Properties

Label 8.8.b.a.5.6
Level $8$
Weight $8$
Character 8.5
Analytic conductor $2.499$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.49908020387\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.6
Root \(5.57668 - 0.949035i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.8.b.a.5.5

$q$-expansion

\(f(q)\) \(=\) \(q+(11.1534 + 1.89807i) q^{2} -76.9497i q^{3} +(120.795 + 42.3397i) q^{4} +338.443i q^{5} +(146.056 - 858.247i) q^{6} -438.996 q^{7} +(1266.90 + 701.506i) q^{8} -3734.25 q^{9} +O(q^{10})\) \(q+(11.1534 + 1.89807i) q^{2} -76.9497i q^{3} +(120.795 + 42.3397i) q^{4} +338.443i q^{5} +(146.056 - 858.247i) q^{6} -438.996 q^{7} +(1266.90 + 701.506i) q^{8} -3734.25 q^{9} +(-642.387 + 3774.77i) q^{10} +1966.58i q^{11} +(3258.02 - 9295.11i) q^{12} -2210.98i q^{13} +(-4896.28 - 833.245i) q^{14} +26043.0 q^{15} +(12798.7 + 10228.8i) q^{16} -12114.9 q^{17} +(-41649.4 - 7087.87i) q^{18} -32872.2i q^{19} +(-14329.5 + 40882.1i) q^{20} +33780.6i q^{21} +(-3732.70 + 21933.9i) q^{22} +19605.1 q^{23} +(53980.7 - 97487.7i) q^{24} -36418.4 q^{25} +(4196.59 - 24659.8i) q^{26} +119060. i q^{27} +(-53028.4 - 18587.0i) q^{28} -160689. i q^{29} +(290467. + 49431.5i) q^{30} -229270. q^{31} +(123333. + 138378. i) q^{32} +151328. q^{33} +(-135122. - 22994.9i) q^{34} -148575. i q^{35} +(-451078. - 158107. i) q^{36} +496284. i q^{37} +(62393.6 - 366635. i) q^{38} -170134. q^{39} +(-237420. + 428774. i) q^{40} +599971. q^{41} +(-64117.9 + 376767. i) q^{42} -88346.0i q^{43} +(-83264.3 + 237552. i) q^{44} -1.26383e6i q^{45} +(218662. + 37211.8i) q^{46} +820344. q^{47} +(787104. - 984856. i) q^{48} -630825. q^{49} +(-406187. - 69124.6i) q^{50} +932236. i q^{51} +(93612.2 - 267075. i) q^{52} +1.53717e6i q^{53} +(-225985. + 1.32792e6i) q^{54} -665574. q^{55} +(-556165. - 307959. i) q^{56} -2.52950e6 q^{57} +(304999. - 1.79222e6i) q^{58} -1.82480e6i q^{59} +(3.14586e6 + 1.10265e6i) q^{60} +484582. i q^{61} +(-2.55713e6 - 435171. i) q^{62} +1.63932e6 q^{63} +(1.11293e6 + 1.77748e6i) q^{64} +748290. q^{65} +(1.68781e6 + 287230. i) q^{66} +79878.2i q^{67} +(-1.46341e6 - 512940. i) q^{68} -1.50860e6i q^{69} +(282006. - 1.65711e6i) q^{70} +1.27078e6 q^{71} +(-4.73093e6 - 2.61960e6i) q^{72} +3.70820e6 q^{73} +(-941981. + 5.53523e6i) q^{74} +2.80238e6i q^{75} +(1.39180e6 - 3.97078e6i) q^{76} -863321. i q^{77} +(-1.89757e6 - 322926. i) q^{78} -2.55846e6 q^{79} +(-3.46187e6 + 4.33163e6i) q^{80} +994857. q^{81} +(6.69169e6 + 1.13879e6i) q^{82} -1.53414e6i q^{83} +(-1.43026e6 + 4.08052e6i) q^{84} -4.10019e6i q^{85} +(167687. - 985355. i) q^{86} -1.23650e7 q^{87} +(-1.37957e6 + 2.49146e6i) q^{88} +1.99492e6 q^{89} +(2.39884e6 - 1.40959e7i) q^{90} +970612. i q^{91} +(2.36819e6 + 830073. i) q^{92} +1.76423e7i q^{93} +(9.14959e6 + 1.55707e6i) q^{94} +1.11253e7 q^{95} +(1.06482e7 - 9.49047e6i) q^{96} -28917.7 q^{97} +(-7.03582e6 - 1.19735e6i) q^{98} -7.34370e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9} - 1656 q^{10} - 4088 q^{12} + 12048 q^{14} + 17872 q^{15} + 35344 q^{16} + 1452 q^{17} - 89062 q^{18} - 114768 q^{20} + 152860 q^{22} - 1296 q^{23} + 282512 q^{24} - 39314 q^{25} - 316968 q^{26} - 480800 q^{28} + 821648 q^{30} - 89280 q^{31} + 817056 q^{32} + 53880 q^{33} - 1009108 q^{34} - 1253556 q^{36} + 974124 q^{38} - 328208 q^{39} + 954464 q^{40} + 521244 q^{41} - 1093088 q^{42} - 1096344 q^{44} + 929840 q^{46} + 1566432 q^{47} + 853920 q^{48} - 511050 q^{49} - 148626 q^{50} + 823952 q^{52} - 1077064 q^{54} - 3270256 q^{55} - 2468928 q^{56} - 1889896 q^{57} + 3130744 q^{58} + 5715168 q^{60} - 7055808 q^{62} + 5776816 q^{63} - 4792768 q^{64} + 1416480 q^{65} + 7926264 q^{66} + 6608040 q^{68} - 7406912 q^{70} - 7597104 q^{71} - 11363944 q^{72} + 2089564 q^{73} + 7744200 q^{74} + 9241288 q^{76} - 9471184 q^{78} + 16015904 q^{79} - 12600384 q^{80} - 723058 q^{81} + 10715932 q^{82} + 4220608 q^{84} - 5639076 q^{86} - 37453776 q^{87} + 1541200 q^{88} + 2169084 q^{89} - 121864 q^{90} + 669600 q^{92} + 15503712 q^{94} + 48537936 q^{95} + 21402176 q^{96} - 1088308 q^{97} - 14983242 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.1534 + 1.89807i 0.985827 + 0.167767i
\(3\) 76.9497i 1.64544i −0.568446 0.822721i \(-0.692455\pi\)
0.568446 0.822721i \(-0.307545\pi\)
\(4\) 120.795 + 42.3397i 0.943708 + 0.330779i
\(5\) 338.443i 1.21085i 0.795903 + 0.605425i \(0.206997\pi\)
−0.795903 + 0.605425i \(0.793003\pi\)
\(6\) 146.056 858.247i 0.276051 1.62212i
\(7\) −438.996 −0.483746 −0.241873 0.970308i \(-0.577762\pi\)
−0.241873 + 0.970308i \(0.577762\pi\)
\(8\) 1266.90 + 701.506i 0.874839 + 0.484414i
\(9\) −3734.25 −1.70748
\(10\) −642.387 + 3774.77i −0.203141 + 1.19369i
\(11\) 1966.58i 0.445489i 0.974877 + 0.222744i \(0.0715015\pi\)
−0.974877 + 0.222744i \(0.928498\pi\)
\(12\) 3258.02 9295.11i 0.544277 1.55282i
\(13\) 2210.98i 0.279115i −0.990214 0.139557i \(-0.955432\pi\)
0.990214 0.139557i \(-0.0445680\pi\)
\(14\) −4896.28 833.245i −0.476890 0.0811568i
\(15\) 26043.0 1.99238
\(16\) 12798.7 + 10228.8i 0.781171 + 0.624317i
\(17\) −12114.9 −0.598064 −0.299032 0.954243i \(-0.596664\pi\)
−0.299032 + 0.954243i \(0.596664\pi\)
\(18\) −41649.4 7087.87i −1.68328 0.286459i
\(19\) 32872.2i 1.09949i −0.835333 0.549744i \(-0.814725\pi\)
0.835333 0.549744i \(-0.185275\pi\)
\(20\) −14329.5 + 40882.1i −0.400523 + 1.14269i
\(21\) 33780.6i 0.795976i
\(22\) −3732.70 + 21933.9i −0.0747384 + 0.439175i
\(23\) 19605.1 0.335986 0.167993 0.985788i \(-0.446271\pi\)
0.167993 + 0.985788i \(0.446271\pi\)
\(24\) 53980.7 97487.7i 0.797074 1.43950i
\(25\) −36418.4 −0.466155
\(26\) 4196.59 24659.8i 0.0468263 0.275159i
\(27\) 119060.i 1.16411i
\(28\) −53028.4 18587.0i −0.456515 0.160013i
\(29\) 160689.i 1.22347i −0.791063 0.611735i \(-0.790472\pi\)
0.791063 0.611735i \(-0.209528\pi\)
\(30\) 290467. + 49431.5i 1.96414 + 0.334256i
\(31\) −229270. −1.38224 −0.691118 0.722742i \(-0.742881\pi\)
−0.691118 + 0.722742i \(0.742881\pi\)
\(32\) 123333. + 138378.i 0.665359 + 0.746523i
\(33\) 151328. 0.733026
\(34\) −135122. 22994.9i −0.589588 0.100336i
\(35\) 148575.i 0.585744i
\(36\) −451078. 158107.i −1.61136 0.564797i
\(37\) 496284.i 1.61074i 0.592775 + 0.805368i \(0.298032\pi\)
−0.592775 + 0.805368i \(0.701968\pi\)
\(38\) 62393.6 366635.i 0.184458 1.08391i
\(39\) −170134. −0.459267
\(40\) −237420. + 428774.i −0.586552 + 1.05930i
\(41\) 599971. 1.35952 0.679762 0.733433i \(-0.262083\pi\)
0.679762 + 0.733433i \(0.262083\pi\)
\(42\) −64117.9 + 376767.i −0.133539 + 0.784695i
\(43\) 88346.0i 0.169452i −0.996404 0.0847262i \(-0.972998\pi\)
0.996404 0.0847262i \(-0.0270015\pi\)
\(44\) −83264.3 + 237552.i −0.147358 + 0.420412i
\(45\) 1.26383e6i 2.06750i
\(46\) 218662. + 37211.8i 0.331224 + 0.0563674i
\(47\) 820344. 1.15253 0.576267 0.817262i \(-0.304509\pi\)
0.576267 + 0.817262i \(0.304509\pi\)
\(48\) 787104. 984856.i 1.02728 1.28537i
\(49\) −630825. −0.765989
\(50\) −406187. 69124.6i −0.459548 0.0782056i
\(51\) 932236.i 0.984080i
\(52\) 93612.2 267075.i 0.0923253 0.263403i
\(53\) 1.53717e6i 1.41826i 0.705077 + 0.709131i \(0.250913\pi\)
−0.705077 + 0.709131i \(0.749087\pi\)
\(54\) −225985. + 1.32792e6i −0.195300 + 1.14761i
\(55\) −665574. −0.539420
\(56\) −556165. 307959.i −0.423200 0.234333i
\(57\) −2.52950e6 −1.80914
\(58\) 304999. 1.79222e6i 0.205258 1.20613i
\(59\) 1.82480e6i 1.15673i −0.815776 0.578367i \(-0.803690\pi\)
0.815776 0.578367i \(-0.196310\pi\)
\(60\) 3.14586e6 + 1.10265e6i 1.88023 + 0.659037i
\(61\) 484582.i 0.273346i 0.990616 + 0.136673i \(0.0436410\pi\)
−0.990616 + 0.136673i \(0.956359\pi\)
\(62\) −2.55713e6 435171.i −1.36264 0.231894i
\(63\) 1.63932e6 0.825986
\(64\) 1.11293e6 + 1.77748e6i 0.530687 + 0.847568i
\(65\) 748290. 0.337966
\(66\) 1.68781e6 + 287230.i 0.722636 + 0.122978i
\(67\) 79878.2i 0.0324464i 0.999868 + 0.0162232i \(0.00516423\pi\)
−0.999868 + 0.0162232i \(0.994836\pi\)
\(68\) −1.46341e6 512940.i −0.564398 0.197827i
\(69\) 1.50860e6i 0.552845i
\(70\) 282006. 1.65711e6i 0.0982686 0.577442i
\(71\) 1.27078e6 0.421373 0.210686 0.977554i \(-0.432430\pi\)
0.210686 + 0.977554i \(0.432430\pi\)
\(72\) −4.73093e6 2.61960e6i −1.49377 0.827125i
\(73\) 3.70820e6 1.11566 0.557832 0.829954i \(-0.311633\pi\)
0.557832 + 0.829954i \(0.311633\pi\)
\(74\) −941981. + 5.53523e6i −0.270229 + 1.58791i
\(75\) 2.80238e6i 0.767031i
\(76\) 1.39180e6 3.97078e6i 0.363687 1.03760i
\(77\) 863321.i 0.215504i
\(78\) −1.89757e6 322926.i −0.452758 0.0770500i
\(79\) −2.55846e6 −0.583827 −0.291914 0.956445i \(-0.594292\pi\)
−0.291914 + 0.956445i \(0.594292\pi\)
\(80\) −3.46187e6 + 4.33163e6i −0.755954 + 0.945880i
\(81\) 994857. 0.208000
\(82\) 6.69169e6 + 1.13879e6i 1.34025 + 0.228083i
\(83\) 1.53414e6i 0.294505i −0.989099 0.147252i \(-0.952957\pi\)
0.989099 0.147252i \(-0.0470430\pi\)
\(84\) −1.43026e6 + 4.08052e6i −0.263292 + 0.751169i
\(85\) 4.10019e6i 0.724166i
\(86\) 167687. 985355.i 0.0284285 0.167051i
\(87\) −1.23650e7 −2.01315
\(88\) −1.37957e6 + 2.49146e6i −0.215801 + 0.389731i
\(89\) 1.99492e6 0.299958 0.149979 0.988689i \(-0.452079\pi\)
0.149979 + 0.988689i \(0.452079\pi\)
\(90\) 2.39884e6 1.40959e7i 0.346858 2.03819i
\(91\) 970612.i 0.135021i
\(92\) 2.36819e6 + 830073.i 0.317073 + 0.111137i
\(93\) 1.76423e7i 2.27439i
\(94\) 9.14959e6 + 1.55707e6i 1.13620 + 0.193357i
\(95\) 1.11253e7 1.33131
\(96\) 1.06482e7 9.49047e6i 1.22836 1.09481i
\(97\) −28917.7 −0.00321708 −0.00160854 0.999999i \(-0.500512\pi\)
−0.00160854 + 0.999999i \(0.500512\pi\)
\(98\) −7.03582e6 1.19735e6i −0.755133 0.128508i
\(99\) 7.34370e6i 0.760662i
\(100\) −4.39915e6 1.54194e6i −0.439915 0.154194i
\(101\) 1.68077e7i 1.62324i −0.584182 0.811622i \(-0.698585\pi\)
0.584182 0.811622i \(-0.301415\pi\)
\(102\) −1.76945e6 + 1.03976e7i −0.165096 + 0.970132i
\(103\) −1.27746e7 −1.15191 −0.575953 0.817483i \(-0.695369\pi\)
−0.575953 + 0.817483i \(0.695369\pi\)
\(104\) 1.55102e6 2.80110e6i 0.135207 0.244181i
\(105\) −1.14328e7 −0.963807
\(106\) −2.91766e6 + 1.71446e7i −0.237938 + 1.39816i
\(107\) 1.35610e7i 1.07016i 0.844803 + 0.535078i \(0.179718\pi\)
−0.844803 + 0.535078i \(0.820282\pi\)
\(108\) −5.04098e6 + 1.43819e7i −0.385063 + 1.09858i
\(109\) 4.74206e6i 0.350731i −0.984503 0.175366i \(-0.943889\pi\)
0.984503 0.175366i \(-0.0561108\pi\)
\(110\) −7.42338e6 1.26331e6i −0.531774 0.0904969i
\(111\) 3.81889e7 2.65037
\(112\) −5.61858e6 4.49041e6i −0.377889 0.302011i
\(113\) −8.06832e6 −0.526028 −0.263014 0.964792i \(-0.584717\pi\)
−0.263014 + 0.964792i \(0.584717\pi\)
\(114\) −2.82124e7 4.80117e6i −1.78350 0.303515i
\(115\) 6.63520e6i 0.406828i
\(116\) 6.80352e6 1.94104e7i 0.404698 1.15460i
\(117\) 8.25635e6i 0.476582i
\(118\) 3.46360e6 2.03527e7i 0.194062 1.14034i
\(119\) 5.31839e6 0.289311
\(120\) 3.29940e7 + 1.82694e7i 1.74301 + 0.965137i
\(121\) 1.56197e7 0.801540
\(122\) −919770. + 5.40471e6i −0.0458585 + 0.269472i
\(123\) 4.61676e7i 2.23702i
\(124\) −2.76946e7 9.70723e6i −1.30443 0.457214i
\(125\) 1.41153e7i 0.646405i
\(126\) 1.82839e7 + 3.11155e6i 0.814279 + 0.138573i
\(127\) −1.12410e7 −0.486960 −0.243480 0.969906i \(-0.578289\pi\)
−0.243480 + 0.969906i \(0.578289\pi\)
\(128\) 9.03913e6 + 2.19373e7i 0.380971 + 0.924587i
\(129\) −6.79820e6 −0.278824
\(130\) 8.34594e6 + 1.42031e6i 0.333176 + 0.0566996i
\(131\) 8.81527e6i 0.342599i 0.985219 + 0.171299i \(0.0547966\pi\)
−0.985219 + 0.171299i \(0.945203\pi\)
\(132\) 1.82796e7 + 6.40716e6i 0.691763 + 0.242469i
\(133\) 1.44308e7i 0.531874i
\(134\) −151614. + 890910.i −0.00544344 + 0.0319865i
\(135\) −4.02951e7 −1.40956
\(136\) −1.53484e7 8.49866e6i −0.523210 0.289711i
\(137\) −3.33729e7 −1.10885 −0.554424 0.832234i \(-0.687061\pi\)
−0.554424 + 0.832234i \(0.687061\pi\)
\(138\) 2.86344e6 1.68260e7i 0.0927493 0.545010i
\(139\) 4.68161e7i 1.47857i 0.673391 + 0.739287i \(0.264837\pi\)
−0.673391 + 0.739287i \(0.735163\pi\)
\(140\) 6.29062e6 1.79471e7i 0.193752 0.552771i
\(141\) 6.31252e7i 1.89643i
\(142\) 1.41735e7 + 2.41203e6i 0.415401 + 0.0706926i
\(143\) 4.34806e6 0.124343
\(144\) −4.77936e7 3.81970e7i −1.33383 1.06601i
\(145\) 5.43840e7 1.48144
\(146\) 4.13589e7 + 7.03843e6i 1.09985 + 0.187172i
\(147\) 4.85418e7i 1.26039i
\(148\) −2.10125e7 + 5.99485e7i −0.532797 + 1.52006i
\(149\) 3.83709e7i 0.950277i 0.879911 + 0.475139i \(0.157602\pi\)
−0.879911 + 0.475139i \(0.842398\pi\)
\(150\) −5.31912e6 + 3.12560e7i −0.128683 + 0.756160i
\(151\) −7.17648e7 −1.69626 −0.848130 0.529788i \(-0.822271\pi\)
−0.848130 + 0.529788i \(0.822271\pi\)
\(152\) 2.30600e7 4.16458e7i 0.532607 0.961875i
\(153\) 4.52400e7 1.02118
\(154\) 1.63864e6 9.62892e6i 0.0361544 0.212449i
\(155\) 7.75948e7i 1.67368i
\(156\) −2.05513e7 7.20343e6i −0.433414 0.151916i
\(157\) 4.03778e7i 0.832710i −0.909202 0.416355i \(-0.863307\pi\)
0.909202 0.416355i \(-0.136693\pi\)
\(158\) −2.85355e7 4.85614e6i −0.575553 0.0979471i
\(159\) 1.18285e8 2.33367
\(160\) −4.68332e7 + 4.17413e7i −0.903927 + 0.805649i
\(161\) −8.60656e6 −0.162532
\(162\) 1.10960e7 + 1.88831e6i 0.205052 + 0.0348956i
\(163\) 9.84512e7i 1.78059i −0.455383 0.890296i \(-0.650498\pi\)
0.455383 0.890296i \(-0.349502\pi\)
\(164\) 7.24733e7 + 2.54026e7i 1.28299 + 0.449702i
\(165\) 5.12157e7i 0.887584i
\(166\) 2.91191e6 1.71108e7i 0.0494083 0.290331i
\(167\) −4.24811e7 −0.705810 −0.352905 0.935659i \(-0.614806\pi\)
−0.352905 + 0.935659i \(0.614806\pi\)
\(168\) −2.36973e7 + 4.27967e7i −0.385582 + 0.696351i
\(169\) 5.78601e7 0.922095
\(170\) 7.78245e6 4.57309e7i 0.121491 0.713902i
\(171\) 1.22753e8i 1.87735i
\(172\) 3.74054e6 1.06717e7i 0.0560512 0.159914i
\(173\) 2.65257e7i 0.389498i 0.980853 + 0.194749i \(0.0623893\pi\)
−0.980853 + 0.194749i \(0.937611\pi\)
\(174\) −1.37911e8 2.34696e7i −1.98461 0.337740i
\(175\) 1.59875e7 0.225501
\(176\) −2.01158e7 + 2.51697e7i −0.278126 + 0.348003i
\(177\) −1.40418e8 −1.90334
\(178\) 2.22501e7 + 3.78650e6i 0.295707 + 0.0503231i
\(179\) 2.42148e7i 0.315570i 0.987474 + 0.157785i \(0.0504353\pi\)
−0.987474 + 0.157785i \(0.949565\pi\)
\(180\) 5.35101e7 1.52664e8i 0.683884 1.95111i
\(181\) 2.78961e7i 0.349679i −0.984597 0.174839i \(-0.944059\pi\)
0.984597 0.174839i \(-0.0559406\pi\)
\(182\) −1.84229e6 + 1.08256e7i −0.0226521 + 0.133107i
\(183\) 3.72884e7 0.449775
\(184\) 2.48377e7 + 1.37531e7i 0.293934 + 0.162756i
\(185\) −1.67964e8 −1.95036
\(186\) −3.34863e7 + 1.96771e8i −0.381567 + 2.24215i
\(187\) 2.38249e7i 0.266431i
\(188\) 9.90932e7 + 3.47331e7i 1.08766 + 0.381234i
\(189\) 5.22671e7i 0.563135i
\(190\) 1.24085e8 + 2.11167e7i 1.31245 + 0.223351i
\(191\) 1.67596e7 0.174039 0.0870195 0.996207i \(-0.472266\pi\)
0.0870195 + 0.996207i \(0.472266\pi\)
\(192\) 1.36776e8 8.56396e7i 1.39462 0.873214i
\(193\) 8.75008e7 0.876116 0.438058 0.898947i \(-0.355667\pi\)
0.438058 + 0.898947i \(0.355667\pi\)
\(194\) −322529. 54887.7i −0.00317148 0.000539721i
\(195\) 5.75806e7i 0.556103i
\(196\) −7.62003e7 2.67089e7i −0.722871 0.253373i
\(197\) 2.56239e7i 0.238789i −0.992847 0.119394i \(-0.961905\pi\)
0.992847 0.119394i \(-0.0380953\pi\)
\(198\) 1.39388e7 8.19069e7i 0.127614 0.749881i
\(199\) 5.31884e7 0.478444 0.239222 0.970965i \(-0.423108\pi\)
0.239222 + 0.970965i \(0.423108\pi\)
\(200\) −4.61385e7 2.55477e7i −0.407811 0.225812i
\(201\) 6.14660e6 0.0533886
\(202\) 3.19022e7 1.87462e8i 0.272327 1.60024i
\(203\) 7.05419e7i 0.591849i
\(204\) −3.94706e7 + 1.12609e8i −0.325513 + 0.928684i
\(205\) 2.03056e8i 1.64618i
\(206\) −1.42480e8 2.42471e7i −1.13558 0.193252i
\(207\) −7.32103e7 −0.573688
\(208\) 2.26157e7 2.82977e7i 0.174256 0.218036i
\(209\) 6.46457e7 0.489810
\(210\) −1.27514e8 2.17002e7i −0.950147 0.161695i
\(211\) 2.01165e7i 0.147423i 0.997280 + 0.0737114i \(0.0234844\pi\)
−0.997280 + 0.0737114i \(0.976516\pi\)
\(212\) −6.50833e7 + 1.85682e8i −0.469131 + 1.33843i
\(213\) 9.77862e7i 0.693344i
\(214\) −2.57396e7 + 1.51250e8i −0.179537 + 1.05499i
\(215\) 2.99001e7 0.205181
\(216\) −8.35217e7 + 1.50838e8i −0.563912 + 1.01841i
\(217\) 1.00649e8 0.668651
\(218\) 9.00076e6 5.28899e7i 0.0588412 0.345760i
\(219\) 2.85345e8i 1.83576i
\(220\) −8.03978e7 2.81802e7i −0.509055 0.178429i
\(221\) 2.67858e7i 0.166929i
\(222\) 4.25934e8 + 7.24852e7i 2.61281 + 0.444645i
\(223\) −1.67012e8 −1.00851 −0.504254 0.863555i \(-0.668232\pi\)
−0.504254 + 0.863555i \(0.668232\pi\)
\(224\) −5.41429e7 6.07476e7i −0.321865 0.361128i
\(225\) 1.35995e8 0.795949
\(226\) −8.99889e7 1.53142e7i −0.518572 0.0882502i
\(227\) 1.37308e8i 0.779122i 0.921001 + 0.389561i \(0.127373\pi\)
−0.921001 + 0.389561i \(0.872627\pi\)
\(228\) −3.05550e8 1.07098e8i −1.70730 0.598426i
\(229\) 2.67935e8i 1.47436i −0.675694 0.737182i \(-0.736156\pi\)
0.675694 0.737182i \(-0.263844\pi\)
\(230\) −1.25941e7 + 7.40047e7i −0.0682525 + 0.401062i
\(231\) −6.64322e7 −0.354599
\(232\) 1.12724e8 2.03577e8i 0.592665 1.07034i
\(233\) 1.98032e8 1.02563 0.512815 0.858499i \(-0.328603\pi\)
0.512815 + 0.858499i \(0.328603\pi\)
\(234\) −1.56711e7 + 9.20861e7i −0.0799549 + 0.469827i
\(235\) 2.77639e8i 1.39554i
\(236\) 7.72615e7 2.20426e8i 0.382623 1.09162i
\(237\) 1.96873e8i 0.960654i
\(238\) 5.93179e7 + 1.00947e7i 0.285211 + 0.0485370i
\(239\) 8.22277e7 0.389606 0.194803 0.980842i \(-0.437593\pi\)
0.194803 + 0.980842i \(0.437593\pi\)
\(240\) 3.33317e8 + 2.66389e8i 1.55639 + 1.24388i
\(241\) −2.70650e8 −1.24551 −0.622757 0.782415i \(-0.713988\pi\)
−0.622757 + 0.782415i \(0.713988\pi\)
\(242\) 1.74213e8 + 2.96473e7i 0.790179 + 0.134472i
\(243\) 1.83831e8i 0.821860i
\(244\) −2.05170e7 + 5.85349e7i −0.0904171 + 0.257959i
\(245\) 2.13498e8i 0.927498i
\(246\) 8.76293e7 5.14923e8i 0.375298 2.20531i
\(247\) −7.26797e7 −0.306884
\(248\) −2.90463e8 1.60835e8i −1.20923 0.669574i
\(249\) −1.18052e8 −0.484591
\(250\) −2.67918e7 + 1.57433e8i −0.108446 + 0.637243i
\(251\) 2.90747e8i 1.16053i −0.814427 0.580266i \(-0.802949\pi\)
0.814427 0.580266i \(-0.197051\pi\)
\(252\) 1.98021e8 + 6.94084e7i 0.779490 + 0.273218i
\(253\) 3.85549e7i 0.149678i
\(254\) −1.25375e8 2.13363e7i −0.480058 0.0816959i
\(255\) −3.15508e8 −1.19157
\(256\) 5.91782e7 + 2.61831e8i 0.220456 + 0.975397i
\(257\) 4.36047e7 0.160239 0.0801193 0.996785i \(-0.474470\pi\)
0.0801193 + 0.996785i \(0.474470\pi\)
\(258\) −7.58227e7 1.29035e7i −0.274872 0.0467775i
\(259\) 2.17867e8i 0.779188i
\(260\) 9.03894e7 + 3.16823e7i 0.318941 + 0.111792i
\(261\) 6.00053e8i 2.08905i
\(262\) −1.67320e7 + 9.83198e7i −0.0574769 + 0.337743i
\(263\) 4.27678e8 1.44968 0.724840 0.688917i \(-0.241914\pi\)
0.724840 + 0.688917i \(0.241914\pi\)
\(264\) 1.91717e8 + 1.06157e8i 0.641280 + 0.355088i
\(265\) −5.20244e8 −1.71730
\(266\) −2.73906e7 + 1.60951e8i −0.0892309 + 0.524335i
\(267\) 1.53509e8i 0.493564i
\(268\) −3.38202e6 + 9.64886e6i −0.0107326 + 0.0306199i
\(269\) 8.26134e7i 0.258772i −0.991594 0.129386i \(-0.958699\pi\)
0.991594 0.129386i \(-0.0413007\pi\)
\(270\) −4.49426e8 7.64830e7i −1.38958 0.236478i
\(271\) 6.15189e7 0.187766 0.0938829 0.995583i \(-0.470072\pi\)
0.0938829 + 0.995583i \(0.470072\pi\)
\(272\) −1.55055e8 1.23921e8i −0.467190 0.373382i
\(273\) 7.46883e7 0.222169
\(274\) −3.72220e8 6.33441e7i −1.09313 0.186028i
\(275\) 7.16196e7i 0.207667i
\(276\) 6.38738e7 1.82231e8i 0.182869 0.521725i
\(277\) 4.39237e7i 0.124171i 0.998071 + 0.0620854i \(0.0197751\pi\)
−0.998071 + 0.0620854i \(0.980225\pi\)
\(278\) −8.88601e7 + 5.22156e8i −0.248056 + 1.45762i
\(279\) 8.56153e8 2.36013
\(280\) 1.04226e8 1.88230e8i 0.283742 0.512432i
\(281\) 5.80931e8 1.56190 0.780948 0.624596i \(-0.214736\pi\)
0.780948 + 0.624596i \(0.214736\pi\)
\(282\) 1.19816e8 7.04058e8i 0.318158 1.86955i
\(283\) 6.03790e8i 1.58356i 0.610810 + 0.791778i \(0.290844\pi\)
−0.610810 + 0.791778i \(0.709156\pi\)
\(284\) 1.53504e8 + 5.38045e7i 0.397653 + 0.139381i
\(285\) 8.56091e8i 2.19060i
\(286\) 4.84955e7 + 8.25293e6i 0.122580 + 0.0208606i
\(287\) −2.63385e8 −0.657665
\(288\) −4.60558e8 5.16740e8i −1.13609 1.27467i
\(289\) −2.63568e8 −0.642319
\(290\) 6.06564e8 + 1.03225e8i 1.46044 + 0.248536i
\(291\) 2.22520e6i 0.00529352i
\(292\) 4.47931e8 + 1.57004e8i 1.05286 + 0.369038i
\(293\) 1.10504e8i 0.256649i −0.991732 0.128325i \(-0.959040\pi\)
0.991732 0.128325i \(-0.0409600\pi\)
\(294\) −9.21357e7 + 5.41404e8i −0.211452 + 1.24253i
\(295\) 6.17591e8 1.40063
\(296\) −3.48146e8 + 6.28743e8i −0.780263 + 1.40913i
\(297\) −2.34142e8 −0.518599
\(298\) −7.28307e7 + 4.27965e8i −0.159425 + 0.936809i
\(299\) 4.33464e7i 0.0937787i
\(300\) −1.18652e8 + 3.38513e8i −0.253718 + 0.723854i
\(301\) 3.87836e7i 0.0819719i
\(302\) −8.00419e8 1.36215e8i −1.67222 0.284577i
\(303\) −1.29335e9 −2.67095
\(304\) 3.36243e8 4.20721e8i 0.686430 0.858888i
\(305\) −1.64003e8 −0.330981
\(306\) 5.04578e8 + 8.58687e7i 1.00671 + 0.171321i
\(307\) 7.03386e8i 1.38742i −0.720252 0.693712i \(-0.755974\pi\)
0.720252 0.693712i \(-0.244026\pi\)
\(308\) 3.65527e7 1.04285e8i 0.0712840 0.203373i
\(309\) 9.83002e8i 1.89539i
\(310\) 1.47280e8 8.65443e8i 0.280788 1.64996i
\(311\) −8.61240e8 −1.62354 −0.811769 0.583978i \(-0.801495\pi\)
−0.811769 + 0.583978i \(0.801495\pi\)
\(312\) −2.15543e8 1.19350e8i −0.401785 0.222475i
\(313\) 2.42056e8 0.446181 0.223090 0.974798i \(-0.428385\pi\)
0.223090 + 0.974798i \(0.428385\pi\)
\(314\) 7.66398e7 4.50348e8i 0.139701 0.820908i
\(315\) 5.54817e8i 1.00014i
\(316\) −3.09049e8 1.08325e8i −0.550963 0.193118i
\(317\) 5.38362e8i 0.949221i 0.880196 + 0.474610i \(0.157411\pi\)
−0.880196 + 0.474610i \(0.842589\pi\)
\(318\) 1.31927e9 + 2.24513e8i 2.30059 + 0.391513i
\(319\) 3.16007e8 0.545042
\(320\) −6.01575e8 + 3.76663e8i −1.02628 + 0.642581i
\(321\) 1.04351e9 1.76088
\(322\) −9.59920e7 1.63358e7i −0.160228 0.0272675i
\(323\) 3.98242e8i 0.657565i
\(324\) 1.20173e8 + 4.21219e7i 0.196291 + 0.0688020i
\(325\) 8.05203e7i 0.130111i
\(326\) 1.86867e8 1.09806e9i 0.298725 1.75535i
\(327\) −3.64900e8 −0.577108
\(328\) 7.60105e8 + 4.20883e8i 1.18936 + 0.658572i
\(329\) −3.60128e8 −0.557534
\(330\) −9.72109e7 + 5.71227e8i −0.148907 + 0.875003i
\(331\) 1.05054e9i 1.59226i −0.605124 0.796131i \(-0.706877\pi\)
0.605124 0.796131i \(-0.293123\pi\)
\(332\) 6.49551e7 1.85316e8i 0.0974160 0.277927i
\(333\) 1.85325e9i 2.75029i
\(334\) −4.73806e8 8.06320e7i −0.695806 0.118412i
\(335\) −2.70342e7 −0.0392877
\(336\) −3.45536e8 + 4.32348e8i −0.496942 + 0.621793i
\(337\) −2.04579e8 −0.291177 −0.145589 0.989345i \(-0.546508\pi\)
−0.145589 + 0.989345i \(0.546508\pi\)
\(338\) 6.45334e8 + 1.09822e8i 0.909026 + 0.154697i
\(339\) 6.20855e8i 0.865548i
\(340\) 1.73601e8 4.95281e8i 0.239539 0.683401i
\(341\) 4.50878e8i 0.615770i
\(342\) −2.32994e8 + 1.36911e9i −0.314958 + 1.85074i
\(343\) 6.38462e8 0.854291
\(344\) 6.19753e7 1.11926e8i 0.0820850 0.148244i
\(345\) 5.10576e8 0.669412
\(346\) −5.03476e7 + 2.95851e8i −0.0653450 + 0.383978i
\(347\) 6.28852e8i 0.807970i 0.914766 + 0.403985i \(0.132375\pi\)
−0.914766 + 0.403985i \(0.867625\pi\)
\(348\) −1.49362e9 5.23529e8i −1.89982 0.665906i
\(349\) 9.86717e8i 1.24252i 0.783604 + 0.621260i \(0.213379\pi\)
−0.783604 + 0.621260i \(0.786621\pi\)
\(350\) 1.78315e8 + 3.03455e7i 0.222305 + 0.0378317i
\(351\) 2.63240e8 0.324921
\(352\) −2.72132e8 + 2.42545e8i −0.332568 + 0.296410i
\(353\) 5.59732e8 0.677281 0.338641 0.940916i \(-0.390033\pi\)
0.338641 + 0.940916i \(0.390033\pi\)
\(354\) −1.56613e9 2.66523e8i −1.87636 0.319318i
\(355\) 4.30087e8i 0.510219i
\(356\) 2.40976e8 + 8.44643e7i 0.283073 + 0.0992198i
\(357\) 4.09248e8i 0.476045i
\(358\) −4.59614e7 + 2.70076e8i −0.0529423 + 0.311097i
\(359\) 1.42390e8 0.162424 0.0812119 0.996697i \(-0.474121\pi\)
0.0812119 + 0.996697i \(0.474121\pi\)
\(360\) 8.86584e8 1.60115e9i 1.00152 1.80873i
\(361\) −1.86707e8 −0.208875
\(362\) 5.29488e7 3.11136e8i 0.0586646 0.344723i
\(363\) 1.20193e9i 1.31889i
\(364\) −4.10954e7 + 1.17245e8i −0.0446620 + 0.127420i
\(365\) 1.25501e9i 1.35090i
\(366\) 4.15891e8 + 7.07760e7i 0.443400 + 0.0754575i
\(367\) 7.13452e8 0.753414 0.376707 0.926333i \(-0.377056\pi\)
0.376707 + 0.926333i \(0.377056\pi\)
\(368\) 2.50920e8 + 2.00537e8i 0.262463 + 0.209762i
\(369\) −2.24044e9 −2.32136
\(370\) −1.87336e9 3.18807e8i −1.92271 0.327206i
\(371\) 6.74812e8i 0.686079i
\(372\) −7.46968e8 + 2.13109e9i −0.752319 + 2.14636i
\(373\) 4.14729e8i 0.413794i −0.978363 0.206897i \(-0.933664\pi\)
0.978363 0.206897i \(-0.0663364\pi\)
\(374\) 4.52212e7 2.65727e8i 0.0446984 0.262655i
\(375\) 1.08617e9 1.06362
\(376\) 1.03930e9 + 5.75476e8i 1.00828 + 0.558303i
\(377\) −3.55280e8 −0.341489
\(378\) 9.92066e7 5.82954e8i 0.0944755 0.555153i
\(379\) 1.23625e8i 0.116646i 0.998298 + 0.0583229i \(0.0185753\pi\)
−0.998298 + 0.0583229i \(0.981425\pi\)
\(380\) 1.34388e9 + 4.71043e8i 1.25637 + 0.440371i
\(381\) 8.64994e8i 0.801264i
\(382\) 1.86926e8 + 3.18109e7i 0.171572 + 0.0291980i
\(383\) −1.35784e9 −1.23496 −0.617480 0.786586i \(-0.711846\pi\)
−0.617480 + 0.786586i \(0.711846\pi\)
\(384\) 1.68807e9 6.95558e8i 1.52135 0.626865i
\(385\) 2.92184e8 0.260942
\(386\) 9.75927e8 + 1.66083e8i 0.863698 + 0.146983i
\(387\) 3.29906e8i 0.289336i
\(388\) −3.49310e6 1.22436e6i −0.00303599 0.00106414i
\(389\) 1.00573e9i 0.866281i −0.901326 0.433141i \(-0.857405\pi\)
0.901326 0.433141i \(-0.142595\pi\)
\(390\) 1.09292e8 6.42217e8i 0.0932959 0.548221i
\(391\) −2.37513e8 −0.200941
\(392\) −7.99194e8 4.42528e8i −0.670117 0.371056i
\(393\) 6.78332e8 0.563726
\(394\) 4.86359e7 2.85793e8i 0.0400609 0.235404i
\(395\) 8.65893e8i 0.706927i
\(396\) 3.10930e8 8.87080e8i 0.251611 0.717843i
\(397\) 2.30080e8i 0.184549i 0.995734 + 0.0922747i \(0.0294138\pi\)
−0.995734 + 0.0922747i \(0.970586\pi\)
\(398\) 5.93229e8 + 1.00955e8i 0.471663 + 0.0802672i
\(399\) 1.11044e9 0.875167
\(400\) −4.66108e8 3.72517e8i −0.364147 0.291029i
\(401\) −1.24791e9 −0.966446 −0.483223 0.875497i \(-0.660534\pi\)
−0.483223 + 0.875497i \(0.660534\pi\)
\(402\) 6.85552e7 + 1.16667e7i 0.0526319 + 0.00895686i
\(403\) 5.06912e8i 0.385802i
\(404\) 7.11633e8 2.03028e9i 0.536935 1.53187i
\(405\) 3.36702e8i 0.251857i
\(406\) −1.33893e8 + 7.86778e8i −0.0992928 + 0.583460i
\(407\) −9.75982e8 −0.717565
\(408\) −6.53969e8 + 1.18105e9i −0.476702 + 0.860911i
\(409\) −1.79923e9 −1.30033 −0.650166 0.759792i \(-0.725301\pi\)
−0.650166 + 0.759792i \(0.725301\pi\)
\(410\) −3.85414e8 + 2.26475e9i −0.276175 + 1.62285i
\(411\) 2.56803e9i 1.82454i
\(412\) −1.54310e9 5.40873e8i −1.08706 0.381026i
\(413\) 8.01081e8i 0.559566i
\(414\) −8.16541e8 1.38958e8i −0.565557 0.0962461i
\(415\) 5.19219e8 0.356601
\(416\) 3.05952e8 2.72688e8i 0.208366 0.185712i
\(417\) 3.60248e9 2.43291
\(418\) 7.21016e8 + 1.22702e8i 0.482868 + 0.0821740i
\(419\) 2.66870e8i 0.177235i 0.996066 + 0.0886177i \(0.0282449\pi\)
−0.996066 + 0.0886177i \(0.971755\pi\)
\(420\) −1.38102e9 4.84061e8i −0.909553 0.318807i
\(421\) 2.70575e9i 1.76726i −0.468185 0.883630i \(-0.655092\pi\)
0.468185 0.883630i \(-0.344908\pi\)
\(422\) −3.81826e7 + 2.24367e8i −0.0247327 + 0.145333i
\(423\) −3.06337e9 −1.96792
\(424\) −1.07833e9 + 1.94745e9i −0.687026 + 1.24075i
\(425\) 4.41204e8 0.278791
\(426\) 1.85605e8 1.09064e9i 0.116320 0.683517i
\(427\) 2.12730e8i 0.132230i
\(428\) −5.74167e8 + 1.63809e9i −0.353985 + 1.00992i
\(429\) 3.34582e8i 0.204598i
\(430\) 3.33486e8 + 5.67524e7i 0.202273 + 0.0344227i
\(431\) 1.78455e9 1.07364 0.536820 0.843697i \(-0.319626\pi\)
0.536820 + 0.843697i \(0.319626\pi\)
\(432\) −1.21785e9 + 1.52382e9i −0.726775 + 0.909370i
\(433\) 1.21276e9 0.717905 0.358953 0.933356i \(-0.383134\pi\)
0.358953 + 0.933356i \(0.383134\pi\)
\(434\) 1.12257e9 + 1.91038e8i 0.659174 + 0.112178i
\(435\) 4.18483e9i 2.43762i
\(436\) 2.00777e8 5.72816e8i 0.116014 0.330988i
\(437\) 6.44461e8i 0.369413i
\(438\) 5.41605e8 3.18256e9i 0.307980 1.80974i
\(439\) −1.76141e9 −0.993654 −0.496827 0.867850i \(-0.665502\pi\)
−0.496827 + 0.867850i \(0.665502\pi\)
\(440\) −8.43217e8 4.66904e8i −0.471905 0.261302i
\(441\) 2.35566e9 1.30791
\(442\) −5.08412e7 + 2.98751e8i −0.0280052 + 0.164563i
\(443\) 8.06208e8i 0.440590i 0.975433 + 0.220295i \(0.0707019\pi\)
−0.975433 + 0.220295i \(0.929298\pi\)
\(444\) 4.61301e9 + 1.61691e9i 2.50118 + 0.876686i
\(445\) 6.75166e8i 0.363204i
\(446\) −1.86274e9 3.16999e8i −0.994214 0.169195i
\(447\) 2.95263e9 1.56363
\(448\) −4.88572e8 7.80307e8i −0.256718 0.410008i
\(449\) 5.85913e8 0.305472 0.152736 0.988267i \(-0.451192\pi\)
0.152736 + 0.988267i \(0.451192\pi\)
\(450\) 1.51681e9 + 2.58129e8i 0.784668 + 0.133534i
\(451\) 1.17989e9i 0.605653i
\(452\) −9.74611e8 3.41610e8i −0.496417 0.173999i
\(453\) 5.52228e9i 2.79110i
\(454\) −2.60620e8 + 1.53145e9i −0.130711 + 0.768079i
\(455\) −3.28496e8 −0.163490
\(456\) −3.20463e9 1.77446e9i −1.58271 0.876374i
\(457\) 5.52640e8 0.270854 0.135427 0.990787i \(-0.456759\pi\)
0.135427 + 0.990787i \(0.456759\pi\)
\(458\) 5.08559e8 2.98837e9i 0.247350 1.45347i
\(459\) 1.44240e9i 0.696213i
\(460\) −2.80932e8 + 8.01496e8i −0.134570 + 0.383927i
\(461\) 1.74101e9i 0.827652i −0.910356 0.413826i \(-0.864192\pi\)
0.910356 0.413826i \(-0.135808\pi\)
\(462\) −7.40942e8 1.26093e8i −0.349573 0.0594900i
\(463\) −2.84431e9 −1.33181 −0.665906 0.746035i \(-0.731955\pi\)
−0.665906 + 0.746035i \(0.731955\pi\)
\(464\) 1.64366e9 2.05661e9i 0.763833 0.955739i
\(465\) −5.97090e9 −2.75394
\(466\) 2.20873e9 + 3.75879e8i 1.01109 + 0.172067i
\(467\) 1.63130e9i 0.741183i 0.928796 + 0.370592i \(0.120845\pi\)
−0.928796 + 0.370592i \(0.879155\pi\)
\(468\) −3.49571e8 + 9.97324e8i −0.157643 + 0.449755i
\(469\) 3.50662e7i 0.0156958i
\(470\) −5.26979e8 + 3.09661e9i −0.234127 + 1.37576i
\(471\) −3.10706e9 −1.37018
\(472\) 1.28011e9 2.31185e9i 0.560338 1.01196i
\(473\) 1.73739e8 0.0754891
\(474\) −3.73678e8 + 2.19579e9i −0.161166 + 0.947038i
\(475\) 1.19715e9i 0.512532i
\(476\) 6.42433e8 + 2.25179e8i 0.273026 + 0.0956981i
\(477\) 5.74018e9i 2.42165i
\(478\) 9.17114e8 + 1.56074e8i 0.384084 + 0.0653630i
\(479\) 3.69345e9 1.53553 0.767765 0.640732i \(-0.221369\pi\)
0.767765 + 0.640732i \(0.221369\pi\)
\(480\) 3.21198e9 + 3.60380e9i 1.32565 + 1.48736i
\(481\) 1.09727e9 0.449580
\(482\) −3.01866e9 5.13713e8i −1.22786 0.208956i
\(483\) 6.62272e8i 0.267437i
\(484\) 1.88678e9 + 6.61335e8i 0.756420 + 0.265132i
\(485\) 9.78697e6i 0.00389540i
\(486\) −3.48925e8 + 2.05034e9i −0.137881 + 0.810211i
\(487\) 1.57153e9 0.616554 0.308277 0.951297i \(-0.400248\pi\)
0.308277 + 0.951297i \(0.400248\pi\)
\(488\) −3.39937e8 + 6.13918e8i −0.132413 + 0.239134i
\(489\) −7.57578e9 −2.92986
\(490\) 4.05234e8 2.38122e9i 0.155604 0.914352i
\(491\) 1.63493e9i 0.623323i 0.950193 + 0.311662i \(0.100886\pi\)
−0.950193 + 0.311662i \(0.899114\pi\)
\(492\) 1.95472e9 5.57680e9i 0.739958 2.11109i
\(493\) 1.94673e9i 0.731713i
\(494\) −8.10622e8 1.37951e8i −0.302534 0.0514850i
\(495\) 2.48542e9 0.921047
\(496\) −2.93436e9 2.34516e9i −1.07976 0.862953i
\(497\) −5.57868e8 −0.203838
\(498\) −1.31667e9 2.24070e8i −0.477722 0.0812984i
\(499\) 6.86870e8i 0.247470i 0.992315 + 0.123735i \(0.0394873\pi\)
−0.992315 + 0.123735i \(0.960513\pi\)
\(500\) −5.97637e8 + 1.70505e9i −0.213817 + 0.610018i
\(501\) 3.26890e9i 1.16137i
\(502\) 5.51858e8 3.24280e9i 0.194699 1.14408i
\(503\) 2.33472e9 0.817990 0.408995 0.912537i \(-0.365879\pi\)
0.408995 + 0.912537i \(0.365879\pi\)
\(504\) 2.07686e9 + 1.14999e9i 0.722604 + 0.400119i
\(505\) 5.68845e9 1.96550
\(506\) −7.31799e7 + 4.30017e8i −0.0251111 + 0.147557i
\(507\) 4.45231e9i 1.51725i
\(508\) −1.35786e9 4.75942e8i −0.459548 0.161076i
\(509\) 6.21342e8i 0.208842i 0.994533 + 0.104421i \(0.0332990\pi\)
−0.994533 + 0.104421i \(0.966701\pi\)
\(510\) −3.51898e9 5.98857e8i −1.17468 0.199907i
\(511\) −1.62789e9 −0.539699
\(512\) 1.63062e8 + 3.03262e9i 0.0536917 + 0.998558i
\(513\) 3.91378e9 1.27993
\(514\) 4.86339e8 + 8.27647e7i 0.157968 + 0.0268828i
\(515\) 4.32347e9i 1.39478i
\(516\) −8.21186e8 2.87834e8i −0.263128 0.0922290i
\(517\) 1.61327e9i 0.513441i
\(518\) 4.13526e8 2.42995e9i 0.130722 0.768144i
\(519\) 2.04114e9 0.640896
\(520\) 9.48010e8 + 5.24930e8i 0.295666 + 0.163715i
\(521\) −1.65562e9 −0.512897 −0.256448 0.966558i \(-0.582552\pi\)
−0.256448 + 0.966558i \(0.582552\pi\)
\(522\) −1.13894e9 + 6.69260e9i −0.350473 + 2.05944i
\(523\) 4.42671e9i 1.35309i −0.736403 0.676543i \(-0.763477\pi\)
0.736403 0.676543i \(-0.236523\pi\)
\(524\) −3.73236e8 + 1.06484e9i −0.113324 + 0.323313i
\(525\) 1.23024e9i 0.371049i
\(526\) 4.77005e9 + 8.11763e8i 1.42913 + 0.243209i
\(527\) 2.77758e9 0.826665
\(528\) 1.93680e9 + 1.54790e9i 0.572618 + 0.457641i
\(529\) −3.02047e9 −0.887113
\(530\) −5.80247e9 9.87459e8i −1.69296 0.288107i
\(531\) 6.81427e9i 1.97510i
\(532\) −6.10994e8 + 1.74316e9i −0.175932 + 0.501933i
\(533\) 1.32652e9i 0.379463i
\(534\) 2.91370e8 1.71213e9i 0.0828038 0.486568i
\(535\) −4.58961e9 −1.29580
\(536\) −5.60350e7 + 1.01198e8i −0.0157175 + 0.0283854i
\(537\) 1.86332e9 0.519252
\(538\) 1.56806e8 9.21417e8i 0.0434135 0.255105i
\(539\) 1.24057e9i 0.341240i
\(540\) −4.86744e9 1.70608e9i −1.33022 0.466253i
\(541\) 3.71878e9i 1.00974i −0.863195 0.504871i \(-0.831540\pi\)
0.863195 0.504871i \(-0.168460\pi\)
\(542\) 6.86143e8 + 1.16767e8i 0.185104 + 0.0315009i
\(543\) −2.14660e9 −0.575376
\(544\) −1.49417e9 1.67644e9i −0.397928 0.446469i
\(545\) 1.60492e9 0.424683
\(546\) 8.33025e8 + 1.41763e8i 0.219020 + 0.0372726i
\(547\) 3.20749e9i 0.837934i 0.908002 + 0.418967i \(0.137608\pi\)
−0.908002 + 0.418967i \(0.862392\pi\)
\(548\) −4.03127e9 1.41300e9i −1.04643 0.366783i
\(549\) 1.80955e9i 0.466732i
\(550\) 1.35939e8 7.98799e8i 0.0348397 0.204724i
\(551\) −5.28219e9 −1.34519
\(552\) 1.05830e9 1.91125e9i 0.267806 0.483651i
\(553\) 1.12316e9 0.282424
\(554\) −8.33702e7 + 4.89897e8i −0.0208318 + 0.122411i
\(555\) 1.29247e10i 3.20920i
\(556\) −1.98218e9 + 5.65513e9i −0.489081 + 1.39534i
\(557\) 4.80739e9i 1.17873i 0.807865 + 0.589367i \(0.200623\pi\)
−0.807865 + 0.589367i \(0.799377\pi\)
\(558\) 9.54898e9 + 1.62504e9i 2.32668 + 0.395953i
\(559\) −1.95331e8 −0.0472967
\(560\) 1.51975e9 1.90157e9i 0.365690 0.457566i
\(561\) −1.83332e9 −0.438397
\(562\) 6.47933e9 + 1.10265e9i 1.53976 + 0.262035i
\(563\) 3.77127e9i 0.890653i −0.895368 0.445326i \(-0.853088\pi\)
0.895368 0.445326i \(-0.146912\pi\)
\(564\) 2.67270e9 7.62519e9i 0.627297 1.78967i
\(565\) 2.73066e9i 0.636940i
\(566\) −1.14603e9 + 6.73428e9i −0.265669 + 1.56111i
\(567\) −4.36739e8 −0.100619
\(568\) 1.60996e9 + 8.91461e8i 0.368633 + 0.204119i
\(569\) 2.09341e9 0.476388 0.238194 0.971218i \(-0.423445\pi\)
0.238194 + 0.971218i \(0.423445\pi\)
\(570\) 1.62492e9 9.54829e9i 0.367511 2.15955i
\(571\) 6.86085e9i 1.54224i −0.636691 0.771119i \(-0.719697\pi\)
0.636691 0.771119i \(-0.280303\pi\)
\(572\) 5.25223e8 + 1.84096e8i 0.117343 + 0.0411299i
\(573\) 1.28965e9i 0.286371i
\(574\) −2.93763e9 4.99923e8i −0.648343 0.110335i
\(575\) −7.13986e8 −0.156622
\(576\) −4.15596e9 6.63755e9i −0.906135 1.44720i
\(577\) 5.70742e9 1.23687 0.618435 0.785836i \(-0.287767\pi\)
0.618435 + 0.785836i \(0.287767\pi\)
\(578\) −2.93967e9 5.00271e8i −0.633215 0.107760i
\(579\) 6.73316e9i 1.44160i
\(580\) 6.56930e9 + 2.30260e9i 1.39804 + 0.490028i
\(581\) 6.73483e8i 0.142466i
\(582\) −4.22359e6 + 2.48185e7i −0.000888078 + 0.00521849i
\(583\) −3.02297e9 −0.631820
\(584\) 4.69793e9 + 2.60133e9i 0.976027 + 0.540443i
\(585\) −2.79430e9 −0.577069
\(586\) 2.09744e8 1.23249e9i 0.0430573 0.253012i
\(587\) 1.56510e9i 0.319380i 0.987167 + 0.159690i \(0.0510495\pi\)
−0.987167 + 0.159690i \(0.948951\pi\)
\(588\) −2.05524e9 + 5.86359e9i −0.416910 + 1.18944i
\(589\) 7.53661e9i 1.51975i
\(590\) 6.88821e9 + 1.17223e9i 1.38078 + 0.234980i
\(591\) −1.97175e9 −0.392913
\(592\) −5.07640e9 + 6.35179e9i −1.00561 + 1.25826i
\(593\) −2.78410e9 −0.548268 −0.274134 0.961692i \(-0.588391\pi\)
−0.274134 + 0.961692i \(0.588391\pi\)
\(594\) −2.61147e9 4.44417e8i −0.511248 0.0870038i
\(595\) 1.79997e9i 0.350312i
\(596\) −1.62461e9 + 4.63500e9i −0.314331 + 0.896784i
\(597\) 4.09283e9i 0.787251i
\(598\) 8.22745e7 4.83458e8i 0.0157330 0.0924496i
\(599\) 6.18885e9 1.17657 0.588283 0.808655i \(-0.299804\pi\)
0.588283 + 0.808655i \(0.299804\pi\)
\(600\) −1.96589e9 + 3.55035e9i −0.371561 + 0.671029i
\(601\) −2.42206e9 −0.455118 −0.227559 0.973764i \(-0.573074\pi\)
−0.227559 + 0.973764i \(0.573074\pi\)
\(602\) −7.36139e7 + 4.32567e8i −0.0137522 + 0.0808101i
\(603\) 2.98285e8i 0.0554014i
\(604\) −8.66881e9 3.03850e9i −1.60077 0.561087i
\(605\) 5.28639e9i 0.970544i
\(606\) −1.44252e10 2.45486e9i −2.63310 0.448098i
\(607\) −4.62465e9 −0.839302 −0.419651 0.907686i \(-0.637848\pi\)
−0.419651 + 0.907686i \(0.637848\pi\)
\(608\) 4.54880e9 4.05424e9i 0.820794 0.731555i
\(609\) 5.42817e9 0.973852
\(610\) −1.82919e9 3.11289e8i −0.326290 0.0555277i
\(611\) 1.81376e9i 0.321689i
\(612\) 5.46475e9 + 1.91545e9i 0.963697 + 0.337785i
\(613\) 5.45433e9i 0.956378i −0.878257 0.478189i \(-0.841293\pi\)
0.878257 0.478189i \(-0.158707\pi\)
\(614\) 1.33508e9 7.84511e9i 0.232764 1.36776i
\(615\) 1.56251e10 2.70869
\(616\) 6.05625e8 1.09374e9i 0.104393 0.188531i
\(617\) −2.32837e9 −0.399074 −0.199537 0.979890i \(-0.563944\pi\)
−0.199537 + 0.979890i \(0.563944\pi\)
\(618\) −1.86581e9 + 1.09638e10i −0.317985 + 1.86853i
\(619\) 9.58626e9i 1.62455i 0.583278 + 0.812273i \(0.301770\pi\)
−0.583278 + 0.812273i \(0.698230\pi\)
\(620\) 3.28534e9 9.37304e9i 0.553617 1.57946i
\(621\) 2.33419e9i 0.391125i
\(622\) −9.60571e9 1.63469e9i −1.60053 0.272377i
\(623\) −8.75763e8 −0.145104
\(624\) −2.17750e9 1.74027e9i −0.358766 0.286728i
\(625\) −7.62240e9 −1.24885
\(626\) 2.69974e9 + 4.59439e8i 0.439857 + 0.0748545i
\(627\) 4.97446e9i 0.805953i
\(628\) 1.70958e9 4.87742e9i 0.275443 0.785835i
\(629\) 6.01242e9i 0.963324i
\(630\) −1.05308e9 + 6.18807e9i −0.167791 + 0.985969i
\(631\) 1.18616e10 1.87949 0.939747 0.341870i \(-0.111060\pi\)
0.939747 + 0.341870i \(0.111060\pi\)
\(632\) −3.24132e9 1.79478e9i −0.510755 0.282814i
\(633\) 1.54796e9 0.242576
\(634\) −1.02185e9 + 6.00455e9i −0.159248 + 0.935767i
\(635\) 3.80445e9i 0.589635i
\(636\) 1.42882e10 + 5.00814e9i 2.20230 + 0.771928i
\(637\) 1.39474e9i 0.213799i
\(638\) 3.52454e9 + 5.99804e8i 0.537317 + 0.0914402i
\(639\) −4.74542e9 −0.719484
\(640\) −7.42451e9 + 3.05923e9i −1.11954 + 0.461298i
\(641\) −1.06130e8 −0.0159161 −0.00795805 0.999968i \(-0.502533\pi\)
−0.00795805 + 0.999968i \(0.502533\pi\)
\(642\) 1.16387e10 + 1.98066e9i 1.73592 + 0.295418i
\(643\) 2.19289e9i 0.325296i 0.986684 + 0.162648i \(0.0520035\pi\)
−0.986684 + 0.162648i \(0.947996\pi\)
\(644\) −1.03963e9 3.64399e8i −0.153383 0.0537621i
\(645\) 2.30080e9i 0.337614i
\(646\) −7.55891e8 + 4.44174e9i −0.110318 + 0.648245i
\(647\) −4.23914e9 −0.615337 −0.307668 0.951494i \(-0.599549\pi\)
−0.307668 + 0.951494i \(0.599549\pi\)
\(648\) 1.26039e9 + 6.97899e8i 0.181966 + 0.100758i
\(649\) 3.58862e9 0.515312
\(650\) −1.52833e8 + 8.98072e8i −0.0218283 + 0.128267i
\(651\) 7.74489e9i 1.10023i
\(652\) 4.16839e9 1.18924e10i 0.588982 1.68036i
\(653\) 9.93257e9i 1.39594i −0.716129 0.697968i \(-0.754088\pi\)
0.716129 0.697968i \(-0.245912\pi\)
\(654\) −4.06986e9 6.92606e8i −0.568928 0.0968198i
\(655\) −2.98346e9 −0.414836
\(656\) 7.67885e9 + 6.13699e9i 1.06202 + 0.848774i
\(657\) −1.38474e10 −1.90497
\(658\) −4.01664e9 6.83548e8i −0.549632 0.0935359i
\(659\) 1.36634e10i 1.85977i 0.367852 + 0.929884i \(0.380093\pi\)
−0.367852 + 0.929884i \(0.619907\pi\)
\(660\) −2.16846e9 + 6.18658e9i −0.293594 + 0.837620i
\(661\) 1.03765e10i 1.39747i 0.715378 + 0.698737i \(0.246254\pi\)
−0.715378 + 0.698737i \(0.753746\pi\)
\(662\) 1.99400e9 1.17170e10i 0.267129 1.56969i
\(663\) 2.06115e9 0.274671
\(664\) 1.07621e9 1.94361e9i 0.142662 0.257644i
\(665\) −4.88398e9 −0.644019
\(666\) 3.51760e9 2.06700e10i 0.461409 2.71131i
\(667\) 3.15032e9i 0.411069i
\(668\) −5.13149e9 1.79863e9i −0.666079 0.233467i
\(669\) 1.28515e10i 1.65944i
\(670\) −3.01522e8 5.13127e7i −0.0387308 0.00659118i
\(671\) −9.52968e8 −0.121773
\(672\) −4.67451e9 + 4.16628e9i −0.594215 + 0.529610i
\(673\) 4.70776e9 0.595336 0.297668 0.954669i \(-0.403791\pi\)
0.297668 + 0.954669i \(0.403791\pi\)
\(674\) −2.28175e9 3.88306e8i −0.287050 0.0488500i
\(675\) 4.33599e9i 0.542657i
\(676\) 6.98919e9 + 2.44978e9i 0.870189 + 0.305009i
\(677\) 9.55050e9i 1.18295i 0.806324 + 0.591474i \(0.201454\pi\)
−0.806324 + 0.591474i \(0.798546\pi\)
\(678\) −1.17843e9 + 6.92462e9i −0.145211 + 0.853280i
\(679\) 1.26947e7 0.00155625
\(680\) 2.87631e9 5.19454e9i 0.350796 0.633528i
\(681\) 1.05658e10 1.28200
\(682\) 8.55798e8 5.02880e9i 0.103306 0.607043i
\(683\) 1.06442e10i 1.27832i 0.769073 + 0.639161i \(0.220718\pi\)
−0.769073 + 0.639161i \(0.779282\pi\)
\(684\) −5.19732e9 + 1.48279e10i −0.620988 + 1.77167i
\(685\) 1.12948e10i 1.34265i
\(686\) 7.12100e9 + 1.21185e9i 0.842183 + 0.143322i
\(687\) −2.06175e10 −2.42598
\(688\) 9.03675e8 1.13071e9i 0.105792 0.132371i
\(689\) 3.39865e9 0.395858
\(690\) 5.69464e9 + 9.69109e8i 0.659924 + 0.112305i
\(691\) 8.41537e9i 0.970287i −0.874435 0.485143i \(-0.838767\pi\)
0.874435 0.485143i \(-0.161233\pi\)
\(692\) −1.12309e9 + 3.20416e9i −0.128838 + 0.367573i
\(693\) 3.22386e9i 0.367967i
\(694\) −1.19360e9 + 7.01381e9i −0.135551 + 0.796519i
\(695\) −1.58445e10 −1.79033
\(696\) −1.56652e10 8.67410e9i −1.76118 0.975196i
\(697\) −7.26858e9 −0.813083
\(698\) −1.87286e9 + 1.10052e10i −0.208454 + 1.22491i
\(699\) 1.52385e10i 1.68761i
\(700\) 1.93121e9 + 6.76907e8i 0.212807 + 0.0745909i
\(701\) 8.95355e9i 0.981707i −0.871242 0.490854i \(-0.836685\pi\)
0.871242 0.490854i \(-0.163315\pi\)
\(702\) 2.93601e9 + 4.99648e8i 0.320316 + 0.0545110i
\(703\) 1.63139e10 1.77099
\(704\) −3.49555e9 + 2.18867e9i −0.377582 + 0.236415i
\(705\) 2.13643e10 2.29629
\(706\) 6.24289e9 + 1.06241e9i 0.667682 + 0.113626i
\(707\) 7.37853e9i 0.785239i
\(708\) −1.69617e10 5.94525e9i −1.79620 0.629584i
\(709\) 8.11796e9i 0.855431i −0.903913 0.427716i \(-0.859318\pi\)
0.903913 0.427716i \(-0.140682\pi\)
\(710\) −8.16334e8 + 4.79691e9i −0.0855980 + 0.502988i
\(711\) 9.55395e9 0.996872
\(712\) 2.52737e9 + 1.39945e9i 0.262415 + 0.145304i
\(713\) −4.49486e9 −0.464412
\(714\) 7.76781e8 4.56449e9i 0.0798647 0.469298i
\(715\) 1.47157e9i 0.150560i
\(716\) −1.02525e9 + 2.92502e9i −0.104384 + 0.297806i
\(717\) 6.32739e9i 0.641073i
\(718\) 1.58813e9 + 2.70266e8i 0.160122 + 0.0272494i
\(719\) 9.54339e8 0.0957528 0.0478764 0.998853i \(-0.484755\pi\)
0.0478764 + 0.998853i \(0.484755\pi\)
\(720\) 1.29275e10 1.61754e10i 1.29077 1.61507i
\(721\) 5.60800e9 0.557231
\(722\) −2.08241e9 3.54383e8i −0.205914 0.0350423i
\(723\) 2.08264e10i 2.04942i
\(724\) 1.18111e9 3.36971e9i 0.115666 0.329995i
\(725\) 5.85203e9i 0.570327i
\(726\) 2.28135e9 1.34056e10i 0.221266 1.30019i
\(727\) 1.75084e10 1.68996 0.844979 0.534799i \(-0.179613\pi\)
0.844979 + 0.534799i \(0.179613\pi\)
\(728\) −6.80890e8 + 1.22967e9i −0.0654059 + 0.118121i
\(729\) 1.63215e10 1.56032
\(730\) −2.38210e9 + 1.39976e10i −0.226637 + 1.33175i
\(731\) 1.07030e9i 0.101343i
\(732\) 4.50424e9 + 1.57878e9i 0.424456 + 0.148776i
\(733\) 1.16062e10i 1.08849i −0.838925 0.544247i \(-0.816815\pi\)
0.838925 0.544247i \(-0.183185\pi\)
\(734\) 7.95738e9 + 1.35418e9i 0.742735 + 0.126398i
\(735\) −1.64286e10 −1.52614
\(736\) 2.41796e9 + 2.71292e9i 0.223551 + 0.250821i
\(737\) −1.57087e8 −0.0144545
\(738\) −2.49885e10 4.25252e9i −2.28845 0.389447i
\(739\) 4.74800e9i 0.432768i −0.976308 0.216384i \(-0.930574\pi\)
0.976308 0.216384i \(-0.0694263\pi\)
\(740\) −2.02891e10 7.11153e9i −1.84057 0.645137i
\(741\) 5.59268e9i 0.504959i
\(742\) 1.28084e9 7.52642e9i 0.115102 0.676355i
\(743\) −4.35857e9 −0.389837 −0.194918 0.980819i \(-0.562444\pi\)
−0.194918 + 0.980819i \(0.562444\pi\)
\(744\) −1.23762e10 + 2.23510e10i −1.10174 + 1.98972i
\(745\) −1.29864e10 −1.15064
\(746\) 7.87185e8 4.62562e9i 0.0694210 0.407929i
\(747\) 5.72888e9i 0.502860i
\(748\) 1.00874e9 2.87792e9i 0.0881297 0.251433i
\(749\) 5.95321e9i 0.517684i
\(750\) 1.21144e10 + 2.06162e9i 1.04855 + 0.178441i
\(751\) −6.10987e9 −0.526371 −0.263186 0.964745i \(-0.584773\pi\)
−0.263186 + 0.964745i \(0.584773\pi\)
\(752\) 1.04993e10 + 8.39115e9i 0.900326 + 0.719547i
\(753\) −2.23729e10 −1.90959
\(754\) −3.96256e9 6.74346e8i −0.336648 0.0572906i
\(755\) 2.42883e10i 2.05391i
\(756\) 2.21297e9 6.31359e9i 0.186273 0.531435i
\(757\) 2.29472e10i 1.92262i 0.275460 + 0.961312i \(0.411170\pi\)
−0.275460 + 0.961312i \(0.588830\pi\)
\(758\) −2.34649e8 + 1.37883e9i −0.0195693 + 0.114993i
\(759\) 2.96679e9 0.246286
\(760\) 1.40947e10 + 7.80449e9i 1.16469 + 0.644907i
\(761\) 7.15151e9 0.588236 0.294118 0.955769i \(-0.404974\pi\)
0.294118 + 0.955769i \(0.404974\pi\)
\(762\) −1.64182e9 + 9.64759e9i −0.134426 + 0.789908i
\(763\) 2.08175e9i 0.169665i
\(764\) 2.02447e9 + 7.09596e8i 0.164242 + 0.0575684i
\(765\) 1.53111e10i 1.23650i
\(766\) −1.51445e10 2.57728e9i −1.21746 0.207186i
\(767\) −4.03460e9 −0.322862