Properties

Label 43.6.c.a.36.9
Level $43$
Weight $6$
Character 43.36
Analytic conductor $6.897$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 36.9
Character \(\chi\) \(=\) 43.36
Dual form 43.6.c.a.6.9

$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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 0.849728 0.527222i \(-0.176766\pi\)
−0.881451 + 0.472275i \(0.843433\pi\)
\(4\) −30.4445 −0.951389
\(5\) 24.3642 + 42.2000i 0.435840 + 0.754896i 0.997364 0.0725640i \(-0.0231182\pi\)
−0.561524 + 0.827460i \(0.689785\pi\)
\(6\) 0.616768 + 1.06827i 0.00699429 + 0.0121145i
\(7\) 83.1429 144.008i 0.641328 1.11081i −0.343809 0.939040i \(-0.611717\pi\)
0.985137 0.171773i \(-0.0549495\pi\)
\(8\) 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 −0.121772 0.992558i \(-0.538858\pi\)
0.920466 0.390821i \(-0.127809\pi\)
\(14\) −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 −0.664306 0.747460i \(-0.731273\pi\)
0.979473 + 0.201576i \(0.0646063\pi\)
\(18\) −150.926 + 261.412i −0.109795 + 0.190171i
\(19\) 283.197 + 490.512i 0.179972 + 0.311721i 0.941871 0.335975i \(-0.109066\pi\)
−0.761899 + 0.647696i \(0.775733\pi\)
\(20\) −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 0.750866 0.660455i \(-0.229636\pi\)
−0.947404 + 0.320042i \(0.896303\pi\)
\(24\) −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 −0.997783 0.0665481i \(-0.978801\pi\)
0.556524 + 0.830832i \(0.312135\pi\)
\(30\) −30.0541 + 52.0552i −0.00609678 + 0.0105599i
\(31\) 3892.30 + 6741.67i 0.727449 + 1.25998i 0.957958 + 0.286909i \(0.0926276\pi\)
−0.230509 + 0.973070i \(0.574039\pi\)
\(32\) −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 −0.959704 0.281014i \(-0.909329\pi\)
0.236486 0.971635i \(-0.424004\pi\)
\(38\) −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 0.809921 0.586539i \(-0.199510\pi\)
−0.912918 + 0.408142i \(0.866177\pi\)
\(54\) 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 −0.515007 0.857186i \(-0.672211\pi\)
0.999848 + 0.0174167i \(0.00554417\pi\)
\(62\) −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 0.935211 0.354090i \(-0.115210\pi\)
−0.774257 + 0.632871i \(0.781876\pi\)
\(68\) −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 −0.0471673 + 0.998887i \(0.515019\pi\)
−0.841478 + 0.540292i \(0.818314\pi\)
\(72\) 9424.52 16323.7i 0.214253 0.371098i
\(73\) 27806.1 48161.5i 0.610707 1.05777i −0.380415 0.924816i \(-0.624219\pi\)
0.991122 0.132959i \(-0.0424478\pi\)
\(74\) 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 0.265131 + 0.964212i \(0.414585\pi\)
−0.967598 + 0.252496i \(0.918749\pi\)
\(80\) 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 0.924255 0.381776i \(-0.124688\pi\)
−0.792755 + 0.609540i \(0.791354\pi\)
\(84\) 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 0.999917 + 0.0128953i \(0.00410481\pi\)
−0.488791 + 0.872401i \(0.662562\pi\)
\(90\) −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 −0.669238 0.743048i \(-0.733379\pi\)
0.978118 + 0.208053i \(0.0667127\pi\)
\(102\) 926.498 0.00881747
\(103\) −18130.1 + 31402.2i −0.168386 + 0.291653i −0.937853 0.347034i \(-0.887189\pi\)
0.769467 + 0.638687i \(0.220522\pi\)
\(104\) 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 0.913430 + 0.406997i \(0.133424\pi\)
−0.104245 + 0.994552i \(0.533243\pi\)
\(110\) 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 0.982088 0.188424i \(-0.0603379\pi\)
−0.654224 + 0.756301i \(0.727005\pi\)
\(140\) −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 0.965425 0.260682i \(-0.0839474\pi\)
−0.708469 + 0.705741i \(0.750614\pi\)
\(150\) 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 −0.997756 0.0669622i \(-0.978669\pi\)
0.556869 + 0.830601i \(0.312003\pi\)
\(158\) 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 −0.880967 0.473178i \(-0.843107\pi\)
0.850267 + 0.526351i \(0.176440\pi\)
\(164\) 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 0.919369 + 0.393395i \(0.128700\pi\)
−0.118994 + 0.992895i \(0.537967\pi\)
\(168\) −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 −0.993772 0.111431i \(-0.964457\pi\)
0.593388 + 0.804917i \(0.297790\pi\)
\(180\) −359041. −0.825968
\(181\) 148436. 257098.i 0.336776 0.583314i −0.647048 0.762449i \(-0.723997\pi\)
0.983824 + 0.179135i \(0.0573300\pi\)
\(182\) 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 −0.962926 0.269767i \(-0.913053\pi\)
0.247838 0.968802i \(-0.420280\pi\)
\(192\) 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 −0.519132 0.854694i \(-0.673745\pi\)
0.999753 + 0.0222339i \(0.00707786\pi\)
\(198\) 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 0.609780 0.792571i \(-0.291258\pi\)
−0.991276 + 0.131799i \(0.957925\pi\)
\(228\) −8527.24 + 14769.6i −0.0108635 + 0.0188162i
\(229\) −197566. + 342194.i −0.248956 + 0.431205i −0.963236 0.268655i \(-0.913421\pi\)
0.714280 + 0.699860i \(0.246754\pi\)
\(230\) −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 −0.958353 0.285587i \(-0.907812\pi\)
0.726502 + 0.687165i \(0.241145\pi\)
\(234\) 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 0.901838 0.432073i \(-0.142218\pi\)
−0.825106 + 0.564978i \(0.808885\pi\)
\(240\) 21135.2 36607.2i 0.0236852 0.0410240i
\(241\) 189808. 328757.i 0.210510 0.364613i −0.741365 0.671103i \(-0.765821\pi\)
0.951874 + 0.306489i \(0.0991544\pi\)
\(242\) −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 −0.701286 0.712880i \(-0.747390\pi\)
0.968015 + 0.250891i \(0.0807236\pi\)
\(252\) 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 0.960272 0.279065i \(-0.0900243\pi\)
−0.721813 + 0.692088i \(0.756691\pi\)
\(264\) 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 −0.957352 0.288923i \(-0.906703\pi\)
0.728891 + 0.684630i \(0.240036\pi\)
\(272\) 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 0.844375 0.535752i \(-0.179972\pi\)
−0.886163 + 0.463374i \(0.846639\pi\)
\(278\) −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 −0.967840 0.251566i \(-0.919054\pi\)
0.266057 0.963957i \(-0.414279\pi\)
\(282\) 5072.67 + 8786.12i 0.00379851 + 0.00657922i
\(283\) 688486. 1.19249e6i 0.511009 0.885094i −0.488909 0.872335i \(-0.662605\pi\)
0.999919 0.0127596i \(-0.00406163\pi\)
\(284\) 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 0.938188 0.346125i \(-0.112503\pi\)
−0.768847 + 0.639432i \(0.779169\pi\)
\(308\) 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 −0.998998 0.0447446i \(-0.985753\pi\)
0.460749 0.887530i \(-0.347581\pi\)
\(312\) −74974.7 −0.0436042
\(313\) 1.10804e6 + 1.91919e6i 0.639286 + 1.10728i 0.985590 + 0.169154i \(0.0541035\pi\)
−0.346303 + 0.938123i \(0.612563\pi\)
\(314\) 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 0.399261 + 0.916837i \(0.369267\pi\)
−0.993635 + 0.112648i \(0.964067\pi\)
\(332\) −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 −0.812638 0.582769i \(-0.801969\pi\)
0.911012 + 0.412381i \(0.135303\pi\)
\(338\) 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 0.840821 + 0.541313i \(0.182072\pi\)
0.0483798 + 0.998829i \(0.484594\pi\)
\(348\) −120348. −0.0532709
\(349\) 2.04771e6 + 3.54674e6i 0.899921 + 1.55871i 0.827593 + 0.561329i \(0.189710\pi\)
0.0723287 + 0.997381i \(0.476957\pi\)
\(350\) 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 0.133407 + 0.991061i \(0.457408\pi\)
−0.924988 + 0.379997i \(0.875925\pi\)
\(354\) 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 −0.984888 0.173194i \(-0.944591\pi\)
0.642434 + 0.766341i \(0.277925\pi\)
\(360\) 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 0.648187 0.761482i \(-0.275528\pi\)
−0.983556 + 0.180605i \(0.942194\pi\)
\(368\) −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 −0.593271 0.805003i \(-0.702164\pi\)
0.993788 + 0.111287i \(0.0354971\pi\)
\(374\) 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 0.876928 0.480621i \(-0.159589\pi\)
−0.854694 + 0.519132i \(0.826255\pi\)
\(398\) −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 −0.0160174 + 0.999872i \(0.505099\pi\)
−0.857906 + 0.513807i \(0.828235\pi\)
\(402\) −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 −0.883976 0.467532i \(-0.845143\pi\)
0.846883 + 0.531780i \(0.178477\pi\)
\(422\) 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 0.765018 0.644009i \(-0.222730\pi\)
−0.940237 + 0.340520i \(0.889397\pi\)
\(434\) −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 −0.787775 0.615963i \(-0.788767\pi\)
0.927327 + 0.374251i \(0.122100\pi\)
\(440\) −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 −0.0897697 0.995963i \(-0.528613\pi\)
0.907414 0.420238i \(-0.138054\pi\)
\(444\) 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 −0.998377 0.0569469i \(-0.981863\pi\)
0.449871 0.893093i \(-0.351470\pi\)
\(450\) 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 0.658112 0.752920i \(-0.271355\pi\)
−0.981104 + 0.193482i \(0.938022\pi\)
\(462\) −89535.4 −0.0195159
\(463\) −3.81961e6 6.61576e6i −0.828069 1.43426i −0.899551 0.436815i \(-0.856106\pi\)
0.0714825 0.997442i \(-0.477227\pi\)
\(464\) −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 0.942071 0.335412i \(-0.108876\pi\)
−0.761511 + 0.648152i \(0.775542\pi\)
\(468\) 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 0.929532 0.368742i \(-0.120211\pi\)
−0.784106 + 0.620627i \(0.786878\pi\)
\(480\) −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 0.0798119 + 0.996810i \(0.474568\pi\)
−0.903169 + 0.429286i \(0.858765\pi\)
\(488\) 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 −0.998151 0.0607798i \(-0.980641\pi\)
0.551712 + 0.834034i \(0.313975\pi\)
\(492\) −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 −0.534899 0.844916i \(-0.679650\pi\)
0.999168 + 0.0407780i \(0.0129837\pi\)
\(500\) −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 −0.0392764 0.999228i \(-0.512505\pi\)
0.884995 0.465600i \(-0.154161\pi\)
\(504\) −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 −0.758331 0.651869i \(-0.773985\pi\)
0.943701 + 0.330800i \(0.107318\pi\)
\(510\) 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 0.844828 + 0.535037i \(0.179702\pi\)
0.0409416 + 0.999162i \(0.486964\pi\)
\(522\) −603231. 1.04483e6i −0.0968964 0.167830i
\(523\) −1.04582e6 + 1.81142e6i −0.167188 + 0.289578i −0.937430 0.348174i \(-0.886802\pi\)
0.770242 + 0.637751i \(0.220135\pi\)
\(524\) −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 −0.181929 0.983312i \(-0.558234\pi\)
0.942538 0.334100i \(-0.108432\pi\)
\(542\) 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 0.729014 0.684499i \(-0.239979\pi\)
−0.957300 + 0.289095i \(0.906646\pi\)
\(548\) 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 0.984730 0.174086i \(-0.0556972\pi\)
−0.643128 + 0.765758i \(0.722364\pi\)
\(570\) −34044.9 −0.00438900
\(571\) 2.48880e6 + 4.31072e6i 0.319447 + 0.553299i 0.980373 0.197153i \(-0.0631695\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(572\) 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 0.263080 0.964774i \(-0.415262\pi\)
0.703979 0.710221i \(-0.251405\pi\)
\(578\) −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 −0.950472 0.310809i \(-0.899400\pi\)
0.744405 + 0.667729i \(0.232733\pi\)
\(588\) 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 0.275307 + 0.961356i \(0.411221\pi\)
−0.970212 + 0.242256i \(0.922113\pi\)
\(594\) −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 0.708900 0.705309i \(-0.249192\pi\)
−0.965266 + 0.261270i \(0.915859\pi\)
\(600\) −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 −0.999712 0.0240121i \(-0.992356\pi\)
0.479061 0.877782i \(-0.340977\pi\)
\(608\) −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 −0.936475 0.350734i \(-0.885932\pi\)
0.771982 + 0.635644i \(0.219265\pi\)
\(618\) −44728.2 −0.00471096
\(619\) −1.44636e6 + 2.50517e6i −0.151722 + 0.262791i −0.931861 0.362816i \(-0.881815\pi\)
0.780138 + 0.625607i \(0.215149\pi\)
\(620\) 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 −0.990614 0.136686i \(-0.956355\pi\)
0.613681 + 0.789554i \(0.289688\pi\)
\(632\) −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 −0.835167 0.549996i \(-0.814629\pi\)
0.893894 + 0.448278i \(0.147963\pi\)
\(660\) 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 −0.982377 0.186908i \(-0.940153\pi\)
0.653056 + 0.757310i \(0.273487\pi\)
\(674\) −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 0.770120 0.637900i \(-0.220197\pi\)
−0.937497 + 0.347993i \(0.886863\pi\)
\(684\) −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 0.809438 + 0.587205i \(0.199772\pi\)
0.103816 + 0.994597i \(0.466895\pi\)
\(692\) −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 −0.394908 0.918721i \(-0.629223\pi\)
0.993089 0.117360i \(-0.0374432\pi\)
\(702\) 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 0.709736 0.704468i \(-0.248814\pi\)
−0.964955 + 0.262416i \(0.915481\pi\)
\(720\) 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 −0.911615 0.411045i \(-0.865164\pi\)
0.0998321 0.995004i \(-0.468169\pi\)
\(744\) 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 0.865257 0.501328i \(-0.167155\pi\)
−0.866792 + 0.498670i \(0.833822\pi\)
\(752\) 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 −0.136339 0.990662i \(-0.543534\pi\)
0.926108 0.377258i \(-0.123133\pi\)
\(758\) 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 0.351282 + 0.936270i \(0.385746\pi\)
−0.986474 + 0.163916i \(0.947587\pi\)
\(762\) 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 0.974504 0.224372i \(-0.0720329\pi\)
−0.681563 + 0.731759i \(0.738700\pi\)
\(770\) 4.41129e6 0.268126
\(771\) 147383. + 255274.i 0.00892915 + 0.0154657i
\(772\) −1.55543e7 −0.939307