Properties

Label 605.2.g.f.511.2
Level $605$
Weight $2$
Character 605.511
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.64000000.2
Defining polynomial: \(x^{8} + 2 x^{6} + 4 x^{4} + 8 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 511.2
Root \(-1.14412 + 0.831254i\) of defining polynomial
Character \(\chi\) \(=\) 605.511
Dual form 605.2.g.f.251.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.746033 + 2.29605i) q^{2} +(2.28825 + 1.66251i) q^{3} +(-3.09726 + 2.25029i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-2.11010 + 6.49422i) q^{6} +(1.61803 - 1.17557i) q^{7} +(-3.57117 - 2.59461i) q^{8} +(1.54508 + 4.75528i) q^{9} +O(q^{10})\) \(q+(0.746033 + 2.29605i) q^{2} +(2.28825 + 1.66251i) q^{3} +(-3.09726 + 2.25029i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-2.11010 + 6.49422i) q^{6} +(1.61803 - 1.17557i) q^{7} +(-3.57117 - 2.59461i) q^{8} +(1.54508 + 4.75528i) q^{9} -2.41421 q^{10} -10.8284 q^{12} +(-0.362036 - 1.11423i) q^{13} +(3.90628 + 2.83808i) q^{14} +(-2.28825 + 1.66251i) q^{15} +(0.927051 - 2.85317i) q^{16} +(2.11010 - 6.49422i) q^{17} +(-9.76570 + 7.09520i) q^{18} +(-1.18305 - 3.64105i) q^{20} +5.65685 q^{21} -2.82843 q^{23} +(-3.85816 - 11.8742i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(2.28825 - 1.66251i) q^{26} +(-1.74806 + 5.37999i) q^{27} +(-2.36610 + 7.28210i) q^{28} +(2.95846 - 2.14944i) q^{29} +(-5.52431 - 4.01365i) q^{30} -1.58579 q^{32} +16.4853 q^{34} +(0.618034 + 1.90211i) q^{35} +(-15.4863 - 11.2515i) q^{36} +(6.19453 - 4.50059i) q^{37} +(1.02399 - 3.15152i) q^{39} +(3.57117 - 2.59461i) q^{40} +(-4.85410 - 3.52671i) q^{41} +(4.22020 + 12.9884i) q^{42} -6.00000 q^{43} -5.00000 q^{45} +(-2.11010 - 6.49422i) q^{46} +(-2.28825 - 1.66251i) q^{47} +(6.86474 - 4.98752i) q^{48} +(-0.927051 + 2.85317i) q^{49} +(0.746033 - 2.29605i) q^{50} +(15.6251 - 11.3523i) q^{51} +(3.62867 + 2.63638i) q^{52} +(3.60217 + 11.0863i) q^{53} -13.6569 q^{54} -8.82843 q^{56} +(7.14235 + 5.18922i) q^{58} +(-1.34042 + 0.973874i) q^{59} +(3.34617 - 10.2984i) q^{60} +(-2.87809 + 8.85786i) q^{61} +(8.09017 + 5.87785i) q^{63} +(-3.03715 - 9.34739i) q^{64} +1.17157 q^{65} +12.4853 q^{67} +(8.07836 + 24.8626i) q^{68} +(-6.47214 - 4.70228i) q^{69} +(-3.90628 + 2.83808i) q^{70} +(3.49613 - 10.7600i) q^{71} +(6.82034 - 20.9908i) q^{72} +(0.947822 - 0.688633i) q^{73} +(14.9549 + 10.8654i) q^{74} +(-0.874032 - 2.68999i) q^{75} +8.00000 q^{78} +(1.23607 + 3.80423i) q^{79} +(2.42705 + 1.76336i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(4.47620 - 13.7763i) q^{82} +(-1.85410 + 5.70634i) q^{83} +(-17.5208 + 12.7296i) q^{84} +(5.52431 + 4.01365i) q^{85} +(-4.47620 - 13.7763i) q^{86} +10.3431 q^{87} -13.3137 q^{89} +(-3.73017 - 11.4803i) q^{90} +(-1.89564 - 1.37727i) q^{91} +(8.76038 - 6.36479i) q^{92} +(2.11010 - 6.49422i) q^{94} +(-3.62867 - 2.63638i) q^{96} +(1.13003 + 3.47788i) q^{97} -7.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - 6 q^{8} - 10 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - 6 q^{8} - 10 q^{9} - 8 q^{10} - 64 q^{12} + 8 q^{13} + 4 q^{14} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 2 q^{20} + 8 q^{24} - 2 q^{25} + 4 q^{28} - 4 q^{29} - 8 q^{30} - 24 q^{32} + 64 q^{34} - 4 q^{35} - 10 q^{36} + 4 q^{37} + 16 q^{39} + 6 q^{40} - 12 q^{41} - 16 q^{42} - 48 q^{43} - 40 q^{45} + 8 q^{46} + 6 q^{49} - 2 q^{50} + 16 q^{51} - 8 q^{52} - 12 q^{53} - 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} - 4 q^{61} + 20 q^{63} + 14 q^{64} + 32 q^{65} + 32 q^{67} - 24 q^{68} - 16 q^{69} - 4 q^{70} - 30 q^{72} + 8 q^{73} + 20 q^{74} + 64 q^{78} - 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} + 12 q^{83} - 32 q^{84} + 8 q^{85} + 12 q^{86} + 128 q^{87} - 16 q^{89} + 10 q^{90} - 16 q^{91} + 16 q^{92} - 8 q^{94} + 8 q^{96} + 4 q^{97} - 24 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.746033 + 2.29605i 0.527525 + 1.62356i 0.759268 + 0.650778i \(0.225557\pi\)
−0.231743 + 0.972777i \(0.574443\pi\)
\(3\) 2.28825 + 1.66251i 1.32112 + 0.959849i 0.999918 + 0.0128385i \(0.00408672\pi\)
0.321202 + 0.947011i \(0.395913\pi\)
\(4\) −3.09726 + 2.25029i −1.54863 + 1.12515i
\(5\) −0.309017 + 0.951057i −0.138197 + 0.425325i
\(6\) −2.11010 + 6.49422i −0.861445 + 2.65125i
\(7\) 1.61803 1.17557i 0.611559 0.444324i −0.238404 0.971166i \(-0.576624\pi\)
0.849963 + 0.526842i \(0.176624\pi\)
\(8\) −3.57117 2.59461i −1.26260 0.917333i
\(9\) 1.54508 + 4.75528i 0.515028 + 1.58509i
\(10\) −2.41421 −0.763441
\(11\) 0 0
\(12\) −10.8284 −3.12590
\(13\) −0.362036 1.11423i −0.100411 0.309032i 0.888215 0.459428i \(-0.151945\pi\)
−0.988626 + 0.150395i \(0.951945\pi\)
\(14\) 3.90628 + 2.83808i 1.04400 + 0.758508i
\(15\) −2.28825 + 1.66251i −0.590822 + 0.429258i
\(16\) 0.927051 2.85317i 0.231763 0.713292i
\(17\) 2.11010 6.49422i 0.511774 1.57508i −0.277301 0.960783i \(-0.589440\pi\)
0.789075 0.614297i \(-0.210560\pi\)
\(18\) −9.76570 + 7.09520i −2.30180 + 1.67235i
\(19\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(20\) −1.18305 3.64105i −0.264538 0.814164i
\(21\) 5.65685 1.23443
\(22\) 0 0
\(23\) −2.82843 −0.589768 −0.294884 0.955533i \(-0.595281\pi\)
−0.294884 + 0.955533i \(0.595281\pi\)
\(24\) −3.85816 11.8742i −0.787544 2.42381i
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) 2.28825 1.66251i 0.448762 0.326045i
\(27\) −1.74806 + 5.37999i −0.336415 + 1.03538i
\(28\) −2.36610 + 7.28210i −0.447151 + 1.37619i
\(29\) 2.95846 2.14944i 0.549372 0.399142i −0.278182 0.960528i \(-0.589732\pi\)
0.827554 + 0.561386i \(0.189732\pi\)
\(30\) −5.52431 4.01365i −1.00860 0.732789i
\(31\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(32\) −1.58579 −0.280330
\(33\) 0 0
\(34\) 16.4853 2.82720
\(35\) 0.618034 + 1.90211i 0.104467 + 0.321516i
\(36\) −15.4863 11.2515i −2.58105 1.87524i
\(37\) 6.19453 4.50059i 1.01837 0.739892i 0.0524248 0.998625i \(-0.483305\pi\)
0.965949 + 0.258733i \(0.0833050\pi\)
\(38\) 0 0
\(39\) 1.02399 3.15152i 0.163970 0.504648i
\(40\) 3.57117 2.59461i 0.564652 0.410244i
\(41\) −4.85410 3.52671i −0.758083 0.550780i 0.140238 0.990118i \(-0.455213\pi\)
−0.898322 + 0.439338i \(0.855213\pi\)
\(42\) 4.22020 + 12.9884i 0.651191 + 2.00416i
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) −5.00000 −0.745356
\(46\) −2.11010 6.49422i −0.311117 0.957521i
\(47\) −2.28825 1.66251i −0.333775 0.242502i 0.408256 0.912868i \(-0.366137\pi\)
−0.742031 + 0.670366i \(0.766137\pi\)
\(48\) 6.86474 4.98752i 0.990839 0.719887i
\(49\) −0.927051 + 2.85317i −0.132436 + 0.407596i
\(50\) 0.746033 2.29605i 0.105505 0.324711i
\(51\) 15.6251 11.3523i 2.18795 1.58964i
\(52\) 3.62867 + 2.63638i 0.503206 + 0.365600i
\(53\) 3.60217 + 11.0863i 0.494796 + 1.52282i 0.817275 + 0.576248i \(0.195484\pi\)
−0.322480 + 0.946576i \(0.604516\pi\)
\(54\) −13.6569 −1.85846
\(55\) 0 0
\(56\) −8.82843 −1.17975
\(57\) 0 0
\(58\) 7.14235 + 5.18922i 0.937836 + 0.681378i
\(59\) −1.34042 + 0.973874i −0.174508 + 0.126788i −0.671611 0.740904i \(-0.734397\pi\)
0.497103 + 0.867692i \(0.334397\pi\)
\(60\) 3.34617 10.2984i 0.431988 1.32952i
\(61\) −2.87809 + 8.85786i −0.368502 + 1.13413i 0.579257 + 0.815145i \(0.303343\pi\)
−0.947759 + 0.318988i \(0.896657\pi\)
\(62\) 0 0
\(63\) 8.09017 + 5.87785i 1.01927 + 0.740540i
\(64\) −3.03715 9.34739i −0.379644 1.16842i
\(65\) 1.17157 0.145316
\(66\) 0 0
\(67\) 12.4853 1.52532 0.762660 0.646800i \(-0.223893\pi\)
0.762660 + 0.646800i \(0.223893\pi\)
\(68\) 8.07836 + 24.8626i 0.979646 + 3.01504i
\(69\) −6.47214 4.70228i −0.779154 0.566088i
\(70\) −3.90628 + 2.83808i −0.466890 + 0.339215i
\(71\) 3.49613 10.7600i 0.414914 1.27697i −0.497414 0.867513i \(-0.665717\pi\)
0.912328 0.409461i \(-0.134283\pi\)
\(72\) 6.82034 20.9908i 0.803784 2.47379i
\(73\) 0.947822 0.688633i 0.110934 0.0805984i −0.530935 0.847413i \(-0.678159\pi\)
0.641869 + 0.766814i \(0.278159\pi\)
\(74\) 14.9549 + 10.8654i 1.73847 + 1.26307i
\(75\) −0.874032 2.68999i −0.100925 0.310614i
\(76\) 0 0
\(77\) 0 0
\(78\) 8.00000 0.905822
\(79\) 1.23607 + 3.80423i 0.139069 + 0.428009i 0.996201 0.0870877i \(-0.0277560\pi\)
−0.857132 + 0.515097i \(0.827756\pi\)
\(80\) 2.42705 + 1.76336i 0.271353 + 0.197149i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 4.47620 13.7763i 0.494313 1.52134i
\(83\) −1.85410 + 5.70634i −0.203514 + 0.626352i 0.796257 + 0.604959i \(0.206810\pi\)
−0.999771 + 0.0213936i \(0.993190\pi\)
\(84\) −17.5208 + 12.7296i −1.91167 + 1.38891i
\(85\) 5.52431 + 4.01365i 0.599196 + 0.435341i
\(86\) −4.47620 13.7763i −0.482681 1.48554i
\(87\) 10.3431 1.10890
\(88\) 0 0
\(89\) −13.3137 −1.41125 −0.705625 0.708585i \(-0.749334\pi\)
−0.705625 + 0.708585i \(0.749334\pi\)
\(90\) −3.73017 11.4803i −0.393194 1.21013i
\(91\) −1.89564 1.37727i −0.198718 0.144377i
\(92\) 8.76038 6.36479i 0.913333 0.663575i
\(93\) 0 0
\(94\) 2.11010 6.49422i 0.217640 0.669828i
\(95\) 0 0
\(96\) −3.62867 2.63638i −0.370349 0.269075i
\(97\) 1.13003 + 3.47788i 0.114737 + 0.353125i 0.991892 0.127083i \(-0.0405614\pi\)
−0.877155 + 0.480207i \(0.840561\pi\)
\(98\) −7.24264 −0.731617
\(99\) 0 0
\(100\) 3.82843 0.382843
\(101\) 2.87809 + 8.85786i 0.286381 + 0.881390i 0.985981 + 0.166856i \(0.0533615\pi\)
−0.699600 + 0.714534i \(0.746639\pi\)
\(102\) 37.7224 + 27.4069i 3.73507 + 2.71369i
\(103\) −5.52431 + 4.01365i −0.544327 + 0.395477i −0.825689 0.564125i \(-0.809214\pi\)
0.281363 + 0.959602i \(0.409214\pi\)
\(104\) −1.59810 + 4.91846i −0.156707 + 0.482294i
\(105\) −1.74806 + 5.37999i −0.170594 + 0.525033i
\(106\) −22.7675 + 16.5415i −2.21137 + 1.60666i
\(107\) −6.19453 4.50059i −0.598847 0.435088i 0.246622 0.969112i \(-0.420679\pi\)
−0.845470 + 0.534024i \(0.820679\pi\)
\(108\) −6.69234 20.5969i −0.643970 1.98194i
\(109\) −7.65685 −0.733394 −0.366697 0.930341i \(-0.619511\pi\)
−0.366697 + 0.930341i \(0.619511\pi\)
\(110\) 0 0
\(111\) 21.6569 2.05558
\(112\) −1.85410 5.70634i −0.175196 0.539198i
\(113\) −15.9027 11.5540i −1.49600 1.08691i −0.971940 0.235230i \(-0.924416\pi\)
−0.524063 0.851679i \(-0.675584\pi\)
\(114\) 0 0
\(115\) 0.874032 2.68999i 0.0815039 0.250843i
\(116\) −4.32624 + 13.3148i −0.401681 + 1.23625i
\(117\) 4.73911 3.44317i 0.438131 0.318321i
\(118\) −3.23607 2.35114i −0.297904 0.216440i
\(119\) −4.22020 12.9884i −0.386865 1.19065i
\(120\) 12.4853 1.13975
\(121\) 0 0
\(122\) −22.4853 −2.03572
\(123\) −5.24419 16.1400i −0.472853 1.45529i
\(124\) 0 0
\(125\) 0.809017 0.587785i 0.0723607 0.0525731i
\(126\) −7.46033 + 22.9605i −0.664619 + 2.04549i
\(127\) 1.34211 4.13058i 0.119093 0.366529i −0.873686 0.486490i \(-0.838277\pi\)
0.992779 + 0.119961i \(0.0382769\pi\)
\(128\) 16.6304 12.0827i 1.46994 1.06797i
\(129\) −13.7295 9.97505i −1.20881 0.878254i
\(130\) 0.874032 + 2.68999i 0.0766577 + 0.235928i
\(131\) −11.3137 −0.988483 −0.494242 0.869325i \(-0.664554\pi\)
−0.494242 + 0.869325i \(0.664554\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 9.31443 + 28.6669i 0.804644 + 2.47644i
\(135\) −4.57649 3.32502i −0.393882 0.286172i
\(136\) −24.3855 + 17.7171i −2.09104 + 1.51923i
\(137\) −3.39009 + 10.4336i −0.289635 + 0.891405i 0.695336 + 0.718685i \(0.255256\pi\)
−0.984971 + 0.172720i \(0.944744\pi\)
\(138\) 5.96826 18.3684i 0.508052 1.56362i
\(139\) 3.23607 2.35114i 0.274480 0.199421i −0.442026 0.897002i \(-0.645740\pi\)
0.716506 + 0.697581i \(0.245740\pi\)
\(140\) −6.19453 4.50059i −0.523533 0.380369i
\(141\) −2.47214 7.60845i −0.208191 0.640747i
\(142\) 27.3137 2.29212
\(143\) 0 0
\(144\) 15.0000 1.25000
\(145\) 1.13003 + 3.47788i 0.0938439 + 0.288822i
\(146\) 2.28825 + 1.66251i 0.189377 + 0.137590i
\(147\) −6.86474 + 4.98752i −0.566194 + 0.411364i
\(148\) −9.05843 + 27.8790i −0.744599 + 2.29164i
\(149\) 0.106038 0.326351i 0.00868696 0.0267357i −0.946619 0.322354i \(-0.895526\pi\)
0.955306 + 0.295619i \(0.0955258\pi\)
\(150\) 5.52431 4.01365i 0.451058 0.327713i
\(151\) 9.70820 + 7.05342i 0.790042 + 0.573999i 0.907976 0.419022i \(-0.137627\pi\)
−0.117934 + 0.993021i \(0.537627\pi\)
\(152\) 0 0
\(153\) 34.1421 2.76023
\(154\) 0 0
\(155\) 0 0
\(156\) 3.92028 + 12.0654i 0.313874 + 0.966004i
\(157\) 11.3262 + 8.22899i 0.903932 + 0.656745i 0.939473 0.342623i \(-0.111315\pi\)
−0.0355408 + 0.999368i \(0.511315\pi\)
\(158\) −7.81256 + 5.67616i −0.621534 + 0.451571i
\(159\) −10.1885 + 31.3569i −0.807998 + 2.48676i
\(160\) 0.490035 1.50817i 0.0387407 0.119232i
\(161\) −4.57649 + 3.32502i −0.360678 + 0.262048i
\(162\) −1.95314 1.41904i −0.153453 0.111490i
\(163\) 5.09423 + 15.6784i 0.399011 + 1.22803i 0.925794 + 0.378030i \(0.123398\pi\)
−0.526782 + 0.850000i \(0.676602\pi\)
\(164\) 22.9706 1.79370
\(165\) 0 0
\(166\) −14.4853 −1.12428
\(167\) −7.09829 21.8463i −0.549283 1.69052i −0.710584 0.703613i \(-0.751569\pi\)
0.161301 0.986905i \(-0.448431\pi\)
\(168\) −20.2016 14.6773i −1.55859 1.13238i
\(169\) 9.40678 6.83442i 0.723598 0.525725i
\(170\) −5.09423 + 15.6784i −0.390710 + 1.20248i
\(171\) 0 0
\(172\) 18.5836 13.5018i 1.41698 1.02950i
\(173\) 17.9134 + 13.0148i 1.36193 + 0.989499i 0.998320 + 0.0579465i \(0.0184553\pi\)
0.363608 + 0.931552i \(0.381545\pi\)
\(174\) 7.71633 + 23.7484i 0.584973 + 1.80036i
\(175\) −2.00000 −0.151186
\(176\) 0 0
\(177\) −4.68629 −0.352243
\(178\) −9.93247 30.5690i −0.744470 2.29124i
\(179\) −7.81256 5.67616i −0.583938 0.424256i 0.256204 0.966623i \(-0.417528\pi\)
−0.840142 + 0.542367i \(0.817528\pi\)
\(180\) 15.4863 11.2515i 1.15428 0.838635i
\(181\) 6.58630 20.2705i 0.489556 1.50670i −0.335717 0.941963i \(-0.608979\pi\)
0.825273 0.564735i \(-0.191021\pi\)
\(182\) 1.74806 5.37999i 0.129575 0.398791i
\(183\) −21.3121 + 15.4841i −1.57543 + 1.14462i
\(184\) 10.1008 + 7.33866i 0.744641 + 0.541014i
\(185\) 2.36610 + 7.28210i 0.173959 + 0.535391i
\(186\) 0 0
\(187\) 0 0
\(188\) 10.8284 0.789744
\(189\) 3.49613 + 10.7600i 0.254306 + 0.782673i
\(190\) 0 0
\(191\) −2.68085 + 1.94775i −0.193979 + 0.140934i −0.680536 0.732715i \(-0.738253\pi\)
0.486556 + 0.873649i \(0.338253\pi\)
\(192\) 8.59036 26.4384i 0.619956 1.90803i
\(193\) −0.362036 + 1.11423i −0.0260599 + 0.0802042i −0.963241 0.268640i \(-0.913426\pi\)
0.937181 + 0.348844i \(0.113426\pi\)
\(194\) −7.14235 + 5.18922i −0.512791 + 0.372564i
\(195\) 2.68085 + 1.94775i 0.191979 + 0.139481i
\(196\) −3.54915 10.9232i −0.253511 0.780225i
\(197\) −10.8284 −0.771493 −0.385747 0.922605i \(-0.626056\pi\)
−0.385747 + 0.922605i \(0.626056\pi\)
\(198\) 0 0
\(199\) 10.3431 0.733206 0.366603 0.930377i \(-0.380521\pi\)
0.366603 + 0.930377i \(0.380521\pi\)
\(200\) 1.36407 + 4.19817i 0.0964541 + 0.296855i
\(201\) 28.5694 + 20.7569i 2.01513 + 1.46408i
\(202\) −18.1910 + 13.2165i −1.27991 + 0.929911i
\(203\) 2.26006 6.95575i 0.158625 0.488198i
\(204\) −22.8491 + 70.3222i −1.59975 + 4.92354i
\(205\) 4.85410 3.52671i 0.339025 0.246316i
\(206\) −13.3369 9.68981i −0.929224 0.675121i
\(207\) −4.37016 13.4500i −0.303747 0.934838i
\(208\) −3.51472 −0.243702
\(209\) 0 0
\(210\) −13.6569 −0.942412
\(211\) −4.94427 15.2169i −0.340378 1.04757i −0.964012 0.265859i \(-0.914345\pi\)
0.623634 0.781716i \(-0.285655\pi\)
\(212\) −36.1043 26.2313i −2.47966 1.80158i
\(213\) 25.8885 18.8091i 1.77385 1.28878i
\(214\) 5.71227 17.5805i 0.390482 1.20178i
\(215\) 1.85410 5.70634i 0.126449 0.389169i
\(216\) 20.2016 14.6773i 1.37455 0.998666i
\(217\) 0 0
\(218\) −5.71227 17.5805i −0.386883 1.19070i
\(219\) 3.31371 0.223920
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 16.1567 + 49.7253i 1.08437 + 3.33734i
\(223\) 8.76038 + 6.36479i 0.586639 + 0.426218i 0.841111 0.540862i \(-0.181902\pi\)
−0.254473 + 0.967080i \(0.581902\pi\)
\(224\) −2.56586 + 1.86420i −0.171438 + 0.124557i
\(225\) 1.54508 4.75528i 0.103006 0.317019i
\(226\) 14.6647 45.1332i 0.975479 3.00222i
\(227\) −20.4792 + 14.8790i −1.35925 + 0.987556i −0.360762 + 0.932658i \(0.617483\pi\)
−0.998492 + 0.0548975i \(0.982517\pi\)
\(228\) 0 0
\(229\) 0.405958 + 1.24941i 0.0268265 + 0.0825634i 0.963573 0.267444i \(-0.0861791\pi\)
−0.936747 + 0.350007i \(0.886179\pi\)
\(230\) 6.82843 0.450253
\(231\) 0 0
\(232\) −16.1421 −1.05978
\(233\) −1.89802 5.84152i −0.124344 0.382691i 0.869437 0.494043i \(-0.164482\pi\)
−0.993781 + 0.111353i \(0.964482\pi\)
\(234\) 11.4412 + 8.31254i 0.747936 + 0.543408i
\(235\) 2.28825 1.66251i 0.149269 0.108450i
\(236\) 1.96014 6.03269i 0.127594 0.392695i
\(237\) −3.49613 + 10.7600i −0.227098 + 0.698936i
\(238\) 26.6737 19.3796i 1.72900 1.25619i
\(239\) 18.8612 + 13.7035i 1.22003 + 0.886403i 0.996102 0.0882033i \(-0.0281125\pi\)
0.223926 + 0.974606i \(0.428113\pi\)
\(240\) 2.62210 + 8.06998i 0.169256 + 0.520915i
\(241\) 6.00000 0.386494 0.193247 0.981150i \(-0.438098\pi\)
0.193247 + 0.981150i \(0.438098\pi\)
\(242\) 0 0
\(243\) 14.1421 0.907218
\(244\) −11.0186 33.9117i −0.705392 2.17097i
\(245\) −2.42705 1.76336i −0.155059 0.112657i
\(246\) 33.1459 24.0819i 2.11330 1.53541i
\(247\) 0 0
\(248\) 0 0
\(249\) −13.7295 + 9.97505i −0.870070 + 0.632143i
\(250\) 1.95314 + 1.41904i 0.123527 + 0.0897479i
\(251\) 3.70820 + 11.4127i 0.234060 + 0.720362i 0.997245 + 0.0741818i \(0.0236345\pi\)
−0.763185 + 0.646180i \(0.776365\pi\)
\(252\) −38.2843 −2.41168
\(253\) 0 0
\(254\) 10.4853 0.657905
\(255\) 5.96826 + 18.3684i 0.373747 + 1.15028i
\(256\) 24.2467 + 17.6163i 1.51542 + 1.10102i
\(257\) 7.53495 5.47446i 0.470017 0.341487i −0.327431 0.944875i \(-0.606183\pi\)
0.797448 + 0.603388i \(0.206183\pi\)
\(258\) 12.6606 38.9653i 0.788215 2.42587i
\(259\) 4.73220 14.5642i 0.294044 0.904975i
\(260\) −3.62867 + 2.63638i −0.225040 + 0.163501i
\(261\) 14.7923 + 10.7472i 0.915620 + 0.665237i
\(262\) −8.44040 25.9769i −0.521450 1.60486i
\(263\) −10.9706 −0.676474 −0.338237 0.941061i \(-0.609831\pi\)
−0.338237 + 0.941061i \(0.609831\pi\)
\(264\) 0 0
\(265\) −11.6569 −0.716075
\(266\) 0 0
\(267\) −30.4650 22.1341i −1.86443 1.35459i
\(268\) −38.6702 + 28.0955i −2.36216 + 1.71621i
\(269\) 5.35023 16.4663i 0.326209 1.00397i −0.644683 0.764450i \(-0.723010\pi\)
0.970892 0.239519i \(-0.0769896\pi\)
\(270\) 4.22020 12.9884i 0.256833 0.790451i
\(271\) −5.91691 + 4.29889i −0.359427 + 0.261139i −0.752813 0.658234i \(-0.771304\pi\)
0.393386 + 0.919373i \(0.371304\pi\)
\(272\) −16.5729 12.0409i −1.00488 0.730090i
\(273\) −2.04798 6.30305i −0.123950 0.381478i
\(274\) −26.4853 −1.60003
\(275\) 0 0
\(276\) 30.6274 1.84355
\(277\) 2.11010 + 6.49422i 0.126784 + 0.390200i 0.994222 0.107345i \(-0.0342350\pi\)
−0.867438 + 0.497545i \(0.834235\pi\)
\(278\) 7.81256 + 5.67616i 0.468566 + 0.340433i
\(279\) 0 0
\(280\) 2.72813 8.39633i 0.163037 0.501777i
\(281\) 5.35023 16.4663i 0.319168 0.982298i −0.654837 0.755770i \(-0.727263\pi\)
0.974005 0.226528i \(-0.0727374\pi\)
\(282\) 15.6251 11.3523i 0.930462 0.676020i
\(283\) −26.3961 19.1779i −1.56909 1.14001i −0.928024 0.372521i \(-0.878493\pi\)
−0.641064 0.767488i \(-0.721507\pi\)
\(284\) 13.3847 + 41.1938i 0.794234 + 2.44440i
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) −2.45017 7.54086i −0.144378 0.444350i
\(289\) −23.9691 17.4146i −1.40995 1.02439i
\(290\) −7.14235 + 5.18922i −0.419413 + 0.304721i
\(291\) −3.19621 + 9.83692i −0.187365 + 0.576650i
\(292\) −1.38603 + 4.26576i −0.0811112 + 0.249634i
\(293\) 7.41996 5.39092i 0.433479 0.314941i −0.349560 0.936914i \(-0.613669\pi\)
0.783038 + 0.621973i \(0.213669\pi\)
\(294\) −16.5729 12.0409i −0.966554 0.702242i
\(295\) −0.511996 1.57576i −0.0298096 0.0917444i
\(296\) −33.7990 −1.96453
\(297\) 0 0
\(298\) 0.828427 0.0479895
\(299\) 1.02399 + 3.15152i 0.0592190 + 0.182257i
\(300\) 8.76038 + 6.36479i 0.505781 + 0.367471i
\(301\) −9.70820 + 7.05342i −0.559572 + 0.406553i
\(302\) −8.95240 + 27.5526i −0.515153 + 1.58548i
\(303\) −8.14048 + 25.0538i −0.467658 + 1.43930i
\(304\) 0 0
\(305\) −7.53495 5.47446i −0.431450 0.313467i
\(306\) 25.4712 + 78.3922i 1.45609 + 4.48138i
\(307\) −16.3431 −0.932753 −0.466376 0.884586i \(-0.654441\pi\)
−0.466376 + 0.884586i \(0.654441\pi\)
\(308\) 0 0
\(309\) −19.3137 −1.09872
\(310\) 0 0
\(311\) −3.79129 2.75453i −0.214984 0.156195i 0.475082 0.879942i \(-0.342419\pi\)
−0.690066 + 0.723746i \(0.742419\pi\)
\(312\) −11.8338 + 8.59778i −0.669959 + 0.486753i
\(313\) −0.405958 + 1.24941i −0.0229461 + 0.0706209i −0.961874 0.273493i \(-0.911821\pi\)
0.938928 + 0.344114i \(0.111821\pi\)
\(314\) −10.4445 + 32.1447i −0.589415 + 1.81403i
\(315\) −8.09017 + 5.87785i −0.455829 + 0.331179i
\(316\) −12.3891 9.00117i −0.696939 0.506355i
\(317\) −0.405958 1.24941i −0.0228009 0.0701739i 0.939009 0.343894i \(-0.111746\pi\)
−0.961810 + 0.273720i \(0.911746\pi\)
\(318\) −79.5980 −4.46363
\(319\) 0 0
\(320\) 9.82843 0.549426
\(321\) −6.69234 20.5969i −0.373530 1.14961i
\(322\) −11.0486 8.02730i −0.615716 0.447344i
\(323\) 0 0
\(324\) 1.18305 3.64105i 0.0657249 0.202281i
\(325\) −0.362036 + 1.11423i −0.0200821 + 0.0618065i
\(326\) −32.1981 + 23.3933i −1.78329 + 1.29563i
\(327\) −17.5208 12.7296i −0.968900 0.703947i
\(328\) 8.18440 + 25.1890i 0.451908 + 1.39083i
\(329\) −5.65685 −0.311872
\(330\) 0 0
\(331\) −7.31371 −0.401998 −0.200999 0.979591i \(-0.564419\pi\)
−0.200999 + 0.979591i \(0.564419\pi\)
\(332\) −7.09829 21.8463i −0.389570 1.19897i
\(333\) 30.9726 + 22.5029i 1.69729 + 1.23315i
\(334\) 44.8647 32.5961i 2.45489 1.78358i
\(335\) −3.85816 + 11.8742i −0.210794 + 0.648757i
\(336\) 5.24419 16.1400i 0.286094 0.880507i
\(337\) 16.5729 12.0409i 0.902786 0.655912i −0.0363944 0.999338i \(-0.511587\pi\)
0.939180 + 0.343425i \(0.111587\pi\)
\(338\) 22.7100 + 16.4998i 1.23526 + 0.897469i
\(339\) −17.1807 52.8768i −0.933129 2.87187i
\(340\) −26.1421 −1.41776
\(341\) 0 0
\(342\) 0 0
\(343\) 6.18034 + 19.0211i 0.333707 + 1.02704i
\(344\) 21.4270 + 15.5677i 1.15527 + 0.839352i
\(345\) 6.47214 4.70228i 0.348448 0.253162i
\(346\) −16.5188 + 50.8395i −0.888054 + 2.73315i
\(347\) 3.39009 10.4336i 0.181990 0.560106i −0.817894 0.575369i \(-0.804858\pi\)
0.999884 + 0.0152627i \(0.00485845\pi\)
\(348\) −32.0354 + 23.2751i −1.71728 + 1.24768i
\(349\) −21.8196 15.8529i −1.16798 0.848586i −0.177213 0.984172i \(-0.556708\pi\)
−0.990766 + 0.135586i \(0.956708\pi\)
\(350\) −1.49207 4.59211i −0.0797543 0.245458i
\(351\) 6.62742 0.353745
\(352\) 0 0
\(353\) 21.3137 1.13441 0.567207 0.823575i \(-0.308024\pi\)
0.567207 + 0.823575i \(0.308024\pi\)
\(354\) −3.49613 10.7600i −0.185817 0.571886i
\(355\) 9.15298 + 6.65003i 0.485790 + 0.352947i
\(356\) 41.2361 29.9597i 2.18551 1.58786i
\(357\) 11.9365 36.7369i 0.631748 1.94432i
\(358\) 7.20433 22.1727i 0.380761 1.17186i
\(359\) −0.555221 + 0.403392i −0.0293035 + 0.0212902i −0.602341 0.798239i \(-0.705765\pi\)
0.573037 + 0.819529i \(0.305765\pi\)
\(360\) 17.8559 + 12.9730i 0.941087 + 0.683740i
\(361\) −5.87132 18.0701i −0.309017 0.951057i
\(362\) 51.4558 2.70446
\(363\) 0 0
\(364\) 8.97056 0.470185
\(365\) 0.362036 + 1.11423i 0.0189498 + 0.0583216i
\(366\) −51.4518 37.3820i −2.68943 1.95399i
\(367\) 6.86474 4.98752i 0.358336 0.260347i −0.394022 0.919101i \(-0.628916\pi\)
0.752358 + 0.658755i \(0.228916\pi\)
\(368\) −2.62210 + 8.06998i −0.136686 + 0.420677i
\(369\) 9.27051 28.5317i 0.482603 1.48530i
\(370\) −14.9549 + 10.8654i −0.777469 + 0.564864i
\(371\) 18.8612 + 13.7035i 0.979224 + 0.711448i
\(372\) 0 0
\(373\) 35.7990 1.85360 0.926801 0.375554i \(-0.122547\pi\)
0.926801 + 0.375554i \(0.122547\pi\)
\(374\) 0 0
\(375\) 2.82843 0.146059
\(376\) 3.85816 + 11.8742i 0.198970 + 0.612366i
\(377\) −3.46605 2.51823i −0.178511 0.129696i
\(378\) −22.0973 + 16.0546i −1.13656 + 0.825759i
\(379\) 10.4005 32.0096i 0.534240 1.64422i −0.211046 0.977476i \(-0.567687\pi\)
0.745286 0.666745i \(-0.232313\pi\)
\(380\) 0 0
\(381\) 9.93818 7.22051i 0.509149 0.369918i
\(382\) −6.47214 4.70228i −0.331143 0.240590i
\(383\) −1.81018 5.57116i −0.0924959 0.284673i 0.894097 0.447873i \(-0.147818\pi\)
−0.986593 + 0.163200i \(0.947818\pi\)
\(384\) 58.1421 2.96705
\(385\) 0 0
\(386\) −2.82843 −0.143963
\(387\) −9.27051 28.5317i −0.471246 1.45035i
\(388\) −11.3262 8.22899i −0.575003 0.417764i
\(389\) −16.6879 + 12.1245i −0.846112 + 0.614736i −0.924071 0.382220i \(-0.875160\pi\)
0.0779595 + 0.996957i \(0.475160\pi\)
\(390\) −2.47214 + 7.60845i −0.125181 + 0.385269i
\(391\) −5.96826 + 18.3684i −0.301828 + 0.928931i
\(392\) 10.7135 7.78383i 0.541115 0.393143i
\(393\) −25.8885 18.8091i −1.30590 0.948795i
\(394\) −8.07836 24.8626i −0.406982 1.25256i
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) −9.31371 −0.467442 −0.233721 0.972304i \(-0.575090\pi\)
−0.233721 + 0.972304i \(0.575090\pi\)
\(398\) 7.71633 + 23.7484i 0.386785 + 1.19040i
\(399\) 0 0
\(400\) −2.42705 + 1.76336i −0.121353 + 0.0881678i
\(401\) −1.64203 + 5.05364i −0.0819989 + 0.252367i −0.983648 0.180102i \(-0.942357\pi\)
0.901649 + 0.432468i \(0.142357\pi\)
\(402\) −26.3452 + 81.0822i −1.31398 + 4.04401i
\(403\) 0 0
\(404\) −28.8470 20.9586i −1.43519 1.04273i
\(405\) −0.309017 0.951057i −0.0153552 0.0472584i
\(406\) 17.6569 0.876295
\(407\) 0 0
\(408\) −85.2548 −4.22074
\(409\) 0.318114 + 0.979053i 0.0157297 + 0.0484111i 0.958613 0.284711i \(-0.0918978\pi\)
−0.942884 + 0.333122i \(0.891898\pi\)
\(410\) 11.7188 + 8.51423i 0.578752 + 0.420488i
\(411\) −25.1033 + 18.2386i −1.23826 + 0.899646i
\(412\) 8.07836 24.8626i 0.397992 1.22489i
\(413\) −1.02399 + 3.15152i −0.0503874 + 0.155076i
\(414\) 27.6216 20.0682i 1.35753 0.986300i
\(415\) −4.85410 3.52671i −0.238278 0.173119i
\(416\) 0.574112 + 1.76693i 0.0281481 + 0.0866311i
\(417\) 11.3137 0.554035
\(418\) 0 0
\(419\) −25.6569 −1.25342 −0.626710 0.779253i \(-0.715599\pi\)
−0.626710 + 0.779253i \(0.715599\pi\)
\(420\) −6.69234 20.5969i −0.326553 1.00503i
\(421\) 4.85410 + 3.52671i 0.236574 + 0.171881i 0.699756 0.714382i \(-0.253292\pi\)
−0.463181 + 0.886264i \(0.653292\pi\)
\(422\) 31.2502 22.7046i 1.52124 1.10524i
\(423\) 4.37016 13.4500i 0.212484 0.653960i
\(424\) 15.9007 48.9374i 0.772208 2.37661i
\(425\) −5.52431 + 4.01365i −0.267969 + 0.194691i
\(426\) 62.5005 + 45.4093i 3.02816 + 2.20009i
\(427\) 5.75619 + 17.7157i 0.278561 + 0.857324i
\(428\) 29.3137 1.41693
\(429\) 0 0
\(430\) 14.4853 0.698542
\(431\) −3.49613 10.7600i −0.168403 0.518290i 0.830868 0.556469i \(-0.187844\pi\)
−0.999271 + 0.0381792i \(0.987844\pi\)
\(432\) 13.7295 + 9.97505i 0.660560 + 0.479925i
\(433\) 6.19453 4.50059i 0.297690 0.216284i −0.428907 0.903349i \(-0.641101\pi\)
0.726596 + 0.687065i \(0.241101\pi\)
\(434\) 0 0
\(435\) −3.19621 + 9.83692i −0.153246 + 0.471644i
\(436\) 23.7153 17.2302i 1.13576 0.825175i
\(437\) 0 0
\(438\) 2.47214 + 7.60845i 0.118123 + 0.363546i
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) −15.0000 −0.714286
\(442\) −5.96826 18.3684i −0.283881 0.873697i
\(443\) 21.7047 + 15.7694i 1.03122 + 0.749225i 0.968552 0.248810i \(-0.0800394\pi\)
0.0626669 + 0.998035i \(0.480039\pi\)
\(444\) −67.0770 + 48.7343i −3.18333 + 2.31283i
\(445\) 4.11416 12.6621i 0.195030 0.600241i
\(446\) −8.07836 + 24.8626i −0.382522 + 1.17728i
\(447\) 0.785202 0.570482i 0.0371388 0.0269829i
\(448\) −15.9027 11.5540i −0.751333 0.545876i
\(449\) 8.84636 + 27.2263i 0.417485 + 1.28489i 0.910009 + 0.414589i \(0.136075\pi\)
−0.492523 + 0.870299i \(0.663925\pi\)
\(450\) 12.0711 0.569036
\(451\) 0 0
\(452\) 75.2548 3.53969
\(453\) 10.4884 + 32.2799i 0.492787 + 1.51664i
\(454\) −49.4412 35.9211i −2.32039 1.68586i
\(455\) 1.89564 1.37727i 0.0888692 0.0645673i
\(456\) 0 0
\(457\) 0.149960 0.461530i 0.00701484 0.0215895i −0.947488 0.319792i \(-0.896387\pi\)
0.954503 + 0.298202i \(0.0963870\pi\)
\(458\) −2.56586 + 1.86420i −0.119895 + 0.0871085i
\(459\) 31.2502 + 22.7046i 1.45864 + 1.05976i
\(460\) 3.34617 + 10.2984i 0.156016 + 0.480168i
\(461\) 12.6274 0.588117 0.294059 0.955787i \(-0.404994\pi\)
0.294059 + 0.955787i \(0.404994\pi\)
\(462\) 0 0
\(463\) −6.14214 −0.285449 −0.142725 0.989762i \(-0.545586\pi\)
−0.142725 + 0.989762i \(0.545586\pi\)
\(464\) −3.39009 10.4336i −0.157381 0.484369i
\(465\) 0 0
\(466\) 11.9964 8.71593i 0.555725 0.403758i
\(467\) −4.58224 + 14.1027i −0.212041 + 0.652594i 0.787310 + 0.616557i \(0.211473\pi\)
−0.999350 + 0.0360364i \(0.988527\pi\)
\(468\) −6.93014 + 21.3288i −0.320346 + 0.985923i
\(469\) 20.2016 14.6773i 0.932824 0.677736i
\(470\) 5.52431 + 4.01365i 0.254818 + 0.185136i
\(471\) 12.2364 + 37.6599i 0.563826 + 1.73528i
\(472\) 7.31371 0.336641
\(473\) 0 0
\(474\) −27.3137 −1.25456
\(475\) 0 0
\(476\) 42.2989 + 30.7319i 1.93877 + 1.40860i
\(477\) −47.1530 + 34.2586i −2.15899 + 1.56860i
\(478\) −17.3928 + 53.5295i −0.795528 + 2.44838i
\(479\) −11.1246 + 34.2380i −0.508296 + 1.56438i 0.286861 + 0.957972i \(0.407388\pi\)
−0.795157 + 0.606403i \(0.792612\pi\)
\(480\) 3.62867 2.63638i 0.165625 0.120334i
\(481\) −7.25734 5.27276i −0.330906 0.240417i
\(482\) 4.47620 + 13.7763i 0.203885 + 0.627494i
\(483\) −16.0000 −0.728025
\(484\) 0 0
\(485\) −3.65685 −0.166049
\(486\) 10.5505 + 32.4711i 0.478580 + 1.47292i
\(487\) 19.8090 + 14.3921i 0.897632 + 0.652168i 0.937857 0.347023i \(-0.112807\pi\)
−0.0402248 + 0.999191i \(0.512807\pi\)
\(488\) 33.2609 24.1654i 1.50565 1.09392i
\(489\) −14.4087 + 44.3453i −0.651582 + 2.00536i
\(490\) 2.23810 6.88816i 0.101107 0.311175i
\(491\) 0.555221 0.403392i 0.0250568 0.0182048i −0.575186 0.818022i \(-0.695070\pi\)
0.600243 + 0.799818i \(0.295070\pi\)
\(492\) 52.5623 + 38.1887i 2.36969 + 1.72168i
\(493\) −7.71633 23.7484i −0.347526 1.06957i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.99226 21.5200i −0.313646 0.965302i
\(498\) −33.1459 24.0819i −1.48530 1.07914i
\(499\) −7.81256 + 5.67616i −0.349738 + 0.254100i −0.748759 0.662842i \(-0.769350\pi\)
0.399021 + 0.916942i \(0.369350\pi\)
\(500\) −1.18305 + 3.64105i −0.0529076 + 0.162833i
\(501\) 20.0770 61.7907i 0.896975 2.76060i
\(502\) −23.4377 + 17.0285i −1.04607 + 0.760018i
\(503\) −13.4519 9.77335i −0.599789 0.435772i 0.246015 0.969266i \(-0.420879\pi\)
−0.845804 + 0.533494i \(0.820879\pi\)
\(504\) −13.6407 41.9817i −0.607604 1.87001i
\(505\) −9.31371 −0.414455
\(506\) 0 0
\(507\) 32.8873 1.46058
\(508\) 5.13815 + 15.8136i 0.227969 + 0.701616i
\(509\) 10.7710 + 7.82560i 0.477417 + 0.346864i 0.800325 0.599567i \(-0.204660\pi\)
−0.322908 + 0.946430i \(0.604660\pi\)
\(510\) −37.7224 + 27.4069i −1.67037 + 1.21360i
\(511\) 0.724072 2.22846i 0.0320311 0.0985814i
\(512\) −9.65451 + 29.7135i −0.426673 + 1.31316i
\(513\) 0 0
\(514\) 18.1910 + 13.2165i 0.802369 + 0.582956i
\(515\) −2.11010 6.49422i −0.0929821 0.286170i
\(516\) 64.9706 2.86017
\(517\) 0 0
\(518\) 36.9706 1.62439
\(519\) 19.3529 + 59.5622i 0.849500 + 2.61449i
\(520\) −4.18389 3.03977i −0.183476 0.133303i
\(521\) −20.4792 + 14.8790i −0.897211 + 0.651862i −0.937748 0.347316i \(-0.887093\pi\)
0.0405372 + 0.999178i \(0.487093\pi\)
\(522\) −13.6407 + 41.9817i −0.597036 + 1.83749i
\(523\) −12.8545 + 39.5620i −0.562087 + 1.72993i 0.114364 + 0.993439i \(0.463517\pi\)
−0.676451 + 0.736488i \(0.736483\pi\)
\(524\) 35.0415 25.4592i 1.53080 1.11219i
\(525\) −4.57649 3.32502i −0.199734 0.145116i
\(526\) −8.18440 25.1890i −0.356857 1.09829i
\(527\) 0 0
\(528\) 0 0
\(529\) −15.0000 −0.652174
\(530\) −8.69640 26.7648i −0.377747 1.16259i
\(531\) −6.70212 4.86937i −0.290847 0.211313i
\(532\) 0 0
\(533\) −2.17222 + 6.68539i −0.0940891 + 0.289576i
\(534\) 28.0933 86.4622i 1.21571 3.74158i
\(535\) 6.19453 4.50059i 0.267813 0.194577i
\(536\) −44.5871 32.3944i −1.92587 1.39923i
\(537\) −8.44040 25.9769i −0.364230 1.12099i
\(538\) 41.7990 1.80208
\(539\) 0 0
\(540\) 21.6569 0.931963
\(541\) 1.85410 + 5.70634i 0.0797141 + 0.245335i 0.982970 0.183768i \(-0.0588297\pi\)
−0.903255 + 0.429103i \(0.858830\pi\)
\(542\) −14.2847 10.3784i −0.613580 0.445792i
\(543\) 48.7710 35.4342i 2.09296 1.52063i
\(544\) −3.34617 + 10.2984i −0.143466 + 0.441542i
\(545\) 2.36610 7.28210i 0.101353 0.311931i
\(546\) 12.9443 9.40456i 0.553964 0.402478i
\(547\) 27.5066 + 19.9847i 1.17610 + 0.854484i 0.991726 0.128373i \(-0.0409754\pi\)
0.184370 + 0.982857i \(0.440975\pi\)
\(548\) −12.9787 39.9444i −0.554423 1.70634i
\(549\) −46.5685 −1.98750
\(550\) 0 0
\(551\) 0 0
\(552\) 10.9125 + 33.5853i 0.464468 + 1.42949i
\(553\) 6.47214 + 4.70228i 0.275223 + 0.199961i
\(554\) −13.3369 + 9.68981i −0.566629 + 0.411680i
\(555\) −6.69234 + 20.5969i −0.284074 + 0.874289i
\(556\) −4.73220 + 14.5642i −0.200690 + 0.617660i
\(557\) −7.97518 + 5.79431i −0.337919 + 0.245513i −0.743783 0.668421i \(-0.766971\pi\)
0.405864 + 0.913933i \(0.366971\pi\)
\(558\) 0 0
\(559\) 2.17222 + 6.68539i 0.0918749 + 0.282762i
\(560\) 6.00000 0.253546
\(561\) 0 0
\(562\) 41.7990 1.76318
\(563\) 0.106038 + 0.326351i 0.00446896 + 0.0137541i 0.953266 0.302132i \(-0.0976983\pi\)
−0.948797 + 0.315886i \(0.897698\pi\)
\(564\) 24.7781 + 18.0023i 1.04335 + 0.758035i
\(565\) 15.9027 11.5540i 0.669033 0.486081i
\(566\) 24.3411 74.9143i 1.02313 3.14888i
\(567\) −0.618034 + 1.90211i −0.0259550 + 0.0798812i
\(568\) −40.4032 + 29.3547i −1.69528 + 1.23169i
\(569\) −25.6109 18.6074i −1.07367 0.780064i −0.0970985 0.995275i \(-0.530956\pi\)
−0.976568 + 0.215211i \(0.930956\pi\)
\(570\) 0 0
\(571\) −21.9411 −0.918208 −0.459104 0.888383i \(-0.651829\pi\)
−0.459104 + 0.888383i \(0.651829\pi\)
\(572\) 0 0
\(573\) −9.37258 −0.391545
\(574\) −8.95240 27.5526i −0.373666 1.15003i
\(575\) 2.28825 + 1.66251i 0.0954264 + 0.0693314i
\(576\) 39.7568 28.8850i 1.65653 1.20354i
\(577\) −8.33436 + 25.6505i −0.346964 + 1.06785i 0.613560 + 0.789648i \(0.289737\pi\)
−0.960524 + 0.278197i \(0.910263\pi\)
\(578\) 22.1030 68.0261i 0.919365 2.82951i
\(579\) −2.68085 + 1.94775i −0.111412 + 0.0809457i
\(580\) −11.3262 8.22899i −0.470296 0.341690i
\(581\) 3.70820 + 11.4127i 0.153842 + 0.473478i
\(582\) −24.9706 −1.03506
\(583\) 0 0
\(584\) −5.17157 −0.214001
\(585\) 1.81018 + 5.57116i 0.0748417 + 0.230339i
\(586\) 17.9134 + 13.0148i 0.739994 + 0.537637i
\(587\) 1.73302 1.25912i 0.0715296 0.0519693i −0.551446 0.834211i \(-0.685924\pi\)
0.622975 + 0.782241i \(0.285924\pi\)
\(588\) 10.0385 30.8953i 0.413981 1.27410i
\(589\) 0 0
\(590\) 3.23607 2.35114i 0.133227 0.0967949i
\(591\) −24.7781 18.0023i −1.01923 0.740517i
\(592\) −7.09829 21.8463i −0.291738 0.897878i
\(593\) 3.51472 0.144332 0.0721661 0.997393i \(-0.477009\pi\)
0.0721661 + 0.997393i \(0.477009\pi\)
\(594\) 0 0
\(595\) 13.6569 0.559876
\(596\) 0.405958 + 1.24941i 0.0166287 + 0.0511779i
\(597\) 23.6677 + 17.1956i 0.968653 + 0.703767i
\(598\) −6.47214 + 4.70228i −0.264665 + 0.192291i
\(599\) −1.74806 + 5.37999i −0.0714240 + 0.219820i −0.980396 0.197036i \(-0.936868\pi\)
0.908972 + 0.416857i \(0.136868\pi\)
\(600\) −3.85816 + 11.8742i −0.157509 + 0.484763i
\(601\) −19.3688 + 14.0722i −0.790069 + 0.574019i −0.907984 0.419005i \(-0.862379\pi\)
0.117915 + 0.993024i \(0.462379\pi\)
\(602\) −23.4377 17.0285i −0.955248 0.694029i
\(603\) 19.2908 + 59.3710i 0.785583 + 2.41778i
\(604\) −45.9411 −1.86932
\(605\) 0 0
\(606\) −63.5980 −2.58349
\(607\) 11.8305 + 36.4105i 0.480185 + 1.47786i 0.838835 + 0.544385i \(0.183237\pi\)
−0.358651 + 0.933472i \(0.616763\pi\)
\(608\) 0 0
\(609\) 16.7356 12.1591i 0.678159 0.492711i
\(610\) 6.94833 21.3848i 0.281330 0.865844i
\(611\) −1.02399 + 3.15152i −0.0414263 + 0.127497i
\(612\) −105.747 + 76.8298i −4.27458 + 3.10566i
\(613\) 20.5942 + 14.9626i 0.831792 + 0.604333i 0.920066 0.391764i \(-0.128135\pi\)
−0.0882735 + 0.996096i \(0.528135\pi\)
\(614\) −12.1925 37.5247i −0.492050 1.51438i
\(615\) 16.9706 0.684319
\(616\) 0 0
\(617\) 0.343146 0.0138145 0.00690726 0.999976i \(-0.497801\pi\)
0.00690726 + 0.999976i \(0.497801\pi\)
\(618\) −14.4087 44.3453i −0.579601 1.78383i
\(619\) 11.6038 + 8.43069i 0.466398 + 0.338858i 0.796036 0.605249i \(-0.206927\pi\)
−0.329638 + 0.944107i \(0.606927\pi\)
\(620\) 0 0
\(621\) 4.94427 15.2169i 0.198407 0.610633i
\(622\) 3.49613 10.7600i 0.140182 0.431436i
\(623\) −21.5420 + 15.6512i −0.863063 + 0.627052i
\(624\) −8.04254 5.84325i −0.321959 0.233917i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) −3.17157 −0.126762
\(627\) 0 0
\(628\) −53.5980 −2.13879
\(629\) −16.1567 49.7253i −0.644211 1.98268i
\(630\) −19.5314 14.1904i −0.778150 0.565359i
\(631\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(632\) 5.45627 16.7927i 0.217039 0.667976i
\(633\) 13.9845 43.0399i 0.555834 1.71068i
\(634\) 2.56586 1.86420i 0.101903 0.0740370i
\(635\) 3.51368 + 2.55284i 0.139436 + 0.101306i
\(636\) −39.0058 120.047i −1.54668 4.76019i
\(637\) 3.51472 0.139258
\(638\) 0 0
\(639\) 56.5685 2.23782
\(640\) 6.35226 + 19.5502i 0.251095 + 0.772791i
\(641\) −24.2705 17.6336i −0.958628 0.696484i −0.00579592 0.999983i \(-0.501845\pi\)
−0.952832 + 0.303500i \(0.901845\pi\)
\(642\) 42.2989 30.7319i 1.66940 1.21289i
\(643\) −0.449881 + 1.38459i −0.0177416 + 0.0546029i −0.959535 0.281588i \(-0.909139\pi\)
0.941794 + 0.336191i \(0.109139\pi\)
\(644\) 6.69234 20.5969i 0.263715 0.811631i
\(645\) 13.7295 9.97505i 0.540597 0.392767i
\(646\) 0 0
\(647\) 8.37828 + 25.7857i 0.329384 + 1.01374i 0.969422 + 0.245398i \(0.0789185\pi\)
−0.640038 + 0.768343i \(0.721081\pi\)
\(648\) 4.41421 0.173407
\(649\) 0 0
\(650\) −2.82843 −0.110940
\(651\) 0 0
\(652\) −51.0592 37.0967i −1.99963 1.45282i
\(653\) −9.43059 + 6.85173i −0.369048 + 0.268129i −0.756816 0.653628i \(-0.773246\pi\)
0.387768 + 0.921757i \(0.373246\pi\)
\(654\) 16.1567 49.7253i 0.631778 1.94441i
\(655\) 3.49613 10.7600i 0.136605 0.420427i
\(656\) −14.5623 + 10.5801i −0.568563 + 0.413085i
\(657\) 4.73911 + 3.44317i 0.184890 + 0.134331i
\(658\) −4.22020 12.9884i −0.164521 0.506342i
\(659\) 45.9411 1.78961 0.894806 0.446455i \(-0.147314\pi\)
0.894806 + 0.446455i \(0.147314\pi\)
\(660\) 0 0
\(661\) 44.6274 1.73581 0.867903 0.496734i \(-0.165468\pi\)
0.867903 + 0.496734i \(0.165468\pi\)
\(662\) −5.45627 16.7927i −0.212064 0.652666i
\(663\) −18.3060 13.3001i −0.710945 0.516532i
\(664\) 21.4270 15.5677i 0.831531 0.604142i
\(665\) 0 0
\(666\) −28.5613 + 87.9027i −1.10673 + 3.40616i
\(667\) −8.36778 + 6.07955i −0.324002 + 0.235401i
\(668\) 71.1459 + 51.6905i 2.75272 + 1.99997i
\(669\) 9.46439 + 29.1284i 0.365915 + 1.12617i
\(670\) −30.1421 −1.16449
\(671\) 0 0
\(672\) −8.97056 −0.346047
\(673\) −3.85816 11.8742i −0.148721 0.457717i 0.848749 0.528795i \(-0.177356\pi\)
−0.997471 + 0.0710781i \(0.977356\pi\)
\(674\) 40.0106 + 29.0694i 1.54115 + 1.11971i
\(675\) 4.57649 3.32502i 0.176149 0.127980i
\(676\) −13.7558 + 42.3360i −0.529069 + 1.62831i
\(677\) 7.05437 21.7111i 0.271122 0.834426i −0.719098 0.694909i \(-0.755445\pi\)
0.990220 0.139518i \(-0.0445552\pi\)
\(678\) 108.591 78.8957i 4.17040 3.02997i
\(679\) 5.91691 + 4.29889i 0.227070 + 0.164976i
\(680\) −9.31443 28.6669i −0.357192 1.09932i
\(681\) −71.5980 −2.74364
\(682\) 0 0
\(683\) −7.79899 −0.298420 −0.149210 0.988806i \(-0.547673\pi\)
−0.149210 + 0.988806i \(0.547673\pi\)
\(684\) 0 0
\(685\) −8.87537 6.44833i −0.339111 0.246378i
\(686\) −39.0628 + 28.3808i −1.49142 + 1.08358i
\(687\) −1.14822 + 3.53387i −0.0438075 + 0.134825i
\(688\) −5.56231 + 17.1190i −0.212061 + 0.652656i
\(689\) 11.0486 8.02730i 0.420919 0.305816i
\(690\) 15.6251 + 11.3523i 0.594838 + 0.432175i
\(691\) −12.1486 37.3896i −0.462155 1.42237i −0.862526 0.506013i \(-0.831119\pi\)
0.400371 0.916353i \(-0.368881\pi\)
\(692\) −84.7696 −3.22245
\(693\) 0 0
\(694\) 26.4853 1.00537
\(695\) 1.23607 + 3.80423i 0.0468867 + 0.144303i
\(696\) −36.9372 26.8364i −1.40010 1.01723i
\(697\) −33.1459 + 24.0819i −1.25549 + 0.912167i
\(698\) 20.1209 61.9259i 0.761588 2.34393i
\(699\) 5.36842 16.5223i 0.203052 0.624931i
\(700\) 6.19453 4.50059i 0.234131 0.170106i
\(701\) 10.2158 + 7.42221i 0.385845 + 0.280333i 0.763751 0.645511i \(-0.223356\pi\)
−0.377906 + 0.925844i \(0.623356\pi\)
\(702\) 4.94427 + 15.2169i 0.186610 + 0.574325i
\(703\) 0 0
\(704\) 0 0
\(705\) 8.00000 0.301297
\(706\) 15.9007 + 48.9374i 0.598432 + 1.84178i
\(707\) 15.0699 + 10.9489i 0.566762 + 0.411777i
\(708\) 14.5147 10.5455i 0.545495 0.396325i
\(709\) 7.61029 23.4221i 0.285810 0.879634i −0.700344 0.713805i \(-0.746970\pi\)
0.986155 0.165829i \(-0.0530299\pi\)
\(710\) −8.44040 + 25.9769i −0.316763 + 0.974895i
\(711\) −16.1803 + 11.7557i −0.606810 + 0.440873i
\(712\) 47.5456 + 34.5439i 1.78185 + 1.29459i
\(713\) 0 0
\(714\) 93.2548 3.48997
\(715\) 0 0
\(716\) 36.9706 1.38165
\(717\) 20.3769 + 62.7137i 0.760990 + 2.34209i
\(718\) −1.34042 0.973874i −0.0500242 0.0363447i
\(719\) −14.8399 + 10.7818i −0.553436 + 0.402094i −0.829051 0.559174i \(-0.811118\pi\)
0.275615 + 0.961268i \(0.411118\pi\)
\(720\) −4.63525 + 14.2658i −0.172746 + 0.531657i
\(721\) −4.22020 + 12.9884i −0.157168 + 0.483715i
\(722\) 37.1097 26.9617i 1.38108 1.00341i
\(723\) 13.7295 + 9.97505i 0.510605 + 0.370976i
\(724\) 25.2152 + 77.6043i 0.937114 + 2.88414i
\(725\) −3.65685 −0.135812
\(726\) 0 0
\(727\) −19.5147 −0.723761 −0.361880 0.932225i \(-0.617865\pi\)
−0.361880 + 0.932225i \(0.617865\pi\)
\(728\) 3.19621 + 9.83692i 0.118459 + 0.364580i
\(729\) 34.7877 + 25.2748i 1.28843 + 0.936102i
\(730\) −2.28825 + 1.66251i −0.0846918 + 0.0615322i
\(731\) −12.6606 + 38.9653i −0.468269 + 1.44118i
\(732\) 31.1652 95.9167i 1.15190 3.54518i
\(733\) 14.1221 10.2603i 0.521611 0.378972i −0.295600 0.955312i \(-0.595519\pi\)
0.817210 + 0.576340i \(0.195519\pi\)
\(734\) 16.5729 + 12.0409i 0.611718 + 0.444439i
\(735\) −2.62210 8.06998i −0.0967175 0.297666i
\(736\) 4.48528 0.165330
\(737\) 0 0
\(738\) 72.4264 2.66605
\(739\) 9.25232 + 28.4757i 0.340352 + 1.04750i 0.964025 + 0.265811i \(0.0856396\pi\)
−0.623673 + 0.781685i \(0.714360\pi\)
\(740\) −23.7153 17.2302i −0.871791 0.633393i
\(741\) 0 0
\(742\) −17.3928 + 53.5295i −0.638510 + 1.96513i
\(743\) −15.3266 + 47.1705i −0.562279 + 1.73052i 0.113621 + 0.993524i \(0.463755\pi\)
−0.675900 + 0.736993i \(0.736245\pi\)
\(744\) 0 0
\(745\) 0.277611 + 0.201696i 0.0101709 + 0.00738957i
\(746\) 26.7072 + 82.1964i 0.977821 + 3.00942i
\(747\) −30.0000 −1.09764
\(748\) 0 0
\(749\) −15.3137 −0.559551
\(750\) 2.11010 + 6.49422i 0.0770500 + 0.237135i
\(751\) 12.9443 + 9.40456i 0.472343 + 0.343177i 0.798354 0.602189i \(-0.205705\pi\)
−0.326011 + 0.945366i \(0.605705\pi\)
\(752\) −6.86474 + 4.98752i −0.250331 + 0.181876i
\(753\) −10.4884 + 32.2799i −0.382218 + 1.17635i
\(754\) 3.19621 9.83692i 0.116399 0.358239i
\(755\) −9.70820 + 7.05342i −0.353318 + 0.256700i
\(756\) −35.0415 25.4592i −1.27445 0.925941i
\(757\) 4.11416 + 12.6621i 0.149532 + 0.460211i 0.997566 0.0697302i \(-0.0222138\pi\)
−0.848034 + 0.529942i \(0.822214\pi\)
\(758\) 81.2548 2.95131
\(759\) 0 0
\(760\) 0 0
\(761\) −9.27051 28.5317i −0.336056 1.03427i −0.966200 0.257795i \(-0.917004\pi\)
0.630144 0.776478i \(-0.282996\pi\)
\(762\) 23.9929 + 17.4319i 0.869171 + 0.631490i
\(763\) −12.3891 + 9.00117i −0.448514 + 0.325864i
\(764\) 3.92028 12.0654i 0.141831 0.436510i
\(765\) −10.5505 + 32.4711i −0.381454 + 1.17400i
\(766\) 11.4412 8.31254i 0.413388 0.300344i
\(767\) 1.57040 + 1.14096i 0.0567040 + 0.0411979i
\(768\) 26.1952 + 80.6206i 0.945239 + 2.90915i
\(769\) −18.9706 −0.684096 −0.342048 0.939682i \(-0.611121\pi\)
−0.342048 + 0.939682i \(0.611121\pi\)
\(770\) 0 0
\(771\) 26.3431 0.948725
\(772\) −1.38603 4.26576i −0.0498842 0.153528i
\(773\) −21.2644 15.4495i −0.764828 0.555680i 0.135559 0.990769i \(-0.456717\pi\)
−0.900387 + 0.435089i \(0.856717\pi\)
\(774\) 58.5942 42.5712i 2.10612 1.53019i
\(775\) 0 0
\(776\) 4.98819 15.3521i 0.179066 0.551108i
\(777\) 35.0415 25.4592i 1.25711 0.913342i
\(778\) −40.2882 29.2711i −1.44440 1.04942i
\(779\) 0 0
\(780\) −12.6863 −0.454242