −83.4847 + 83.4847i −0.678738 + 0.678738i
\(124\) 48.5555i 0.391576i
\(125\) −3.21264 + 124.959i −0.0257011 + 0.999670i
\(126\) −3.59746 −0.0285513
\(127\) 52.1973 + 52.1973i 0.411002 + 0.411002i 0.882088 0.471085i \(-0.156138\pi\)
−0.471085 + 0.882088i \(0.656138\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 39.2886i 0.304563i
\(130\) −0.892992 + 104.222i −0.00686917 + 0.801705i
\(131\) −184.660 −1.40962 −0.704809 0.709397i \(-0.748967\pi\)
−0.704809 + 0.709397i \(0.748967\pi\)
\(132\) −6.84066 6.84066i −0.0518232 0.0518232i
\(133\) −11.8493 + 11.8493i −0.0890928 + 0.0890928i
\(134\) 80.2396i 0.598803i
\(135\) 18.5279 18.2131i 0.137244 0.134912i
\(136\) 32.4967 0.238946
\(137\) 126.402 + 126.402i 0.922642 + 0.922642i 0.997216 0.0745733i \(-0.0237595\pi\)
−0.0745733 + 0.997216i \(0.523759\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 217.770i 1.56669i −0.621589 0.783344i \(-0.713513\pi\)
0.621589 0.783344i \(-0.286487\pi\)
\(140\) 5.94417 + 6.04691i 0.0424584 + 0.0431922i
\(141\) 24.5482 0.174101
\(142\) −117.779 117.779i −0.829428 0.829428i
\(143\) 29.1069 29.1069i 0.203545 0.203545i
\(144\) 12.0000i 0.0833333i
\(145\) −269.386 2.30816i −1.85784 0.0159183i
\(146\) −150.784 −1.03277
\(147\) 59.1319 + 59.1319i 0.402258 + 0.402258i
\(148\) −42.7867 + 42.7867i −0.289099 + 0.289099i
\(149\) 75.9518i 0.509744i −0.966975 0.254872i \(-0.917967\pi\)
0.966975 0.254872i \(-0.0820333\pi\)
\(150\) −61.2283 1.04931i −0.408188 0.00699539i
\(151\) 36.4482 0.241379 0.120689 0.992690i \(-0.461489\pi\)
0.120689 + 0.992690i \(0.461489\pi\)
\(152\) 39.5257 + 39.5257i 0.260038 + 0.260038i
\(153\) 24.3725 24.3725i 0.159298 0.159298i
\(154\) 3.34886i 0.0217458i
\(155\) −1.04004 + 121.384i −0.00670996 + 0.783124i
\(156\) −51.0599 −0.327307
\(157\) 172.089 + 172.089i 1.09611 + 1.09611i 0.994862 + 0.101244i \(0.0322822\pi\)
0.101244 + 0.994862i \(0.467718\pi\)
\(158\) −84.1235 + 84.1235i −0.532427 + 0.532427i
\(159\) 49.9153i 0.313933i
\(160\) 20.1706 19.8279i 0.126066 0.123924i
\(161\) −4.06652 −0.0252579
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −81.8088 + 81.8088i −0.501895 + 0.501895i −0.912026 0.410132i \(-0.865483\pi\)
0.410132 + 0.912026i \(0.365483\pi\)
\(164\) 136.330i 0.831281i
\(165\) 16.9545 + 17.2476i 0.102755 + 0.104531i
\(166\) 157.197 0.946967
\(167\) 47.7793 + 47.7793i 0.286103 + 0.286103i 0.835537 0.549434i \(-0.185157\pi\)
−0.549434 + 0.835537i \(0.685157\pi\)
\(168\) −2.93731 + 2.93731i −0.0174840 + 0.0174840i
\(169\) 48.2591i 0.285557i
\(170\) −81.2388 0.696070i −0.477875 0.00409453i
\(171\) 59.2886 0.346717
\(172\) −32.0790 32.0790i −0.186506 0.186506i
\(173\) 115.524 115.524i 0.667770 0.667770i −0.289429 0.957199i \(-0.593466\pi\)
0.957199 + 0.289429i \(0.0934655\pi\)
\(174\) 131.977i 0.758487i
\(175\) −14.7304 15.2441i −0.0841735 0.0871089i
\(176\) −11.1708 −0.0634702
\(177\) 139.199 + 139.199i 0.786436 + 0.786436i
\(178\) −67.9727 + 67.9727i −0.381869 + 0.381869i
\(179\) 55.5826i 0.310518i −0.987874 0.155259i \(-0.950379\pi\)
0.987874 0.155259i \(-0.0496211\pi\)
\(180\) 0.257036 29.9989i 0.00142798 0.166661i
\(181\) 25.4089 0.140381 0.0701903 0.997534i \(-0.477639\pi\)
0.0701903 + 0.997534i \(0.477639\pi\)
\(182\) −12.4982 12.4982i −0.0686716 0.0686716i
\(183\) 86.1256 86.1256i 0.470632 0.470632i
\(184\) 13.5647i 0.0737210i
\(185\) 107.879 106.046i 0.583131 0.573223i
\(186\) −59.4681 −0.319721
\(187\) 22.6883 + 22.6883i 0.121328 + 0.121328i
\(188\) 20.0436 20.0436i 0.106615 0.106615i
\(189\) 4.40597i 0.0233120i
\(190\) −97.9640 99.6573i −0.515600 0.524512i
\(191\) 80.7623 0.422839 0.211420 0.977395i \(-0.432191\pi\)
0.211420 + 0.977395i \(0.432191\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −171.972 + 171.972i −0.891047 + 0.891047i −0.994622 0.103575i \(-0.966972\pi\)
0.103575 + 0.994622i \(0.466972\pi\)
\(194\) 149.391i 0.770057i
\(195\) 127.645 + 1.09369i 0.654590 + 0.00560865i
\(196\) 96.5620 0.492663
\(197\) −85.6447 85.6447i −0.434745 0.434745i 0.455494 0.890239i \(-0.349463\pi\)
−0.890239 + 0.455494i \(0.849463\pi\)
\(198\) −8.37807 + 8.37807i −0.0423135 + 0.0423135i
\(199\) 309.137i 1.55345i 0.629838 + 0.776726i \(0.283121\pi\)
−0.629838 + 0.776726i \(0.716879\pi\)
\(200\) −50.8494 + 49.1359i −0.254247 + 0.245680i
\(201\) 98.2730 0.488920
\(202\) 50.8982 + 50.8982i 0.251971 + 0.251971i
\(203\) 32.3047 32.3047i 0.159137 0.159137i
\(204\) 39.8002i 0.195099i
\(205\) 2.92015 340.813i 0.0142446 1.66250i
\(206\) 31.7524 0.154138
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −41.6902 + 41.6902i −0.200434 + 0.200434i
\(209\) 55.1915i 0.264074i
\(210\) 7.40593 7.28009i 0.0352663 0.0346671i
\(211\) 166.044 0.786937 0.393469 0.919338i \(-0.371275\pi\)
0.393469 + 0.919338i \(0.371275\pi\)
\(212\) 40.7557 + 40.7557i 0.192244 + 0.192244i
\(213\) −144.249 + 144.249i −0.677225 + 0.677225i
\(214\) 67.4370i 0.315126i
\(215\) 79.5074 + 80.8817i 0.369802 + 0.376194i
\(216\) 14.6969 0.0680414
\(217\) −14.5564 14.5564i −0.0670800 0.0670800i
\(218\) −136.307 + 136.307i −0.625263 + 0.625263i
\(219\) 184.672i 0.843249i
\(220\) 27.9259 + 0.239274i 0.126936 + 0.00108761i
\(221\) 169.349 0.766287
\(222\) 52.4028 + 52.4028i 0.236048 + 0.236048i
\(223\) 33.5693 33.5693i 0.150535 0.150535i −0.627822 0.778357i \(-0.716053\pi\)
0.778357 + 0.627822i \(0.216053\pi\)
\(224\) 4.79661i 0.0214134i
\(225\) −1.28514 + 74.9890i −0.00571171 + 0.333284i
\(226\) −133.079 −0.588846
\(227\) 201.604 + 201.604i 0.888125 + 0.888125i 0.994343 0.106218i \(-0.0338742\pi\)
−0.106218 + 0.994343i \(0.533874\pi\)
\(228\) 48.4089 48.4089i 0.212320 0.212320i
\(229\) 91.1570i 0.398066i 0.979993 + 0.199033i \(0.0637800\pi\)
−0.979993 + 0.199033i \(0.936220\pi\)
\(230\) 0.290551 33.9104i 0.00126327 0.147437i
\(231\) −4.10150 −0.0177554
\(232\) −107.759 107.759i −0.464476 0.464476i
\(233\) −186.981 + 186.981i −0.802495 + 0.802495i −0.983485 0.180990i \(-0.942070\pi\)
0.180990 + 0.983485i \(0.442070\pi\)
\(234\) 62.5353i 0.267245i
\(235\) −50.5364 + 49.6777i −0.215048 + 0.211395i
\(236\) 227.311 0.963183
\(237\) 103.030 + 103.030i 0.434725 + 0.434725i
\(238\) 9.74213 9.74213i 0.0409333 0.0409333i
\(239\) 171.742i 0.718586i 0.933225 + 0.359293i \(0.116982\pi\)
−0.933225 + 0.359293i \(0.883018\pi\)
\(240\) −24.2841 24.7039i −0.101184 0.102933i
\(241\) −119.663 −0.496527 −0.248263 0.968693i \(-0.579860\pi\)
−0.248263 + 0.968693i \(0.579860\pi\)
\(242\) 113.201 + 113.201i 0.467772 + 0.467772i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 140.643i 0.576404i
\(245\) −241.396 2.06833i −0.985291 0.00844216i
\(246\) 166.969 0.678738
\(247\) 205.979 + 205.979i 0.833925 + 0.833925i
\(248\) −48.5555 + 48.5555i −0.195788 + 0.195788i
\(249\) 192.526i 0.773196i
\(250\) 128.171 121.746i 0.512685 0.486984i
\(251\) 353.988 1.41031 0.705156 0.709052i \(-0.250877\pi\)
0.705156 + 0.709052i \(0.250877\pi\)
\(252\) 3.59746 + 3.59746i 0.0142756 + 0.0142756i
\(253\) −9.47047 + 9.47047i −0.0374327 + 0.0374327i
\(254\) 104.395i 0.411002i
\(255\) −0.852508 + 99.4968i −0.00334317 + 0.390184i
\(256\) 16.0000 0.0625000
\(257\) 121.719 + 121.719i 0.473614 + 0.473614i 0.903082 0.429468i \(-0.141299\pi\)
−0.429468 + 0.903082i \(0.641299\pi\)
\(258\) −39.2886 + 39.2886i −0.152281 + 0.152281i
\(259\) 25.6539i 0.0990497i
\(260\) 105.115 103.329i 0.404287 0.397418i
\(261\) −161.638 −0.619302
\(262\) 184.660 + 184.660i 0.704809 + 0.704809i
\(263\) 325.892 325.892i 1.23913 1.23913i 0.278775 0.960356i \(-0.410072\pi\)
0.960356 0.278775i \(-0.0899284\pi\)
\(264\) 13.6813i 0.0518232i
\(265\) −101.012 102.758i −0.381179 0.387768i
\(266\) 23.6987 0.0890928
\(267\) 83.2493 + 83.2493i 0.311795 + 0.311795i
\(268\) 80.2396 80.2396i 0.299401 0.299401i
\(269\) 510.361i 1.89725i −0.316400 0.948626i \(-0.602474\pi\)
0.316400 0.948626i \(-0.397526\pi\)
\(270\) −36.7410 0.314804i −0.136078 0.00116594i
\(271\) 57.8719 0.213550 0.106775 0.994283i \(-0.465948\pi\)
0.106775 + 0.994283i \(0.465948\pi\)
\(272\) −32.4967 32.4967i −0.119473 0.119473i
\(273\) −15.3071 + 15.3071i −0.0560701 + 0.0560701i
\(274\) 252.804i 0.922642i
\(275\) −69.8070 1.19633i −0.253844 0.00435028i
\(276\) 16.6132 0.0601929
\(277\) 210.527 + 210.527i 0.760027 + 0.760027i 0.976327 0.216300i \(-0.0693989\pi\)
−0.216300 + 0.976327i \(0.569399\pi\)
\(278\) −217.770 + 217.770i −0.783344 + 0.783344i
\(279\) 72.8332i 0.261051i
\(280\) 0.102742 11.9911i 0.000366936 0.0428253i
\(281\) 34.0038 0.121010 0.0605049 0.998168i \(-0.480729\pi\)
0.0605049 + 0.998168i \(0.480729\pi\)
\(282\) −24.5482 24.5482i −0.0870505 0.0870505i
\(283\) 172.081 172.081i 0.608060 0.608060i −0.334379 0.942439i \(-0.608526\pi\)
0.942439 + 0.334379i \(0.108526\pi\)
\(284\) 235.557i 0.829428i
\(285\) −122.055 + 119.981i −0.428262 + 0.420986i
\(286\) −58.2139 −0.203545
\(287\) 40.8701 + 40.8701i 0.142405 + 0.142405i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 156.995i 0.543237i
\(290\) 267.078 + 271.695i 0.920959 + 0.936878i
\(291\) 182.966 0.628749
\(292\) 150.784 + 150.784i 0.516383 + 0.516383i
\(293\) 66.0033 66.0033i 0.225267 0.225267i −0.585445 0.810712i \(-0.699080\pi\)
0.810712 + 0.585445i \(0.199080\pi\)
\(294\) 118.264i 0.402258i
\(295\) −568.257 4.86894i −1.92630 0.0165049i
\(296\) 85.5733 0.289099
\(297\) 10.2610 + 10.2610i 0.0345488 + 0.0345488i
\(298\) −75.9518 + 75.9518i −0.254872 + 0.254872i
\(299\) 70.6892i 0.236419i
\(300\) 60.1789 + 62.2776i 0.200596 + 0.207592i
\(301\) −19.2338 −0.0638997
\(302\) −36.4482 36.4482i −0.120689 0.120689i
\(303\) 62.3373 62.3373i 0.205734 0.205734i
\(304\) 79.0514i 0.260038i
\(305\) −3.01252 + 351.594i −0.00987712 + 1.15277i
\(306\) −48.7451 −0.159298
\(307\) −182.604 182.604i −0.594801 0.594801i 0.344123 0.938924i \(-0.388176\pi\)
−0.938924 + 0.344123i \(0.888176\pi\)
\(308\) −3.34886 + 3.34886i −0.0108729 + 0.0108729i
\(309\) 38.8886i 0.125853i
\(310\) 122.424 120.344i 0.394917 0.388207i
\(311\) −412.663 −1.32689 −0.663446 0.748224i \(-0.730907\pi\)
−0.663446 + 0.748224i \(0.730907\pi\)
\(312\) 51.0599 + 51.0599i 0.163653 + 0.163653i
\(313\) −417.460 + 417.460i −1.33374 + 1.33374i −0.431743 + 0.901997i \(0.642101\pi\)
−0.901997 + 0.431743i \(0.857899\pi\)
\(314\) 344.177i 1.09611i
\(315\) −8.91626 9.07037i −0.0283056 0.0287948i
\(316\) 168.247 0.532427
\(317\) −290.923 290.923i −0.917738 0.917738i 0.0791268 0.996865i \(-0.474787\pi\)
−0.996865 + 0.0791268i \(0.974787\pi\)
\(318\) 49.9153 49.9153i 0.156966 0.156966i
\(319\) 150.468i 0.471687i
\(320\) −39.9985 0.342715i −0.124995 0.00107099i
\(321\) 82.5931 0.257299
\(322\) 4.06652 + 4.06652i 0.0126290 + 0.0126290i
\(323\) −160.557 + 160.557i −0.497080 + 0.497080i
\(324\) 18.0000i 0.0555556i
\(325\) −264.990 + 256.061i −0.815355 + 0.787879i
\(326\) 163.618 0.501895
\(327\) 166.942 + 166.942i 0.510525 + 0.510525i
\(328\) 136.330 136.330i 0.415640 0.415640i
\(329\) 12.0176i 0.0365278i
\(330\) 0.293050 34.2021i 0.000888030 0.103643i
\(331\) 52.5667 0.158812 0.0794058 0.996842i \(-0.474698\pi\)
0.0794058 + 0.996842i \(0.474698\pi\)
\(332\) −157.197 157.197i −0.473484 0.473484i
\(333\) 64.1800 64.1800i 0.192733 0.192733i
\(334\) 95.5585i 0.286103i
\(335\) −202.310 + 198.873i −0.603911 + 0.593650i
\(336\) 5.87462 0.0174840
\(337\) −52.9222 52.9222i −0.157039 0.157039i 0.624214 0.781253i \(-0.285419\pi\)
−0.781253 + 0.624214i \(0.785419\pi\)
\(338\) −48.2591 + 48.2591i −0.142778 + 0.142778i
\(339\) 162.988i 0.480790i
\(340\) 80.5427 + 81.9349i 0.236890 + 0.240985i
\(341\) −67.8002 −0.198827
\(342\) −59.2886 59.2886i −0.173358 0.173358i
\(343\) 58.3274 58.3274i 0.170051 0.170051i
\(344\) 64.1580i 0.186506i
\(345\) −41.5316 0.355851i −0.120381 0.00103145i
\(346\) −231.048 −0.667770
\(347\) −118.619 118.619i −0.341843 0.341843i 0.515217 0.857060i \(-0.327711\pi\)
−0.857060 + 0.515217i \(0.827711\pi\)
\(348\) −131.977 + 131.977i −0.379243 + 0.379243i
\(349\) 398.115i 1.14073i 0.821391 + 0.570366i \(0.193199\pi\)
−0.821391 + 0.570366i \(0.806801\pi\)
\(350\) −0.513691 + 29.9744i −0.00146769 + 0.0856412i
\(351\) 76.5898 0.218205
\(352\) 11.1708 + 11.1708i 0.0317351 + 0.0317351i
\(353\) 171.724 171.724i 0.486470 0.486470i −0.420721 0.907190i \(-0.638223\pi\)
0.907190 + 0.420721i \(0.138223\pi\)
\(354\) 278.398i 0.786436i
\(355\) 5.04557 588.872i 0.0142129 1.65879i
\(356\) 135.945 0.381869
\(357\) −11.9316 11.9316i −0.0334219 0.0334219i
\(358\) −55.5826 + 55.5826i −0.155259 + 0.155259i
\(359\) 544.606i 1.51701i 0.651669 + 0.758504i \(0.274069\pi\)
−0.651669 + 0.758504i \(0.725931\pi\)
\(360\) −30.2559 + 29.7419i −0.0840443 + 0.0826163i
\(361\) −29.5704 −0.0819126
\(362\) −25.4089 25.4089i −0.0701903 0.0701903i
\(363\) 138.642 138.642i 0.381934 0.381934i
\(364\) 24.9965i 0.0686716i
\(365\) −373.716 380.175i −1.02388 1.04158i
\(366\) −172.251 −0.470632
\(367\) 98.8242 + 98.8242i 0.269276 + 0.269276i 0.828808 0.559533i \(-0.189019\pi\)
−0.559533 + 0.828808i \(0.689019\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 204.495i 0.554187i
\(370\) −213.925 1.83296i −0.578177 0.00495393i
\(371\) 24.4361 0.0658656
\(372\) 59.4681 + 59.4681i 0.159860 + 0.159860i
\(373\) −407.257 + 407.257i −1.09184 + 1.09184i −0.0965103 + 0.995332i \(0.530768\pi\)
−0.995332 + 0.0965103i \(0.969232\pi\)
\(374\) 45.3766i 0.121328i
\(375\) −149.108 156.977i −0.397621 0.418606i
\(376\) −40.0871 −0.106615
\(377\) −561.559 561.559i −1.48955 1.48955i
\(378\) 4.40597 4.40597i 0.0116560 0.0116560i
\(379\) 237.240i 0.625962i 0.949759 + 0.312981i \(0.101328\pi\)
−0.949759 + 0.312981i \(0.898672\pi\)
\(380\) −1.69326 + 197.621i −0.00445594 + 0.520056i
\(381\) −127.857 −0.335582
\(382\) −80.7623 80.7623i −0.211420 0.211420i
\(383\) −204.845 + 204.845i −0.534842 + 0.534842i −0.922010 0.387167i \(-0.873454\pi\)
0.387167 + 0.922010i \(0.373454\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 8.44357 8.30011i 0.0219314 0.0215587i
\(386\) 343.944 0.891047
\(387\) 48.1185 + 48.1185i 0.124337 + 0.124337i
\(388\) 149.391 149.391i 0.385029 0.385029i
\(389\) 398.431i 1.02425i −0.858912 0.512123i \(-0.828859\pi\)
0.858912 0.512123i \(-0.171141\pi\)
\(390\) −126.551 128.739i −0.324490 0.330099i
\(391\) −55.1009 −0.140923
\(392\) −96.5620 96.5620i −0.246332 0.246332i
\(393\) 226.161 226.161i 0.575474 0.575474i
\(394\) 171.289i 0.434745i
\(395\) −420.602 3.60380i −1.06482 0.00912355i
\(396\) 16.7561 0.0423135
\(397\) 257.697 + 257.697i 0.649112 + 0.649112i 0.952778 0.303666i \(-0.0982108\pi\)
−0.303666 + 0.952778i \(0.598211\pi\)
\(398\) 309.137 309.137i 0.776726 0.776726i
\(399\) 29.0248i 0.0727439i
\(400\) 99.9853 + 1.71351i 0.249963 + 0.00428378i
\(401\) −415.912 −1.03719 −0.518594 0.855021i \(-0.673544\pi\)
−0.518594 + 0.855021i \(0.673544\pi\)
\(402\) −98.2730 98.2730i −0.244460 0.244460i
\(403\) −253.036 + 253.036i −0.627881 + 0.627881i
\(404\) 101.796i 0.251971i
\(405\) −0.385555 + 44.9983i −0.000951987 + 0.111107i
\(406\) −64.6094 −0.159137
\(407\) 59.7449 + 59.7449i 0.146793 + 0.146793i
\(408\) −39.8002 + 39.8002i −0.0975495 + 0.0975495i
\(409\) 287.346i 0.702557i 0.936271 + 0.351278i \(0.114253\pi\)
−0.936271 + 0.351278i \(0.885747\pi\)
\(410\) −343.733 + 337.892i −0.838372 + 0.824128i
\(411\) −309.620 −0.753334
\(412\) −31.7524 31.7524i −0.0770690 0.0770690i
\(413\) 68.1452 68.1452i 0.165001 0.165001i
\(414\) 20.3470i 0.0491473i
\(415\) 389.610 + 396.344i 0.938819 + 0.955046i
\(416\) 83.3804 0.200434
\(417\) 266.712 + 266.712i 0.639597 + 0.639597i
\(418\) 55.1915 55.1915i 0.132037 0.132037i
\(419\) 832.842i 1.98769i −0.110778 0.993845i \(-0.535334\pi\)
0.110778 0.993845i \(-0.464666\pi\)
\(420\) −14.6860 0.125833i −0.0349667 0.000299602i
\(421\) 503.773 1.19661 0.598305 0.801269i \(-0.295841\pi\)
0.598305 + 0.801269i \(0.295841\pi\)
\(422\) −166.044 166.044i −0.393469 0.393469i
\(423\) −30.0653 + 30.0653i −0.0710764 + 0.0710764i
\(424\) 81.5113i 0.192244i
\(425\) −199.594 206.555i −0.469634 0.486011i
\(426\) 288.498 0.677225
\(427\) −42.1630 42.1630i −0.0987423 0.0987423i
\(428\) 67.4370 67.4370i 0.157563 0.157563i
\(429\) 71.2972i 0.166194i
\(430\) 1.37425 160.389i 0.00319592 0.372998i
\(431\) 213.988 0.496492 0.248246 0.968697i \(-0.420146\pi\)
0.248246 + 0.968697i \(0.420146\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 4.82654 4.82654i 0.0111467 0.0111467i −0.701511 0.712658i \(-0.747491\pi\)
0.712658 + 0.701511i \(0.247491\pi\)
\(434\) 29.1127i 0.0670800i
\(435\) 332.757 327.103i 0.764958 0.751960i
\(436\) 272.615 0.625263
\(437\) −67.0191 67.0191i −0.153362 0.153362i
\(438\) 184.672 184.672i 0.421625 0.421625i
\(439\) 770.632i 1.75543i −0.479187 0.877713i \(-0.659068\pi\)
0.479187 0.877713i \(-0.340932\pi\)
\(440\) −27.6866 28.1651i −0.0629241 0.0640117i
\(441\) −144.843 −0.328442
\(442\) −169.349 169.349i −0.383143 0.383143i
\(443\) 83.6593 83.6593i 0.188847 0.188847i −0.606350 0.795198i \(-0.707367\pi\)
0.795198 + 0.606350i \(0.207367\pi\)
\(444\) 104.806i 0.236048i
\(445\) −339.851 2.91191i −0.763711 0.00654362i
\(446\) −67.1385 −0.150535
\(447\) 93.0216 + 93.0216i 0.208102 + 0.208102i
\(448\) 4.79661 4.79661i 0.0107067 0.0107067i
\(449\) 544.988i 1.21378i 0.794785 + 0.606891i \(0.207584\pi\)
−0.794785 + 0.606891i \(0.792416\pi\)
\(450\) 76.2741 73.7039i 0.169498 0.163786i
\(451\) 190.364 0.422092
\(452\) 133.079 + 133.079i 0.294423 + 0.294423i
\(453\) −44.6398 + 44.6398i −0.0985425 + 0.0985425i
\(454\) 403.209i 0.888125i
\(455\) 0.535417 62.4888i 0.00117674 0.137338i
\(456\) −96.8178 −0.212320
\(457\) −429.596 429.596i −0.940035 0.940035i 0.0582661 0.998301i \(-0.481443\pi\)
−0.998301 + 0.0582661i \(0.981443\pi\)
\(458\) 91.1570 91.1570i 0.199033 0.199033i
\(459\) 59.7003i 0.130066i
\(460\) −34.2010 + 33.6199i −0.0743499 + 0.0730866i
\(461\) 327.982 0.711458 0.355729 0.934589i \(-0.384233\pi\)
0.355729 + 0.934589i \(0.384233\pi\)
\(462\) 4.10150 + 4.10150i 0.00887770 + 0.00887770i
\(463\) 412.976 412.976i 0.891957 0.891957i −0.102750 0.994707i \(-0.532764\pi\)
0.994707 + 0.102750i \(0.0327641\pi\)
\(464\) 215.517i 0.464476i
\(465\) −147.391 149.939i −0.316970 0.322448i
\(466\) 373.963 0.802495
\(467\) 553.078 + 553.078i 1.18432 + 1.18432i 0.978613 + 0.205708i \(0.0659496\pi\)
0.205708 + 0.978613i \(0.434050\pi\)
\(468\) 62.5353 62.5353i 0.133622 0.133622i
\(469\) 48.1097i 0.102579i
\(470\) 100.214 + 0.858654i 0.213221 + 0.00182692i
\(471\) −421.529 −0.894966
\(472\) −227.311 227.311i −0.481592 0.481592i
\(473\) −44.7933 + 44.7933i −0.0947005 + 0.0947005i
\(474\) 206.060i 0.434725i
\(475\) 8.46598 493.999i 0.0178231 1.04000i
\(476\) −19.4843 −0.0409333
\(477\) −61.1335 61.1335i −0.128162 0.128162i
\(478\) 171.742 171.742i 0.359293 0.359293i
\(479\) 560.923i 1.17103i −0.810662 0.585514i \(-0.800893\pi\)
0.810662 0.585514i \(-0.199107\pi\)
\(480\) −0.419739 + 48.9880i −0.000874456 + 0.102058i
\(481\) 445.946 0.927123
\(482\) 119.663 + 119.663i 0.248263 + 0.248263i
\(483\) 4.98045 4.98045i 0.0103115 0.0103115i
\(484\) 226.402i 0.467772i
\(485\) −376.664 + 370.264i −0.776627 + 0.763431i
\(486\) −22.0454 −0.0453609
\(487\) 455.931 + 455.931i 0.936203 + 0.936203i 0.998084 0.0618802i \(-0.0197097\pi\)
−0.0618802 + 0.998084i \(0.519710\pi\)
\(488\) −140.643 + 140.643i −0.288202 + 0.288202i
\(489\) 200.390i 0.409795i
\(490\) 239.328 + 243.465i 0.488424 + 0.496866i
\(491\) −419.688 −0.854762 −0.427381 0.904072i \(-0.640564\pi\)
−0.427381 + 0.904072i \(0.640564\pi\)
\(492\) −166.969 166.969i −0.339369 0.339369i
\(493\) 437.725 437.725i 0.887880 0.887880i
\(494\) 411.959i 0.833925i
\(495\) −41.8888 0.358911i −0.0846238 0.000725074i
\(496\) 97.1110 0.195788
\(497\) 70.6173 + 70.6173i 0.142087 + 0.142087i
\(498\) −192.526 + 192.526i −0.386598 + 0.386598i
\(499\) 338.152i 0.677659i 0.940848 + 0.338830i \(0.110031\pi\)
−0.940848 + 0.338830i \(0.889969\pi\)
\(500\) −249.917 6.42528i −0.499835 0.0128506i
\(501\) −117.035 −0.233602
\(502\) −353.988 353.988i −0.705156 0.705156i
\(503\) −153.284 + 153.284i −0.304740 + 0.304740i −0.842865 0.538125i \(-0.819133\pi\)
0.538125 + 0.842865i \(0.319133\pi\)
\(504\) 7.19492i 0.0142756i
\(505\) −2.18045 + 254.481i −0.00431772 + 0.503924i
\(506\) 18.9409 0.0374327
\(507\) 59.1051 + 59.1051i 0.116578 + 0.116578i
\(508\) −104.395 + 104.395i −0.205501 + 0.205501i
\(509\) 706.177i 1.38738i 0.720273 + 0.693691i \(0.244017\pi\)
−0.720273 + 0.693691i \(0.755983\pi\)
\(510\) 100.349 98.6443i 0.196763 0.193420i
\(511\) 90.4064 0.176920
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −72.6134 + 72.6134i −0.141547 + 0.141547i
\(514\) 243.438i 0.473614i
\(515\) 78.6980 + 80.0583i 0.152812 + 0.155453i
\(516\) 78.5772 0.152281
\(517\) −27.9877 27.9877i −0.0541348 0.0541348i
\(518\) 25.6539 25.6539i 0.0495248 0.0495248i
\(519\) 282.975i 0.545232i
\(520\) −208.443 1.78598i −0.400853 0.00343458i
\(521\) −701.348 −1.34616 −0.673079 0.739571i \(-0.735028\pi\)
−0.673079 + 0.739571i \(0.735028\pi\)
\(522\) 161.638 + 161.638i 0.309651 + 0.309651i
\(523\) 467.174 467.174i 0.893258 0.893258i −0.101571 0.994828i \(-0.532387\pi\)
0.994828 + 0.101571i \(0.0323868\pi\)
\(524\) 369.320i 0.704809i
\(525\) 36.7110 + 0.629140i 0.0699257 + 0.00119836i
\(526\) −651.783 −1.23913
\(527\) −197.237 197.237i −0.374263 0.374263i
\(528\) 13.6813 13.6813i 0.0259116 0.0259116i
\(529\) 23.0000i 0.0434783i
\(530\) −1.74595 + 203.771i −0.00329424 + 0.384473i
\(531\) −340.967 −0.642122
\(532\) −23.6987 23.6987i −0.0445464 0.0445464i
\(533\) 710.453 710.453i 1.33293 1.33293i
\(534\) 166.499i 0.311795i
\(535\) −170.031 + 167.142i −0.317815 + 0.312415i
\(536\) −160.479 −0.299401
\(537\) 68.0746 + 68.0746i 0.126768 + 0.126768i
\(538\) −510.361 + 510.361i −0.948626 + 0.948626i
\(539\) 134.834i 0.250156i
\(540\) 36.4262 + 37.0558i 0.0674559 + 0.0686219i
\(541\) −397.941 −0.735565 −0.367783 0.929912i \(-0.619883\pi\)
−0.367783 + 0.929912i \(0.619883\pi\)
\(542\) −57.8719 57.8719i −0.106775 0.106775i
\(543\) −31.1194 + 31.1194i −0.0573101 + 0.0573101i
\(544\) 64.9934i 0.119473i
\(545\) −681.512 5.83932i −1.25048 0.0107144i
\(546\) 30.6143 0.0560701
\(547\) 266.491 + 266.491i 0.487187 + 0.487187i 0.907417 0.420230i \(-0.138051\pi\)
−0.420230 + 0.907417i \(0.638051\pi\)
\(548\) −252.804 + 252.804i −0.461321 + 0.461321i
\(549\) 210.964i 0.384269i
\(550\) 68.6106 + 71.0033i 0.124747 + 0.129097i
\(551\) 1064.81 1.93250
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 50.4384 50.4384i 0.0912088 0.0912088i
\(554\) 421.055i 0.760027i
\(555\) −2.24490 + 262.004i −0.00404487 + 0.472080i
\(556\) 435.539 0.783344
\(557\) 218.918 + 218.918i 0.393031 + 0.393031i 0.875766 0.482736i \(-0.160357\pi\)
−0.482736 + 0.875766i \(0.660357\pi\)
\(558\) 72.8332 72.8332i 0.130525 0.130525i
\(559\) 334.345i 0.598113i
\(560\) −12.0938 + 11.8883i −0.0215961 + 0.0212292i
\(561\) −55.5748 −0.0990638
\(562\) −34.0038 34.0038i −0.0605049 0.0605049i
\(563\) 144.453 144.453i 0.256577 0.256577i −0.567083 0.823660i \(-0.691928\pi\)
0.823660 + 0.567083i \(0.191928\pi\)
\(564\) 49.0965i 0.0870505i
\(565\) −329.835 335.536i −0.583779 0.593869i
\(566\) −344.162 −0.608060
\(567\) −5.39619 5.39619i −0.00951708 0.00951708i
\(568\) 235.557 235.557i 0.414714 0.414714i
\(569\) 282.359i 0.496238i −0.968730 0.248119i \(-0.920188\pi\)
0.968730 0.248119i \(-0.0798124\pi\)
\(570\) 242.036 + 2.07381i 0.424624 + 0.00363826i
\(571\) 234.186 0.410133 0.205067 0.978748i \(-0.434259\pi\)
0.205067 + 0.978748i \(0.434259\pi\)
\(572\) 58.2139 + 58.2139i 0.101773 + 0.101773i
\(573\) −98.9132 + 98.9132i −0.172623 + 0.172623i
\(574\) 81.7402i 0.142405i
\(575\) 86.2194 83.3140i 0.149947 0.144894i
\(576\) −24.0000 −0.0416667
\(577\) 501.679 + 501.679i 0.869461 + 0.869461i 0.992413 0.122952i \(-0.0392361\pi\)
−0.122952 + 0.992413i \(0.539236\pi\)
\(578\) −156.995 + 156.995i −0.271618 + 0.271618i
\(579\) 421.244i 0.727537i
\(580\) 4.61631 538.773i 0.00795916 0.928919i
\(581\) −94.2513 −0.162223
\(582\) −182.966 182.966i −0.314375 0.314375i
\(583\) 56.9090 56.9090i 0.0976140 0.0976140i
\(584\) 301.568i 0.516383i
\(585\) −157.672 + 154.993i −0.269525 + 0.264945i
\(586\) −132.007 −0.225267
\(587\) −729.488 729.488i −1.24274 1.24274i −0.958860 0.283880i \(-0.908378\pi\)
−0.283880 0.958860i \(-0.591622\pi\)
\(588\) −118.264 + 118.264i −0.201129 + 0.201129i
\(589\) 479.797i 0.814597i
\(590\) 563.388 + 573.126i 0.954895 + 0.971400i
\(591\) 209.786 0.354968
\(592\) −85.5733 85.5733i −0.144550 0.144550i
\(593\) 223.415 223.415i 0.376754 0.376754i −0.493176 0.869930i \(-0.664164\pi\)
0.869930 + 0.493176i \(0.164164\pi\)
\(594\) 20.5220i 0.0345488i
\(595\) 48.7089 + 0.417347i 0.0818636 + 0.000701424i
\(596\) 151.904 0.254872
\(597\) −378.614 378.614i −0.634194 0.634194i
\(598\) 70.6892 70.6892i 0.118209 0.118209i
\(599\) 267.169i 0.446024i 0.974816 + 0.223012i \(0.0715890\pi\)
−0.974816 + 0.223012i \(0.928411\pi\)
\(600\) 2.09862 122.457i 0.00349769 0.204094i
\(601\) −123.350 −0.205240 −0.102620 0.994721i \(-0.532723\pi\)
−0.102620 + 0.994721i \(0.532723\pi\)
\(602\) 19.2338 + 19.2338i 0.0319498 + 0.0319498i
\(603\) −120.359 + 120.359i −0.199601 + 0.199601i
\(604\) 72.8964i 0.120689i
\(605\) −4.84946 + 565.984i −0.00801563 + 0.935510i
\(606\) −124.675 −0.205734
\(607\) 328.996 + 328.996i 0.542003 + 0.542003i 0.924116 0.382113i \(-0.124803\pi\)
−0.382113 + 0.924116i \(0.624803\pi\)
\(608\) −79.0514 + 79.0514i −0.130019 + 0.130019i
\(609\) 79.1301i 0.129934i
\(610\) 354.606 348.581i 0.581321 0.571444i
\(611\) −208.905 −0.341907
\(612\) 48.7451 + 48.7451i 0.0796488 + 0.0796488i
\(613\) −218.431 + 218.431i −0.356331 + 0.356331i −0.862459 0.506128i \(-0.831076\pi\)
0.506128 + 0.862459i \(0.331076\pi\)
\(614\) 365.208i 0.594801i
\(615\) 413.832 + 420.985i 0.672897 + 0.684528i
\(616\) 6.69772 0.0108729
\(617\) −746.090 746.090i −1.20922 1.20922i −0.971279 0.237943i \(-0.923527\pi\)
−0.237943 0.971279i \(-0.576473\pi\)
\(618\) −38.8886 + 38.8886i −0.0629266 + 0.0629266i
\(619\) 545.374i 0.881056i 0.897739 + 0.440528i \(0.145209\pi\)
−0.897739 + 0.440528i \(0.854791\pi\)
\(620\) −242.768 2.08009i −0.391562 0.00335498i
\(621\) −24.9199 −0.0401286
\(622\) 412.663 + 412.663i 0.663446 + 0.663446i
\(623\) 40.7548 40.7548i 0.0654171 0.0654171i
\(624\) 102.120i 0.163653i
\(625\) 624.633 + 21.4158i 0.999413 + 0.0342652i
\(626\) 834.921 1.33374
\(627\) −67.5955 67.5955i −0.107808 0.107808i
\(628\) −344.177 + 344.177i −0.548053 + 0.548053i
\(629\) 347.607i 0.552634i
\(630\) −0.154113 + 17.9866i −0.000244624 + 0.0285502i
\(631\) −794.740 −1.25949 −0.629746 0.776801i \(-0.716841\pi\)
−0.629746 + 0.776801i \(0.716841\pi\)
\(632\) −168.247 168.247i −0.266214 0.266214i
\(633\) −203.361 + 203.361i −0.321266 + 0.321266i
\(634\) 581.846i 0.917738i
\(635\) 263.213 258.741i 0.414509 0.407466i
\(636\) −99.8306 −0.156966
\(637\) −503.211 503.211i −0.789971 0.789971i
\(638\) −150.468 + 150.468i −0.235843 + 0.235843i
\(639\) 353.336i 0.552952i
\(640\) 39.6558 + 40.3412i 0.0619622 + 0.0630332i
\(641\) 1123.20 1.75226 0.876128 0.482079i \(-0.160118\pi\)
0.876128 + 0.482079i \(0.160118\pi\)
\(642\) −82.5931 82.5931i −0.128650 0.128650i
\(643\) −274.942 + 274.942i −0.427593 + 0.427593i −0.887808 0.460215i \(-0.847772\pi\)
0.460215 + 0.887808i \(0.347772\pi\)
\(644\) 8.13305i 0.0126290i
\(645\) −196.436 1.68310i −0.304552 0.00260946i
\(646\) 321.114 0.497080
\(647\) 73.7474 + 73.7474i 0.113984 + 0.113984i 0.761798 0.647815i \(-0.224317\pi\)
−0.647815 + 0.761798i \(0.724317\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 317.405i 0.489067i
\(650\) 521.051 + 8.92959i 0.801617 + 0.0137378i
\(651\) 35.6556 0.0547706
\(652\) −163.618 163.618i −0.250947 0.250947i
\(653\) 606.822 606.822i 0.929284 0.929284i −0.0683758 0.997660i \(-0.521782\pi\)
0.997660 + 0.0683758i \(0.0217817\pi\)
\(654\) 333.883i 0.510525i
\(655\) −7.91073 + 923.266i −0.0120774 + 1.40957i
\(656\) −272.660 −0.415640
\(657\) −226.176 226.176i −0.344255 0.344255i
\(658\) −12.0176 + 12.0176i −0.0182639 + 0.0182639i
\(659\) 377.512i 0.572856i 0.958102 + 0.286428i \(0.0924678\pi\)
−0.958102 + 0.286428i \(0.907532\pi\)
\(660\) −34.4951 + 33.9090i −0.0522653 + 0.0513773i
\(661\) 1170.11 1.77020 0.885102 0.465396i \(-0.154088\pi\)
0.885102 + 0.465396i \(0.154088\pi\)
\(662\) −52.5667 52.5667i −0.0794058 0.0794058i
\(663\) −207.410 + 207.410i −0.312835 + 0.312835i
\(664\) 314.393i 0.473484i
\(665\) 58.7369 + 59.7521i 0.0883262 + 0.0898528i
\(666\) −128.360 −0.192733
\(667\) 182.713 + 182.713i 0.273933 + 0.273933i
\(668\) −95.5585 + 95.5585i −0.143052 + 0.143052i
\(669\) 82.2275i 0.122911i
\(670\) 401.183 + 3.43742i 0.598781 + 0.00513047i
\(671\) −196.385 −0.292676
\(672\) −5.87462 5.87462i −0.00874200 0.00874200i
\(673\) −245.453 + 245.453i −0.364715 + 0.364715i −0.865545 0.500831i \(-0.833028\pi\)
0.500831 + 0.865545i \(0.333028\pi\)
\(674\) 105.844i 0.157039i
\(675\) −90.2684 93.4163i −0.133731 0.138395i
\(676\) 96.5182 0.142778
\(677\) −121.820 121.820i −0.179940 0.179940i 0.611389 0.791330i \(-0.290611\pi\)
−0.791330 + 0.611389i \(0.790611\pi\)
\(678\) 162.988 162.988i 0.240395 0.240395i
\(679\) 89.5714i 0.131917i
\(680\) 1.39214 162.478i 0.00204726 0.238938i
\(681\) −493.828 −0.725151
\(682\) 67.8002 + 67.8002i 0.0994137 + 0.0994137i
\(683\) 293.160 293.160i 0.429224 0.429224i −0.459140 0.888364i \(-0.651842\pi\)
0.888364 + 0.459140i \(0.151842\pi\)
\(684\) 118.577i 0.173358i
\(685\) 637.402 626.572i 0.930513 0.914703i
\(686\) −116.655 −0.170051
\(687\) −111.644 111.644i −0.162510 0.162510i
\(688\) 64.1580 64.1580i 0.0932529 0.0932529i
\(689\) 424.778i 0.616514i
\(690\) 41.1757 + 41.8874i 0.0596750 + 0.0607064i
\(691\) 711.388 1.02950 0.514752 0.857339i \(-0.327884\pi\)
0.514752 + 0.857339i \(0.327884\pi\)
\(692\) 231.048 + 231.048i 0.333885 + 0.333885i
\(693\) 5.02329 5.02329i 0.00724862 0.00724862i
\(694\) 237.239i 0.341843i
\(695\) −1088.81 9.32912i −1.56663 0.0134232i
\(696\) 263.953 0.379243
\(697\) 553.785 + 553.785i 0.794526 + 0.794526i
\(698\) 398.115 398.115i 0.570366 0.570366i
\(699\) 458.009i 0.655235i
\(700\) 30.4881 29.4607i 0.0435544 0.0420867i
\(701\) −78.4101 −0.111855 −0.0559273 0.998435i \(-0.517812\pi\)
−0.0559273 + 0.998435i \(0.517812\pi\)
\(702\) −76.5898 76.5898i −0.109102 0.109102i
\(703\) −422.793 + 422.793i −0.601413 + 0.601413i
\(704\) 22.3415i 0.0317351i
\(705\) 1.05163 122.737i 0.00149168 0.174095i
\(706\) −343.448 −0.486470
\(707\) −30.5173 30.5173i −0.0431645 0.0431645i
\(708\) −278.398 + 278.398i −0.393218 + 0.393218i
\(709\) 398.925i 0.562659i 0.959611 + 0.281330i \(0.0907754\pi\)
−0.959611 + 0.281330i \(0.909225\pi\)
\(710\) −593.917 + 583.826i −0.836504 + 0.822291i
\(711\) −252.370 −0.354951
\(712\) −135.945 135.945i −0.190935 0.190935i
\(713\) 82.3298 82.3298i 0.115470 0.115470i
\(714\) 23.8632i 0.0334219i
\(715\) −144.282 146.776i −0.201794 0.205282i
\(716\) 111.165 0.155259
\(717\) −210.340 210.340i −0.293361 0.293361i
\(718\) 544.606 544.606i 0.758504 0.758504i
\(719\) 774.146i 1.07670i 0.842722 + 0.538349i \(0.180952\pi\)
−0.842722 + 0.538349i \(0.819048\pi\)
\(720\) 59.9978 + 0.514073i 0.0833303 + 0.000713990i
\(721\) −19.0380 −0.0264050
\(722\) 29.5704 + 29.5704i 0.0409563 + 0.0409563i
\(723\) 146.557 146.557i 0.202706 0.202706i
\(724\) 50.8178i 0.0701903i
\(725\) −23.0807 + 1346.78i −0.0318355 + 1.85763i
\(726\) −277.284 −0.381934
\(727\) 832.259 + 832.259i 1.14479 + 1.14479i 0.987563 + 0.157223i \(0.0502541\pi\)
0.157223 + 0.987563i \(0.449746\pi\)
\(728\) 24.9965 24.9965i 0.0343358 0.0343358i
\(729\) 27.0000i 0.0370370i
\(730\) −6.45949 + 753.891i −0.00884861 + 1.03273i
\(731\) −260.616 −0.356519
\(732\) 172.251 + 172.251i 0.235316 + 0.235316i
\(733\) −56.0242 + 56.0242i −0.0764313 + 0.0764313i −0.744289 0.667858i \(-0.767211\pi\)
0.667858 + 0.744289i \(0.267211\pi\)
\(734\) 197.648i 0.269276i
\(735\) 298.182 293.116i 0.405690 0.398797i
\(736\) −27.1293 −0.0368605
\(737\) −112.042 112.042i −0.152025 0.152025i
\(738\) −204.495 + 204.495i −0.277094 + 0.277094i
\(739\) 717.045i 0.970291i 0.874433 + 0.485145i \(0.161233\pi\)
−0.874433 + 0.485145i \(0.838767\pi\)
\(740\) 212.093 + 215.758i 0.286612 + 0.291565i
\(741\) −504.544 −0.680897
\(742\) −24.4361 24.4361i −0.0329328 0.0329328i
\(743\) 305.067 305.067i 0.410588 0.410588i −0.471355 0.881943i \(-0.656235\pi\)
0.881943 + 0.471355i \(0.156235\pi\)
\(744\) 118.936i 0.159860i
\(745\) −379.745 3.25373i −0.509725 0.00436742i
\(746\) 814.514 1.09184
\(747\) 235.795 + 235.795i 0.315656 + 0.315656i
\(748\) −45.3766 + 45.3766i −0.0606639 + 0.0606639i
\(749\) 40.4336i 0.0539835i
\(750\) −7.86933 + 306.085i −0.0104924 + 0.408113i
\(751\) 1169.74 1.55757 0.778786 0.627290i \(-0.215836\pi\)
0.778786 + 0.627290i \(0.215836\pi\)
\(752\) 40.0871 + 40.0871i 0.0533073 + 0.0533073i
\(753\) −433.545 + 433.545i −0.575757 + 0.575757i
\(754\) 1123.12i 1.48955i
\(755\) 1.56142 182.234i 0.00206811 0.241370i
\(756\) −8.81194 −0.0116560
\(757\) −405.514 405.514i −0.535685 0.535685i 0.386573 0.922259i \(-0.373659\pi\)
−0.922259 + 0.386573i \(0.873659\pi\)
\(758\) 237.240 237.240i 0.312981 0.312981i
\(759\) 23.1978i 0.0305637i
\(760\) 199.315 195.928i 0.262256 0.257800i
\(761\) −327.256 −0.430034 −0.215017 0.976610i \(-0.568981\pi\)
−0.215017 + 0.976610i \(0.568981\pi\)
\(762\) 127.857 + 127.857i 0.167791 + 0.167791i
\(763\) 81.7266 81.7266i 0.107112 0.107112i
\(764\) 161.525i 0.211420i
\(765\) −120.814 122.902i −0.157927 0.160657i
\(766\) 409.689 0.534842
\(767\) −1184.58 1184.58i −1.54443 1.54443i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 75.4942i 0.0981719i −0.998795 0.0490860i \(-0.984369\pi\)
0.998795 0.0490860i \(-0.0156308\pi\)
\(770\) −16.7437 0.143463i −0.0217450 0.000186316i
\(771\) −298.149 −0.386704
\(772\) −343.944 343.944i −0.445523 0.445523i
\(773\) 734.361 734.361i 0.950015 0.950015i −0.0487940 0.998809i \(-0.515538\pi\)
0.998809 + 0.0487940i \(0.0155378\pi\)
\(774\) 96.2370i 0.124337i
\(775\) 606.854 + 10.4001i 0.783038 + 0.0134194i
\(776\) −298.782 −0.385029
\(777\) −31.4194 31.4194i −0.0404369 0.0404369i
\(778\) −398.431 + 398.431i −0.512123 + 0.512123i