Properties

Label 60.7.c.a.31.10
Level $60$
Weight $7$
Character 60.31
Analytic conductor $13.803$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.10
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36400 + 7.88286i) q^{2} -15.5885i q^{3} +(-60.2790 - 21.5045i) q^{4} -55.9017 q^{5} +(122.882 + 21.2627i) q^{6} -86.8984i q^{7} +(251.737 - 445.839i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(-1.36400 + 7.88286i) q^{2} -15.5885i q^{3} +(-60.2790 - 21.5045i) q^{4} -55.9017 q^{5} +(122.882 + 21.2627i) q^{6} -86.8984i q^{7} +(251.737 - 445.839i) q^{8} -243.000 q^{9} +(76.2500 - 440.665i) q^{10} +1545.70i q^{11} +(-335.221 + 939.657i) q^{12} +3187.34 q^{13} +(685.008 + 118.530i) q^{14} +871.421i q^{15} +(3171.12 + 2592.54i) q^{16} +4062.12 q^{17} +(331.452 - 1915.54i) q^{18} -536.854i q^{19} +(3369.70 + 1202.14i) q^{20} -1354.61 q^{21} +(-12184.5 - 2108.34i) q^{22} +18107.3i q^{23} +(-6949.94 - 3924.20i) q^{24} +3125.00 q^{25} +(-4347.53 + 25125.3i) q^{26} +3788.00i q^{27} +(-1868.70 + 5238.15i) q^{28} +14939.5 q^{29} +(-6869.29 - 1188.62i) q^{30} +11771.9i q^{31} +(-24762.0 + 21461.2i) q^{32} +24095.1 q^{33} +(-5540.73 + 32021.1i) q^{34} +4857.77i q^{35} +(14647.8 + 5225.59i) q^{36} -34906.3 q^{37} +(4231.95 + 732.270i) q^{38} -49685.7i q^{39} +(-14072.5 + 24923.2i) q^{40} +108362. q^{41} +(1847.69 - 10678.2i) q^{42} -91972.0i q^{43} +(33239.4 - 93173.2i) q^{44} +13584.1 q^{45} +(-142737. - 24698.4i) q^{46} +17272.4i q^{47} +(40413.6 - 49432.8i) q^{48} +110098. q^{49} +(-4262.50 + 24633.9i) q^{50} -63322.2i q^{51} +(-192130. - 68542.0i) q^{52} +238792. q^{53} +(-29860.2 - 5166.83i) q^{54} -86407.2i q^{55} +(-38742.7 - 21875.6i) q^{56} -8368.73 q^{57} +(-20377.5 + 117766. i) q^{58} -95677.8i q^{59} +(18739.4 - 52528.4i) q^{60} -144057. q^{61} +(-92796.3 - 16056.9i) q^{62} +21116.3i q^{63} +(-135401. - 224469. i) q^{64} -178178. q^{65} +(-32865.7 + 189938. i) q^{66} +494031. i q^{67} +(-244860. - 87353.7i) q^{68} +282265. q^{69} +(-38293.1 - 6626.01i) q^{70} -263745. i q^{71} +(-61172.2 + 108339. i) q^{72} -225002. q^{73} +(47612.3 - 275162. i) q^{74} -48713.9i q^{75} +(-11544.8 + 32361.0i) q^{76} +134319. q^{77} +(391665. + 67771.3i) q^{78} -318736. i q^{79} +(-177271. - 144927. i) q^{80} +59049.0 q^{81} +(-147806. + 854203. i) q^{82} +880209. i q^{83} +(81654.7 + 29130.2i) q^{84} -227079. q^{85} +(725003. + 125450. i) q^{86} -232883. i q^{87} +(689133. + 389110. i) q^{88} -198618. q^{89} +(-18528.7 + 107082. i) q^{90} -276975. i q^{91} +(389388. - 1.09149e6i) q^{92} +183506. q^{93} +(-136156. - 23559.5i) q^{94} +30011.1i q^{95} +(334548. + 386001. i) q^{96} -141679. q^{97} +(-150173. + 867885. i) q^{98} -375605. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} + O(q^{10}) \) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} - 750q^{10} + 5040q^{13} - 2596q^{14} + 4194q^{16} - 4860q^{18} + 7000q^{20} + 19440q^{21} + 45780q^{22} + 24786q^{24} + 75000q^{25} + 75852q^{26} + 54300q^{28} + 132800q^{29} - 10700q^{32} - 173484q^{34} + 59778q^{36} - 69840q^{37} + 215800q^{38} - 14250q^{40} - 70448q^{41} - 189540q^{42} - 395668q^{44} - 158760q^{46} + 252720q^{48} - 642984q^{49} + 62500q^{50} - 210240q^{52} - 644320q^{53} - 39366q^{54} - 917708q^{56} + 408240q^{57} - 1345020q^{58} + 222750q^{60} - 222864q^{61} + 1948520q^{62} + 935922q^{64} + 266000q^{65} - 640548q^{66} + 572680q^{68} - 541728q^{69} + 220500q^{70} + 82620q^{72} + 771120q^{73} - 589164q^{74} - 191544q^{76} + 1383840q^{77} - 693360q^{78} - 946000q^{80} + 1417176q^{81} + 2672520q^{82} + 1256796q^{84} - 372000q^{85} + 1781528q^{86} + 956940q^{88} - 1566224q^{89} + 182250q^{90} - 3040560q^{92} + 1496880q^{93} - 3788352q^{94} - 413262q^{96} - 1666800q^{97} - 2709660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36400 + 7.88286i −0.170500 + 0.985358i
\(3\) 15.5885i 0.577350i
\(4\) −60.2790 21.5045i −0.941859 0.336007i
\(5\) −55.9017 −0.447214
\(6\) 122.882 + 21.2627i 0.568897 + 0.0984383i
\(7\) 86.8984i 0.253348i −0.991944 0.126674i \(-0.959570\pi\)
0.991944 0.126674i \(-0.0404302\pi\)
\(8\) 251.737 445.839i 0.491675 0.870779i
\(9\) −243.000 −0.333333
\(10\) 76.2500 440.665i 0.0762500 0.440665i
\(11\) 1545.70i 1.16131i 0.814151 + 0.580653i \(0.197203\pi\)
−0.814151 + 0.580653i \(0.802797\pi\)
\(12\) −335.221 + 939.657i −0.193994 + 0.543783i
\(13\) 3187.34 1.45077 0.725384 0.688344i \(-0.241662\pi\)
0.725384 + 0.688344i \(0.241662\pi\)
\(14\) 685.008 + 118.530i 0.249639 + 0.0431959i
\(15\) 871.421i 0.258199i
\(16\) 3171.12 + 2592.54i 0.774198 + 0.632943i
\(17\) 4062.12 0.826810 0.413405 0.910547i \(-0.364339\pi\)
0.413405 + 0.910547i \(0.364339\pi\)
\(18\) 331.452 1915.54i 0.0568334 0.328453i
\(19\) 536.854i 0.0782701i −0.999234 0.0391350i \(-0.987540\pi\)
0.999234 0.0391350i \(-0.0124602\pi\)
\(20\) 3369.70 + 1202.14i 0.421212 + 0.150267i
\(21\) −1354.61 −0.146271
\(22\) −12184.5 2108.34i −1.14430 0.198003i
\(23\) 18107.3i 1.48823i 0.668052 + 0.744115i \(0.267129\pi\)
−0.668052 + 0.744115i \(0.732871\pi\)
\(24\) −6949.94 3924.20i −0.502745 0.283868i
\(25\) 3125.00 0.200000
\(26\) −4347.53 + 25125.3i −0.247356 + 1.42953i
\(27\) 3788.00i 0.192450i
\(28\) −1868.70 + 5238.15i −0.0851269 + 0.238618i
\(29\) 14939.5 0.612549 0.306275 0.951943i \(-0.400917\pi\)
0.306275 + 0.951943i \(0.400917\pi\)
\(30\) −6869.29 1188.62i −0.254418 0.0440230i
\(31\) 11771.9i 0.395150i 0.980288 + 0.197575i \(0.0633066\pi\)
−0.980288 + 0.197575i \(0.936693\pi\)
\(32\) −24762.0 + 21461.2i −0.755676 + 0.654945i
\(33\) 24095.1 0.670481
\(34\) −5540.73 + 32021.1i −0.140971 + 0.814704i
\(35\) 4857.77i 0.113301i
\(36\) 14647.8 + 5225.59i 0.313953 + 0.112002i
\(37\) −34906.3 −0.689127 −0.344563 0.938763i \(-0.611973\pi\)
−0.344563 + 0.938763i \(0.611973\pi\)
\(38\) 4231.95 + 732.270i 0.0771240 + 0.0133451i
\(39\) 49685.7i 0.837602i
\(40\) −14072.5 + 24923.2i −0.219884 + 0.389424i
\(41\) 108362. 1.57226 0.786132 0.618058i \(-0.212081\pi\)
0.786132 + 0.618058i \(0.212081\pi\)
\(42\) 1847.69 10678.2i 0.0249392 0.144129i
\(43\) 91972.0i 1.15678i −0.815761 0.578389i \(-0.803681\pi\)
0.815761 0.578389i \(-0.196319\pi\)
\(44\) 33239.4 93173.2i 0.390207 1.09379i
\(45\) 13584.1 0.149071
\(46\) −142737. 24698.4i −1.46644 0.253743i
\(47\) 17272.4i 0.166363i 0.996534 + 0.0831817i \(0.0265082\pi\)
−0.996534 + 0.0831817i \(0.973492\pi\)
\(48\) 40413.6 49432.8i 0.365430 0.446984i
\(49\) 110098. 0.935815
\(50\) −4262.50 + 24633.9i −0.0341000 + 0.197072i
\(51\) 63322.2i 0.477359i
\(52\) −192130. 68542.0i −1.36642 0.487469i
\(53\) 238792. 1.60395 0.801977 0.597355i \(-0.203781\pi\)
0.801977 + 0.597355i \(0.203781\pi\)
\(54\) −29860.2 5166.83i −0.189632 0.0328128i
\(55\) 86407.2i 0.519352i
\(56\) −38742.7 21875.6i −0.220610 0.124565i
\(57\) −8368.73 −0.0451892
\(58\) −20377.5 + 117766.i −0.104440 + 0.603580i
\(59\) 95677.8i 0.465860i −0.972494 0.232930i \(-0.925169\pi\)
0.972494 0.232930i \(-0.0748312\pi\)
\(60\) 18739.4 52528.4i 0.0867567 0.243187i
\(61\) −144057. −0.634666 −0.317333 0.948314i \(-0.602787\pi\)
−0.317333 + 0.948314i \(0.602787\pi\)
\(62\) −92796.3 16056.9i −0.389364 0.0673731i
\(63\) 21116.3i 0.0844494i
\(64\) −135401. 224469.i −0.516512 0.856280i
\(65\) −178178. −0.648803
\(66\) −32865.7 + 189938.i −0.114317 + 0.660663i
\(67\) 494031.i 1.64259i 0.570501 + 0.821297i \(0.306749\pi\)
−0.570501 + 0.821297i \(0.693251\pi\)
\(68\) −244860. 87353.7i −0.778739 0.277814i
\(69\) 282265. 0.859230
\(70\) −38293.1 6626.01i −0.111642 0.0193178i
\(71\) 263745.i 0.736902i −0.929647 0.368451i \(-0.879888\pi\)
0.929647 0.368451i \(-0.120112\pi\)
\(72\) −61172.2 + 108339.i −0.163892 + 0.290260i
\(73\) −225002. −0.578386 −0.289193 0.957271i \(-0.593387\pi\)
−0.289193 + 0.957271i \(0.593387\pi\)
\(74\) 47612.3 275162.i 0.117496 0.679036i
\(75\) 48713.9i 0.115470i
\(76\) −11544.8 + 32361.0i −0.0262993 + 0.0737194i
\(77\) 134319. 0.294215
\(78\) 391665. + 67771.3i 0.825337 + 0.142811i
\(79\) 318736.i 0.646471i −0.946318 0.323236i \(-0.895229\pi\)
0.946318 0.323236i \(-0.104771\pi\)
\(80\) −177271. 144927.i −0.346232 0.283061i
\(81\) 59049.0 0.111111
\(82\) −147806. + 854203.i −0.268071 + 1.54924i
\(83\) 880209.i 1.53940i 0.638406 + 0.769700i \(0.279594\pi\)
−0.638406 + 0.769700i \(0.720406\pi\)
\(84\) 81654.7 + 29130.2i 0.137766 + 0.0491480i
\(85\) −227079. −0.369761
\(86\) 725003. + 125450.i 1.13984 + 0.197231i
\(87\) 232883.i 0.353656i
\(88\) 689133. + 389110.i 1.01124 + 0.570985i
\(89\) −198618. −0.281740 −0.140870 0.990028i \(-0.544990\pi\)
−0.140870 + 0.990028i \(0.544990\pi\)
\(90\) −18528.7 + 107082.i −0.0254167 + 0.146888i
\(91\) 276975.i 0.367550i
\(92\) 389388. 1.09149e6i 0.500056 1.40170i
\(93\) 183506. 0.228140
\(94\) −136156. 23559.5i −0.163928 0.0283650i
\(95\) 30011.1i 0.0350034i
\(96\) 334548. + 386001.i 0.378133 + 0.436290i
\(97\) −141679. −0.155235 −0.0776175 0.996983i \(-0.524731\pi\)
−0.0776175 + 0.996983i \(0.524731\pi\)
\(98\) −150173. + 867885.i −0.159557 + 0.922112i
\(99\) 375605.i 0.387102i
\(100\) −188372. 67201.5i −0.188372 0.0672015i
\(101\) 1.23128e6 1.19506 0.597532 0.801845i \(-0.296148\pi\)
0.597532 + 0.801845i \(0.296148\pi\)
\(102\) 499160. + 86371.5i 0.470369 + 0.0813898i
\(103\) 1.34540e6i 1.23123i 0.788047 + 0.615615i \(0.211092\pi\)
−0.788047 + 0.615615i \(0.788908\pi\)
\(104\) 802372. 1.42104e6i 0.713306 1.26330i
\(105\) 75725.1 0.0654142
\(106\) −325713. + 1.88236e6i −0.273475 + 1.58047i
\(107\) 1.09887e6i 0.897006i 0.893781 + 0.448503i \(0.148043\pi\)
−0.893781 + 0.448503i \(0.851957\pi\)
\(108\) 81458.8 228337.i 0.0646646 0.181261i
\(109\) −1.90361e6 −1.46994 −0.734968 0.678101i \(-0.762803\pi\)
−0.734968 + 0.678101i \(0.762803\pi\)
\(110\) 681136. + 117860.i 0.511747 + 0.0885496i
\(111\) 544136.i 0.397867i
\(112\) 225287. 275565.i 0.160355 0.196142i
\(113\) −2.70511e6 −1.87478 −0.937389 0.348284i \(-0.886764\pi\)
−0.937389 + 0.348284i \(0.886764\pi\)
\(114\) 11415.0 65969.5i 0.00770477 0.0445276i
\(115\) 1.01223e6i 0.665557i
\(116\) −900536. 321265.i −0.576935 0.205821i
\(117\) −774523. −0.483589
\(118\) 754215. + 130505.i 0.459038 + 0.0794291i
\(119\) 352992.i 0.209471i
\(120\) 388513. + 219369.i 0.224834 + 0.126950i
\(121\) −617624. −0.348632
\(122\) 196494. 1.13558e6i 0.108211 0.625373i
\(123\) 1.68920e6i 0.907747i
\(124\) 253149. 709599.i 0.132773 0.372176i
\(125\) −174693. −0.0894427
\(126\) −166457. 28802.7i −0.0832129 0.0143986i
\(127\) 1.50271e6i 0.733606i −0.930299 0.366803i \(-0.880452\pi\)
0.930299 0.366803i \(-0.119548\pi\)
\(128\) 1.95414e6 761169.i 0.931807 0.362953i
\(129\) −1.43370e6 −0.667867
\(130\) 243035. 1.40455e6i 0.110621 0.639303i
\(131\) 4.39609e6i 1.95547i 0.209832 + 0.977737i \(0.432708\pi\)
−0.209832 + 0.977737i \(0.567292\pi\)
\(132\) −1.45243e6 518151.i −0.631498 0.225286i
\(133\) −46651.8 −0.0198296
\(134\) −3.89438e6 673860.i −1.61854 0.280063i
\(135\) 211755.i 0.0860663i
\(136\) 1.02259e6 1.81105e6i 0.406522 0.719969i
\(137\) 2.14601e6 0.834584 0.417292 0.908772i \(-0.362979\pi\)
0.417292 + 0.908772i \(0.362979\pi\)
\(138\) −385010. + 2.22505e6i −0.146499 + 0.846649i
\(139\) 3.06053e6i 1.13960i −0.821784 0.569800i \(-0.807021\pi\)
0.821784 0.569800i \(-0.192979\pi\)
\(140\) 104464. 292822.i 0.0380699 0.106713i
\(141\) 269249. 0.0960500
\(142\) 2.07907e6 + 359749.i 0.726112 + 0.125642i
\(143\) 4.92666e6i 1.68479i
\(144\) −770581. 629986.i −0.258066 0.210981i
\(145\) −835141. −0.273940
\(146\) 306903. 1.77366e6i 0.0986150 0.569917i
\(147\) 1.71625e6i 0.540293i
\(148\) 2.10412e6 + 750642.i 0.649060 + 0.231552i
\(149\) −1.56754e6 −0.473871 −0.236936 0.971525i \(-0.576143\pi\)
−0.236936 + 0.971525i \(0.576143\pi\)
\(150\) 384005. + 66445.9i 0.113779 + 0.0196877i
\(151\) 5.43173e6i 1.57764i −0.614626 0.788819i \(-0.710693\pi\)
0.614626 0.788819i \(-0.289307\pi\)
\(152\) −239351. 135146.i −0.0681559 0.0384834i
\(153\) −987095. −0.275603
\(154\) −183211. + 1.05882e6i −0.0501637 + 0.289907i
\(155\) 658070.i 0.176716i
\(156\) −1.06846e6 + 2.99500e6i −0.281440 + 0.788903i
\(157\) 6.05232e6 1.56395 0.781976 0.623309i \(-0.214212\pi\)
0.781976 + 0.623309i \(0.214212\pi\)
\(158\) 2.51255e6 + 434756.i 0.637006 + 0.110223i
\(159\) 3.72240e6i 0.926044i
\(160\) 1.38424e6 1.19972e6i 0.337949 0.292900i
\(161\) 1.57350e6 0.377040
\(162\) −80542.9 + 465475.i −0.0189445 + 0.109484i
\(163\) 1.11984e6i 0.258578i 0.991607 + 0.129289i \(0.0412695\pi\)
−0.991607 + 0.129289i \(0.958731\pi\)
\(164\) −6.53195e6 2.33027e6i −1.48085 0.528292i
\(165\) −1.34695e6 −0.299848
\(166\) −6.93856e6 1.20061e6i −1.51686 0.262468i
\(167\) 2.51799e6i 0.540636i −0.962771 0.270318i \(-0.912871\pi\)
0.962771 0.270318i \(-0.0871288\pi\)
\(168\) −341007. + 603939.i −0.0719176 + 0.127369i
\(169\) 5.33232e6 1.10473
\(170\) 309736. 1.79003e6i 0.0630443 0.364347i
\(171\) 130456.i 0.0260900i
\(172\) −1.97781e6 + 5.54398e6i −0.388686 + 1.08952i
\(173\) 4153.24 0.000802137 0.000401069 1.00000i \(-0.499872\pi\)
0.000401069 1.00000i \(0.499872\pi\)
\(174\) 1.83579e6 + 317653.i 0.348477 + 0.0602983i
\(175\) 271558.i 0.0506696i
\(176\) −4.00728e6 + 4.90159e6i −0.735041 + 0.899081i
\(177\) −1.49147e6 −0.268964
\(178\) 270916. 1.56568e6i 0.0480368 0.277615i
\(179\) 3.95787e6i 0.690084i 0.938587 + 0.345042i \(0.112135\pi\)
−0.938587 + 0.345042i \(0.887865\pi\)
\(180\) −818837. 292119.i −0.140404 0.0500890i
\(181\) 9.51906e6 1.60531 0.802654 0.596446i \(-0.203421\pi\)
0.802654 + 0.596446i \(0.203421\pi\)
\(182\) 2.18335e6 + 377794.i 0.362168 + 0.0626673i
\(183\) 2.24563e6i 0.366424i
\(184\) 8.07293e6 + 4.55828e6i 1.29592 + 0.731725i
\(185\) 1.95132e6 0.308187
\(186\) −250302. + 1.44655e6i −0.0388979 + 0.224799i
\(187\) 6.27881e6i 0.960180i
\(188\) 371433. 1.04116e6i 0.0558993 0.156691i
\(189\) 329171. 0.0487569
\(190\) −236573. 40935.1i −0.0344909 0.00596809i
\(191\) 6.63547e6i 0.952295i 0.879365 + 0.476148i \(0.157967\pi\)
−0.879365 + 0.476148i \(0.842033\pi\)
\(192\) −3.49912e6 + 2.11069e6i −0.494373 + 0.298208i
\(193\) −4.88164e6 −0.679037 −0.339519 0.940599i \(-0.610264\pi\)
−0.339519 + 0.940599i \(0.610264\pi\)
\(194\) 193250. 1.11683e6i 0.0264676 0.152962i
\(195\) 2.77751e6i 0.374587i
\(196\) −6.63658e6 2.36759e6i −0.881406 0.314441i
\(197\) 3.69499e6 0.483297 0.241649 0.970364i \(-0.422312\pi\)
0.241649 + 0.970364i \(0.422312\pi\)
\(198\) 2.96084e6 + 512325.i 0.381434 + 0.0660010i
\(199\) 137140.i 0.0174023i 0.999962 + 0.00870113i \(0.00276969\pi\)
−0.999962 + 0.00870113i \(0.997230\pi\)
\(200\) 786679. 1.39325e6i 0.0983349 0.174156i
\(201\) 7.70119e6 0.948352
\(202\) −1.67946e6 + 9.70598e6i −0.203759 + 1.17757i
\(203\) 1.29822e6i 0.155188i
\(204\) −1.36171e6 + 3.81700e6i −0.160396 + 0.449605i
\(205\) −6.05762e6 −0.703138
\(206\) −1.06056e7 1.83513e6i −1.21320 0.209925i
\(207\) 4.40007e6i 0.496077i
\(208\) 1.01074e7 + 8.26329e6i 1.12318 + 0.918254i
\(209\) 829815. 0.0908955
\(210\) −103289. + 596931.i −0.0111531 + 0.0644564i
\(211\) 372967.i 0.0397029i −0.999803 0.0198515i \(-0.993681\pi\)
0.999803 0.0198515i \(-0.00631933\pi\)
\(212\) −1.43941e7 5.13509e6i −1.51070 0.538940i
\(213\) −4.11138e6 −0.425451
\(214\) −8.66225e6 1.49886e6i −0.883872 0.152940i
\(215\) 5.14139e6i 0.517327i
\(216\) 1.68884e6 + 953580.i 0.167582 + 0.0946228i
\(217\) 1.02296e6 0.100111
\(218\) 2.59653e6 1.50059e7i 0.250625 1.44841i
\(219\) 3.50744e6i 0.333931i
\(220\) −1.85814e6 + 5.20854e6i −0.174506 + 0.489157i
\(221\) 1.29473e7 1.19951
\(222\) −4.28935e6 742202.i −0.392042 0.0678365i
\(223\) 1.01313e7i 0.913591i −0.889572 0.456795i \(-0.848997\pi\)
0.889572 0.456795i \(-0.151003\pi\)
\(224\) 1.86495e6 + 2.15178e6i 0.165929 + 0.191449i
\(225\) −759375. −0.0666667
\(226\) 3.68978e6 2.13240e7i 0.319650 1.84733i
\(227\) 4.30252e6i 0.367829i −0.982942 0.183914i \(-0.941123\pi\)
0.982942 0.183914i \(-0.0588769\pi\)
\(228\) 504459. + 179965.i 0.0425619 + 0.0151839i
\(229\) 1.34915e7 1.12345 0.561724 0.827325i \(-0.310138\pi\)
0.561724 + 0.827325i \(0.310138\pi\)
\(230\) 7.97926e6 + 1.38068e6i 0.655811 + 0.113478i
\(231\) 2.09382e6i 0.169865i
\(232\) 3.76082e6 6.66059e6i 0.301175 0.533395i
\(233\) −2.26239e7 −1.78855 −0.894273 0.447521i \(-0.852307\pi\)
−0.894273 + 0.447521i \(0.852307\pi\)
\(234\) 1.05645e6 6.10546e6i 0.0824521 0.476509i
\(235\) 965554.i 0.0744000i
\(236\) −2.05750e6 + 5.76736e6i −0.156532 + 0.438774i
\(237\) −4.96860e6 −0.373240
\(238\) 2.78258e6 + 481481.i 0.206404 + 0.0357148i
\(239\) 4.98771e6i 0.365348i −0.983173 0.182674i \(-0.941525\pi\)
0.983173 0.182674i \(-0.0584754\pi\)
\(240\) −2.25919e6 + 2.76338e6i −0.163425 + 0.199897i
\(241\) 3.64828e6 0.260637 0.130319 0.991472i \(-0.458400\pi\)
0.130319 + 0.991472i \(0.458400\pi\)
\(242\) 842439. 4.86864e6i 0.0594419 0.343528i
\(243\) 920483.i 0.0641500i
\(244\) 8.68361e6 + 3.09787e6i 0.597766 + 0.213252i
\(245\) −6.15465e6 −0.418509
\(246\) 1.33157e7 + 2.30407e6i 0.894456 + 0.154771i
\(247\) 1.71114e6i 0.113552i
\(248\) 5.24838e6 + 2.96343e6i 0.344088 + 0.194285i
\(249\) 1.37211e7 0.888773
\(250\) 238281. 1.37708e6i 0.0152500 0.0881331i
\(251\) 9.91942e6i 0.627285i −0.949541 0.313643i \(-0.898451\pi\)
0.949541 0.313643i \(-0.101549\pi\)
\(252\) 454095. 1.27287e6i 0.0283756 0.0795395i
\(253\) −2.79884e7 −1.72829
\(254\) 1.18456e7 + 2.04969e6i 0.722865 + 0.125080i
\(255\) 3.53982e6i 0.213481i
\(256\) 3.33473e6 + 1.64425e7i 0.198766 + 0.980047i
\(257\) 1.34441e7 0.792015 0.396008 0.918247i \(-0.370395\pi\)
0.396008 + 0.918247i \(0.370395\pi\)
\(258\) 1.95557e6 1.13017e7i 0.113871 0.658087i
\(259\) 3.03331e6i 0.174589i
\(260\) 1.07404e7 + 3.83161e6i 0.611082 + 0.218003i
\(261\) −3.63029e6 −0.204183
\(262\) −3.46537e7 5.99627e6i −1.92684 0.333409i
\(263\) 2.04971e7i 1.12674i −0.826204 0.563371i \(-0.809504\pi\)
0.826204 0.563371i \(-0.190496\pi\)
\(264\) 6.06563e6 1.07425e7i 0.329658 0.583840i
\(265\) −1.33489e7 −0.717310
\(266\) 63633.1 367750.i 0.00338095 0.0195392i
\(267\) 3.09615e6i 0.162663i
\(268\) 1.06239e7 2.97797e7i 0.551924 1.54709i
\(269\) −2.45721e7 −1.26237 −0.631183 0.775634i \(-0.717430\pi\)
−0.631183 + 0.775634i \(0.717430\pi\)
\(270\) 1.66924e6 + 288835.i 0.0848061 + 0.0146743i
\(271\) 1.41101e7i 0.708962i −0.935063 0.354481i \(-0.884658\pi\)
0.935063 0.354481i \(-0.115342\pi\)
\(272\) 1.28814e7 + 1.05312e7i 0.640115 + 0.523324i
\(273\) −4.31761e6 −0.212205
\(274\) −2.92716e6 + 1.69167e7i −0.142297 + 0.822364i
\(275\) 4.83031e6i 0.232261i
\(276\) −1.70146e7 6.06995e6i −0.809274 0.288708i
\(277\) −3.78003e7 −1.77851 −0.889255 0.457412i \(-0.848777\pi\)
−0.889255 + 0.457412i \(0.848777\pi\)
\(278\) 2.41257e7 + 4.17457e6i 1.12291 + 0.194302i
\(279\) 2.86057e6i 0.131717i
\(280\) 2.16578e6 + 1.22288e6i 0.0986599 + 0.0557071i
\(281\) 1.02523e7 0.462066 0.231033 0.972946i \(-0.425790\pi\)
0.231033 + 0.972946i \(0.425790\pi\)
\(282\) −367257. + 2.12246e6i −0.0163765 + 0.0946436i
\(283\) 3.79250e7i 1.67327i 0.547762 + 0.836635i \(0.315480\pi\)
−0.547762 + 0.836635i \(0.684520\pi\)
\(284\) −5.67170e6 + 1.58983e7i −0.247604 + 0.694058i
\(285\) 467826. 0.0202092
\(286\) −3.88362e7 6.71998e6i −1.66012 0.287256i
\(287\) 9.41649e6i 0.398330i
\(288\) 6.01717e6 5.21508e6i 0.251892 0.218315i
\(289\) −7.63676e6 −0.316385
\(290\) 1.13913e6 6.58330e6i 0.0467069 0.269929i
\(291\) 2.20855e6i 0.0896250i
\(292\) 1.35629e7 + 4.83855e6i 0.544759 + 0.194342i
\(293\) −1.51174e7 −0.601000 −0.300500 0.953782i \(-0.597153\pi\)
−0.300500 + 0.953782i \(0.597153\pi\)
\(294\) 1.35290e7 + 2.34097e6i 0.532382 + 0.0921200i
\(295\) 5.34855e6i 0.208339i
\(296\) −8.78723e6 + 1.55626e7i −0.338826 + 0.600077i
\(297\) −5.85510e6 −0.223494
\(298\) 2.13813e6 1.23567e7i 0.0807951 0.466932i
\(299\) 5.77141e7i 2.15908i
\(300\) −1.04757e6 + 2.93643e6i −0.0387988 + 0.108757i
\(301\) −7.99222e6 −0.293068
\(302\) 4.28176e7 + 7.40889e6i 1.55454 + 0.268988i
\(303\) 1.91937e7i 0.689971i
\(304\) 1.39181e6 1.70243e6i 0.0495405 0.0605965i
\(305\) 8.05303e6 0.283831
\(306\) 1.34640e6 7.78113e6i 0.0469904 0.271568i
\(307\) 3.85776e7i 1.33328i 0.745382 + 0.666638i \(0.232267\pi\)
−0.745382 + 0.666638i \(0.767733\pi\)
\(308\) −8.09660e6 2.88845e6i −0.277109 0.0988584i
\(309\) 2.09727e7 0.710851
\(310\) 5.18747e6 + 897608.i 0.174129 + 0.0301302i
\(311\) 4.61860e7i 1.53543i −0.640794 0.767713i \(-0.721395\pi\)
0.640794 0.767713i \(-0.278605\pi\)
\(312\) −2.21518e7 1.25077e7i −0.729366 0.411827i
\(313\) −1.41773e7 −0.462339 −0.231170 0.972913i \(-0.574255\pi\)
−0.231170 + 0.972913i \(0.574255\pi\)
\(314\) −8.25538e6 + 4.77096e7i −0.266654 + 1.54105i
\(315\) 1.18044e6i 0.0377669i
\(316\) −6.85424e6 + 1.92131e7i −0.217219 + 0.608885i
\(317\) 6.05126e7 1.89963 0.949813 0.312817i \(-0.101273\pi\)
0.949813 + 0.312817i \(0.101273\pi\)
\(318\) 2.93431e7 + 5.07736e6i 0.912484 + 0.157891i
\(319\) 2.30919e7i 0.711357i
\(320\) 7.56912e6 + 1.25482e7i 0.230991 + 0.382940i
\(321\) 1.71297e7 0.517887
\(322\) −2.14625e6 + 1.24036e7i −0.0642854 + 0.371520i
\(323\) 2.18077e6i 0.0647145i
\(324\) −3.55941e6 1.26982e6i −0.104651 0.0373341i
\(325\) 9.96043e6 0.290154
\(326\) −8.82750e6 1.52746e6i −0.254792 0.0440876i
\(327\) 2.96744e7i 0.848668i
\(328\) 2.72788e7 4.83120e7i 0.773042 1.36909i
\(329\) 1.50094e6 0.0421479
\(330\) 1.83725e6 1.06179e7i 0.0511241 0.295458i
\(331\) 1.01477e7i 0.279824i 0.990164 + 0.139912i \(0.0446820\pi\)
−0.990164 + 0.139912i \(0.955318\pi\)
\(332\) 1.89284e7 5.30581e7i 0.517250 1.44990i
\(333\) 8.48224e6 0.229709
\(334\) 1.98490e7 + 3.43454e6i 0.532720 + 0.0921785i
\(335\) 2.76172e7i 0.734590i
\(336\) −4.29563e6 3.51188e6i −0.113242 0.0925810i
\(337\) 5.39701e7 1.41014 0.705072 0.709136i \(-0.250915\pi\)
0.705072 + 0.709136i \(0.250915\pi\)
\(338\) −7.27329e6 + 4.20339e7i −0.188356 + 1.08855i
\(339\) 4.21685e7i 1.08240i
\(340\) 1.36881e7 + 4.88322e6i 0.348263 + 0.124242i
\(341\) −1.81958e7 −0.458890
\(342\) −1.02836e6 177942.i −0.0257080 0.00444835i
\(343\) 1.97908e7i 0.490435i
\(344\) −4.10047e7 2.31528e7i −1.00730 0.568759i
\(345\) −1.57791e7 −0.384259
\(346\) −5665.02 + 32739.4i −0.000136765 + 0.000790392i
\(347\) 4.90499e7i 1.17395i −0.809605 0.586975i \(-0.800319\pi\)
0.809605 0.586975i \(-0.199681\pi\)
\(348\) −5.00803e6 + 1.40380e7i −0.118831 + 0.333094i
\(349\) 2.30969e7 0.543346 0.271673 0.962390i \(-0.412423\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(350\) 2.14065e6 + 370405.i 0.0499277 + 0.00863918i
\(351\) 1.20736e7i 0.279201i
\(352\) −3.31726e7 3.82746e7i −0.760592 0.877572i
\(353\) −8.59041e7 −1.95294 −0.976472 0.215642i \(-0.930816\pi\)
−0.976472 + 0.215642i \(0.930816\pi\)
\(354\) 2.03437e6 1.17570e7i 0.0458584 0.265026i
\(355\) 1.47438e7i 0.329553i
\(356\) 1.19725e7 + 4.27118e6i 0.265360 + 0.0946668i
\(357\) −5.50260e6 −0.120938
\(358\) −3.11993e7 5.39854e6i −0.679980 0.117660i
\(359\) 4.12084e7i 0.890640i −0.895371 0.445320i \(-0.853090\pi\)
0.895371 0.445320i \(-0.146910\pi\)
\(360\) 3.41963e6 6.05633e6i 0.0732945 0.129808i
\(361\) 4.67577e7 0.993874
\(362\) −1.29840e7 + 7.50374e7i −0.273705 + 1.58180i
\(363\) 9.62780e6i 0.201283i
\(364\) −5.95619e6 + 1.66958e7i −0.123499 + 0.346180i
\(365\) 1.25780e7 0.258662
\(366\) −1.77020e7 3.06304e6i −0.361059 0.0624754i
\(367\) 5.40236e7i 1.09291i −0.837488 0.546456i \(-0.815977\pi\)
0.837488 0.546456i \(-0.184023\pi\)
\(368\) −4.69438e7 + 5.74203e7i −0.941965 + 1.15218i
\(369\) −2.63320e7 −0.524088
\(370\) −2.66161e6 + 1.53820e7i −0.0525459 + 0.303674i
\(371\) 2.07506e7i 0.406359i
\(372\) −1.10616e7 3.94620e6i −0.214876 0.0766567i
\(373\) 5.45778e7 1.05169 0.525847 0.850579i \(-0.323748\pi\)
0.525847 + 0.850579i \(0.323748\pi\)
\(374\) −4.94950e7 8.56431e6i −0.946121 0.163711i
\(375\) 2.72319e6i 0.0516398i
\(376\) 7.70069e6 + 4.34810e6i 0.144866 + 0.0817967i
\(377\) 4.76171e7 0.888667
\(378\) −448990. + 2.59481e6i −0.00831306 + 0.0480430i
\(379\) 7.14006e7i 1.31155i −0.754957 0.655774i \(-0.772342\pi\)
0.754957 0.655774i \(-0.227658\pi\)
\(380\) 645372. 1.80904e6i 0.0117614 0.0329683i
\(381\) −2.34249e7 −0.423548
\(382\) −5.23065e7 9.05079e6i −0.938352 0.162367i
\(383\) 2.38242e7i 0.424055i −0.977264 0.212028i \(-0.931993\pi\)
0.977264 0.212028i \(-0.0680067\pi\)
\(384\) −1.18654e7 3.04621e7i −0.209551 0.537979i
\(385\) −7.50865e6 −0.131577
\(386\) 6.65856e6 3.84813e7i 0.115776 0.669095i
\(387\) 2.23492e7i 0.385593i
\(388\) 8.54026e6 + 3.04673e6i 0.146210 + 0.0521601i
\(389\) −3.32214e7 −0.564377 −0.282188 0.959359i \(-0.591060\pi\)
−0.282188 + 0.959359i \(0.591060\pi\)
\(390\) −2.18948e7 3.78853e6i −0.369102 0.0638671i
\(391\) 7.35540e7i 1.23048i
\(392\) 2.77157e7 4.90858e7i 0.460116 0.814888i
\(393\) 6.85282e7 1.12899
\(394\) −5.03997e6 + 2.91271e7i −0.0824023 + 0.476221i
\(395\) 1.78179e7i 0.289111i
\(396\) −8.07718e6 + 2.26411e7i −0.130069 + 0.364596i
\(397\) −4.02591e7 −0.643417 −0.321709 0.946839i \(-0.604257\pi\)
−0.321709 + 0.946839i \(0.604257\pi\)
\(398\) −1.08106e6 187059.i −0.0171474 0.00296709i
\(399\) 727230.i 0.0114486i
\(400\) 9.90974e6 + 8.10167e6i 0.154840 + 0.126589i
\(401\) 3.97745e7 0.616839 0.308420 0.951250i \(-0.400200\pi\)
0.308420 + 0.951250i \(0.400200\pi\)
\(402\) −1.05044e7 + 6.07074e7i −0.161694 + 0.934466i
\(403\) 3.75211e7i 0.573271i
\(404\) −7.42201e7 2.64779e7i −1.12558 0.401550i
\(405\) −3.30094e6 −0.0496904
\(406\) 1.02337e7 + 1.77077e6i 0.152916 + 0.0264596i
\(407\) 5.39547e7i 0.800287i
\(408\) −2.82315e7 1.59406e7i −0.415674 0.234705i
\(409\) −1.31428e7 −0.192097 −0.0960483 0.995377i \(-0.530620\pi\)
−0.0960483 + 0.995377i \(0.530620\pi\)
\(410\) 8.26260e6 4.77514e7i 0.119885 0.692842i
\(411\) 3.34530e7i 0.481847i
\(412\) 2.89321e7 8.10993e7i 0.413702 1.15965i
\(413\) −8.31425e6 −0.118025
\(414\) 3.46852e7 + 6.00170e6i 0.488813 + 0.0845811i
\(415\) 4.92052e7i 0.688440i
\(416\) −7.89249e7 + 6.84042e7i −1.09631 + 0.950174i
\(417\) −4.77089e7 −0.657948
\(418\) −1.13187e6 + 6.54132e6i −0.0154977 + 0.0895646i
\(419\) 7.92855e6i 0.107783i −0.998547 0.0538917i \(-0.982837\pi\)
0.998547 0.0538917i \(-0.0171626\pi\)
\(420\) −4.56464e6 1.62843e6i −0.0616110 0.0219797i
\(421\) 9.38186e7 1.25731 0.628655 0.777684i \(-0.283606\pi\)
0.628655 + 0.777684i \(0.283606\pi\)
\(422\) 2.94004e6 + 508727.i 0.0391216 + 0.00676936i
\(423\) 4.19718e6i 0.0554545i
\(424\) 6.01129e7 1.06463e8i 0.788624 1.39669i
\(425\) 1.26941e7 0.165362
\(426\) 5.60793e6 3.24095e7i 0.0725394 0.419221i
\(427\) 1.25183e7i 0.160791i
\(428\) 2.36306e7 6.62388e7i 0.301401 0.844854i
\(429\) 7.67991e7 0.972712
\(430\) −4.05289e7 7.01287e6i −0.509752 0.0882044i
\(431\) 2.86716e7i 0.358114i −0.983839 0.179057i \(-0.942695\pi\)
0.983839 0.179057i \(-0.0573046\pi\)
\(432\) −9.82051e6 + 1.20122e7i −0.121810 + 0.148995i
\(433\) 8.16883e7 1.00623 0.503114 0.864220i \(-0.332188\pi\)
0.503114 + 0.864220i \(0.332188\pi\)
\(434\) −1.39532e6 + 8.06386e6i −0.0170689 + 0.0986447i
\(435\) 1.30186e7i 0.158160i
\(436\) 1.14748e8 + 4.09361e7i 1.38447 + 0.493910i
\(437\) 9.72098e6 0.116484
\(438\) −2.76486e7 4.78415e6i −0.329042 0.0569354i
\(439\) 1.61778e8i 1.91217i −0.293085 0.956086i \(-0.594682\pi\)
0.293085 0.956086i \(-0.405318\pi\)
\(440\) −3.85237e7 2.17519e7i −0.452241 0.255352i
\(441\) −2.67537e7 −0.311938
\(442\) −1.76602e7 + 1.02062e8i −0.204517 + 1.18195i
\(443\) 1.00373e8i 1.15453i 0.816556 + 0.577266i \(0.195880\pi\)
−0.816556 + 0.577266i \(0.804120\pi\)
\(444\) 1.17014e7 3.28000e7i 0.133686 0.374735i
\(445\) 1.11031e7 0.125998
\(446\) 7.98638e7 + 1.38191e7i 0.900214 + 0.155767i
\(447\) 2.44356e7i 0.273590i
\(448\) −1.95060e7 + 1.17661e7i −0.216937 + 0.130857i
\(449\) −4.56145e7 −0.503922 −0.251961 0.967737i \(-0.581075\pi\)
−0.251961 + 0.967737i \(0.581075\pi\)
\(450\) 1.03579e6 5.98605e6i 0.0113667 0.0656905i
\(451\) 1.67495e8i 1.82588i
\(452\) 1.63061e8 + 5.81720e7i 1.76578 + 0.629939i
\(453\) −8.46723e7 −0.910850
\(454\) 3.39162e7 + 5.86865e6i 0.362443 + 0.0627149i
\(455\) 1.54834e7i 0.164373i
\(456\) −2.10672e6 + 3.73111e6i −0.0222184 + 0.0393498i
\(457\) −1.29981e8 −1.36186 −0.680928 0.732350i \(-0.738423\pi\)
−0.680928 + 0.732350i \(0.738423\pi\)
\(458\) −1.84024e7 + 1.06351e8i −0.191548 + 1.10700i
\(459\) 1.53873e7i 0.159120i
\(460\) −2.17674e7 + 6.10161e7i −0.223632 + 0.626861i
\(461\) −1.24776e8 −1.27358 −0.636791 0.771036i \(-0.719739\pi\)
−0.636791 + 0.771036i \(0.719739\pi\)
\(462\) 1.65053e7 + 2.85598e6i 0.167378 + 0.0289620i
\(463\) 1.12030e8i 1.12874i 0.825523 + 0.564369i \(0.190880\pi\)
−0.825523 + 0.564369i \(0.809120\pi\)
\(464\) 4.73748e7 + 3.87311e7i 0.474235 + 0.387709i
\(465\) −1.02583e7 −0.102027
\(466\) 3.08591e7 1.78341e8i 0.304947 1.76236i
\(467\) 1.67693e8i 1.64651i 0.567670 + 0.823256i \(0.307845\pi\)
−0.567670 + 0.823256i \(0.692155\pi\)
\(468\) 4.66875e7 + 1.66557e7i 0.455473 + 0.162490i
\(469\) 4.29306e7 0.416148
\(470\) 7.61133e6 + 1.31702e6i 0.0733106 + 0.0126852i
\(471\) 9.43464e7i 0.902948i
\(472\) −4.26569e7 2.40857e7i −0.405661 0.229051i
\(473\) 1.42161e8 1.34337
\(474\) 6.77717e6 3.91668e7i 0.0636376 0.367775i
\(475\) 1.67767e6i 0.0156540i
\(476\) −7.59090e6 + 2.12780e7i −0.0703837 + 0.197292i
\(477\) −5.80264e7 −0.534651
\(478\) 3.93174e7 + 6.80324e6i 0.359999 + 0.0622920i
\(479\) 7.64619e7i 0.695726i 0.937545 + 0.347863i \(0.113093\pi\)
−0.937545 + 0.347863i \(0.886907\pi\)
\(480\) −1.87018e7 2.15781e7i −0.169106 0.195115i
\(481\) −1.11258e8 −0.999763
\(482\) −4.97625e6 + 2.87588e7i −0.0444387 + 0.256821i
\(483\) 2.45284e7i 0.217684i
\(484\) 3.72297e7 + 1.32817e7i 0.328363 + 0.117143i
\(485\) 7.92009e6 0.0694232
\(486\) 7.25604e6 + 1.25554e6i 0.0632107 + 0.0109376i
\(487\) 4.97455e7i 0.430692i −0.976538 0.215346i \(-0.930912\pi\)
0.976538 0.215346i \(-0.0690880\pi\)
\(488\) −3.62645e7 + 6.42262e7i −0.312049 + 0.552653i
\(489\) 1.74565e7 0.149290
\(490\) 8.39495e6 4.85162e7i 0.0713559 0.412381i
\(491\) 1.85343e8i 1.56578i 0.622158 + 0.782891i \(0.286256\pi\)
−0.622158 + 0.782891i \(0.713744\pi\)
\(492\) −3.63253e7 + 1.01823e8i −0.305010 + 0.854970i
\(493\) 6.06859e7 0.506462
\(494\) 1.34886e7 + 2.33399e6i 0.111889 + 0.0193606i
\(495\) 2.09969e7i 0.173117i
\(496\) −3.05191e7 + 3.73301e7i −0.250107 + 0.305924i
\(497\) −2.29191e7 −0.186693
\(498\) −1.87156e7 + 1.08161e8i −0.151536 + 0.875759i
\(499\) 1.92003e8i 1.54527i −0.634848 0.772637i \(-0.718937\pi\)
0.634848 0.772637i \(-0.281063\pi\)
\(500\) 1.05303e7 + 3.75668e6i 0.0842425 + 0.0300534i
\(501\) −3.92516e7 −0.312136
\(502\) 7.81934e7 + 1.35301e7i 0.618100 + 0.106952i
\(503\) 8.45476e7i 0.664351i −0.943218 0.332175i \(-0.892217\pi\)
0.943218 0.332175i \(-0.107783\pi\)
\(504\) 9.41448e6 + 5.31577e6i 0.0735368 + 0.0415216i
\(505\) −6.88304e7 −0.534449
\(506\) 3.81762e7 2.20629e8i 0.294674 1.70298i
\(507\) 8.31226e7i 0.637816i
\(508\) −3.23149e7 + 9.05817e7i −0.246497 + 0.690954i
\(509\) −1.50345e8 −1.14008 −0.570040 0.821617i \(-0.693072\pi\)
−0.570040 + 0.821617i \(0.693072\pi\)
\(510\) −2.79039e7 4.82831e6i −0.210356 0.0363986i
\(511\) 1.95523e7i 0.146533i
\(512\) −1.34162e8 + 3.85971e6i −0.999586 + 0.0287571i
\(513\) 2.03360e6 0.0150631
\(514\) −1.83378e7 + 1.05978e8i −0.135039 + 0.780418i
\(515\) 7.52101e7i 0.550623i
\(516\) 8.64221e7 + 3.08310e7i 0.629036 + 0.224408i
\(517\) −2.66979e7 −0.193199
\(518\) −2.39111e7 4.13743e6i −0.172033 0.0297675i
\(519\) 64742.6i 0.000463114i
\(520\) −4.48540e7 + 7.94385e7i −0.319000 + 0.564964i
\(521\) −2.12869e8 −1.50521 −0.752607 0.658470i \(-0.771204\pi\)
−0.752607 + 0.658470i \(0.771204\pi\)
\(522\) 4.95172e6 2.86171e7i 0.0348133 0.201193i
\(523\) 1.22260e7i 0.0854635i −0.999087 0.0427317i \(-0.986394\pi\)
0.999087 0.0427317i \(-0.0136061\pi\)
\(524\) 9.45355e7 2.64992e8i 0.657054 1.84178i
\(525\) −4.23316e6 −0.0292541
\(526\) 1.61575e8 + 2.79580e7i 1.11024 + 0.192110i
\(527\) 4.78189e7i 0.326714i
\(528\) 7.64082e7 + 6.24673e7i 0.519085 + 0.424376i
\(529\) −1.79838e8 −1.21483
\(530\) 1.82079e7 1.05227e8i 0.122302 0.706807i
\(531\) 2.32497e7i 0.155287i
\(532\) 2.81212e6 + 1.00322e6i 0.0186767 + 0.00666288i
\(533\) 3.45386e8 2.28099
\(534\) −2.44065e7 4.22316e6i −0.160281 0.0277341i
\(535\) 6.14288e7i 0.401153i
\(536\) 2.20258e8 + 1.24366e8i 1.43034 + 0.807622i
\(537\) 6.16971e7 0.398420
\(538\) 3.35164e7 1.93699e8i 0.215234 1.24388i
\(539\) 1.70178e8i 1.08677i
\(540\) −4.55369e6 + 1.27644e7i −0.0289189 + 0.0810623i
\(541\) −2.07093e8 −1.30790 −0.653949 0.756539i \(-0.726889\pi\)
−0.653949 + 0.756539i \(0.726889\pi\)
\(542\) 1.11228e8 + 1.92462e7i 0.698581 + 0.120878i
\(543\) 1.48387e8i 0.926824i
\(544\) −1.00586e8 + 8.71781e7i −0.624801 + 0.541515i
\(545\) 1.06415e8 0.657376
\(546\) 5.88922e6 3.40351e7i 0.0361810 0.209098i
\(547\) 1.70930e8i 1.04438i 0.852831 + 0.522188i \(0.174884\pi\)
−0.852831 + 0.522188i \(0.825116\pi\)
\(548\) −1.29359e8 4.61488e7i −0.786061 0.280426i
\(549\) 3.50059e7 0.211555
\(550\) −3.80767e7 6.58855e6i −0.228860 0.0396006i
\(551\) 8.02032e6i 0.0479443i
\(552\) 7.10566e7 1.25845e8i 0.422461 0.748199i
\(553\) −2.76976e7 −0.163782
\(554\) 5.15597e7 2.97975e8i 0.303236 1.75247i
\(555\) 3.04181e7i 0.177932i
\(556\) −6.58151e7 + 1.84486e8i −0.382914 + 1.07334i
\(557\) −1.13400e8 −0.656215 −0.328107 0.944640i \(-0.606411\pi\)
−0.328107 + 0.944640i \(0.606411\pi\)
\(558\) 2.25495e7 + 3.90183e6i 0.129788 + 0.0224577i
\(559\) 2.93146e8i 1.67822i
\(560\) −1.25939e7 + 1.54046e7i −0.0717130 + 0.0877172i
\(561\) 9.78770e7 0.554360
\(562\) −1.39842e7 + 8.08177e7i −0.0787823 + 0.455300i
\(563\) 1.29905e8i 0.727947i −0.931409 0.363973i \(-0.881420\pi\)
0.931409 0.363973i \(-0.118580\pi\)
\(564\) −1.62301e7 5.79007e6i −0.0904656 0.0322735i
\(565\) 1.51220e8 0.838426
\(566\) −2.98957e8 5.17297e7i −1.64877 0.285293i
\(567\) 5.13127e6i 0.0281498i
\(568\) −1.17588e8 6.63946e7i −0.641679 0.362316i
\(569\) 1.43283e8 0.777783 0.388892 0.921284i \(-0.372858\pi\)
0.388892 + 0.921284i \(0.372858\pi\)
\(570\) −638116. + 3.68781e6i −0.00344568 + 0.0199133i
\(571\) 1.43037e8i 0.768318i −0.923267 0.384159i \(-0.874491\pi\)
0.923267 0.384159i \(-0.125509\pi\)
\(572\) 1.05945e8 2.96974e8i 0.566101 1.58683i
\(573\) 1.03437e8 0.549808
\(574\) 7.42289e7 + 1.28441e7i 0.392498 + 0.0679154i
\(575\) 5.65853e7i 0.297646i
\(576\) 3.29023e7 + 5.45459e7i 0.172171 + 0.285427i
\(577\) −2.37146e8 −1.23449 −0.617245 0.786771i \(-0.711751\pi\)
−0.617245 + 0.786771i \(0.711751\pi\)
\(578\) 1.04166e7 6.01996e7i 0.0539437 0.311752i
\(579\) 7.60972e7i 0.392042i
\(580\) 5.03415e7 + 1.79593e7i 0.258013 + 0.0920460i
\(581\) 7.64888e7 0.390004
\(582\) −1.74097e7 3.01247e6i −0.0883127 0.0152811i
\(583\) 3.69100e8i 1.86268i
\(584\) −5.66414e7 + 1.00315e8i −0.284378 + 0.503647i
\(585\) 4.32972e7 0.216268
\(586\) 2.06201e7 1.19168e8i 0.102471 0.592199i
\(587\) 2.64831e8i 1.30935i −0.755912 0.654674i \(-0.772806\pi\)
0.755912 0.654674i \(-0.227194\pi\)
\(588\) −3.69071e7 + 1.03454e8i −0.181542 + 0.508880i
\(589\) 6.31980e6 0.0309284
\(590\) −4.21619e7 7.29543e6i −0.205288 0.0355218i
\(591\) 5.75992e7i 0.279032i
\(592\) −1.10692e8 9.04959e7i −0.533521 0.436178i
\(593\) −1.78125e8 −0.854200 −0.427100 0.904204i \(-0.640465\pi\)
−0.427100 + 0.904204i \(0.640465\pi\)
\(594\) 7.98636e6 4.61549e7i 0.0381057 0.220221i
\(595\) 1.97328e7i 0.0936782i
\(596\) 9.44898e7 + 3.37091e7i 0.446320 + 0.159224i
\(597\) 2.13780e6 0.0100472
\(598\) −4.54952e8 7.87221e7i −2.12746 0.368123i
\(599\) 1.67621e8i 0.779915i 0.920833 + 0.389958i \(0.127510\pi\)
−0.920833 + 0.389958i \(0.872490\pi\)
\(600\) −2.17186e7 1.22631e7i −0.100549 0.0567737i
\(601\) 2.23815e7 0.103102 0.0515508 0.998670i \(-0.483584\pi\)
0.0515508 + 0.998670i \(0.483584\pi\)
\(602\) 1.09014e7 6.30016e7i 0.0499681 0.288777i
\(603\) 1.20050e8i 0.547531i
\(604\) −1.16806e8 + 3.27419e8i −0.530098 + 1.48591i
\(605\) 3.45262e7 0.155913
\(606\) 1.51301e8 + 2.61802e7i 0.679868 + 0.117640i
\(607\) 2.34167e8i 1.04703i −0.852017 0.523515i \(-0.824620\pi\)
0.852017 0.523515i \(-0.175380\pi\)
\(608\) 1.15216e7 + 1.32936e7i 0.0512626 + 0.0591468i
\(609\) −2.02372e7 −0.0895980
\(610\) −1.09843e7 + 6.34809e7i −0.0483932 + 0.279675i
\(611\) 5.50528e7i 0.241355i
\(612\) 5.95011e7 + 2.12269e7i 0.259580 + 0.0926047i
\(613\) 3.31792e8 1.44040 0.720202 0.693765i \(-0.244049\pi\)
0.720202 + 0.693765i \(0.244049\pi\)
\(614\) −3.04102e8 5.26199e7i −1.31375 0.227324i
\(615\) 9.44290e7i 0.405957i
\(616\) 3.38131e7 5.98845e7i 0.144658 0.256196i
\(617\) 2.84884e8 1.21287 0.606433 0.795135i \(-0.292600\pi\)
0.606433 + 0.795135i \(0.292600\pi\)
\(618\) −2.86068e7 + 1.65325e8i −0.121200 + 0.700443i
\(619\) 2.80053e8i 1.18078i 0.807119 + 0.590389i \(0.201026\pi\)
−0.807119 + 0.590389i \(0.798974\pi\)
\(620\) −1.41514e7 + 3.96678e7i −0.0593780 + 0.166442i
\(621\) −6.85903e7 −0.286410
\(622\) 3.64078e8 + 6.29977e7i 1.51294 + 0.261790i
\(623\) 1.72596e7i 0.0713784i
\(624\) 1.28812e8 1.57559e8i 0.530154 0.648470i
\(625\) 9.76562e6 0.0400000
\(626\) 1.93379e7 1.11758e8i 0.0788289 0.455570i
\(627\) 1.29355e7i 0.0524785i
\(628\) −3.64828e8 1.30152e8i −1.47302 0.525499i
\(629\) −1.41794e8 −0.569777
\(630\) 9.30523e6 + 1.61012e6i 0.0372139 + 0.00643927i
\(631\) 1.42135e8i 0.565733i −0.959159 0.282867i \(-0.908715\pi\)
0.959159 0.282867i \(-0.0912854\pi\)
\(632\) −1.42105e8 8.02377e7i −0.562934 0.317854i
\(633\) −5.81397e6 −0.0229225
\(634\) −8.25393e7 + 4.77013e8i −0.323887 + 1.87181i
\(635\) 8.40039e7i 0.328079i
\(636\) −8.00482e7 + 2.24382e8i −0.311157 + 0.872203i
\(637\) 3.50918e8 1.35765
\(638\) −1.82030e8 3.14974e7i −0.700941 0.121287i
\(639\) 6.40901e7i 0.245634i
\(640\) −1.09240e8 + 4.25506e7i −0.416717 + 0.162318i
\(641\) 2.05020e8 0.778435 0.389217 0.921146i \(-0.372745\pi\)
0.389217 + 0.921146i \(0.372745\pi\)
\(642\) −2.33649e7 + 1.35031e8i −0.0882998 + 0.510304i
\(643\) 8.84803e7i 0.332823i −0.986056 0.166412i \(-0.946782\pi\)
0.986056 0.166412i \(-0.0532180\pi\)
\(644\) −9.48487e7 3.38372e7i −0.355119 0.126688i
\(645\) 8.01464e7 0.298679
\(646\) 1.71907e7 + 2.97457e6i 0.0637669 + 0.0110338i
\(647\) 3.76256e8i 1.38922i 0.719387 + 0.694609i \(0.244423\pi\)
−0.719387 + 0.694609i \(0.755577\pi\)
\(648\) 1.48648e7 2.63263e7i 0.0546305 0.0967532i
\(649\) 1.47889e8 0.541006
\(650\) −1.35860e7 + 7.85167e7i −0.0494713 + 0.285905i
\(651\) 1.59464e7i 0.0577988i
\(652\) 2.40815e7 6.75025e7i 0.0868840 0.243544i
\(653\) 1.08922e8 0.391180 0.195590 0.980686i \(-0.437338\pi\)
0.195590 + 0.980686i \(0.437338\pi\)
\(654\) −2.33919e8 4.04759e7i −0.836242 0.144698i
\(655\) 2.45749e8i 0.874515i
\(656\) 3.43629e8 + 2.80932e8i 1.21724 + 0.995154i
\(657\) 5.46755e7 0.192795
\(658\) −2.04729e6 + 1.18317e7i −0.00718622 + 0.0415308i
\(659\) 2.73716e8i 0.956410i 0.878248 + 0.478205i \(0.158712\pi\)
−0.878248 + 0.478205i \(0.841288\pi\)
\(660\) 8.11931e7 + 2.89655e7i 0.282415 + 0.100751i
\(661\) −3.25447e8 −1.12687 −0.563437 0.826159i \(-0.690521\pi\)
−0.563437 + 0.826159i \(0.690521\pi\)
\(662\) −7.99932e7 1.38415e7i −0.275727 0.0477101i
\(663\) 2.01829e8i 0.692537i
\(664\) 3.92431e8 + 2.21581e8i 1.34048 + 0.756884i
\(665\) 2.60792e6 0.00886806
\(666\) −1.15698e7 + 6.68643e7i −0.0391654 + 0.226345i
\(667\) 2.70513e8i 0.911614i
\(668\) −5.41481e7 + 1.51782e8i −0.181658 + 0.509203i
\(669\) −1.57932e8 −0.527462
\(670\) 2.17703e8 + 3.76699e7i 0.723834 + 0.125248i
\(671\) 2.22669e8i 0.737041i
\(672\) 3.35429e7 2.90717e7i 0.110533 0.0957993i
\(673\) −1.53428e7 −0.0503339 −0.0251669 0.999683i \(-0.508012\pi\)
−0.0251669 + 0.999683i \(0.508012\pi\)
\(674\) −7.36153e7 + 4.25439e8i −0.240430 + 1.38950i
\(675\) 1.18375e7i 0.0384900i
\(676\) −3.21427e8 1.14669e8i −1.04050 0.371197i
\(677\) −1.41403e8 −0.455715 −0.227857 0.973694i \(-0.573172\pi\)
−0.227857 + 0.973694i \(0.573172\pi\)
\(678\) −3.32409e8 5.75179e7i −1.06655 0.184550i
\(679\) 1.23117e7i 0.0393285i
\(680\) −5.71643e7 + 1.01241e8i −0.181802 + 0.321980i
\(681\) −6.70697e7 −0.212366
\(682\) 2.48191e7 1.43435e8i 0.0782408 0.452171i
\(683\) 2.86757e8i 0.900020i −0.893024 0.450010i \(-0.851420\pi\)
0.893024 0.450010i \(-0.148580\pi\)
\(684\) 2.80538e6 7.86373e6i 0.00876644 0.0245731i
\(685\) −1.19966e8 −0.373237
\(686\) 1.56008e8 + 2.69947e7i 0.483254 + 0.0836193i
\(687\) 2.10311e8i 0.648623i
\(688\) 2.38441e8 2.91654e8i 0.732175 0.895576i
\(689\) 7.61111e8 2.32697
\(690\) 2.15227e7 1.24384e8i 0.0655163 0.378633i
\(691\) 7.86675e7i 0.238430i 0.992868 + 0.119215i \(0.0380378\pi\)
−0.992868 + 0.119215i \(0.961962\pi\)
\(692\) −250353. 89313.2i −0.000755500 0.000269524i
\(693\) −3.26395e7 −0.0980716
\(694\) 3.86653e8 + 6.69041e7i 1.15676 + 0.200159i
\(695\) 1.71089e8i 0.509644i
\(696\) −1.03828e8 5.86254e7i −0.307956 0.173883i
\(697\) 4.40179e8 1.29996
\(698\) −3.15041e7 + 1.82069e8i −0.0926406 + 0.535390i
\(699\) 3.52672e8i 1.03262i
\(700\) −5.83970e6 + 1.63692e7i −0.0170254 + 0.0477237i
\(701\) −3.28382e8 −0.953290 −0.476645 0.879096i \(-0.658147\pi\)
−0.476645 + 0.879096i \(0.658147\pi\)
\(702\) −9.51747e7 1.64684e7i −0.275112 0.0476037i
\(703\) 1.87396e7i 0.0539380i
\(704\) 3.46961e8 2.09289e8i 0.994403 0.599829i
\(705\) −1.50515e7 −0.0429549
\(706\) 1.17173e8 6.77170e8i 0.332977 1.92435i
\(707\) 1.06996e8i 0.302768i
\(708\) 8.99043e7 + 3.20732e7i 0.253326 + 0.0903739i
\(709\) −2.06210e8 −0.578591 −0.289296 0.957240i \(-0.593421\pi\)
−0.289296 + 0.957240i \(0.593421\pi\)
\(710\) −1.16223e8 2.01106e7i −0.324727 0.0561888i
\(711\) 7.74528e7i 0.215490i
\(712\) −4.99996e7 + 8.85517e7i −0.138525 + 0.245334i
\(713\) −2.13157e8 −0.588074
\(714\) 7.50555e6 4.33762e7i 0.0206200 0.119167i
\(715\) 2.75409e8i 0.753459i
\(716\) 8.51118e7 2.38576e8i 0.231873 0.649962i
\(717\) −7.77507e7 −0.210934
\(718\) 3.24840e8 + 5.62083e7i 0.877599 + 0.151854i
\(719\) 1.06671e8i 0.286986i 0.989651 + 0.143493i \(0.0458334\pi\)
−0.989651 + 0.143493i \(0.954167\pi\)
\(720\) 4.30768e7 + 3.52173e7i 0.115411 + 0.0943536i
\(721\) 1.16913e8 0.311930
\(722\) −6.37775e7 + 3.68584e8i −0.169456 + 0.979321i
\(723\) 5.68710e7i 0.150479i
\(724\) −5.73799e8 2.04702e8i −1.51197 0.539395i
\(725\) 4.66858e7 0.122510
\(726\) −7.58946e7 1.31323e7i −0.198336 0.0343188i
\(727\) 4.85082e8i 1.26244i 0.775602 + 0.631222i \(0.217446\pi\)
−0.775602 + 0.631222i \(0.782554\pi\)
\(728\) −1.23486e8 6.97249e7i −0.320054 0.180715i
\(729\) −1.43489e7 −0.0370370
\(730\) −1.71564e7 + 9.91506e7i −0.0441020 + 0.254875i
\(731\) 3.73601e8i 0.956436i
\(732\) 4.82910e7 1.35364e8i 0.123121 0.345120i
\(733\) 2.57203e8 0.653077 0.326538 0.945184i \(-0.394118\pi\)
0.326538 + 0.945184i \(0.394118\pi\)
\(734\) 4.25860e8 + 7.36883e7i 1.07691 + 0.186342i
\(735\) 9.59414e7i 0.241626i
\(736\) −3.88605e8 4.48373e8i −0.974709 1.12462i
\(737\) −7.63624e8 −1.90755
\(738\) 3.59168e7 2.07571e8i 0.0893571 0.516414i
\(739\) 7.60588e8i 1.88459i −0.334787 0.942294i \(-0.608664\pi\)
0.334787 0.942294i \(-0.391336\pi\)
\(740\) −1.17624e8 4.19622e7i −0.290269 0.103553i
\(741\) −2.66740e7 −0.0655591
\(742\) 1.63574e8 + 2.83039e7i 0.400409 + 0.0692843i
\(743\) 2.14669e8i 0.523363i −0.965154 0.261682i \(-0.915723\pi\)
0.965154 0.261682i \(-0.0842770\pi\)
\(744\) 4.61953e7 8.18141e7i 0.112171 0.198659i
\(745\) 8.76282e7 0.211922
\(746\) −7.44442e7 + 4.30229e8i −0.179314 + 1.03630i
\(747\) 2.13891e8i 0.513133i
\(748\) 1.35022e8 3.78480e8i 0.322627 0.904354i
\(749\) 9.54902e7 0.227255
\(750\) −2.14665e7 3.71444e6i −0.0508837 0.00880459i
\(751\) 3.72415e8i 0.879239i 0.898184 + 0.439620i \(0.144887\pi\)
−0.898184 + 0.439620i \(0.855113\pi\)
\(752\) −4.47792e7 + 5.47726e7i −0.105299 + 0.128798i
\(753\) −1.54628e8 −0.362163
\(754\) −6.49498e7 + 3.75359e8i −0.151518 + 0.875655i
\(755\) 3.03643e8i 0.705541i
\(756\) −1.98421e7 7.07864e6i −0.0459221 0.0163827i
\(757\) −2.17431e8 −0.501227 −0.250613 0.968087i \(-0.580632\pi\)
−0.250613 + 0.968087i \(0.580632\pi\)
\(758\) 5.62841e8 + 9.73906e7i 1.29234 + 0.223619i
\(759\) 4.36296e8i 0.997829i
\(760\) 1.33801e7 + 7.55491e6i 0.0304803 + 0.0172103i
\(761\) −3.79154e7 −0.0860322 −0.0430161 0.999074i \(-0.513697\pi\)
−0.0430161 + 0.999074i \(0.513697\pi\)
\(762\) 3.19516e7 1.84655e8i 0.0722150 0.417346i
\(763\) 1.65421e8i 0.372406i
\(764\) 1.42692e8 3.99980e8i 0.319978 0.896928i
\(765\) 5.51803e7 0.123254
\(766\) 1.87803e8 + 3.24963e7i 0.417846 + 0.0723015i
\(767\) 3.04957e8i 0.675854i
\(768\) 2.56313e8 5.19834e7i 0.565830 0.114757i
\(769\) −4.55616e8 −1.00189 −0.500945 0.865479i \(-0.667014\pi\)
−0.500945 + 0.865479i \(0.667014\pi\)
\(770\) 1.02418e7 5.91896e7i 0.0224339 0.129650i
\(771\) 2.09573e8i 0.457270i
\(772\) 2.94260e8 + 1.04977e8i 0.639558 + 0.228162i
\(773\) −5.34167e8 −1.15648