Properties

Label 605.2.g.l.251.1
Level $605$
Weight $2$
Character 605.251
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 251.1
Root \(1.14412 - 0.831254i\) of defining polynomial
Character \(\chi\) \(=\) 605.251
Dual form 605.2.g.l.511.1

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + 6q^{8} - 10q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + 6q^{8} - 10q^{9} + 8q^{10} - 64q^{12} - 8q^{13} + 4q^{14} - 6q^{16} + 8q^{17} + 10q^{18} + 2q^{20} - 8q^{24} - 2q^{25} - 4q^{28} + 4q^{29} + 8q^{30} + 24q^{32} + 64q^{34} + 4q^{35} - 10q^{36} + 4q^{37} - 16q^{39} - 6q^{40} + 12q^{41} - 16q^{42} + 48q^{43} - 40q^{45} - 8q^{46} + 6q^{49} + 2q^{50} - 16q^{51} + 8q^{52} - 12q^{53} + 64q^{54} - 48q^{56} + 12q^{58} + 8q^{59} - 16q^{60} + 4q^{61} - 20q^{63} + 14q^{64} - 32q^{65} + 32q^{67} + 24q^{68} - 16q^{69} - 4q^{70} + 30q^{72} - 8q^{73} - 20q^{74} + 64q^{78} + 8q^{79} + 6q^{80} - 2q^{81} - 12q^{82} - 12q^{83} + 32q^{84} - 8q^{85} + 12q^{86} - 128q^{87} - 16q^{89} - 10q^{90} - 16q^{91} + 16q^{92} + 8q^{94} - 8q^{96} + 4q^{97} + 24q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 0.231743 + 0.972777i \(0.425557\pi\)
−0.759268 + 0.650778i \(0.774443\pi\)
\(3\) 2.28825 1.66251i 1.32112 0.959849i 0.321202 0.947011i \(-0.395913\pi\)
0.999918 0.0128385i \(-0.00408672\pi\)
\(4\) −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 \(-0.423376\pi\)
−0.849963 + 0.526842i \(0.823376\pi\)
\(8\) 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 \(-0.848055\pi\)
0.988626 + 0.150395i \(0.0480546\pi\)
\(14\) 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 −0.789075 0.614297i \(-0.789440\pi\)
0.277301 0.960783i \(-0.410560\pi\)
\(18\) 9.76570 + 7.09520i 2.30180 + 1.67235i
\(19\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(20\) −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 \(-0.410268\pi\)
−0.827554 + 0.561386i \(0.810268\pi\)
\(30\) 5.52431 4.01365i 1.00860 0.732789i
\(31\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(32\) 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 0.965949 0.258733i \(-0.0833050\pi\)
0.0524248 + 0.998625i \(0.483305\pi\)
\(38\) 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 \(-0.544787\pi\)
0.898322 + 0.439338i \(0.144787\pi\)
\(42\) 4.22020 12.9884i 0.651191 2.00416i
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 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 −0.742031 0.670366i \(-0.766137\pi\)
0.408256 + 0.912868i \(0.366137\pi\)
\(48\) 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 −0.322480 0.946576i \(-0.604516\pi\)
0.817275 0.576248i \(-0.195484\pi\)
\(54\) 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 0.497103 0.867692i \(-0.334397\pi\)
−0.671611 + 0.740904i \(0.734397\pi\)
\(60\) 3.34617 + 10.2984i 0.431988 + 1.32952i
\(61\) 2.87809 + 8.85786i 0.368502 + 1.13413i 0.947759 + 0.318988i \(0.103343\pi\)
−0.579257 + 0.815145i \(0.696657\pi\)
\(62\) 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 0.912328 + 0.409461i \(0.134283\pi\)
−0.497414 + 0.867513i \(0.665717\pi\)
\(72\) −6.82034 20.9908i −0.803784 2.47379i
\(73\) −0.947822 0.688633i −0.110934 0.0805984i 0.530935 0.847413i \(-0.321841\pi\)
−0.641869 + 0.766814i \(0.721841\pi\)
\(74\) −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 \(-0.972244\pi\)
0.857132 + 0.515097i \(0.172244\pi\)
\(80\) 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 0.999771 + 0.0213936i \(0.00681031\pi\)
−0.796257 + 0.604959i \(0.793190\pi\)
\(84\) 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 −0.877155 0.480207i \(-0.840561\pi\)
0.991892 + 0.127083i \(0.0405614\pi\)
\(98\) 7.24264 0.731617
\(99\) 0 0
\(100\) 3.82843 0.382843
\(101\) −2.87809 + 8.85786i −0.286381 + 0.881390i 0.699600 + 0.714534i \(0.253361\pi\)
−0.985981 + 0.166856i \(0.946639\pi\)
\(102\) 37.7224 27.4069i 3.73507 2.71369i
\(103\) −5.52431 4.01365i −0.544327 0.395477i 0.281363 0.959602i \(-0.409214\pi\)
−0.825689 + 0.564125i \(0.809214\pi\)
\(104\) −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 \(-0.579321\pi\)
0.845470 + 0.534024i \(0.179321\pi\)
\(108\) −6.69234 + 20.5969i −0.643970 + 1.98194i
\(109\) 7.65685 0.733394 0.366697 0.930341i \(-0.380489\pi\)
0.366697 + 0.930341i \(0.380489\pi\)
\(110\) 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 −0.524063 + 0.851679i \(0.675584\pi\)
−0.971940 + 0.235230i \(0.924416\pi\)
\(114\) 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 \(-0.161723\pi\)
−0.992779 + 0.119961i \(0.961723\pi\)
\(128\) −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 \(-0.335446\pi\)
0.494242 + 0.869325i \(0.335446\pi\)
\(132\) 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 −0.984971 0.172720i \(-0.944744\pi\)
0.695336 0.718685i \(-0.255256\pi\)
\(138\) −5.96826 18.3684i −0.508052 1.56362i
\(139\) −3.23607 2.35114i −0.274480 0.199421i 0.442026 0.897002i \(-0.354260\pi\)
−0.716506 + 0.697581i \(0.754260\pi\)
\(140\) 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 \(-0.104474\pi\)
−0.955306 + 0.295619i \(0.904474\pi\)
\(150\) −5.52431 4.01365i −0.451058 0.327713i
\(151\) −9.70820 + 7.05342i −0.790042 + 0.573999i −0.907976 0.419022i \(-0.862373\pi\)
0.117934 + 0.993021i \(0.462373\pi\)
\(152\) 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 −0.0355408 0.999368i \(-0.511315\pi\)
0.939473 + 0.342623i \(0.111315\pi\)
\(158\) −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 −0.526782 0.850000i \(-0.676602\pi\)
0.925794 0.378030i \(-0.123398\pi\)
\(164\) −22.9706 −1.79370
\(165\) 0 0
\(166\) −14.4853 −1.12428
\(167\) 7.09829 21.8463i 0.549283 1.69052i −0.161301 0.986905i \(-0.551569\pi\)
0.710584 0.703613i \(-0.248431\pi\)
\(168\) −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 −0.363608 + 0.931552i \(0.618455\pi\)
−0.998320 + 0.0579465i \(0.981545\pi\)
\(174\) 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 −0.840142 0.542367i \(-0.817528\pi\)
0.256204 + 0.966623i \(0.417528\pi\)
\(180\) 15.4863 + 11.2515i 1.15428 + 0.838635i
\(181\) 6.58630 + 20.2705i 0.489556 + 1.50670i 0.825273 + 0.564735i \(0.191021\pi\)
−0.335717 + 0.941963i \(0.608979\pi\)
\(182\) −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 0.486556 0.873649i \(-0.338253\pi\)
−0.680536 + 0.732715i \(0.738253\pi\)
\(192\) 8.59036 + 26.4384i 0.619956 + 1.90803i
\(193\) 0.362036 + 1.11423i 0.0260599 + 0.0802042i 0.963241 0.268640i \(-0.0865742\pi\)
−0.937181 + 0.348844i \(0.886574\pi\)
\(194\) 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 \(-0.373944\pi\)
0.385747 + 0.922605i \(0.373944\pi\)
\(198\) 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 −0.623634 0.781716i \(-0.714345\pi\)
0.964012 0.265859i \(-0.0856555\pi\)
\(212\) −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 −0.254473 0.967080i \(-0.581902\pi\)
0.841111 + 0.540862i \(0.181902\pi\)
\(224\) −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 0.998492 + 0.0548975i \(0.0174832\pi\)
0.360762 + 0.932658i \(0.382517\pi\)
\(228\) 0 0
\(229\) 0.405958 1.24941i 0.0268265 0.0825634i −0.936747 0.350007i \(-0.886179\pi\)
0.963573 + 0.267444i \(0.0861791\pi\)
\(230\) −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 \(-0.835518\pi\)
0.993781 + 0.111353i \(0.0355184\pi\)
\(234\) 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 \(-0.971887\pi\)
−0.223926 + 0.974606i \(0.571887\pi\)
\(240\) 2.62210 8.06998i 0.169256 0.520915i
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) 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 −0.763185 0.646180i \(-0.776365\pi\)
0.997245 0.0741818i \(-0.0236345\pi\)
\(252\) 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 0.797448 0.603388i \(-0.206183\pi\)
−0.327431 + 0.944875i \(0.606183\pi\)
\(258\) 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 \(-0.390169\pi\)
0.338237 + 0.941061i \(0.390169\pi\)
\(264\) 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 0.970892 + 0.239519i \(0.0769896\pi\)
−0.644683 + 0.764450i \(0.723010\pi\)
\(270\) −4.22020 12.9884i −0.256833 0.790451i
\(271\) 5.91691 + 4.29889i 0.359427 + 0.261139i 0.752813 0.658234i \(-0.228696\pi\)
−0.393386 + 0.919373i \(0.628696\pi\)
\(272\) 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 \(-0.965765\pi\)
0.867438 + 0.497545i \(0.165765\pi\)
\(278\) 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 −0.974005 0.226528i \(-0.927263\pi\)
0.654837 0.755770i \(-0.272737\pi\)
\(282\) −15.6251 11.3523i −0.930462 0.676020i
\(283\) 26.3961 19.1779i 1.56909 1.14001i 0.641064 0.767488i \(-0.278493\pi\)
0.928024 0.372521i \(-0.121507\pi\)
\(284\) 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 \(-0.386331\pi\)
−0.783038 + 0.621973i \(0.786331\pi\)
\(294\) 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 \(-0.345559\pi\)
0.466376 + 0.884586i \(0.345559\pi\)
\(308\) 0 0
\(309\) −19.3137 −1.09872
\(310\) 0 0
\(311\) −3.79129 + 2.75453i −0.214984 + 0.156195i −0.690066 0.723746i \(-0.742419\pi\)
0.475082 + 0.879942i \(0.342419\pi\)
\(312\) −11.8338 8.59778i −0.669959 0.486753i
\(313\) −0.405958 1.24941i −0.0229461 0.0706209i 0.938928 0.344114i \(-0.111821\pi\)
−0.961874 + 0.273493i \(0.911821\pi\)
\(314\) 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 −0.961810 0.273720i \(-0.911746\pi\)
0.939009 + 0.343894i \(0.111746\pi\)
\(318\) 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 \(-0.488413\pi\)
−0.939180 + 0.343425i \(0.888413\pi\)
\(338\) −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 \(-0.195142\pi\)
−0.999884 + 0.0152627i \(0.995142\pi\)
\(348\) 32.0354 + 23.2751i 1.71728 + 1.24768i
\(349\) 21.8196 15.8529i 1.16798 0.848586i 0.177213 0.984172i \(-0.443292\pi\)
0.990766 + 0.135586i \(0.0432918\pi\)
\(350\) −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 \(-0.294235\pi\)
−0.573037 + 0.819529i \(0.694235\pi\)
\(360\) −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 0.752358 0.658755i \(-0.228916\pi\)
−0.394022 + 0.919101i \(0.628916\pi\)
\(368\) −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 \(-0.877453\pi\)
−0.926801 + 0.375554i \(0.877453\pi\)
\(374\) 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 0.745286 + 0.666745i \(0.232313\pi\)
−0.211046 + 0.977476i \(0.567687\pi\)
\(380\) 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 −0.986593 0.163200i \(-0.947818\pi\)
0.894097 + 0.447873i \(0.147818\pi\)
\(384\) −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 0.0779595 0.996957i \(-0.475160\pi\)
−0.924071 + 0.382220i \(0.875160\pi\)
\(390\) −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 0.901649 0.432468i \(-0.142357\pi\)
−0.983648 + 0.180102i \(0.942357\pi\)
\(402\) 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 \(-0.908102\pi\)
0.942884 + 0.333122i \(0.108102\pi\)
\(410\) 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 −0.463181 0.886264i \(-0.653292\pi\)
0.699756 + 0.714382i \(0.253292\pi\)
\(422\) 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 \(-0.812156\pi\)
0.999271 + 0.0381792i \(0.0121558\pi\)
\(432\) 13.7295 9.97505i 0.660560 0.479925i
\(433\) 6.19453 + 4.50059i 0.297690 + 0.216284i 0.726596 0.687065i \(-0.241101\pi\)
−0.428907 + 0.903349i \(0.641101\pi\)
\(434\) 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 \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 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 0.0626669 0.998035i \(-0.480039\pi\)
0.968552 + 0.248810i \(0.0800394\pi\)
\(444\) −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 −0.492523 0.870299i \(-0.663925\pi\)
0.910009 0.414589i \(-0.136075\pi\)
\(450\) −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 \(-0.103613\pi\)
−0.954503 + 0.298202i \(0.903613\pi\)
\(458\) 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 \(-0.595006\pi\)
−0.294059 + 0.955787i \(0.595006\pi\)
\(462\) 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 −0.999350 0.0360364i \(-0.988527\pi\)
0.787310 0.616557i \(-0.211473\pi\)
\(468\) 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 0.795157 + 0.606403i \(0.207388\pi\)
−0.286861 + 0.957972i \(0.592612\pi\)
\(480\) −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 −0.0402248 0.999191i \(-0.512807\pi\)
0.937857 + 0.347023i \(0.112807\pi\)
\(488\) 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 \(-0.304930\pi\)
−0.600243 + 0.799818i \(0.704930\pi\)
\(492\) −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 0.399021 0.916942i \(-0.369350\pi\)
−0.748759 + 0.662842i \(0.769350\pi\)
\(500\) −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 \(-0.579121\pi\)
0.845804 + 0.533494i \(0.179121\pi\)
\(504\) −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 −0.322908 0.946430i \(-0.604660\pi\)
0.800325 + 0.599567i \(0.204660\pi\)
\(510\) −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 0.0405372 0.999178i \(-0.487093\pi\)
−0.937748 + 0.347316i \(0.887093\pi\)
\(522\) −13.6407 41.9817i −0.597036 1.83749i
\(523\) 12.8545 + 39.5620i 0.562087 + 1.72993i 0.676451 + 0.736488i \(0.263517\pi\)
−0.114364 + 0.993439i \(0.536483\pi\)
\(524\) −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 \(-0.941170\pi\)
0.903255 + 0.429103i \(0.141170\pi\)
\(542\) −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 \(-0.959025\pi\)
−0.184370 + 0.982857i \(0.559025\pi\)
\(548\) −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 \(-0.233029\pi\)
−0.405864 + 0.913933i \(0.633029\pi\)
\(558\) 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 \(-0.902302\pi\)
0.948797 + 0.315886i \(0.102302\pi\)
\(564\) 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 \(-0.469044\pi\)
0.976568 + 0.215211i \(0.0690438\pi\)
\(570\) 0 0
\(571\) 21.9411 0.918208 0.459104 0.888383i \(-0.348171\pi\)
0.459104 + 0.888383i \(0.348171\pi\)
\(572\) 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 −0.960524 0.278197i \(-0.910263\pi\)
0.613560 0.789648i \(-0.289737\pi\)
\(578\) −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 0.622975 0.782241i \(-0.285924\pi\)
−0.551446 + 0.834211i \(0.685924\pi\)
\(588\) 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 \(-0.522991\pi\)
−0.0721661 + 0.997393i \(0.522991\pi\)
\(594\) 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 0.908972 0.416857i \(-0.136868\pi\)
−0.980396 + 0.197036i \(0.936868\pi\)
\(600\) 3.85816 + 11.8742i 0.157509 + 0.484763i
\(601\) 19.3688 + 14.0722i 0.790069 + 0.574019i 0.907984 0.419005i \(-0.137621\pi\)
−0.117915 + 0.993024i \(0.537621\pi\)
\(602\) 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 0.358651 + 0.933472i \(0.383237\pi\)
−0.838835 + 0.544385i \(0.816763\pi\)
\(608\) 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 \(-0.871865\pi\)
0.0882735 + 0.996096i \(0.471865\pi\)
\(614\) −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 −0.329638 0.944107i \(-0.606927\pi\)
0.796036 + 0.605249i \(0.206927\pi\)
\(620\) 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 \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(632\) 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 −0.952832 0.303500i \(-0.901845\pi\)
−0.00579592 + 0.999983i \(0.501845\pi\)
\(642\) 42.2989 + 30.7319i 1.66940 + 1.21289i
\(643\) −0.449881 1.38459i −0.0177416 0.0546029i 0.941794 0.336191i \(-0.109139\pi\)
−0.959535 + 0.281588i \(0.909139\pi\)
\(644\) −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 −0.640038 0.768343i \(-0.721081\pi\)
0.969422 0.245398i \(-0.0789185\pi\)
\(648\) −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 0.387768 0.921757i \(-0.373246\pi\)
−0.756816 + 0.653628i \(0.773246\pi\)
\(654\) 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 \(-0.852686\pi\)
−0.894806 + 0.446455i \(0.852686\pi\)
\(660\) 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 \(-0.822644\pi\)
0.997471 + 0.0710781i \(0.0226440\pi\)
\(674\) 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 −0.990220 0.139518i \(-0.955445\pi\)
0.719098 0.694909i \(-0.244555\pi\)
\(678\) −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 0.400371 + 0.916353i \(0.368881\pi\)
−0.862526 + 0.506013i \(0.831119\pi\)
\(692\) 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 \(-0.776644\pi\)
0.377906 + 0.925844i \(0.376644\pi\)
\(702\) 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 0.986155 + 0.165829i \(0.0530299\pi\)
−0.700344 + 0.713805i \(0.746970\pi\)
\(710\) 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 0.275615 0.961268i \(-0.411118\pi\)
−0.829051 + 0.559174i \(0.811118\pi\)
\(720\) −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 \(-0.404481\pi\)
−0.817210 + 0.576340i \(0.804481\pi\)
\(734\) −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 0.623673 + 0.781685i \(0.285640\pi\)
−0.964025 + 0.265811i \(0.914360\pi\)
\(740\) −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 0.675900 + 0.736993i \(0.263755\pi\)
−0.113621 + 0.993524i \(0.536245\pi\)
\(744\) 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 −0.326011 0.945366i \(-0.605705\pi\)
0.798354 + 0.602189i \(0.205705\pi\)
\(752\) −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 −0.848034 0.529942i \(-0.822214\pi\)
0.997566 + 0.0697302i \(0.0222138\pi\)
\(758\) −81.2548 −2.95131
\(759\) 0 0
\(760\) 0 0
\(761\) 9.27051 28.5317i 0.336056 1.03427i −0.630144 0.776478i \(-0.717004\pi\)
0.966200 0.257795i \(-0.0829959\pi\)
\(762\) 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 \(-0.388879\pi\)
0.342048 + 0.939682i \(0.388879\pi\)
\(770\) 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 −0.900387 0.435089i \(-0.856717\pi\)
0.135559 + 0.990769i \(0.456717\pi\)
\(774\) 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