Properties

Label 43.6.c.a.6.9
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 6.9
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.24721 q^{2} +(-0.494517 + 0.856528i) q^{3} -30.4445 q^{4} +(24.3642 - 42.2000i) q^{5} +(0.616768 - 1.06827i) q^{6} +(83.1429 + 144.008i) q^{7} +77.8815 q^{8} +(121.011 + 209.597i) q^{9} +O(q^{10})\) \(q-1.24721 q^{2} +(-0.494517 + 0.856528i) q^{3} -30.4445 q^{4} +(24.3642 - 42.2000i) q^{5} +(0.616768 - 1.06827i) q^{6} +(83.1429 + 144.008i) q^{7} +77.8815 q^{8} +(121.011 + 209.597i) q^{9} +(-30.3873 + 52.6324i) q^{10} -436.503 q^{11} +(15.0553 - 26.0765i) q^{12} +(486.675 + 842.946i) q^{13} +(-103.697 - 179.608i) q^{14} +(24.0970 + 41.7372i) q^{15} +877.088 q^{16} +(375.545 + 650.464i) q^{17} +(-150.926 - 261.412i) q^{18} +(283.197 - 490.512i) q^{19} +(-741.754 + 1284.76i) q^{20} -164.462 q^{21} +544.413 q^{22} +(-498.615 + 863.626i) q^{23} +(-38.5137 + 66.7078i) q^{24} +(375.274 + 649.994i) q^{25} +(-606.988 - 1051.33i) q^{26} -479.703 q^{27} +(-2531.24 - 4384.24i) q^{28} +(-1998.43 - 3461.38i) q^{29} +(-30.0541 - 52.0552i) q^{30} +(3892.30 - 6741.67i) q^{31} -3586.12 q^{32} +(215.858 - 373.877i) q^{33} +(-468.385 - 811.267i) q^{34} +8102.83 q^{35} +(-3684.11 - 6381.07i) q^{36} +(-6022.45 + 10431.2i) q^{37} +(-353.207 + 611.773i) q^{38} -962.676 q^{39} +(1897.52 - 3286.60i) q^{40} -15533.0 q^{41} +205.120 q^{42} +(3632.24 + 11567.9i) q^{43} +13289.1 q^{44} +11793.3 q^{45} +(621.879 - 1077.13i) q^{46} +8224.60 q^{47} +(-433.735 + 751.251i) q^{48} +(-5421.99 + 9391.16i) q^{49} +(-468.047 - 810.680i) q^{50} -742.854 q^{51} +(-14816.6 - 25663.0i) q^{52} +(-2106.28 + 3648.19i) q^{53} +598.292 q^{54} +(-10635.0 + 18420.4i) q^{55} +(6475.30 + 11215.5i) q^{56} +(280.092 + 485.133i) q^{57} +(2492.47 + 4317.08i) q^{58} +38108.9 q^{59} +(-733.620 - 1270.67i) q^{60} +(14090.4 + 24405.3i) q^{61} +(-4854.53 + 8408.30i) q^{62} +(-20122.4 + 34853.0i) q^{63} -23594.1 q^{64} +47429.7 q^{65} +(-269.221 + 466.305i) q^{66} +(5914.11 - 10243.5i) q^{67} +(-11433.3 - 19803.0i) q^{68} +(-493.147 - 854.156i) q^{69} -10106.0 q^{70} +(-37746.3 - 65378.5i) q^{71} +(9424.52 + 16323.7i) q^{72} +(27806.1 + 48161.5i) q^{73} +(7511.28 - 13009.9i) q^{74} -742.317 q^{75} +(-8621.79 + 14933.4i) q^{76} +(-36292.2 - 62859.9i) q^{77} +1200.66 q^{78} +(-38966.7 - 67492.3i) q^{79} +(21369.5 - 37013.1i) q^{80} +(-29168.4 + 50521.2i) q^{81} +19372.9 q^{82} +(8253.14 - 14294.9i) q^{83} +5006.97 q^{84} +36599.4 q^{85} +(-4530.18 - 14427.6i) q^{86} +3953.03 q^{87} -33995.6 q^{88} +(38194.7 - 66155.2i) q^{89} -14708.8 q^{90} +(-80927.2 + 140170. i) q^{91} +(15180.1 - 26292.6i) q^{92} +(3849.62 + 6667.74i) q^{93} -10257.8 q^{94} +(-13799.7 - 23901.8i) q^{95} +(1773.40 - 3071.62i) q^{96} -1066.68 q^{97} +(6762.38 - 11712.8i) q^{98} +(-52821.7 - 91489.8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24721 −0.220478 −0.110239 0.993905i \(-0.535162\pi\)
−0.110239 + 0.993905i \(0.535162\pi\)
\(3\) −0.494517 + 0.856528i −0.0317233 + 0.0549463i −0.881451 0.472275i \(-0.843433\pi\)
0.849728 + 0.527222i \(0.176766\pi\)
\(4\) −30.4445 −0.951389
\(5\) 24.3642 42.2000i 0.435840 0.754896i −0.561524 0.827460i \(-0.689785\pi\)
0.997364 + 0.0725640i \(0.0231182\pi\)
\(6\) 0.616768 1.06827i 0.00699429 0.0121145i
\(7\) 83.1429 + 144.008i 0.641328 + 1.11081i 0.985137 + 0.171773i \(0.0549495\pi\)
−0.343809 + 0.939040i \(0.611717\pi\)
\(8\) 77.8815 0.430239
\(9\) 121.011 + 209.597i 0.497987 + 0.862539i
\(10\) −30.3873 + 52.6324i −0.0960931 + 0.166438i
\(11\) −436.503 −1.08769 −0.543846 0.839185i \(-0.683032\pi\)
−0.543846 + 0.839185i \(0.683032\pi\)
\(12\) 15.0553 26.0765i 0.0301812 0.0522753i
\(13\) 486.675 + 842.946i 0.798695 + 1.38338i 0.920466 + 0.390821i \(0.127809\pi\)
−0.121772 + 0.992558i \(0.538858\pi\)
\(14\) −103.697 179.608i −0.141399 0.244910i
\(15\) 24.0970 + 41.7372i 0.0276525 + 0.0478956i
\(16\) 877.088 0.856531
\(17\) 375.545 + 650.464i 0.315167 + 0.545885i 0.979473 0.201576i \(-0.0646063\pi\)
−0.664306 + 0.747460i \(0.731273\pi\)
\(18\) −150.926 261.412i −0.109795 0.190171i
\(19\) 283.197 490.512i 0.179972 0.311721i −0.761899 0.647696i \(-0.775733\pi\)
0.941871 + 0.335975i \(0.109066\pi\)
\(20\) −741.754 + 1284.76i −0.414653 + 0.718200i
\(21\) −164.462 −0.0813801
\(22\) 544.413 0.239812
\(23\) −498.615 + 863.626i −0.196538 + 0.340413i −0.947404 0.320042i \(-0.896303\pi\)
0.750866 + 0.660455i \(0.229636\pi\)
\(24\) −38.5137 + 66.7078i −0.0136486 + 0.0236400i
\(25\) 375.274 + 649.994i 0.120088 + 0.207998i
\(26\) −606.988 1051.33i −0.176095 0.305005i
\(27\) −479.703 −0.126638
\(28\) −2531.24 4384.24i −0.610153 1.05682i
\(29\) −1998.43 3461.38i −0.441259 0.764283i 0.556524 0.830832i \(-0.312135\pi\)
−0.997783 + 0.0665481i \(0.978801\pi\)
\(30\) −30.0541 52.0552i −0.00609678 0.0105599i
\(31\) 3892.30 6741.67i 0.727449 1.25998i −0.230509 0.973070i \(-0.574039\pi\)
0.957958 0.286909i \(-0.0926276\pi\)
\(32\) −3586.12 −0.619085
\(33\) 215.858 373.877i 0.0345051 0.0597647i
\(34\) −468.385 811.267i −0.0694874 0.120356i
\(35\) 8102.83 1.11806
\(36\) −3684.11 6381.07i −0.473780 0.820611i
\(37\) −6022.45 + 10431.2i −0.723217 + 1.25265i 0.236486 + 0.971635i \(0.424004\pi\)
−0.959704 + 0.281014i \(0.909329\pi\)
\(38\) −353.207 + 611.773i −0.0396799 + 0.0687276i
\(39\) −962.676 −0.101349
\(40\) 1897.52 3286.60i 0.187515 0.324786i
\(41\) −15533.0 −1.44310 −0.721548 0.692364i \(-0.756569\pi\)
−0.721548 + 0.692364i \(0.756569\pi\)
\(42\) 205.120 0.0179425
\(43\) 3632.24 + 11567.9i 0.299573 + 0.954073i
\(44\) 13289.1 1.03482
\(45\) 11793.3 0.868170
\(46\) 621.879 1077.13i 0.0433323 0.0750537i
\(47\) 8224.60 0.543088 0.271544 0.962426i \(-0.412466\pi\)
0.271544 + 0.962426i \(0.412466\pi\)
\(48\) −433.735 + 751.251i −0.0271720 + 0.0470632i
\(49\) −5421.99 + 9391.16i −0.322603 + 0.558765i
\(50\) −468.047 810.680i −0.0264767 0.0458590i
\(51\) −742.854 −0.0399925
\(52\) −14816.6 25663.0i −0.759870 1.31613i
\(53\) −2106.28 + 3648.19i −0.102998 + 0.178397i −0.912918 0.408142i \(-0.866177\pi\)
0.809921 + 0.586539i \(0.199510\pi\)
\(54\) 598.292 0.0279209
\(55\) −10635.0 + 18420.4i −0.474059 + 0.821095i
\(56\) 6475.30 + 11215.5i 0.275924 + 0.477915i
\(57\) 280.092 + 485.133i 0.0114186 + 0.0197776i
\(58\) 2492.47 + 4317.08i 0.0972880 + 0.168508i
\(59\) 38108.9 1.42527 0.712634 0.701536i \(-0.247502\pi\)
0.712634 + 0.701536i \(0.247502\pi\)
\(60\) −733.620 1270.67i −0.0263083 0.0455673i
\(61\) 14090.4 + 24405.3i 0.484841 + 0.839769i 0.999848 0.0174167i \(-0.00554417\pi\)
−0.515007 + 0.857186i \(0.672211\pi\)
\(62\) −4854.53 + 8408.30i −0.160387 + 0.277798i
\(63\) −20122.4 + 34853.0i −0.638746 + 1.10634i
\(64\) −23594.1 −0.720036
\(65\) 47429.7 1.39241
\(66\) −269.221 + 466.305i −0.00760763 + 0.0131768i
\(67\) 5914.11 10243.5i 0.160954 0.278781i −0.774257 0.632871i \(-0.781876\pi\)
0.935211 + 0.354090i \(0.115210\pi\)
\(68\) −11433.3 19803.0i −0.299846 0.519349i
\(69\) −493.147 854.156i −0.0124696 0.0215980i
\(70\) −10106.0 −0.246509
\(71\) −37746.3 65378.5i −0.888645 1.53918i −0.841478 0.540292i \(-0.818314\pi\)
−0.0471673 0.998887i \(-0.515019\pi\)
\(72\) 9424.52 + 16323.7i 0.214253 + 0.371098i
\(73\) 27806.1 + 48161.5i 0.610707 + 1.05777i 0.991122 + 0.132959i \(0.0424478\pi\)
−0.380415 + 0.924816i \(0.624219\pi\)
\(74\) 7511.28 13009.9i 0.159454 0.276182i
\(75\) −742.317 −0.0152383
\(76\) −8621.79 + 14933.4i −0.171223 + 0.296568i
\(77\) −36292.2 62859.9i −0.697567 1.20822i
\(78\) 1200.66 0.0223452
\(79\) −38966.7 67492.3i −0.702467 1.21671i −0.967598 0.252496i \(-0.918749\pi\)
0.265131 0.964212i \(-0.414585\pi\)
\(80\) 21369.5 37013.1i 0.373310 0.646592i
\(81\) −29168.4 + 50521.2i −0.493970 + 0.855581i
\(82\) 19372.9 0.318171
\(83\) 8253.14 14294.9i 0.131499 0.227764i −0.792755 0.609540i \(-0.791354\pi\)
0.924255 + 0.381776i \(0.124688\pi\)
\(84\) 5006.97 0.0774242
\(85\) 36599.4 0.549448
\(86\) −4530.18 14427.6i −0.0660494 0.210352i
\(87\) 3953.03 0.0559928
\(88\) −33995.6 −0.467967
\(89\) 38194.7 66155.2i 0.511126 0.885296i −0.488791 0.872401i \(-0.662562\pi\)
0.999917 0.0128953i \(-0.00410481\pi\)
\(90\) −14708.8 −0.191413
\(91\) −80927.2 + 140170.i −1.02445 + 1.77440i
\(92\) 15180.1 26292.6i 0.186984 0.323865i
\(93\) 3849.62 + 6667.74i 0.0461541 + 0.0799413i
\(94\) −10257.8 −0.119739
\(95\) −13799.7 23901.8i −0.156878 0.271720i
\(96\) 1773.40 3071.62i 0.0196394 0.0340165i
\(97\) −1066.68 −0.0115108 −0.00575540 0.999983i \(-0.501832\pi\)
−0.00575540 + 0.999983i \(0.501832\pi\)
\(98\) 6762.38 11712.8i 0.0711270 0.123196i
\(99\) −52821.7 91489.8i −0.541657 0.938177i
\(100\) −11425.0 19788.7i −0.114250 0.197887i
\(101\) 31666.0 + 54847.0i 0.308880 + 0.534995i 0.978118 0.208053i \(-0.0667127\pi\)
−0.669238 + 0.743048i \(0.733379\pi\)
\(102\) 926.498 0.00881747
\(103\) −18130.1 31402.2i −0.168386 0.291653i 0.769467 0.638687i \(-0.220522\pi\)
−0.937853 + 0.347034i \(0.887189\pi\)
\(104\) 37903.0 + 65649.9i 0.343629 + 0.595184i
\(105\) −4006.99 + 6940.31i −0.0354687 + 0.0614335i
\(106\) 2626.98 4550.07i 0.0227087 0.0393326i
\(107\) 117719. 0.994001 0.497000 0.867750i \(-0.334435\pi\)
0.497000 + 0.867750i \(0.334435\pi\)
\(108\) 14604.3 0.120482
\(109\) 100372. 173850.i 0.809184 1.40155i −0.104245 0.994552i \(-0.533243\pi\)
0.913430 0.406997i \(-0.133424\pi\)
\(110\) 13264.2 22974.2i 0.104520 0.181033i
\(111\) −5956.41 10316.8i −0.0458856 0.0794763i
\(112\) 72923.6 + 126307.i 0.549317 + 0.951446i
\(113\) −194153. −1.43037 −0.715185 0.698935i \(-0.753658\pi\)
−0.715185 + 0.698935i \(0.753658\pi\)
\(114\) −349.334 605.064i −0.00251755 0.00436053i
\(115\) 24296.7 + 42083.1i 0.171318 + 0.296731i
\(116\) 60841.1 + 105380.i 0.419809 + 0.727131i
\(117\) −117786. + 204011.i −0.795479 + 1.37781i
\(118\) −47530.0 −0.314241
\(119\) −62447.9 + 108163.i −0.404250 + 0.700182i
\(120\) 1876.71 + 3250.56i 0.0118972 + 0.0206065i
\(121\) 29484.1 0.183073
\(122\) −17573.8 30438.6i −0.106897 0.185151i
\(123\) 7681.33 13304.4i 0.0457798 0.0792929i
\(124\) −118499. + 205246.i −0.692087 + 1.19873i
\(125\) 188849. 1.08104
\(126\) 25096.9 43469.1i 0.140830 0.243924i
\(127\) 68255.9 0.375518 0.187759 0.982215i \(-0.439878\pi\)
0.187759 + 0.982215i \(0.439878\pi\)
\(128\) 144183. 0.777838
\(129\) −11704.4 2609.38i −0.0619263 0.0138059i
\(130\) −59155.0 −0.306996
\(131\) 202347. 1.03019 0.515095 0.857133i \(-0.327757\pi\)
0.515095 + 0.857133i \(0.327757\pi\)
\(132\) −6571.69 + 11382.5i −0.0328278 + 0.0568595i
\(133\) 94183.4 0.461684
\(134\) −7376.16 + 12775.9i −0.0354869 + 0.0614651i
\(135\) −11687.6 + 20243.5i −0.0551937 + 0.0955983i
\(136\) 29248.1 + 50659.1i 0.135597 + 0.234861i
\(137\) −45140.4 −0.205477 −0.102739 0.994708i \(-0.532761\pi\)
−0.102739 + 0.994708i \(0.532761\pi\)
\(138\) 615.059 + 1065.31i 0.00274928 + 0.00476190i
\(139\) 74684.5 129357.i 0.327864 0.567877i −0.654224 0.756301i \(-0.727005\pi\)
0.982088 + 0.188424i \(0.0603379\pi\)
\(140\) −246686. −1.06371
\(141\) −4067.20 + 7044.60i −0.0172285 + 0.0298407i
\(142\) 47077.7 + 81540.9i 0.195927 + 0.339355i
\(143\) −212435. 367949.i −0.868734 1.50469i
\(144\) 106137. + 183835.i 0.426542 + 0.738792i
\(145\) −194760. −0.769273
\(146\) −34680.1 60067.7i −0.134647 0.233216i
\(147\) −5362.53 9288.18i −0.0204681 0.0354517i
\(148\) 183350. 317572.i 0.688061 1.19176i
\(149\) 69634.3 120610.i 0.256955 0.445060i −0.708469 0.705741i \(-0.750614\pi\)
0.965425 + 0.260682i \(0.0839474\pi\)
\(150\) 925.828 0.00335971
\(151\) −345221. −1.23213 −0.616063 0.787697i \(-0.711273\pi\)
−0.616063 + 0.787697i \(0.711273\pi\)
\(152\) 22055.8 38201.8i 0.0774310 0.134114i
\(153\) −90890.2 + 157426.i −0.313898 + 0.543687i
\(154\) 45264.1 + 78399.6i 0.153798 + 0.266387i
\(155\) −189666. 328510.i −0.634102 1.09830i
\(156\) 29308.2 0.0964222
\(157\) −136168. 235851.i −0.440887 0.763638i 0.556869 0.830601i \(-0.312003\pi\)
−0.997756 + 0.0669622i \(0.978669\pi\)
\(158\) 48599.8 + 84177.3i 0.154879 + 0.268258i
\(159\) −2083.18 3608.18i −0.00653484 0.0113187i
\(160\) −87373.0 + 151334.i −0.269822 + 0.467345i
\(161\) −165825. −0.504180
\(162\) 36379.2 63010.7i 0.108910 0.188637i
\(163\) −10413.6 18036.9i −0.0306996 0.0531733i 0.850267 0.526351i \(-0.176440\pi\)
−0.880967 + 0.473178i \(0.843107\pi\)
\(164\) 472893. 1.37295
\(165\) −10518.4 18218.4i −0.0300774 0.0520956i
\(166\) −10293.4 + 17828.7i −0.0289928 + 0.0502169i
\(167\) 288459. 499626.i 0.800375 1.38629i −0.118994 0.992895i \(-0.537967\pi\)
0.919369 0.393395i \(-0.128700\pi\)
\(168\) −12808.6 −0.0350129
\(169\) −288059. + 498932.i −0.775826 + 1.34377i
\(170\) −45647.3 −0.121141
\(171\) 137080. 0.358495
\(172\) −110582. 352177.i −0.285011 0.907695i
\(173\) 677893. 1.72205 0.861026 0.508562i \(-0.169823\pi\)
0.861026 + 0.508562i \(0.169823\pi\)
\(174\) −4930.27 −0.0123452
\(175\) −62402.7 + 108085.i −0.154031 + 0.266790i
\(176\) −382852. −0.931642
\(177\) −18845.5 + 32641.4i −0.0452142 + 0.0783133i
\(178\) −47636.9 + 82509.6i −0.112692 + 0.195189i
\(179\) −171637. 297283.i −0.400384 0.693486i 0.593388 0.804917i \(-0.297790\pi\)
−0.993772 + 0.111431i \(0.964457\pi\)
\(180\) −359041. −0.825968
\(181\) 148436. + 257098.i 0.336776 + 0.583314i 0.983824 0.179135i \(-0.0573300\pi\)
−0.647048 + 0.762449i \(0.723997\pi\)
\(182\) 100933. 174822.i 0.225869 0.391217i
\(183\) −27871.8 −0.0615230
\(184\) −38832.9 + 67260.6i −0.0845581 + 0.146459i
\(185\) 293464. + 508295.i 0.630413 + 1.09191i
\(186\) −4801.30 8316.09i −0.0101760 0.0176253i
\(187\) −163927. 283930.i −0.342804 0.593754i
\(188\) −250393. −0.516688
\(189\) −39883.9 69081.0i −0.0812163 0.140671i
\(190\) 17211.2 + 29810.7i 0.0345882 + 0.0599084i
\(191\) −360531. + 624458.i −0.715088 + 1.23857i 0.247838 + 0.968802i \(0.420280\pi\)
−0.962926 + 0.269767i \(0.913053\pi\)
\(192\) 11667.7 20209.1i 0.0228419 0.0395633i
\(193\) 510908. 0.987300 0.493650 0.869661i \(-0.335662\pi\)
0.493650 + 0.869661i \(0.335662\pi\)
\(194\) 1330.38 0.00253788
\(195\) −23454.8 + 40624.9i −0.0441718 + 0.0765079i
\(196\) 165070. 285909.i 0.306921 0.531603i
\(197\) 261799. + 453450.i 0.480621 + 0.832460i 0.999753 0.0222339i \(-0.00707786\pi\)
−0.519132 + 0.854694i \(0.673745\pi\)
\(198\) 65879.9 + 114107.i 0.119423 + 0.206848i
\(199\) 434612. 0.777980 0.388990 0.921242i \(-0.372824\pi\)
0.388990 + 0.921242i \(0.372824\pi\)
\(200\) 29226.9 + 50622.5i 0.0516664 + 0.0894888i
\(201\) 5849.26 + 10131.2i 0.0102120 + 0.0176877i
\(202\) −39494.2 68406.0i −0.0681012 0.117955i
\(203\) 332311. 575579.i 0.565984 0.980313i
\(204\) 22615.8 0.0380484
\(205\) −378448. + 655492.i −0.628959 + 1.08939i
\(206\) 22612.0 + 39165.2i 0.0371255 + 0.0643032i
\(207\) −241351. −0.391493
\(208\) 426857. + 739338.i 0.684107 + 1.18491i
\(209\) −123617. + 214110.i −0.195754 + 0.339056i
\(210\) 4997.57 8656.04i 0.00782007 0.0135448i
\(211\) −544697. −0.842265 −0.421133 0.906999i \(-0.638367\pi\)
−0.421133 + 0.906999i \(0.638367\pi\)
\(212\) 64124.6 111067.i 0.0979908 0.169725i
\(213\) 74664.7 0.112763
\(214\) −146821. −0.219156
\(215\) 576660. + 128561.i 0.850792 + 0.189676i
\(216\) −37360.0 −0.0544845
\(217\) 1.29447e6 1.86613
\(218\) −125186. + 216828.i −0.178408 + 0.309011i
\(219\) −55002.3 −0.0774945
\(220\) 323778. 560800.i 0.451015 0.781181i
\(221\) −365537. + 633129.i −0.503444 + 0.871990i
\(222\) 7428.91 + 12867.2i 0.0101168 + 0.0175228i
\(223\) −672053. −0.904985 −0.452492 0.891768i \(-0.649465\pi\)
−0.452492 + 0.891768i \(0.649465\pi\)
\(224\) −298161. 516430.i −0.397037 0.687688i
\(225\) −90824.5 + 157313.i −0.119604 + 0.207161i
\(226\) 242151. 0.315366
\(227\) −296180. + 512999.i −0.381497 + 0.660772i −0.991276 0.131799i \(-0.957925\pi\)
0.609780 + 0.792571i \(0.291258\pi\)
\(228\) −8527.24 14769.6i −0.0108635 0.0188162i
\(229\) −197566. 342194.i −0.248956 0.431205i 0.714280 0.699860i \(-0.246754\pi\)
−0.963236 + 0.268655i \(0.913421\pi\)
\(230\) −30303.1 52486.6i −0.0377718 0.0654227i
\(231\) 71788.3 0.0885165
\(232\) −155641. 269578.i −0.189847 0.328824i
\(233\) −192132. 332782.i −0.231851 0.401578i 0.726502 0.687165i \(-0.241145\pi\)
−0.958353 + 0.285587i \(0.907812\pi\)
\(234\) 146904. 254446.i 0.175386 0.303777i
\(235\) 200385. 347078.i 0.236699 0.409975i
\(236\) −1.16021e6 −1.35599
\(237\) 77078.7 0.0891382
\(238\) 77885.8 134902.i 0.0891284 0.154375i
\(239\) 67760.2 117364.i 0.0767326 0.132905i −0.825106 0.564978i \(-0.808885\pi\)
0.901838 + 0.432073i \(0.142218\pi\)
\(240\) 21135.2 + 36607.2i 0.0236852 + 0.0410240i
\(241\) 189808. + 328757.i 0.210510 + 0.364613i 0.951874 0.306489i \(-0.0991544\pi\)
−0.741365 + 0.671103i \(0.765821\pi\)
\(242\) −36773.0 −0.0403637
\(243\) −87132.5 150918.i −0.0946595 0.163955i
\(244\) −428975. 743007.i −0.461272 0.798947i
\(245\) 264205. + 457616.i 0.281206 + 0.487064i
\(246\) −9580.25 + 16593.5i −0.0100934 + 0.0174823i
\(247\) 551300. 0.574971
\(248\) 303139. 525052.i 0.312977 0.542092i
\(249\) 8162.63 + 14138.1i 0.00834318 + 0.0144508i
\(250\) −235535. −0.238345
\(251\) 266229. + 461122.i 0.266730 + 0.461989i 0.968015 0.250891i \(-0.0807236\pi\)
−0.701286 + 0.712880i \(0.747390\pi\)
\(252\) 612616. 1.06108e6i 0.607696 1.05256i
\(253\) 217647. 376976.i 0.213772 0.370265i
\(254\) −85129.7 −0.0827936
\(255\) −18099.0 + 31348.4i −0.0174303 + 0.0301902i
\(256\) 575186. 0.548540
\(257\) −298033. −0.281470 −0.140735 0.990047i \(-0.544947\pi\)
−0.140735 + 0.990047i \(0.544947\pi\)
\(258\) 14597.9 + 3254.46i 0.0136534 + 0.00304389i
\(259\) −2.00290e6 −1.85528
\(260\) −1.44397e6 −1.32472
\(261\) 483663. 837730.i 0.439483 0.761207i
\(262\) −252369. −0.227135
\(263\) 267487. 463302.i 0.238459 0.413023i −0.721813 0.692088i \(-0.756691\pi\)
0.960272 + 0.279065i \(0.0900243\pi\)
\(264\) 16811.4 29118.2i 0.0148455 0.0257131i
\(265\) 102636. + 177770.i 0.0897808 + 0.155505i
\(266\) −117467. −0.101791
\(267\) 37775.8 + 65429.7i 0.0324292 + 0.0561690i
\(268\) −180052. + 311859.i −0.153130 + 0.265229i
\(269\) 398325. 0.335627 0.167814 0.985819i \(-0.446329\pi\)
0.167814 + 0.985819i \(0.446329\pi\)
\(270\) 14576.9 25247.9i 0.0121690 0.0210773i
\(271\) −276209. 478407.i −0.228462 0.395708i 0.728891 0.684630i \(-0.240036\pi\)
−0.957352 + 0.288923i \(0.906703\pi\)
\(272\) 329386. + 570514.i 0.269950 + 0.467567i
\(273\) −80039.7 138633.i −0.0649978 0.112580i
\(274\) 56299.6 0.0453032
\(275\) −163808. 283724.i −0.130618 0.226238i
\(276\) 15013.6 + 26004.3i 0.0118635 + 0.0205481i
\(277\) −53363.6 + 92428.5i −0.0417874 + 0.0723780i −0.886163 0.463374i \(-0.846639\pi\)
0.844375 + 0.535752i \(0.179972\pi\)
\(278\) −93147.5 + 161336.i −0.0722869 + 0.125204i
\(279\) 1.88405e6 1.44904
\(280\) 631061. 0.481035
\(281\) −928899. + 1.60890e6i −0.701783 + 1.21552i 0.266057 + 0.963957i \(0.414279\pi\)
−0.967840 + 0.251566i \(0.919054\pi\)
\(282\) 5072.67 8786.12i 0.00379851 0.00657922i
\(283\) 688486. + 1.19249e6i 0.511009 + 0.885094i 0.999919 + 0.0127596i \(0.00406163\pi\)
−0.488909 + 0.872335i \(0.662605\pi\)
\(284\) 1.14917e6 + 1.99041e6i 0.845448 + 1.46436i
\(285\) 27296.8 0.0199067
\(286\) 264952. + 458910.i 0.191537 + 0.331751i
\(287\) −1.29146e6 2.23687e6i −0.925498 1.60301i
\(288\) −433960. 751641.i −0.308297 0.533985i
\(289\) 427860. 741075.i 0.301340 0.521936i
\(290\) 242908. 0.169608
\(291\) 527.492 913.644i 0.000365161 0.000632477i
\(292\) −846541. 1.46625e6i −0.581020 1.00636i
\(293\) −2.36069e6 −1.60646 −0.803230 0.595669i \(-0.796887\pi\)
−0.803230 + 0.595669i \(0.796887\pi\)
\(294\) 6688.22 + 11584.3i 0.00451276 + 0.00781633i
\(295\) 928493. 1.60820e6i 0.621188 1.07593i
\(296\) −469038. + 812397.i −0.311156 + 0.538938i
\(297\) 209392. 0.137743
\(298\) −86848.8 + 150427.i −0.0566530 + 0.0981259i
\(299\) −970654. −0.627894
\(300\) 22599.4 0.0144976
\(301\) −1.36387e6 + 1.48486e6i −0.867672 + 0.944644i
\(302\) 430564. 0.271657
\(303\) −62637.4 −0.0391947
\(304\) 248389. 430222.i 0.154152 0.266999i
\(305\) 1.37321e6 0.845251
\(306\) 113359. 196344.i 0.0692076 0.119871i
\(307\) 279645. 484360.i 0.169341 0.293307i −0.768847 0.639432i \(-0.779169\pi\)
0.938188 + 0.346125i \(0.112503\pi\)
\(308\) 1.10490e6 + 1.91373e6i 0.663658 + 1.14949i
\(309\) 35862.5 0.0213670
\(310\) 236553. + 409723.i 0.139806 + 0.242151i
\(311\) −918088. + 1.59018e6i −0.538249 + 0.932275i 0.460749 + 0.887530i \(0.347581\pi\)
−0.998998 + 0.0447446i \(0.985753\pi\)
\(312\) −74974.7 −0.0436042
\(313\) 1.10804e6 1.91919e6i 0.639286 1.10728i −0.346303 0.938123i \(-0.612563\pi\)
0.985590 0.169154i \(-0.0541035\pi\)
\(314\) 169831. + 294156.i 0.0972059 + 0.168366i
\(315\) 980531. + 1.69833e6i 0.556782 + 0.964375i
\(316\) 1.18632e6 + 2.05477e6i 0.668319 + 1.15756i
\(317\) 2.22654e6 1.24447 0.622233 0.782832i \(-0.286226\pi\)
0.622233 + 0.782832i \(0.286226\pi\)
\(318\) 2598.17 + 4500.17i 0.00144079 + 0.00249552i
\(319\) 872321. + 1.51090e6i 0.479954 + 0.831305i
\(320\) −574852. + 995673.i −0.313820 + 0.543553i
\(321\) −58214.0 + 100830.i −0.0315330 + 0.0546167i
\(322\) 206819. 0.111161
\(323\) 425414. 0.226885
\(324\) 888017. 1.53809e6i 0.469958 0.813991i
\(325\) −365273. + 632671.i −0.191827 + 0.332254i
\(326\) 12988.0 + 22495.9i 0.00676860 + 0.0117236i
\(327\) 99271.6 + 171943.i 0.0513400 + 0.0889234i
\(328\) −1.20973e6 −0.620876
\(329\) 683817. + 1.18441e6i 0.348297 + 0.603269i
\(330\) 13118.7 + 22722.3i 0.00663141 + 0.0114859i
\(331\) −1.18476e6 2.05206e6i −0.594374 1.02949i −0.993635 0.112648i \(-0.964067\pi\)
0.399261 0.916837i \(-0.369267\pi\)
\(332\) −251262. + 435199.i −0.125107 + 0.216692i
\(333\) −2.91513e6 −1.44061
\(334\) −359770. + 623140.i −0.176465 + 0.305647i
\(335\) −288185. 499151.i −0.140300 0.243008i
\(336\) −144248. −0.0697046
\(337\) 205094. + 355233.i 0.0983735 + 0.170388i 0.911012 0.412381i \(-0.135303\pi\)
−0.812638 + 0.582769i \(0.801969\pi\)
\(338\) 359271. 622275.i 0.171053 0.296272i
\(339\) 96012.1 166298.i 0.0453760 0.0785936i
\(340\) −1.11425e6 −0.522739
\(341\) −1.69900e6 + 2.94276e6i −0.791240 + 1.37047i
\(342\) −170968. −0.0790404
\(343\) 991566. 0.455078
\(344\) 282884. + 900922.i 0.128888 + 0.410479i
\(345\) −48060.5 −0.0217390
\(346\) −845477. −0.379675
\(347\) 1.99445e6 3.45449e6i 0.889201 1.54014i 0.0483798 0.998829i \(-0.484594\pi\)
0.840821 0.541313i \(-0.182072\pi\)
\(348\) −120348. −0.0532709
\(349\) 2.04771e6 3.54674e6i 0.899921 1.55871i 0.0723287 0.997381i \(-0.476957\pi\)
0.827593 0.561329i \(-0.189710\pi\)
\(350\) 77829.5 134805.i 0.0339605 0.0588213i
\(351\) −233459. 404364.i −0.101145 0.175188i
\(352\) 1.56536e6 0.673374
\(353\) −1.85324e6 3.20991e6i −0.791581 1.37106i −0.924988 0.379997i \(-0.875925\pi\)
0.133407 0.991061i \(-0.457408\pi\)
\(354\) 23504.4 40710.8i 0.00996874 0.0172664i
\(355\) −3.67863e6 −1.54923
\(356\) −1.16282e6 + 2.01406e6i −0.486280 + 0.842262i
\(357\) −61763.1 106977.i −0.0256483 0.0444241i
\(358\) 214067. + 370775.i 0.0882760 + 0.152899i
\(359\) −836253. 1.44843e6i −0.342453 0.593147i 0.642434 0.766341i \(-0.277925\pi\)
−0.984888 + 0.173194i \(0.944591\pi\)
\(360\) 918482. 0.373521
\(361\) 1.07765e6 + 1.86654e6i 0.435220 + 0.753823i
\(362\) −185131. 320656.i −0.0742519 0.128608i
\(363\) −14580.4 + 25254.0i −0.00580769 + 0.0100592i
\(364\) 2.46378e6 4.26740e6i 0.974651 1.68815i
\(365\) 2.70989e6 1.06468
\(366\) 34762.1 0.0135645
\(367\) −865343. + 1.49882e6i −0.335369 + 0.580876i −0.983556 0.180605i \(-0.942194\pi\)
0.648187 + 0.761482i \(0.275528\pi\)
\(368\) −437329. + 757476.i −0.168341 + 0.291574i
\(369\) −1.87966e6 3.25567e6i −0.718644 1.24473i
\(370\) −366012. 633952.i −0.138992 0.240742i
\(371\) −700490. −0.264221
\(372\) −117200. 202996.i −0.0439106 0.0760553i
\(373\) 1.07620e6 + 1.86403e6i 0.400517 + 0.693716i 0.993788 0.111287i \(-0.0354971\pi\)
−0.593271 + 0.805003i \(0.702164\pi\)
\(374\) 204452. + 354121.i 0.0755808 + 0.130910i
\(375\) −93389.1 + 161755.i −0.0342940 + 0.0593989i
\(376\) 640544. 0.233657
\(377\) 1.94517e6 3.36914e6i 0.704863 1.22086i
\(378\) 49743.7 + 86158.7i 0.0179064 + 0.0310148i
\(379\) −526611. −0.188318 −0.0941591 0.995557i \(-0.530016\pi\)
−0.0941591 + 0.995557i \(0.530016\pi\)
\(380\) 420126. + 727679.i 0.149252 + 0.258512i
\(381\) −33753.7 + 58463.1i −0.0119127 + 0.0206333i
\(382\) 449659. 778832.i 0.157661 0.273077i
\(383\) −3.64301e6 −1.26900 −0.634502 0.772921i \(-0.718795\pi\)
−0.634502 + 0.772921i \(0.718795\pi\)
\(384\) −71300.9 + 123497.i −0.0246756 + 0.0427393i
\(385\) −3.53691e6 −1.21611
\(386\) −637211. −0.217678
\(387\) −1.98505e6 + 2.16114e6i −0.673742 + 0.733510i
\(388\) 32474.6 0.0109513
\(389\) 1.77768e6 0.595636 0.297818 0.954623i \(-0.403741\pi\)
0.297818 + 0.954623i \(0.403741\pi\)
\(390\) 29253.1 50667.9i 0.00973893 0.0168683i
\(391\) −749010. −0.247768
\(392\) −422273. + 731398.i −0.138796 + 0.240402i
\(393\) −100064. + 173316.i −0.0326810 + 0.0566052i
\(394\) −326520. 565548.i −0.105967 0.183539i
\(395\) −3.79756e6 −1.22465
\(396\) 1.60813e6 + 2.78536e6i 0.515326 + 0.892571i
\(397\) 69822.7 120937.i 0.0222342 0.0385107i −0.854694 0.519132i \(-0.826255\pi\)
0.876928 + 0.480621i \(0.159589\pi\)
\(398\) −542053. −0.171528
\(399\) −46575.3 + 80670.8i −0.0146461 + 0.0253679i
\(400\) 329148. + 570101.i 0.102859 + 0.178157i
\(401\) −2.81406e6 4.87410e6i −0.873923 1.51368i −0.857906 0.513807i \(-0.828235\pi\)
−0.0160174 0.999872i \(-0.505099\pi\)
\(402\) −7295.27 12635.8i −0.00225152 0.00389975i
\(403\) 7.57715e6 2.32404
\(404\) −964053. 1.66979e6i −0.293865 0.508989i
\(405\) 1.42133e6 + 2.46181e6i 0.430583 + 0.745792i
\(406\) −414462. + 717869.i −0.124787 + 0.216138i
\(407\) 2.62882e6 4.55325e6i 0.786637 1.36250i
\(408\) −57854.6 −0.0172063
\(409\) 269707. 0.0797232 0.0398616 0.999205i \(-0.487308\pi\)
0.0398616 + 0.999205i \(0.487308\pi\)
\(410\) 472006. 817538.i 0.138672 0.240186i
\(411\) 22322.7 38664.0i 0.00651841 0.0112902i
\(412\) 551960. + 956022.i 0.160201 + 0.277476i
\(413\) 3.16849e6 + 5.48798e6i 0.914065 + 1.58321i
\(414\) 301017. 0.0863157
\(415\) −402162. 696564.i −0.114625 0.198537i
\(416\) −1.74528e6 3.02291e6i −0.494460 0.856430i
\(417\) 73865.5 + 127939.i 0.0208018 + 0.0360298i
\(418\) 154176. 267041.i 0.0431595 0.0747545i
\(419\) 1.57291e6 0.437692 0.218846 0.975759i \(-0.429771\pi\)
0.218846 + 0.975759i \(0.429771\pi\)
\(420\) 121991. 211294.i 0.0337445 0.0584472i
\(421\) −134897. 233649.i −0.0370935 0.0642478i 0.846883 0.531780i \(-0.178477\pi\)
−0.883976 + 0.467532i \(0.845143\pi\)
\(422\) 679353. 0.185701
\(423\) 995266. + 1.72385e6i 0.270451 + 0.468434i
\(424\) −164040. + 284126.i −0.0443135 + 0.0767533i
\(425\) −281865. + 488204.i −0.0756952 + 0.131108i
\(426\) −93122.8 −0.0248618
\(427\) −2.34304e6 + 4.05826e6i −0.621884 + 1.07713i
\(428\) −3.58389e6 −0.945682
\(429\) 420211. 0.110236
\(430\) −719218. 160343.i −0.187581 0.0418194i
\(431\) 6.42657e6 1.66643 0.833213 0.552952i \(-0.186499\pi\)
0.833213 + 0.552952i \(0.186499\pi\)
\(432\) −420742. −0.108469
\(433\) −683599. + 1.18403e6i −0.175219 + 0.303489i −0.940237 0.340520i \(-0.889397\pi\)
0.765018 + 0.644009i \(0.222730\pi\)
\(434\) −1.61448e6 −0.411442
\(435\) 96312.3 166818.i 0.0244039 0.0422687i
\(436\) −3.05578e6 + 5.29277e6i −0.769849 + 1.33342i
\(437\) 282413. + 489153.i 0.0707426 + 0.122530i
\(438\) 68599.6 0.0170858
\(439\) 563506. + 976022.i 0.139552 + 0.241712i 0.927327 0.374251i \(-0.122100\pi\)
−0.787775 + 0.615963i \(0.788767\pi\)
\(440\) −828274. + 1.43461e6i −0.203959 + 0.353267i
\(441\) −2.62448e6 −0.642609
\(442\) 455903. 789647.i 0.110998 0.192255i
\(443\) 3.37733e6 + 5.84971e6i 0.817644 + 1.41620i 0.907414 + 0.420238i \(0.138054\pi\)
−0.0897697 + 0.995963i \(0.528613\pi\)
\(444\) 181340. + 314089.i 0.0436551 + 0.0756129i
\(445\) −1.86116e6 3.22363e6i −0.445538 0.771694i
\(446\) 838193. 0.199529
\(447\) 68870.7 + 119288.i 0.0163029 + 0.0282375i
\(448\) −1.96169e6 3.39774e6i −0.461779 0.799825i
\(449\) −2.34313e6 + 4.05843e6i −0.548506 + 0.950040i 0.449871 + 0.893093i \(0.351470\pi\)
−0.998377 + 0.0569469i \(0.981863\pi\)
\(450\) 113277. 196202.i 0.0263701 0.0456744i
\(451\) 6.78020e6 1.56964
\(452\) 5.91089e6 1.36084
\(453\) 170718. 295692.i 0.0390871 0.0677008i
\(454\) 369399. 639819.i 0.0841117 0.145686i
\(455\) 3.94345e6 + 6.83025e6i 0.892992 + 1.54671i
\(456\) 21814.0 + 37782.9i 0.00491273 + 0.00850909i
\(457\) −1.94840e6 −0.436403 −0.218202 0.975904i \(-0.570019\pi\)
−0.218202 + 0.975904i \(0.570019\pi\)
\(458\) 246406. + 426789.i 0.0548894 + 0.0950712i
\(459\) −180150. 312029.i −0.0399120 0.0691296i
\(460\) −739699. 1.28120e6i −0.162990 0.282307i
\(461\) −1.47382e6 + 2.55272e6i −0.322991 + 0.559437i −0.981104 0.193482i \(-0.938022\pi\)
0.658112 + 0.752920i \(0.271355\pi\)
\(462\) −89535.4 −0.0195159
\(463\) −3.81961e6 + 6.61576e6i −0.828069 + 1.43426i 0.0714825 + 0.997442i \(0.477227\pi\)
−0.899551 + 0.436815i \(0.856106\pi\)
\(464\) −1.75280e6 3.03594e6i −0.377952 0.654632i
\(465\) 375171. 0.0804632
\(466\) 239629. + 415050.i 0.0511181 + 0.0885391i
\(467\) 850970. 1.47392e6i 0.180560 0.312740i −0.761511 0.648152i \(-0.775542\pi\)
0.942071 + 0.335412i \(0.108876\pi\)
\(468\) 3.58593e6 6.21101e6i 0.756811 1.31083i
\(469\) 1.96687e6 0.412898
\(470\) −249923. + 432880.i −0.0521870 + 0.0903905i
\(471\) 269350. 0.0559455
\(472\) 2.96798e6 0.613206
\(473\) −1.58548e6 5.04941e6i −0.325843 1.03774i
\(474\) −96133.6 −0.0196530
\(475\) 425106. 0.0864497
\(476\) 1.90119e6 3.29296e6i 0.384599 0.666146i
\(477\) −1.01953e6 −0.205166
\(478\) −84511.4 + 146378.i −0.0169179 + 0.0293026i
\(479\) 730267. 1.26486e6i 0.145426 0.251886i −0.784106 0.620627i \(-0.786878\pi\)
0.929532 + 0.368742i \(0.120211\pi\)
\(480\) −86414.8 149675.i −0.0171193 0.0296514i
\(481\) −1.17239e7 −2.31052
\(482\) −236731. 410030.i −0.0464128 0.0803893i
\(483\) 82003.4 142034.i 0.0159943 0.0277029i
\(484\) −897629. −0.174174
\(485\) −25988.8 + 45014.0i −0.00501687 + 0.00868947i
\(486\) 108673. + 188227.i 0.0208704 + 0.0361485i
\(487\) −4.30934e6 7.46399e6i −0.823357 1.42610i −0.903169 0.429286i \(-0.858765\pi\)
0.0798119 0.996810i \(-0.474568\pi\)
\(488\) 1.09738e6 + 1.90072e6i 0.208597 + 0.361301i
\(489\) 20598.9 0.00389557
\(490\) −329520. 570745.i −0.0619999 0.107387i
\(491\) −2.38488e6 4.13072e6i −0.446439 0.773255i 0.551712 0.834034i \(-0.313975\pi\)
−0.998151 + 0.0607798i \(0.980641\pi\)
\(492\) −233854. + 405047.i −0.0435544 + 0.0754384i
\(493\) 1.50100e6 2.59981e6i 0.278140 0.481753i
\(494\) −687589. −0.126769
\(495\) −5.14782e6 −0.944302
\(496\) 3.41389e6 5.91304e6i 0.623083 1.07921i
\(497\) 6.27667e6 1.08715e7i 1.13983 1.97424i
\(498\) −10180.5 17633.2i −0.00183949 0.00318609i
\(499\) 2.58239e6 + 4.47283e6i 0.464269 + 0.804138i 0.999168 0.0407780i \(-0.0129837\pi\)
−0.534899 + 0.844916i \(0.679650\pi\)
\(500\) −5.74941e6 −1.02849
\(501\) 285296. + 494147.i 0.0507810 + 0.0879553i
\(502\) −332044. 575118.i −0.0588081 0.101859i
\(503\) 4.79895e6 + 8.31202e6i 0.845719 + 1.46483i 0.884995 + 0.465600i \(0.154161\pi\)
−0.0392764 + 0.999228i \(0.512505\pi\)
\(504\) −1.56716e6 + 2.71441e6i −0.274813 + 0.475991i
\(505\) 3.08606e6 0.538488
\(506\) −271452. + 470169.i −0.0471321 + 0.0816353i
\(507\) −284900. 493461.i −0.0492235 0.0852576i
\(508\) −2.07801e6 −0.357264
\(509\) 1.08351e6 + 1.87670e6i 0.185370 + 0.321070i 0.943701 0.330800i \(-0.107318\pi\)
−0.758331 + 0.651869i \(0.773985\pi\)
\(510\) 22573.3 39098.2i 0.00384300 0.00665627i
\(511\) −4.62376e6 + 8.00858e6i −0.783326 + 1.35676i
\(512\) −5.33123e6 −0.898779
\(513\) −135851. + 235300.i −0.0227912 + 0.0394756i
\(514\) 371711. 0.0620580
\(515\) −1.76690e6 −0.293557
\(516\) 356334. + 79441.3i 0.0589160 + 0.0131348i
\(517\) −3.59006e6 −0.590712
\(518\) 2.49804e6 0.409048
\(519\) −335230. + 580635.i −0.0546291 + 0.0946204i
\(520\) 3.69390e6 0.599069
\(521\) 5.48802e6 9.50552e6i 0.885770 1.53420i 0.0409416 0.999162i \(-0.486964\pi\)
0.844828 0.535037i \(-0.179702\pi\)
\(522\) −603231. + 1.04483e6i −0.0968964 + 0.167830i
\(523\) −1.04582e6 1.81142e6i −0.167188 0.289578i 0.770242 0.637751i \(-0.220135\pi\)
−0.937430 + 0.348174i \(0.886802\pi\)
\(524\) −6.16033e6 −0.980112
\(525\) −61718.4 106899.i −0.00977275 0.0169269i
\(526\) −333614. + 577836.i −0.0525751 + 0.0910627i
\(527\) 5.84695e6 0.917071
\(528\) 189327. 327923.i 0.0295547 0.0511903i
\(529\) 2.72094e6 + 4.71280e6i 0.422746 + 0.732217i
\(530\) −128009. 221717.i −0.0197947 0.0342854i
\(531\) 4.61160e6 + 7.98752e6i 0.709766 + 1.22935i
\(532\) −2.86736e6 −0.439242
\(533\) −7.55952e6 1.30935e7i −1.15259 1.99635i
\(534\) −47114.5 81604.8i −0.00714993 0.0123840i
\(535\) 2.86812e6 4.96774e6i 0.433225 0.750368i
\(536\) 460600. 797783.i 0.0692488 0.119942i
\(537\) 339509. 0.0508060
\(538\) −496796. −0.0739985
\(539\) 2.36672e6 4.09927e6i 0.350893 0.607764i
\(540\) 355822. 616301.i 0.0525107 0.0909512i
\(541\) 5.17791e6 + 8.96840e6i 0.760608 + 1.31741i 0.942538 + 0.334100i \(0.108432\pi\)
−0.181929 + 0.983312i \(0.558234\pi\)
\(542\) 344491. + 596676.i 0.0503709 + 0.0872449i
\(543\) −293616. −0.0427346
\(544\) −1.34675e6 2.33264e6i −0.195115 0.337949i
\(545\) −4.89098e6 8.47142e6i −0.705349 1.22170i
\(546\) 99826.6 + 172905.i 0.0143306 + 0.0248213i
\(547\) −1.59753e6 + 2.76700e6i −0.228287 + 0.395404i −0.957300 0.289095i \(-0.906646\pi\)
0.729014 + 0.684499i \(0.239979\pi\)
\(548\) 1.37427e6 0.195489
\(549\) −3.41019e6 + 5.90662e6i −0.482889 + 0.836389i
\(550\) 204304. + 353865.i 0.0287985 + 0.0498805i
\(551\) −2.26380e6 −0.317657
\(552\) −38407.1 66523.0i −0.00536492 0.00929232i
\(553\) 6.47961e6 1.12230e7i 0.901023 1.56062i
\(554\) 66555.8 115278.i 0.00921322 0.0159578i
\(555\) −580492. −0.0799951
\(556\) −2.27373e6 + 3.93822e6i −0.311926 + 0.540272i
\(557\) 7.52794e6 1.02811 0.514053 0.857758i \(-0.328143\pi\)
0.514053 + 0.857758i \(0.328143\pi\)
\(558\) −2.34981e6 −0.319482
\(559\) −7.98336e6 + 8.69157e6i −1.08058 + 1.17644i
\(560\) 7.10690e6 0.957657
\(561\) 324258. 0.0434995
\(562\) 1.15853e6 2.00664e6i 0.154728 0.267996i
\(563\) −1.99120e6 −0.264754 −0.132377 0.991199i \(-0.542261\pi\)
−0.132377 + 0.991199i \(0.542261\pi\)
\(564\) 123824. 214469.i 0.0163910 0.0283901i
\(565\) −4.73038e6 + 8.19327e6i −0.623412 + 1.07978i
\(566\) −858689. 1.48729e6i −0.112666 0.195144i
\(567\) −9.70059e6 −1.26719
\(568\) −2.93974e6 5.09178e6i −0.382330 0.662214i
\(569\) 2.63816e6 4.56943e6i 0.341602 0.591672i −0.643128 0.765758i \(-0.722364\pi\)
0.984730 + 0.174086i \(0.0556972\pi\)
\(570\) −34044.9 −0.00438900
\(571\) 2.48880e6 4.31072e6i 0.319447 0.553299i −0.660926 0.750451i \(-0.729836\pi\)
0.980373 + 0.197153i \(0.0631695\pi\)
\(572\) 6.46748e6 + 1.12020e7i 0.826504 + 1.43155i
\(573\) −356577. 617610.i −0.0453699 0.0785829i
\(574\) 1.61072e6 + 2.78985e6i 0.204052 + 0.353429i
\(575\) −748469. −0.0944070
\(576\) −2.85515e6 4.94526e6i −0.358569 0.621060i
\(577\) 7.73379e6 + 1.33953e7i 0.967059 + 1.67499i 0.703979 + 0.710221i \(0.251405\pi\)
0.263080 + 0.964774i \(0.415262\pi\)
\(578\) −533632. + 924278.i −0.0664389 + 0.115076i
\(579\) −252652. + 437607.i −0.0313204 + 0.0542485i
\(580\) 5.92937e6 0.731878
\(581\) 2.74476e6 0.337337
\(582\) −657.896 + 1139.51i −8.05099e−5 + 0.000139447i
\(583\) 919399. 1.59245e6i 0.112030 0.194041i
\(584\) 2.16558e6 + 3.75090e6i 0.262750 + 0.455096i
\(585\) 5.73952e6 + 9.94113e6i 0.693403 + 1.20101i
\(586\) 2.94428e6 0.354189
\(587\) −1.72030e6 2.97965e6i −0.206068 0.356920i 0.744405 0.667729i \(-0.232733\pi\)
−0.950472 + 0.310809i \(0.899400\pi\)
\(588\) 163259. + 282774.i 0.0194731 + 0.0337284i
\(589\) −2.20458e6 3.81844e6i −0.261841 0.453522i
\(590\) −1.15803e6 + 2.00576e6i −0.136959 + 0.237219i
\(591\) −517857. −0.0609875
\(592\) −5.28222e6 + 9.14907e6i −0.619458 + 1.07293i
\(593\) −5.95063e6 1.03068e7i −0.694906 1.20361i −0.970212 0.242256i \(-0.922113\pi\)
0.275307 0.961356i \(-0.411221\pi\)
\(594\) −261156. −0.0303693
\(595\) 3.04298e6 + 5.27060e6i 0.352377 + 0.610334i
\(596\) −2.11998e6 + 3.67191e6i −0.244465 + 0.423425i
\(597\) −214923. + 372257.i −0.0246801 + 0.0427472i
\(598\) 1.21061e6 0.138437
\(599\) −2.25127e6 + 3.89931e6i −0.256366 + 0.444039i −0.965266 0.261270i \(-0.915859\pi\)
0.708900 + 0.705309i \(0.249192\pi\)
\(600\) −57812.8 −0.00655611
\(601\) 2.84128e6 0.320869 0.160434 0.987047i \(-0.448711\pi\)
0.160434 + 0.987047i \(0.448711\pi\)
\(602\) 1.70103e6 1.85193e6i 0.191303 0.208273i
\(603\) 2.86269e6 0.320613
\(604\) 1.05101e7 1.17223
\(605\) 718357. 1.24423e6i 0.0797906 0.138201i
\(606\) 78122.2 0.00864157
\(607\) −4.72627e6 + 8.18614e6i −0.520651 + 0.901794i 0.479061 + 0.877782i \(0.340977\pi\)
−0.999712 + 0.0240121i \(0.992356\pi\)
\(608\) −1.01558e6 + 1.75904e6i −0.111418 + 0.192982i
\(609\) 328666. + 569267.i 0.0359097 + 0.0621975i
\(610\) −1.71268e6 −0.186360
\(611\) 4.00271e6 + 6.93289e6i 0.433761 + 0.751296i
\(612\) 2.76710e6 4.79276e6i 0.298639 0.517258i
\(613\) −9.44159e6 −1.01483 −0.507416 0.861701i \(-0.669399\pi\)
−0.507416 + 0.861701i \(0.669399\pi\)
\(614\) −348777. + 604100.i −0.0373360 + 0.0646678i
\(615\) −374298. 648304.i −0.0399053 0.0691179i
\(616\) −2.82649e6 4.89562e6i −0.300120 0.519824i
\(617\) −1.55546e6 2.69414e6i −0.164493 0.284909i 0.771982 0.635644i \(-0.219265\pi\)
−0.936475 + 0.350734i \(0.885932\pi\)
\(618\) −44728.2 −0.00471096
\(619\) −1.44636e6 2.50517e6i −0.151722 0.262791i 0.780138 0.625607i \(-0.215149\pi\)
−0.931861 + 0.362816i \(0.881815\pi\)
\(620\) 5.77427e6 + 1.00013e7i 0.603278 + 1.04491i
\(621\) 239187. 414284.i 0.0248891 0.0431091i
\(622\) 1.14505e6 1.98329e6i 0.118672 0.205546i
\(623\) 1.27025e7 1.31120
\(624\) −844352. −0.0868084
\(625\) 3.42842e6 5.93820e6i 0.351070 0.608071i
\(626\) −1.38196e6 + 2.39363e6i −0.140949 + 0.244130i
\(627\) −122261. 211762.i −0.0124199 0.0215119i
\(628\) 4.14557e6 + 7.18034e6i 0.419455 + 0.726517i
\(629\) −9.04681e6 −0.911736
\(630\) −1.22293e6 2.11818e6i −0.122758 0.212624i
\(631\) −3.76998e6 6.52979e6i −0.376934 0.652868i 0.613681 0.789554i \(-0.289688\pi\)
−0.990614 + 0.136686i \(0.956355\pi\)
\(632\) −3.03479e6 5.25640e6i −0.302228 0.523475i
\(633\) 269362. 466549.i 0.0267194 0.0462794i
\(634\) −2.77697e6 −0.274378
\(635\) 1.66300e6 2.88040e6i 0.163666 0.283477i
\(636\) 63421.4 + 109849.i 0.00621718 + 0.0107685i
\(637\) −1.05550e7 −1.03065
\(638\) −1.08797e6 1.88442e6i −0.105819 0.183285i
\(639\) 9.13543e6 1.58230e7i 0.885068 1.53298i
\(640\) 3.51290e6 6.08452e6i 0.339012 0.587187i
\(641\) −6.12124e6 −0.588429 −0.294214 0.955739i \(-0.595058\pi\)
−0.294214 + 0.955739i \(0.595058\pi\)
\(642\) 72605.3 125756.i 0.00695233 0.0120418i
\(643\) −8.80693e6 −0.840035 −0.420017 0.907516i \(-0.637976\pi\)
−0.420017 + 0.907516i \(0.637976\pi\)
\(644\) 5.04846e6 0.479672
\(645\) −395284. + 430350.i −0.0374119 + 0.0407308i
\(646\) −530582. −0.0500231
\(647\) 1.51956e7 1.42711 0.713557 0.700598i \(-0.247083\pi\)
0.713557 + 0.700598i \(0.247083\pi\)
\(648\) −2.27168e6 + 3.93467e6i −0.212525 + 0.368104i
\(649\) −1.66347e7 −1.55025
\(650\) 455573. 789076.i 0.0422936 0.0732547i
\(651\) −640137. + 1.10875e6i −0.0591999 + 0.102537i
\(652\) 317037. + 549125.i 0.0292073 + 0.0505885i
\(653\) 1.10998e7 1.01867 0.509335 0.860568i \(-0.329891\pi\)
0.509335 + 0.860568i \(0.329891\pi\)
\(654\) −123813. 214450.i −0.0113193 0.0196057i
\(655\) 4.93001e6 8.53902e6i 0.448998 0.777687i
\(656\) −1.36238e7 −1.23606
\(657\) −6.72968e6 + 1.16561e7i −0.608248 + 1.05352i
\(658\) −852865. 1.47721e6i −0.0767920 0.133008i
\(659\) 654712. + 1.13399e6i 0.0587268 + 0.101718i 0.893894 0.448278i \(-0.147963\pi\)
−0.835167 + 0.549996i \(0.814629\pi\)
\(660\) 320228. + 554650.i 0.0286153 + 0.0495632i
\(661\) 7.77181e6 0.691861 0.345930 0.938260i \(-0.387563\pi\)
0.345930 + 0.938260i \(0.387563\pi\)
\(662\) 1.47765e6 + 2.55936e6i 0.131046 + 0.226979i
\(663\) −361529. 626186.i −0.0319418 0.0553248i
\(664\) 642767. 1.11331e6i 0.0565761 0.0979928i
\(665\) 2.29470e6 3.97454e6i 0.201220 0.348524i
\(666\) 3.63579e6 0.317624
\(667\) 3.98579e6 0.346896
\(668\) −8.78199e6 + 1.52109e7i −0.761468 + 1.31890i
\(669\) 332341. 575632.i 0.0287091 0.0497256i
\(670\) 359428. + 622547.i 0.0309332 + 0.0535779i
\(671\) −6.15051e6 1.06530e7i −0.527357 0.913410i
\(672\) 589782. 0.0503812
\(673\) −3.86953e6 6.70222e6i −0.329322 0.570402i 0.653056 0.757310i \(-0.273487\pi\)
−0.982377 + 0.186908i \(0.940153\pi\)
\(674\) −255796. 443052.i −0.0216892 0.0375668i
\(675\) −180020. 311804.i −0.0152076 0.0263404i
\(676\) 8.76979e6 1.51897e7i 0.738113 1.27845i
\(677\) −2.00333e7 −1.67989 −0.839944 0.542673i \(-0.817412\pi\)
−0.839944 + 0.542673i \(0.817412\pi\)
\(678\) −119748. + 207409.i −0.0100044 + 0.0173282i
\(679\) −88687.1 153611.i −0.00738220 0.0127864i
\(680\) 2.85042e6 0.236394
\(681\) −292932. 507373.i −0.0242047 0.0419237i
\(682\) 2.11902e6 3.67025e6i 0.174451 0.302158i
\(683\) −2.04056e6 + 3.53435e6i −0.167377 + 0.289906i −0.937497 0.347993i \(-0.886863\pi\)
0.770120 + 0.637900i \(0.220197\pi\)
\(684\) −4.17332e6 −0.341068
\(685\) −1.09981e6 + 1.90492e6i −0.0895551 + 0.155114i
\(686\) −1.23669e6 −0.100335
\(687\) 390798. 0.0315908
\(688\) 3.18579e6 + 1.01460e7i 0.256594 + 0.817193i
\(689\) −4.10030e6 −0.329054
\(690\) 59941.7 0.00479299
\(691\) 1.14627e7 1.98540e7i 0.913254 1.58180i 0.103816 0.994597i \(-0.466895\pi\)
0.809438 0.587205i \(-0.199772\pi\)
\(692\) −2.06381e7 −1.63834
\(693\) 8.78349e6 1.52135e7i 0.694759 1.20336i
\(694\) −2.48751e6 + 4.30849e6i −0.196049 + 0.339568i
\(695\) −3.63925e6 6.30337e6i −0.285792 0.495007i
\(696\) 307868. 0.0240903
\(697\) −5.83334e6 1.01036e7i −0.454816 0.787764i
\(698\) −2.55393e6 + 4.42353e6i −0.198413 + 0.343662i
\(699\) 380049. 0.0294203
\(700\) 1.89982e6 3.29058e6i 0.146544 0.253821i
\(701\) 7.78266e6 + 1.34800e7i 0.598182 + 1.03608i 0.993089 + 0.117360i \(0.0374432\pi\)
−0.394908 + 0.918721i \(0.629223\pi\)
\(702\) 291174. + 504328.i 0.0223002 + 0.0386251i
\(703\) 3.41108e6 + 5.90817e6i 0.260318 + 0.450884i
\(704\) 1.02989e7 0.783178
\(705\) 198188. + 343272.i 0.0150177 + 0.0260115i
\(706\) 2.31139e6 + 4.00344e6i 0.174526 + 0.302288i
\(707\) −5.26560e6 + 9.12029e6i −0.396186 + 0.686215i
\(708\) 573741. 993749.i 0.0430163 0.0745064i
\(709\) 2.09179e7 1.56279 0.781397 0.624034i \(-0.214507\pi\)
0.781397 + 0.624034i \(0.214507\pi\)
\(710\) 4.58803e6 0.341571
\(711\) 9.43079e6 1.63346e7i 0.699639 1.21181i
\(712\) 2.97466e6 5.15227e6i 0.219906 0.380889i
\(713\) 3.88152e6 + 6.72299e6i 0.285942 + 0.495267i
\(714\) 77031.7 + 133423.i 0.00565489 + 0.00979455i
\(715\) −2.07032e7 −1.51451
\(716\) 5.22538e6 + 9.05063e6i 0.380921 + 0.659775i
\(717\) 67017.2 + 116077.i 0.00486842 + 0.00843235i
\(718\) 1.04299e6 + 1.80650e6i 0.0755035 + 0.130776i
\(719\) −3.53782e6 + 6.12768e6i −0.255219 + 0.442052i −0.964955 0.262416i \(-0.915481\pi\)
0.709736 + 0.704468i \(0.248814\pi\)
\(720\) 1.03438e7 0.743615
\(721\) 3.01477e6 5.22174e6i 0.215981 0.374091i
\(722\) −1.34406e6 2.32797e6i −0.0959565 0.166202i
\(723\) −375453. −0.0267122
\(724\) −4.51904e6 7.82721e6i −0.320406 0.554959i
\(725\) 1.49992e6 2.59793e6i 0.105980 0.183562i
\(726\) 18184.9 31497.1i 0.00128047 0.00221784i
\(727\) −1.38648e7 −0.972919 −0.486460 0.873703i \(-0.661712\pi\)
−0.486460 + 0.873703i \(0.661712\pi\)
\(728\) −6.30273e6 + 1.09167e7i −0.440758 + 0.763416i
\(729\) −1.40035e7 −0.975928
\(730\) −3.37981e6 −0.234739
\(731\) −6.16040e6 + 6.70689e6i −0.426398 + 0.464224i
\(732\) 848542. 0.0585323
\(733\) −5.59992e6 −0.384965 −0.192483 0.981300i \(-0.561654\pi\)
−0.192483 + 0.981300i \(0.561654\pi\)
\(734\) 1.07927e6 1.86934e6i 0.0739416 0.128071i
\(735\) −522615. −0.0356832
\(736\) 1.78810e6 3.09707e6i 0.121674 0.210745i
\(737\) −2.58153e6 + 4.47134e6i −0.175069 + 0.303228i
\(738\) 2.34434e6 + 4.06051e6i 0.158445 + 0.274435i
\(739\) 9.61223e6 0.647460 0.323730 0.946149i \(-0.395063\pi\)
0.323730 + 0.946149i \(0.395063\pi\)
\(740\) −8.93435e6 1.54748e7i −0.599769 1.03883i
\(741\) −272627. + 472204.i −0.0182400 + 0.0315925i
\(742\) 873660. 0.0582549
\(743\) −1.22155e7 + 2.11579e7i −0.811783 + 1.40605i 0.0998321 + 0.995004i \(0.468169\pi\)
−0.911615 + 0.411045i \(0.865164\pi\)
\(744\) 299814. + 519294.i 0.0198573 + 0.0343939i
\(745\) −3.39316e6 5.87713e6i −0.223983 0.387949i
\(746\) −1.34225e6 2.32485e6i −0.0883053 0.152949i
\(747\) 3.99488e6 0.261940
\(748\) 4.99066e6 + 8.64408e6i 0.326140 + 0.564891i
\(749\) 9.78749e6 + 1.69524e7i 0.637481 + 1.10415i
\(750\) 116476. 201742.i 0.00756107 0.0130962i
\(751\) −23719.0 + 41082.5i −0.00153461 + 0.00265802i −0.866792 0.498670i \(-0.833822\pi\)
0.865257 + 0.501328i \(0.167155\pi\)
\(752\) 7.21369e6 0.465171
\(753\) −526619. −0.0338461
\(754\) −2.42604e6 + 4.20203e6i −0.155407 + 0.269173i
\(755\) −8.41103e6 + 1.45683e7i −0.537009 + 0.930128i
\(756\) 1.21424e6 + 2.10313e6i 0.0772683 + 0.133833i
\(757\) 1.24520e7 + 2.15675e7i 0.789769 + 1.36792i 0.926108 + 0.377258i \(0.123133\pi\)
−0.136339 + 0.990662i \(0.543534\pi\)
\(758\) 656797. 0.0415200
\(759\) 215260. + 372842.i 0.0135631 + 0.0234920i
\(760\) −1.07474e6 1.86151e6i −0.0674950 0.116905i
\(761\) −1.01477e7 1.75763e7i −0.635193 1.10019i −0.986474 0.163916i \(-0.947587\pi\)
0.351282 0.936270i \(-0.385746\pi\)
\(762\) 42098.1 72916.0i 0.00262648 0.00454920i
\(763\) 3.33810e7 2.07581
\(764\) 1.09762e7 1.90113e7i 0.680327 1.17836i
\(765\) 4.42893e6 + 7.67113e6i 0.273618 + 0.473921i
\(766\) 4.54360e6 0.279788
\(767\) 1.85467e7 + 3.21238e7i 1.13835 + 1.97169i
\(768\) −284439. + 492663.i −0.0174015 + 0.0301403i
\(769\) 4.80391e6 8.32062e6i 0.292940 0.507388i −0.681563 0.731759i \(-0.738700\pi\)
0.974504 + 0.224372i \(0.0720329\pi\)
\(770\) 4.41129e6 0.268126
\(771\) 147383. 255274.i 0.00892915 0.0154657i
\(772\) −1.55543e7 −0.939307
\(773\) 1.99799e7