Properties

Label 91.2.e.c.53.2
Level $91$
Weight $2$
Character 91.53
Analytic conductor $0.727$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 53.2
Root \(-0.606661 - 1.05077i\) of defining polynomial
Character \(\chi\) \(=\) 91.53
Dual form 91.2.e.c.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.10666 - 1.91679i) q^{2} +(-1.23721 + 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(1.06140 + 1.83839i) q^{5} +5.47671 q^{6} +(2.63169 + 0.272389i) q^{7} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +O(q^{10})\) \(q+(-1.10666 - 1.91679i) q^{2} +(-1.23721 + 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(1.06140 + 1.83839i) q^{5} +5.47671 q^{6} +(2.63169 + 0.272389i) q^{7} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +(2.34921 - 4.06896i) q^{10} +(-2.39448 + 4.14736i) q^{11} +(-3.58643 - 6.21188i) q^{12} +1.00000 q^{13} +(-2.39028 - 5.34585i) q^{14} -5.25271 q^{15} +(0.697291 + 1.20774i) q^{16} +(1.88914 - 3.27208i) q^{17} +(-3.45588 + 5.98575i) q^{18} +(1.78362 + 3.08931i) q^{19} -6.15355 q^{20} +(-3.83967 + 5.30250i) q^{21} +10.5995 q^{22} +(-2.23721 - 3.87497i) q^{23} +(-2.46122 + 4.26295i) q^{24} +(0.246870 - 0.427591i) q^{25} +(-1.10666 - 1.91679i) q^{26} +0.303848 q^{27} +(-4.49818 + 6.21188i) q^{28} -5.90107 q^{29} +(5.81296 + 10.0683i) q^{30} +(1.88558 - 3.26592i) q^{31} +(3.53265 - 6.11873i) q^{32} +(-5.92496 - 10.2623i) q^{33} -8.36254 q^{34} +(2.29251 + 5.12720i) q^{35} +9.05234 q^{36} +(-2.81285 - 4.87200i) q^{37} +(3.94772 - 6.83765i) q^{38} +(-1.23721 + 2.14292i) q^{39} +(2.11146 + 3.65716i) q^{40} +10.3948 q^{41} +(14.4130 + 1.49180i) q^{42} +3.40733 q^{43} +(-6.94110 - 12.0223i) q^{44} +(3.31453 - 5.74093i) q^{45} +(-4.95168 + 8.57655i) q^{46} +(3.55438 + 6.15636i) q^{47} -3.45079 q^{48} +(6.85161 + 1.43369i) q^{49} -1.09280 q^{50} +(4.67454 + 8.09654i) q^{51} +(-1.44940 + 2.51043i) q^{52} +(6.19003 - 10.7214i) q^{53} +(-0.336257 - 0.582415i) q^{54} -10.1660 q^{55} +(5.23528 + 0.541869i) q^{56} -8.82686 q^{57} +(6.53049 + 11.3111i) q^{58} +(-2.39448 + 4.14736i) q^{59} +(7.61326 - 13.1865i) q^{60} +(-1.60348 - 2.77732i) q^{61} -8.34680 q^{62} +(-3.37246 - 7.54251i) q^{63} -12.8486 q^{64} +(1.06140 + 1.83839i) q^{65} +(-13.1139 + 22.7139i) q^{66} +(1.44978 - 2.51109i) q^{67} +(5.47622 + 9.48510i) q^{68} +11.0717 q^{69} +(7.29075 - 10.0683i) q^{70} -2.53876 q^{71} +(-3.10612 - 5.37996i) q^{72} +(-3.85035 + 6.66901i) q^{73} +(-6.22574 + 10.7833i) q^{74} +(0.610862 + 1.05804i) q^{75} -10.3407 q^{76} +(-7.43122 + 10.2623i) q^{77} +5.47671 q^{78} +(2.58925 + 4.48471i) q^{79} +(-1.48021 + 2.56379i) q^{80} +(4.30827 - 7.46214i) q^{81} +(-11.5035 - 19.9247i) q^{82} +3.46731 q^{83} +(-7.74633 - 17.3247i) q^{84} +8.02051 q^{85} +(-3.77076 - 6.53115i) q^{86} +(7.30089 - 12.6455i) q^{87} +(-4.76338 + 8.25042i) q^{88} +(-1.83216 - 3.17339i) q^{89} -14.6722 q^{90} +(2.63169 + 0.272389i) q^{91} +12.9704 q^{92} +(4.66574 + 8.08129i) q^{93} +(7.86698 - 13.6260i) q^{94} +(-3.78625 + 6.55798i) q^{95} +(8.74129 + 15.1404i) q^{96} -5.40733 q^{97} +(-4.83432 - 14.7197i) q^{98} +14.9549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{2} - 8q^{4} - 2q^{5} - 10q^{6} + q^{7} + 18q^{8} - 3q^{9} + O(q^{10}) \) \( 10q - 4q^{2} - 8q^{4} - 2q^{5} - 10q^{6} + q^{7} + 18q^{8} - 3q^{9} + 5q^{10} - 11q^{11} - 5q^{12} + 10q^{13} + 10q^{14} - 10q^{16} + 5q^{17} - 9q^{18} - 9q^{19} + 2q^{20} + 2q^{21} + 16q^{22} - 10q^{23} - 9q^{25} - 4q^{26} + 37q^{28} - 6q^{29} + 13q^{30} + 6q^{31} - 22q^{32} - 8q^{33} - 44q^{34} - 4q^{35} + 14q^{36} - 4q^{37} + 10q^{38} - 28q^{40} + 28q^{41} + 52q^{42} + 4q^{43} + 32q^{45} - 3q^{46} - q^{47} - 46q^{48} - 11q^{49} + 18q^{50} + 8q^{51} - 8q^{52} - 17q^{53} - 23q^{54} - 21q^{56} - 32q^{57} + 27q^{58} - 11q^{59} + 29q^{60} + 11q^{61} - 46q^{62} + 5q^{63} + 18q^{64} - 2q^{65} - 21q^{66} - 13q^{67} + 32q^{68} + 36q^{69} + 49q^{70} + 30q^{71} + 19q^{72} + 33q^{74} + 20q^{75} + 16q^{76} - 46q^{77} - 10q^{78} - 2q^{79} - 55q^{80} + 19q^{81} - 34q^{82} + 12q^{83} - 23q^{84} - 44q^{85} - 28q^{86} + 8q^{87} + 3q^{88} + 4q^{89} - 68q^{90} + q^{91} + 42q^{92} - 18q^{93} - 20q^{94} + 12q^{95} + 37q^{96} - 24q^{97} - 7q^{98} + 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10666 1.91679i −0.782527 1.35538i −0.930465 0.366381i \(-0.880597\pi\)
0.147938 0.988997i \(-0.452737\pi\)
\(3\) −1.23721 + 2.14292i −0.714306 + 1.23721i 0.248921 + 0.968524i \(0.419924\pi\)
−0.963227 + 0.268690i \(0.913409\pi\)
\(4\) −1.44940 + 2.51043i −0.724699 + 1.25521i
\(5\) 1.06140 + 1.83839i 0.474671 + 0.822155i 0.999579 0.0290040i \(-0.00923354\pi\)
−0.524908 + 0.851159i \(0.675900\pi\)
\(6\) 5.47671 2.23586
\(7\) 2.63169 + 0.272389i 0.994686 + 0.102953i
\(8\) 1.98932 0.703331
\(9\) −1.56140 2.70442i −0.520466 0.901473i
\(10\) 2.34921 4.06896i 0.742887 1.28672i
\(11\) −2.39448 + 4.14736i −0.721962 + 1.25048i 0.238250 + 0.971204i \(0.423426\pi\)
−0.960212 + 0.279272i \(0.909907\pi\)
\(12\) −3.58643 6.21188i −1.03531 1.79321i
\(13\) 1.00000 0.277350
\(14\) −2.39028 5.34585i −0.638829 1.42874i
\(15\) −5.25271 −1.35624
\(16\) 0.697291 + 1.20774i 0.174323 + 0.301936i
\(17\) 1.88914 3.27208i 0.458183 0.793597i −0.540682 0.841227i \(-0.681834\pi\)
0.998865 + 0.0476304i \(0.0151670\pi\)
\(18\) −3.45588 + 5.98575i −0.814558 + 1.41086i
\(19\) 1.78362 + 3.08931i 0.409190 + 0.708737i 0.994799 0.101856i \(-0.0324781\pi\)
−0.585609 + 0.810593i \(0.699145\pi\)
\(20\) −6.15355 −1.37597
\(21\) −3.83967 + 5.30250i −0.837886 + 1.15710i
\(22\) 10.5995 2.25982
\(23\) −2.23721 3.87497i −0.466491 0.807987i 0.532776 0.846256i \(-0.321149\pi\)
−0.999267 + 0.0382695i \(0.987815\pi\)
\(24\) −2.46122 + 4.26295i −0.502394 + 0.870171i
\(25\) 0.246870 0.427591i 0.0493740 0.0855182i
\(26\) −1.10666 1.91679i −0.217034 0.375914i
\(27\) 0.303848 0.0584757
\(28\) −4.49818 + 6.21188i −0.850076 + 1.17393i
\(29\) −5.90107 −1.09580 −0.547901 0.836543i \(-0.684573\pi\)
−0.547901 + 0.836543i \(0.684573\pi\)
\(30\) 5.81296 + 10.0683i 1.06130 + 1.83822i
\(31\) 1.88558 3.26592i 0.338660 0.586577i −0.645521 0.763743i \(-0.723360\pi\)
0.984181 + 0.177166i \(0.0566929\pi\)
\(32\) 3.53265 6.11873i 0.624490 1.08165i
\(33\) −5.92496 10.2623i −1.03140 1.78644i
\(34\) −8.36254 −1.43416
\(35\) 2.29251 + 5.12720i 0.387505 + 0.866655i
\(36\) 9.05234 1.50872
\(37\) −2.81285 4.87200i −0.462429 0.800951i 0.536652 0.843804i \(-0.319689\pi\)
−0.999081 + 0.0428524i \(0.986355\pi\)
\(38\) 3.94772 6.83765i 0.640404 1.10921i
\(39\) −1.23721 + 2.14292i −0.198113 + 0.343141i
\(40\) 2.11146 + 3.65716i 0.333851 + 0.578247i
\(41\) 10.3948 1.62340 0.811698 0.584077i \(-0.198543\pi\)
0.811698 + 0.584077i \(0.198543\pi\)
\(42\) 14.4130 + 1.49180i 2.22398 + 0.230189i
\(43\) 3.40733 0.519613 0.259807 0.965661i \(-0.416341\pi\)
0.259807 + 0.965661i \(0.416341\pi\)
\(44\) −6.94110 12.0223i −1.04641 1.81244i
\(45\) 3.31453 5.74093i 0.494101 0.855807i
\(46\) −4.95168 + 8.57655i −0.730085 + 1.26454i
\(47\) 3.55438 + 6.15636i 0.518459 + 0.897998i 0.999770 + 0.0214479i \(0.00682759\pi\)
−0.481311 + 0.876550i \(0.659839\pi\)
\(48\) −3.45079 −0.498079
\(49\) 6.85161 + 1.43369i 0.978801 + 0.204813i
\(50\) −1.09280 −0.154546
\(51\) 4.67454 + 8.09654i 0.654566 + 1.13374i
\(52\) −1.44940 + 2.51043i −0.200995 + 0.348134i
\(53\) 6.19003 10.7214i 0.850266 1.47270i −0.0307027 0.999529i \(-0.509774\pi\)
0.880968 0.473175i \(-0.156892\pi\)
\(54\) −0.336257 0.582415i −0.0457588 0.0792566i
\(55\) −10.1660 −1.37078
\(56\) 5.23528 + 0.541869i 0.699594 + 0.0724103i
\(57\) −8.82686 −1.16915
\(58\) 6.53049 + 11.3111i 0.857495 + 1.48522i
\(59\) −2.39448 + 4.14736i −0.311734 + 0.539940i −0.978738 0.205115i \(-0.934243\pi\)
0.667003 + 0.745055i \(0.267577\pi\)
\(60\) 7.61326 13.1865i 0.982867 1.70238i
\(61\) −1.60348 2.77732i −0.205305 0.355599i 0.744925 0.667148i \(-0.232485\pi\)
−0.950230 + 0.311550i \(0.899152\pi\)
\(62\) −8.34680 −1.06004
\(63\) −3.37246 7.54251i −0.424890 0.950267i
\(64\) −12.8486 −1.60608
\(65\) 1.06140 + 1.83839i 0.131650 + 0.228025i
\(66\) −13.1139 + 22.7139i −1.61420 + 2.79588i
\(67\) 1.44978 2.51109i 0.177118 0.306778i −0.763774 0.645484i \(-0.776656\pi\)
0.940892 + 0.338706i \(0.109989\pi\)
\(68\) 5.47622 + 9.48510i 0.664090 + 1.15024i
\(69\) 11.0717 1.33287
\(70\) 7.29075 10.0683i 0.871411 1.20340i
\(71\) −2.53876 −0.301295 −0.150648 0.988588i \(-0.548136\pi\)
−0.150648 + 0.988588i \(0.548136\pi\)
\(72\) −3.10612 5.37996i −0.366060 0.634034i
\(73\) −3.85035 + 6.66901i −0.450650 + 0.780548i −0.998426 0.0560762i \(-0.982141\pi\)
0.547777 + 0.836625i \(0.315474\pi\)
\(74\) −6.22574 + 10.7833i −0.723727 + 1.25353i
\(75\) 0.610862 + 1.05804i 0.0705362 + 0.122172i
\(76\) −10.3407 −1.18616
\(77\) −7.43122 + 10.2623i −0.846867 + 1.16950i
\(78\) 5.47671 0.620115
\(79\) 2.58925 + 4.48471i 0.291313 + 0.504569i 0.974120 0.226029i \(-0.0725745\pi\)
−0.682807 + 0.730598i \(0.739241\pi\)
\(80\) −1.48021 + 2.56379i −0.165492 + 0.286641i
\(81\) 4.30827 7.46214i 0.478696 0.829126i
\(82\) −11.5035 19.9247i −1.27035 2.20032i
\(83\) 3.46731 0.380587 0.190294 0.981727i \(-0.439056\pi\)
0.190294 + 0.981727i \(0.439056\pi\)
\(84\) −7.74633 17.3247i −0.845194 1.89027i
\(85\) 8.02051 0.869946
\(86\) −3.77076 6.53115i −0.406612 0.704272i
\(87\) 7.30089 12.6455i 0.782738 1.35574i
\(88\) −4.76338 + 8.25042i −0.507778 + 0.879498i
\(89\) −1.83216 3.17339i −0.194209 0.336379i 0.752432 0.658670i \(-0.228881\pi\)
−0.946641 + 0.322291i \(0.895547\pi\)
\(90\) −14.6722 −1.54659
\(91\) 2.63169 + 0.272389i 0.275876 + 0.0285541i
\(92\) 12.9704 1.35226
\(93\) 4.66574 + 8.08129i 0.483814 + 0.837991i
\(94\) 7.86698 13.6260i 0.811417 1.40542i
\(95\) −3.78625 + 6.55798i −0.388461 + 0.672835i
\(96\) 8.74129 + 15.1404i 0.892154 + 1.54526i
\(97\) −5.40733 −0.549031 −0.274516 0.961583i \(-0.588518\pi\)
−0.274516 + 0.961583i \(0.588518\pi\)
\(98\) −4.83432 14.7197i −0.488340 1.48692i
\(99\) 14.9549 1.50303
\(100\) 0.715625 + 1.23950i 0.0715625 + 0.123950i
\(101\) −4.65862 + 8.06897i −0.463550 + 0.802892i −0.999135 0.0415891i \(-0.986758\pi\)
0.535585 + 0.844482i \(0.320091\pi\)
\(102\) 10.3463 17.9202i 1.02443 1.77437i
\(103\) −3.65318 6.32749i −0.359958 0.623466i 0.627995 0.778217i \(-0.283876\pi\)
−0.987953 + 0.154751i \(0.950542\pi\)
\(104\) 1.98932 0.195069
\(105\) −13.8235 1.43078i −1.34904 0.139630i
\(106\) −27.4011 −2.66143
\(107\) −3.37365 5.84333i −0.326143 0.564896i 0.655600 0.755108i \(-0.272416\pi\)
−0.981743 + 0.190212i \(0.939082\pi\)
\(108\) −0.440397 + 0.762790i −0.0423772 + 0.0733995i
\(109\) −2.08822 + 3.61691i −0.200016 + 0.346437i −0.948533 0.316678i \(-0.897433\pi\)
0.748518 + 0.663115i \(0.230766\pi\)
\(110\) 11.2503 + 19.4861i 1.07267 + 1.85792i
\(111\) 13.9204 1.32126
\(112\) 1.50608 + 3.36834i 0.142311 + 0.318278i
\(113\) 5.90107 0.555126 0.277563 0.960707i \(-0.410473\pi\)
0.277563 + 0.960707i \(0.410473\pi\)
\(114\) 9.76834 + 16.9193i 0.914889 + 1.58463i
\(115\) 4.74915 8.22577i 0.442860 0.767057i
\(116\) 8.55300 14.8142i 0.794126 1.37547i
\(117\) −1.56140 2.70442i −0.144351 0.250024i
\(118\) 10.5995 0.975763
\(119\) 5.86291 8.09654i 0.537452 0.742208i
\(120\) −10.4493 −0.953888
\(121\) −5.96705 10.3352i −0.542459 0.939567i
\(122\) −3.54903 + 6.14709i −0.321314 + 0.556532i
\(123\) −12.8606 + 22.2752i −1.15960 + 2.00849i
\(124\) 5.46591 + 9.46724i 0.490853 + 0.850183i
\(125\) 11.6621 1.04309
\(126\) −10.7253 + 14.8113i −0.955482 + 1.31950i
\(127\) −10.5268 −0.934100 −0.467050 0.884231i \(-0.654683\pi\)
−0.467050 + 0.884231i \(0.654683\pi\)
\(128\) 7.15377 + 12.3907i 0.632309 + 1.09519i
\(129\) −4.21560 + 7.30163i −0.371163 + 0.642873i
\(130\) 2.34921 4.06896i 0.206040 0.356871i
\(131\) −2.71204 4.69740i −0.236952 0.410413i 0.722886 0.690967i \(-0.242815\pi\)
−0.959838 + 0.280554i \(0.909482\pi\)
\(132\) 34.3505 2.98983
\(133\) 3.85243 + 8.61596i 0.334048 + 0.747099i
\(134\) −6.41765 −0.554400
\(135\) 0.322504 + 0.558593i 0.0277567 + 0.0480761i
\(136\) 3.75810 6.50922i 0.322255 0.558161i
\(137\) −11.1224 + 19.2645i −0.950248 + 1.64588i −0.205363 + 0.978686i \(0.565837\pi\)
−0.744886 + 0.667192i \(0.767496\pi\)
\(138\) −12.2526 21.2221i −1.04301 1.80654i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −16.1942 1.67616i −1.36866 0.141661i
\(141\) −17.5901 −1.48135
\(142\) 2.80955 + 4.86628i 0.235772 + 0.408369i
\(143\) −2.39448 + 4.14736i −0.200236 + 0.346819i
\(144\) 2.17750 3.77153i 0.181458 0.314294i
\(145\) −6.26338 10.8485i −0.520146 0.900919i
\(146\) 17.0441 1.41058
\(147\) −11.5492 + 12.9087i −0.952561 + 1.06469i
\(148\) 16.3077 1.34049
\(149\) −1.47736 2.55887i −0.121030 0.209630i 0.799144 0.601140i \(-0.205286\pi\)
−0.920174 + 0.391509i \(0.871953\pi\)
\(150\) 1.35203 2.34179i 0.110393 0.191206i
\(151\) 9.27736 16.0689i 0.754981 1.30766i −0.190403 0.981706i \(-0.560980\pi\)
0.945384 0.325959i \(-0.105687\pi\)
\(152\) 3.54818 + 6.14564i 0.287796 + 0.498477i
\(153\) −11.7988 −0.953875
\(154\) 27.8946 + 2.88719i 2.24781 + 0.232656i
\(155\) 8.00541 0.643010
\(156\) −3.58643 6.21188i −0.287144 0.497348i
\(157\) 4.89982 8.48673i 0.391048 0.677315i −0.601540 0.798843i \(-0.705446\pi\)
0.992588 + 0.121528i \(0.0387793\pi\)
\(158\) 5.73084 9.92610i 0.455921 0.789678i
\(159\) 15.3168 + 26.5294i 1.21470 + 2.10392i
\(160\) 14.9982 1.18571
\(161\) −4.83216 10.8071i −0.380828 0.851720i
\(162\) −19.0712 −1.49837
\(163\) −6.91709 11.9808i −0.541788 0.938405i −0.998801 0.0489451i \(-0.984414\pi\)
0.457013 0.889460i \(-0.348919\pi\)
\(164\) −15.0662 + 26.0954i −1.17647 + 2.03771i
\(165\) 12.5775 21.7848i 0.979156 1.69595i
\(166\) −3.83714 6.64612i −0.297820 0.515839i
\(167\) 17.3534 1.34285 0.671424 0.741073i \(-0.265683\pi\)
0.671424 + 0.741073i \(0.265683\pi\)
\(168\) −7.63834 + 10.5484i −0.589311 + 0.813824i
\(169\) 1.00000 0.0769231
\(170\) −8.87598 15.3737i −0.680757 1.17911i
\(171\) 5.56987 9.64730i 0.425939 0.737747i
\(172\) −4.93858 + 8.55387i −0.376563 + 0.652226i
\(173\) 1.48069 + 2.56463i 0.112575 + 0.194985i 0.916808 0.399329i \(-0.130757\pi\)
−0.804233 + 0.594314i \(0.797424\pi\)
\(174\) −32.3184 −2.45005
\(175\) 0.766156 1.05804i 0.0579160 0.0799806i
\(176\) −6.67859 −0.503418
\(177\) −5.92496 10.2623i −0.445348 0.771365i
\(178\) −4.05516 + 7.02374i −0.303947 + 0.526452i
\(179\) 2.83444 4.90939i 0.211856 0.366945i −0.740440 0.672123i \(-0.765383\pi\)
0.952295 + 0.305178i \(0.0987159\pi\)
\(180\) 9.60813 + 16.6418i 0.716148 + 1.24040i
\(181\) 7.17645 0.533421 0.266711 0.963777i \(-0.414063\pi\)
0.266711 + 0.963777i \(0.414063\pi\)
\(182\) −2.39028 5.34585i −0.177179 0.396261i
\(183\) 7.93541 0.586603
\(184\) −4.45054 7.70855i −0.328098 0.568282i
\(185\) 5.97110 10.3423i 0.439004 0.760377i
\(186\) 10.3268 17.8865i 0.757196 1.31150i
\(187\) 9.04700 + 15.6699i 0.661582 + 1.14589i
\(188\) −20.6068 −1.50291
\(189\) 0.799636 + 0.0827650i 0.0581649 + 0.00602027i
\(190\) 16.7604 1.21593
\(191\) −5.94088 10.2899i −0.429867 0.744552i 0.566994 0.823722i \(-0.308106\pi\)
−0.996861 + 0.0791703i \(0.974773\pi\)
\(192\) 15.8965 27.5335i 1.14723 1.98706i
\(193\) −11.4851 + 19.8927i −0.826714 + 1.43191i 0.0738876 + 0.997267i \(0.476459\pi\)
−0.900602 + 0.434645i \(0.856874\pi\)
\(194\) 5.98408 + 10.3647i 0.429632 + 0.744145i
\(195\) −5.25271 −0.376154
\(196\) −13.5299 + 15.1225i −0.966420 + 1.08018i
\(197\) 16.9216 1.20561 0.602806 0.797888i \(-0.294049\pi\)
0.602806 + 0.797888i \(0.294049\pi\)
\(198\) −16.5500 28.6655i −1.17616 2.03717i
\(199\) −5.02953 + 8.71140i −0.356534 + 0.617535i −0.987379 0.158374i \(-0.949375\pi\)
0.630845 + 0.775909i \(0.282708\pi\)
\(200\) 0.491103 0.850616i 0.0347262 0.0601476i
\(201\) 3.58737 + 6.21351i 0.253034 + 0.438267i
\(202\) 20.6221 1.45096
\(203\) −15.5298 1.60739i −1.08998 0.112817i
\(204\) −27.1010 −1.89745
\(205\) 11.0330 + 19.1098i 0.770580 + 1.33468i
\(206\) −8.08566 + 14.0048i −0.563355 + 0.975759i
\(207\) −6.98636 + 12.1007i −0.485586 + 0.841059i
\(208\) 0.697291 + 1.20774i 0.0483484 + 0.0837419i
\(209\) −17.0833 −1.18168
\(210\) 12.5554 + 28.0802i 0.866406 + 1.93772i
\(211\) −24.4609 −1.68396 −0.841978 0.539512i \(-0.818609\pi\)
−0.841978 + 0.539512i \(0.818609\pi\)
\(212\) 17.9436 + 31.0793i 1.23237 + 2.13453i
\(213\) 3.14099 5.44035i 0.215217 0.372767i
\(214\) −7.46697 + 12.9332i −0.510431 + 0.884093i
\(215\) 3.61654 + 6.26402i 0.246646 + 0.427203i
\(216\) 0.604452 0.0411277
\(217\) 5.85187 8.08129i 0.397251 0.548594i
\(218\) 9.24382 0.626071
\(219\) −9.52742 16.5020i −0.643804 1.11510i
\(220\) 14.7345 25.5210i 0.993402 1.72062i
\(221\) 1.88914 3.27208i 0.127077 0.220104i
\(222\) −15.4051 26.6825i −1.03393 1.79081i
\(223\) −29.2625 −1.95956 −0.979780 0.200076i \(-0.935881\pi\)
−0.979780 + 0.200076i \(0.935881\pi\)
\(224\) 10.9635 15.1404i 0.732531 1.01161i
\(225\) −1.54185 −0.102790
\(226\) −6.53049 11.3111i −0.434401 0.752405i
\(227\) 5.03685 8.72408i 0.334307 0.579038i −0.649044 0.760751i \(-0.724831\pi\)
0.983352 + 0.181713i \(0.0581643\pi\)
\(228\) 12.7936 22.1592i 0.847279 1.46753i
\(229\) 5.56997 + 9.64748i 0.368074 + 0.637523i 0.989264 0.146137i \(-0.0466839\pi\)
−0.621190 + 0.783660i \(0.713351\pi\)
\(230\) −21.0228 −1.38620
\(231\) −12.7973 28.6212i −0.842003 1.88314i
\(232\) −11.7391 −0.770711
\(233\) 8.54166 + 14.7946i 0.559583 + 0.969226i 0.997531 + 0.0702257i \(0.0223720\pi\)
−0.437948 + 0.899000i \(0.644295\pi\)
\(234\) −3.45588 + 5.98575i −0.225918 + 0.391301i
\(235\) −7.54522 + 13.0687i −0.492196 + 0.852508i
\(236\) −6.94110 12.0223i −0.451827 0.782587i
\(237\) −12.8138 −0.832347
\(238\) −22.0076 2.27787i −1.42654 0.147652i
\(239\) 6.92142 0.447710 0.223855 0.974622i \(-0.428136\pi\)
0.223855 + 0.974622i \(0.428136\pi\)
\(240\) −3.66266 6.34392i −0.236424 0.409498i
\(241\) −3.24812 + 5.62592i −0.209230 + 0.362397i −0.951472 0.307735i \(-0.900429\pi\)
0.742242 + 0.670132i \(0.233762\pi\)
\(242\) −13.2070 + 22.8752i −0.848978 + 1.47047i
\(243\) 11.1163 + 19.2539i 0.713109 + 1.23514i
\(244\) 9.29634 0.595137
\(245\) 4.63660 + 14.1177i 0.296221 + 0.901945i
\(246\) 56.9293 3.62968
\(247\) 1.78362 + 3.08931i 0.113489 + 0.196568i
\(248\) 3.75103 6.49697i 0.238190 0.412558i
\(249\) −4.28981 + 7.43017i −0.271856 + 0.470868i
\(250\) −12.9060 22.3538i −0.816246 1.41378i
\(251\) −9.86804 −0.622865 −0.311433 0.950268i \(-0.600809\pi\)
−0.311433 + 0.950268i \(0.600809\pi\)
\(252\) 23.8230 + 2.46576i 1.50071 + 0.155328i
\(253\) 21.4278 1.34716
\(254\) 11.6496 + 20.1776i 0.730959 + 1.26606i
\(255\) −9.92309 + 17.1873i −0.621408 + 1.07631i
\(256\) 2.98497 5.17012i 0.186560 0.323132i
\(257\) −3.43234 5.94499i −0.214104 0.370838i 0.738891 0.673825i \(-0.235350\pi\)
−0.952995 + 0.302986i \(0.902016\pi\)
\(258\) 18.6610 1.16178
\(259\) −6.07547 13.5878i −0.377511 0.844304i
\(260\) −6.15355 −0.381627
\(261\) 9.21392 + 15.9590i 0.570327 + 0.987836i
\(262\) −6.00262 + 10.3969i −0.370843 + 0.642320i
\(263\) 0.0632753 0.109596i 0.00390172 0.00675798i −0.864068 0.503375i \(-0.832091\pi\)
0.867970 + 0.496617i \(0.165425\pi\)
\(264\) −11.7867 20.4151i −0.725418 1.25646i
\(265\) 26.2803 1.61439
\(266\) 12.2517 16.9193i 0.751199 1.03739i
\(267\) 9.06710 0.554897
\(268\) 4.20261 + 7.27913i 0.256715 + 0.444643i
\(269\) 2.12154 3.67462i 0.129353 0.224045i −0.794073 0.607822i \(-0.792043\pi\)
0.923426 + 0.383777i \(0.125377\pi\)
\(270\) 0.713805 1.23635i 0.0434408 0.0752417i
\(271\) −0.783616 1.35726i −0.0476013 0.0824479i 0.841243 0.540657i \(-0.181824\pi\)
−0.888844 + 0.458209i \(0.848491\pi\)
\(272\) 5.26911 0.319487
\(273\) −3.83967 + 5.30250i −0.232388 + 0.320922i
\(274\) 49.2348 2.97438
\(275\) 1.18225 + 2.04771i 0.0712923 + 0.123482i
\(276\) −16.0472 + 27.7946i −0.965929 + 1.67304i
\(277\) 6.37260 11.0377i 0.382892 0.663189i −0.608582 0.793491i \(-0.708261\pi\)
0.991474 + 0.130302i \(0.0415947\pi\)
\(278\) 4.42664 + 7.66717i 0.265492 + 0.459846i
\(279\) −11.7766 −0.705045
\(280\) 4.56054 + 10.1996i 0.272545 + 0.609546i
\(281\) 4.62986 0.276194 0.138097 0.990419i \(-0.455901\pi\)
0.138097 + 0.990419i \(0.455901\pi\)
\(282\) 19.4663 + 33.7166i 1.15920 + 2.00779i
\(283\) −1.82416 + 3.15954i −0.108435 + 0.187815i −0.915136 0.403144i \(-0.867917\pi\)
0.806701 + 0.590959i \(0.201251\pi\)
\(284\) 3.67967 6.37338i 0.218348 0.378190i
\(285\) −9.36881 16.2273i −0.554960 0.961220i
\(286\) 10.5995 0.626762
\(287\) 27.3559 + 2.83143i 1.61477 + 0.167134i
\(288\) −22.0635 −1.30010
\(289\) 1.36231 + 2.35959i 0.0801360 + 0.138800i
\(290\) −13.8629 + 24.0112i −0.814057 + 1.40999i
\(291\) 6.69003 11.5875i 0.392176 0.679269i
\(292\) −11.1614 19.3321i −0.653171 1.13132i
\(293\) −21.0415 −1.22926 −0.614630 0.788816i \(-0.710695\pi\)
−0.614630 + 0.788816i \(0.710695\pi\)
\(294\) 37.5242 + 7.85189i 2.18846 + 0.457932i
\(295\) −10.1660 −0.591886
\(296\) −5.59566 9.69196i −0.325241 0.563334i
\(297\) −0.727559 + 1.26017i −0.0422172 + 0.0731224i
\(298\) −3.26988 + 5.66359i −0.189419 + 0.328083i
\(299\) −2.23721 3.87497i −0.129381 0.224095i
\(300\) −3.54152 −0.204470
\(301\) 8.96705 + 0.928120i 0.516852 + 0.0534960i
\(302\) −41.0676 −2.36317
\(303\) −11.5274 19.9661i −0.662233 1.14702i
\(304\) −2.48740 + 4.30830i −0.142662 + 0.247098i
\(305\) 3.40387 5.89567i 0.194905 0.337585i
\(306\) 13.0573 + 22.6158i 0.746434 + 1.29286i
\(307\) −4.95861 −0.283003 −0.141502 0.989938i \(-0.545193\pi\)
−0.141502 + 0.989938i \(0.545193\pi\)
\(308\) −14.9921 33.5298i −0.854253 1.91054i
\(309\) 18.0791 1.02848
\(310\) −8.85927 15.3447i −0.503173 0.871521i
\(311\) 1.21079 2.09715i 0.0686575 0.118918i −0.829653 0.558279i \(-0.811462\pi\)
0.898311 + 0.439361i \(0.144795\pi\)
\(312\) −2.46122 + 4.26295i −0.139339 + 0.241342i
\(313\) −6.98026 12.0902i −0.394548 0.683377i 0.598496 0.801126i \(-0.295765\pi\)
−0.993043 + 0.117749i \(0.962432\pi\)
\(314\) −21.6897 −1.22402
\(315\) 10.2866 14.2055i 0.579583 0.800390i
\(316\) −15.0114 −0.844457
\(317\) −1.53431 2.65750i −0.0861753 0.149260i 0.819716 0.572770i \(-0.194131\pi\)
−0.905891 + 0.423510i \(0.860798\pi\)
\(318\) 33.9010 58.7182i 1.90107 3.29275i
\(319\) 14.1300 24.4739i 0.791127 1.37027i
\(320\) −13.6375 23.6208i −0.762359 1.32044i
\(321\) 16.6957 0.931863
\(322\) −15.3674 + 21.2221i −0.856394 + 1.18266i
\(323\) 13.4780 0.749936
\(324\) 12.4888 + 21.6312i 0.693821 + 1.20173i
\(325\) 0.246870 0.427591i 0.0136939 0.0237185i
\(326\) −15.3098 + 26.5173i −0.847929 + 1.46866i
\(327\) −5.16716 8.94978i −0.285745 0.494924i
\(328\) 20.6786 1.14179
\(329\) 7.67710 + 17.1698i 0.423252 + 0.946603i
\(330\) −55.6761 −3.06487
\(331\) −6.80261 11.7825i −0.373905 0.647623i 0.616257 0.787545i \(-0.288648\pi\)
−0.990162 + 0.139922i \(0.955315\pi\)
\(332\) −5.02551 + 8.70445i −0.275811 + 0.477719i
\(333\) −8.78395 + 15.2142i −0.481358 + 0.833736i
\(334\) −19.2044 33.2629i −1.05082 1.82007i
\(335\) 6.15516 0.336292
\(336\) −9.08142 0.939958i −0.495432 0.0512789i
\(337\) −35.1646 −1.91554 −0.957769 0.287538i \(-0.907163\pi\)
−0.957769 + 0.287538i \(0.907163\pi\)
\(338\) −1.10666 1.91679i −0.0601944 0.104260i
\(339\) −7.30089 + 12.6455i −0.396530 + 0.686810i
\(340\) −11.6249 + 20.1349i −0.630449 + 1.09197i
\(341\) 9.02997 + 15.6404i 0.489000 + 0.846973i
\(342\) −24.6558 −1.33323
\(343\) 17.6408 + 5.63933i 0.952514 + 0.304495i
\(344\) 6.77828 0.365460
\(345\) 11.7514 + 20.3541i 0.632676 + 1.09583i
\(346\) 3.27724 5.67635i 0.176186 0.305162i
\(347\) 2.73551 4.73804i 0.146850 0.254351i −0.783212 0.621755i \(-0.786420\pi\)
0.930062 + 0.367404i \(0.119753\pi\)
\(348\) 21.1638 + 36.6567i 1.13450 + 1.96501i
\(349\) 4.34196 0.232420 0.116210 0.993225i \(-0.462925\pi\)
0.116210 + 0.993225i \(0.462925\pi\)
\(350\) −2.87593 0.297668i −0.153725 0.0159110i
\(351\) 0.303848 0.0162182
\(352\) 16.9177 + 29.3023i 0.901717 + 1.56182i
\(353\) −13.7996 + 23.9016i −0.734479 + 1.27216i 0.220472 + 0.975393i \(0.429240\pi\)
−0.954951 + 0.296762i \(0.904093\pi\)
\(354\) −13.1139 + 22.7139i −0.696993 + 1.20723i
\(355\) −2.69463 4.66724i −0.143016 0.247712i
\(356\) 10.6221 0.562971
\(357\) 10.0965 + 22.5809i 0.534365 + 1.19511i
\(358\) −12.5470 −0.663132
\(359\) −3.31427 5.74049i −0.174921 0.302971i 0.765213 0.643777i \(-0.222634\pi\)
−0.940134 + 0.340806i \(0.889300\pi\)
\(360\) 6.59366 11.4206i 0.347516 0.601916i
\(361\) 3.13742 5.43418i 0.165128 0.286009i
\(362\) −7.94189 13.7558i −0.417417 0.722987i
\(363\) 29.5301 1.54993
\(364\) −4.49818 + 6.21188i −0.235769 + 0.325591i
\(365\) −16.3470 −0.855643
\(366\) −8.78181 15.2105i −0.459033 0.795068i
\(367\) −15.6037 + 27.0264i −0.814506 + 1.41077i 0.0951768 + 0.995460i \(0.469658\pi\)
−0.909682 + 0.415305i \(0.863675\pi\)
\(368\) 3.11998 5.40396i 0.162640 0.281701i
\(369\) −16.2304 28.1119i −0.844923 1.46345i
\(370\) −26.4319 −1.37413
\(371\) 19.2107 26.5294i 0.997368 1.37734i
\(372\) −27.0500 −1.40248
\(373\) 7.88730 + 13.6612i 0.408389 + 0.707350i 0.994709 0.102729i \(-0.0327574\pi\)
−0.586321 + 0.810079i \(0.699424\pi\)
\(374\) 20.0239 34.6825i 1.03541 1.79339i
\(375\) −14.4285 + 24.9909i −0.745084 + 1.29052i
\(376\) 7.07080 + 12.2470i 0.364649 + 0.631590i
\(377\) −5.90107 −0.303921
\(378\) −0.726282 1.62433i −0.0373559 0.0835465i
\(379\) 31.6512 1.62581 0.812907 0.582393i \(-0.197884\pi\)
0.812907 + 0.582393i \(0.197884\pi\)
\(380\) −10.9756 19.0102i −0.563035 0.975205i
\(381\) 13.0239 22.5580i 0.667233 1.15568i
\(382\) −13.1491 + 22.7749i −0.672766 + 1.16526i
\(383\) −6.19675 10.7331i −0.316639 0.548435i 0.663145 0.748491i \(-0.269221\pi\)
−0.979785 + 0.200055i \(0.935888\pi\)
\(384\) −35.4030 −1.80665
\(385\) −26.7537 2.76910i −1.36350 0.141126i
\(386\) 50.8404 2.58771
\(387\) −5.32020 9.21486i −0.270441 0.468418i
\(388\) 7.83737 13.5747i 0.397882 0.689152i
\(389\) 7.03705 12.1885i 0.356792 0.617983i −0.630631 0.776083i \(-0.717204\pi\)
0.987423 + 0.158100i \(0.0505370\pi\)
\(390\) 5.81296 + 10.0683i 0.294351 + 0.509831i
\(391\) −16.9056 −0.854954
\(392\) 13.6300 + 2.85207i 0.688421 + 0.144051i
\(393\) 13.4215 0.677026
\(394\) −18.7265 32.4352i −0.943425 1.63406i
\(395\) −5.49644 + 9.52012i −0.276556 + 0.479009i
\(396\) −21.6756 + 37.5433i −1.08924 + 1.88662i
\(397\) 3.48652 + 6.03884i 0.174984 + 0.303081i 0.940156 0.340745i \(-0.110679\pi\)
−0.765172 + 0.643826i \(0.777346\pi\)
\(398\) 22.2639 1.11599
\(399\) −23.2296 2.40434i −1.16293 0.120368i
\(400\) 0.688560 0.0344280
\(401\) −1.36841 2.37016i −0.0683352 0.118360i 0.829833 0.558011i \(-0.188435\pi\)
−0.898169 + 0.439651i \(0.855102\pi\)
\(402\) 7.94000 13.7525i 0.396011 0.685912i
\(403\) 1.88558 3.26592i 0.0939275 0.162687i
\(404\) −13.5044 23.3903i −0.671868 1.16371i
\(405\) 18.2911 0.908894
\(406\) 14.1052 + 31.5463i 0.700029 + 1.56561i
\(407\) 26.9412 1.33543
\(408\) 9.29915 + 16.1066i 0.460377 + 0.797396i
\(409\) 12.2577 21.2309i 0.606104 1.04980i −0.385772 0.922594i \(-0.626065\pi\)
0.991876 0.127208i \(-0.0406017\pi\)
\(410\) 24.4196 42.2961i 1.20600 2.08885i
\(411\) −27.5215 47.6686i −1.35754 2.35132i
\(412\) 21.1796 1.04345
\(413\) −7.43122 + 10.2623i −0.365667 + 0.504977i
\(414\) 30.9261 1.51994
\(415\) 3.68020 + 6.37429i 0.180654 + 0.312902i
\(416\) 3.53265 6.11873i 0.173202 0.299995i
\(417\) 4.94886 8.57167i 0.242347 0.419757i
\(418\) 18.9054 + 32.7452i 0.924696 + 1.60162i
\(419\) −3.01252 −0.147171 −0.0735856 0.997289i \(-0.523444\pi\)
−0.0735856 + 0.997289i \(0.523444\pi\)
\(420\) 23.6276 32.6292i 1.15291 1.59214i
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 27.0699 + 46.8864i 1.31774 + 2.28240i
\(423\) 11.0996 19.2251i 0.539681 0.934755i
\(424\) 12.3140 21.3284i 0.598018 1.03580i
\(425\) −0.932742 1.61556i −0.0452447 0.0783660i
\(426\) −13.9040 −0.673653
\(427\) −3.46337 7.74581i −0.167604 0.374846i
\(428\) 19.5590 0.945421
\(429\) −5.92496 10.2623i −0.286060 0.495470i
\(430\) 8.00456 13.8643i 0.386014 0.668596i
\(431\) 9.39711 16.2763i 0.452643 0.784001i −0.545906 0.837846i \(-0.683815\pi\)
0.998549 + 0.0538455i \(0.0171478\pi\)
\(432\) 0.211871 + 0.366971i 0.0101936 + 0.0176559i
\(433\) −7.76911 −0.373360 −0.186680 0.982421i \(-0.559773\pi\)
−0.186680 + 0.982421i \(0.559773\pi\)
\(434\) −21.9662 2.27358i −1.05441 0.109135i
\(435\) 30.9966 1.48617
\(436\) −6.05333 10.4847i −0.289902 0.502125i
\(437\) 7.98066 13.8229i 0.381767 0.661240i
\(438\) −21.0873 + 36.5242i −1.00759 + 1.74519i
\(439\) 18.9841 + 32.8814i 0.906060 + 1.56934i 0.819488 + 0.573096i \(0.194258\pi\)
0.0865713 + 0.996246i \(0.472409\pi\)
\(440\) −20.2234 −0.964112
\(441\) −6.82079 20.7682i −0.324799 0.988961i
\(442\) −8.36254 −0.397766
\(443\) −17.8135 30.8539i −0.846344 1.46591i −0.884449 0.466637i \(-0.845465\pi\)
0.0381050 0.999274i \(-0.487868\pi\)
\(444\) −20.1762 + 34.9461i −0.957518 + 1.65847i
\(445\) 3.88930 6.73647i 0.184371 0.319339i
\(446\) 32.3837 + 56.0901i 1.53341 + 2.65594i
\(447\) 7.31125 0.345810
\(448\) −33.8136 3.49982i −1.59754 0.165351i
\(449\) −8.05285 −0.380038 −0.190019 0.981780i \(-0.560855\pi\)
−0.190019 + 0.981780i \(0.560855\pi\)
\(450\) 1.70630 + 2.95540i 0.0804359 + 0.139319i
\(451\) −24.8901 + 43.1110i −1.17203 + 2.03002i
\(452\) −8.55300 + 14.8142i −0.402299 + 0.696803i
\(453\) 22.9562 + 39.7612i 1.07857 + 1.86815i
\(454\) −22.2963 −1.04642
\(455\) 2.29251 + 5.12720i 0.107475 + 0.240367i
\(456\) −17.5595 −0.822297
\(457\) −7.79881 13.5079i −0.364813 0.631875i 0.623933 0.781478i \(-0.285534\pi\)
−0.988746 + 0.149603i \(0.952200\pi\)
\(458\) 12.3281 21.3530i 0.576056 0.997759i
\(459\) 0.574012 0.994218i 0.0267926 0.0464061i
\(460\) 13.7668 + 23.8448i 0.641880 + 1.11177i
\(461\) −25.6991 −1.19692 −0.598462 0.801151i \(-0.704221\pi\)
−0.598462 + 0.801151i \(0.704221\pi\)
\(462\) −40.6986 + 56.2038i −1.89347 + 2.61484i
\(463\) −20.5209 −0.953685 −0.476842 0.878989i \(-0.658219\pi\)
−0.476842 + 0.878989i \(0.658219\pi\)
\(464\) −4.11476 7.12698i −0.191023 0.330862i
\(465\) −9.90440 + 17.1549i −0.459306 + 0.795541i
\(466\) 18.9054 32.7452i 0.875778 1.51689i
\(467\) −5.91241 10.2406i −0.273594 0.473878i 0.696186 0.717862i \(-0.254879\pi\)
−0.969779 + 0.243984i \(0.921546\pi\)
\(468\) 9.05234 0.418445
\(469\) 4.49936 6.21351i 0.207761 0.286913i
\(470\) 33.4000 1.54063
\(471\) 12.1242 + 20.9998i 0.558656 + 0.967620i
\(472\) −4.76338 + 8.25042i −0.219253 + 0.379757i
\(473\) −8.15878 + 14.1314i −0.375141 + 0.649764i
\(474\) 14.1805 + 24.5614i 0.651334 + 1.12814i
\(475\) 1.76128 0.0808133
\(476\) 11.8281 + 26.4535i 0.542140 + 1.21250i
\(477\) −38.6604 −1.77014
\(478\) −7.65967 13.2669i −0.350345 0.606816i
\(479\) −11.3276 + 19.6200i −0.517571 + 0.896459i 0.482221 + 0.876050i \(0.339830\pi\)
−0.999792 + 0.0204092i \(0.993503\pi\)
\(480\) −18.5560 + 32.1399i −0.846960 + 1.46698i
\(481\) −2.81285 4.87200i −0.128255 0.222144i
\(482\) 14.3783 0.654913
\(483\) 29.1372 + 3.01580i 1.32579 + 0.137224i
\(484\) 34.5945 1.57248
\(485\) −5.73933 9.94081i −0.260610 0.451389i
\(486\) 24.6039 42.6152i 1.11606 1.93306i
\(487\) 16.3584 28.3335i 0.741268 1.28391i −0.210650 0.977562i \(-0.567558\pi\)
0.951918 0.306353i \(-0.0991087\pi\)
\(488\) −3.18984 5.52497i −0.144397 0.250104i
\(489\) 34.2317 1.54801
\(490\) 21.9295 24.5109i 0.990675 1.10729i
\(491\) 6.17281 0.278575 0.139288 0.990252i \(-0.455519\pi\)
0.139288 + 0.990252i \(0.455519\pi\)
\(492\) −37.2803 64.5713i −1.68072 2.91110i
\(493\) −11.1479 + 19.3088i −0.502078 + 0.869625i
\(494\) 3.94772 6.83765i 0.177616 0.307640i
\(495\) 15.8731 + 27.4931i 0.713444 + 1.23572i
\(496\) 5.25919 0.236145
\(497\) −6.68123 0.691531i −0.299694 0.0310194i
\(498\) 18.9895 0.850938
\(499\) 7.31934 + 12.6775i 0.327659 + 0.567521i 0.982047 0.188637i \(-0.0604071\pi\)
−0.654388 + 0.756159i \(0.727074\pi\)
\(500\) −16.9030 + 29.2768i −0.755925 + 1.30930i
\(501\) −21.4699 + 37.1870i −0.959205 + 1.66139i
\(502\) 10.9206 + 18.9150i 0.487409 + 0.844218i
\(503\) 12.7787 0.569774 0.284887 0.958561i \(-0.408044\pi\)
0.284887 + 0.958561i \(0.408044\pi\)
\(504\) −6.70891 15.0045i −0.298839 0.668352i
\(505\) −19.7786 −0.880136
\(506\) −23.7134 41.0727i −1.05419 1.82591i
\(507\) −1.23721 + 2.14292i −0.0549466 + 0.0951703i
\(508\) 15.2575 26.4267i 0.676941 1.17250i
\(509\) −5.84263 10.1197i −0.258970 0.448549i 0.706996 0.707217i \(-0.250050\pi\)
−0.965966 + 0.258668i \(0.916716\pi\)
\(510\) 43.9260 1.94507
\(511\) −11.9495 + 16.5020i −0.528615 + 0.730005i
\(512\) 15.4017 0.680664
\(513\) 0.541949 + 0.938683i 0.0239276 + 0.0414439i
\(514\) −7.59688 + 13.1582i −0.335084 + 0.580382i
\(515\) 7.75495 13.4320i 0.341724 0.591883i
\(516\) −12.2202 21.1659i −0.537962 0.931778i
\(517\) −34.0435 −1.49723
\(518\) −19.3215 + 26.6825i −0.848937 + 1.17236i
\(519\) −7.32772 −0.321651
\(520\) 2.11146 + 3.65716i 0.0925937 + 0.160377i
\(521\) −4.23838 + 7.34108i −0.185687 + 0.321619i −0.943808 0.330495i \(-0.892784\pi\)
0.758121 + 0.652114i \(0.226118\pi\)
\(522\) 20.3934 35.3224i 0.892594 1.54602i
\(523\) −16.3554 28.3284i −0.715172 1.23871i −0.962893 0.269883i \(-0.913015\pi\)
0.247721 0.968831i \(-0.420318\pi\)
\(524\) 15.7233 0.686876
\(525\) 1.31940 + 2.95084i 0.0575833 + 0.128785i
\(526\) −0.280097 −0.0122128
\(527\) −7.12425 12.3396i −0.310337 0.537520i
\(528\) 8.26284 14.3117i 0.359594 0.622835i
\(529\) 1.48975 2.58032i 0.0647716 0.112188i
\(530\) −29.0834 50.3739i −1.26330 2.18810i
\(531\) 14.9549 0.648989
\(532\) −27.2135 2.81669i −1.17985 0.122119i
\(533\) 10.3948 0.450249
\(534\) −10.0342 17.3797i −0.434222 0.752095i
\(535\) 7.16156 12.4042i 0.309621 0.536280i
\(536\) 2.88407 4.99536i 0.124573 0.215767i
\(537\) 7.01361 + 12.1479i 0.302660 + 0.524222i
\(538\) −9.39131 −0.404888
\(539\) −22.3520 + 24.9831i −0.962771 + 1.07610i
\(540\) −1.86975 −0.0804610
\(541\) 14.0853 + 24.3964i 0.605573 + 1.04888i 0.991961 + 0.126547i \(0.0403893\pi\)
−0.386388 + 0.922336i \(0.626277\pi\)
\(542\) −1.73440 + 3.00406i −0.0744987 + 0.129035i
\(543\) −8.87880 + 15.3785i −0.381026 + 0.659956i
\(544\) −13.3473 23.1182i −0.572262 0.991187i
\(545\) −8.86574 −0.379767
\(546\) 14.4130 + 1.49180i 0.616820 + 0.0638430i
\(547\) −18.5377 −0.792615 −0.396307 0.918118i \(-0.629709\pi\)
−0.396307 + 0.918118i \(0.629709\pi\)
\(548\) −32.2415 55.8438i −1.37729 2.38553i
\(549\) −5.00735 + 8.67299i −0.213709 + 0.370154i
\(550\) 2.61670 4.53225i 0.111576 0.193256i
\(551\) −10.5252 18.2303i −0.448391 0.776635i
\(552\) 22.0251 0.937449
\(553\) 5.59252 + 12.5077i 0.237818 + 0.531880i
\(554\) −28.2092 −1.19850
\(555\) 14.7751 + 25.5912i 0.627167 + 1.08628i
\(556\) 5.79759 10.0417i 0.245873 0.425864i
\(557\) −2.00142 + 3.46655i −0.0848027 + 0.146883i −0.905307 0.424758i \(-0.860359\pi\)
0.820504 + 0.571640i \(0.193693\pi\)
\(558\) 13.0327 + 22.5732i 0.551717 + 0.955602i
\(559\) 3.40733 0.144115
\(560\) −4.59379 + 6.34392i −0.194123 + 0.268079i
\(561\) −44.7723 −1.89029
\(562\) −5.12368 8.87448i −0.216129 0.374347i
\(563\) 8.93100 15.4689i 0.376397 0.651938i −0.614138 0.789199i \(-0.710496\pi\)
0.990535 + 0.137260i \(0.0438296\pi\)
\(564\) 25.4951 44.1587i 1.07354 1.85942i
\(565\) 6.26338 + 10.8485i 0.263503 + 0.456400i
\(566\) 8.07490 0.339413
\(567\) 13.3706 18.4645i 0.561514 0.775437i
\(568\) −5.05041 −0.211910
\(569\) 18.7336 + 32.4475i 0.785353 + 1.36027i 0.928788 + 0.370612i \(0.120852\pi\)
−0.143434 + 0.989660i \(0.545815\pi\)
\(570\) −20.7362 + 35.9161i −0.868544 + 1.50436i
\(571\) −8.78514 + 15.2163i −0.367646 + 0.636782i −0.989197 0.146592i \(-0.953170\pi\)
0.621551 + 0.783374i \(0.286503\pi\)
\(572\) −6.94110 12.0223i −0.290222 0.502679i
\(573\) 29.4006 1.22823
\(574\) −24.8465 55.5691i −1.03707 2.31941i
\(575\) −2.20920 −0.0921301
\(576\) 20.0618 + 34.7481i 0.835908 + 1.44784i
\(577\) 17.1247 29.6608i 0.712910 1.23480i −0.250850 0.968026i \(-0.580710\pi\)
0.963760 0.266770i \(-0.0859565\pi\)
\(578\) 3.01524 5.22254i 0.125417 0.217229i
\(579\) −28.4190 49.2232i −1.18105 2.04565i
\(580\) 36.3125 1.50780
\(581\) 9.12490 + 0.944459i 0.378565 + 0.0391828i
\(582\) −29.6144 −1.22756
\(583\) 29.6438 + 51.3445i 1.22772 + 2.12647i
\(584\) −7.65959 + 13.2668i −0.316956 + 0.548984i
\(585\) 3.31453 5.74093i 0.137039 0.237358i
\(586\) 23.2859 + 40.3323i 0.961930 + 1.66611i
\(587\) −29.4494 −1.21551 −0.607754 0.794126i \(-0.707929\pi\)
−0.607754 + 0.794126i \(0.707929\pi\)
\(588\) −15.6669 47.7032i −0.646092 1.96725i
\(589\) 13.4526 0.554305
\(590\) 11.2503 + 19.4861i 0.463167 + 0.802229i
\(591\) −20.9356 + 36.2616i −0.861176 + 1.49160i
\(592\) 3.92275 6.79439i 0.161224 0.279248i
\(593\) 17.0001 + 29.4450i 0.698109 + 1.20916i 0.969121 + 0.246584i \(0.0793081\pi\)
−0.271013 + 0.962576i \(0.587359\pi\)
\(594\) 3.22064 0.132145
\(595\) 21.1075 + 2.18470i 0.865324 + 0.0895640i
\(596\) 8.56514 0.350842
\(597\) −12.4452 21.5557i −0.509349 0.882218i
\(598\) −4.95168 + 8.57655i −0.202489 + 0.350721i
\(599\) −10.7209 + 18.5691i −0.438043 + 0.758713i −0.997539 0.0701203i \(-0.977662\pi\)
0.559495 + 0.828834i \(0.310995\pi\)
\(600\) 1.21520 + 2.10479i 0.0496103 + 0.0859276i
\(601\) 40.4039 1.64811 0.824054 0.566511i \(-0.191707\pi\)
0.824054 + 0.566511i \(0.191707\pi\)
\(602\) −8.14447 18.2151i −0.331944 0.742392i
\(603\) −9.05472 −0.368737
\(604\) 26.8931 + 46.5803i 1.09427 + 1.89533i
\(605\) 12.6668 21.9396i 0.514980 0.891971i
\(606\) −25.5139 + 44.1914i −1.03643 + 1.79515i
\(607\) 21.9456 + 38.0110i 0.890746 + 1.54282i 0.838983 + 0.544158i \(0.183151\pi\)
0.0517636 + 0.998659i \(0.483516\pi\)
\(608\) 25.2036 1.02214
\(609\) 22.6582 31.2904i 0.918156 1.26795i
\(610\) −15.0677 −0.610074
\(611\) 3.55438 + 6.15636i 0.143795 + 0.249060i
\(612\) 17.1011 29.6200i 0.691272 1.19732i
\(613\) 7.15777 12.3976i 0.289100 0.500735i −0.684496 0.729017i \(-0.739977\pi\)
0.973595 + 0.228282i \(0.0733108\pi\)
\(614\) 5.48750 + 9.50464i 0.221458 + 0.383576i
\(615\) −54.6009 −2.20172
\(616\) −14.7831 + 20.4151i −0.595628 + 0.822547i
\(617\) −36.9097 −1.48593 −0.742965 0.669330i \(-0.766581\pi\)
−0.742965 + 0.669330i \(0.766581\pi\)
\(618\) −20.0074 34.6538i −0.804815 1.39398i
\(619\) −7.14646 + 12.3780i −0.287240 + 0.497515i −0.973150 0.230172i \(-0.926071\pi\)
0.685910 + 0.727687i \(0.259405\pi\)
\(620\) −11.6030 + 20.0970i −0.465988 + 0.807115i
\(621\) −0.679774 1.17740i −0.0272784 0.0472476i
\(622\) −5.35973 −0.214906
\(623\) −3.95728 8.85046i −0.158545 0.354586i
\(624\) −3.45079 −0.138142
\(625\) 11.1438 + 19.3016i 0.445750 + 0.772062i
\(626\) −15.4496 + 26.7594i −0.617489 + 1.06952i
\(627\) 21.1357 36.6082i 0.844080 1.46199i
\(628\) 14.2036 + 24.6013i 0.566784 + 0.981698i
\(629\) −21.2554 −0.847510
\(630\) −38.6128 3.99656i −1.53837 0.159227i
\(631\) −0.0431064 −0.00171604 −0.000858019 1.00000i \(-0.500273\pi\)
−0.000858019 1.00000i \(0.500273\pi\)
\(632\) 5.15084 + 8.92152i 0.204890 + 0.354879i
\(633\) 30.2633 52.4176i 1.20286 2.08341i
\(634\) −3.39592 + 5.88190i −0.134869 + 0.233600i
\(635\) −11.1731 19.3524i −0.443390 0.767975i
\(636\) −88.8004 −3.52116
\(637\) 6.85161 + 1.43369i 0.271471 + 0.0568048i
\(638\) −62.5484 −2.47632
\(639\) 3.96401 + 6.86587i 0.156814 + 0.271610i
\(640\) −15.1860 + 26.3029i −0.600279 + 1.03971i
\(641\) −21.3328 + 36.9494i −0.842594 + 1.45942i 0.0451008 + 0.998982i \(0.485639\pi\)
−0.887695 + 0.460433i \(0.847694\pi\)
\(642\) −18.4765 32.0022i −0.729208 1.26303i
\(643\) −5.49737 −0.216795 −0.108398 0.994108i \(-0.534572\pi\)
−0.108398 + 0.994108i \(0.534572\pi\)
\(644\) 34.1342 + 3.53301i 1.34508 + 0.139220i
\(645\) −17.8977 −0.704722
\(646\) −14.9156 25.8345i −0.586845 1.01645i
\(647\) 19.0933 33.0706i 0.750637 1.30014i −0.196877 0.980428i \(-0.563080\pi\)
0.947514 0.319713i \(-0.103587\pi\)
\(648\) 8.57053 14.8446i 0.336682 0.583150i
\(649\) −11.4671 19.8615i −0.450121 0.779633i
\(650\) −1.09280 −0.0428633
\(651\) 10.0775 + 22.5384i 0.394969 + 0.883348i
\(652\) 40.1024 1.57053
\(653\) −19.2510 33.3437i −0.753349 1.30484i −0.946191 0.323608i \(-0.895104\pi\)
0.192843 0.981230i \(-0.438229\pi\)
\(654\) −11.4366 + 19.8088i −0.447206 + 0.774584i
\(655\) 5.75711 9.97161i 0.224949 0.389623i
\(656\) 7.24820 + 12.5543i 0.282995 + 0.490161i
\(657\) 24.0477 0.938192
\(658\) 24.4151 33.7166i 0.951798 1.31441i
\(659\) 19.4843 0.759002 0.379501 0.925191i \(-0.376096\pi\)
0.379501 + 0.925191i \(0.376096\pi\)
\(660\) 36.4595 + 63.1498i 1.41919 + 2.45810i
\(661\) 20.8334 36.0844i 0.810324 1.40352i −0.102314 0.994752i \(-0.532625\pi\)
0.912638 0.408770i \(-0.134042\pi\)
\(662\) −15.0564 + 26.0784i −0.585182 + 1.01356i
\(663\) 4.67454 + 8.09654i 0.181544 + 0.314443i
\(664\) 6.89760 0.267679
\(665\) −11.7506 + 16.2273i −0.455668 + 0.629266i
\(666\) 38.8834 1.50670
\(667\) 13.2020 + 22.8665i 0.511182 + 0.885393i
\(668\) −25.1520 + 43.5645i −0.973160 + 1.68556i
\(669\) 36.2040 62.7071i 1.39973 2.42440i
\(670\) −6.81168 11.7982i −0.263158 0.455803i
\(671\) 15.3580 0.592890
\(672\) 18.8803 + 42.2258i 0.728324 + 1.62889i
\(673\) −14.3157 −0.551830 −0.275915 0.961182i \(-0.588981\pi\)
−0.275915 + 0.961182i \(0.588981\pi\)
\(674\) 38.9153 + 67.4033i 1.49896 + 2.59628i
\(675\) 0.0750110 0.129923i 0.00288718 0.00500073i
\(676\) −1.44940 + 2.51043i −0.0557460 + 0.0965550i
\(677\) 14.7641 + 25.5721i 0.567429 + 0.982815i 0.996819 + 0.0796963i \(0.0253950\pi\)
−0.429391 + 0.903119i \(0.641272\pi\)
\(678\) 32.3184 1.24118
\(679\) −14.2304 1.47290i −0.546114 0.0565247i
\(680\) 15.9554 0.611860
\(681\) 12.4633 + 21.5871i 0.477596 + 0.827220i
\(682\) 19.9862 34.6172i 0.765312 1.32556i
\(683\) −23.5349 + 40.7637i −0.900539 + 1.55978i −0.0737441 + 0.997277i \(0.523495\pi\)
−0.826795 + 0.562503i \(0.809839\pi\)
\(684\) 16.1459 + 27.9655i 0.617354 + 1.06929i
\(685\) −47.2210 −1.80422
\(686\) −8.71296 40.0546i −0.332662 1.52929i
\(687\) −27.5650 −1.05167
\(688\) 2.37590 + 4.11518i 0.0905804 + 0.156890i
\(689\) 6.19003 10.7214i 0.235821 0.408454i
\(690\) 26.0097 45.0501i 0.990172 1.71503i
\(691\) 15.4334 + 26.7314i 0.587113 + 1.01691i 0.994608 + 0.103703i \(0.0330690\pi\)
−0.407495 + 0.913207i \(0.633598\pi\)
\(692\) −8.58442 −0.326331
\(693\) 39.3568 + 4.07356i 1.49504 + 0.154742i
\(694\) −12.1091 −0.459656
\(695\) −4.24559 7.35358i −0.161044 0.278937i
\(696\) 14.5238 25.1560i 0.550524 0.953535i
\(697\) 19.6372 34.0127i 0.743813 1.28832i
\(698\) −4.80508 8.32264i −0.181875 0.315017i
\(699\) −42.2715 −1.59885
\(700\) 1.54568 + 3.45691i 0.0584211 + 0.130659i
\(701\) 6.48958 0.245108 0.122554 0.992462i \(-0.460892\pi\)
0.122554 + 0.992462i \(0.460892\pi\)
\(702\) −0.336257 0.582415i −0.0126912 0.0219818i
\(703\) 10.0341 17.3795i 0.378443 0.655482i
\(704\) 30.7657 53.2878i 1.15953 2.00836i
\(705\) −18.6701 32.3376i −0.703157 1.21790i
\(706\) 61.0860 2.29900
\(707\) −14.4580 + 19.9661i −0.543747 + 0.750902i
\(708\) 34.3505 1.29097
\(709\) 6.68689 + 11.5820i 0.251131 + 0.434972i 0.963838 0.266490i \(-0.0858641\pi\)
−0.712706 + 0.701463i \(0.752531\pi\)
\(710\) −5.96409 + 10.3301i −0.223828 + 0.387682i
\(711\) 8.08569 14.0048i 0.303237 0.525222i
\(712\) −3.64475 6.31290i −0.136593 0.236586i
\(713\) −16.8738 −0.631929
\(714\) 32.1094 44.3424i 1.20167 1.65947i
\(715\) −10.1660 −0.380186
\(716\) 8.21645 + 14.2313i 0.307063 + 0.531849i
\(717\) −8.56328 + 14.8320i −0.319802 + 0.553913i
\(718\) −7.33555 + 12.7055i −0.273760 + 0.474167i
\(719\) 8.37048 + 14.4981i 0.312166 + 0.540688i 0.978831 0.204670i \(-0.0656120\pi\)
−0.666665 + 0.745358i \(0.732279\pi\)
\(720\) 9.24476 0.344532
\(721\) −7.89050 17.6471i −0.293858 0.657212i
\(722\) −13.8883 −0.516868
\(723\) −8.03725 13.9209i −0.298909 0.517725i
\(724\) −10.4015 + 18.0160i −0.386570 + 0.669558i
\(725\) −1.45680 + 2.52325i −0.0541041 + 0.0937110i
\(726\) −32.6798 56.6030i −1.21286 2.10074i
\(727\) 38.8138 1.43952 0.719761 0.694221i \(-0.244251\pi\)
0.719761 + 0.694221i \(0.244251\pi\)
\(728\) 5.23528 + 0.541869i 0.194032 + 0.0200830i
\(729\) −29.1632 −1.08012
\(730\) 18.0906 + 31.3339i 0.669564 + 1.15972i
\(731\) 6.43692 11.1491i 0.238078 0.412364i
\(732\) −11.5016 + 19.9213i −0.425110 + 0.736312i
\(733\) −18.8639 32.6733i −0.696756 1.20682i −0.969585 0.244754i \(-0.921293\pi\)
0.272830 0.962062i \(-0.412040\pi\)
\(734\) 69.0719 2.54949
\(735\) −35.9895 7.53074i −1.32749 0.277776i
\(736\) −31.6132 −1.16528
\(737\) 6.94292 + 12.0255i 0.255746 + 0.442965i
\(738\) −35.9232 + 62.2208i −1.32235 + 2.29038i
\(739\) 4.61476 7.99300i 0.169757 0.294027i −0.768578 0.639757i \(-0.779035\pi\)
0.938334 + 0.345729i \(0.112368\pi\)
\(740\) 17.3090 + 29.9801i 0.636291 + 1.10209i
\(741\) −8.82686 −0.324263
\(742\) −72.1111 7.46375i −2.64728 0.274003i
\(743\) −3.56327 −0.130724 −0.0653619 0.997862i \(-0.520820\pi\)
−0.0653619 + 0.997862i \(0.520820\pi\)
\(744\) 9.28164 + 16.0763i 0.340282 + 0.589385i
\(745\) 3.13614 5.43195i 0.114899 0.199011i
\(746\) 17.4571 30.2366i 0.639151 1.10704i
\(747\) −5.41386 9.37707i −0.198083 0.343089i
\(748\) −52.4508 −1.91779
\(749\) −7.28674 16.2968i −0.266252 0.595472i
\(750\) 63.8698 2.33220
\(751\) −25.6053 44.3496i −0.934350 1.61834i −0.775789 0.630992i \(-0.782648\pi\)
−0.158561 0.987349i \(-0.550685\pi\)
\(752\) −4.95687 + 8.58555i −0.180758 + 0.313083i
\(753\) 12.2089 21.1464i 0.444916 0.770618i
\(754\) 6.53049 + 11.3111i 0.237826 + 0.411927i
\(755\) 39.3879 1.43347
\(756\) −1.36677 + 1.88747i −0.0497088 + 0.0686466i
\(757\) 25.2305 0.917019 0.458509 0.888690i \(-0.348384\pi\)
0.458509 + 0.888690i \(0.348384\pi\)
\(758\) −35.0272 60.6688i −1.27224 2.20359i
\(759\) −26.5108 + 45.9181i −0.962282 + 1.66672i
\(760\) −7.53207 + 13.0459i −0.273217 + 0.473226i
\(761\) −1.82372 3.15878i −0.0661099 0.114506i 0.831076 0.556159i \(-0.187725\pi\)
−0.897186 + 0.441653i \(0.854392\pi\)
\(762\) −57.6520 −2.08851
\(763\) −6.48077 + 8.94978i −0.234620 + 0.324004i
\(764\) 34.4428 1.24610
\(765\) −12.5232 21.6908i −0.452777 0.784233i
\(766\) −13.7154 + 23.7558i −0.495558 + 0.858331i
\(767\) −2.39448 + 4.14736i −0.0864596 + 0.149752i
\(768\) 7.38609 + 12.7931i 0.266523 + 0.461631i
\(769\) 21.9882 0.792914 0.396457 0.918053i \(-0.370240\pi\)
0.396457 + 0.918053i \(0.370240\pi\)
\(770\) 24.2995 + 54.3458i 0.875693 + 1.95849i
\(771\) 16.9862 0.611742
\(772\) −33.2929 57.6650i −1.19824 2.07541i
\(773\) −10.9295 + 18.9305i −0.393108 + 0.680882i −0.992858 0.119305i \(-0.961933\pi\)
0.599750 + 0.800187i \(0.295267\pi\)
\(774\) −11.7753 + 20.3954i −0.423255 + 0.733099i
\(775\) −0.930986 1.61252i −0.0334420 0.0579233i
\(776\) −10.7569 −0.386151
\(777\) 36.6342