Properties

Label 43.6.c.a.6.8
Level $43$
Weight $6$
Character 43.6
Analytic conductor $6.897$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.8
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.8

$q$-expansion

\(f(q)\) \(=\) \(q-2.35784 q^{2} +(-4.70904 + 8.15629i) q^{3} -26.4406 q^{4} +(15.5528 - 26.9382i) q^{5} +(11.1032 - 19.2313i) q^{6} +(-36.1175 - 62.5573i) q^{7} +137.794 q^{8} +(77.1499 + 133.628i) q^{9} +O(q^{10})\) \(q-2.35784 q^{2} +(-4.70904 + 8.15629i) q^{3} -26.4406 q^{4} +(15.5528 - 26.9382i) q^{5} +(11.1032 - 19.2313i) q^{6} +(-36.1175 - 62.5573i) q^{7} +137.794 q^{8} +(77.1499 + 133.628i) q^{9} +(-36.6710 + 63.5160i) q^{10} +785.739 q^{11} +(124.510 - 215.657i) q^{12} +(-374.054 - 647.881i) q^{13} +(85.1594 + 147.500i) q^{14} +(146.477 + 253.706i) q^{15} +521.202 q^{16} +(198.545 + 343.889i) q^{17} +(-181.907 - 315.073i) q^{18} +(1247.23 - 2160.26i) q^{19} +(-411.224 + 712.261i) q^{20} +680.315 q^{21} -1852.65 q^{22} +(628.566 - 1088.71i) q^{23} +(-648.876 + 1123.89i) q^{24} +(1078.72 + 1868.40i) q^{25} +(881.961 + 1527.60i) q^{26} -3741.80 q^{27} +(954.967 + 1654.05i) q^{28} +(-2011.40 - 3483.85i) q^{29} +(-345.370 - 598.199i) q^{30} +(-3397.41 + 5884.48i) q^{31} -5638.31 q^{32} +(-3700.07 + 6408.72i) q^{33} +(-468.137 - 810.838i) q^{34} -2246.91 q^{35} +(-2039.89 - 3533.19i) q^{36} +(5808.25 - 10060.2i) q^{37} +(-2940.77 + 5093.56i) q^{38} +7045.74 q^{39} +(2143.07 - 3711.91i) q^{40} +18171.5 q^{41} -1604.08 q^{42} +(-11480.7 + 3898.98i) q^{43} -20775.4 q^{44} +4799.58 q^{45} +(-1482.06 + 2567.01i) q^{46} +17311.6 q^{47} +(-2454.36 + 4251.08i) q^{48} +(5794.55 - 10036.5i) q^{49} +(-2543.46 - 4405.40i) q^{50} -3739.82 q^{51} +(9890.21 + 17130.3i) q^{52} +(10053.7 - 17413.5i) q^{53} +8822.58 q^{54} +(12220.4 - 21166.4i) q^{55} +(-4976.76 - 8620.01i) q^{56} +(11746.5 + 20345.5i) q^{57} +(4742.57 + 8214.37i) q^{58} -27080.7 q^{59} +(-3872.94 - 6708.13i) q^{60} +(23684.1 + 41022.1i) q^{61} +(8010.56 - 13874.7i) q^{62} +(5572.92 - 9652.58i) q^{63} -3384.21 q^{64} -23270.3 q^{65} +(8724.20 - 15110.8i) q^{66} +(18579.1 - 32179.9i) q^{67} +(-5249.64 - 9092.63i) q^{68} +(5919.89 + 10253.5i) q^{69} +5297.85 q^{70} +(-25191.9 - 43633.6i) q^{71} +(10630.8 + 18413.0i) q^{72} +(17654.3 + 30578.2i) q^{73} +(-13695.0 + 23720.4i) q^{74} -20319.0 q^{75} +(-32977.4 + 57118.6i) q^{76} +(-28378.9 - 49153.7i) q^{77} -16612.8 q^{78} +(4905.21 + 8496.08i) q^{79} +(8106.13 - 14040.2i) q^{80} +(-1127.14 + 1952.26i) q^{81} -42845.5 q^{82} +(-24391.4 + 42247.2i) q^{83} -17987.9 q^{84} +12351.7 q^{85} +(27069.7 - 9193.18i) q^{86} +37887.0 q^{87} +108270. q^{88} +(-36792.6 + 63726.6i) q^{89} -11316.7 q^{90} +(-27019.8 + 46799.6i) q^{91} +(-16619.7 + 28786.1i) q^{92} +(-31997.1 - 55420.5i) q^{93} -40818.0 q^{94} +(-38795.7 - 67196.1i) q^{95} +(26551.0 - 45987.7i) q^{96} -14665.7 q^{97} +(-13662.7 + 23664.4i) q^{98} +(60619.7 + 104996. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} + O(q^{10}) \) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} - 317q^{10} + 1326q^{11} - 648q^{12} + 1006q^{13} - 1272q^{14} + 683q^{15} + 3574q^{16} + 200q^{17} + 1861q^{18} + 3361q^{19} + 3825q^{20} - 1320q^{21} - 8768q^{22} + 560q^{23} - 7382q^{24} - 3232q^{25} - 3201q^{26} - 122q^{27} + 13934q^{28} + 8887q^{29} - 19449q^{30} - 6749q^{31} - 19086q^{32} + 7106q^{33} + 8423q^{34} + 31118q^{35} - 14112q^{36} - 4514q^{37} + 7072q^{38} - 5404q^{39} - 18519q^{40} - 28996q^{41} + 58118q^{42} - 14998q^{43} + 71050q^{44} - 92096q^{45} + 20052q^{46} - 10742q^{47} + 32927q^{48} + 7472q^{49} + 20362q^{50} + 20250q^{51} + 59532q^{52} - 50572q^{53} - 230084q^{54} + 38544q^{55} - 40355q^{56} - 18087q^{57} - 33436q^{58} + 112654q^{59} + 134093q^{60} - 20120q^{61} - 31491q^{62} + 188227q^{63} + 125164q^{64} - 36578q^{65} + 8803q^{66} - 73824q^{67} - 128456q^{68} + 8005q^{69} - 141610q^{70} + 142842q^{71} + 98466q^{72} - 91624q^{73} - 99720q^{74} + 298358q^{75} + 258288q^{76} + 68051q^{77} - 201116q^{78} + 99734q^{79} - 31261q^{80} - 28441q^{81} - 147772q^{82} - 47340q^{83} - 624232q^{84} - 71734q^{85} - 115526q^{86} - 215924q^{87} - 720684q^{88} + 60402q^{89} + 676108q^{90} + 164172q^{91} + 78997q^{92} - 40793q^{93} - 341874q^{94} + 123541q^{95} - 442140q^{96} + 318476q^{97} + 217473q^{98} - 134770q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35784 −0.416812 −0.208406 0.978042i \(-0.566828\pi\)
−0.208406 + 0.978042i \(0.566828\pi\)
\(3\) −4.70904 + 8.15629i −0.302085 + 0.523227i −0.976608 0.215027i \(-0.931016\pi\)
0.674523 + 0.738254i \(0.264349\pi\)
\(4\) −26.4406 −0.826268
\(5\) 15.5528 26.9382i 0.278216 0.481885i −0.692725 0.721202i \(-0.743590\pi\)
0.970942 + 0.239317i \(0.0769235\pi\)
\(6\) 11.1032 19.2313i 0.125913 0.218087i
\(7\) −36.1175 62.5573i −0.278594 0.482540i 0.692441 0.721474i \(-0.256535\pi\)
−0.971036 + 0.238935i \(0.923202\pi\)
\(8\) 137.794 0.761210
\(9\) 77.1499 + 133.628i 0.317489 + 0.549908i
\(10\) −36.6710 + 63.5160i −0.115964 + 0.200855i
\(11\) 785.739 1.95793 0.978963 0.204037i \(-0.0654063\pi\)
0.978963 + 0.204037i \(0.0654063\pi\)
\(12\) 124.510 215.657i 0.249603 0.432325i
\(13\) −374.054 647.881i −0.613870 1.06325i −0.990582 0.136923i \(-0.956279\pi\)
0.376712 0.926330i \(-0.377055\pi\)
\(14\) 85.1594 + 147.500i 0.116121 + 0.201128i
\(15\) 146.477 + 253.706i 0.168090 + 0.291140i
\(16\) 521.202 0.508986
\(17\) 198.545 + 343.889i 0.166623 + 0.288600i 0.937231 0.348710i \(-0.113380\pi\)
−0.770607 + 0.637310i \(0.780047\pi\)
\(18\) −181.907 315.073i −0.132333 0.229208i
\(19\) 1247.23 2160.26i 0.792614 1.37285i −0.131729 0.991286i \(-0.542053\pi\)
0.924343 0.381562i \(-0.124614\pi\)
\(20\) −411.224 + 712.261i −0.229881 + 0.398166i
\(21\) 680.315 0.336637
\(22\) −1852.65 −0.816087
\(23\) 628.566 1088.71i 0.247760 0.429133i −0.715144 0.698977i \(-0.753639\pi\)
0.962904 + 0.269844i \(0.0869722\pi\)
\(24\) −648.876 + 1123.89i −0.229950 + 0.398285i
\(25\) 1078.72 + 1868.40i 0.345191 + 0.597889i
\(26\) 881.961 + 1527.60i 0.255868 + 0.443177i
\(27\) −3741.80 −0.987805
\(28\) 954.967 + 1654.05i 0.230194 + 0.398707i
\(29\) −2011.40 3483.85i −0.444123 0.769244i 0.553867 0.832605i \(-0.313151\pi\)
−0.997991 + 0.0633608i \(0.979818\pi\)
\(30\) −345.370 598.199i −0.0700619 0.121351i
\(31\) −3397.41 + 5884.48i −0.634956 + 1.09978i 0.351569 + 0.936162i \(0.385648\pi\)
−0.986525 + 0.163614i \(0.947685\pi\)
\(32\) −5638.31 −0.973362
\(33\) −3700.07 + 6408.72i −0.591460 + 1.02444i
\(34\) −468.137 810.838i −0.0694506 0.120292i
\(35\) −2246.91 −0.310038
\(36\) −2039.89 3533.19i −0.262331 0.454371i
\(37\) 5808.25 10060.2i 0.697495 1.20810i −0.271837 0.962343i \(-0.587631\pi\)
0.969332 0.245754i \(-0.0790356\pi\)
\(38\) −2940.77 + 5093.56i −0.330371 + 0.572219i
\(39\) 7045.74 0.741763
\(40\) 2143.07 3711.91i 0.211781 0.366815i
\(41\) 18171.5 1.68823 0.844113 0.536166i \(-0.180128\pi\)
0.844113 + 0.536166i \(0.180128\pi\)
\(42\) −1604.08 −0.140314
\(43\) −11480.7 + 3898.98i −0.946885 + 0.321573i
\(44\) −20775.4 −1.61777
\(45\) 4799.58 0.353323
\(46\) −1482.06 + 2567.01i −0.103269 + 0.178868i
\(47\) 17311.6 1.14312 0.571560 0.820560i \(-0.306338\pi\)
0.571560 + 0.820560i \(0.306338\pi\)
\(48\) −2454.36 + 4251.08i −0.153757 + 0.266315i
\(49\) 5794.55 10036.5i 0.344770 0.597160i
\(50\) −2543.46 4405.40i −0.143880 0.249207i
\(51\) −3739.82 −0.201338
\(52\) 9890.21 + 17130.3i 0.507221 + 0.878532i
\(53\) 10053.7 17413.5i 0.491626 0.851521i −0.508328 0.861164i \(-0.669736\pi\)
0.999954 + 0.00964287i \(0.00306947\pi\)
\(54\) 8822.58 0.411729
\(55\) 12220.4 21166.4i 0.544727 0.943495i
\(56\) −4976.76 8620.01i −0.212069 0.367314i
\(57\) 11746.5 + 20345.5i 0.478874 + 0.829433i
\(58\) 4742.57 + 8214.37i 0.185116 + 0.320630i
\(59\) −27080.7 −1.01281 −0.506407 0.862294i \(-0.669027\pi\)
−0.506407 + 0.862294i \(0.669027\pi\)
\(60\) −3872.94 6708.13i −0.138887 0.240560i
\(61\) 23684.1 + 41022.1i 0.814953 + 1.41154i 0.909362 + 0.416006i \(0.136571\pi\)
−0.0944089 + 0.995534i \(0.530096\pi\)
\(62\) 8010.56 13874.7i 0.264657 0.458400i
\(63\) 5572.92 9652.58i 0.176901 0.306402i
\(64\) −3384.21 −0.103278
\(65\) −23270.3 −0.683154
\(66\) 8724.20 15110.8i 0.246528 0.426998i
\(67\) 18579.1 32179.9i 0.505635 0.875785i −0.494344 0.869266i \(-0.664592\pi\)
0.999979 0.00651894i \(-0.00207506\pi\)
\(68\) −5249.64 9092.63i −0.137676 0.238461i
\(69\) 5919.89 + 10253.5i 0.149689 + 0.259269i
\(70\) 5297.85 0.129227
\(71\) −25191.9 43633.6i −0.593082 1.02725i −0.993814 0.111053i \(-0.964578\pi\)
0.400732 0.916195i \(-0.368756\pi\)
\(72\) 10630.8 + 18413.0i 0.241676 + 0.418595i
\(73\) 17654.3 + 30578.2i 0.387743 + 0.671590i 0.992146 0.125089i \(-0.0399216\pi\)
−0.604403 + 0.796679i \(0.706588\pi\)
\(74\) −13695.0 + 23720.4i −0.290724 + 0.503549i
\(75\) −20319.0 −0.417109
\(76\) −32977.4 + 57118.6i −0.654911 + 1.13434i
\(77\) −28378.9 49153.7i −0.545467 0.944777i
\(78\) −16612.8 −0.309176
\(79\) 4905.21 + 8496.08i 0.0884281 + 0.153162i 0.906847 0.421460i \(-0.138482\pi\)
−0.818419 + 0.574622i \(0.805149\pi\)
\(80\) 8106.13 14040.2i 0.141608 0.245273i
\(81\) −1127.14 + 1952.26i −0.0190882 + 0.0330618i
\(82\) −42845.5 −0.703672
\(83\) −24391.4 + 42247.2i −0.388635 + 0.673136i −0.992266 0.124128i \(-0.960387\pi\)
0.603631 + 0.797264i \(0.293720\pi\)
\(84\) −17987.9 −0.278152
\(85\) 12351.7 0.185429
\(86\) 27069.7 9193.18i 0.394673 0.134035i
\(87\) 37887.0 0.536652
\(88\) 108270. 1.49039
\(89\) −36792.6 + 63726.6i −0.492363 + 0.852797i −0.999961 0.00879659i \(-0.997200\pi\)
0.507599 + 0.861594i \(0.330533\pi\)
\(90\) −11316.7 −0.147269
\(91\) −27019.8 + 46799.6i −0.342041 + 0.592433i
\(92\) −16619.7 + 28786.1i −0.204716 + 0.354579i
\(93\) −31997.1 55420.5i −0.383621 0.664451i
\(94\) −40818.0 −0.476466
\(95\) −38795.7 67196.1i −0.441036 0.763897i
\(96\) 26551.0 45987.7i 0.294038 0.509289i
\(97\) −14665.7 −0.158261 −0.0791305 0.996864i \(-0.525214\pi\)
−0.0791305 + 0.996864i \(0.525214\pi\)
\(98\) −13662.7 + 23664.4i −0.143704 + 0.248903i
\(99\) 60619.7 + 104996.i 0.621621 + 1.07668i
\(100\) −28522.1 49401.7i −0.285221 0.494017i
\(101\) −24764.9 42894.1i −0.241565 0.418402i 0.719596 0.694393i \(-0.244327\pi\)
−0.961160 + 0.275991i \(0.910994\pi\)
\(102\) 8817.91 0.0839199
\(103\) 19879.4 + 34432.1i 0.184633 + 0.319794i 0.943453 0.331507i \(-0.107557\pi\)
−0.758820 + 0.651301i \(0.774224\pi\)
\(104\) −51542.3 89273.9i −0.467284 0.809359i
\(105\) 10580.8 18326.4i 0.0936578 0.162220i
\(106\) −23705.0 + 41058.2i −0.204915 + 0.354924i
\(107\) −118895. −1.00394 −0.501968 0.864886i \(-0.667390\pi\)
−0.501968 + 0.864886i \(0.667390\pi\)
\(108\) 98935.3 0.816192
\(109\) 26664.4 46184.1i 0.214964 0.372328i −0.738298 0.674475i \(-0.764370\pi\)
0.953261 + 0.302147i \(0.0977033\pi\)
\(110\) −28813.8 + 49907.0i −0.227049 + 0.393260i
\(111\) 54702.6 + 94747.7i 0.421406 + 0.729896i
\(112\) −18824.5 32605.0i −0.141801 0.245606i
\(113\) −15529.6 −0.114410 −0.0572052 0.998362i \(-0.518219\pi\)
−0.0572052 + 0.998362i \(0.518219\pi\)
\(114\) −27696.4 47971.5i −0.199600 0.345718i
\(115\) −19551.9 33864.9i −0.137862 0.238784i
\(116\) 53182.6 + 92114.9i 0.366965 + 0.635602i
\(117\) 57716.5 99967.9i 0.389794 0.675143i
\(118\) 63852.1 0.422153
\(119\) 14341.9 24840.8i 0.0928407 0.160805i
\(120\) 20183.6 + 34959.1i 0.127952 + 0.221619i
\(121\) 456334. 2.83348
\(122\) −55843.4 96723.7i −0.339682 0.588347i
\(123\) −85570.2 + 148212.i −0.509987 + 0.883324i
\(124\) 89829.4 155589.i 0.524644 0.908709i
\(125\) 164313. 0.940584
\(126\) −13140.1 + 22759.3i −0.0737346 + 0.127712i
\(127\) −155519. −0.855604 −0.427802 0.903872i \(-0.640712\pi\)
−0.427802 + 0.903872i \(0.640712\pi\)
\(128\) 188405. 1.01641
\(129\) 22261.9 112000.i 0.117784 0.592578i
\(130\) 54867.7 0.284747
\(131\) 87048.1 0.443181 0.221591 0.975140i \(-0.428875\pi\)
0.221591 + 0.975140i \(0.428875\pi\)
\(132\) 97832.1 169450.i 0.488705 0.846461i
\(133\) −180187. −0.883271
\(134\) −43806.6 + 75875.2i −0.210755 + 0.365038i
\(135\) −58195.3 + 100797.i −0.274823 + 0.476008i
\(136\) 27358.2 + 47385.8i 0.126835 + 0.219685i
\(137\) −157426. −0.716596 −0.358298 0.933607i \(-0.616643\pi\)
−0.358298 + 0.933607i \(0.616643\pi\)
\(138\) −13958.2 24176.3i −0.0623923 0.108067i
\(139\) −59373.3 + 102838.i −0.260648 + 0.451455i −0.966414 0.256989i \(-0.917269\pi\)
0.705766 + 0.708445i \(0.250603\pi\)
\(140\) 59409.5 0.256174
\(141\) −81520.9 + 141198.i −0.345320 + 0.598111i
\(142\) 59398.5 + 102881.i 0.247204 + 0.428169i
\(143\) −293909. 509065.i −1.20191 2.08177i
\(144\) 40210.7 + 69647.0i 0.161598 + 0.279896i
\(145\) −125131. −0.494249
\(146\) −41626.1 72098.5i −0.161616 0.279927i
\(147\) 54573.6 + 94524.2i 0.208300 + 0.360786i
\(148\) −153574. + 265997.i −0.576318 + 0.998212i
\(149\) −50677.4 + 87775.9i −0.187003 + 0.323899i −0.944250 0.329230i \(-0.893211\pi\)
0.757247 + 0.653129i \(0.226544\pi\)
\(150\) 47909.0 0.173856
\(151\) −273662. −0.976724 −0.488362 0.872641i \(-0.662405\pi\)
−0.488362 + 0.872641i \(0.662405\pi\)
\(152\) 171860. 297671.i 0.603346 1.04503i
\(153\) −30635.4 + 53062.1i −0.105802 + 0.183255i
\(154\) 66913.0 + 115897.i 0.227357 + 0.393794i
\(155\) 105678. + 183040.i 0.353310 + 0.611951i
\(156\) −186293. −0.612895
\(157\) −85576.5 148223.i −0.277080 0.479917i 0.693578 0.720382i \(-0.256033\pi\)
−0.970658 + 0.240465i \(0.922700\pi\)
\(158\) −11565.7 20032.4i −0.0368579 0.0638397i
\(159\) 94686.2 + 164001.i 0.297026 + 0.514463i
\(160\) −87691.3 + 151886.i −0.270805 + 0.469048i
\(161\) −90808.9 −0.276098
\(162\) 2657.62 4603.14i 0.00795620 0.0137805i
\(163\) −195306. 338280.i −0.575767 0.997258i −0.995958 0.0898219i \(-0.971370\pi\)
0.420191 0.907436i \(-0.361963\pi\)
\(164\) −480464. −1.39493
\(165\) 115093. + 199346.i 0.329108 + 0.570031i
\(166\) 57511.2 99612.3i 0.161988 0.280571i
\(167\) −324947. + 562825.i −0.901616 + 1.56164i −0.0762185 + 0.997091i \(0.524285\pi\)
−0.825397 + 0.564553i \(0.809049\pi\)
\(168\) 93743.1 0.256251
\(169\) −94186.5 + 163136.i −0.253672 + 0.439372i
\(170\) −29123.3 −0.0772891
\(171\) 384894. 1.00659
\(172\) 303556. 103091.i 0.782381 0.265705i
\(173\) 113478. 0.288269 0.144135 0.989558i \(-0.453960\pi\)
0.144135 + 0.989558i \(0.453960\pi\)
\(174\) −89331.7 −0.223683
\(175\) 77921.5 134964.i 0.192337 0.333137i
\(176\) 409529. 0.996558
\(177\) 127524. 220878.i 0.305956 0.529931i
\(178\) 86751.1 150257.i 0.205223 0.355456i
\(179\) −55577.1 96262.3i −0.129647 0.224556i 0.793893 0.608058i \(-0.208051\pi\)
−0.923540 + 0.383502i \(0.874718\pi\)
\(180\) −126904. −0.291939
\(181\) 31209.6 + 54056.6i 0.0708095 + 0.122646i 0.899256 0.437422i \(-0.144108\pi\)
−0.828447 + 0.560068i \(0.810775\pi\)
\(182\) 63708.4 110346.i 0.142567 0.246933i
\(183\) −446118. −0.984740
\(184\) 86612.5 150017.i 0.188598 0.326661i
\(185\) −180669. 312928.i −0.388109 0.672225i
\(186\) 75444.1 + 130673.i 0.159898 + 0.276951i
\(187\) 156004. + 270207.i 0.326236 + 0.565058i
\(188\) −457728. −0.944524
\(189\) 135144. + 234077.i 0.275197 + 0.476655i
\(190\) 91474.1 + 158438.i 0.183829 + 0.318401i
\(191\) 80509.0 139446.i 0.159684 0.276581i −0.775071 0.631874i \(-0.782286\pi\)
0.934755 + 0.355294i \(0.115619\pi\)
\(192\) 15936.4 27602.6i 0.0311987 0.0540377i
\(193\) 386516. 0.746919 0.373460 0.927646i \(-0.378171\pi\)
0.373460 + 0.927646i \(0.378171\pi\)
\(194\) 34579.5 0.0659651
\(195\) 109581. 189799.i 0.206371 0.357444i
\(196\) −153211. + 265370.i −0.284873 + 0.493414i
\(197\) −164469. 284868.i −0.301938 0.522972i 0.674637 0.738150i \(-0.264300\pi\)
−0.976575 + 0.215178i \(0.930967\pi\)
\(198\) −142932. 247565.i −0.259099 0.448772i
\(199\) 309184. 0.553457 0.276729 0.960948i \(-0.410750\pi\)
0.276729 + 0.960948i \(0.410750\pi\)
\(200\) 148641. + 257454.i 0.262763 + 0.455119i
\(201\) 174979. + 303073.i 0.305489 + 0.529123i
\(202\) 58391.8 + 101138.i 0.100687 + 0.174395i
\(203\) −145293. + 251656.i −0.247460 + 0.428614i
\(204\) 98882.9 0.166359
\(205\) 282616. 489506.i 0.469692 0.813530i
\(206\) −46872.5 81185.6i −0.0769573 0.133294i
\(207\) 193975. 0.314645
\(208\) −194958. 337677.i −0.312451 0.541182i
\(209\) 979995. 1.69740e6i 1.55188 2.68793i
\(210\) −24947.8 + 43210.9i −0.0390377 + 0.0676153i
\(211\) 146655. 0.226772 0.113386 0.993551i \(-0.463830\pi\)
0.113386 + 0.993551i \(0.463830\pi\)
\(212\) −265825. + 460422.i −0.406215 + 0.703584i
\(213\) 474518. 0.716645
\(214\) 280337. 0.418452
\(215\) −73525.3 + 369909.i −0.108478 + 0.545756i
\(216\) −515597. −0.751927
\(217\) 490823. 0.707580
\(218\) −62870.4 + 108895.i −0.0895994 + 0.155191i
\(219\) −332539. −0.468525
\(220\) −323114. + 559651.i −0.450090 + 0.779579i
\(221\) 148533. 257267.i 0.204570 0.354326i
\(222\) −128980. 223400.i −0.175647 0.304229i
\(223\) −794062. −1.06928 −0.534641 0.845079i \(-0.679553\pi\)
−0.534641 + 0.845079i \(0.679553\pi\)
\(224\) 203642. + 352718.i 0.271173 + 0.469686i
\(225\) −166447. + 288294.i −0.219189 + 0.379647i
\(226\) 36616.5 0.0476876
\(227\) −18433.1 + 31927.0i −0.0237429 + 0.0411239i −0.877653 0.479297i \(-0.840892\pi\)
0.853910 + 0.520421i \(0.174225\pi\)
\(228\) −310584. 537947.i −0.395678 0.685334i
\(229\) 217075. + 375985.i 0.273540 + 0.473786i 0.969766 0.244037i \(-0.0784720\pi\)
−0.696226 + 0.717823i \(0.745139\pi\)
\(230\) 46100.3 + 79848.0i 0.0574624 + 0.0995279i
\(231\) 534549. 0.659110
\(232\) −277158. 480052.i −0.338071 0.585556i
\(233\) 677907. + 1.17417e6i 0.818051 + 1.41691i 0.907116 + 0.420881i \(0.138279\pi\)
−0.0890646 + 0.996026i \(0.528388\pi\)
\(234\) −136086. + 235709.i −0.162471 + 0.281408i
\(235\) 269243. 466342.i 0.318035 0.550852i
\(236\) 716029. 0.836856
\(237\) −92395.4 −0.106851
\(238\) −33815.9 + 58570.8i −0.0386971 + 0.0670253i
\(239\) −460249. + 797175.i −0.521193 + 0.902733i 0.478503 + 0.878086i \(0.341179\pi\)
−0.999696 + 0.0246469i \(0.992154\pi\)
\(240\) 76344.2 + 132232.i 0.0855555 + 0.148186i
\(241\) 524551. + 908549.i 0.581761 + 1.00764i 0.995271 + 0.0971404i \(0.0309696\pi\)
−0.413509 + 0.910500i \(0.635697\pi\)
\(242\) −1.07596e6 −1.18103
\(243\) −465244. 805827.i −0.505435 0.875439i
\(244\) −626221. 1.08465e6i −0.673369 1.16631i
\(245\) −180243. 312189.i −0.191841 0.332279i
\(246\) 201761. 349460.i 0.212569 0.368180i
\(247\) −1.86612e6 −1.94625
\(248\) −468142. + 810845.i −0.483335 + 0.837160i
\(249\) −229720. 397888.i −0.234802 0.406689i
\(250\) −387425. −0.392047
\(251\) 583378. + 1.01044e6i 0.584475 + 1.01234i 0.994941 + 0.100464i \(0.0320328\pi\)
−0.410466 + 0.911876i \(0.634634\pi\)
\(252\) −147351. + 255220.i −0.146168 + 0.253170i
\(253\) 493889. 855440.i 0.485096 0.840211i
\(254\) 366689. 0.356626
\(255\) −58164.5 + 100744.i −0.0560154 + 0.0970216i
\(256\) −335936. −0.320374
\(257\) −234774. −0.221726 −0.110863 0.993836i \(-0.535361\pi\)
−0.110863 + 0.993836i \(0.535361\pi\)
\(258\) −52490.0 + 264079.i −0.0490939 + 0.246993i
\(259\) −839118. −0.777273
\(260\) 615280. 0.564468
\(261\) 310359. 537557.i 0.282009 0.488454i
\(262\) −205246. −0.184723
\(263\) 1.07763e6 1.86652e6i 0.960686 1.66396i 0.239903 0.970797i \(-0.422884\pi\)
0.720783 0.693160i \(-0.243782\pi\)
\(264\) −509847. + 883081.i −0.450225 + 0.779813i
\(265\) −312724. 541655.i −0.273557 0.473814i
\(266\) 424853. 0.368158
\(267\) −346515. 600182.i −0.297471 0.515234i
\(268\) −491241. + 850855.i −0.417790 + 0.723633i
\(269\) −374180. −0.315282 −0.157641 0.987496i \(-0.550389\pi\)
−0.157641 + 0.987496i \(0.550389\pi\)
\(270\) 137216. 237664.i 0.114550 0.198406i
\(271\) 1.00118e6 + 1.73410e6i 0.828112 + 1.43433i 0.899517 + 0.436885i \(0.143918\pi\)
−0.0714049 + 0.997447i \(0.522748\pi\)
\(272\) 103482. + 179236.i 0.0848091 + 0.146894i
\(273\) −254474. 440763.i −0.206651 0.357930i
\(274\) 371185. 0.298686
\(275\) 847594. + 1.46808e6i 0.675859 + 1.17062i
\(276\) −156525. 271110.i −0.123683 0.214226i
\(277\) 66019.1 114348.i 0.0516976 0.0895428i −0.839019 0.544103i \(-0.816870\pi\)
0.890716 + 0.454560i \(0.150203\pi\)
\(278\) 139993. 242475.i 0.108641 0.188172i
\(279\) −1.04844e6 −0.806367
\(280\) −309610. −0.236004
\(281\) −700236. + 1.21285e6i −0.529028 + 0.916304i 0.470399 + 0.882454i \(0.344110\pi\)
−0.999427 + 0.0338498i \(0.989223\pi\)
\(282\) 192214. 332924.i 0.143933 0.249300i
\(283\) 289462. + 501362.i 0.214845 + 0.372122i 0.953225 0.302263i \(-0.0977421\pi\)
−0.738380 + 0.674385i \(0.764409\pi\)
\(284\) 666088. + 1.15370e6i 0.490045 + 0.848782i
\(285\) 730761. 0.532922
\(286\) 692991. + 1.20030e6i 0.500971 + 0.867707i
\(287\) −656308. 1.13676e6i −0.470330 0.814636i
\(288\) −434995. 753434.i −0.309032 0.535259i
\(289\) 631089. 1.09308e6i 0.444473 0.769850i
\(290\) 295040. 0.206009
\(291\) 69061.4 119618.i 0.0478083 0.0828064i
\(292\) −466790. 808504.i −0.320379 0.554913i
\(293\) 357984. 0.243610 0.121805 0.992554i \(-0.461132\pi\)
0.121805 + 0.992554i \(0.461132\pi\)
\(294\) −128676. 222873.i −0.0868219 0.150380i
\(295\) −421180. + 729505.i −0.281781 + 0.488060i
\(296\) 800341. 1.38623e6i 0.530941 0.919616i
\(297\) −2.94008e6 −1.93405
\(298\) 119489. 206962.i 0.0779451 0.135005i
\(299\) −940471. −0.608370
\(300\) 537246. 0.344643
\(301\) 658563. + 577380.i 0.418968 + 0.367321i
\(302\) 645252. 0.407110
\(303\) 466476. 0.291892
\(304\) 650058. 1.12593e6i 0.403430 0.698761i
\(305\) 1.47341e6 0.906932
\(306\) 72233.5 125112.i 0.0440996 0.0763828i
\(307\) 27911.1 48343.5i 0.0169017 0.0292747i −0.857451 0.514566i \(-0.827953\pi\)
0.874353 + 0.485291i \(0.161286\pi\)
\(308\) 750354. + 1.29965e6i 0.450702 + 0.780639i
\(309\) −374451. −0.223100
\(310\) −249173. 431580.i −0.147264 0.255068i
\(311\) 245116. 424553.i 0.143704 0.248903i −0.785184 0.619262i \(-0.787432\pi\)
0.928889 + 0.370359i \(0.120765\pi\)
\(312\) 970859. 0.564638
\(313\) −1.08613e6 + 1.88123e6i −0.626644 + 1.08538i 0.361577 + 0.932342i \(0.382239\pi\)
−0.988221 + 0.153036i \(0.951095\pi\)
\(314\) 201776. + 349486.i 0.115490 + 0.200035i
\(315\) −173349. 300249.i −0.0984337 0.170492i
\(316\) −129697. 224641.i −0.0730653 0.126553i
\(317\) 853939. 0.477286 0.238643 0.971107i \(-0.423297\pi\)
0.238643 + 0.971107i \(0.423297\pi\)
\(318\) −223255. 386689.i −0.123804 0.214434i
\(319\) −1.58043e6 2.73739e6i −0.869561 1.50612i
\(320\) −52633.7 + 91164.3i −0.0287336 + 0.0497680i
\(321\) 559883. 969746.i 0.303274 0.525286i
\(322\) 214113. 0.115081
\(323\) 990522. 0.528272
\(324\) 29802.2 51619.0i 0.0157720 0.0273179i
\(325\) 807002. 1.39777e6i 0.423805 0.734052i
\(326\) 460501. + 797612.i 0.239987 + 0.415669i
\(327\) 251127. + 434965.i 0.129875 + 0.224950i
\(328\) 2.50391e6 1.28509
\(329\) −625251. 1.08297e6i −0.318467 0.551601i
\(330\) −271371. 470028.i −0.137176 0.237596i
\(331\) 896639. + 1.55303e6i 0.449829 + 0.779127i 0.998375 0.0569935i \(-0.0181514\pi\)
−0.548545 + 0.836121i \(0.684818\pi\)
\(332\) 644924. 1.11704e6i 0.321117 0.556191i
\(333\) 1.79243e6 0.885789
\(334\) 766174. 1.32705e6i 0.375804 0.650912i
\(335\) −577912. 1.00097e6i −0.281352 0.487315i
\(336\) 354581. 0.171344
\(337\) 1.47938e6 + 2.56236e6i 0.709584 + 1.22904i 0.965011 + 0.262208i \(0.0844506\pi\)
−0.255427 + 0.966828i \(0.582216\pi\)
\(338\) 222077. 384649.i 0.105733 0.183136i
\(339\) 73129.7 126664.i 0.0345617 0.0598626i
\(340\) −326585. −0.153214
\(341\) −2.66947e6 + 4.62367e6i −1.24320 + 2.15328i
\(342\) −907520. −0.419557
\(343\) −2.05119e6 −0.941393
\(344\) −1.58197e6 + 537255.i −0.720778 + 0.244785i
\(345\) 368282. 0.166584
\(346\) −267564. −0.120154
\(347\) 340583. 589907.i 0.151845 0.263002i −0.780061 0.625703i \(-0.784812\pi\)
0.931906 + 0.362701i \(0.118145\pi\)
\(348\) −1.00176e6 −0.443418
\(349\) 898075. 1.55551e6i 0.394683 0.683612i −0.598377 0.801214i \(-0.704188\pi\)
0.993061 + 0.117603i \(0.0375209\pi\)
\(350\) −183727. + 318224.i −0.0801683 + 0.138855i
\(351\) 1.39964e6 + 2.42424e6i 0.606383 + 1.05029i
\(352\) −4.43024e6 −1.90577
\(353\) 445.726 + 772.021i 0.000190384 + 0.000329756i 0.866121 0.499835i \(-0.166606\pi\)
−0.865930 + 0.500165i \(0.833273\pi\)
\(354\) −300682. + 520796.i −0.127526 + 0.220882i
\(355\) −1.56721e6 −0.660020
\(356\) 972816. 1.68497e6i 0.406823 0.704639i
\(357\) 135073. + 233953.i 0.0560916 + 0.0971534i
\(358\) 131042. + 226972.i 0.0540385 + 0.0935974i
\(359\) −7293.51 12632.7i −0.00298676 0.00517322i 0.864528 0.502584i \(-0.167617\pi\)
−0.867515 + 0.497411i \(0.834284\pi\)
\(360\) 661352. 0.268953
\(361\) −1.87310e6 3.24431e6i −0.756474 1.31025i
\(362\) −73587.3 127457.i −0.0295142 0.0511201i
\(363\) −2.14889e6 + 3.72200e6i −0.855950 + 1.48255i
\(364\) 714419. 1.23741e6i 0.282618 0.489508i
\(365\) 1.09829e6 0.431505
\(366\) 1.05188e6 0.410451
\(367\) 219283. 379809.i 0.0849845 0.147197i −0.820400 0.571790i \(-0.806249\pi\)
0.905385 + 0.424592i \(0.139583\pi\)
\(368\) 327610. 567437.i 0.126107 0.218423i
\(369\) 1.40193e6 + 2.42821e6i 0.535993 + 0.928368i
\(370\) 425989. + 737834.i 0.161768 + 0.280191i
\(371\) −1.45245e6 −0.547857
\(372\) 846020. + 1.46535e6i 0.316974 + 0.549015i
\(373\) −1.84218e6 3.19074e6i −0.685582 1.18746i −0.973254 0.229733i \(-0.926215\pi\)
0.287672 0.957729i \(-0.407119\pi\)
\(374\) −367834. 637106.i −0.135979 0.235523i
\(375\) −773758. + 1.34019e6i −0.284136 + 0.492139i
\(376\) 2.38543e6 0.870155
\(377\) −1.50475e6 + 2.60630e6i −0.545267 + 0.944431i
\(378\) −318649. 551917.i −0.114705 0.198675i
\(379\) −4.33977e6 −1.55192 −0.775959 0.630784i \(-0.782734\pi\)
−0.775959 + 0.630784i \(0.782734\pi\)
\(380\) 1.02578e6 + 1.77670e6i 0.364414 + 0.631184i
\(381\) 732343. 1.26846e6i 0.258465 0.447675i
\(382\) −189828. + 328791.i −0.0665581 + 0.115282i
\(383\) 826932. 0.288053 0.144027 0.989574i \(-0.453995\pi\)
0.144027 + 0.989574i \(0.453995\pi\)
\(384\) −887209. + 1.53669e6i −0.307042 + 0.531812i
\(385\) −1.76548e6 −0.607031
\(386\) −911343. −0.311325
\(387\) −1.40675e6 1.23333e6i −0.477461 0.418603i
\(388\) 387770. 0.130766
\(389\) −2.23266e6 −0.748080 −0.374040 0.927413i \(-0.622028\pi\)
−0.374040 + 0.927413i \(0.622028\pi\)
\(390\) −258374. + 447517.i −0.0860177 + 0.148987i
\(391\) 499194. 0.165131
\(392\) 798453. 1.38296e6i 0.262443 0.454564i
\(393\) −409913. + 709990.i −0.133878 + 0.231884i
\(394\) 387791. + 671674.i 0.125851 + 0.217981i
\(395\) 305159. 0.0984085
\(396\) −1.60282e6 2.77616e6i −0.513625 0.889625i
\(397\) −1.86790e6 + 3.23529e6i −0.594808 + 1.03024i 0.398766 + 0.917053i \(0.369438\pi\)
−0.993574 + 0.113184i \(0.963895\pi\)
\(398\) −729007. −0.230687
\(399\) 848507. 1.46966e6i 0.266823 0.462151i
\(400\) 562233. + 973816.i 0.175698 + 0.304317i
\(401\) −894571. 1.54944e6i −0.277814 0.481188i 0.693027 0.720911i \(-0.256276\pi\)
−0.970841 + 0.239724i \(0.922943\pi\)
\(402\) −412574. 714598.i −0.127332 0.220545i
\(403\) 5.08326e6 1.55912
\(404\) 654798. + 1.13414e6i 0.199597 + 0.345712i
\(405\) 35060.3 + 60726.2i 0.0106213 + 0.0183966i
\(406\) 342579. 593365.i 0.103144 0.178651i
\(407\) 4.56377e6 7.90468e6i 1.36564 2.36537i
\(408\) −515324. −0.153260
\(409\) −531028. −0.156967 −0.0784836 0.996915i \(-0.525008\pi\)
−0.0784836 + 0.996915i \(0.525008\pi\)
\(410\) −666366. + 1.15418e6i −0.195773 + 0.339089i
\(411\) 741324. 1.28401e6i 0.216473 0.374942i
\(412\) −525622. 910405.i −0.152557 0.264236i
\(413\) 978087. + 1.69410e6i 0.282164 + 0.488723i
\(414\) −457364. −0.131148
\(415\) 758708. + 1.31412e6i 0.216249 + 0.374555i
\(416\) 2.10903e6 + 3.65295e6i 0.597517 + 1.03493i
\(417\) −559182. 968532.i −0.157476 0.272756i
\(418\) −2.31067e6 + 4.00221e6i −0.646842 + 1.12036i
\(419\) −4.56915e6 −1.27145 −0.635726 0.771915i \(-0.719299\pi\)
−0.635726 + 0.771915i \(0.719299\pi\)
\(420\) −279762. + 484561.i −0.0773864 + 0.134037i
\(421\) 1.50987e6 + 2.61516e6i 0.415177 + 0.719107i 0.995447 0.0953168i \(-0.0303864\pi\)
−0.580270 + 0.814424i \(0.697053\pi\)
\(422\) −345789. −0.0945214
\(423\) 1.33559e6 + 2.31330e6i 0.362929 + 0.628611i
\(424\) 1.38533e6 2.39947e6i 0.374231 0.648186i
\(425\) −428350. + 741923.i −0.115034 + 0.199245i
\(426\) −1.11884e6 −0.298706
\(427\) 1.71082e6 2.96323e6i 0.454083 0.786494i
\(428\) 3.14366e6 0.829519
\(429\) 5.53611e6 1.45232
\(430\) 173361. 872187.i 0.0452148 0.227478i
\(431\) −453602. −0.117620 −0.0588101 0.998269i \(-0.518731\pi\)
−0.0588101 + 0.998269i \(0.518731\pi\)
\(432\) −1.95023e6 −0.502779
\(433\) 2.91468e6 5.04838e6i 0.747087 1.29399i −0.202126 0.979360i \(-0.564785\pi\)
0.949213 0.314634i \(-0.101882\pi\)
\(434\) −1.15728e6 −0.294928
\(435\) 589248. 1.02061e6i 0.149305 0.258604i
\(436\) −705021. + 1.22113e6i −0.177618 + 0.307643i
\(437\) −1.56793e6 2.71574e6i −0.392756 0.680274i
\(438\) 784076. 0.195287
\(439\) 3.31046e6 + 5.73388e6i 0.819835 + 1.42000i 0.905803 + 0.423698i \(0.139268\pi\)
−0.0859683 + 0.996298i \(0.527398\pi\)
\(440\) 1.68390e6 2.91659e6i 0.414652 0.718198i
\(441\) 1.78820e6 0.437844
\(442\) −350217. + 606594.i −0.0852672 + 0.147687i
\(443\) −1.63844e6 2.83786e6i −0.396662 0.687039i 0.596650 0.802502i \(-0.296498\pi\)
−0.993312 + 0.115463i \(0.963165\pi\)
\(444\) −1.44637e6 2.50518e6i −0.348194 0.603090i
\(445\) 1.14445e6 + 1.98225e6i 0.273967 + 0.474524i
\(446\) 1.87228e6 0.445690
\(447\) −477284. 826680.i −0.112982 0.195690i
\(448\) 122229. + 211707.i 0.0287726 + 0.0498356i
\(449\) 1.03947e6 1.80042e6i 0.243331 0.421462i −0.718330 0.695703i \(-0.755093\pi\)
0.961661 + 0.274241i \(0.0884265\pi\)
\(450\) 392456. 679753.i 0.0913607 0.158241i
\(451\) 1.42780e7 3.30542
\(452\) 410613. 0.0945336
\(453\) 1.28868e6 2.23207e6i 0.295054 0.511048i
\(454\) 43462.3 75278.9i 0.00989631 0.0171409i
\(455\) 840465. + 1.45573e6i 0.190323 + 0.329649i
\(456\) 1.61859e6 + 2.80348e6i 0.364523 + 0.631373i
\(457\) −7.10479e6 −1.59133 −0.795665 0.605736i \(-0.792879\pi\)
−0.795665 + 0.605736i \(0.792879\pi\)
\(458\) −511829. 886514.i −0.114015 0.197479i
\(459\) −742915. 1.28677e6i −0.164591 0.285081i
\(460\) 516963. + 895406.i 0.113911 + 0.197299i
\(461\) −386731. + 669838.i −0.0847534 + 0.146797i −0.905286 0.424802i \(-0.860344\pi\)
0.820533 + 0.571600i \(0.193677\pi\)
\(462\) −1.26038e6 −0.274725
\(463\) −1.35158e6 + 2.34100e6i −0.293014 + 0.507516i −0.974521 0.224296i \(-0.927992\pi\)
0.681507 + 0.731812i \(0.261325\pi\)
\(464\) −1.04835e6 1.81579e6i −0.226053 0.391535i
\(465\) −1.99057e6 −0.426919
\(466\) −1.59840e6 2.76851e6i −0.340974 0.590583i
\(467\) 1.45585e6 2.52161e6i 0.308905 0.535039i −0.669218 0.743066i \(-0.733371\pi\)
0.978123 + 0.208027i \(0.0667043\pi\)
\(468\) −1.52606e6 + 2.64321e6i −0.322074 + 0.557849i
\(469\) −2.68412e6 −0.563468
\(470\) −634833. + 1.09956e6i −0.132561 + 0.229602i
\(471\) 1.61193e6 0.334807
\(472\) −3.73155e6 −0.770965
\(473\) −9.02083e6 + 3.06358e6i −1.85393 + 0.629616i
\(474\) 217854. 0.0445369
\(475\) 5.38165e6 1.09441
\(476\) −379207. + 656806.i −0.0767113 + 0.132868i
\(477\) 3.10256e6 0.624344
\(478\) 1.08520e6 1.87962e6i 0.217239 0.376270i
\(479\) −2.26063e6 + 3.91553e6i −0.450185 + 0.779743i −0.998397 0.0565964i \(-0.981975\pi\)
0.548212 + 0.836339i \(0.315309\pi\)
\(480\) −825884. 1.43047e6i −0.163612 0.283385i
\(481\) −8.69041e6 −1.71268
\(482\) −1.23681e6 2.14222e6i −0.242485 0.419996i
\(483\) 427623. 740664.i 0.0834052 0.144462i
\(484\) −1.20657e7 −2.34121
\(485\) −228092. + 395068.i −0.0440308 + 0.0762636i
\(486\) 1.09697e6 + 1.90001e6i 0.210671 + 0.364893i
\(487\) −2.41774e6 4.18764e6i −0.461941 0.800105i 0.537117 0.843508i \(-0.319513\pi\)
−0.999058 + 0.0434028i \(0.986180\pi\)
\(488\) 3.26352e6 + 5.65259e6i 0.620350 + 1.07448i
\(489\) 3.67882e6 0.695722
\(490\) 424984. + 736094.i 0.0799618 + 0.138498i
\(491\) 3.77568e6 + 6.53967e6i 0.706792 + 1.22420i 0.966041 + 0.258389i \(0.0831916\pi\)
−0.259249 + 0.965810i \(0.583475\pi\)
\(492\) 2.26252e6 3.91881e6i 0.421386 0.729862i
\(493\) 798706. 1.38340e6i 0.148003 0.256348i
\(494\) 4.40003e6 0.811219
\(495\) 3.77121e6 0.691780
\(496\) −1.77074e6 + 3.06701e6i −0.323184 + 0.559771i
\(497\) −1.81974e6 + 3.15187e6i −0.330459 + 0.572371i
\(498\) 541645. + 938157.i 0.0978682 + 0.169513i
\(499\) 4.16824e6 + 7.21960e6i 0.749379 + 1.29796i 0.948121 + 0.317910i \(0.102981\pi\)
−0.198742 + 0.980052i \(0.563686\pi\)
\(500\) −4.34454e6 −0.777174
\(501\) −3.06038e6 5.30073e6i −0.544729 0.943498i
\(502\) −1.37551e6 2.38246e6i −0.243616 0.421955i
\(503\) −5.50014e6 9.52651e6i −0.969289 1.67886i −0.697620 0.716468i \(-0.745758\pi\)
−0.271669 0.962391i \(-0.587576\pi\)
\(504\) 767914. 1.33007e6i 0.134659 0.233237i
\(505\) −1.54065e6 −0.268829
\(506\) −1.16451e6 + 2.01699e6i −0.202194 + 0.350210i
\(507\) −887056. 1.53643e6i −0.153261 0.265456i
\(508\) 4.11200e6 0.706958
\(509\) −525773. 910665.i −0.0899505 0.155799i 0.817540 0.575873i \(-0.195338\pi\)
−0.907490 + 0.420074i \(0.862004\pi\)
\(510\) 137143. 237538.i 0.0233479 0.0404397i
\(511\) 1.27526e6 2.20881e6i 0.216046 0.374202i
\(512\) −5.23689e6 −0.882874
\(513\) −4.66688e6 + 8.08327e6i −0.782948 + 1.35611i
\(514\) 553560. 0.0924180
\(515\) 1.23672e6 0.205472
\(516\) −588616. + 2.96135e6i −0.0973213 + 0.489628i
\(517\) 1.36024e7 2.23815
\(518\) 1.97851e6 0.323977
\(519\) −534374. + 925563.i −0.0870818 + 0.150830i
\(520\) −3.20650e6 −0.520024
\(521\) −286252. + 495803.i −0.0462013 + 0.0800230i −0.888201 0.459455i \(-0.848045\pi\)
0.842000 + 0.539478i \(0.181378\pi\)
\(522\) −731777. + 1.26748e6i −0.117545 + 0.203593i
\(523\) 2.93659e6 + 5.08632e6i 0.469450 + 0.813111i 0.999390 0.0349242i \(-0.0111190\pi\)
−0.529940 + 0.848035i \(0.677786\pi\)
\(524\) −2.30160e6 −0.366186
\(525\) 733871. + 1.27110e6i 0.116204 + 0.201271i
\(526\) −2.54089e6 + 4.40095e6i −0.400425 + 0.693557i
\(527\) −2.69815e6 −0.423194
\(528\) −1.92849e6 + 3.34024e6i −0.301045 + 0.521426i
\(529\) 2.42798e6 + 4.20539e6i 0.377230 + 0.653381i
\(530\) 737355. + 1.27714e6i 0.114022 + 0.197491i
\(531\) −2.08927e6 3.61873e6i −0.321558 0.556954i
\(532\) 4.76424e6 0.729819
\(533\) −6.79711e6 1.17729e7i −1.03635 1.79501i
\(534\) 817029. + 1.41514e6i 0.123989 + 0.214756i
\(535\) −1.84915e6 + 3.20283e6i −0.279311 + 0.483781i
\(536\) 2.56008e6 4.43419e6i 0.384894 0.666657i
\(537\) 1.04686e6 0.156658
\(538\) 882258. 0.131413
\(539\) 4.55301e6 7.88604e6i 0.675035 1.16919i
\(540\) 1.53872e6 2.66514e6i 0.227078 0.393310i
\(541\) 163410. + 283035.i 0.0240042 + 0.0415764i 0.877778 0.479068i \(-0.159025\pi\)
−0.853774 + 0.520644i \(0.825692\pi\)
\(542\) −2.36063e6 4.08873e6i −0.345167 0.597847i
\(543\) −587868. −0.0855619
\(544\) −1.11946e6 1.93896e6i −0.162185 0.280912i
\(545\) −829409. 1.43658e6i −0.119613 0.207175i
\(546\) 600011. + 1.03925e6i 0.0861346 + 0.149190i
\(547\) −691457. + 1.19764e6i −0.0988090 + 0.171142i −0.911192 0.411982i \(-0.864837\pi\)
0.812383 + 0.583124i \(0.198170\pi\)
\(548\) 4.16243e6 0.592100
\(549\) −3.65445e6 + 6.32970e6i −0.517478 + 0.896298i
\(550\) −1.99850e6 3.46150e6i −0.281706 0.487929i
\(551\) −1.00347e7 −1.40807
\(552\) 815723. + 1.41287e6i 0.113945 + 0.197358i
\(553\) 354328. 613714.i 0.0492711 0.0853401i
\(554\) −155663. + 269616.i −0.0215482 + 0.0373225i
\(555\) 3.40311e6 0.468968
\(556\) 1.56986e6 2.71908e6i 0.215365 0.373023i
\(557\) −9.53674e6 −1.30245 −0.651226 0.758883i \(-0.725745\pi\)
−0.651226 + 0.758883i \(0.725745\pi\)
\(558\) 2.47205e6 0.336103
\(559\) 6.82047e6 + 5.97970e6i 0.923177 + 0.809375i
\(560\) −1.17109e6 −0.157805
\(561\) −2.93852e6 −0.394204
\(562\) 1.65105e6 2.85970e6i 0.220505 0.381926i
\(563\) −5.53863e6 −0.736430 −0.368215 0.929741i \(-0.620031\pi\)
−0.368215 + 0.929741i \(0.620031\pi\)
\(564\) 2.15546e6 3.73337e6i 0.285327 0.494200i
\(565\) −241529. + 418340.i −0.0318308 + 0.0551326i
\(566\) −682506. 1.18213e6i −0.0895499 0.155105i
\(567\) 162838. 0.0212715
\(568\) −3.47128e6 6.01244e6i −0.451460 0.781952i
\(569\) 4.21862e6 7.30687e6i 0.546248 0.946130i −0.452279 0.891876i \(-0.649389\pi\)
0.998527 0.0542531i \(-0.0172778\pi\)
\(570\) −1.72302e6 −0.222128
\(571\) −1.00713e6 + 1.74439e6i −0.129269 + 0.223900i −0.923393 0.383855i \(-0.874596\pi\)
0.794125 + 0.607755i \(0.207930\pi\)
\(572\) 7.77112e6 + 1.34600e7i 0.993101 + 1.72010i
\(573\) 758240. + 1.31331e6i 0.0964762 + 0.167102i
\(574\) 1.54747e6 + 2.68030e6i 0.196039 + 0.339550i
\(575\) 2.71220e6 0.342099
\(576\) −261091. 452223.i −0.0327896 0.0567932i
\(577\) 3.63995e6 + 6.30458e6i 0.455152 + 0.788346i 0.998697 0.0510342i \(-0.0162517\pi\)
−0.543545 + 0.839380i \(0.682918\pi\)
\(578\) −1.48801e6 + 2.57731e6i −0.185262 + 0.320883i
\(579\) −1.82012e6 + 3.15254e6i −0.225633 + 0.390808i
\(580\) 3.30854e6 0.408382
\(581\) 3.52383e6 0.433086
\(582\) −162836. + 282040.i −0.0199271 + 0.0345147i
\(583\) 7.89955e6 1.36824e7i 0.962567 1.66722i
\(584\) 2.43265e6 + 4.21348e6i 0.295154 + 0.511221i
\(585\) −1.79530e6 3.10955e6i −0.216894 0.375672i
\(586\) −844070. −0.101539
\(587\) −2.18347e6 3.78187e6i −0.261548 0.453014i 0.705106 0.709102i \(-0.250900\pi\)
−0.966653 + 0.256088i \(0.917566\pi\)
\(588\) −1.44296e6 2.49927e6i −0.172112 0.298106i
\(589\) 8.47468e6 + 1.46786e7i 1.00655 + 1.74340i
\(590\) 993076. 1.72006e6i 0.117450 0.203429i
\(591\) 3.09796e6 0.364844
\(592\) 3.02727e6 5.24339e6i 0.355016 0.614905i
\(593\) −2.44473e6 4.23439e6i −0.285492 0.494486i 0.687237 0.726434i \(-0.258824\pi\)
−0.972728 + 0.231947i \(0.925490\pi\)
\(594\) 6.93224e6 0.806135
\(595\) −446111. 772687.i −0.0516596 0.0894770i
\(596\) 1.33994e6 2.32084e6i 0.154515 0.267627i
\(597\) −1.45596e6 + 2.52179e6i −0.167191 + 0.289583i
\(598\) 2.21748e6 0.253576
\(599\) −100075. + 173334.i −0.0113961 + 0.0197387i −0.871667 0.490098i \(-0.836961\pi\)
0.860271 + 0.509837i \(0.170294\pi\)
\(600\) −2.79983e6 −0.317507
\(601\) −3.52160e6 −0.397699 −0.198849 0.980030i \(-0.563720\pi\)
−0.198849 + 0.980030i \(0.563720\pi\)
\(602\) −1.55279e6 1.36137e6i −0.174631 0.153104i
\(603\) 5.73350e6 0.642135
\(604\) 7.23578e6 0.807036
\(605\) 7.09725e6 1.22928e7i 0.788319 1.36541i
\(606\) −1.09988e6 −0.121664
\(607\) −869571. + 1.50614e6i −0.0957929 + 0.165918i −0.909939 0.414742i \(-0.863872\pi\)
0.814146 + 0.580660i \(0.197205\pi\)
\(608\) −7.03226e6 + 1.21802e7i −0.771500 + 1.33628i
\(609\) −1.36838e6 2.37011e6i −0.149508 0.258956i
\(610\) −3.47408e6 −0.378020
\(611\) −6.47547e6 1.12158e7i −0.701727 1.21543i
\(612\) 810018. 1.40299e6i 0.0874210 0.151418i
\(613\) 3.79841e6 0.408273 0.204136 0.978942i \(-0.434561\pi\)
0.204136 + 0.978942i \(0.434561\pi\)
\(614\) −65810.0 + 113986.i −0.00704484 + 0.0122020i
\(615\) 2.66170e6 + 4.61021e6i 0.283774 + 0.491510i
\(616\) −3.91043e6 6.77307e6i −0.415215 0.719174i
\(617\) 8.10025e6 + 1.40300e7i 0.856615 + 1.48370i 0.875139 + 0.483872i \(0.160770\pi\)
−0.0185241 + 0.999828i \(0.505897\pi\)
\(618\) 882898. 0.0929906
\(619\) −6.36414e6 1.10230e7i −0.667595 1.15631i −0.978575 0.205892i \(-0.933990\pi\)
0.310980 0.950417i \(-0.399343\pi\)
\(620\) −2.79419e6 4.83968e6i −0.291929 0.505635i
\(621\) −2.35197e6 + 4.07373e6i −0.244739 + 0.423900i
\(622\) −577945. + 1.00103e6i −0.0598977 + 0.103746i
\(623\) 5.31542e6 0.548678
\(624\) 3.67226e6 0.377547
\(625\) −815485. + 1.41246e6i −0.0835057 + 0.144636i
\(626\) 2.56092e6 4.43565e6i 0.261193 0.452399i
\(627\) 9.22967e6 + 1.59863e7i 0.937599 + 1.62397i
\(628\) 2.26269e6 + 3.91910e6i 0.228942 + 0.396540i
\(629\) 4.61279e6 0.464876
\(630\) 408729. + 707939.i 0.0410283 + 0.0710632i
\(631\) −5.58801e6 9.67872e6i −0.558707 0.967708i −0.997605 0.0691716i \(-0.977964\pi\)
0.438898 0.898537i \(-0.355369\pi\)
\(632\) 675908. + 1.17071e6i 0.0673124 + 0.116588i
\(633\) −690603. + 1.19616e6i −0.0685045 + 0.118653i
\(634\) −2.01346e6 −0.198938
\(635\) −2.41874e6 + 4.18939e6i −0.238043 + 0.412303i
\(636\) −2.50356e6 4.33629e6i −0.245423 0.425085i
\(637\) −8.66991e6 −0.846576
\(638\) 3.72642e6 + 6.45435e6i 0.362443 + 0.627770i
\(639\) 3.88710e6 6.73266e6i 0.376594 0.652281i
\(640\) 2.93022e6 5.07530e6i 0.282782 0.489792i
\(641\) −1.39604e7 −1.34200 −0.671002 0.741456i \(-0.734136\pi\)
−0.671002 + 0.741456i \(0.734136\pi\)
\(642\) −1.32012e6 + 2.28651e6i −0.126408 + 0.218945i
\(643\) −1.15185e7 −1.09867 −0.549337 0.835601i \(-0.685120\pi\)
−0.549337 + 0.835601i \(0.685120\pi\)
\(644\) 2.40104e6 0.228131
\(645\) −2.67085e6 2.34161e6i −0.252785 0.221623i
\(646\) −2.33550e6 −0.220190
\(647\) 7.86031e6 0.738209 0.369104 0.929388i \(-0.379665\pi\)
0.369104 + 0.929388i \(0.379665\pi\)
\(648\) −155313. + 269010.i −0.0145302 + 0.0251670i
\(649\) −2.12784e7 −1.98302
\(650\) −1.90278e6 + 3.29572e6i −0.176647 + 0.305962i
\(651\) −2.31131e6 + 4.00330e6i −0.213749 + 0.370225i
\(652\) 5.16400e6 + 8.94432e6i 0.475738 + 0.824002i
\(653\) −1.39211e7 −1.27758 −0.638792 0.769379i \(-0.720566\pi\)
−0.638792 + 0.769379i \(0.720566\pi\)
\(654\) −592119. 1.02558e6i −0.0541333 0.0937616i
\(655\) 1.35384e6 2.34492e6i 0.123300 0.213562i
\(656\) 9.47101e6 0.859284
\(657\) −2.72406e6 + 4.71820e6i −0.246208 + 0.426445i
\(658\) 1.47424e6 + 2.55347e6i 0.132741 + 0.229914i
\(659\) −6.30343e6 1.09179e7i −0.565410 0.979319i −0.997011 0.0772545i \(-0.975385\pi\)
0.431601 0.902064i \(-0.357949\pi\)
\(660\) −3.04312e6 5.27083e6i −0.271931 0.470998i
\(661\) −111996. −0.00997012 −0.00498506 0.999988i \(-0.501587\pi\)
−0.00498506 + 0.999988i \(0.501587\pi\)
\(662\) −2.11414e6 3.66179e6i −0.187494 0.324750i
\(663\) 1.39889e6 + 2.42296e6i 0.123595 + 0.214073i
\(664\) −3.36099e6 + 5.82140e6i −0.295833 + 0.512398i
\(665\) −2.80240e6 + 4.85391e6i −0.245740 + 0.425635i
\(666\) −4.22626e6 −0.369207
\(667\) −5.05719e6 −0.440144
\(668\) 8.59178e6 1.48814e7i 0.744976 1.29034i
\(669\) 3.73927e6 6.47661e6i 0.323014 0.559477i
\(670\) 1.36263e6 + 2.36014e6i 0.117271 + 0.203119i
\(671\) 1.86095e7 + 3.22326e7i 1.59562 + 2.76369i
\(672\) −3.83583e6 −0.327669
\(673\) 6.26611e6 + 1.08532e7i 0.533286 + 0.923678i 0.999244 + 0.0388717i \(0.0123764\pi\)
−0.465958 + 0.884807i \(0.654290\pi\)
\(674\) −3.48814e6 6.04163e6i −0.295763 0.512277i
\(675\) −4.03637e6 6.99119e6i −0.340982 0.590598i
\(676\) 2.49035e6 4.31341e6i 0.209601 0.363039i
\(677\) 1.27948e7 1.07291 0.536455 0.843929i \(-0.319763\pi\)
0.536455 + 0.843929i \(0.319763\pi\)
\(678\) −172428. + 298655.i −0.0144057 + 0.0249514i
\(679\) 529689. + 917448.i 0.0440906 + 0.0763672i
\(680\) 1.70198e6 0.141151
\(681\) −173604. 300691.i −0.0143447 0.0248458i
\(682\) 6.29420e6 1.09019e7i 0.518179 0.897512i
\(683\) −1.94779e6 + 3.37367e6i −0.159768 + 0.276727i −0.934785 0.355214i \(-0.884408\pi\)
0.775017 + 0.631941i \(0.217741\pi\)
\(684\) −1.01768e7 −0.831710
\(685\) −2.44841e6 + 4.24076e6i −0.199369 + 0.345317i
\(686\) 4.83639e6 0.392384
\(687\) −4.08886e6 −0.330530
\(688\) −5.98376e6 + 2.03215e6i −0.481952 + 0.163676i
\(689\) −1.50425e7 −1.20718
\(690\) −868352. −0.0694342
\(691\) 284444. 492671.i 0.0226622 0.0392520i −0.854472 0.519498i \(-0.826119\pi\)
0.877134 + 0.480246i \(0.159452\pi\)
\(692\) −3.00043e6 −0.238187
\(693\) 4.37886e6 7.58441e6i 0.346360 0.599913i
\(694\) −803041. + 1.39091e6i −0.0632906 + 0.109623i
\(695\) 1.84684e6 + 3.19882e6i 0.145033 + 0.251204i
\(696\) 5.22060e6 0.408505
\(697\) 3.60785e6 + 6.24898e6i 0.281298 + 0.487222i
\(698\) −2.11752e6 + 3.66765e6i −0.164509 + 0.284937i
\(699\) −1.27692e7 −0.988484
\(700\) −2.06029e6 + 3.56853e6i −0.158922 + 0.275260i
\(701\) 6.57247e6 + 1.13839e7i 0.505166 + 0.874973i 0.999982 + 0.00597517i \(0.00190197\pi\)
−0.494816 + 0.868998i \(0.664765\pi\)
\(702\) −3.30012e6 5.71598e6i −0.252748 0.437772i
\(703\) −1.44884e7 2.50947e7i −1.10569 1.91511i
\(704\) −2.65910e6 −0.202210
\(705\) 2.53575e6 + 4.39205e6i 0.192147 + 0.332808i
\(706\) −1050.95 1820.30i −7.93545e−5 0.000137446i
\(707\) −1.78889e6 + 3.09845e6i −0.134597 + 0.233129i
\(708\) −3.37181e6 + 5.84015e6i −0.252802 + 0.437865i
\(709\) 1.54954e7 1.15767 0.578836 0.815444i \(-0.303507\pi\)
0.578836 + 0.815444i \(0.303507\pi\)
\(710\) 3.69524e6 0.275104
\(711\) −756874. + 1.31094e6i −0.0561500 + 0.0972546i
\(712\) −5.06979e6 + 8.78113e6i −0.374791 + 0.649158i
\(713\) 4.27099e6 + 7.39758e6i 0.314633 + 0.544961i
\(714\) −318481. 551625.i −0.0233796 0.0404947i
\(715\) −1.82844e7 −1.33757
\(716\) 1.46949e6 + 2.54523e6i 0.107123 + 0.185543i
\(717\) −4.33467e6 7.50786e6i −0.314889 0.545404i
\(718\) 17197.0 + 29786.0i 0.00124492 + 0.00215626i
\(719\) −6.63582e6 + 1.14936e7i −0.478710 + 0.829150i −0.999702 0.0244114i \(-0.992229\pi\)
0.520992 + 0.853562i \(0.325562\pi\)
\(720\) 2.50155e6 0.179836
\(721\) 1.43599e6 2.48720e6i 0.102876 0.178186i
\(722\) 4.41649e6 + 7.64958e6i 0.315307 + 0.546128i
\(723\) −9.88052e6 −0.702966
\(724\) −825199. 1.42929e6i −0.0585076 0.101338i
\(725\) 4.33949e6 7.51621e6i 0.306615 0.531073i
\(726\) 5.06676e6 8.77588e6i 0.356770 0.617944i
\(727\) 7.27001e6 0.510151 0.255076 0.966921i \(-0.417900\pi\)
0.255076 + 0.966921i \(0.417900\pi\)
\(728\) −3.72316e6 + 6.44870e6i −0.260365 + 0.450966i
\(729\) 8.21562e6 0.572561
\(730\) −2.58960e6 −0.179856
\(731\) −3.62025e6 3.17397e6i −0.250579 0.219690i
\(732\) 1.17956e7 0.813659
\(733\) 1.00580e7 0.691438 0.345719 0.938338i \(-0.387635\pi\)
0.345719 + 0.938338i \(0.387635\pi\)
\(734\) −517035. + 895531.i −0.0354225 + 0.0613536i
\(735\) 3.39508e6 0.231810
\(736\) −3.54405e6 + 6.13848e6i −0.241160 + 0.417702i
\(737\) 1.45983e7 2.52850e7i 0.989996 1.71472i
\(738\) −3.30552e6 5.72534e6i −0.223408 0.386955i
\(739\) 7.58208e6 0.510713 0.255357 0.966847i \(-0.417807\pi\)
0.255357 + 0.966847i \(0.417807\pi\)
\(740\) 4.77699e6 + 8.27398e6i 0.320682 + 0.555438i
\(741\) 8.78765e6 1.52206e7i 0.587932 1.01833i
\(742\) 3.42466e6 0.228353
\(743\) 3.36685e6 5.83156e6i 0.223744 0.387536i −0.732198 0.681092i \(-0.761505\pi\)
0.955942 + 0.293556i \(0.0948386\pi\)
\(744\) −4.40899e6 7.63660e6i −0.292016 0.505787i
\(745\) 1.57635e6 + 2.73031e6i 0.104055 + 0.180228i
\(746\) 4.34356e6 + 7.52327e6i 0.285759 + 0.494948i
\(747\) −7.52719e6 −0.493550
\(748\) −4.12484e6 7.14443e6i −0.269559 0.466889i
\(749\) 4.29420e6 + 7.43778e6i 0.279691 + 0.484438i
\(750\) 1.82440e6 3.15995e6i 0.118431 0.205129i
\(751\) 6.84753e6 1.18603e7i 0.443031 0.767352i −0.554882 0.831929i \(-0.687237\pi\)
0.997913 + 0.0645774i \(0.0205699\pi\)
\(752\) 9.02283e6 0.581833
\(753\) −1.09886e7 −0.706244
\(754\) 3.54795e6 6.14524e6i 0.227274 0.393650i
\(755\) −4.25620e6 + 7.37195e6i −0.271741 + 0.470668i
\(756\) −3.57330e6 6.18913e6i −0.227386 0.393845i
\(757\) −254645. 441058.i −0.0161508 0.0279741i 0.857837 0.513922i \(-0.171808\pi\)
−0.873988 + 0.485948i \(0.838475\pi\)
\(758\) 1.02325e7 0.646858
\(759\) 4.65148e6 + 8.05660e6i 0.293081 + 0.507630i
\(760\) −5.34580e6 9.25920e6i −0.335721 0.581486i
\(761\) −2.37927e6 4.12102e6i −0.148930 0.257955i 0.781902 0.623401i \(-0.214250\pi\)
−0.930832 + 0.365446i \(0.880916\pi\)
\(762\) −1.72675e6 + 2.99082e6i −0.107731 + 0.186596i
\(763\) −3.85220e6 −0.239551
\(764\) −2.12870e6 + 3.68702e6i −0.131942 + 0.228530i
\(765\) 952930. + 1.65052e6i 0.0588718 + 0.101969i
\(766\) −1.94978e6 −0.120064
\(767\) 1.01296e7 + 1.75451e7i 0.621736 + 1.07688i
\(768\) 1.58194e6 2.73999e6i 0.0967801 0.167628i
\(769\) −6.90091e6 + 1.19527e7i −0.420814 + 0.728871i −0.996019 0.0891377i \(-0.971589\pi\)
0.575205 + 0.818009i \(0.304922\pi\)
\(770\) 4.16273e6 0.253018
\(771\) 1.10556e6 1.91488e6i 0.0669801 0.116013i
\(772\) −1.02197e7 −0.617156
\(773\)