Properties

Label 72.8.d.b.37.1
Level $72$
Weight $8$
Character 72.37
Analytic conductor $22.492$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 72.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.4917218349\)
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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.1
Root \(5.57668 - 0.949035i\) of defining polynomial
Character \(\chi\) \(=\) 72.37
Dual form 72.8.d.b.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-11.1534 - 1.89807i) q^{2} +(120.795 + 42.3397i) q^{4} -338.443i q^{5} -438.996 q^{7} +(-1266.90 - 701.506i) q^{8} +O(q^{10})\) \(q+(-11.1534 - 1.89807i) q^{2} +(120.795 + 42.3397i) q^{4} -338.443i q^{5} -438.996 q^{7} +(-1266.90 - 701.506i) q^{8} +(-642.387 + 3774.77i) q^{10} -1966.58i q^{11} -2210.98i q^{13} +(4896.28 + 833.245i) q^{14} +(12798.7 + 10228.8i) q^{16} +12114.9 q^{17} -32872.2i q^{19} +(14329.5 - 40882.1i) q^{20} +(-3732.70 + 21933.9i) q^{22} -19605.1 q^{23} -36418.4 q^{25} +(-4196.59 + 24659.8i) q^{26} +(-53028.4 - 18587.0i) q^{28} +160689. i q^{29} -229270. q^{31} +(-123333. - 138378. i) q^{32} +(-135122. - 22994.9i) q^{34} +148575. i q^{35} +496284. i q^{37} +(-62393.6 + 366635. i) q^{38} +(-237420. + 428774. i) q^{40} -599971. q^{41} -88346.0i q^{43} +(83264.3 - 237552. i) q^{44} +(218662. + 37211.8i) q^{46} -820344. q^{47} -630825. q^{49} +(406187. + 69124.6i) q^{50} +(93612.2 - 267075. i) q^{52} -1.53717e6i q^{53} -665574. q^{55} +(556165. + 307959. i) q^{56} +(304999. - 1.79222e6i) q^{58} +1.82480e6i q^{59} +484582. i q^{61} +(2.55713e6 + 435171. i) q^{62} +(1.11293e6 + 1.77748e6i) q^{64} -748290. q^{65} +79878.2i q^{67} +(1.46341e6 + 512940. i) q^{68} +(282006. - 1.65711e6i) q^{70} -1.27078e6 q^{71} +3.70820e6 q^{73} +(941981. - 5.53523e6i) q^{74} +(1.39180e6 - 3.97078e6i) q^{76} +863321. i q^{77} -2.55846e6 q^{79} +(3.46187e6 - 4.33163e6i) q^{80} +(6.69169e6 + 1.13879e6i) q^{82} +1.53414e6i q^{83} -4.10019e6i q^{85} +(-167687. + 985355. i) q^{86} +(-1.37957e6 + 2.49146e6i) q^{88} -1.99492e6 q^{89} +970612. i q^{91} +(-2.36819e6 - 830073. i) q^{92} +(9.14959e6 + 1.55707e6i) q^{94} -1.11253e7 q^{95} -28917.7 q^{97} +(7.03582e6 + 1.19735e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8} - 1656 q^{10} - 12048 q^{14} + 35344 q^{16} - 1452 q^{17} + 114768 q^{20} + 152860 q^{22} + 1296 q^{23} - 39314 q^{25} + 316968 q^{26} - 480800 q^{28} - 89280 q^{31} - 817056 q^{32} - 1009108 q^{34} - 974124 q^{38} + 954464 q^{40} - 521244 q^{41} + 1096344 q^{44} + 929840 q^{46} - 1566432 q^{47} - 511050 q^{49} + 148626 q^{50} + 823952 q^{52} - 3270256 q^{55} + 2468928 q^{56} + 3130744 q^{58} + 7055808 q^{62} - 4792768 q^{64} - 1416480 q^{65} - 6608040 q^{68} - 7406912 q^{70} + 7597104 q^{71} + 2089564 q^{73} - 7744200 q^{74} + 9241288 q^{76} + 16015904 q^{79} + 12600384 q^{80} + 10715932 q^{82} + 5639076 q^{86} + 1541200 q^{88} - 2169084 q^{89} - 669600 q^{92} + 15503712 q^{94} - 48537936 q^{95} - 1088308 q^{97} + 14983242 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.1534 1.89807i −0.985827 0.167767i
\(3\) 0 0
\(4\) 120.795 + 42.3397i 0.943708 + 0.330779i
\(5\) 338.443i 1.21085i −0.795903 0.605425i \(-0.793003\pi\)
0.795903 0.605425i \(-0.206997\pi\)
\(6\) 0 0
\(7\) −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
\(9\) 0 0
\(10\) −642.387 + 3774.77i −0.203141 + 1.19369i
\(11\) 1966.58i 0.445489i −0.974877 0.222744i \(-0.928498\pi\)
0.974877 0.222744i \(-0.0715015\pi\)
\(12\) 0 0
\(13\) 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
\(15\) 0 0
\(16\) 12798.7 + 10228.8i 0.781171 + 0.624317i
\(17\) 12114.9 0.598064 0.299032 0.954243i \(-0.403336\pi\)
0.299032 + 0.954243i \(0.403336\pi\)
\(18\) 0 0
\(19\) 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
\(21\) 0 0
\(22\) −3732.70 + 21933.9i −0.0747384 + 0.439175i
\(23\) −19605.1 −0.335986 −0.167993 0.985788i \(-0.553729\pi\)
−0.167993 + 0.985788i \(0.553729\pi\)
\(24\) 0 0
\(25\) −36418.4 −0.466155
\(26\) −4196.59 + 24659.8i −0.0468263 + 0.275159i
\(27\) 0 0
\(28\) −53028.4 18587.0i −0.456515 0.160013i
\(29\) 160689.i 1.22347i 0.791063 + 0.611735i \(0.209528\pi\)
−0.791063 + 0.611735i \(0.790472\pi\)
\(30\) 0 0
\(31\) −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
\(33\) 0 0
\(34\) −135122. 22994.9i −0.589588 0.100336i
\(35\) 148575.i 0.585744i
\(36\) 0 0
\(37\) 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
\(39\) 0 0
\(40\) −237420. + 428774.i −0.586552 + 1.05930i
\(41\) −599971. −1.35952 −0.679762 0.733433i \(-0.737917\pi\)
−0.679762 + 0.733433i \(0.737917\pi\)
\(42\) 0 0
\(43\) 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
\(45\) 0 0
\(46\) 218662. + 37211.8i 0.331224 + 0.0563674i
\(47\) −820344. −1.15253 −0.576267 0.817262i \(-0.695491\pi\)
−0.576267 + 0.817262i \(0.695491\pi\)
\(48\) 0 0
\(49\) −630825. −0.765989
\(50\) 406187. + 69124.6i 0.459548 + 0.0782056i
\(51\) 0 0
\(52\) 93612.2 267075.i 0.0923253 0.263403i
\(53\) 1.53717e6i 1.41826i −0.705077 0.709131i \(-0.749087\pi\)
0.705077 0.709131i \(-0.250913\pi\)
\(54\) 0 0
\(55\) −665574. −0.539420
\(56\) 556165. + 307959.i 0.423200 + 0.234333i
\(57\) 0 0
\(58\) 304999. 1.79222e6i 0.205258 1.20613i
\(59\) 1.82480e6i 1.15673i 0.815776 + 0.578367i \(0.196310\pi\)
−0.815776 + 0.578367i \(0.803690\pi\)
\(60\) 0 0
\(61\) 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
\(63\) 0 0
\(64\) 1.11293e6 + 1.77748e6i 0.530687 + 0.847568i
\(65\) −748290. −0.337966
\(66\) 0 0
\(67\) 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
\(69\) 0 0
\(70\) 282006. 1.65711e6i 0.0982686 0.577442i
\(71\) −1.27078e6 −0.421373 −0.210686 0.977554i \(-0.567570\pi\)
−0.210686 + 0.977554i \(0.567570\pi\)
\(72\) 0 0
\(73\) 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
\(75\) 0 0
\(76\) 1.39180e6 3.97078e6i 0.363687 1.03760i
\(77\) 863321.i 0.215504i
\(78\) 0 0
\(79\) −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
\(81\) 0 0
\(82\) 6.69169e6 + 1.13879e6i 1.34025 + 0.228083i
\(83\) 1.53414e6i 0.294505i 0.989099 + 0.147252i \(0.0470430\pi\)
−0.989099 + 0.147252i \(0.952957\pi\)
\(84\) 0 0
\(85\) 4.10019e6i 0.724166i
\(86\) −167687. + 985355.i −0.0284285 + 0.167051i
\(87\) 0 0
\(88\) −1.37957e6 + 2.49146e6i −0.215801 + 0.389731i
\(89\) −1.99492e6 −0.299958 −0.149979 0.988689i \(-0.547921\pi\)
−0.149979 + 0.988689i \(0.547921\pi\)
\(90\) 0 0
\(91\) 970612.i 0.135021i
\(92\) −2.36819e6 830073.i −0.317073 0.111137i
\(93\) 0 0
\(94\) 9.14959e6 + 1.55707e6i 1.13620 + 0.193357i
\(95\) −1.11253e7 −1.33131
\(96\) 0 0
\(97\) −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
\(99\) 0 0
\(100\) −4.39915e6 1.54194e6i −0.439915 0.154194i
\(101\) 1.68077e7i 1.62324i 0.584182 + 0.811622i \(0.301415\pi\)
−0.584182 + 0.811622i \(0.698585\pi\)
\(102\) 0 0
\(103\) −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
\(105\) 0 0
\(106\) −2.91766e6 + 1.71446e7i −0.237938 + 1.39816i
\(107\) 1.35610e7i 1.07016i −0.844803 0.535078i \(-0.820282\pi\)
0.844803 0.535078i \(-0.179718\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) −5.61858e6 4.49041e6i −0.377889 0.302011i
\(113\) 8.06832e6 0.526028 0.263014 0.964792i \(-0.415283\pi\)
0.263014 + 0.964792i \(0.415283\pi\)
\(114\) 0 0
\(115\) 6.63520e6i 0.406828i
\(116\) −6.80352e6 + 1.94104e7i −0.404698 + 1.15460i
\(117\) 0 0
\(118\) 3.46360e6 2.03527e7i 0.194062 1.14034i
\(119\) −5.31839e6 −0.289311
\(120\) 0 0
\(121\) 1.56197e7 0.801540
\(122\) 919770. 5.40471e6i 0.0458585 0.269472i
\(123\) 0 0
\(124\) −2.76946e7 9.70723e6i −1.30443 0.457214i
\(125\) 1.41153e7i 0.646405i
\(126\) 0 0
\(127\) −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
\(129\) 0 0
\(130\) 8.34594e6 + 1.42031e6i 0.333176 + 0.0566996i
\(131\) 8.81527e6i 0.342599i −0.985219 0.171299i \(-0.945203\pi\)
0.985219 0.171299i \(-0.0547966\pi\)
\(132\) 0 0
\(133\) 1.44308e7i 0.531874i
\(134\) 151614. 890910.i 0.00544344 0.0319865i
\(135\) 0 0
\(136\) −1.53484e7 8.49866e6i −0.523210 0.289711i
\(137\) 3.33729e7 1.10885 0.554424 0.832234i \(-0.312939\pi\)
0.554424 + 0.832234i \(0.312939\pi\)
\(138\) 0 0
\(139\) 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
\(141\) 0 0
\(142\) 1.41735e7 + 2.41203e6i 0.415401 + 0.0706926i
\(143\) −4.34806e6 −0.124343
\(144\) 0 0
\(145\) 5.43840e7 1.48144
\(146\) −4.13589e7 7.03843e6i −1.09985 0.187172i
\(147\) 0 0
\(148\) −2.10125e7 + 5.99485e7i −0.532797 + 1.52006i
\(149\) 3.83709e7i 0.950277i −0.879911 0.475139i \(-0.842398\pi\)
0.879911 0.475139i \(-0.157602\pi\)
\(150\) 0 0
\(151\) −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
\(153\) 0 0
\(154\) 1.63864e6 9.62892e6i 0.0361544 0.212449i
\(155\) 7.75948e7i 1.67368i
\(156\) 0 0
\(157\) 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
\(159\) 0 0
\(160\) −4.68332e7 + 4.17413e7i −0.903927 + 0.805649i
\(161\) 8.60656e6 0.162532
\(162\) 0 0
\(163\) 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
\(165\) 0 0
\(166\) 2.91191e6 1.71108e7i 0.0494083 0.290331i
\(167\) 4.24811e7 0.705810 0.352905 0.935659i \(-0.385194\pi\)
0.352905 + 0.935659i \(0.385194\pi\)
\(168\) 0 0
\(169\) 5.78601e7 0.922095
\(170\) −7.78245e6 + 4.57309e7i −0.121491 + 0.713902i
\(171\) 0 0
\(172\) 3.74054e6 1.06717e7i 0.0560512 0.159914i
\(173\) 2.65257e7i 0.389498i −0.980853 0.194749i \(-0.937611\pi\)
0.980853 0.194749i \(-0.0623893\pi\)
\(174\) 0 0
\(175\) 1.59875e7 0.225501
\(176\) 2.01158e7 2.51697e7i 0.278126 0.348003i
\(177\) 0 0
\(178\) 2.22501e7 + 3.78650e6i 0.295707 + 0.0503231i
\(179\) 2.42148e7i 0.315570i −0.987474 0.157785i \(-0.949565\pi\)
0.987474 0.157785i \(-0.0504353\pi\)
\(180\) 0 0
\(181\) 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
\(183\) 0 0
\(184\) 2.48377e7 + 1.37531e7i 0.293934 + 0.162756i
\(185\) 1.67964e8 1.95036
\(186\) 0 0
\(187\) 2.38249e7i 0.266431i
\(188\) −9.90932e7 3.47331e7i −1.08766 0.381234i
\(189\) 0 0
\(190\) 1.24085e8 + 2.11167e7i 1.31245 + 0.223351i
\(191\) −1.67596e7 −0.174039 −0.0870195 0.996207i \(-0.527734\pi\)
−0.0870195 + 0.996207i \(0.527734\pi\)
\(192\) 0 0
\(193\) 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
\(195\) 0 0
\(196\) −7.62003e7 2.67089e7i −0.722871 0.253373i
\(197\) 2.56239e7i 0.238789i 0.992847 + 0.119394i \(0.0380953\pi\)
−0.992847 + 0.119394i \(0.961905\pi\)
\(198\) 0 0
\(199\) 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
\(201\) 0 0
\(202\) 3.19022e7 1.87462e8i 0.272327 1.60024i
\(203\) 7.05419e7i 0.591849i
\(204\) 0 0
\(205\) 2.03056e8i 1.64618i
\(206\) 1.42480e8 + 2.42471e7i 1.13558 + 0.193252i
\(207\) 0 0
\(208\) 2.26157e7 2.82977e7i 0.174256 0.218036i
\(209\) −6.46457e7 −0.489810
\(210\) 0 0
\(211\) 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
\(213\) 0 0
\(214\) −2.57396e7 + 1.51250e8i −0.179537 + 1.05499i
\(215\) −2.99001e7 −0.205181
\(216\) 0 0
\(217\) 1.00649e8 0.668651
\(218\) −9.00076e6 + 5.28899e7i −0.0588412 + 0.345760i
\(219\) 0 0
\(220\) −8.03978e7 2.81802e7i −0.509055 0.178429i
\(221\) 2.67858e7i 0.166929i
\(222\) 0 0
\(223\) −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
\(225\) 0 0
\(226\) −8.99889e7 1.53142e7i −0.518572 0.0882502i
\(227\) 1.37308e8i 0.779122i −0.921001 0.389561i \(-0.872627\pi\)
0.921001 0.389561i \(-0.127373\pi\)
\(228\) 0 0
\(229\) 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
\(231\) 0 0
\(232\) 1.12724e8 2.03577e8i 0.592665 1.07034i
\(233\) −1.98032e8 −1.02563 −0.512815 0.858499i \(-0.671397\pi\)
−0.512815 + 0.858499i \(0.671397\pi\)
\(234\) 0 0
\(235\) 2.77639e8i 1.39554i
\(236\) −7.72615e7 + 2.20426e8i −0.382623 + 1.09162i
\(237\) 0 0
\(238\) 5.93179e7 + 1.00947e7i 0.285211 + 0.0485370i
\(239\) −8.22277e7 −0.389606 −0.194803 0.980842i \(-0.562407\pi\)
−0.194803 + 0.980842i \(0.562407\pi\)
\(240\) 0 0
\(241\) −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
\(243\) 0 0
\(244\) −2.05170e7 + 5.85349e7i −0.0904171 + 0.257959i
\(245\) 2.13498e8i 0.927498i
\(246\) 0 0
\(247\) −7.26797e7 −0.306884
\(248\) 2.90463e8 + 1.60835e8i 1.20923 + 0.669574i
\(249\) 0 0
\(250\) −2.67918e7 + 1.57433e8i −0.108446 + 0.637243i
\(251\) 2.90747e8i 1.16053i 0.814427 + 0.580266i \(0.197051\pi\)
−0.814427 + 0.580266i \(0.802949\pi\)
\(252\) 0 0
\(253\) 3.85549e7i 0.149678i
\(254\) 1.25375e8 + 2.13363e7i 0.480058 + 0.0816959i
\(255\) 0 0
\(256\) 5.91782e7 + 2.61831e8i 0.220456 + 0.975397i
\(257\) −4.36047e7 −0.160239 −0.0801193 0.996785i \(-0.525530\pi\)
−0.0801193 + 0.996785i \(0.525530\pi\)
\(258\) 0 0
\(259\) 2.17867e8i 0.779188i
\(260\) −9.03894e7 3.16823e7i −0.318941 0.111792i
\(261\) 0 0
\(262\) −1.67320e7 + 9.83198e7i −0.0574769 + 0.337743i
\(263\) −4.27678e8 −1.44968 −0.724840 0.688917i \(-0.758086\pi\)
−0.724840 + 0.688917i \(0.758086\pi\)
\(264\) 0 0
\(265\) −5.20244e8 −1.71730
\(266\) 2.73906e7 1.60951e8i 0.0892309 0.524335i
\(267\) 0 0
\(268\) −3.38202e6 + 9.64886e6i −0.0107326 + 0.0306199i
\(269\) 8.26134e7i 0.258772i 0.991594 + 0.129386i \(0.0413007\pi\)
−0.991594 + 0.129386i \(0.958699\pi\)
\(270\) 0 0
\(271\) 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
\(273\) 0 0
\(274\) −3.72220e8 6.33441e7i −1.09313 0.186028i
\(275\) 7.16196e7i 0.207667i
\(276\) 0 0
\(277\) 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
\(279\) 0 0
\(280\) 1.04226e8 1.88230e8i 0.283742 0.512432i
\(281\) −5.80931e8 −1.56190 −0.780948 0.624596i \(-0.785264\pi\)
−0.780948 + 0.624596i \(0.785264\pi\)
\(282\) 0 0
\(283\) 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
\(285\) 0 0
\(286\) 4.84955e7 + 8.25293e6i 0.122580 + 0.0208606i
\(287\) 2.63385e8 0.657665
\(288\) 0 0
\(289\) −2.63568e8 −0.642319
\(290\) −6.06564e8 1.03225e8i −1.46044 0.248536i
\(291\) 0 0
\(292\) 4.47931e8 + 1.57004e8i 1.05286 + 0.369038i
\(293\) 1.10504e8i 0.256649i 0.991732 + 0.128325i \(0.0409600\pi\)
−0.991732 + 0.128325i \(0.959040\pi\)
\(294\) 0 0
\(295\) 6.17591e8 1.40063
\(296\) 3.48146e8 6.28743e8i 0.780263 1.40913i
\(297\) 0 0
\(298\) −7.28307e7 + 4.27965e8i −0.159425 + 0.936809i
\(299\) 4.33464e7i 0.0937787i
\(300\) 0 0
\(301\) 3.87836e7i 0.0819719i
\(302\) 8.00419e8 + 1.36215e8i 1.67222 + 0.284577i
\(303\) 0 0
\(304\) 3.36243e8 4.20721e8i 0.686430 0.858888i
\(305\) 1.64003e8 0.330981
\(306\) 0 0
\(307\) 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
\(309\) 0 0
\(310\) 1.47280e8 8.65443e8i 0.280788 1.64996i
\(311\) 8.61240e8 1.62354 0.811769 0.583978i \(-0.198505\pi\)
0.811769 + 0.583978i \(0.198505\pi\)
\(312\) 0 0
\(313\) 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
\(315\) 0 0
\(316\) −3.09049e8 1.08325e8i −0.550963 0.193118i
\(317\) 5.38362e8i 0.949221i −0.880196 0.474610i \(-0.842589\pi\)
0.880196 0.474610i \(-0.157411\pi\)
\(318\) 0 0
\(319\) 3.16007e8 0.545042
\(320\) 6.01575e8 3.76663e8i 1.02628 0.642581i
\(321\) 0 0
\(322\) −9.59920e7 1.63358e7i −0.160228 0.0272675i
\(323\) 3.98242e8i 0.657565i
\(324\) 0 0
\(325\) 8.05203e7i 0.130111i
\(326\) −1.86867e8 + 1.09806e9i −0.298725 + 1.75535i
\(327\) 0 0
\(328\) 7.60105e8 + 4.20883e8i 1.18936 + 0.658572i
\(329\) 3.60128e8 0.557534
\(330\) 0 0
\(331\) 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
\(333\) 0 0
\(334\) −4.73806e8 8.06320e7i −0.695806 0.118412i
\(335\) 2.70342e7 0.0392877
\(336\) 0 0
\(337\) −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
\(339\) 0 0
\(340\) 1.73601e8 4.95281e8i 0.239539 0.683401i
\(341\) 4.50878e8i 0.615770i
\(342\) 0 0
\(343\) 6.38462e8 0.854291
\(344\) −6.19753e7 + 1.11926e8i −0.0820850 + 0.148244i
\(345\) 0 0
\(346\) −5.03476e7 + 2.95851e8i −0.0653450 + 0.383978i
\(347\) 6.28852e8i 0.807970i −0.914766 0.403985i \(-0.867625\pi\)
0.914766 0.403985i \(-0.132375\pi\)
\(348\) 0 0
\(349\) 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
\(351\) 0 0
\(352\) −2.72132e8 + 2.42545e8i −0.332568 + 0.296410i
\(353\) −5.59732e8 −0.677281 −0.338641 0.940916i \(-0.609967\pi\)
−0.338641 + 0.940916i \(0.609967\pi\)
\(354\) 0 0
\(355\) 4.30087e8i 0.510219i
\(356\) −2.40976e8 8.44643e7i −0.283073 0.0992198i
\(357\) 0 0
\(358\) −4.59614e7 + 2.70076e8i −0.0529423 + 0.311097i
\(359\) −1.42390e8 −0.162424 −0.0812119 0.996697i \(-0.525879\pi\)
−0.0812119 + 0.996697i \(0.525879\pi\)
\(360\) 0 0
\(361\) −1.86707e8 −0.208875
\(362\) −5.29488e7 + 3.11136e8i −0.0586646 + 0.344723i
\(363\) 0 0
\(364\) −4.10954e7 + 1.17245e8i −0.0446620 + 0.127420i
\(365\) 1.25501e9i 1.35090i
\(366\) 0 0
\(367\) 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
\(369\) 0 0
\(370\) −1.87336e9 3.18807e8i −1.92271 0.327206i
\(371\) 6.74812e8i 0.686079i
\(372\) 0 0
\(373\) 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
\(375\) 0 0
\(376\) 1.03930e9 + 5.75476e8i 1.00828 + 0.558303i
\(377\) 3.55280e8 0.341489
\(378\) 0 0
\(379\) 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
\(381\) 0 0
\(382\) 1.86926e8 + 3.18109e7i 0.171572 + 0.0291980i
\(383\) 1.35784e9 1.23496 0.617480 0.786586i \(-0.288154\pi\)
0.617480 + 0.786586i \(0.288154\pi\)
\(384\) 0 0
\(385\) 2.92184e8 0.260942
\(386\) −9.75927e8 1.66083e8i −0.863698 0.146983i
\(387\) 0 0
\(388\) −3.49310e6 1.22436e6i −0.00303599 0.00106414i
\(389\) 1.00573e9i 0.866281i 0.901326 + 0.433141i \(0.142595\pi\)
−0.901326 + 0.433141i \(0.857405\pi\)
\(390\) 0 0
\(391\) −2.37513e8 −0.200941
\(392\) 7.99194e8 + 4.42528e8i 0.670117 + 0.371056i
\(393\) 0 0
\(394\) 4.86359e7 2.85793e8i 0.0400609 0.235404i
\(395\) 8.65893e8i 0.706927i
\(396\) 0 0
\(397\) 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
\(399\) 0 0
\(400\) −4.66108e8 3.72517e8i −0.364147 0.291029i
\(401\) 1.24791e9 0.966446 0.483223 0.875497i \(-0.339466\pi\)
0.483223 + 0.875497i \(0.339466\pi\)
\(402\) 0 0
\(403\) 5.06912e8i 0.385802i
\(404\) −7.11633e8 + 2.03028e9i −0.536935 + 1.53187i
\(405\) 0 0
\(406\) −1.33893e8 + 7.86778e8i −0.0992928 + 0.583460i
\(407\) 9.75982e8 0.717565
\(408\) 0 0
\(409\) −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
\(411\) 0 0
\(412\) −1.54310e9 5.40873e8i −1.08706 0.381026i
\(413\) 8.01081e8i 0.559566i
\(414\) 0 0
\(415\) 5.19219e8 0.356601
\(416\) −3.05952e8 + 2.72688e8i −0.208366 + 0.185712i
\(417\) 0 0
\(418\) 7.21016e8 + 1.22702e8i 0.482868 + 0.0821740i
\(419\) 2.66870e8i 0.177235i −0.996066 0.0886177i \(-0.971755\pi\)
0.996066 0.0886177i \(-0.0282449\pi\)
\(420\) 0 0
\(421\) 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
\(423\) 0 0
\(424\) −1.07833e9 + 1.94745e9i −0.687026 + 1.24075i
\(425\) −4.41204e8 −0.278791
\(426\) 0 0
\(427\) 2.12730e8i 0.132230i
\(428\) 5.74167e8 1.63809e9i 0.353985 1.00992i
\(429\) 0 0
\(430\) 3.33486e8 + 5.67524e7i 0.202273 + 0.0344227i
\(431\) −1.78455e9 −1.07364 −0.536820 0.843697i \(-0.680374\pi\)
−0.536820 + 0.843697i \(0.680374\pi\)
\(432\) 0 0
\(433\) 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
\(435\) 0 0
\(436\) 2.00777e8 5.72816e8i 0.116014 0.330988i
\(437\) 6.44461e8i 0.369413i
\(438\) 0 0
\(439\) −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
\(441\) 0 0
\(442\) −5.08412e7 + 2.98751e8i −0.0280052 + 0.164563i
\(443\) 8.06208e8i 0.440590i −0.975433 0.220295i \(-0.929298\pi\)
0.975433 0.220295i \(-0.0707019\pi\)
\(444\) 0 0
\(445\) 6.75166e8i 0.363204i
\(446\) 1.86274e9 + 3.16999e8i 0.994214 + 0.169195i
\(447\) 0 0
\(448\) −4.88572e8 7.80307e8i −0.256718 0.410008i
\(449\) −5.85913e8 −0.305472 −0.152736 0.988267i \(-0.548808\pi\)
−0.152736 + 0.988267i \(0.548808\pi\)
\(450\) 0 0
\(451\) 1.17989e9i 0.605653i
\(452\) 9.74611e8 + 3.41610e8i 0.496417 + 0.173999i
\(453\) 0 0
\(454\) −2.60620e8 + 1.53145e9i −0.130711 + 0.768079i
\(455\) 3.28496e8 0.163490
\(456\) 0 0
\(457\) 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
\(459\) 0 0
\(460\) −2.80932e8 + 8.01496e8i −0.134570 + 0.383927i
\(461\) 1.74101e9i 0.827652i 0.910356 + 0.413826i \(0.135808\pi\)
−0.910356 + 0.413826i \(0.864192\pi\)
\(462\) 0 0
\(463\) −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
\(465\) 0 0
\(466\) 2.20873e9 + 3.75879e8i 1.01109 + 0.172067i
\(467\) 1.63130e9i 0.741183i −0.928796 0.370592i \(-0.879155\pi\)
0.928796 0.370592i \(-0.120845\pi\)
\(468\) 0 0
\(469\) 3.50662e7i 0.0156958i
\(470\) 5.26979e8 3.09661e9i 0.234127 1.37576i
\(471\) 0 0
\(472\) 1.28011e9 2.31185e9i 0.560338 1.01196i
\(473\) −1.73739e8 −0.0754891
\(474\) 0 0
\(475\) 1.19715e9i 0.512532i
\(476\) −6.42433e8 2.25179e8i −0.273026 0.0956981i
\(477\) 0 0
\(478\) 9.17114e8 + 1.56074e8i 0.384084 + 0.0653630i
\(479\) −3.69345e9 −1.53553 −0.767765 0.640732i \(-0.778631\pi\)
−0.767765 + 0.640732i \(0.778631\pi\)
\(480\) 0 0
\(481\) 1.09727e9 0.449580
\(482\) 3.01866e9 + 5.13713e8i 1.22786 + 0.208956i
\(483\) 0 0
\(484\) 1.88678e9 + 6.61335e8i 0.756420 + 0.265132i
\(485\) 9.78697e6i 0.00389540i
\(486\) 0 0
\(487\) 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
\(489\) 0 0
\(490\) 4.05234e8 2.38122e9i 0.155604 0.914352i
\(491\) 1.63493e9i 0.623323i −0.950193 0.311662i \(-0.899114\pi\)
0.950193 0.311662i \(-0.100886\pi\)
\(492\) 0 0
\(493\) 1.94673e9i 0.731713i
\(494\) 8.10622e8 + 1.37951e8i 0.302534 + 0.0514850i
\(495\) 0 0
\(496\) −2.93436e9 2.34516e9i −1.07976 0.862953i
\(497\) 5.57868e8 0.203838
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) 5.51858e8 3.24280e9i 0.194699 1.14408i
\(503\) −2.33472e9 −0.817990 −0.408995 0.912537i \(-0.634121\pi\)
−0.408995 + 0.912537i \(0.634121\pi\)
\(504\) 0 0
\(505\) 5.68845e9 1.96550
\(506\) 7.31799e7 4.30017e8i 0.0251111 0.147557i
\(507\) 0 0
\(508\) −1.35786e9 4.75942e8i −0.459548 0.161076i
\(509\) 6.21342e8i 0.208842i −0.994533 0.104421i \(-0.966701\pi\)
0.994533 0.104421i \(-0.0332990\pi\)
\(510\) 0 0
\(511\) −1.62789e9 −0.539699
\(512\) −1.63062e8 3.03262e9i −0.0536917 0.998558i
\(513\) 0 0
\(514\) 4.86339e8 + 8.27647e7i 0.157968 + 0.0268828i
\(515\) 4.32347e9i 1.39478i
\(516\) 0 0
\(517\) 1.61327e9i 0.513441i
\(518\) −4.13526e8 + 2.42995e9i −0.130722 + 0.768144i
\(519\) 0 0
\(520\) 9.48010e8 + 5.24930e8i 0.295666 + 0.163715i
\(521\) 1.65562e9 0.512897 0.256448 0.966558i \(-0.417448\pi\)
0.256448 + 0.966558i \(0.417448\pi\)
\(522\) 0 0
\(523\) 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
\(525\) 0 0
\(526\) 4.77005e9 + 8.11763e8i 1.42913 + 0.243209i
\(527\) −2.77758e9 −0.826665
\(528\) 0 0
\(529\) −3.02047e9 −0.887113
\(530\) 5.80247e9 + 9.87459e8i 1.69296 + 0.288107i
\(531\) 0 0
\(532\) −6.10994e8 + 1.74316e9i −0.175932 + 0.501933i
\(533\) 1.32652e9i 0.379463i
\(534\) 0 0
\(535\) −4.58961e9 −1.29580
\(536\) 5.60350e7 1.01198e8i 0.0157175 0.0283854i
\(537\) 0 0
\(538\) 1.56806e8 9.21417e8i 0.0434135 0.255105i
\(539\) 1.24057e9i 0.341240i
\(540\) 0 0
\(541\) 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
\(543\) 0 0
\(544\) −1.49417e9 1.67644e9i −0.397928 0.446469i
\(545\) −1.60492e9 −0.424683
\(546\) 0 0
\(547\) 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
\(549\) 0 0
\(550\) 1.35939e8 7.98799e8i 0.0348397 0.204724i
\(551\) 5.28219e9 1.34519
\(552\) 0 0
\(553\) 1.12316e9 0.282424
\(554\) 8.33702e7 4.89897e8i 0.0208318 0.122411i
\(555\) 0 0
\(556\) −1.98218e9 + 5.65513e9i −0.489081 + 1.39534i
\(557\) 4.80739e9i 1.17873i −0.807865 0.589367i \(-0.799377\pi\)
0.807865 0.589367i \(-0.200623\pi\)
\(558\) 0 0
\(559\) −1.95331e8 −0.0472967
\(560\) −1.51975e9 + 1.90157e9i −0.365690 + 0.457566i
\(561\) 0 0
\(562\) 6.47933e9 + 1.10265e9i 1.53976 + 0.262035i
\(563\) 3.77127e9i 0.890653i 0.895368 + 0.445326i \(0.146912\pi\)
−0.895368 + 0.445326i \(0.853088\pi\)
\(564\) 0 0
\(565\) 2.73066e9i 0.636940i
\(566\) 1.14603e9 6.73428e9i 0.265669 1.56111i
\(567\) 0 0
\(568\) 1.60996e9 + 8.91461e8i 0.368633 + 0.204119i
\(569\) −2.09341e9 −0.476388 −0.238194 0.971218i \(-0.576555\pi\)
−0.238194 + 0.971218i \(0.576555\pi\)
\(570\) 0 0
\(571\) 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
\(573\) 0 0
\(574\) −2.93763e9 4.99923e8i −0.648343 0.110335i
\(575\) 7.13986e8 0.156622
\(576\) 0 0
\(577\) 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
\(579\) 0 0
\(580\) 6.56930e9 + 2.30260e9i 1.39804 + 0.490028i
\(581\) 6.73483e8i 0.142466i
\(582\) 0 0
\(583\) −3.02297e9 −0.631820
\(584\) −4.69793e9 2.60133e9i −0.976027 0.540443i
\(585\) 0 0
\(586\) 2.09744e8 1.23249e9i 0.0430573 0.253012i
\(587\) 1.56510e9i 0.319380i −0.987167 0.159690i \(-0.948951\pi\)
0.987167 0.159690i \(-0.0510495\pi\)
\(588\) 0 0
\(589\) 7.53661e9i 1.51975i
\(590\) −6.88821e9 1.17223e9i −1.38078 0.234980i
\(591\) 0 0
\(592\) −5.07640e9 + 6.35179e9i −1.00561 + 1.25826i
\(593\) 2.78410e9 0.548268 0.274134 0.961692i \(-0.411609\pi\)
0.274134 + 0.961692i \(0.411609\pi\)
\(594\) 0 0
\(595\) 1.79997e9i 0.350312i
\(596\) 1.62461e9 4.63500e9i 0.314331 0.896784i
\(597\) 0 0
\(598\) 8.22745e7 4.83458e8i 0.0157330 0.0924496i
\(599\) −6.18885e9 −1.17657 −0.588283 0.808655i \(-0.700196\pi\)
−0.588283 + 0.808655i \(0.700196\pi\)
\(600\) 0 0
\(601\) −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
\(603\) 0 0
\(604\) −8.66881e9 3.03850e9i −1.60077 0.561087i
\(605\) 5.28639e9i 0.970544i
\(606\) 0 0
\(607\) −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
\(609\) 0 0
\(610\) −1.82919e9 3.11289e8i −0.326290 0.0555277i
\(611\) 1.81376e9i 0.321689i
\(612\) 0 0
\(613\) 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
\(615\) 0 0
\(616\) 6.05625e8 1.09374e9i 0.104393 0.188531i
\(617\) 2.32837e9 0.399074 0.199537 0.979890i \(-0.436056\pi\)
0.199537 + 0.979890i \(0.436056\pi\)
\(618\) 0 0
\(619\) 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
\(621\) 0 0
\(622\) −9.60571e9 1.63469e9i −1.60053 0.272377i
\(623\) 8.75763e8 0.145104
\(624\) 0 0
\(625\) −7.62240e9 −1.24885
\(626\) −2.69974e9 4.59439e8i −0.439857 0.0748545i
\(627\) 0 0
\(628\) 1.70958e9 4.87742e9i 0.275443 0.785835i
\(629\) 6.01242e9i 0.963324i
\(630\) 0 0
\(631\) 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
\(633\) 0 0
\(634\) −1.02185e9 + 6.00455e9i −0.159248 + 0.935767i
\(635\) 3.80445e9i 0.589635i
\(636\) 0 0
\(637\) 1.39474e9i 0.213799i
\(638\) −3.52454e9 5.99804e8i −0.537317 0.0914402i
\(639\) 0 0
\(640\) −7.42451e9 + 3.05923e9i −1.11954 + 0.461298i
\(641\) 1.06130e8 0.0159161 0.00795805 0.999968i \(-0.497467\pi\)
0.00795805 + 0.999968i \(0.497467\pi\)
\(642\) 0 0
\(643\) 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
\(645\) 0 0
\(646\) −7.55891e8 + 4.44174e9i −0.110318 + 0.648245i
\(647\) 4.23914e9 0.615337 0.307668 0.951494i \(-0.400451\pi\)
0.307668 + 0.951494i \(0.400451\pi\)
\(648\) 0 0
\(649\) 3.58862e9 0.515312
\(650\) 1.52833e8 8.98072e8i 0.0218283 0.128267i
\(651\) 0 0
\(652\) 4.16839e9 1.18924e10i 0.588982 1.68036i
\(653\) 9.93257e9i 1.39594i 0.716129 + 0.697968i \(0.245912\pi\)
−0.716129 + 0.697968i \(0.754088\pi\)
\(654\) 0 0
\(655\) −2.98346e9 −0.414836
\(656\) −7.67885e9 6.13699e9i −1.06202 0.848774i
\(657\) 0 0
\(658\) −4.01664e9 6.83548e8i −0.549632 0.0935359i
\(659\) 1.36634e10i 1.85977i −0.367852 0.929884i \(-0.619907\pi\)
0.367852 0.929884i \(-0.380093\pi\)
\(660\) 0 0
\(661\) 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
\(663\) 0 0
\(664\) 1.07621e9 1.94361e9i 0.142662 0.257644i
\(665\) 4.88398e9 0.644019
\(666\) 0 0
\(667\) 3.15032e9i 0.411069i
\(668\) 5.13149e9 + 1.79863e9i 0.666079 + 0.233467i
\(669\) 0 0
\(670\) −3.01522e8 5.13127e7i −0.0387308 0.00659118i
\(671\) 9.52968e8 0.121773
\(672\) 0 0
\(673\) 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
\(675\) 0 0
\(676\) 6.98919e9 + 2.44978e9i 0.870189 + 0.305009i
\(677\) 9.55050e9i 1.18295i −0.806324 0.591474i \(-0.798546\pi\)
0.806324 0.591474i \(-0.201454\pi\)
\(678\) 0 0
\(679\) 1.26947e7 0.00155625
\(680\) −2.87631e9 + 5.19454e9i −0.350796 + 0.633528i
\(681\) 0 0
\(682\) 8.55798e8 5.02880e9i 0.103306 0.607043i
\(683\) 1.06442e10i 1.27832i −0.769073 0.639161i \(-0.779282\pi\)
0.769073 0.639161i \(-0.220718\pi\)
\(684\) 0 0
\(685\) 1.12948e10i 1.34265i
\(686\) −7.12100e9 1.21185e9i −0.842183 0.143322i
\(687\) 0 0
\(688\) 9.03675e8 1.13071e9i 0.105792 0.132371i
\(689\) −3.39865e9 −0.395858
\(690\) 0 0
\(691\) 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
\(693\) 0 0
\(694\) −1.19360e9 + 7.01381e9i −0.135551 + 0.796519i
\(695\) 1.58445e10 1.79033
\(696\) 0 0
\(697\) −7.26858e9 −0.813083
\(698\) 1.87286e9 1.10052e10i 0.208454 1.22491i
\(699\) 0 0
\(700\) 1.93121e9 + 6.76907e8i 0.212807 + 0.0745909i
\(701\) 8.95355e9i 0.981707i 0.871242 + 0.490854i \(0.163315\pi\)
−0.871242 + 0.490854i \(0.836685\pi\)
\(702\) 0 0
\(703\) 1.63139e10 1.77099
\(704\) 3.49555e9 2.18867e9i 0.377582 0.236415i
\(705\) 0 0
\(706\) 6.24289e9 + 1.06241e9i 0.667682 + 0.113626i
\(707\) 7.37853e9i 0.785239i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) 2.52737e9 + 1.39945e9i 0.262415 + 0.145304i
\(713\) 4.49486e9 0.464412
\(714\) 0 0
\(715\) 1.47157e9i 0.150560i
\(716\) 1.02525e9 2.92502e9i 0.104384 0.297806i
\(717\) 0 0
\(718\) 1.58813e9 + 2.70266e8i 0.160122 + 0.0272494i
\(719\) −9.54339e8 −0.0957528 −0.0478764 0.998853i \(-0.515245\pi\)
−0.0478764 + 0.998853i \(0.515245\pi\)
\(720\) 0 0
\(721\) 5.60800e9 0.557231
\(722\) 2.08241e9 + 3.54383e8i 0.205914 + 0.0350423i
\(723\) 0 0
\(724\) 1.18111e9 3.36971e9i 0.115666 0.329995i
\(725\) 5.85203e9i 0.570327i
\(726\) 0 0
\(727\) 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
\(729\) 0 0
\(730\) −2.38210e9 + 1.39976e10i −0.226637 + 1.33175i
\(731\) 1.07030e9i 0.101343i
\(732\) 0 0
\(733\) 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
\(735\) 0 0
\(736\) 2.41796e9 + 2.71292e9i 0.223551 + 0.250821i
\(737\) 1.57087e8 0.0144545
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) 1.28084e9 7.52642e9i 0.115102 0.676355i
\(743\) 4.35857e9 0.389837 0.194918 0.980819i \(-0.437556\pi\)
0.194918 + 0.980819i \(0.437556\pi\)
\(744\) 0 0
\(745\) −1.29864e10 −1.15064
\(746\) −7.87185e8 + 4.62562e9i −0.0694210 + 0.407929i
\(747\) 0 0
\(748\) 1.00874e9 2.87792e9i 0.0881297 0.251433i
\(749\) 5.95321e9i 0.517684i
\(750\) 0 0
\(751\) −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
\(753\) 0 0
\(754\) −3.96256e9 6.74346e8i −0.336648 0.0572906i
\(755\) 2.42883e10i 2.05391i
\(756\) 0 0
\(757\) 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
\(759\) 0 0
\(760\) 1.40947e10 + 7.80449e9i 1.16469 + 0.644907i
\(761\) −7.15151e9 −0.588236 −0.294118 0.955769i \(-0.595026\pi\)
−0.294118 + 0.955769i \(0.595026\pi\)
\(762\) 0 0
\(763\) 2.08175e9i 0.169665i
\(764\) −2.02447e9 7.09596e8i −0.164242 0.0575684i
\(765\) 0 0
\(766\) −1.51445e10 2.57728e9i −1.21746 0.207186i
\(767\) 4.03460e9 0.322862
\(768\) 0 0
\(769\) −1.85381e10 −1.47002 −0.735011 0.678055i \(-0.762823\pi\)
−0.735011 + 0.678055i \(0.762823\pi\)
\(770\) −3.25884e9 5.54586e8i −0.257244 0.0437776i
\(771\) 0 0
\(772\) 1.05696e10 + 3.70476e9i 0.826798 + 0.289800i
\(773\) 8.25535e9i 0.642846i −0.946936 0.321423i \(-0.895839\pi\)
0.946936 0.321423i \(-0.104161\pi\)
\(774\) 0 0
\(775\) 8.34966e9 0.644336
\(776\) 3.66358e7 + 2.02859e7i 0.00281443 + 0.00155840i
\(777\) 0 0
\(778\) 1.90895e9 1.12173e10i 0.145334 0.854003i
\(779\)