Properties

Label 570.2.d.c.229.5
Level $570$
Weight $2$
Character 570.229
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.5
Root \(-0.854638 + 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.c.229.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +1.07838i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +1.07838i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.17009 - 0.539189i) q^{10} +6.34017 q^{11} -1.00000i q^{12} +3.41855i q^{13} -1.07838 q^{14} +(2.17009 - 0.539189i) q^{15} +1.00000 q^{16} +5.41855i q^{17} -1.00000i q^{18} -1.00000 q^{19} +(0.539189 + 2.17009i) q^{20} -1.07838 q^{21} +6.34017i q^{22} +6.34017i q^{23} +1.00000 q^{24} +(-4.41855 + 2.34017i) q^{25} -3.41855 q^{26} -1.00000i q^{27} -1.07838i q^{28} +0.340173 q^{29} +(0.539189 + 2.17009i) q^{30} +1.07838 q^{31} +1.00000i q^{32} +6.34017i q^{33} -5.41855 q^{34} +(2.34017 - 0.581449i) q^{35} +1.00000 q^{36} -3.41855i q^{37} -1.00000i q^{38} -3.41855 q^{39} +(-2.17009 + 0.539189i) q^{40} +7.60197 q^{41} -1.07838i q^{42} -11.1773i q^{43} -6.34017 q^{44} +(0.539189 + 2.17009i) q^{45} -6.34017 q^{46} +6.34017i q^{47} +1.00000i q^{48} +5.83710 q^{49} +(-2.34017 - 4.41855i) q^{50} -5.41855 q^{51} -3.41855i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(-3.41855 - 13.7587i) q^{55} +1.07838 q^{56} -1.00000i q^{57} +0.340173i q^{58} -0.738205 q^{59} +(-2.17009 + 0.539189i) q^{60} -2.68035 q^{61} +1.07838i q^{62} -1.07838i q^{63} -1.00000 q^{64} +(7.41855 - 1.84324i) q^{65} -6.34017 q^{66} -2.83710i q^{67} -5.41855i q^{68} -6.34017 q^{69} +(0.581449 + 2.34017i) q^{70} -2.83710 q^{71} +1.00000i q^{72} +6.83710i q^{73} +3.41855 q^{74} +(-2.34017 - 4.41855i) q^{75} +1.00000 q^{76} +6.83710i q^{77} -3.41855i q^{78} +1.07838 q^{79} +(-0.539189 - 2.17009i) q^{80} +1.00000 q^{81} +7.60197i q^{82} +0.894960i q^{83} +1.07838 q^{84} +(11.7587 - 2.92162i) q^{85} +11.1773 q^{86} +0.340173i q^{87} -6.34017i q^{88} -6.92162 q^{89} +(-2.17009 + 0.539189i) q^{90} -3.68649 q^{91} -6.34017i q^{92} +1.07838i q^{93} -6.34017 q^{94} +(0.539189 + 2.17009i) q^{95} -1.00000 q^{96} +3.65983i q^{97} +5.83710i q^{98} -6.34017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + 2q^{10} + 16q^{11} + 2q^{15} + 6q^{16} - 6q^{19} + 6q^{24} + 2q^{25} + 8q^{26} - 20q^{29} - 4q^{34} - 8q^{35} + 6q^{36} + 8q^{39} - 2q^{40} + 8q^{41} - 16q^{44} - 16q^{46} - 22q^{49} + 8q^{50} - 4q^{51} + 6q^{54} + 8q^{55} - 20q^{59} - 2q^{60} + 28q^{61} - 6q^{64} + 16q^{65} - 16q^{66} - 16q^{69} + 32q^{70} + 40q^{71} - 8q^{74} + 8q^{75} + 6q^{76} + 6q^{81} + 20q^{85} - 12q^{86} - 48q^{89} - 2q^{90} - 48q^{91} - 16q^{94} - 6q^{96} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −0.539189 2.17009i −0.241133 0.970492i
\(6\) −1.00000 −0.408248
\(7\) 1.07838i 0.407588i 0.979014 + 0.203794i \(0.0653274\pi\)
−0.979014 + 0.203794i \(0.934673\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.17009 0.539189i 0.686242 0.170506i
\(11\) 6.34017 1.91163 0.955817 0.293962i \(-0.0949740\pi\)
0.955817 + 0.293962i \(0.0949740\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.41855i 0.948135i 0.880488 + 0.474068i \(0.157215\pi\)
−0.880488 + 0.474068i \(0.842785\pi\)
\(14\) −1.07838 −0.288209
\(15\) 2.17009 0.539189i 0.560314 0.139218i
\(16\) 1.00000 0.250000
\(17\) 5.41855i 1.31419i 0.753807 + 0.657096i \(0.228215\pi\)
−0.753807 + 0.657096i \(0.771785\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.00000 −0.229416
\(20\) 0.539189 + 2.17009i 0.120566 + 0.485246i
\(21\) −1.07838 −0.235321
\(22\) 6.34017i 1.35173i
\(23\) 6.34017i 1.32202i 0.750378 + 0.661009i \(0.229871\pi\)
−0.750378 + 0.661009i \(0.770129\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.41855 + 2.34017i −0.883710 + 0.468035i
\(26\) −3.41855 −0.670433
\(27\) 1.00000i 0.192450i
\(28\) 1.07838i 0.203794i
\(29\) 0.340173 0.0631685 0.0315843 0.999501i \(-0.489945\pi\)
0.0315843 + 0.999501i \(0.489945\pi\)
\(30\) 0.539189 + 2.17009i 0.0984420 + 0.396202i
\(31\) 1.07838 0.193682 0.0968412 0.995300i \(-0.469126\pi\)
0.0968412 + 0.995300i \(0.469126\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.34017i 1.10368i
\(34\) −5.41855 −0.929274
\(35\) 2.34017 0.581449i 0.395561 0.0982829i
\(36\) 1.00000 0.166667
\(37\) 3.41855i 0.562006i −0.959707 0.281003i \(-0.909333\pi\)
0.959707 0.281003i \(-0.0906671\pi\)
\(38\) 1.00000i 0.162221i
\(39\) −3.41855 −0.547406
\(40\) −2.17009 + 0.539189i −0.343121 + 0.0852532i
\(41\) 7.60197 1.18723 0.593614 0.804750i \(-0.297701\pi\)
0.593614 + 0.804750i \(0.297701\pi\)
\(42\) 1.07838i 0.166397i
\(43\) 11.1773i 1.70452i −0.523120 0.852259i \(-0.675232\pi\)
0.523120 0.852259i \(-0.324768\pi\)
\(44\) −6.34017 −0.955817
\(45\) 0.539189 + 2.17009i 0.0803775 + 0.323497i
\(46\) −6.34017 −0.934808
\(47\) 6.34017i 0.924809i 0.886669 + 0.462405i \(0.153013\pi\)
−0.886669 + 0.462405i \(0.846987\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 5.83710 0.833872
\(50\) −2.34017 4.41855i −0.330950 0.624877i
\(51\) −5.41855 −0.758749
\(52\) 3.41855i 0.474068i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 1.00000 0.136083
\(55\) −3.41855 13.7587i −0.460957 1.85523i
\(56\) 1.07838 0.144104
\(57\) 1.00000i 0.132453i
\(58\) 0.340173i 0.0446669i
\(59\) −0.738205 −0.0961061 −0.0480530 0.998845i \(-0.515302\pi\)
−0.0480530 + 0.998845i \(0.515302\pi\)
\(60\) −2.17009 + 0.539189i −0.280157 + 0.0696090i
\(61\) −2.68035 −0.343183 −0.171592 0.985168i \(-0.554891\pi\)
−0.171592 + 0.985168i \(0.554891\pi\)
\(62\) 1.07838i 0.136954i
\(63\) 1.07838i 0.135863i
\(64\) −1.00000 −0.125000
\(65\) 7.41855 1.84324i 0.920158 0.228626i
\(66\) −6.34017 −0.780421
\(67\) 2.83710i 0.346607i −0.984868 0.173304i \(-0.944556\pi\)
0.984868 0.173304i \(-0.0554442\pi\)
\(68\) 5.41855i 0.657096i
\(69\) −6.34017 −0.763267
\(70\) 0.581449 + 2.34017i 0.0694965 + 0.279704i
\(71\) −2.83710 −0.336702 −0.168351 0.985727i \(-0.553844\pi\)
−0.168351 + 0.985727i \(0.553844\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 6.83710i 0.800222i 0.916467 + 0.400111i \(0.131028\pi\)
−0.916467 + 0.400111i \(0.868972\pi\)
\(74\) 3.41855 0.397398
\(75\) −2.34017 4.41855i −0.270220 0.510210i
\(76\) 1.00000 0.114708
\(77\) 6.83710i 0.779160i
\(78\) 3.41855i 0.387075i
\(79\) 1.07838 0.121327 0.0606635 0.998158i \(-0.480678\pi\)
0.0606635 + 0.998158i \(0.480678\pi\)
\(80\) −0.539189 2.17009i −0.0602831 0.242623i
\(81\) 1.00000 0.111111
\(82\) 7.60197i 0.839497i
\(83\) 0.894960i 0.0982347i 0.998793 + 0.0491173i \(0.0156408\pi\)
−0.998793 + 0.0491173i \(0.984359\pi\)
\(84\) 1.07838 0.117661
\(85\) 11.7587 2.92162i 1.27541 0.316894i
\(86\) 11.1773 1.20528
\(87\) 0.340173i 0.0364704i
\(88\) 6.34017i 0.675865i
\(89\) −6.92162 −0.733690 −0.366845 0.930282i \(-0.619562\pi\)
−0.366845 + 0.930282i \(0.619562\pi\)
\(90\) −2.17009 + 0.539189i −0.228747 + 0.0568355i
\(91\) −3.68649 −0.386449
\(92\) 6.34017i 0.661009i
\(93\) 1.07838i 0.111823i
\(94\) −6.34017 −0.653939
\(95\) 0.539189 + 2.17009i 0.0553196 + 0.222646i
\(96\) −1.00000 −0.102062
\(97\) 3.65983i 0.371599i 0.982588 + 0.185800i \(0.0594875\pi\)
−0.982588 + 0.185800i \(0.940512\pi\)
\(98\) 5.83710i 0.589636i
\(99\) −6.34017 −0.637211
\(100\) 4.41855 2.34017i 0.441855 0.234017i
\(101\) 19.6020 1.95047 0.975234 0.221174i \(-0.0709889\pi\)
0.975234 + 0.221174i \(0.0709889\pi\)
\(102\) 5.41855i 0.536516i
\(103\) 11.7587i 1.15862i −0.815107 0.579311i \(-0.803322\pi\)
0.815107 0.579311i \(-0.196678\pi\)
\(104\) 3.41855 0.335216
\(105\) 0.581449 + 2.34017i 0.0567436 + 0.228377i
\(106\) −6.00000 −0.582772
\(107\) 6.15676i 0.595196i −0.954691 0.297598i \(-0.903814\pi\)
0.954691 0.297598i \(-0.0961855\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −17.9155 −1.71599 −0.857996 0.513657i \(-0.828291\pi\)
−0.857996 + 0.513657i \(0.828291\pi\)
\(110\) 13.7587 3.41855i 1.31184 0.325946i
\(111\) 3.41855 0.324474
\(112\) 1.07838i 0.101897i
\(113\) 13.2039i 1.24212i −0.783762 0.621061i \(-0.786702\pi\)
0.783762 0.621061i \(-0.213298\pi\)
\(114\) 1.00000 0.0936586
\(115\) 13.7587 3.41855i 1.28301 0.318781i
\(116\) −0.340173 −0.0315843
\(117\) 3.41855i 0.316045i
\(118\) 0.738205i 0.0679573i
\(119\) −5.84324 −0.535649
\(120\) −0.539189 2.17009i −0.0492210 0.198101i
\(121\) 29.1978 2.65434
\(122\) 2.68035i 0.242667i
\(123\) 7.60197i 0.685446i
\(124\) −1.07838 −0.0968412
\(125\) 7.46081 + 8.32684i 0.667315 + 0.744775i
\(126\) 1.07838 0.0960695
\(127\) 0.921622i 0.0817808i 0.999164 + 0.0408904i \(0.0130194\pi\)
−0.999164 + 0.0408904i \(0.986981\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 11.1773 0.984104
\(130\) 1.84324 + 7.41855i 0.161663 + 0.650650i
\(131\) 10.6537 0.930817 0.465408 0.885096i \(-0.345907\pi\)
0.465408 + 0.885096i \(0.345907\pi\)
\(132\) 6.34017i 0.551841i
\(133\) 1.07838i 0.0935072i
\(134\) 2.83710 0.245088
\(135\) −2.17009 + 0.539189i −0.186771 + 0.0464060i
\(136\) 5.41855 0.464637
\(137\) 20.6225i 1.76190i −0.473211 0.880949i \(-0.656905\pi\)
0.473211 0.880949i \(-0.343095\pi\)
\(138\) 6.34017i 0.539711i
\(139\) −18.8371 −1.59774 −0.798871 0.601502i \(-0.794569\pi\)
−0.798871 + 0.601502i \(0.794569\pi\)
\(140\) −2.34017 + 0.581449i −0.197781 + 0.0491414i
\(141\) −6.34017 −0.533939
\(142\) 2.83710i 0.238084i
\(143\) 21.6742i 1.81249i
\(144\) −1.00000 −0.0833333
\(145\) −0.183417 0.738205i −0.0152320 0.0613046i
\(146\) −6.83710 −0.565843
\(147\) 5.83710i 0.481436i
\(148\) 3.41855i 0.281003i
\(149\) 5.44521 0.446089 0.223045 0.974808i \(-0.428400\pi\)
0.223045 + 0.974808i \(0.428400\pi\)
\(150\) 4.41855 2.34017i 0.360773 0.191074i
\(151\) −23.1194 −1.88143 −0.940716 0.339196i \(-0.889845\pi\)
−0.940716 + 0.339196i \(0.889845\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 5.41855i 0.438064i
\(154\) −6.83710 −0.550949
\(155\) −0.581449 2.34017i −0.0467031 0.187967i
\(156\) 3.41855 0.273703
\(157\) 9.73206i 0.776703i 0.921511 + 0.388352i \(0.126955\pi\)
−0.921511 + 0.388352i \(0.873045\pi\)
\(158\) 1.07838i 0.0857911i
\(159\) −6.00000 −0.475831
\(160\) 2.17009 0.539189i 0.171560 0.0426266i
\(161\) −6.83710 −0.538839
\(162\) 1.00000i 0.0785674i
\(163\) 6.49693i 0.508879i −0.967089 0.254439i \(-0.918109\pi\)
0.967089 0.254439i \(-0.0818909\pi\)
\(164\) −7.60197 −0.593614
\(165\) 13.7587 3.41855i 1.07112 0.266134i
\(166\) −0.894960 −0.0694624
\(167\) 20.9939i 1.62455i −0.583272 0.812277i \(-0.698228\pi\)
0.583272 0.812277i \(-0.301772\pi\)
\(168\) 1.07838i 0.0831986i
\(169\) 1.31351 0.101039
\(170\) 2.92162 + 11.7587i 0.224078 + 0.901853i
\(171\) 1.00000 0.0764719
\(172\) 11.1773i 0.852259i
\(173\) 6.99386i 0.531733i −0.964010 0.265867i \(-0.914342\pi\)
0.964010 0.265867i \(-0.0856581\pi\)
\(174\) −0.340173 −0.0257884
\(175\) −2.52359 4.76487i −0.190766 0.360190i
\(176\) 6.34017 0.477909
\(177\) 0.738205i 0.0554869i
\(178\) 6.92162i 0.518798i
\(179\) 4.73820 0.354150 0.177075 0.984197i \(-0.443336\pi\)
0.177075 + 0.984197i \(0.443336\pi\)
\(180\) −0.539189 2.17009i −0.0401888 0.161749i
\(181\) −12.0722 −0.897322 −0.448661 0.893702i \(-0.648099\pi\)
−0.448661 + 0.893702i \(0.648099\pi\)
\(182\) 3.68649i 0.273261i
\(183\) 2.68035i 0.198137i
\(184\) 6.34017 0.467404
\(185\) −7.41855 + 1.84324i −0.545423 + 0.135518i
\(186\) −1.07838 −0.0790705
\(187\) 34.3545i 2.51225i
\(188\) 6.34017i 0.462405i
\(189\) 1.07838 0.0784404
\(190\) −2.17009 + 0.539189i −0.157435 + 0.0391169i
\(191\) −7.26180 −0.525445 −0.262723 0.964871i \(-0.584620\pi\)
−0.262723 + 0.964871i \(0.584620\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 18.8638i 1.35784i −0.734211 0.678922i \(-0.762448\pi\)
0.734211 0.678922i \(-0.237552\pi\)
\(194\) −3.65983 −0.262760
\(195\) 1.84324 + 7.41855i 0.131997 + 0.531253i
\(196\) −5.83710 −0.416936
\(197\) 17.7009i 1.26113i −0.776135 0.630567i \(-0.782822\pi\)
0.776135 0.630567i \(-0.217178\pi\)
\(198\) 6.34017i 0.450576i
\(199\) 0.313511 0.0222242 0.0111121 0.999938i \(-0.496463\pi\)
0.0111121 + 0.999938i \(0.496463\pi\)
\(200\) 2.34017 + 4.41855i 0.165475 + 0.312439i
\(201\) 2.83710 0.200114
\(202\) 19.6020i 1.37919i
\(203\) 0.366835i 0.0257468i
\(204\) 5.41855 0.379374
\(205\) −4.09890 16.4969i −0.286279 1.15220i
\(206\) 11.7587 0.819269
\(207\) 6.34017i 0.440672i
\(208\) 3.41855i 0.237034i
\(209\) −6.34017 −0.438559
\(210\) −2.34017 + 0.581449i −0.161487 + 0.0401238i
\(211\) 14.8371 1.02143 0.510714 0.859751i \(-0.329381\pi\)
0.510714 + 0.859751i \(0.329381\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 2.83710i 0.194395i
\(214\) 6.15676 0.420867
\(215\) −24.2557 + 6.02666i −1.65422 + 0.411015i
\(216\) −1.00000 −0.0680414
\(217\) 1.16290i 0.0789427i
\(218\) 17.9155i 1.21339i
\(219\) −6.83710 −0.462009
\(220\) 3.41855 + 13.7587i 0.230479 + 0.927613i
\(221\) −18.5236 −1.24603
\(222\) 3.41855i 0.229438i
\(223\) 1.28846i 0.0862815i 0.999069 + 0.0431407i \(0.0137364\pi\)
−0.999069 + 0.0431407i \(0.986264\pi\)
\(224\) −1.07838 −0.0720521
\(225\) 4.41855 2.34017i 0.294570 0.156012i
\(226\) 13.2039 0.878313
\(227\) 20.9939i 1.39341i −0.717357 0.696706i \(-0.754648\pi\)
0.717357 0.696706i \(-0.245352\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) 2.36683 0.156405 0.0782024 0.996938i \(-0.475082\pi\)
0.0782024 + 0.996938i \(0.475082\pi\)
\(230\) 3.41855 + 13.7587i 0.225413 + 0.907223i
\(231\) −6.83710 −0.449848
\(232\) 0.340173i 0.0223334i
\(233\) 5.10504i 0.334442i 0.985919 + 0.167221i \(0.0534794\pi\)
−0.985919 + 0.167221i \(0.946521\pi\)
\(234\) 3.41855 0.223478
\(235\) 13.7587 3.41855i 0.897520 0.223002i
\(236\) 0.738205 0.0480530
\(237\) 1.07838i 0.0700482i
\(238\) 5.84324i 0.378761i
\(239\) −10.4124 −0.673523 −0.336761 0.941590i \(-0.609332\pi\)
−0.336761 + 0.941590i \(0.609332\pi\)
\(240\) 2.17009 0.539189i 0.140078 0.0348045i
\(241\) 3.36069 0.216481 0.108241 0.994125i \(-0.465478\pi\)
0.108241 + 0.994125i \(0.465478\pi\)
\(242\) 29.1978i 1.87691i
\(243\) 1.00000i 0.0641500i
\(244\) 2.68035 0.171592
\(245\) −3.14730 12.6670i −0.201074 0.809266i
\(246\) −7.60197 −0.484684
\(247\) 3.41855i 0.217517i
\(248\) 1.07838i 0.0684771i
\(249\) −0.894960 −0.0567158
\(250\) −8.32684 + 7.46081i −0.526636 + 0.471863i
\(251\) 21.8576 1.37964 0.689820 0.723981i \(-0.257689\pi\)
0.689820 + 0.723981i \(0.257689\pi\)
\(252\) 1.07838i 0.0679314i
\(253\) 40.1978i 2.52721i
\(254\) −0.921622 −0.0578277
\(255\) 2.92162 + 11.7587i 0.182959 + 0.736360i
\(256\) 1.00000 0.0625000
\(257\) 26.8781i 1.67661i 0.545200 + 0.838306i \(0.316454\pi\)
−0.545200 + 0.838306i \(0.683546\pi\)
\(258\) 11.1773i 0.695867i
\(259\) 3.68649 0.229067
\(260\) −7.41855 + 1.84324i −0.460079 + 0.114313i
\(261\) −0.340173 −0.0210562
\(262\) 10.6537i 0.658187i
\(263\) 22.3402i 1.37755i 0.724973 + 0.688777i \(0.241852\pi\)
−0.724973 + 0.688777i \(0.758148\pi\)
\(264\) 6.34017 0.390211
\(265\) 13.0205 3.23513i 0.799844 0.198733i
\(266\) 1.07838 0.0661196
\(267\) 6.92162i 0.423596i
\(268\) 2.83710i 0.173304i
\(269\) 17.3340 1.05687 0.528437 0.848972i \(-0.322778\pi\)
0.528437 + 0.848972i \(0.322778\pi\)
\(270\) −0.539189 2.17009i −0.0328140 0.132067i
\(271\) −13.3607 −0.811604 −0.405802 0.913961i \(-0.633008\pi\)
−0.405802 + 0.913961i \(0.633008\pi\)
\(272\) 5.41855i 0.328548i
\(273\) 3.68649i 0.223116i
\(274\) 20.6225 1.24585
\(275\) −28.0144 + 14.8371i −1.68933 + 0.894711i
\(276\) 6.34017 0.381634
\(277\) 0.738205i 0.0443544i −0.999754 0.0221772i \(-0.992940\pi\)
0.999754 0.0221772i \(-0.00705980\pi\)
\(278\) 18.8371i 1.12977i
\(279\) −1.07838 −0.0645608
\(280\) −0.581449 2.34017i −0.0347482 0.139852i
\(281\) −31.7998 −1.89701 −0.948507 0.316755i \(-0.897407\pi\)
−0.948507 + 0.316755i \(0.897407\pi\)
\(282\) 6.34017i 0.377552i
\(283\) 4.70701i 0.279803i −0.990165 0.139901i \(-0.955321\pi\)
0.990165 0.139901i \(-0.0446785\pi\)
\(284\) 2.83710 0.168351
\(285\) −2.17009 + 0.539189i −0.128545 + 0.0319388i
\(286\) −21.6742 −1.28162
\(287\) 8.19779i 0.483900i
\(288\) 1.00000i 0.0589256i
\(289\) −12.3607 −0.727100
\(290\) 0.738205 0.183417i 0.0433489 0.0107706i
\(291\) −3.65983 −0.214543
\(292\) 6.83710i 0.400111i
\(293\) 26.1978i 1.53049i 0.643738 + 0.765246i \(0.277383\pi\)
−0.643738 + 0.765246i \(0.722617\pi\)
\(294\) −5.83710 −0.340427
\(295\) 0.398032 + 1.60197i 0.0231743 + 0.0932702i
\(296\) −3.41855 −0.198699
\(297\) 6.34017i 0.367894i
\(298\) 5.44521i 0.315433i
\(299\) −21.6742 −1.25345
\(300\) 2.34017 + 4.41855i 0.135110 + 0.255105i
\(301\) 12.0533 0.694742
\(302\) 23.1194i 1.33037i
\(303\) 19.6020i 1.12610i
\(304\) −1.00000 −0.0573539
\(305\) 1.44521 + 5.81658i 0.0827526 + 0.333057i
\(306\) 5.41855 0.309758
\(307\) 32.1978i 1.83763i −0.394694 0.918813i \(-0.629149\pi\)
0.394694 0.918813i \(-0.370851\pi\)
\(308\) 6.83710i 0.389580i
\(309\) 11.7587 0.668930
\(310\) 2.34017 0.581449i 0.132913 0.0330241i
\(311\) 16.7382 0.949137 0.474568 0.880219i \(-0.342604\pi\)
0.474568 + 0.880219i \(0.342604\pi\)
\(312\) 3.41855i 0.193537i
\(313\) 14.1568i 0.800187i −0.916474 0.400094i \(-0.868978\pi\)
0.916474 0.400094i \(-0.131022\pi\)
\(314\) −9.73206 −0.549212
\(315\) −2.34017 + 0.581449i −0.131854 + 0.0327610i
\(316\) −1.07838 −0.0606635
\(317\) 21.8843i 1.22914i 0.788861 + 0.614572i \(0.210671\pi\)
−0.788861 + 0.614572i \(0.789329\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 2.15676 0.120755
\(320\) 0.539189 + 2.17009i 0.0301416 + 0.121312i
\(321\) 6.15676 0.343637
\(322\) 6.83710i 0.381017i
\(323\) 5.41855i 0.301496i
\(324\) −1.00000 −0.0555556
\(325\) −8.00000 15.1050i −0.443760 0.837877i
\(326\) 6.49693 0.359832
\(327\) 17.9155i 0.990728i
\(328\) 7.60197i 0.419748i
\(329\) −6.83710 −0.376942
\(330\) 3.41855 + 13.7587i 0.188185 + 0.757393i
\(331\) −26.1568 −1.43771 −0.718853 0.695162i \(-0.755332\pi\)
−0.718853 + 0.695162i \(0.755332\pi\)
\(332\) 0.894960i 0.0491173i
\(333\) 3.41855i 0.187335i
\(334\) 20.9939 1.14873
\(335\) −6.15676 + 1.52973i −0.336379 + 0.0835783i
\(336\) −1.07838 −0.0588303
\(337\) 29.7009i 1.61791i 0.587871 + 0.808955i \(0.299966\pi\)
−0.587871 + 0.808955i \(0.700034\pi\)
\(338\) 1.31351i 0.0714456i
\(339\) 13.2039 0.717139
\(340\) −11.7587 + 2.92162i −0.637706 + 0.158447i
\(341\) 6.83710 0.370250
\(342\) 1.00000i 0.0540738i
\(343\) 13.8432i 0.747465i
\(344\) −11.1773 −0.602638
\(345\) 3.41855 + 13.7587i 0.184049 + 0.740745i
\(346\) 6.99386 0.375992
\(347\) 23.4186i 1.25717i −0.777739 0.628587i \(-0.783634\pi\)
0.777739 0.628587i \(-0.216366\pi\)
\(348\) 0.340173i 0.0182352i
\(349\) −6.48255 −0.347003 −0.173502 0.984834i \(-0.555508\pi\)
−0.173502 + 0.984834i \(0.555508\pi\)
\(350\) 4.76487 2.52359i 0.254693 0.134892i
\(351\) 3.41855 0.182469
\(352\) 6.34017i 0.337932i
\(353\) 2.58145i 0.137397i 0.997637 + 0.0686983i \(0.0218846\pi\)
−0.997637 + 0.0686983i \(0.978115\pi\)
\(354\) 0.738205 0.0392351
\(355\) 1.52973 + 6.15676i 0.0811898 + 0.326767i
\(356\) 6.92162 0.366845
\(357\) 5.84324i 0.309257i
\(358\) 4.73820i 0.250422i
\(359\) −28.1399 −1.48517 −0.742584 0.669752i \(-0.766400\pi\)
−0.742584 + 0.669752i \(0.766400\pi\)
\(360\) 2.17009 0.539189i 0.114374 0.0284177i
\(361\) 1.00000 0.0526316
\(362\) 12.0722i 0.634503i
\(363\) 29.1978i 1.53249i
\(364\) 3.68649 0.193225
\(365\) 14.8371 3.68649i 0.776609 0.192960i
\(366\) 2.68035 0.140104
\(367\) 10.5548i 0.550955i −0.961307 0.275478i \(-0.911164\pi\)
0.961307 0.275478i \(-0.0888360\pi\)
\(368\) 6.34017i 0.330504i
\(369\) −7.60197 −0.395743
\(370\) −1.84324 7.41855i −0.0958257 0.385672i
\(371\) −6.47027 −0.335919
\(372\) 1.07838i 0.0559113i
\(373\) 17.8888i 0.926248i 0.886294 + 0.463124i \(0.153272\pi\)
−0.886294 + 0.463124i \(0.846728\pi\)
\(374\) −34.3545 −1.77643
\(375\) −8.32684 + 7.46081i −0.429996 + 0.385275i
\(376\) 6.34017 0.326969
\(377\) 1.16290i 0.0598923i
\(378\) 1.07838i 0.0554658i
\(379\) −4.36683 −0.224309 −0.112155 0.993691i \(-0.535775\pi\)
−0.112155 + 0.993691i \(0.535775\pi\)
\(380\) −0.539189 2.17009i −0.0276598 0.111323i
\(381\) −0.921622 −0.0472161
\(382\) 7.26180i 0.371546i
\(383\) 22.5236i 1.15090i 0.817836 + 0.575451i \(0.195173\pi\)
−0.817836 + 0.575451i \(0.804827\pi\)
\(384\) 1.00000 0.0510310
\(385\) 14.8371 3.68649i 0.756169 0.187881i
\(386\) 18.8638 0.960140
\(387\) 11.1773i 0.568173i
\(388\) 3.65983i 0.185800i
\(389\) 9.07838 0.460292 0.230146 0.973156i \(-0.426080\pi\)
0.230146 + 0.973156i \(0.426080\pi\)
\(390\) −7.41855 + 1.84324i −0.375653 + 0.0933363i
\(391\) −34.3545 −1.73738
\(392\) 5.83710i 0.294818i
\(393\) 10.6537i 0.537407i
\(394\) 17.7009 0.891757
\(395\) −0.581449 2.34017i −0.0292559 0.117747i
\(396\) 6.34017 0.318606
\(397\) 3.74435i 0.187923i 0.995576 + 0.0939617i \(0.0299531\pi\)
−0.995576 + 0.0939617i \(0.970047\pi\)
\(398\) 0.313511i 0.0157149i
\(399\) 1.07838 0.0539864
\(400\) −4.41855 + 2.34017i −0.220928 + 0.117009i
\(401\) −11.9155 −0.595031 −0.297515 0.954717i \(-0.596158\pi\)
−0.297515 + 0.954717i \(0.596158\pi\)
\(402\) 2.83710i 0.141502i
\(403\) 3.68649i 0.183637i
\(404\) −19.6020 −0.975234
\(405\) −0.539189 2.17009i −0.0267925 0.107832i
\(406\) −0.366835 −0.0182057
\(407\) 21.6742i 1.07435i
\(408\) 5.41855i 0.268258i
\(409\) 2.99386 0.148037 0.0740183 0.997257i \(-0.476418\pi\)
0.0740183 + 0.997257i \(0.476418\pi\)
\(410\) 16.4969 4.09890i 0.814725 0.202430i
\(411\) 20.6225 1.01723
\(412\) 11.7587i 0.579311i
\(413\) 0.796064i 0.0391717i
\(414\) 6.34017 0.311603
\(415\) 1.94214 0.482553i 0.0953360 0.0236876i
\(416\) −3.41855 −0.167608
\(417\) 18.8371i 0.922457i
\(418\) 6.34017i 0.310108i
\(419\) 33.5441 1.63874 0.819368 0.573267i \(-0.194324\pi\)
0.819368 + 0.573267i \(0.194324\pi\)
\(420\) −0.581449 2.34017i −0.0283718 0.114189i
\(421\) 31.5897 1.53959 0.769793 0.638293i \(-0.220359\pi\)
0.769793 + 0.638293i \(0.220359\pi\)
\(422\) 14.8371i 0.722259i
\(423\) 6.34017i 0.308270i
\(424\) 6.00000 0.291386
\(425\) −12.6803 23.9421i −0.615087 1.16136i
\(426\) 2.83710 0.137458
\(427\) 2.89043i 0.139877i
\(428\) 6.15676i 0.297598i
\(429\) −21.6742 −1.04644
\(430\) −6.02666 24.2557i −0.290631 1.16971i
\(431\) −40.5113 −1.95136 −0.975680 0.219198i \(-0.929656\pi\)
−0.975680 + 0.219198i \(0.929656\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 5.13624i 0.246832i 0.992355 + 0.123416i \(0.0393849\pi\)
−0.992355 + 0.123416i \(0.960615\pi\)
\(434\) −1.16290 −0.0558209
\(435\) 0.738205 0.183417i 0.0353942 0.00879420i
\(436\) 17.9155 0.857996
\(437\) 6.34017i 0.303292i
\(438\) 6.83710i 0.326689i
\(439\) 17.7054 0.845033 0.422516 0.906355i \(-0.361147\pi\)
0.422516 + 0.906355i \(0.361147\pi\)
\(440\) −13.7587 + 3.41855i −0.655921 + 0.162973i
\(441\) −5.83710 −0.277957
\(442\) 18.5236i 0.881077i
\(443\) 6.73820i 0.320142i 0.987106 + 0.160071i \(0.0511723\pi\)
−0.987106 + 0.160071i \(0.948828\pi\)
\(444\) −3.41855 −0.162237
\(445\) 3.73206 + 15.0205i 0.176917 + 0.712041i
\(446\) −1.28846 −0.0610102
\(447\) 5.44521i 0.257550i
\(448\) 1.07838i 0.0509486i
\(449\) 36.2290 1.70975 0.854876 0.518833i \(-0.173633\pi\)
0.854876 + 0.518833i \(0.173633\pi\)
\(450\) 2.34017 + 4.41855i 0.110317 + 0.208292i
\(451\) 48.1978 2.26955
\(452\) 13.2039i 0.621061i
\(453\) 23.1194i 1.08624i
\(454\) 20.9939 0.985291
\(455\) 1.98771 + 8.00000i 0.0931855 + 0.375046i
\(456\) −1.00000 −0.0468293
\(457\) 8.00000i 0.374224i 0.982339 + 0.187112i \(0.0599128\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) 2.36683i 0.110595i
\(459\) 5.41855 0.252916
\(460\) −13.7587 + 3.41855i −0.641504 + 0.159391i
\(461\) 35.7464 1.66488 0.832439 0.554117i \(-0.186944\pi\)
0.832439 + 0.554117i \(0.186944\pi\)
\(462\) 6.83710i 0.318091i
\(463\) 37.3295i 1.73485i −0.497569 0.867424i \(-0.665774\pi\)
0.497569 0.867424i \(-0.334226\pi\)
\(464\) 0.340173 0.0157921
\(465\) 2.34017 0.581449i 0.108523 0.0269641i
\(466\) −5.10504 −0.236486
\(467\) 12.0989i 0.559870i 0.960019 + 0.279935i \(0.0903129\pi\)
−0.960019 + 0.279935i \(0.909687\pi\)
\(468\) 3.41855i 0.158023i
\(469\) 3.05947 0.141273
\(470\) 3.41855 + 13.7587i 0.157686 + 0.634643i
\(471\) −9.73206 −0.448430
\(472\) 0.738205i 0.0339786i
\(473\) 70.8659i 3.25842i
\(474\) −1.07838 −0.0495315
\(475\) 4.41855 2.34017i 0.202737 0.107375i
\(476\) 5.84324 0.267825
\(477\) 6.00000i 0.274721i
\(478\) 10.4124i 0.476252i
\(479\) 34.6102 1.58138 0.790690 0.612216i \(-0.209722\pi\)
0.790690 + 0.612216i \(0.209722\pi\)
\(480\) 0.539189 + 2.17009i 0.0246105 + 0.0990504i
\(481\) 11.6865 0.532858
\(482\) 3.36069i 0.153075i
\(483\) 6.83710i 0.311099i
\(484\) −29.1978 −1.32717
\(485\) 7.94214 1.97334i 0.360634 0.0896047i
\(486\) −1.00000 −0.0453609
\(487\) 30.2823i 1.37222i −0.727497 0.686111i \(-0.759316\pi\)
0.727497 0.686111i \(-0.240684\pi\)
\(488\) 2.68035i 0.121334i
\(489\) 6.49693 0.293801
\(490\) 12.6670 3.14730i 0.572237 0.142181i
\(491\) −27.0205 −1.21942 −0.609709 0.792625i \(-0.708714\pi\)
−0.609709 + 0.792625i \(0.708714\pi\)
\(492\) 7.60197i 0.342723i
\(493\) 1.84324i 0.0830156i
\(494\) 3.41855 0.153808
\(495\) 3.41855 + 13.7587i 0.153652 + 0.618409i
\(496\) 1.07838 0.0484206
\(497\) 3.05947i 0.137236i
\(498\) 0.894960i 0.0401041i
\(499\) 35.0349 1.56838 0.784189 0.620522i \(-0.213079\pi\)
0.784189 + 0.620522i \(0.213079\pi\)
\(500\) −7.46081 8.32684i −0.333658 0.372388i
\(501\) 20.9939 0.937936
\(502\) 21.8576i 0.975553i
\(503\) 29.5441i 1.31731i −0.752447 0.658653i \(-0.771126\pi\)
0.752447 0.658653i \(-0.228874\pi\)
\(504\) −1.07838 −0.0480348
\(505\) −10.5692 42.5380i −0.470322 1.89291i
\(506\) −40.1978 −1.78701
\(507\) 1.31351i 0.0583351i
\(508\) 0.921622i 0.0408904i
\(509\) −29.2183 −1.29508 −0.647539 0.762032i \(-0.724202\pi\)
−0.647539 + 0.762032i \(0.724202\pi\)
\(510\) −11.7587 + 2.92162i −0.520685 + 0.129372i
\(511\) −7.37298 −0.326161
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) −26.8781 −1.18554
\(515\) −25.5174 + 6.34017i −1.12443 + 0.279381i
\(516\) −11.1773 −0.492052
\(517\) 40.1978i 1.76790i
\(518\) 3.68649i 0.161975i
\(519\) 6.99386 0.306996
\(520\) −1.84324 7.41855i −0.0808316 0.325325i
\(521\) −16.3980 −0.718411 −0.359205 0.933259i \(-0.616952\pi\)
−0.359205 + 0.933259i \(0.616952\pi\)
\(522\) 0.340173i 0.0148890i
\(523\) 13.8432i 0.605323i −0.953098 0.302661i \(-0.902125\pi\)
0.953098 0.302661i \(-0.0978751\pi\)
\(524\) −10.6537 −0.465408
\(525\) 4.76487 2.52359i 0.207956 0.110139i
\(526\) −22.3402 −0.974078
\(527\) 5.84324i 0.254536i
\(528\) 6.34017i 0.275921i
\(529\) −17.1978 −0.747730
\(530\) 3.23513 + 13.0205i 0.140525 + 0.565575i
\(531\) 0.738205 0.0320354
\(532\) 1.07838i 0.0467536i
\(533\) 25.9877i 1.12565i
\(534\) 6.92162 0.299528
\(535\) −13.3607 + 3.31965i −0.577633 + 0.143521i
\(536\) −2.83710 −0.122544
\(537\) 4.73820i 0.204469i
\(538\) 17.3340i 0.747323i
\(539\) 37.0082 1.59406
\(540\) 2.17009 0.539189i 0.0933857 0.0232030i
\(541\) −5.20394 −0.223735 −0.111867 0.993723i \(-0.535683\pi\)
−0.111867 + 0.993723i \(0.535683\pi\)
\(542\) 13.3607i 0.573891i
\(543\) 12.0722i 0.518069i
\(544\) −5.41855 −0.232318
\(545\) 9.65983 + 38.8781i 0.413782 + 1.66536i
\(546\) 3.68649 0.157767
\(547\) 19.8843i 0.850191i −0.905149 0.425095i \(-0.860241\pi\)
0.905149 0.425095i \(-0.139759\pi\)
\(548\) 20.6225i 0.880949i
\(549\) 2.68035 0.114394
\(550\) −14.8371 28.0144i −0.632656 1.19454i
\(551\) −0.340173 −0.0144919
\(552\) 6.34017i 0.269856i
\(553\) 1.16290i 0.0494515i
\(554\) 0.738205 0.0313633
\(555\) −1.84324 7.41855i −0.0782414 0.314900i
\(556\) 18.8371 0.798871
\(557\) 17.0205i 0.721183i −0.932724 0.360591i \(-0.882575\pi\)
0.932724 0.360591i \(-0.117425\pi\)
\(558\) 1.07838i 0.0456514i
\(559\) 38.2101 1.61611
\(560\) 2.34017 0.581449i 0.0988904 0.0245707i
\(561\) −34.3545 −1.45045
\(562\) 31.7998i 1.34139i
\(563\) 12.6270i 0.532166i 0.963950 + 0.266083i \(0.0857294\pi\)
−0.963950 + 0.266083i \(0.914271\pi\)
\(564\) 6.34017 0.266969
\(565\) −28.6537 + 7.11942i −1.20547 + 0.299516i
\(566\) 4.70701 0.197850
\(567\) 1.07838i 0.0452876i
\(568\) 2.83710i 0.119042i
\(569\) 31.9155 1.33797 0.668983 0.743277i \(-0.266730\pi\)
0.668983 + 0.743277i \(0.266730\pi\)
\(570\) −0.539189 2.17009i −0.0225841 0.0908949i
\(571\) 24.5113 1.02577 0.512883 0.858458i \(-0.328577\pi\)
0.512883 + 0.858458i \(0.328577\pi\)
\(572\) 21.6742i 0.906244i
\(573\) 7.26180i 0.303366i
\(574\) −8.19779 −0.342169
\(575\) −14.8371 28.0144i −0.618750 1.16828i
\(576\) 1.00000 0.0416667
\(577\) 32.0000i 1.33218i 0.745873 + 0.666089i \(0.232033\pi\)
−0.745873 + 0.666089i \(0.767967\pi\)
\(578\) 12.3607i 0.514137i
\(579\) 18.8638 0.783951
\(580\) 0.183417 + 0.738205i 0.00761600 + 0.0306523i
\(581\) −0.965105 −0.0400393
\(582\) 3.65983i 0.151705i
\(583\) 38.0410i 1.57550i
\(584\) 6.83710 0.282921
\(585\) −7.41855 + 1.84324i −0.306719 + 0.0762088i
\(586\) −26.1978 −1.08222
\(587\) 8.58145i 0.354194i 0.984193 + 0.177097i \(0.0566707\pi\)
−0.984193 + 0.177097i \(0.943329\pi\)
\(588\) 5.83710i 0.240718i
\(589\) −1.07838 −0.0444338
\(590\) −1.60197 + 0.398032i −0.0659520 + 0.0163867i
\(591\) 17.7009 0.728116
\(592\) 3.41855i 0.140502i
\(593\) 10.7792i 0.442650i −0.975200 0.221325i \(-0.928962\pi\)
0.975200 0.221325i \(-0.0710382\pi\)
\(594\) 6.34017 0.260140
\(595\) 3.15061 + 12.6803i 0.129163 + 0.519844i
\(596\) −5.44521 −0.223045
\(597\) 0.313511i 0.0128312i
\(598\) 21.6742i 0.886324i
\(599\) 18.2101 0.744044 0.372022 0.928224i \(-0.378665\pi\)
0.372022 + 0.928224i \(0.378665\pi\)
\(600\) −4.41855 + 2.34017i −0.180387 + 0.0955372i
\(601\) −32.0410 −1.30698 −0.653491 0.756935i \(-0.726696\pi\)
−0.653491 + 0.756935i \(0.726696\pi\)
\(602\) 12.0533i 0.491257i
\(603\) 2.83710i 0.115536i
\(604\) 23.1194 0.940716
\(605\) −15.7431 63.3617i −0.640049 2.57602i
\(606\) −19.6020 −0.796276
\(607\) 11.5609i 0.469244i −0.972087 0.234622i \(-0.924615\pi\)
0.972087 0.234622i \(-0.0753852\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −0.366835 −0.0148649
\(610\) −5.81658 + 1.44521i −0.235507 + 0.0585150i
\(611\) −21.6742 −0.876844
\(612\) 5.41855i 0.219032i
\(613\) 2.58145i 0.104264i −0.998640 0.0521319i \(-0.983398\pi\)
0.998640 0.0521319i \(-0.0166016\pi\)
\(614\) 32.1978 1.29940
\(615\) 16.4969 4.09890i 0.665220 0.165283i
\(616\) 6.83710 0.275475
\(617\) 9.90110i 0.398603i 0.979938 + 0.199302i \(0.0638674\pi\)
−0.979938 + 0.199302i \(0.936133\pi\)
\(618\) 11.7587i 0.473005i
\(619\) −11.2039 −0.450324 −0.225162 0.974321i \(-0.572291\pi\)
−0.225162 + 0.974321i \(0.572291\pi\)
\(620\) 0.581449 + 2.34017i 0.0233516 + 0.0939836i
\(621\) 6.34017 0.254422
\(622\) 16.7382i 0.671141i
\(623\) 7.46412i 0.299044i
\(624\) −3.41855 −0.136852
\(625\) 14.0472 20.6803i 0.561887 0.827214i
\(626\) 14.1568 0.565818
\(627\) 6.34017i 0.253202i
\(628\) 9.73206i 0.388352i
\(629\) 18.5236 0.738584
\(630\) −0.581449 2.34017i −0.0231655 0.0932347i
\(631\) −23.3197 −0.928341 −0.464170 0.885746i \(-0.653647\pi\)
−0.464170 + 0.885746i \(0.653647\pi\)
\(632\) 1.07838i 0.0428956i
\(633\) 14.8371i 0.589722i
\(634\) −21.8843 −0.869136
\(635\) 2.00000 0.496928i 0.0793676 0.0197200i
\(636\) 6.00000 0.237915
\(637\) 19.9544i 0.790623i
\(638\) 2.15676i 0.0853868i
\(639\) 2.83710 0.112234
\(640\) −2.17009 + 0.539189i −0.0857802 + 0.0213133i
\(641\) −19.2885 −0.761848 −0.380924 0.924606i \(-0.624394\pi\)
−0.380924 + 0.924606i \(0.624394\pi\)
\(642\) 6.15676i 0.242988i
\(643\) 31.3751i 1.23731i 0.785662 + 0.618656i \(0.212323\pi\)
−0.785662 + 0.618656i \(0.787677\pi\)
\(644\) 6.83710 0.269420
\(645\) −6.02666 24.2557i −0.237300 0.955065i
\(646\) 5.41855 0.213190
\(647\) 33.2306i 1.30643i −0.757173 0.653215i \(-0.773420\pi\)
0.757173 0.653215i \(-0.226580\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −4.68035 −0.183720
\(650\) 15.1050 8.00000i 0.592468 0.313786i
\(651\) −1.16290 −0.0455776
\(652\) 6.49693i 0.254439i
\(653\) 7.85762i 0.307492i 0.988110 + 0.153746i \(0.0491338\pi\)
−0.988110 + 0.153746i \(0.950866\pi\)
\(654\) 17.9155 0.700551
\(655\) −5.74435 23.1194i −0.224450 0.903350i
\(656\) 7.60197 0.296807
\(657\) 6.83710i 0.266741i
\(658\) 6.83710i 0.266538i
\(659\) 25.4186 0.990166 0.495083 0.868846i \(-0.335138\pi\)
0.495083 + 0.868846i \(0.335138\pi\)
\(660\) −13.7587 + 3.41855i −0.535558 + 0.133067i
\(661\) 30.9093 1.20223 0.601117 0.799161i \(-0.294723\pi\)
0.601117 + 0.799161i \(0.294723\pi\)
\(662\) 26.1568i 1.01661i
\(663\) 18.5236i 0.719397i
\(664\) 0.894960 0.0347312
\(665\) −2.34017 + 0.581449i −0.0907480 + 0.0225476i
\(666\) −3.41855 −0.132466
\(667\) 2.15676i 0.0835099i
\(668\) 20.9939i 0.812277i
\(669\) −1.28846 −0.0498146
\(670\) −1.52973 6.15676i −0.0590988 0.237856i
\(671\) −16.9939 −0.656041
\(672\) 1.07838i 0.0415993i
\(673\) 27.9733i 1.07829i −0.842212 0.539146i \(-0.818747\pi\)
0.842212 0.539146i \(-0.181253\pi\)
\(674\) −29.7009 −1.14403
\(675\) 2.34017 + 4.41855i 0.0900733 + 0.170070i
\(676\) −1.31351 −0.0505197
\(677\) 4.15676i 0.159757i 0.996805 + 0.0798785i \(0.0254532\pi\)
−0.996805 + 0.0798785i \(0.974547\pi\)
\(678\) 13.2039i 0.507094i
\(679\) −3.94668 −0.151460
\(680\) −2.92162 11.7587i −0.112039 0.450926i
\(681\) 20.9939 0.804486
\(682\) 6.83710i 0.261806i
\(683\) 19.5708i 0.748855i −0.927256 0.374427i \(-0.877839\pi\)
0.927256 0.374427i \(-0.122161\pi\)
\(684\) −1.00000 −0.0382360
\(685\) −44.7526 + 11.1194i −1.70991 + 0.424851i
\(686\) −13.8432 −0.528538
\(687\) 2.36683i 0.0903004i
\(688\) 11.1773i 0.426130i
\(689\) −20.5113 −0.781418
\(690\) −13.7587 + 3.41855i −0.523786 + 0.130142i
\(691\) −10.8371 −0.412263 −0.206131 0.978524i \(-0.566087\pi\)
−0.206131 + 0.978524i \(0.566087\pi\)
\(692\) 6.99386i 0.265867i
\(693\) 6.83710i 0.259720i
\(694\) 23.4186 0.888956
\(695\) 10.1568 + 40.8781i 0.385268 + 1.55060i
\(696\) 0.340173 0.0128942
\(697\) 41.1917i 1.56025i
\(698\) 6.48255i 0.245368i
\(699\) −5.10504 −0.193090
\(700\) 2.52359 + 4.76487i 0.0953828 + 0.180095i
\(701\) −42.0098 −1.58669 −0.793345 0.608772i \(-0.791662\pi\)
−0.793345 + 0.608772i \(0.791662\pi\)
\(702\) 3.41855i 0.129025i
\(703\) 3.41855i 0.128933i
\(704\) −6.34017 −0.238954
\(705\) 3.41855 + 13.7587i 0.128750 + 0.518184i
\(706\) −2.58145 −0.0971541
\(707\) 21.1383i 0.794989i
\(708\) 0.738205i 0.0277434i
\(709\) −23.6209 −0.887101 −0.443550 0.896249i \(-0.646281\pi\)
−0.443550 + 0.896249i \(0.646281\pi\)
\(710\) −6.15676 + 1.52973i −0.231059 + 0.0574099i
\(711\) −1.07838 −0.0404423
\(712\) 6.92162i 0.259399i
\(713\) 6.83710i 0.256051i
\(714\) 5.84324 0.218678
\(715\) 47.0349 11.6865i 1.75901 0.437050i
\(716\) −4.73820 −0.177075
\(717\) 10.4124i 0.388858i
\(718\) 28.1399i 1.05017i
\(719\) −30.9770 −1.15525 −0.577624 0.816303i \(-0.696020\pi\)
−0.577624 + 0.816303i \(0.696020\pi\)
\(720\) 0.539189 + 2.17009i 0.0200944 + 0.0808743i
\(721\) 12.6803 0.472241
\(722\) 1.00000i 0.0372161i
\(723\) 3.36069i 0.124985i
\(724\) 12.0722 0.448661
\(725\) −1.50307 + 0.796064i −0.0558227 + 0.0295651i
\(726\) −29.1978 −1.08363
\(727\) 23.7464i 0.880707i −0.897825 0.440353i \(-0.854853\pi\)
0.897825 0.440353i \(-0.145147\pi\)
\(728\) 3.68649i 0.136630i
\(729\) −1.00000 −0.0370370
\(730\) 3.68649 + 14.8371i 0.136443 + 0.549146i
\(731\) 60.5646 2.24006
\(732\) 2.68035i 0.0990684i
\(733\) 41.9832i 1.55068i 0.631542 + 0.775342i \(0.282423\pi\)
−0.631542 + 0.775342i \(0.717577\pi\)
\(734\) 10.5548 0.389584
\(735\) 12.6670 3.14730i 0.467230 0.116090i
\(736\) −6.34017 −0.233702
\(737\) 17.9877i 0.662586i
\(738\) 7.60197i 0.279832i
\(739\) 41.3074 1.51952 0.759758 0.650206i \(-0.225317\pi\)
0.759758 + 0.650206i \(0.225317\pi\)
\(740\) 7.41855 1.84324i 0.272711 0.0677590i
\(741\) 3.41855 0.125584
\(742\) 6.47027i 0.237531i
\(743\) 28.3668i 1.04068i 0.853960 + 0.520339i \(0.174194\pi\)
−0.853960 + 0.520339i \(0.825806\pi\)
\(744\) 1.07838 0.0395352
\(745\) −2.93600 11.8166i −0.107567 0.432926i
\(746\) −17.8888 −0.654956
\(747\) 0.894960i 0.0327449i
\(748\) 34.3545i 1.25613i
\(749\) 6.63931 0.242595
\(750\) −7.46081 8.32684i −0.272430 0.304053i
\(751\) 5.75872 0.210139 0.105069 0.994465i \(-0.466494\pi\)
0.105069 + 0.994465i \(0.466494\pi\)
\(752\) 6.34017i 0.231202i
\(753\) 21.8576i 0.796536i
\(754\) −1.16290 −0.0423503
\(755\) 12.4657 + 50.1711i 0.453674 + 1.82591i
\(756\) −1.07838 −0.0392202
\(757\) 32.3090i 1.17429i 0.809482 + 0.587145i \(0.199748\pi\)
−0.809482 + 0.587145i \(0.800252\pi\)
\(758\) 4.36683i 0.158611i
\(759\) −40.1978 −1.45909
\(760\) 2.17009 0.539189i 0.0787173 0.0195584i
\(761\) 33.5708 1.21694 0.608470 0.793577i \(-0.291784\pi\)
0.608470 + 0.793577i \(0.291784\pi\)
\(762\) 0.921622i 0.0333869i
\(763\) 19.3197i 0.699418i
\(764\) 7.26180 0.262723
\(765\) −11.7587 + 2.92162i −0.425138 + 0.105631i
\(766\) −22.5236 −0.813810
\(767\) 2.52359i 0.0911216i
\(768\) 1.00000i 0.0360844i
\(769\) 17.8843 0.644924 0.322462 0.946582i \(-0.395490\pi\)
0.322462 + 0.946582i \(0.395490\pi\)
\(770\) 3.68649 + 14.8371i 0.132852 + 0.534692i
\(771\) −26.8781 −0.967993
\(772\) 18.8638i 0.678922i
\(773\) 46.5113i 1.67290i −0.548047 0.836448i \(-0.684628\pi\)
0.548047 0.836448i \(-0.315372\pi\)
\(774\) −11.1773 −0.401759
\(775\) −4.76487 + 2.52359i −0.171159 + 0.0906500i
\(776\) 3.65983 0.131380
\(777\) 3.68649i 0.132252i
\(778\) 9.07838i 0.325476i
\(779\) −7.60197 −0.272369
\(780\) −1.84324 7.41855i −0.0659987 0.265627i
\(781\) −17.9877 −0.643651
\(782\) 34.3545i 1.22852i
\(783\) 0.340173i 0.0121568i
\(784\) 5.83710 0.208468
\(785\) 21.1194 5.24742i 0.753784 0.187288i
\(786\) −10.6537 −0.380004
\(787\) 41.9877i 1.49670i 0.663304 + 0.748350i \(0.269154\pi\)
−0.663304 + 0.748350i \(0.730846\pi\)
\(788\) 1