Properties

Label 13.7.f.a.7.1
Level 13
Weight 7
Character 13.7
Analytic conductor 2.991
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 13.f (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 7.1
Character \(\chi\) = 13.7
Dual form 13.7.f.a.2.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-14.0703 + 3.77014i) q^{2} +(-17.8024 + 30.8347i) q^{3} +(128.335 - 74.0942i) q^{4} +(-91.2022 - 91.2022i) q^{5} +(134.235 - 500.973i) q^{6} +(284.589 + 76.2554i) q^{7} +(-867.158 + 867.158i) q^{8} +(-269.354 - 466.535i) q^{9} +O(q^{10})\) \(q+(-14.0703 + 3.77014i) q^{2} +(-17.8024 + 30.8347i) q^{3} +(128.335 - 74.0942i) q^{4} +(-91.2022 - 91.2022i) q^{5} +(134.235 - 500.973i) q^{6} +(284.589 + 76.2554i) q^{7} +(-867.158 + 867.158i) q^{8} +(-269.354 - 466.535i) q^{9} +(1627.09 + 939.401i) q^{10} +(-518.109 - 1933.61i) q^{11} +5276.23i q^{12} +(-2114.15 - 597.648i) q^{13} -4291.76 q^{14} +(4435.82 - 1188.57i) q^{15} +(4189.87 - 7257.08i) q^{16} +(1546.69 - 892.984i) q^{17} +(5548.81 + 5548.81i) q^{18} +(1479.88 - 5523.00i) q^{19} +(-18462.0 - 4946.87i) q^{20} +(-7417.70 + 7417.70i) q^{21} +(14579.9 + 25253.2i) q^{22} +(-2626.58 - 1516.45i) q^{23} +(-11301.1 - 42176.1i) q^{24} +1010.68i q^{25} +(32000.0 + 438.474i) q^{26} -6775.31 q^{27} +(42172.8 - 11300.2i) q^{28} +(-14059.7 + 24352.1i) q^{29} +(-57932.4 + 33447.3i) q^{30} +(-15990.4 - 15990.4i) q^{31} +(-11279.1 + 42094.1i) q^{32} +(68846.0 + 18447.2i) q^{33} +(-18395.8 + 18395.8i) q^{34} +(-19000.5 - 32909.8i) q^{35} +(-69135.1 - 39915.2i) q^{36} +(-8297.74 - 30967.6i) q^{37} +83289.9i q^{38} +(56065.3 - 54549.7i) q^{39} +158173. q^{40} +(-20896.3 + 5599.14i) q^{41} +(76403.8 - 132335. i) q^{42} +(-11378.7 + 6569.51i) q^{43} +(-209761. - 209761. i) q^{44} +(-17983.3 + 67114.7i) q^{45} +(42674.1 + 11434.5i) q^{46} +(-22393.2 + 22393.2i) q^{47} +(149180. + 258387. i) q^{48} +(-26710.9 - 15421.6i) q^{49} +(-3810.41 - 14220.6i) q^{50} +63589.2i q^{51} +(-315601. + 79947.1i) q^{52} +135916. q^{53} +(95330.9 - 25543.8i) q^{54} +(-129097. + 223602. i) q^{55} +(-312909. + 180658. i) q^{56} +(143955. + 143955. i) q^{57} +(106014. - 395649. i) q^{58} +(41611.9 + 11149.9i) q^{59} +(481204. - 481204. i) q^{60} +(-74209.0 - 128534. i) q^{61} +(285276. + 164704. i) q^{62} +(-41079.5 - 153311. i) q^{63} -98498.1i q^{64} +(138308. + 247322. i) q^{65} -1.03823e6 q^{66} +(-440137. + 117934. i) q^{67} +(132330. - 229202. i) q^{68} +(93519.0 - 53993.2i) q^{69} +(391418. + 391418. i) q^{70} +(111253. - 415201. i) q^{71} +(638132. + 170987. i) q^{72} +(-160166. + 160166. i) q^{73} +(233504. + 404441. i) q^{74} +(-31164.1 - 17992.6i) q^{75} +(-219302. - 818445. i) q^{76} -589793. i q^{77} +(-583199. + 978906. i) q^{78} +812939. q^{79} +(-1.04399e6 + 279736. i) q^{80} +(316976. - 549019. i) q^{81} +(272908. - 157564. i) q^{82} +(-475555. - 475555. i) q^{83} +(-402341. + 1.50156e6i) q^{84} +(-222504. - 59619.7i) q^{85} +(135334. - 135334. i) q^{86} +(-500594. - 867054. i) q^{87} +(2.12603e6 + 1.22746e6i) q^{88} +(339904. + 1.26854e6i) q^{89} -1.01213e6i q^{90} +(-556090. - 331299. i) q^{91} -449442. q^{92} +(777726. - 208391. i) q^{93} +(230654. - 399505. i) q^{94} +(-638679. + 368741. i) q^{95} +(-1.09717e6 - 1.09717e6i) q^{96} +(-399838. + 1.49221e6i) q^{97} +(433973. + 116283. i) q^{98} +(-762542. + 762542. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + O(q^{10}) \) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + 4674q^{10} + 228q^{11} - 1552q^{13} - 14616q^{14} + 7486q^{15} - 2138q^{16} + 20898q^{17} - 5630q^{18} - 14036q^{19} - 14634q^{20} - 314q^{21} + 37852q^{22} + 29634q^{23} + 47154q^{24} + 510q^{26} - 107060q^{27} - 40572q^{28} + 1026q^{29} - 247734q^{30} - 118116q^{31} + 180876q^{32} + 306046q^{33} + 101898q^{34} + 104862q^{35} + 105066q^{36} - 31470q^{37} + 28510q^{39} - 275328q^{40} - 357216q^{41} - 25636q^{42} - 480486q^{43} - 797712q^{44} + 464248q^{45} + 1012050q^{46} + 140028q^{47} + 676102q^{48} + 854562q^{49} + 756714q^{50} - 771704q^{52} - 1397076q^{53} - 1271048q^{54} - 205490q^{55} - 1461108q^{56} - 1483394q^{57} + 1133806q^{58} + 1568052q^{59} + 886808q^{60} + 768676q^{61} + 3741966q^{62} + 1336264q^{63} - 946968q^{65} - 5076928q^{66} - 1489892q^{67} - 569052q^{68} - 1475766q^{69} - 2626556q^{70} + 2136948q^{71} + 4787052q^{72} + 326326q^{73} + 2159718q^{74} + 3466008q^{75} + 1522158q^{76} - 1573544q^{78} - 1734344q^{79} - 5214300q^{80} - 773072q^{81} - 3540426q^{82} - 3642132q^{83} + 2952364q^{84} + 3509916q^{85} - 132324q^{86} + 531698q^{87} + 4478052q^{88} + 632754q^{89} - 2946788q^{91} - 1656060q^{92} - 295514q^{93} + 1552210q^{94} - 2753718q^{95} - 3979208q^{96} + 2258214q^{97} + 4984308q^{98} + 4336480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −14.0703 + 3.77014i −1.75879 + 0.471267i −0.986467 0.163960i \(-0.947573\pi\)
−0.772326 + 0.635227i \(0.780907\pi\)
\(3\) −17.8024 + 30.8347i −0.659350 + 1.14203i 0.321434 + 0.946932i \(0.395835\pi\)
−0.980784 + 0.195096i \(0.937498\pi\)
\(4\) 128.335 74.0942i 2.00523 1.15772i
\(5\) −91.2022 91.2022i −0.729618 0.729618i 0.240926 0.970544i \(-0.422549\pi\)
−0.970544 + 0.240926i \(0.922549\pi\)
\(6\) 134.235 500.973i 0.621460 2.31932i
\(7\) 284.589 + 76.2554i 0.829706 + 0.222319i 0.648585 0.761142i \(-0.275361\pi\)
0.181121 + 0.983461i \(0.442028\pi\)
\(8\) −867.158 + 867.158i −1.69367 + 1.69367i
\(9\) −269.354 466.535i −0.369485 0.639966i
\(10\) 1627.09 + 939.401i 1.62709 + 0.939401i
\(11\) −518.109 1933.61i −0.389263 1.45275i −0.831336 0.555770i \(-0.812423\pi\)
0.442073 0.896979i \(-0.354243\pi\)
\(12\) 5276.23i 3.05338i
\(13\) −2114.15 597.648i −0.962289 0.272029i
\(14\) −4291.76 −1.56405
\(15\) 4435.82 1188.57i 1.31432 0.352170i
\(16\) 4189.87 7257.08i 1.02292 1.77175i
\(17\) 1546.69 892.984i 0.314816 0.181759i −0.334263 0.942480i \(-0.608487\pi\)
0.649080 + 0.760720i \(0.275154\pi\)
\(18\) 5548.81 + 5548.81i 0.951442 + 0.951442i
\(19\) 1479.88 5523.00i 0.215758 0.805220i −0.770140 0.637875i \(-0.779814\pi\)
0.985898 0.167345i \(-0.0535195\pi\)
\(20\) −18462.0 4946.87i −2.30775 0.618359i
\(21\) −7417.70 + 7417.70i −0.800961 + 0.800961i
\(22\) 14579.9 + 25253.2i 1.36927 + 2.37164i
\(23\) −2626.58 1516.45i −0.215877 0.124637i 0.388163 0.921591i \(-0.373110\pi\)
−0.604040 + 0.796954i \(0.706443\pi\)
\(24\) −11301.1 42176.1i −0.817496 3.05094i
\(25\) 1010.68i 0.0646837i
\(26\) 32000.0 + 438.474i 1.82067 + 0.0249473i
\(27\) −6775.31 −0.344221
\(28\) 42172.8 11300.2i 1.92114 0.514767i
\(29\) −14059.7 + 24352.1i −0.576477 + 0.998487i 0.419403 + 0.907800i \(0.362239\pi\)
−0.995879 + 0.0906865i \(0.971094\pi\)
\(30\) −57932.4 + 33447.3i −2.14564 + 1.23879i
\(31\) −15990.4 15990.4i −0.536752 0.536752i 0.385822 0.922573i \(-0.373918\pi\)
−0.922573 + 0.385822i \(0.873918\pi\)
\(32\) −11279.1 + 42094.1i −0.344210 + 1.28461i
\(33\) 68846.0 + 18447.2i 1.91574 + 0.513321i
\(34\) −18395.8 + 18395.8i −0.468040 + 0.468040i
\(35\) −19000.5 32909.8i −0.443160 0.767576i
\(36\) −69135.1 39915.2i −1.48181 0.855521i
\(37\) −8297.74 30967.6i −0.163815 0.611367i −0.998188 0.0601668i \(-0.980837\pi\)
0.834373 0.551200i \(-0.185830\pi\)
\(38\) 83289.9i 1.51789i
\(39\) 56065.3 54549.7i 0.945150 0.919598i
\(40\) 158173. 2.47146
\(41\) −20896.3 + 5599.14i −0.303192 + 0.0812399i −0.407207 0.913336i \(-0.633497\pi\)
0.104016 + 0.994576i \(0.466831\pi\)
\(42\) 76403.8 132335.i 1.03126 1.78619i
\(43\) −11378.7 + 6569.51i −0.143116 + 0.0826280i −0.569848 0.821750i \(-0.692998\pi\)
0.426732 + 0.904378i \(0.359665\pi\)
\(44\) −209761. 209761.i −2.46244 2.46244i
\(45\) −17983.3 + 67114.7i −0.197348 + 0.736513i
\(46\) 42674.1 + 11434.5i 0.438420 + 0.117474i
\(47\) −22393.2 + 22393.2i −0.215686 + 0.215686i −0.806678 0.590992i \(-0.798737\pi\)
0.590992 + 0.806678i \(0.298737\pi\)
\(48\) 149180. + 258387.i 1.34892 + 2.33640i
\(49\) −26710.9 15421.6i −0.227039 0.131081i
\(50\) −3810.41 14220.6i −0.0304833 0.113765i
\(51\) 63589.2i 0.479372i
\(52\) −315601. + 79947.1i −2.24455 + 0.568582i
\(53\) 135916. 0.912944 0.456472 0.889738i \(-0.349113\pi\)
0.456472 + 0.889738i \(0.349113\pi\)
\(54\) 95330.9 25543.8i 0.605414 0.162220i
\(55\) −129097. + 223602.i −0.775938 + 1.34396i
\(56\) −312909. + 180658.i −1.78178 + 1.02871i
\(57\) 143955. + 143955.i 0.777323 + 0.777323i
\(58\) 106014. 395649.i 0.543349 2.02781i
\(59\) 41611.9 + 11149.9i 0.202610 + 0.0542893i 0.358697 0.933454i \(-0.383221\pi\)
−0.156086 + 0.987743i \(0.549888\pi\)
\(60\) 481204. 481204.i 2.22780 2.22780i
\(61\) −74209.0 128534.i −0.326939 0.566276i 0.654964 0.755660i \(-0.272684\pi\)
−0.981903 + 0.189385i \(0.939351\pi\)
\(62\) 285276. + 164704.i 1.19699 + 0.691081i
\(63\) −41079.5 153311.i −0.164287 0.613127i
\(64\) 98498.1i 0.375741i
\(65\) 138308. + 247322.i 0.503626 + 0.900580i
\(66\) −1.03823e6 −3.61130
\(67\) −440137. + 117934.i −1.46340 + 0.392117i −0.900663 0.434519i \(-0.856919\pi\)
−0.562738 + 0.826636i \(0.690252\pi\)
\(68\) 132330. 229202.i 0.420854 0.728940i
\(69\) 93519.0 53993.2i 0.284677 0.164358i
\(70\) 391418. + 391418.i 1.14116 + 1.14116i
\(71\) 111253. 415201.i 0.310839 1.16007i −0.616962 0.786993i \(-0.711637\pi\)
0.927801 0.373074i \(-0.121696\pi\)
\(72\) 638132. + 170987.i 1.70967 + 0.458106i
\(73\) −160166. + 160166.i −0.411720 + 0.411720i −0.882337 0.470618i \(-0.844031\pi\)
0.470618 + 0.882337i \(0.344031\pi\)
\(74\) 233504. + 404441.i 0.576234 + 0.998067i
\(75\) −31164.1 17992.6i −0.0738706 0.0426492i
\(76\) −219302. 818445.i −0.499576 1.86444i
\(77\) 589793.i 1.29190i
\(78\) −583199. + 978906.i −1.22895 + 2.06280i
\(79\) 812939. 1.64883 0.824417 0.565983i \(-0.191503\pi\)
0.824417 + 0.565983i \(0.191503\pi\)
\(80\) −1.04399e6 + 279736.i −2.03904 + 0.546358i
\(81\) 316976. 549019.i 0.596447 1.03308i
\(82\) 272908. 157564.i 0.494965 0.285768i
\(83\) −475555. 475555.i −0.831699 0.831699i 0.156050 0.987749i \(-0.450124\pi\)
−0.987749 + 0.156050i \(0.950124\pi\)
\(84\) −402341. + 1.50156e6i −0.678824 + 2.53340i
\(85\) −222504. 59619.7i −0.362310 0.0970808i
\(86\) 135334. 135334.i 0.212771 0.212771i
\(87\) −500594. 867054.i −0.760199 1.31670i
\(88\) 2.12603e6 + 1.22746e6i 3.11976 + 1.80119i
\(89\) 339904. + 1.26854e6i 0.482155 + 1.79943i 0.592544 + 0.805538i \(0.298124\pi\)
−0.110389 + 0.993888i \(0.535210\pi\)
\(90\) 1.01213e6i 1.38838i
\(91\) −556090. 331299.i −0.737940 0.439639i
\(92\) −449442. −0.577179
\(93\) 777726. 208391.i 0.966892 0.259078i
\(94\) 230654. 399505.i 0.277701 0.480992i
\(95\) −638679. + 368741.i −0.744924 + 0.430082i
\(96\) −1.09717e6 1.09717e6i −1.24011 1.24011i
\(97\) −399838. + 1.49221e6i −0.438095 + 1.63499i 0.295454 + 0.955357i \(0.404529\pi\)
−0.733549 + 0.679636i \(0.762138\pi\)
\(98\) 433973. + 116283.i 0.461089 + 0.123548i
\(99\) −762542. + 762542.i −0.785883 + 0.785883i
\(100\) 74885.7 + 129706.i 0.0748857 + 0.129706i
\(101\) −382178. 220651.i −0.370939 0.214161i 0.302930 0.953013i \(-0.402035\pi\)
−0.673868 + 0.738851i \(0.735369\pi\)
\(102\) −239740. 894721.i −0.225912 0.843116i
\(103\) 673740.i 0.616567i −0.951295 0.308284i \(-0.900245\pi\)
0.951295 0.308284i \(-0.0997546\pi\)
\(104\) 2.35156e6 1.31505e6i 2.09052 1.16907i
\(105\) 1.35302e6 1.16879
\(106\) −1.91239e6 + 512423.i −1.60568 + 0.430241i
\(107\) 451255. 781596.i 0.368358 0.638015i −0.620951 0.783849i \(-0.713253\pi\)
0.989309 + 0.145834i \(0.0465867\pi\)
\(108\) −869509. + 502011.i −0.690244 + 0.398513i
\(109\) 550926. + 550926.i 0.425416 + 0.425416i 0.887064 0.461647i \(-0.152741\pi\)
−0.461647 + 0.887064i \(0.652741\pi\)
\(110\) 973425. 3.63287e6i 0.731348 2.72943i
\(111\) 1.10260e6 + 295440.i 0.806209 + 0.216023i
\(112\) 1.74578e6 1.74578e6i 1.24261 1.24261i
\(113\) 451409. + 781863.i 0.312849 + 0.541870i 0.978978 0.203966i \(-0.0653833\pi\)
−0.666129 + 0.745837i \(0.732050\pi\)
\(114\) −2.56822e6 1.48276e6i −1.73348 1.00082i
\(115\) 101246. + 377854.i 0.0665706 + 0.248445i
\(116\) 4.16697e6i 2.66960i
\(117\) 290631. + 1.14730e6i 0.181462 + 0.716343i
\(118\) −627530. −0.381934
\(119\) 508267. 136190.i 0.301614 0.0808171i
\(120\) −2.81587e6 + 4.87724e6i −1.62956 + 2.82248i
\(121\) −1.93619e6 + 1.11786e6i −1.09293 + 0.631003i
\(122\) 1.52874e6 + 1.52874e6i 0.841886 + 0.841886i
\(123\) 199357. 744009.i 0.107131 0.399819i
\(124\) −3.23692e6 867329.i −1.69772 0.454903i
\(125\) −1.33286e6 + 1.33286e6i −0.682423 + 0.682423i
\(126\) 1.15600e6 + 2.00226e6i 0.577893 + 1.00094i
\(127\) −1.58068e6 912605.i −0.771671 0.445524i 0.0617994 0.998089i \(-0.480316\pi\)
−0.833470 + 0.552564i \(0.813649\pi\)
\(128\) −350510. 1.30812e6i −0.167136 0.623760i
\(129\) 467813.i 0.217923i
\(130\) −2.87848e6 2.95846e6i −1.31019 1.34659i
\(131\) 1.92948e6 0.858277 0.429138 0.903239i \(-0.358817\pi\)
0.429138 + 0.903239i \(0.358817\pi\)
\(132\) 1.02022e7 2.73366e6i 4.43579 1.18857i
\(133\) 842318. 1.45894e6i 0.358032 0.620129i
\(134\) 5.74825e6 3.31875e6i 2.38903 1.37930i
\(135\) 617923. + 617923.i 0.251150 + 0.251150i
\(136\) −566869. + 2.11559e6i −0.225355 + 0.841035i
\(137\) −2.16536e6 580208.i −0.842111 0.225643i −0.188121 0.982146i \(-0.560240\pi\)
−0.653990 + 0.756503i \(0.726906\pi\)
\(138\) −1.11228e6 + 1.11228e6i −0.423231 + 0.423231i
\(139\) −1.90441e6 3.29853e6i −0.709114 1.22822i −0.965186 0.261563i \(-0.915762\pi\)
0.256073 0.966658i \(-0.417571\pi\)
\(140\) −4.87685e6 2.81565e6i −1.77728 1.02611i
\(141\) −291834. 1.08914e6i −0.104107 0.388532i
\(142\) 6.26145e6i 2.18681i
\(143\) −60257.1 + 4.39758e6i −0.0206063 + 1.50386i
\(144\) −4.51424e6 −1.51181
\(145\) 3.50324e6 938690.i 1.14912 0.307906i
\(146\) 1.64974e6 2.85744e6i 0.530100 0.918160i
\(147\) 951039. 549083.i 0.299396 0.172857i
\(148\) −3.35941e6 3.35941e6i −1.03628 1.03628i
\(149\) 1.29914e6 4.84845e6i 0.392732 1.46570i −0.432876 0.901453i \(-0.642501\pi\)
0.825608 0.564244i \(-0.190832\pi\)
\(150\) 506325. + 135669.i 0.150022 + 0.0401983i
\(151\) −1.29429e6 + 1.29429e6i −0.375923 + 0.375923i −0.869629 0.493706i \(-0.835642\pi\)
0.493706 + 0.869629i \(0.335642\pi\)
\(152\) 3.50602e6 + 6.07261e6i 0.998353 + 1.72920i
\(153\) −833217. 481058.i −0.232640 0.134315i
\(154\) 2.22360e6 + 8.29859e6i 0.608828 + 2.27218i
\(155\) 2.91671e6i 0.783247i
\(156\) 3.15333e6 1.11547e7i 0.830606 2.93823i
\(157\) 168653. 0.0435807 0.0217904 0.999763i \(-0.493063\pi\)
0.0217904 + 0.999763i \(0.493063\pi\)
\(158\) −1.14383e7 + 3.06489e6i −2.89996 + 0.777041i
\(159\) −2.41964e6 + 4.19095e6i −0.601950 + 1.04261i
\(160\) 4.86775e6 2.81040e6i 1.18842 0.686132i
\(161\) −631857. 631857.i −0.151405 0.151405i
\(162\) −2.39009e6 + 8.91993e6i −0.562172 + 2.09805i
\(163\) 6.10637e6 + 1.63620e6i 1.41000 + 0.377810i 0.881927 0.471386i \(-0.156246\pi\)
0.528078 + 0.849196i \(0.322913\pi\)
\(164\) −2.26686e6 + 2.26686e6i −0.513917 + 0.513917i
\(165\) −4.59648e6 7.96133e6i −1.02323 1.77229i
\(166\) 8.48412e6 + 4.89831e6i 1.85474 + 1.07083i
\(167\) −1.22102e6 4.55691e6i −0.262164 0.978410i −0.963963 0.266035i \(-0.914286\pi\)
0.701799 0.712375i \(-0.252380\pi\)
\(168\) 1.28646e7i 2.71312i
\(169\) 4.11244e6 + 2.52703e6i 0.852001 + 0.523541i
\(170\) 3.35548e6 0.682980
\(171\) −2.97529e6 + 797226.i −0.595033 + 0.159439i
\(172\) −973525. + 1.68619e6i −0.191321 + 0.331377i
\(173\) −2.67944e6 + 1.54697e6i −0.517494 + 0.298775i −0.735909 0.677081i \(-0.763245\pi\)
0.218415 + 0.975856i \(0.429911\pi\)
\(174\) 1.03124e7 + 1.03124e7i 1.95755 + 1.95755i
\(175\) −77070.0 + 287629.i −0.0143804 + 0.0536684i
\(176\) −1.62032e7 4.34162e6i −2.97209 0.796369i
\(177\) −1.08460e6 + 1.08460e6i −0.195591 + 0.195591i
\(178\) −9.56514e6 1.65673e7i −1.69602 2.93759i
\(179\) 2.95727e6 + 1.70738e6i 0.515623 + 0.297695i 0.735142 0.677913i \(-0.237116\pi\)
−0.219519 + 0.975608i \(0.570449\pi\)
\(180\) 2.66492e6 + 9.94563e6i 0.456948 + 1.70535i
\(181\) 3.11821e6i 0.525859i −0.964815 0.262930i \(-0.915311\pi\)
0.964815 0.262930i \(-0.0846887\pi\)
\(182\) 9.07342e6 + 2.56496e6i 1.50507 + 0.425468i
\(183\) 5.28441e6 0.862270
\(184\) 3.59266e6 962651.i 0.576717 0.154531i
\(185\) −2.06754e6 + 3.58108e6i −0.326542 + 0.565587i
\(186\) −1.01572e7 + 5.86427e6i −1.57847 + 0.911329i
\(187\) −2.52804e6 2.52804e6i −0.386597 0.386597i
\(188\) −1.21462e6 + 4.53303e6i −0.182796 + 0.682205i
\(189\) −1.92818e6 516654.i −0.285603 0.0765270i
\(190\) 7.59622e6 7.59622e6i 1.10748 1.10748i
\(191\) 5.01644e6 + 8.68872e6i 0.719938 + 1.24697i 0.961024 + 0.276466i \(0.0891633\pi\)
−0.241085 + 0.970504i \(0.577503\pi\)
\(192\) 3.03717e6 + 1.75351e6i 0.429106 + 0.247745i
\(193\) 844237. + 3.15074e6i 0.117434 + 0.438268i 0.999457 0.0329365i \(-0.0104859\pi\)
−0.882024 + 0.471205i \(0.843819\pi\)
\(194\) 2.25034e7i 3.08207i
\(195\) −1.00883e7 138233.i −1.36055 0.0186427i
\(196\) −4.57059e6 −0.607022
\(197\) −4.75466e6 + 1.27401e6i −0.621900 + 0.166638i −0.555991 0.831188i \(-0.687661\pi\)
−0.0659086 + 0.997826i \(0.520995\pi\)
\(198\) 7.85434e6 1.36041e7i 1.01185 1.75257i
\(199\) 1.06199e7 6.13141e6i 1.34760 0.778039i 0.359693 0.933071i \(-0.382881\pi\)
0.987910 + 0.155032i \(0.0495479\pi\)
\(200\) −876421. 876421.i −0.109553 0.109553i
\(201\) 4.19904e6 1.56710e7i 0.517085 1.92979i
\(202\) 6.20926e6 + 1.66377e6i 0.753331 + 0.201855i
\(203\) −5.85821e6 + 5.85821e6i −0.700289 + 0.700289i
\(204\) 4.71159e6 + 8.16071e6i 0.554980 + 0.961253i
\(205\) 2.41644e6 + 1.39513e6i 0.280488 + 0.161940i
\(206\) 2.54009e6 + 9.47974e6i 0.290568 + 1.08441i
\(207\) 1.63385e6i 0.184205i
\(208\) −1.31952e7 + 1.28385e7i −1.46631 + 1.42667i
\(209\) −1.14461e7 −1.25377
\(210\) −1.90375e7 + 5.10107e6i −2.05566 + 0.550813i
\(211\) 2.30135e6 3.98606e6i 0.244983 0.424323i −0.717144 0.696925i \(-0.754551\pi\)
0.962127 + 0.272602i \(0.0878843\pi\)
\(212\) 1.74428e7 1.00706e7i 1.83067 1.05694i
\(213\) 1.08220e7 + 1.08220e7i 1.11988 + 1.11988i
\(214\) −3.40258e6 + 1.26986e7i −0.347190 + 1.29573i
\(215\) 1.63692e6 + 438611.i 0.164707 + 0.0441330i
\(216\) 5.87526e6 5.87526e6i 0.582997 0.582997i
\(217\) −3.33133e6 5.77004e6i −0.326016 0.564676i
\(218\) −9.82879e6 5.67465e6i −0.948704 0.547734i
\(219\) −2.08733e6 7.79002e6i −0.198728 0.741663i
\(220\) 3.82613e7i 3.59328i
\(221\) −3.80363e6 + 963523.i −0.352388 + 0.0892659i
\(222\) −1.66278e7 −1.51976
\(223\) 1.62138e7 4.34447e6i 1.46208 0.391762i 0.561869 0.827226i \(-0.310082\pi\)
0.900206 + 0.435464i \(0.143416\pi\)
\(224\) −6.41981e6 + 1.11194e7i −0.571187 + 0.989324i
\(225\) 471519. 272232.i 0.0413954 0.0238996i
\(226\) −9.29921e6 9.29921e6i −0.805602 0.805602i
\(227\) −104400. + 389626.i −0.00892530 + 0.0333097i −0.970245 0.242126i \(-0.922155\pi\)
0.961320 + 0.275435i \(0.0888220\pi\)
\(228\) 2.91407e7 + 7.80822e6i 2.45864 + 0.658790i
\(229\) −3.04556e6 + 3.04556e6i −0.253606 + 0.253606i −0.822447 0.568841i \(-0.807392\pi\)
0.568841 + 0.822447i \(0.307392\pi\)
\(230\) −2.84912e6 4.93482e6i −0.234168 0.405590i
\(231\) 1.81861e7 + 1.04998e7i 1.47538 + 0.851811i
\(232\) −8.92514e6 3.33091e7i −0.714745 2.66746i
\(233\) 446782.i 0.0353206i −0.999844 0.0176603i \(-0.994378\pi\)
0.999844 0.0176603i \(-0.00562173\pi\)
\(234\) −8.41478e6 1.50472e7i −0.656742 1.17438i
\(235\) 4.08461e6 0.314736
\(236\) 6.16640e6 1.65228e6i 0.469133 0.125704i
\(237\) −1.44723e7 + 2.50668e7i −1.08716 + 1.88301i
\(238\) −6.63804e6 + 3.83247e6i −0.492389 + 0.284281i
\(239\) −6.94208e6 6.94208e6i −0.508506 0.508506i 0.405562 0.914068i \(-0.367076\pi\)
−0.914068 + 0.405562i \(0.867076\pi\)
\(240\) 9.95995e6 3.71711e7i 0.720483 2.68888i
\(241\) −1.79684e7 4.81461e6i −1.28368 0.343961i −0.448424 0.893821i \(-0.648015\pi\)
−0.835257 + 0.549859i \(0.814681\pi\)
\(242\) 2.30284e7 2.30284e7i 1.62486 1.62486i
\(243\) 8.81631e6 + 1.52703e7i 0.614424 + 1.06421i
\(244\) −1.90472e7 1.09969e7i −1.31118 0.757010i
\(245\) 1.02961e6 + 3.84257e6i 0.0700126 + 0.261291i
\(246\) 1.12201e7i 0.753685i
\(247\) −6.42951e6 + 1.07920e7i −0.426665 + 0.716162i
\(248\) 2.77323e7 1.81816
\(249\) 2.31296e7 6.19757e6i 1.49820 0.401442i
\(250\) 1.37287e7 2.37788e7i 0.878637 1.52184i
\(251\) −2.24171e7 + 1.29425e7i −1.41761 + 0.818460i −0.996089 0.0883562i \(-0.971839\pi\)
−0.421526 + 0.906816i \(0.638505\pi\)
\(252\) −1.66314e7 1.66314e7i −1.03926 1.03926i
\(253\) −1.57138e6 + 5.86446e6i −0.0970329 + 0.362132i
\(254\) 2.56813e7 + 6.88129e6i 1.56717 + 0.419922i
\(255\) 5.79947e6 5.79947e6i 0.349758 0.349758i
\(256\) 1.30155e7 + 2.25436e7i 0.775786 + 1.34370i
\(257\) −1.59072e7 9.18403e6i −0.937118 0.541046i −0.0480626 0.998844i \(-0.515305\pi\)
−0.889056 + 0.457799i \(0.848638\pi\)
\(258\) 1.76372e6 + 6.58229e6i 0.102700 + 0.383281i
\(259\) 9.44578e6i 0.543674i
\(260\) 3.60749e7 + 2.14922e7i 2.05251 + 1.22281i
\(261\) 1.51481e7 0.851997
\(262\) −2.71485e7 + 7.27442e6i −1.50953 + 0.404478i
\(263\) 1.04516e7 1.81027e7i 0.574534 0.995122i −0.421558 0.906802i \(-0.638517\pi\)
0.996092 0.0883210i \(-0.0281501\pi\)
\(264\) −7.56970e7 + 4.37037e7i −4.11402 + 2.37523i
\(265\) −1.23959e7 1.23959e7i −0.666100 0.666100i
\(266\) −6.35131e6 + 2.37034e7i −0.337457 + 1.25941i
\(267\) −4.51662e7 1.21023e7i −2.37290 0.635818i
\(268\) −4.77467e7 + 4.77467e7i −2.48050 + 2.48050i
\(269\) 8.68622e6 + 1.50450e7i 0.446245 + 0.772920i 0.998138 0.0609954i \(-0.0194275\pi\)
−0.551893 + 0.833915i \(0.686094\pi\)
\(270\) −1.10240e7 6.36473e6i −0.560079 0.323362i
\(271\) −96105.5 358671.i −0.00482881 0.0180214i 0.963469 0.267818i \(-0.0863027\pi\)
−0.968298 + 0.249797i \(0.919636\pi\)
\(272\) 1.49660e7i 0.743700i
\(273\) 2.01153e7 1.12490e7i 0.988641 0.552872i
\(274\) 3.26549e7 1.58744
\(275\) 1.95427e6 523644.i 0.0939692 0.0251790i
\(276\) 8.00117e6 1.38584e7i 0.380563 0.659154i
\(277\) 3.59088e7 2.07320e7i 1.68952 0.975442i 0.734630 0.678468i \(-0.237356\pi\)
0.954885 0.296974i \(-0.0959776\pi\)
\(278\) 3.92316e7 + 3.92316e7i 1.82600 + 1.82600i
\(279\) −3.15300e6 + 1.17671e7i −0.145181 + 0.541824i
\(280\) 4.50144e7 + 1.20616e7i 2.05059 + 0.549453i
\(281\) 2.30364e7 2.30364e7i 1.03823 1.03823i 0.0389956 0.999239i \(-0.487584\pi\)
0.999239 0.0389956i \(-0.0124158\pi\)
\(282\) 8.21241e6 + 1.42243e7i 0.366204 + 0.634285i
\(283\) 3.55194e6 + 2.05072e6i 0.156714 + 0.0904786i 0.576306 0.817234i \(-0.304494\pi\)
−0.419592 + 0.907713i \(0.637827\pi\)
\(284\) −1.64864e7 6.15280e7i −0.719730 2.68607i
\(285\) 2.62580e7i 1.13430i
\(286\) −1.57317e7 6.21027e7i −0.672475 2.65468i
\(287\) −6.37381e6 −0.269621
\(288\) 2.26765e7 6.07614e6i 0.949287 0.254361i
\(289\) −1.04739e7 + 1.81414e7i −0.433927 + 0.751584i
\(290\) −4.57528e7 + 2.64154e7i −1.87596 + 1.08309i
\(291\) −3.88940e7 3.88940e7i −1.57835 1.57835i
\(292\) −8.68752e6 + 3.24223e7i −0.348937 + 1.30225i
\(293\) −7.31674e6 1.96052e6i −0.290881 0.0779412i 0.110428 0.993884i \(-0.464778\pi\)
−0.401309 + 0.915943i \(0.631445\pi\)
\(294\) −1.13113e7 + 1.13113e7i −0.445114 + 0.445114i
\(295\) −2.77820e6 4.81199e6i −0.108218 0.187439i
\(296\) 3.40492e7 + 1.96583e7i 1.31290 + 0.758004i
\(297\) 3.51035e6 + 1.31008e7i 0.133993 + 0.500067i
\(298\) 7.31173e7i 2.76294i
\(299\) 4.64667e6 + 4.77578e6i 0.173831 + 0.178661i
\(300\) −5.33260e6 −0.197504
\(301\) −3.73922e6 + 1.00192e6i −0.137114 + 0.0367396i
\(302\) 1.33314e7 2.30907e7i 0.484011 0.838331i
\(303\) 1.36074e7 7.85625e6i 0.489157 0.282415i
\(304\) −3.38803e7 3.38803e7i −1.20594 1.20594i
\(305\) −4.95454e6 + 1.84906e7i −0.174624 + 0.651705i
\(306\) 1.35373e7 + 3.62731e6i 0.472463 + 0.126596i
\(307\) 2.89205e6 2.89205e6i 0.0999519 0.0999519i −0.655363 0.755314i \(-0.727484\pi\)
0.755314 + 0.655363i \(0.227484\pi\)
\(308\) −4.37002e7 7.56910e7i −1.49566 2.59055i
\(309\) 2.07746e7 + 1.19942e7i 0.704137 + 0.406533i
\(310\) −1.09964e7 4.10391e7i −0.369118 1.37757i
\(311\) 2.81073e7i 0.934411i 0.884149 + 0.467206i \(0.154739\pi\)
−0.884149 + 0.467206i \(0.845261\pi\)
\(312\) −1.31433e6 + 9.59207e7i −0.0432755 + 3.15826i
\(313\) −3.23820e7 −1.05602 −0.528008 0.849239i \(-0.677061\pi\)
−0.528008 + 0.849239i \(0.677061\pi\)
\(314\) −2.37300e6 + 635844.i −0.0766494 + 0.0205381i
\(315\) −1.02357e7 + 1.77288e7i −0.327482 + 0.567215i
\(316\) 1.04328e8 6.02341e7i 3.30630 1.90889i
\(317\) −6.51606e6 6.51606e6i −0.204554 0.204554i 0.597394 0.801948i \(-0.296203\pi\)
−0.801948 + 0.597394i \(0.796203\pi\)
\(318\) 1.82448e7 6.80905e7i 0.567358 2.11741i
\(319\) 5.43719e7 + 1.45689e7i 1.67495 + 0.448802i
\(320\) −8.98325e6 + 8.98325e6i −0.274147 + 0.274147i
\(321\) 1.60669e7 + 2.78286e7i 0.485754 + 0.841350i
\(322\) 1.12726e7 + 6.50826e6i 0.337643 + 0.194938i
\(323\) −2.64303e6 9.86391e6i −0.0784321 0.292713i
\(324\) 9.39444e7i 2.76208i
\(325\) 604032. 2.13673e6i 0.0175958 0.0622444i
\(326\) −9.20875e7 −2.65796
\(327\) −2.67955e7 + 7.17984e6i −0.766335 + 0.205339i
\(328\) 1.32650e7 2.29757e7i 0.375912 0.651099i
\(329\) −8.08045e6 + 4.66525e6i −0.226907 + 0.131005i
\(330\) 9.46893e7 + 9.46893e7i 2.63487 + 2.63487i
\(331\) 3.17249e6 1.18399e7i 0.0874814 0.326485i −0.908291 0.418339i \(-0.862613\pi\)
0.995773 + 0.0918536i \(0.0292792\pi\)
\(332\) −9.62661e7 2.57944e7i −2.63063 0.704874i
\(333\) −1.22124e7 + 1.22124e7i −0.330727 + 0.330727i
\(334\) 3.43603e7 + 5.95139e7i 0.922185 + 1.59727i
\(335\) 5.08973e7 + 2.93856e7i 1.35382 + 0.781627i
\(336\) 2.27516e7 + 8.49101e7i 0.599782 + 2.23842i
\(337\) 2.28964e7i 0.598243i 0.954215 + 0.299121i \(0.0966935\pi\)
−0.954215 + 0.299121i \(0.903306\pi\)
\(338\) −6.73907e7 2.00517e7i −1.74522 0.519280i
\(339\) −3.21447e7 −0.825108
\(340\) −3.29725e7 + 8.83496e6i −0.838910 + 0.224785i
\(341\) −2.26344e7 + 3.92039e7i −0.570828 + 0.988703i
\(342\) 3.88577e7 2.24345e7i 0.971401 0.560839i
\(343\) −3.09359e7 3.09359e7i −0.766621 0.766621i
\(344\) 4.17035e6 1.55639e7i 0.102446 0.382335i
\(345\) −1.34534e7 3.60484e6i −0.327624 0.0877866i
\(346\) 3.18683e7 3.18683e7i 0.769362 0.769362i
\(347\) −1.27477e7 2.20797e7i −0.305101 0.528451i 0.672183 0.740385i \(-0.265357\pi\)
−0.977284 + 0.211935i \(0.932024\pi\)
\(348\) −1.28487e8 7.41822e7i −3.04875 1.76020i
\(349\) 1.93822e7 + 7.23352e7i 0.455959 + 1.70166i 0.685253 + 0.728305i \(0.259692\pi\)
−0.229294 + 0.973357i \(0.573642\pi\)
\(350\) 4.33761e6i 0.101169i
\(351\) 1.43240e7 + 4.04925e6i 0.331240 + 0.0936382i
\(352\) 8.72374e7 2.00020
\(353\) 6.83814e7 1.83227e7i 1.55458 0.416549i 0.623639 0.781712i \(-0.285654\pi\)
0.930943 + 0.365163i \(0.118987\pi\)
\(354\) 1.11716e7 1.93497e7i 0.251828 0.436180i
\(355\) −4.80137e7 + 2.77207e7i −1.07320 + 0.619612i
\(356\) 1.37613e8 + 1.37613e8i 3.05007 + 3.05007i
\(357\) −4.84902e6 + 1.80968e7i −0.106574 + 0.397738i
\(358\) −4.80469e7 1.28741e7i −1.04717 0.280588i
\(359\) 3.88671e7 3.88671e7i 0.840037 0.840037i −0.148826 0.988863i \(-0.547550\pi\)
0.988863 + 0.148826i \(0.0475495\pi\)
\(360\) −4.26047e7 7.37935e7i −0.913166 1.58165i
\(361\) 1.24294e7 + 7.17612e6i 0.264198 + 0.152535i
\(362\) 1.17561e7 + 4.38743e7i 0.247820 + 0.924877i
\(363\) 7.96026e7i 1.66421i
\(364\) −9.59132e7 1.31423e6i −1.98872 0.0272501i
\(365\) 2.92150e7 0.600796
\(366\) −7.43534e7 + 1.99229e7i −1.51655 + 0.406359i
\(367\) −6.79518e6 + 1.17696e7i −0.137468 + 0.238102i −0.926538 0.376202i \(-0.877230\pi\)
0.789069 + 0.614304i \(0.210563\pi\)
\(368\) −2.20101e7 + 1.27075e7i −0.441649 + 0.254986i
\(369\) 8.24069e6 + 8.24069e6i 0.164015 + 0.164015i
\(370\) 1.55898e7 5.81820e7i 0.307777 1.14864i
\(371\) 3.86803e7 + 1.03644e7i 0.757475 + 0.202965i
\(372\) 8.43689e7 8.43689e7i 1.63890 1.63890i
\(373\) −2.61575e7 4.53060e7i −0.504045 0.873031i −0.999989 0.00467673i \(-0.998511\pi\)
0.495944 0.868354i \(-0.334822\pi\)
\(374\) 4.51014e7 + 2.60393e7i 0.862135 + 0.497754i
\(375\) −1.73702e7 6.48265e7i −0.329390 1.22930i
\(376\) 3.88368e7i 0.730601i
\(377\) 4.42782e7 4.30812e7i 0.826354 0.804014i
\(378\) 2.90780e7 0.538380
\(379\) −5.12623e7 + 1.37357e7i −0.941631 + 0.252309i −0.696807 0.717258i \(-0.745397\pi\)
−0.244824 + 0.969568i \(0.578730\pi\)
\(380\) −5.46432e7 + 9.46448e7i −0.995831 + 1.72483i
\(381\) 5.62799e7 3.24932e7i 1.01760 0.587513i
\(382\) −1.03341e8 1.03341e8i −1.85388 1.85388i
\(383\) 9.20297e6 3.43459e7i 0.163807 0.611335i −0.834383 0.551186i \(-0.814176\pi\)
0.998189 0.0601493i \(-0.0191577\pi\)
\(384\) 4.65755e7 + 1.24799e7i 0.822553 + 0.220402i
\(385\) −5.37904e7 + 5.37904e7i −0.942590 + 0.942590i
\(386\) −2.37574e7 4.11491e7i −0.413083 0.715481i
\(387\) 6.12981e6 + 3.53905e6i 0.105758 + 0.0610595i
\(388\) 5.92513e7 + 2.21129e8i 1.01438 + 3.78574i
\(389\) 7.69333e7i 1.30697i −0.756939 0.653485i \(-0.773306\pi\)
0.756939 0.653485i \(-0.226694\pi\)
\(390\) 1.42467e8 3.60894e7i 2.40172 0.608395i
\(391\) −5.41668e6 −0.0906155
\(392\) 3.65355e7 9.78966e6i 0.606537 0.162521i
\(393\) −3.43495e7 + 5.94952e7i −0.565905 + 0.980176i
\(394\) 6.20965e7 3.58514e7i 1.01526 0.586162i
\(395\) −7.41418e7 7.41418e7i −1.20302 1.20302i
\(396\) −4.13608e7 + 1.54361e8i −0.666045 + 2.48571i
\(397\) −5.60953e7 1.50307e7i −0.896510 0.240219i −0.218993 0.975726i \(-0.570277\pi\)
−0.677517 + 0.735507i \(0.736944\pi\)
\(398\) −1.26310e8 + 1.26310e8i −2.00349 + 2.00349i
\(399\) 2.99907e7 + 5.19453e7i 0.472136 + 0.817764i
\(400\) 7.33460e6 + 4.23463e6i 0.114603 + 0.0661662i
\(401\) 2.34543e6 + 8.75325e6i 0.0363738 + 0.135749i 0.981725 0.190305i \(-0.0609476\pi\)
−0.945351 + 0.326054i \(0.894281\pi\)
\(402\) 2.36328e8i 3.63778i
\(403\) 2.42494e7 + 4.33626e7i 0.370498 + 0.662522i
\(404\) −6.53958e7 −0.991758
\(405\) −7.89807e7 + 2.11628e7i −1.18893 + 0.318573i
\(406\) 6.03408e7 1.04513e8i 0.901640 1.56169i
\(407\) −5.55800e7 + 3.20892e7i −0.824396 + 0.475965i
\(408\) −5.51419e7 5.51419e7i −0.811897 0.811897i
\(409\) 8.63637e6 3.22314e7i 0.126230 0.471095i −0.873651 0.486553i \(-0.838254\pi\)
0.999881 + 0.0154580i \(0.00492063\pi\)
\(410\) −3.92600e7 1.05197e7i −0.569637 0.152634i
\(411\) 5.64393e7 5.64393e7i 0.812936 0.812936i
\(412\) −4.99202e7 8.64643e7i −0.713813 1.23636i
\(413\) 1.09921e7 + 6.34627e6i 0.156038 + 0.0900883i
\(414\) −6.15985e6 2.29889e7i −0.0868099 0.323979i
\(415\) 8.67433e7i 1.21364i
\(416\) 4.90031e7 8.22523e7i 0.680681 1.14253i
\(417\) 1.35613e8 1.87022
\(418\) 1.61050e8 4.31533e7i 2.20512 0.590860i
\(419\) −1.30180e6 + 2.25479e6i −0.0176972 + 0.0306524i −0.874738 0.484595i \(-0.838967\pi\)
0.857041 + 0.515248i \(0.172300\pi\)
\(420\) 1.73640e8 1.00251e8i 2.34370 1.35313i
\(421\) 2.01304e7 + 2.01304e7i 0.269778 + 0.269778i 0.829011 0.559233i \(-0.188904\pi\)
−0.559233 + 0.829011i \(0.688904\pi\)
\(422\) −1.73528e7 + 6.47616e7i −0.230905 + 0.861748i
\(423\) 1.64789e7 + 4.41550e6i 0.217724 + 0.0583390i
\(424\) −1.17861e8 + 1.17861e8i −1.54622 + 1.54622i
\(425\) 902523. + 1.56322e6i 0.0117569 + 0.0203635i
\(426\) −1.93070e8 1.11469e8i −2.49739 1.44187i
\(427\) −1.13177e7 4.22382e7i −0.145370 0.542527i
\(428\) 1.33741e8i 1.70583i
\(429\) −1.34526e8 8.01458e7i −1.70386 1.01510i
\(430\) −2.46856e7 −0.310483
\(431\) 6.96328e7 1.86580e7i 0.869725 0.233042i 0.203756 0.979022i \(-0.434685\pi\)
0.665969 + 0.745980i \(0.268018\pi\)
\(432\) −2.83877e7 + 4.91689e7i −0.352110 + 0.609873i
\(433\) −1.05530e7 + 6.09278e6i −0.129991 + 0.0750502i −0.563585 0.826058i \(-0.690578\pi\)
0.433594 + 0.901108i \(0.357245\pi\)
\(434\) 6.86268e7 + 6.86268e7i 0.839508 + 0.839508i
\(435\) −3.34220e7 + 1.24732e8i −0.406036 + 1.51535i
\(436\) 1.11524e8 + 2.98826e7i 1.34557 + 0.360545i
\(437\) −1.22624e7 + 1.22624e7i −0.146937 + 0.146937i
\(438\) 5.87389e7 + 1.01739e8i 0.699042 + 1.21078i
\(439\) −2.99649e7 1.73003e7i −0.354176 0.204484i 0.312347 0.949968i \(-0.398885\pi\)
−0.666523 + 0.745484i \(0.732218\pi\)
\(440\) −8.19511e7 3.05846e8i −0.962048 3.59041i
\(441\) 1.66154e7i 0.193730i
\(442\) 4.98858e7 2.78973e7i 0.577710 0.323069i
\(443\) 3.95248e7 0.454630 0.227315 0.973821i \(-0.427005\pi\)
0.227315 + 0.973821i \(0.427005\pi\)
\(444\) 1.63392e8 4.37808e7i 1.86673 0.500190i
\(445\) 8.46936e7 1.46694e8i 0.961105 1.66468i
\(446\) −2.11754e8 + 1.22256e8i −2.38686 + 1.37806i
\(447\) 1.26373e8 + 1.26373e8i 1.41492 + 1.41492i
\(448\) 7.51102e6 2.80315e7i 0.0835343 0.311754i
\(449\) −1.17491e8 3.14815e7i −1.29797 0.347790i −0.457287 0.889319i \(-0.651179\pi\)
−0.840682 + 0.541529i \(0.817846\pi\)
\(450\) −5.60808e6 + 5.60808e6i −0.0615428 + 0.0615428i
\(451\) 2.16531e7 + 3.75042e7i 0.236042 + 0.408838i
\(452\) 1.15863e8 + 6.68936e7i 1.25467 + 0.724384i
\(453\) −1.68675e7 6.29504e7i −0.181450 0.677180i
\(454\) 5.87577e6i 0.0627910i
\(455\) 2.05014e7 + 8.09319e7i 0.217645 + 0.859182i
\(456\) −2.49663e8 −2.63306
\(457\) 6.27379e7 1.68106e7i 0.657327 0.176130i 0.0852877 0.996356i \(-0.472819\pi\)
0.572040 + 0.820226i \(0.306152\pi\)
\(458\) 3.13698e7 5.43342e7i 0.326525 0.565557i
\(459\) −1.04793e7 + 6.05024e6i −0.108367 + 0.0625655i
\(460\) 4.09901e7 + 4.09901e7i 0.421120 + 0.421120i
\(461\) 3.05452e6 1.13996e7i 0.0311774 0.116356i −0.948584 0.316527i \(-0.897483\pi\)
0.979761 + 0.200171i \(0.0641499\pi\)
\(462\) −2.95470e8 7.91710e7i −2.99632 0.802861i
\(463\) −3.15292e6 + 3.15292e6i −0.0317666 + 0.0317666i −0.722812 0.691045i \(-0.757151\pi\)
0.691045 + 0.722812i \(0.257151\pi\)
\(464\) 1.17817e8 + 2.04064e8i 1.17938 + 2.04274i
\(465\) −8.99361e7 5.19246e7i −0.894489 0.516434i
\(466\) 1.68443e6 + 6.28637e6i 0.0166454 + 0.0621215i
\(467\) 8.19686e7i 0.804817i 0.915460 + 0.402408i \(0.131827\pi\)
−0.915460 + 0.402408i \(0.868173\pi\)
\(468\) 1.22307e8 + 1.25705e8i 1.19320 + 1.22635i
\(469\) −1.34251e8 −1.30137
\(470\) −5.74719e7 + 1.53995e7i −0.553556 + 0.148325i
\(471\) −3.00243e6 + 5.20036e6i −0.0287349 + 0.0497704i
\(472\) −4.57528e7 + 2.64154e7i −0.435103 + 0.251207i
\(473\) 1.85983e7 + 1.85983e7i 0.175748 + 0.175748i
\(474\) 1.09125e8 4.07261e8i 1.02468 3.82417i
\(475\) 5.58200e6 + 1.49569e6i 0.0520846 + 0.0139560i
\(476\) 5.51375e7 5.51375e7i 0.511242 0.511242i
\(477\) −3.66097e7 6.34098e7i −0.337319 0.584253i
\(478\) 1.23850e8 + 7.15049e7i 1.13400 + 0.654715i
\(479\) 1.32130e7 + 4.93114e7i 0.120225 + 0.448684i 0.999625 0.0273994i \(-0.00872261\pi\)
−0.879400 + 0.476084i \(0.842056\pi\)
\(480\) 2.00128e8i 1.80961i
\(481\) −965042. + 7.04292e7i −0.00867184 + 0.632874i
\(482\) 2.70973e8 2.41983
\(483\) 3.07318e7 8.23455e6i 0.272738 0.0730800i
\(484\) −1.65654e8 + 2.86921e8i −1.46105 + 2.53062i
\(485\) 1.72559e8 9.96272e7i 1.51256 0.873278i
\(486\) −1.81620e8 1.81620e8i −1.58217 1.58217i
\(487\) 5.25395e7 1.96080e8i 0.454882 1.69764i −0.233551 0.972344i \(-0.575035\pi\)
0.688434 0.725299i \(-0.258299\pi\)
\(488\) 1.75810e8 + 4.71082e7i 1.51281 + 0.405356i
\(489\) −1.59160e8 + 1.59160e8i −1.36116 + 1.36116i
\(490\) −2.89741e7 5.01845e7i −0.246275 0.426562i
\(491\) −1.59223e8 9.19275e7i −1.34512 0.776607i −0.357568 0.933887i \(-0.616394\pi\)
−0.987554 + 0.157280i \(0.949727\pi\)
\(492\) −2.95424e7 1.10254e8i −0.248056 0.925758i
\(493\) 5.02203e7i 0.419120i
\(494\) 4.97780e7 1.76087e8i 0.412911 1.46065i
\(495\) 1.39091e8 1.14679
\(496\) −1.83041e8 + 4.90457e7i −1.50004 + 0.401935i
\(497\) 6.33226e7 1.09678e8i 0.515810 0.893409i
\(498\) −3.02076e8 + 1.74404e8i −2.44584 + 1.41211i
\(499\) 8.31949e7 + 8.31949e7i 0.669569 + 0.669569i 0.957616 0.288047i \(-0.0930061\pi\)
−0.288047 + 0.957616i \(0.593006\pi\)
\(500\) −7.22952e7 + 2.69809e8i −0.578361 + 2.15847i
\(501\) 1.62248e8 + 4.34743e7i 1.29023 + 0.345716i
\(502\) 2.66621e8 2.66621e8i 2.10758 2.10758i
\(503\) 3.96197e7 + 6.86234e7i 0.311320 + 0.539223i 0.978648 0.205541i \(-0.0658954\pi\)
−0.667328 + 0.744764i \(0.732562\pi\)
\(504\) 1.68567e8 + 9.73221e7i 1.31668 + 0.760186i
\(505\) 1.47317e7 + 5.49794e7i 0.114387 + 0.426899i
\(506\) 8.84393e7i 0.682643i
\(507\) −1.51132e8 + 8.18188e7i −1.15966 + 0.627811i
\(508\) −2.70475e8 −2.06317
\(509\) 1.98754e6 532561.i 0.0150717 0.00403846i −0.251275 0.967916i \(-0.580850\pi\)
0.266347 + 0.963877i \(0.414183\pi\)
\(510\) −5.97358e7 + 1.03465e8i −0.450323 + 0.779982i
\(511\) −5.77950e7 + 3.33680e7i −0.433140 + 0.250073i
\(512\) −2.06838e8 2.06838e8i −1.54106 1.54106i
\(513\) −1.00267e7 + 3.74201e7i −0.0742685 + 0.277174i
\(514\) 2.58445e8 + 6.92501e7i 1.90317 + 0.509954i
\(515\) −6.14465e7 + 6.14465e7i −0.449858 + 0.449858i
\(516\) −3.46622e7 6.00368e7i −0.252294 0.436987i
\(517\) 5.49017e7 + 3.16975e7i 0.397296 + 0.229379i
\(518\) 3.56119e7 + 1.32905e8i 0.256216 + 0.956210i
\(519\) 1.10160e8i 0.787990i
\(520\) −3.34402e8 9.45320e7i −2.37826 0.672309i
\(521\) −1.66884e8 −1.18005 −0.590026 0.807385i \(-0.700882\pi\)
−0.590026 + 0.807385i \(0.700882\pi\)
\(522\) −2.13140e8 + 5.71106e7i −1.49849 + 0.401518i
\(523\) 7.27066e7 1.25931e8i 0.508240 0.880297i −0.491715 0.870756i \(-0.663630\pi\)
0.999954 0.00954052i \(-0.00303689\pi\)
\(524\) 2.47620e8 1.42964e8i 1.72105 0.993646i
\(525\) −7.49694e6 7.49694e6i −0.0518091 0.0518091i
\(526\) −7.88080e7 + 2.94115e8i −0.541518 + 2.02097i
\(527\) −3.90113e7 1.04531e7i −0.266538 0.0714186i
\(528\) 4.22329e8 4.22329e8i 2.86912 2.86912i
\(529\) −6.94187e7 1.20237e8i −0.468931 0.812213i
\(530\) 2.21148e8 + 1.27680e8i 1.48544 + 0.857621i
\(531\) −6.00653e6 2.24167e7i −0.0401181 0.149723i
\(532\) 2.49644e8i 1.65800i
\(533\) 4.75241e7 + 651190.i 0.313857 + 0.00430057i
\(534\) 6.81132e8 4.47309
\(535\) −1.12439e8 + 3.01278e7i −0.734268 + 0.196746i
\(536\) 2.79400e8 4.83936e8i 1.81440 3.14263i
\(537\) −1.05293e8 + 6.07911e7i −0.679951 + 0.392570i
\(538\) −1.78940e8 1.78940e8i −1.14910 1.14910i
\(539\) −1.59801e7 + 5.96385e7i −0.102050 + 0.380856i
\(540\) 1.25086e8 + 3.35166e7i 0.794376 + 0.212852i
\(541\) −5.40118e7 + 5.40118e7i −0.341112 + 0.341112i −0.856785 0.515673i \(-0.827542\pi\)
0.515673 + 0.856785i \(0.327542\pi\)
\(542\) 2.70447e6 + 4.68429e6i 0.0169858 + 0.0294202i
\(543\) 9.61491e7 + 5.55117e7i 0.600546 + 0.346725i
\(544\) 2.01441e7 + 7.51787e7i 0.125127 + 0.466980i
\(545\) 1.00491e8i 0.620782i
\(546\) −2.40619e8 + 2.34114e8i −1.47826 + 1.43830i
\(547\) 2.16091e8 1.32031 0.660154 0.751130i \(-0.270491\pi\)
0.660154 + 0.751130i \(0.270491\pi\)
\(548\) −3.20882e8 + 8.59801e7i −1.94986 + 0.522464i
\(549\) −3.99770e7 + 6.92423e7i −0.241598 + 0.418460i
\(550\) −2.55230e7 + 1.47357e7i −0.153406 + 0.0885692i
\(551\) 1.13690e8 + 1.13690e8i 0.679622 + 0.679622i
\(552\) −3.42751e7 + 1.27916e8i −0.203780 + 0.760517i
\(553\) 2.31354e8 + 6.19910e7i 1.36805 + 0.366567i
\(554\) −4.27087e8 + 4.27087e8i −2.51181 + 2.51181i
\(555\) −7.36145e7 1.27504e8i −0.430610 0.745839i
\(556\) −4.88805e8 2.82211e8i −2.84388 1.64191i
\(557\) 5.89088e7 + 2.19851e8i 0.340890 + 1.27222i 0.897341 + 0.441339i \(0.145496\pi\)
−0.556451 + 0.830881i \(0.687837\pi\)
\(558\) 1.77455e8i 1.02138i
\(559\) 2.79826e7 7.08845e6i 0.160196 0.0405804i
\(560\) −3.18439e8 −1.81327
\(561\) 1.22957e8 3.29461e7i 0.696407 0.186602i
\(562\) −2.37280e8 + 4.10980e8i −1.33675 + 2.31533i
\(563\) 6.28453e6 3.62838e6i 0.0352166 0.0203323i −0.482288 0.876013i \(-0.660194\pi\)
0.517505 + 0.855680i \(0.326861\pi\)
\(564\) −1.18152e8 1.18152e8i −0.658570 0.658570i
\(565\) 3.01382e7 1.12477e8i 0.167098 0.623618i
\(566\) −5.77085e7 1.54630e7i −0.318266 0.0852792i
\(567\) 1.32074e8 1.32074e8i 0.724548 0.724548i
\(568\) 2.63571e8 + 4.56518e8i 1.43831 + 2.49123i
\(569\) −1.80180e8 1.04027e8i −0.978071 0.564690i −0.0763840 0.997078i \(-0.524337\pi\)
−0.901687 + 0.432389i \(0.857671\pi\)
\(570\) 9.89962e7 + 3.69459e8i 0.534557 + 1.99499i
\(571\) 5.10219e7i 0.274062i −0.990567 0.137031i \(-0.956244\pi\)
0.990567 0.137031i \(-0.0437559\pi\)
\(572\) 3.18102e8 + 5.68828e8i 1.69973 + 3.03944i
\(573\) −3.57219e8 −1.89876
\(574\) 8.96817e7 2.40302e7i 0.474207 0.127064i
\(575\) 1.53265e6 2.65464e6i 0.00806196 0.0139637i
\(576\) −4.59529e7 + 2.65309e7i −0.240461 + 0.138830i
\(577\) 1.25381e8 + 1.25381e8i 0.652687 + 0.652687i 0.953639 0.300952i \(-0.0973044\pi\)
−0.300952 + 0.953639i \(0.597304\pi\)
\(578\) 7.89764e7 2.94744e8i 0.408991 1.52638i
\(579\) −1.12182e8 3.00590e7i −0.577944 0.154860i
\(580\) 3.80036e8 3.80036e8i 1.94779 1.94779i
\(581\) −9.90741e7 1.71601e8i −0.505163 0.874968i
\(582\) 6.93887e8 + 4.00616e8i 3.51981 + 2.03217i
\(583\) −7.04195e7 2.62809e8i −0.355375 1.32628i
\(584\) 2.77778e8i 1.39463i
\(585\) 7.81304e7 1.31143e8i 0.390259 0.655054i
\(586\) 1.10340e8 0.548330
\(587\) −1.83522e8 + 4.91746e7i −0.907348 + 0.243123i −0.682169 0.731194i \(-0.738963\pi\)
−0.225179 + 0.974317i \(0.572297\pi\)
\(588\) 8.13677e7 1.40933e8i 0.400240 0.693235i
\(589\) −1.11979e8 + 6.46510e7i −0.548012 + 0.316395i
\(590\) 5.72322e7 + 5.72322e7i 0.278666 + 0.278666i
\(591\) 4.53609e7 1.69289e8i 0.219745 0.820099i
\(592\) −2.59500e8 6.95329e7i −1.25076 0.335139i
\(593\) 9.96558e7 9.96558e7i 0.477902 0.477902i −0.426558 0.904460i \(-0.640274\pi\)
0.904460 + 0.426558i \(0.140274\pi\)
\(594\) −9.87836e7 1.71098e8i −0.471331 0.816368i
\(595\) −5.87759e7 3.39343e7i −0.279028 0.161097i
\(596\) −1.92517e8 7.18484e8i −0.909350 3.39374i
\(597\) 4.36617e8i 2.05200i
\(598\) −8.33856e7 4.96783e7i −0.389931 0.232307i
\(599\) −2.64623e8 −1.23125 −0.615625 0.788039i \(-0.711097\pi\)
−0.615625 + 0.788039i \(0.711097\pi\)
\(600\) 4.26267e7 1.14218e7i 0.197346 0.0528786i
\(601\) −8.09719e7 + 1.40247e8i −0.373002 + 0.646058i −0.990026 0.140887i \(-0.955005\pi\)
0.617024 + 0.786944i \(0.288338\pi\)
\(602\) 4.88347e7 2.81947e7i 0.223841 0.129235i
\(603\) 1.73573e8 + 1.73573e8i 0.791645 + 0.791645i
\(604\) −7.02030e7 + 2.62001e8i −0.318599 + 1.18903i
\(605\) 2.78536e8 + 7.46335e7i 1.25781 + 0.337030i
\(606\) −1.61842e8 + 1.61842e8i −0.727232 + 0.727232i
\(607\) −1.40686e8 2.43676e8i −0.629051 1.08955i −0.987743 0.156092i \(-0.950110\pi\)
0.358692 0.933456i \(-0.383223\pi\)
\(608\) 2.15794e8 + 1.24589e8i 0.960128 + 0.554330i
\(609\) −7.63460e7 2.84927e8i −0.338014 1.26148i
\(610\) 2.78848e8i 1.22851i
\(611\) 6.07257e7 3.39593e7i 0.266225 0.148879i
\(612\) −1.42574e8 −0.621996
\(613\) −3.09771e7 + 8.30029e6i −0.134480 + 0.0360339i −0.325431 0.945566i \(-0.605510\pi\)
0.190951 + 0.981600i \(0.438843\pi\)
\(614\) −2.97887e7 + 5.15956e7i −0.128691 + 0.222899i
\(615\) −8.60370e7 + 4.96735e7i −0.369879 + 0.213550i
\(616\) 5.11444e8 + 5.11444e8i 2.18804 + 2.18804i
\(617\) 6.76791e7 2.52582e8i 0.288137 1.07534i −0.658379 0.752686i \(-0.728758\pi\)
0.946516 0.322656i \(-0.104576\pi\)
\(618\) −3.37525e8 9.04396e7i −1.43002 0.383172i
\(619\) 5.75929e7 5.75929e7i 0.242827 0.242827i −0.575192 0.818019i \(-0.695073\pi\)
0.818019 + 0.575192i \(0.195073\pi\)
\(620\) 2.16112e8 + 3.74316e8i 0.906782 + 1.57059i
\(621\) 1.77959e7 + 1.02744e7i 0.0743095 + 0.0429026i
\(622\) −1.05968e8 3.95479e8i −0.440357 1.64344i
\(623\) 3.86932e8i 1.60019i
\(624\) −1.60964e8 6.35427e8i −0.662484 2.61524i
\(625\) 2.58911e8 1.06050
\(626\) 4.55626e8 1.22085e8i 1.85731 0.497666i
\(627\) 2.03768e8 3.52937e8i 0.826673 1.43184i
\(628\) 2.16440e7 1.24962e7i 0.0873895 0.0504543i
\(629\) −4.04876e7 4.04876e7i −0.162693 0.162693i
\(630\) 7.71802e7 2.88040e8i 0.308663 1.15194i
\(631\) −4.42001e7 1.18434e7i −0.175928 0.0471398i 0.169779 0.985482i \(-0.445694\pi\)
−0.345708 + 0.938342i \(0.612361\pi\)
\(632\) −7.04947e8 + 7.04947e8i −2.79258 + 2.79258i
\(633\) 8.19394e7 + 1.41923e8i 0.323059 + 0.559554i
\(634\) 1.16250e8 + 6.71167e7i 0.456167 + 0.263368i
\(635\) 6.09297e7 + 2.27393e8i 0.237962 + 0.888087i
\(636\) 7.17127e8i 2.78756i
\(637\) 4.72542e7 + 4.85672e7i 0.182819 + 0.187899i
\(638\) −8.19958e8 −3.15740
\(639\) −2.23672e8 + 5.99328e7i −0.857254 + 0.229700i
\(640\) −8.73362e7 + 1.51271e8i −0.333161 + 0.577052i
\(641\) 1.13878e8 6.57475e7i 0.432380 0.249635i −0.267980 0.963424i \(-0.586356\pi\)
0.700360 + 0.713790i \(0.253023\pi\)
\(642\) −3.30984e8 3.30984e8i −1.25084 1.25084i
\(643\) −6.76378e7 + 2.52428e8i −0.254423 + 0.949520i 0.713987 + 0.700158i \(0.246887\pi\)
−0.968411 + 0.249361i \(0.919779\pi\)
\(644\) −1.27906e8 3.42724e7i −0.478889 0.128318i
\(645\) −4.26656e7 + 4.26656e7i −0.159001 + 0.159001i
\(646\) 7.43765e7 + 1.28824e8i 0.275892 + 0.477858i
\(647\) −1.32388e8 7.64342e7i −0.488805 0.282212i 0.235274 0.971929i \(-0.424401\pi\)
−0.724079 + 0.689717i \(0.757735\pi\)
\(648\) 2.01218e8 + 7.50955e8i 0.739505 + 2.75987i
\(649\) 8.62380e7i 0.315475i
\(650\) −443158. + 3.23419e7i −0.00161368 + 0.117767i
\(651\) 2.37223e8 0.859834
\(652\) 9.04894e8 2.42466e8i 3.26479 0.874797i
\(653\) 2.22198e8 3.84859e8i 0.797997 1.38217i −0.122922 0.992416i \(-0.539227\pi\)
0.920919 0.389755i \(-0.127440\pi\)
\(654\) 3.49953e8 2.02045e8i 1.25106 0.722297i
\(655\) −1.75973e8 1.75973e8i −0.626214 0.626214i
\(656\) −4.69194e7 + 1.75105e8i −0.166204 + 0.620281i
\(657\) 1.17864e8 + 3.15817e7i 0.415611 + 0.111363i
\(658\) 9.61061e7 9.61061e7i 0.337344 0.337344i
\(659\) 1.85896e8 + 3.21981e8i 0.649551 + 1.12506i 0.983230 + 0.182369i \(0.0583764\pi\)
−0.333679 + 0.942687i \(0.608290\pi\)
\(660\) −1.17978e9 6.81144e8i −4.10363 2.36923i
\(661\) 9.01155e7 + 3.36315e8i 0.312029 + 1.16451i 0.926724 + 0.375743i \(0.122612\pi\)
−0.614695 + 0.788765i \(0.710721\pi\)
\(662\) 1.78552e8i 0.615447i
\(663\) 3.80039e7 1.34437e8i 0.130403 0.461294i
\(664\) 8.24762e8 2.81724
\(665\) −2.09880e8 + 5.62371e7i −0.713683 + 0.191231i
\(666\) 1.25791e8 2.17876e8i 0.425819 0.737541i
\(667\) 7.38577e7 4.26418e7i 0.248896 0.143700i
\(668\) −4.94340e8 4.94340e8i −1.65843 1.65843i
\(669\) −1.54684e8 + 5.77290e8i −0.516616 + 1.92804i
\(670\) −8.26930e8 2.21575e8i −2.74944 0.736710i
\(671\) −2.10086e8 + 2.10086e8i −0.695391 + 0.695391i
\(672\) −2.28577e8 3.95906e8i −0.753224 1.30462i
\(673\) 1.17116e8 + 6.76168e7i 0.384211 + 0.221824i 0.679649 0.733538i \(-0.262132\pi\)
−0.295438 + 0.955362i \(0.595466\pi\)
\(674\) −8.63225e7 3.22160e8i −0.281932 1.05218i
\(675\) 6.84769e6i 0.0222655i
\(676\) 7.15009e8 + 1.95982e7i 2.31457 + 0.0634420i
\(677\) 3.59883e8 1.15983 0.579917 0.814676i \(-0.303085\pi\)
0.579917 + 0.814676i \(0.303085\pi\)
\(678\) 4.52287e8 1.21190e8i 1.45119 0.388846i
\(679\) −2.27579e8 + 3.94178e8i −0.726980 + 1.25917i
\(680\) 2.44646e8 1.41246e8i 0.778056 0.449211i
\(681\) −1.01554e7 1.01554e7i −0.0321557 0.0321557i
\(682\) 1.70669e8 6.36946e8i 0.538025 2.00794i
\(683\) −3.44365e8 9.22722e7i −1.08083 0.289607i −0.325893 0.945407i \(-0.605665\pi\)
−0.754935 + 0.655800i \(0.772331\pi\)
\(684\) −3.22764e8 + 3.22764e8i −1.00859 + 1.00859i
\(685\) 1.44570e8 + 2.50402e8i 0.449786 + 0.779052i
\(686\) 5.51912e8 + 3.18646e8i 1.70961 + 0.987044i
\(687\) −3.96906e7 1.48127e8i −0.122410 0.456841i
\(688\) 1.10102e8i 0.338087i
\(689\) −2.87348e8 8.12301e7i −0.878516 0.248347i
\(690\) 2.02885e8 0.617594
\(691\) −7.78186e7 + 2.08514e7i −0.235857 + 0.0631978i −0.374812 0.927101i \(-0.622293\pi\)
0.138954 + 0.990299i \(0.455626\pi\)
\(692\) −2.29244e8 + 3.97062e8i −0.691797 + 1.19823i
\(693\) −2.75159e8 + 1.58863e8i −0.826769 + 0.477335i
\(694\) 2.62608e8 + 2.62608e8i 0.785651 + 0.785651i
\(695\) −1.27147e8 + 4.74520e8i −0.378750 + 1.41351i
\(696\) 1.18597e9 + 3.17779e8i 3.51758 + 0.942534i
\(697\) −2.73202e7 + 2.73202e7i −0.0806836 + 0.0806836i
\(698\) −5.45427e8 9.44708e8i −1.60388 2.77799i
\(699\) 1.37764e7 + 7.95381e6i 0.0403371 + 0.0232886i
\(700\) 1.14209e7 + 4.26233e7i 0.0332971 + 0.124266i
\(701\) 3.75084e8i 1.08887i −0.838804 0.544433i \(-0.816745\pi\)
0.838804 0.544433i \(-0.183255\pi\)
\(702\) −2.16810e8 2.97080e6i −0.626712 0.00858740i
\(703\) −1.83314e8 −0.527629
\(704\) −1.90457e8 + 5.10328e7i −0.545857 + 0.146262i
\(705\) −7.27161e7 + 1.25948e8i −0.207521 + 0.359438i
\(706\) −8.93070e8 + 5.15614e8i −2.53788 + 1.46525i
\(707\) −9.19380e7 9.19380e7i −0.260158 0.260158i
\(708\) −5.88294e7 + 2.19554e8i −0.165766 + 0.618646i
\(709\) 3.97885e8 + 1.06613e8i 1.11640 + 0.299138i 0.769425 0.638737i \(-0.220543\pi\)
0.346973 + 0.937875i \(0.387209\pi\)
\(710\) 5.71058e8 5.71058e8i 1.59553 1.59553i
\(711\) −2.18969e8 3.79265e8i −0.609218 1.05520i
\(712\) −1.39478e9 8.05274e8i −3.86424 2.23102i
\(713\) 1.77513e7 + 6.62486e7i 0.0489734 + 0.182771i
\(714\) 2.72910e8i 0.749763i
\(715\) 4.06565e8 3.95574e8i 1.11227 1.08220i
\(716\) 5.06028e8 1.37859
\(717\) 3.37643e8 9.04713e7i 0.916011 0.245445i
\(718\) −4.00339e8 + 6.93407e8i −1.08157 + 1.87333i
\(719\) 5.03062e8 2.90443e8i 1.35343 0.781401i 0.364699 0.931125i \(-0.381172\pi\)
0.988728 + 0.149724i \(0.0478385\pi\)
\(720\) 4.11709e8 + 4.11709e8i 1.10304 + 1.10304i
\(721\) 5.13763e7 1.91739e8i 0.137075 0.511569i
\(722\) −2.01941e8 5.41099e7i −0.536553 0.143769i
\(723\) 4.68338e8 4.68338e8i 1.23921 1.23921i
\(724\) −2.31041e8 4.00175e8i −0.608799 1.05447i
\(725\) −2.46122e7 1.42099e7i −0.0645858 0.0372886i
\(726\) 3.00113e8 + 1.12004e9i 0.784286 + 2.92699i
\(727\) 1.59369e8i 0.414762i −0.978260 0.207381i \(-0.933506\pi\)
0.978260 0.207381i \(-0.0664940\pi\)
\(728\) 7.69507e8 1.94929e8i 1.99443 0.505222i
\(729\) −1.65656e8 −0.427587
\(730\) −4.11065e8 + 1.10144e8i −1.05668 + 0.283135i
\(731\) −1.17329e7 + 2.03220e7i −0.0300368 + 0.0520253i
\(732\) 6.78174e8 3.91544e8i 1.72905 0.998269i
\(733\) −1.65813e8 1.65813e8i −0.421024 0.421024i 0.464532 0.885556i \(-0.346223\pi\)
−0.885556 + 0.464532i \(0.846223\pi\)
\(734\) 5.12375e7 1.91221e8i 0.129569 0.483557i
\(735\) −1.36814e8 3.66593e7i −0.344564 0.0923257i
\(736\) 9.34592e7 9.34592e7i 0.234417 0.234417i
\(737\) 4.56078e8 + 7.89950e8i 1.13930 + 1.97332i
\(738\) −1.47018e8 8.48808e7i −0.365764 0.211174i
\(739\) −9.08333e7 3.38994e8i −0.225067 0.839961i −0.982378 0.186907i \(-0.940154\pi\)
0.757311 0.653055i \(-0.226513\pi\)
\(740\) 6.12771e8i 1.51218i
\(741\) −2.18308e8 3.90376e8i −0.536555 0.959464i
\(742\) −5.83321e8 −1.42789
\(743\) −2.80605e8 + 7.51879e7i −0.684115 + 0.183308i −0.584105 0.811678i \(-0.698554\pi\)
−0.100010 + 0.994986i \(0.531888\pi\)
\(744\) −4.93704e8 + 8.55120e8i −1.19880 + 2.07639i
\(745\) −5.60674e8 + 3.23705e8i −1.35594 + 0.782854i
\(746\) 5.38854e8 + 5.38854e8i 1.29794 + 1.29794i
\(747\) −9.37703e7 + 3.49956e8i −0.224959 + 0.839559i
\(748\) −5.11748e8 1.37123e8i −1.22279 0.327645i
\(749\) 1.88023e8 1.88023e8i 0.447472 0.447472i
\(750\) 4.88809e8 + 8.46642e8i 1.15866 + 2.00686i
\(751\) −3.24188e8 1.87170e8i −0.765379 0.441892i 0.0658446 0.997830i \(-0.479026\pi\)
−0.831224 + 0.555938i \(0.812359\pi\)
\(752\) 6.86843e7 + 2.56333e8i 0.161512 + 0.602770i
\(753\) 9.21634e8i 2.15861i
\(754\) −4.60588e8 + 7.73102e8i −1.07448 + 1.80353i
\(755\) 2.36083e8 0.548560
\(756\) −2.85734e8 + 7.65622e7i −0.661297 + 0.177194i
\(757\) 3.02153e8 5.23344e8i 0.696529 1.20642i −0.273133 0.961976i \(-0.588060\pi\)
0.969662 0.244448i \(-0.0786067\pi\)
\(758\) 6.69493e8 3.86532e8i 1.53723 0.887519i
\(759\) −1.52855e8 1.52855e8i −0.349586 0.349586i
\(760\) 2.34078e8 8.73593e8i 0.533237 1.99007i
\(761\) −3.12034e8 8.36092e7i −0.708024 0.189714i −0.113202 0.993572i \(-0.536111\pi\)
−0.594822 + 0.803858i \(0.702777\pi\)
\(762\) −6.69373e8 + 6.69373e8i −1.51288 + 1.51288i
\(763\) 1.14777e8 + 1.98799e8i 0.258392 + 0.447549i