Properties

Label 450.2.h.a.271.1
Level $450$
Weight $2$
Character 450.271
Analytic conductor $3.593$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 271.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 450.271
Dual form 450.2.h.a.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} -3.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-1.80902 + 1.31433i) q^{10} +(-1.30902 + 4.02874i) q^{11} +(0.309017 + 0.951057i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.927051 - 0.673542i) q^{17} +(-4.73607 + 3.44095i) q^{19} +(0.690983 + 2.12663i) q^{20} +(3.42705 + 2.48990i) q^{22} +(0.545085 - 1.67760i) q^{23} +(1.54508 + 4.75528i) q^{25} +1.00000 q^{26} +(2.42705 + 1.76336i) q^{28} +(-7.66312 - 5.56758i) q^{29} +(0.190983 - 0.138757i) q^{31} +1.00000 q^{32} +(-0.354102 - 1.08981i) q^{34} +(5.42705 + 3.94298i) q^{35} +(-2.57295 - 7.91872i) q^{37} +(1.80902 + 5.56758i) q^{38} +2.23607 q^{40} +(-0.454915 - 1.40008i) q^{41} -6.23607 q^{43} +(3.42705 - 2.48990i) q^{44} +(-1.42705 - 1.03681i) q^{46} +(-9.66312 - 7.02067i) q^{47} +2.00000 q^{49} +5.00000 q^{50} +(0.309017 - 0.951057i) q^{52} +(8.47214 + 6.15537i) q^{53} +(7.66312 - 5.56758i) q^{55} +(2.42705 - 1.76336i) q^{56} +(-7.66312 + 5.56758i) q^{58} +(1.38197 + 4.25325i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(-0.0729490 - 0.224514i) q^{62} +(0.309017 - 0.951057i) q^{64} +(0.690983 - 2.12663i) q^{65} +(8.28115 - 6.01661i) q^{67} -1.14590 q^{68} +(5.42705 - 3.94298i) q^{70} +(-2.42705 - 1.76336i) q^{71} +(2.38197 - 7.33094i) q^{73} -8.32624 q^{74} +5.85410 q^{76} +(3.92705 - 12.0862i) q^{77} +(5.85410 + 4.25325i) q^{79} +(0.690983 - 2.12663i) q^{80} -1.47214 q^{82} +(-3.66312 + 2.66141i) q^{83} -2.56231 q^{85} +(-1.92705 + 5.93085i) q^{86} +(-1.30902 - 4.02874i) q^{88} +(-1.38197 + 4.25325i) q^{89} +(-0.927051 - 2.85317i) q^{91} +(-1.42705 + 1.03681i) q^{92} +(-9.66312 + 7.02067i) q^{94} +13.0902 q^{95} +(-7.73607 - 5.62058i) q^{97} +(0.618034 - 1.90211i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} - q^{4} - 5q^{5} - 12q^{7} - q^{8} + O(q^{10}) \) \( 4q - q^{2} - q^{4} - 5q^{5} - 12q^{7} - q^{8} - 5q^{10} - 3q^{11} - q^{13} + 3q^{14} - q^{16} - 3q^{17} - 10q^{19} + 5q^{20} + 7q^{22} - 9q^{23} - 5q^{25} + 4q^{26} + 3q^{28} - 15q^{29} + 3q^{31} + 4q^{32} + 12q^{34} + 15q^{35} - 17q^{37} + 5q^{38} - 13q^{41} - 16q^{43} + 7q^{44} + q^{46} - 23q^{47} + 8q^{49} + 20q^{50} - q^{52} + 16q^{53} + 15q^{55} + 3q^{56} - 15q^{58} + 10q^{59} - 2q^{61} - 7q^{62} - q^{64} + 5q^{65} + 13q^{67} - 18q^{68} + 15q^{70} - 3q^{71} + 14q^{73} - 2q^{74} + 10q^{76} + 9q^{77} + 10q^{79} + 5q^{80} + 12q^{82} + q^{83} + 30q^{85} - q^{86} - 3q^{88} - 10q^{89} + 3q^{91} + q^{92} - 23q^{94} + 30q^{95} - 22q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) 0 0
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) −1.80902 1.31433i −0.809017 0.587785i
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 0 0
\(10\) −1.80902 + 1.31433i −0.572061 + 0.415627i
\(11\) −1.30902 + 4.02874i −0.394683 + 1.21471i 0.534524 + 0.845153i \(0.320491\pi\)
−0.929208 + 0.369558i \(0.879509\pi\)
\(12\) 0 0
\(13\) 0.309017 + 0.951057i 0.0857059 + 0.263776i 0.984720 0.174143i \(-0.0557156\pi\)
−0.899014 + 0.437919i \(0.855716\pi\)
\(14\) −0.927051 + 2.85317i −0.247765 + 0.762542i
\(15\) 0 0
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 0.927051 0.673542i 0.224843 0.163358i −0.469661 0.882847i \(-0.655624\pi\)
0.694504 + 0.719489i \(0.255624\pi\)
\(18\) 0 0
\(19\) −4.73607 + 3.44095i −1.08653 + 0.789409i −0.978810 0.204772i \(-0.934355\pi\)
−0.107719 + 0.994181i \(0.534355\pi\)
\(20\) 0.690983 + 2.12663i 0.154508 + 0.475528i
\(21\) 0 0
\(22\) 3.42705 + 2.48990i 0.730650 + 0.530848i
\(23\) 0.545085 1.67760i 0.113658 0.349804i −0.878007 0.478648i \(-0.841127\pi\)
0.991665 + 0.128845i \(0.0411269\pi\)
\(24\) 0 0
\(25\) 1.54508 + 4.75528i 0.309017 + 0.951057i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 2.42705 + 1.76336i 0.458670 + 0.333243i
\(29\) −7.66312 5.56758i −1.42301 1.03387i −0.991266 0.131875i \(-0.957900\pi\)
−0.431739 0.901998i \(-0.642100\pi\)
\(30\) 0 0
\(31\) 0.190983 0.138757i 0.0343016 0.0249215i −0.570502 0.821296i \(-0.693251\pi\)
0.604804 + 0.796374i \(0.293251\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −0.354102 1.08981i −0.0607280 0.186902i
\(35\) 5.42705 + 3.94298i 0.917339 + 0.666486i
\(36\) 0 0
\(37\) −2.57295 7.91872i −0.422990 1.30183i −0.904906 0.425612i \(-0.860059\pi\)
0.481915 0.876218i \(-0.339941\pi\)
\(38\) 1.80902 + 5.56758i 0.293461 + 0.903181i
\(39\) 0 0
\(40\) 2.23607 0.353553
\(41\) −0.454915 1.40008i −0.0710458 0.218656i 0.909229 0.416297i \(-0.136672\pi\)
−0.980275 + 0.197640i \(0.936672\pi\)
\(42\) 0 0
\(43\) −6.23607 −0.950991 −0.475496 0.879718i \(-0.657731\pi\)
−0.475496 + 0.879718i \(0.657731\pi\)
\(44\) 3.42705 2.48990i 0.516647 0.375366i
\(45\) 0 0
\(46\) −1.42705 1.03681i −0.210407 0.152870i
\(47\) −9.66312 7.02067i −1.40951 1.02407i −0.993393 0.114759i \(-0.963391\pi\)
−0.416117 0.909311i \(-0.636609\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) 0.309017 0.951057i 0.0428529 0.131888i
\(53\) 8.47214 + 6.15537i 1.16374 + 0.845505i 0.990246 0.139331i \(-0.0444951\pi\)
0.173491 + 0.984835i \(0.444495\pi\)
\(54\) 0 0
\(55\) 7.66312 5.56758i 1.03329 0.750733i
\(56\) 2.42705 1.76336i 0.324328 0.235638i
\(57\) 0 0
\(58\) −7.66312 + 5.56758i −1.00622 + 0.731059i
\(59\) 1.38197 + 4.25325i 0.179917 + 0.553727i 0.999824 0.0187700i \(-0.00597502\pi\)
−0.819907 + 0.572496i \(0.805975\pi\)
\(60\) 0 0
\(61\) −2.73607 + 8.42075i −0.350318 + 1.07817i 0.608357 + 0.793663i \(0.291829\pi\)
−0.958675 + 0.284504i \(0.908171\pi\)
\(62\) −0.0729490 0.224514i −0.00926453 0.0285133i
\(63\) 0 0
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 0.690983 2.12663i 0.0857059 0.263776i
\(66\) 0 0
\(67\) 8.28115 6.01661i 1.01170 0.735046i 0.0471381 0.998888i \(-0.484990\pi\)
0.964566 + 0.263843i \(0.0849899\pi\)
\(68\) −1.14590 −0.138961
\(69\) 0 0
\(70\) 5.42705 3.94298i 0.648657 0.471277i
\(71\) −2.42705 1.76336i −0.288038 0.209272i 0.434378 0.900731i \(-0.356968\pi\)
−0.722416 + 0.691459i \(0.756968\pi\)
\(72\) 0 0
\(73\) 2.38197 7.33094i 0.278788 0.858021i −0.709404 0.704802i \(-0.751036\pi\)
0.988192 0.153219i \(-0.0489641\pi\)
\(74\) −8.32624 −0.967905
\(75\) 0 0
\(76\) 5.85410 0.671512
\(77\) 3.92705 12.0862i 0.447529 1.37735i
\(78\) 0 0
\(79\) 5.85410 + 4.25325i 0.658638 + 0.478528i 0.866203 0.499693i \(-0.166554\pi\)
−0.207565 + 0.978221i \(0.566554\pi\)
\(80\) 0.690983 2.12663i 0.0772542 0.237764i
\(81\) 0 0
\(82\) −1.47214 −0.162570
\(83\) −3.66312 + 2.66141i −0.402080 + 0.292128i −0.770387 0.637576i \(-0.779937\pi\)
0.368308 + 0.929704i \(0.379937\pi\)
\(84\) 0 0
\(85\) −2.56231 −0.277921
\(86\) −1.92705 + 5.93085i −0.207799 + 0.639540i
\(87\) 0 0
\(88\) −1.30902 4.02874i −0.139542 0.429465i
\(89\) −1.38197 + 4.25325i −0.146488 + 0.450844i −0.997199 0.0747893i \(-0.976172\pi\)
0.850711 + 0.525633i \(0.176172\pi\)
\(90\) 0 0
\(91\) −0.927051 2.85317i −0.0971813 0.299093i
\(92\) −1.42705 + 1.03681i −0.148780 + 0.108095i
\(93\) 0 0
\(94\) −9.66312 + 7.02067i −0.996675 + 0.724126i
\(95\) 13.0902 1.34302
\(96\) 0 0
\(97\) −7.73607 5.62058i −0.785479 0.570684i 0.121140 0.992635i \(-0.461345\pi\)
−0.906618 + 0.421952i \(0.861345\pi\)
\(98\) 0.618034 1.90211i 0.0624309 0.192142i
\(99\) 0 0
\(100\) 1.54508 4.75528i 0.154508 0.475528i
\(101\) −0.618034 −0.0614967 −0.0307483 0.999527i \(-0.509789\pi\)
−0.0307483 + 0.999527i \(0.509789\pi\)
\(102\) 0 0
\(103\) 10.6353 + 7.72696i 1.04792 + 0.761360i 0.971816 0.235739i \(-0.0757511\pi\)
0.0761065 + 0.997100i \(0.475751\pi\)
\(104\) −0.809017 0.587785i −0.0793306 0.0576371i
\(105\) 0 0
\(106\) 8.47214 6.15537i 0.822887 0.597862i
\(107\) 1.09017 0.105391 0.0526954 0.998611i \(-0.483219\pi\)
0.0526954 + 0.998611i \(0.483219\pi\)
\(108\) 0 0
\(109\) −4.63525 14.2658i −0.443977 1.36642i −0.883602 0.468239i \(-0.844889\pi\)
0.439625 0.898181i \(-0.355111\pi\)
\(110\) −2.92705 9.00854i −0.279083 0.858930i
\(111\) 0 0
\(112\) −0.927051 2.85317i −0.0875981 0.269599i
\(113\) −1.16312 3.57971i −0.109417 0.336751i 0.881325 0.472511i \(-0.156652\pi\)
−0.990742 + 0.135760i \(0.956652\pi\)
\(114\) 0 0
\(115\) −3.19098 + 2.31838i −0.297561 + 0.216191i
\(116\) 2.92705 + 9.00854i 0.271770 + 0.836422i
\(117\) 0 0
\(118\) 4.47214 0.411693
\(119\) −2.78115 + 2.02063i −0.254948 + 0.185230i
\(120\) 0 0
\(121\) −5.61803 4.08174i −0.510730 0.371067i
\(122\) 7.16312 + 5.20431i 0.648518 + 0.471176i
\(123\) 0 0
\(124\) −0.236068 −0.0211995
\(125\) 3.45492 10.6331i 0.309017 0.951057i
\(126\) 0 0
\(127\) −1.09017 + 3.35520i −0.0967369 + 0.297726i −0.987702 0.156345i \(-0.950029\pi\)
0.890966 + 0.454071i \(0.150029\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) 0 0
\(130\) −1.80902 1.31433i −0.158661 0.115274i
\(131\) −13.2812 + 9.64932i −1.16038 + 0.843065i −0.989826 0.142283i \(-0.954556\pi\)
−0.170554 + 0.985348i \(0.554556\pi\)
\(132\) 0 0
\(133\) 14.2082 10.3229i 1.23201 0.895106i
\(134\) −3.16312 9.73508i −0.273252 0.840983i
\(135\) 0 0
\(136\) −0.354102 + 1.08981i −0.0303640 + 0.0934508i
\(137\) −1.57295 4.84104i −0.134386 0.413598i 0.861108 0.508422i \(-0.169771\pi\)
−0.995494 + 0.0948243i \(0.969771\pi\)
\(138\) 0 0
\(139\) −1.64590 + 5.06555i −0.139603 + 0.429655i −0.996278 0.0862030i \(-0.972527\pi\)
0.856674 + 0.515858i \(0.172527\pi\)
\(140\) −2.07295 6.37988i −0.175196 0.539198i
\(141\) 0 0
\(142\) −2.42705 + 1.76336i −0.203674 + 0.147978i
\(143\) −4.23607 −0.354238
\(144\) 0 0
\(145\) 6.54508 + 20.1437i 0.543540 + 1.67284i
\(146\) −6.23607 4.53077i −0.516101 0.374969i
\(147\) 0 0
\(148\) −2.57295 + 7.91872i −0.211495 + 0.650915i
\(149\) −2.23607 −0.183186 −0.0915929 0.995797i \(-0.529196\pi\)
−0.0915929 + 0.995797i \(0.529196\pi\)
\(150\) 0 0
\(151\) −9.70820 −0.790042 −0.395021 0.918672i \(-0.629263\pi\)
−0.395021 + 0.918672i \(0.629263\pi\)
\(152\) 1.80902 5.56758i 0.146731 0.451591i
\(153\) 0 0
\(154\) −10.2812 7.46969i −0.828479 0.601925i
\(155\) −0.527864 −0.0423991
\(156\) 0 0
\(157\) 4.56231 0.364112 0.182056 0.983288i \(-0.441725\pi\)
0.182056 + 0.983288i \(0.441725\pi\)
\(158\) 5.85410 4.25325i 0.465727 0.338371i
\(159\) 0 0
\(160\) −1.80902 1.31433i −0.143015 0.103907i
\(161\) −1.63525 + 5.03280i −0.128876 + 0.396640i
\(162\) 0 0
\(163\) 0.572949 + 1.76336i 0.0448768 + 0.138117i 0.970984 0.239143i \(-0.0768664\pi\)
−0.926108 + 0.377260i \(0.876866\pi\)
\(164\) −0.454915 + 1.40008i −0.0355229 + 0.109328i
\(165\) 0 0
\(166\) 1.39919 + 4.30625i 0.108598 + 0.334230i
\(167\) 10.8262 7.86572i 0.837759 0.608668i −0.0839844 0.996467i \(-0.526765\pi\)
0.921744 + 0.387799i \(0.126765\pi\)
\(168\) 0 0
\(169\) 9.70820 7.05342i 0.746785 0.542571i
\(170\) −0.791796 + 2.43690i −0.0607280 + 0.186902i
\(171\) 0 0
\(172\) 5.04508 + 3.66547i 0.384684 + 0.279489i
\(173\) 0.381966 1.17557i 0.0290403 0.0893770i −0.935486 0.353364i \(-0.885038\pi\)
0.964526 + 0.263987i \(0.0850377\pi\)
\(174\) 0 0
\(175\) −4.63525 14.2658i −0.350392 1.07840i
\(176\) −4.23607 −0.319306
\(177\) 0 0
\(178\) 3.61803 + 2.62866i 0.271183 + 0.197026i
\(179\) 9.04508 + 6.57164i 0.676061 + 0.491187i 0.872049 0.489419i \(-0.162791\pi\)
−0.195987 + 0.980606i \(0.562791\pi\)
\(180\) 0 0
\(181\) −4.38197 + 3.18368i −0.325709 + 0.236641i −0.738608 0.674136i \(-0.764516\pi\)
0.412899 + 0.910777i \(0.364516\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) 0.545085 + 1.67760i 0.0401842 + 0.123674i
\(185\) −5.75329 + 17.7068i −0.422990 + 1.30183i
\(186\) 0 0
\(187\) 1.50000 + 4.61653i 0.109691 + 0.337594i
\(188\) 3.69098 + 11.3597i 0.269193 + 0.828490i
\(189\) 0 0
\(190\) 4.04508 12.4495i 0.293461 0.903181i
\(191\) 4.21885 + 12.9843i 0.305265 + 0.939509i 0.979578 + 0.201064i \(0.0644398\pi\)
−0.674313 + 0.738446i \(0.735560\pi\)
\(192\) 0 0
\(193\) −14.6525 −1.05471 −0.527354 0.849646i \(-0.676816\pi\)
−0.527354 + 0.849646i \(0.676816\pi\)
\(194\) −7.73607 + 5.62058i −0.555417 + 0.403534i
\(195\) 0 0
\(196\) −1.61803 1.17557i −0.115574 0.0839693i
\(197\) 9.70820 + 7.05342i 0.691681 + 0.502536i 0.877212 0.480103i \(-0.159401\pi\)
−0.185531 + 0.982638i \(0.559401\pi\)
\(198\) 0 0
\(199\) 2.56231 0.181637 0.0908185 0.995867i \(-0.471052\pi\)
0.0908185 + 0.995867i \(0.471052\pi\)
\(200\) −4.04508 2.93893i −0.286031 0.207813i
\(201\) 0 0
\(202\) −0.190983 + 0.587785i −0.0134375 + 0.0413564i
\(203\) 22.9894 + 16.7027i 1.61354 + 1.17230i
\(204\) 0 0
\(205\) −1.01722 + 3.13068i −0.0710458 + 0.218656i
\(206\) 10.6353 7.72696i 0.740993 0.538363i
\(207\) 0 0
\(208\) −0.809017 + 0.587785i −0.0560952 + 0.0407556i
\(209\) −7.66312 23.5847i −0.530069 1.63138i
\(210\) 0 0
\(211\) −6.88197 + 21.1805i −0.473774 + 1.45813i 0.373830 + 0.927497i \(0.378044\pi\)
−0.847604 + 0.530629i \(0.821956\pi\)
\(212\) −3.23607 9.95959i −0.222254 0.684028i
\(213\) 0 0
\(214\) 0.336881 1.03681i 0.0230287 0.0708751i
\(215\) 11.2812 + 8.19624i 0.769368 + 0.558979i
\(216\) 0 0
\(217\) −0.572949 + 0.416272i −0.0388943 + 0.0282584i
\(218\) −15.0000 −1.01593
\(219\) 0 0
\(220\) −9.47214 −0.638611
\(221\) 0.927051 + 0.673542i 0.0623602 + 0.0453073i
\(222\) 0 0
\(223\) −2.78115 + 8.55951i −0.186240 + 0.573187i −0.999968 0.00805911i \(-0.997435\pi\)
0.813728 + 0.581246i \(0.197435\pi\)
\(224\) −3.00000 −0.200446
\(225\) 0 0
\(226\) −3.76393 −0.250373
\(227\) −9.07295 + 27.9237i −0.602193 + 1.85336i −0.0871483 + 0.996195i \(0.527775\pi\)
−0.515044 + 0.857163i \(0.672225\pi\)
\(228\) 0 0
\(229\) 2.07295 + 1.50609i 0.136984 + 0.0995249i 0.654167 0.756350i \(-0.273019\pi\)
−0.517183 + 0.855875i \(0.673019\pi\)
\(230\) 1.21885 + 3.75123i 0.0803684 + 0.247348i
\(231\) 0 0
\(232\) 9.47214 0.621876
\(233\) 11.5623 8.40051i 0.757472 0.550336i −0.140662 0.990058i \(-0.544923\pi\)
0.898134 + 0.439722i \(0.144923\pi\)
\(234\) 0 0
\(235\) 8.25329 + 25.4010i 0.538385 + 1.65698i
\(236\) 1.38197 4.25325i 0.0899583 0.276863i
\(237\) 0 0
\(238\) 1.06231 + 3.26944i 0.0688591 + 0.211926i
\(239\) 2.13525 6.57164i 0.138118 0.425084i −0.857944 0.513743i \(-0.828258\pi\)
0.996062 + 0.0886595i \(0.0282583\pi\)
\(240\) 0 0
\(241\) 4.82624 + 14.8536i 0.310885 + 0.956807i 0.977415 + 0.211328i \(0.0677789\pi\)
−0.666530 + 0.745478i \(0.732221\pi\)
\(242\) −5.61803 + 4.08174i −0.361141 + 0.262384i
\(243\) 0 0
\(244\) 7.16312 5.20431i 0.458572 0.333172i
\(245\) −3.61803 2.62866i −0.231148 0.167939i
\(246\) 0 0
\(247\) −4.73607 3.44095i −0.301349 0.218943i
\(248\) −0.0729490 + 0.224514i −0.00463227 + 0.0142567i
\(249\) 0 0
\(250\) −9.04508 6.57164i −0.572061 0.415627i
\(251\) −0.819660 −0.0517365 −0.0258682 0.999665i \(-0.508235\pi\)
−0.0258682 + 0.999665i \(0.508235\pi\)
\(252\) 0 0
\(253\) 6.04508 + 4.39201i 0.380051 + 0.276123i
\(254\) 2.85410 + 2.07363i 0.179082 + 0.130111i
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −25.7426 −1.60578 −0.802891 0.596126i \(-0.796706\pi\)
−0.802891 + 0.596126i \(0.796706\pi\)
\(258\) 0 0
\(259\) 7.71885 + 23.7562i 0.479626 + 1.47614i
\(260\) −1.80902 + 1.31433i −0.112190 + 0.0815111i
\(261\) 0 0
\(262\) 5.07295 + 15.6129i 0.313408 + 0.964570i
\(263\) −1.42705 4.39201i −0.0879957 0.270823i 0.897369 0.441280i \(-0.145476\pi\)
−0.985365 + 0.170457i \(0.945476\pi\)
\(264\) 0 0
\(265\) −7.23607 22.2703i −0.444508 1.36806i
\(266\) −5.42705 16.7027i −0.332754 1.02411i
\(267\) 0 0
\(268\) −10.2361 −0.625267
\(269\) 1.54508 1.12257i 0.0942055 0.0684443i −0.539685 0.841867i \(-0.681457\pi\)
0.633891 + 0.773422i \(0.281457\pi\)
\(270\) 0 0
\(271\) −23.0623 16.7557i −1.40094 1.01784i −0.994564 0.104131i \(-0.966794\pi\)
−0.406372 0.913708i \(-0.633206\pi\)
\(272\) 0.927051 + 0.673542i 0.0562107 + 0.0408395i
\(273\) 0 0
\(274\) −5.09017 −0.307508
\(275\) −21.1803 −1.27722
\(276\) 0 0
\(277\) 0.0901699 0.277515i 0.00541779 0.0166742i −0.948311 0.317342i \(-0.897210\pi\)
0.953729 + 0.300668i \(0.0972096\pi\)
\(278\) 4.30902 + 3.13068i 0.258438 + 0.187766i
\(279\) 0 0
\(280\) −6.70820 −0.400892
\(281\) 2.57295 1.86936i 0.153489 0.111516i −0.508390 0.861127i \(-0.669759\pi\)
0.661879 + 0.749610i \(0.269759\pi\)
\(282\) 0 0
\(283\) 9.94427 7.22494i 0.591126 0.429478i −0.251592 0.967833i \(-0.580954\pi\)
0.842718 + 0.538355i \(0.180954\pi\)
\(284\) 0.927051 + 2.85317i 0.0550104 + 0.169304i
\(285\) 0 0
\(286\) −1.30902 + 4.02874i −0.0774038 + 0.238224i
\(287\) 1.36475 + 4.20025i 0.0805584 + 0.247933i
\(288\) 0 0
\(289\) −4.84752 + 14.9191i −0.285148 + 0.877597i
\(290\) 21.1803 1.24375
\(291\) 0 0
\(292\) −6.23607 + 4.53077i −0.364938 + 0.265143i
\(293\) −8.56231 −0.500215 −0.250108 0.968218i \(-0.580466\pi\)
−0.250108 + 0.968218i \(0.580466\pi\)
\(294\) 0 0
\(295\) 3.09017 9.51057i 0.179917 0.553727i
\(296\) 6.73607 + 4.89404i 0.391526 + 0.284460i
\(297\) 0 0
\(298\) −0.690983 + 2.12663i −0.0400276 + 0.123192i
\(299\) 1.76393 0.102011
\(300\) 0 0
\(301\) 18.7082 1.07832
\(302\) −3.00000 + 9.23305i −0.172631 + 0.531302i
\(303\) 0 0
\(304\) −4.73607 3.44095i −0.271632 0.197352i
\(305\) 16.0172 11.6372i 0.917143 0.666344i
\(306\) 0 0
\(307\) −23.1246 −1.31979 −0.659896 0.751357i \(-0.729400\pi\)
−0.659896 + 0.751357i \(0.729400\pi\)
\(308\) −10.2812 + 7.46969i −0.585823 + 0.425625i
\(309\) 0 0
\(310\) −0.163119 + 0.502029i −0.00926453 + 0.0285133i
\(311\) 3.06231 9.42481i 0.173647 0.534432i −0.825922 0.563785i \(-0.809345\pi\)
0.999569 + 0.0293530i \(0.00934470\pi\)
\(312\) 0 0
\(313\) −5.11803 15.7517i −0.289288 0.890338i −0.985080 0.172095i \(-0.944946\pi\)
0.695792 0.718243i \(-0.255054\pi\)
\(314\) 1.40983 4.33901i 0.0795613 0.244865i
\(315\) 0 0
\(316\) −2.23607 6.88191i −0.125789 0.387138i
\(317\) 6.78115 4.92680i 0.380867 0.276716i −0.380835 0.924643i \(-0.624364\pi\)
0.761703 + 0.647926i \(0.224364\pi\)
\(318\) 0 0
\(319\) 32.4615 23.5847i 1.81749 1.32049i
\(320\) −1.80902 + 1.31433i −0.101127 + 0.0734732i
\(321\) 0 0
\(322\) 4.28115 + 3.11044i 0.238579 + 0.173338i
\(323\) −2.07295 + 6.37988i −0.115342 + 0.354986i
\(324\) 0 0
\(325\) −4.04508 + 2.93893i −0.224381 + 0.163022i
\(326\) 1.85410 0.102689
\(327\) 0 0
\(328\) 1.19098 + 0.865300i 0.0657610 + 0.0477782i
\(329\) 28.9894 + 21.0620i 1.59823 + 1.16119i
\(330\) 0 0
\(331\) 12.5902 9.14729i 0.692018 0.502781i −0.185305 0.982681i \(-0.559327\pi\)
0.877323 + 0.479900i \(0.159327\pi\)
\(332\) 4.52786 0.248499
\(333\) 0 0
\(334\) −4.13525 12.7270i −0.226271 0.696391i
\(335\) −22.8885 −1.25053
\(336\) 0 0
\(337\) −1.41641 4.35926i −0.0771567 0.237464i 0.905038 0.425331i \(-0.139842\pi\)
−0.982194 + 0.187868i \(0.939842\pi\)
\(338\) −3.70820 11.4127i −0.201700 0.620768i
\(339\) 0 0
\(340\) 2.07295 + 1.50609i 0.112421 + 0.0816790i
\(341\) 0.309017 + 0.951057i 0.0167342 + 0.0515026i
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 5.04508 3.66547i 0.272013 0.197629i
\(345\) 0 0
\(346\) −1.00000 0.726543i −0.0537603 0.0390592i
\(347\) −17.0623 12.3965i −0.915953 0.665478i 0.0265607 0.999647i \(-0.491544\pi\)
−0.942513 + 0.334169i \(0.891544\pi\)
\(348\) 0 0
\(349\) −17.7639 −0.950881 −0.475441 0.879748i \(-0.657711\pi\)
−0.475441 + 0.879748i \(0.657711\pi\)
\(350\) −15.0000 −0.801784
\(351\) 0 0
\(352\) −1.30902 + 4.02874i −0.0697708 + 0.214733i
\(353\) −17.1803 12.4822i −0.914417 0.664363i 0.0277109 0.999616i \(-0.491178\pi\)
−0.942128 + 0.335253i \(0.891178\pi\)
\(354\) 0 0
\(355\) 2.07295 + 6.37988i 0.110021 + 0.338609i
\(356\) 3.61803 2.62866i 0.191755 0.139318i
\(357\) 0 0
\(358\) 9.04508 6.57164i 0.478048 0.347322i
\(359\) 2.50000 + 7.69421i 0.131945 + 0.406085i 0.995102 0.0988502i \(-0.0315165\pi\)
−0.863157 + 0.504935i \(0.831516\pi\)
\(360\) 0 0
\(361\) 4.71885 14.5231i 0.248360 0.764375i
\(362\) 1.67376 + 5.15131i 0.0879710 + 0.270747i
\(363\) 0 0
\(364\) −0.927051 + 2.85317i −0.0485907 + 0.149547i
\(365\) −13.9443 + 10.1311i −0.729877 + 0.530286i
\(366\) 0 0
\(367\) −28.7533 + 20.8905i −1.50091 + 1.09047i −0.530892 + 0.847440i \(0.678143\pi\)
−0.970018 + 0.243035i \(0.921857\pi\)
\(368\) 1.76393 0.0919513
\(369\) 0 0
\(370\) 15.0623 + 10.9434i 0.783052 + 0.568921i
\(371\) −25.4164 18.4661i −1.31955 0.958712i
\(372\) 0 0
\(373\) −3.63525 + 11.1882i −0.188226 + 0.579301i −0.999989 0.00468631i \(-0.998508\pi\)
0.811763 + 0.583987i \(0.198508\pi\)
\(374\) 4.85410 0.251000
\(375\) 0 0
\(376\) 11.9443 0.615979
\(377\) 2.92705 9.00854i 0.150751 0.463963i
\(378\) 0 0
\(379\) −7.66312 5.56758i −0.393628 0.285987i 0.373313 0.927706i \(-0.378222\pi\)
−0.766941 + 0.641718i \(0.778222\pi\)
\(380\) −10.5902 7.69421i −0.543264 0.394705i
\(381\) 0 0
\(382\) 13.6525 0.698521
\(383\) 9.16312 6.65740i 0.468214 0.340177i −0.328531 0.944493i \(-0.606554\pi\)
0.796745 + 0.604316i \(0.206554\pi\)
\(384\) 0 0
\(385\) −22.9894 + 16.7027i −1.17165 + 0.851251i
\(386\) −4.52786 + 13.9353i −0.230462 + 0.709290i
\(387\) 0 0
\(388\) 2.95492 + 9.09429i 0.150013 + 0.461693i
\(389\) −5.62868 + 17.3233i −0.285385 + 0.878326i 0.700898 + 0.713262i \(0.252783\pi\)
−0.986283 + 0.165064i \(0.947217\pi\)
\(390\) 0 0
\(391\) −0.624612 1.92236i −0.0315880 0.0972178i
\(392\) −1.61803 + 1.17557i −0.0817231 + 0.0593753i
\(393\) 0 0
\(394\) 9.70820 7.05342i 0.489092 0.355346i
\(395\) −5.00000 15.3884i −0.251577 0.774275i
\(396\) 0 0
\(397\) 8.28115 + 6.01661i 0.415619 + 0.301965i 0.775873 0.630889i \(-0.217310\pi\)
−0.360254 + 0.932854i \(0.617310\pi\)
\(398\) 0.791796 2.43690i 0.0396892 0.122151i
\(399\) 0 0
\(400\) −4.04508 + 2.93893i −0.202254 + 0.146946i
\(401\) 14.1803 0.708132 0.354066 0.935220i \(-0.384799\pi\)
0.354066 + 0.935220i \(0.384799\pi\)
\(402\) 0 0
\(403\) 0.190983 + 0.138757i 0.00951354 + 0.00691199i
\(404\) 0.500000 + 0.363271i 0.0248759 + 0.0180734i
\(405\) 0 0
\(406\) 22.9894 16.7027i 1.14094 0.828943i
\(407\) 35.2705 1.74829
\(408\) 0 0
\(409\) −2.07295 6.37988i −0.102501 0.315465i 0.886635 0.462470i \(-0.153037\pi\)
−0.989136 + 0.147005i \(0.953037\pi\)
\(410\) 2.66312 + 1.93487i 0.131522 + 0.0955564i
\(411\) 0 0
\(412\) −4.06231 12.5025i −0.200135 0.615954i
\(413\) −4.14590 12.7598i −0.204006 0.627867i
\(414\) 0 0
\(415\) 10.1246 0.496998
\(416\) 0.309017 + 0.951057i 0.0151508 + 0.0466294i
\(417\) 0 0
\(418\) −24.7984 −1.21293
\(419\) 18.4164 13.3803i 0.899700 0.653671i −0.0386886 0.999251i \(-0.512318\pi\)
0.938389 + 0.345581i \(0.112318\pi\)
\(420\) 0 0
\(421\) −17.2082 12.5025i −0.838677 0.609334i 0.0833241 0.996522i \(-0.473446\pi\)
−0.922001 + 0.387188i \(0.873446\pi\)
\(422\) 18.0172 + 13.0903i 0.877065 + 0.637225i
\(423\) 0 0
\(424\) −10.4721 −0.508572
\(425\) 4.63525 + 3.36771i 0.224843 + 0.163358i
\(426\) 0 0
\(427\) 8.20820 25.2623i 0.397223 1.22253i
\(428\) −0.881966 0.640786i −0.0426314 0.0309736i
\(429\) 0 0
\(430\) 11.2812 8.19624i 0.544026 0.395258i
\(431\) 21.0902 15.3229i 1.01588 0.738078i 0.0504440 0.998727i \(-0.483936\pi\)
0.965434 + 0.260649i \(0.0839364\pi\)
\(432\) 0 0
\(433\) 17.2812 12.5555i 0.830479 0.603378i −0.0892157 0.996012i \(-0.528436\pi\)
0.919695 + 0.392634i \(0.128436\pi\)
\(434\) 0.218847 + 0.673542i 0.0105050 + 0.0323310i
\(435\) 0 0
\(436\) −4.63525 + 14.2658i −0.221988 + 0.683210i
\(437\) 3.19098 + 9.82084i 0.152645 + 0.469794i
\(438\) 0 0
\(439\) 7.92705 24.3970i 0.378338 1.16440i −0.562862 0.826551i \(-0.690300\pi\)
0.941199 0.337852i \(-0.109700\pi\)
\(440\) −2.92705 + 9.00854i −0.139542 + 0.429465i
\(441\) 0 0
\(442\) 0.927051 0.673542i 0.0440953 0.0320371i
\(443\) −19.4164 −0.922501 −0.461251 0.887270i \(-0.652599\pi\)
−0.461251 + 0.887270i \(0.652599\pi\)
\(444\) 0 0
\(445\) 8.09017 5.87785i 0.383511 0.278637i
\(446\) 7.28115 + 5.29007i 0.344773 + 0.250492i
\(447\) 0 0
\(448\) −0.927051 + 2.85317i −0.0437990 + 0.134800i
\(449\) 3.94427 0.186142 0.0930709 0.995659i \(-0.470332\pi\)
0.0930709 + 0.995659i \(0.470332\pi\)
\(450\) 0 0
\(451\) 6.23607 0.293645
\(452\) −1.16312 + 3.57971i −0.0547085 + 0.168375i
\(453\) 0 0
\(454\) 23.7533 + 17.2578i 1.11480 + 0.809947i
\(455\) −2.07295 + 6.37988i −0.0971813 + 0.299093i
\(456\) 0 0
\(457\) 40.2148 1.88117 0.940584 0.339561i \(-0.110278\pi\)
0.940584 + 0.339561i \(0.110278\pi\)
\(458\) 2.07295 1.50609i 0.0968625 0.0703748i
\(459\) 0 0
\(460\) 3.94427 0.183903
\(461\) −1.79837 + 5.53483i −0.0837586 + 0.257783i −0.984161 0.177275i \(-0.943272\pi\)
0.900403 + 0.435057i \(0.143272\pi\)
\(462\) 0 0
\(463\) −10.8090 33.2667i −0.502338 1.54604i −0.805201 0.593002i \(-0.797943\pi\)
0.302863 0.953034i \(-0.402057\pi\)
\(464\) 2.92705 9.00854i 0.135885 0.418211i
\(465\) 0 0
\(466\) −4.41641 13.5923i −0.204586 0.629651i
\(467\) −15.5172 + 11.2739i −0.718051 + 0.521695i −0.885761 0.464142i \(-0.846363\pi\)
0.167710 + 0.985836i \(0.446363\pi\)
\(468\) 0 0
\(469\) −24.8435 + 18.0498i −1.14716 + 0.833464i
\(470\) 26.7082 1.23196
\(471\) 0 0
\(472\) −3.61803 2.62866i −0.166534 0.120994i
\(473\) 8.16312 25.1235i 0.375341 1.15518i
\(474\) 0 0
\(475\) −23.6803 17.2048i −1.08653 0.789409i
\(476\) 3.43769 0.157566
\(477\) 0 0
\(478\) −5.59017 4.06150i −0.255688 0.185769i
\(479\) −12.2984 8.93529i −0.561927 0.408264i 0.270237 0.962794i \(-0.412898\pi\)
−0.832164 + 0.554530i \(0.812898\pi\)
\(480\) 0 0
\(481\) 6.73607 4.89404i 0.307138 0.223149i
\(482\) 15.6180 0.711382
\(483\) 0 0
\(484\) 2.14590 + 6.60440i 0.0975408 + 0.300200i
\(485\) 6.60739 + 20.3355i 0.300026 + 0.923386i
\(486\) 0 0
\(487\) 6.83688 + 21.0418i 0.309809 + 0.953493i 0.977839 + 0.209359i \(0.0671377\pi\)
−0.668030 + 0.744134i \(0.732862\pi\)
\(488\) −2.73607 8.42075i −0.123856 0.381190i
\(489\) 0 0
\(490\) −3.61803 + 2.62866i −0.163446 + 0.118751i
\(491\) −5.94427 18.2946i −0.268261 0.825623i −0.990924 0.134423i \(-0.957082\pi\)
0.722663 0.691201i \(-0.242918\pi\)
\(492\) 0 0
\(493\) −10.8541 −0.488844
\(494\) −4.73607 + 3.44095i −0.213086 + 0.154816i
\(495\) 0 0
\(496\) 0.190983 + 0.138757i 0.00857539 + 0.00623039i
\(497\) 7.28115 + 5.29007i 0.326604 + 0.237292i
\(498\) 0 0
\(499\) 34.1459 1.52858 0.764290 0.644873i \(-0.223090\pi\)
0.764290 + 0.644873i \(0.223090\pi\)
\(500\) −9.04508 + 6.57164i −0.404508 + 0.293893i
\(501\) 0 0
\(502\) −0.253289 + 0.779543i −0.0113048 + 0.0347927i
\(503\) −24.6803 17.9313i −1.10044 0.799518i −0.119310 0.992857i \(-0.538068\pi\)
−0.981132 + 0.193339i \(0.938068\pi\)
\(504\) 0 0
\(505\) 1.11803 + 0.812299i 0.0497519 + 0.0361468i
\(506\) 6.04508 4.39201i 0.268737 0.195249i
\(507\) 0 0
\(508\) 2.85410 2.07363i 0.126630 0.0920023i
\(509\) 0.590170 + 1.81636i 0.0261588 + 0.0805086i 0.963284 0.268486i \(-0.0865232\pi\)
−0.937125 + 0.348994i \(0.886523\pi\)
\(510\) 0 0
\(511\) −7.14590 + 21.9928i −0.316116 + 0.972905i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) 0 0
\(514\) −7.95492 + 24.4827i −0.350876 + 1.07989i
\(515\) −9.08359 27.9564i −0.400271 1.23191i
\(516\) 0 0
\(517\) 40.9336 29.7400i 1.80026 1.30796i
\(518\) 24.9787 1.09750
\(519\) 0 0
\(520\) 0.690983 + 2.12663i 0.0303016 + 0.0932588i
\(521\) −18.9721 13.7841i −0.831184 0.603891i 0.0887098 0.996058i \(-0.471726\pi\)
−0.919894 + 0.392167i \(0.871726\pi\)
\(522\) 0 0
\(523\) −1.43769 + 4.42477i −0.0628660 + 0.193482i −0.977557 0.210673i \(-0.932434\pi\)
0.914691 + 0.404155i \(0.132434\pi\)
\(524\) 16.4164 0.717154
\(525\) 0 0
\(526\) −4.61803 −0.201356
\(527\) 0.0835921 0.257270i 0.00364133 0.0112069i
\(528\) 0 0
\(529\) 16.0902 + 11.6902i 0.699573 + 0.508269i
\(530\) −23.4164 −1.01714
\(531\) 0 0
\(532\) −17.5623 −0.761423
\(533\) 1.19098 0.865300i 0.0515872 0.0374803i
\(534\) 0 0
\(535\) −1.97214 1.43284i −0.0852629 0.0619471i
\(536\) −3.16312 + 9.73508i −0.136626 + 0.420491i
\(537\) 0 0
\(538\) −0.590170 1.81636i −0.0254440 0.0783087i
\(539\) −2.61803 + 8.05748i −0.112767 + 0.347060i
\(540\) 0 0
\(541\) 4.72542 + 14.5434i 0.203162 + 0.625268i 0.999784 + 0.0207902i \(0.00661819\pi\)
−0.796622 + 0.604478i \(0.793382\pi\)
\(542\) −23.0623 + 16.7557i −0.990611 + 0.719721i
\(543\) 0 0
\(544\) 0.927051 0.673542i 0.0397470 0.0288779i
\(545\) −10.3647 + 31.8994i −0.443977 + 1.36642i
\(546\) 0 0
\(547\) −6.78115 4.92680i −0.289941 0.210655i 0.433301 0.901249i \(-0.357349\pi\)
−0.723242 + 0.690595i \(0.757349\pi\)
\(548\) −1.57295 + 4.84104i −0.0671931 + 0.206799i
\(549\) 0 0
\(550\) −6.54508 + 20.1437i −0.279083 + 0.858930i
\(551\) 55.4508 2.36229
\(552\) 0 0
\(553\) −17.5623 12.7598i −0.746825 0.542600i
\(554\) −0.236068 0.171513i −0.0100296 0.00728691i
\(555\) 0 0
\(556\) 4.30902 3.13068i 0.182743 0.132771i
\(557\) −24.8885 −1.05456 −0.527281 0.849691i \(-0.676788\pi\)
−0.527281 + 0.849691i \(0.676788\pi\)
\(558\) 0 0
\(559\) −1.92705 5.93085i −0.0815056 0.250848i
\(560\) −2.07295 + 6.37988i −0.0875981 + 0.269599i
\(561\) 0 0
\(562\) −0.982779 3.02468i −0.0414560 0.127589i
\(563\) 8.69756 + 26.7683i 0.366558 + 1.12815i 0.948999 + 0.315278i \(0.102098\pi\)
−0.582441 + 0.812873i \(0.697902\pi\)
\(564\) 0 0
\(565\) −2.60081 + 8.00448i −0.109417 + 0.336751i
\(566\) −3.79837 11.6902i −0.159658 0.491375i
\(567\) 0 0
\(568\) 3.00000 0.125877
\(569\) 14.3713 10.4414i 0.602477 0.437725i −0.244280 0.969705i \(-0.578552\pi\)
0.846757 + 0.531979i \(0.178552\pi\)
\(570\) 0 0
\(571\) −14.0172 10.1841i −0.586602 0.426192i 0.254496 0.967074i \(-0.418090\pi\)
−0.841098 + 0.540882i \(0.818090\pi\)
\(572\) 3.42705 + 2.48990i 0.143292 + 0.104108i
\(573\) 0 0
\(574\) 4.41641 0.184337
\(575\) 8.81966 0.367805
\(576\) 0 0
\(577\) −13.2877 + 40.8954i −0.553175 + 1.70250i 0.147538 + 0.989056i \(0.452865\pi\)
−0.700714 + 0.713443i \(0.747135\pi\)
\(578\) 12.6910 + 9.22054i 0.527875 + 0.383524i
\(579\) 0 0
\(580\) 6.54508 20.1437i 0.271770 0.836422i
\(581\) 10.9894 7.98424i 0.455915 0.331242i
\(582\) 0 0
\(583\) −35.8885 + 26.0746i −1.48635 + 1.07990i
\(584\) 2.38197 + 7.33094i 0.0985665 + 0.303356i
\(585\) 0 0
\(586\) −2.64590 + 8.14324i −0.109301 + 0.336394i
\(587\) 10.5623 + 32.5074i 0.435953 + 1.34173i 0.892107 + 0.451824i \(0.149227\pi\)
−0.456154 + 0.889901i \(0.650773\pi\)
\(588\) 0 0
\(589\) −0.427051 + 1.31433i −0.0175963 + 0.0541559i
\(590\) −8.09017 5.87785i −0.333067 0.241987i
\(591\) 0 0
\(592\) 6.73607 4.89404i 0.276851 0.201144i
\(593\) −29.0132 −1.19143 −0.595714 0.803197i \(-0.703131\pi\)
−0.595714 + 0.803197i \(0.703131\pi\)
\(594\) 0 0
\(595\) 7.68692 0.315133
\(596\) 1.80902 + 1.31433i 0.0741002 + 0.0538370i
\(597\) 0 0
\(598\) 0.545085 1.67760i 0.0222902 0.0686021i
\(599\) −8.94427 −0.365453 −0.182727 0.983164i \(-0.558492\pi\)
−0.182727 + 0.983164i \(0.558492\pi\)
\(600\) 0 0
\(601\) 38.8328 1.58402 0.792012 0.610506i \(-0.209034\pi\)
0.792012 + 0.610506i \(0.209034\pi\)
\(602\) 5.78115 17.7926i 0.235622 0.725171i
\(603\) 0 0
\(604\) 7.85410 + 5.70634i 0.319579 + 0.232188i
\(605\) 4.79837 + 14.7679i 0.195082 + 0.600400i
\(606\) 0 0
\(607\) −33.8541 −1.37410 −0.687048 0.726612i \(-0.741094\pi\)
−0.687048 + 0.726612i \(0.741094\pi\)
\(608\) −4.73607 + 3.44095i −0.192073 + 0.139549i
\(609\) 0 0
\(610\) −6.11803 18.8294i −0.247712 0.762379i
\(611\) 3.69098 11.3597i 0.149321 0.459563i
\(612\) 0 0
\(613\) −6.62461 20.3885i −0.267566 0.823482i −0.991091 0.133185i \(-0.957480\pi\)
0.723526 0.690297i \(-0.242520\pi\)
\(614\) −7.14590 + 21.9928i −0.288385 + 0.887558i
\(615\) 0 0
\(616\) 3.92705 + 12.0862i 0.158225 + 0.486968i
\(617\) 11.6180 8.44100i 0.467724 0.339822i −0.328829 0.944389i \(-0.606654\pi\)
0.796554 + 0.604568i \(0.206654\pi\)
\(618\) 0 0
\(619\) −37.9894 + 27.6009i −1.52692 + 1.10937i −0.569002 + 0.822336i \(0.692670\pi\)
−0.957920 + 0.287037i \(0.907330\pi\)
\(620\) 0.427051 + 0.310271i 0.0171508 + 0.0124608i
\(621\) 0 0
\(622\) −8.01722 5.82485i −0.321461 0.233555i
\(623\) 4.14590 12.7598i 0.166102 0.511209i
\(624\) 0 0
\(625\) −20.2254 + 14.6946i −0.809017 + 0.587785i
\(626\) −16.5623 −0.661963
\(627\) 0 0
\(628\) −3.69098 2.68166i −0.147286 0.107010i
\(629\) −7.71885 5.60807i −0.307771 0.223608i
\(630\) 0 0
\(631\) 36.2705 26.3521i 1.44391 1.04906i 0.456698 0.889622i \(-0.349032\pi\)
0.987208 0.159438i \(-0.0509681\pi\)
\(632\) −7.23607 −0.287835
\(633\) 0 0
\(634\) −2.59017 7.97172i −0.102869 0.316598i
\(635\) 6.38197 4.63677i 0.253261 0.184005i
\(636\) 0 0
\(637\) 0.618034 + 1.90211i 0.0244874 + 0.0753645i
\(638\) −12.3992 38.1608i −0.490889 1.51080i
\(639\) 0 0
\(640\) 0.690983 + 2.12663i 0.0273135 + 0.0840623i
\(641\) 9.38197 + 28.8747i 0.370565 + 1.14048i 0.946422 + 0.322932i \(0.104669\pi\)
−0.575857 + 0.817551i \(0.695331\pi\)
\(642\) 0 0
\(643\) −31.7639 −1.25265 −0.626324 0.779563i \(-0.715441\pi\)
−0.626324 + 0.779563i \(0.715441\pi\)
\(644\) 4.28115 3.11044i 0.168701 0.122568i
\(645\) 0 0
\(646\) 5.42705 + 3.94298i 0.213524 + 0.155135i
\(647\) −19.1353 13.9026i −0.752284 0.546567i 0.144250 0.989541i \(-0.453923\pi\)
−0.896534 + 0.442975i \(0.853923\pi\)
\(648\) 0 0
\(649\) −18.9443 −0.743628
\(650\) 1.54508 + 4.75528i 0.0606032 + 0.186518i
\(651\) 0 0
\(652\) 0.572949 1.76336i 0.0224384 0.0690583i
\(653\) −6.95492 5.05304i −0.272167 0.197741i 0.443327 0.896360i \(-0.353798\pi\)
−0.715494 + 0.698619i \(0.753798\pi\)
\(654\) 0 0
\(655\) 36.7082 1.43431
\(656\) 1.19098 0.865300i 0.0465001 0.0337843i
\(657\) 0 0
\(658\) 28.9894 21.0620i 1.13012 0.821082i
\(659\) 7.92705 + 24.3970i 0.308794 + 0.950370i 0.978234 + 0.207504i \(0.0665341\pi\)
−0.669440 + 0.742866i \(0.733466\pi\)
\(660\) 0 0
\(661\) −8.42705 + 25.9358i −0.327774 + 1.00879i 0.642398 + 0.766371i \(0.277939\pi\)
−0.970173 + 0.242415i \(0.922061\pi\)
\(662\) −4.80902 14.8006i −0.186908 0.575243i
\(663\) 0 0
\(664\) 1.39919 4.30625i 0.0542990 0.167115i
\(665\) −39.2705 −1.52285
\(666\) 0 0
\(667\) −13.5172 + 9.82084i −0.523389 + 0.380264i
\(668\) −13.3820 −0.517764
\(669\) 0 0
\(670\) −7.07295 + 21.7683i −0.273252 + 0.840983i
\(671\) −30.3435 22.0458i −1.17140 0.851069i
\(672\) 0 0
\(673\) 1.00000 3.07768i 0.0385472 0.118636i −0.929931 0.367733i \(-0.880134\pi\)
0.968478 + 0.249097i \(0.0801339\pi\)
\(674\) −4.58359 −0.176553
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −2.59017 + 7.97172i −0.0995483 + 0.306378i −0.988412 0.151793i \(-0.951495\pi\)
0.888864 + 0.458171i \(0.151495\pi\)
\(678\) 0 0
\(679\) 23.2082 + 16.8617i 0.890649 + 0.647094i
\(680\) 2.07295 1.50609i 0.0794940 0.0577557i
\(681\) 0 0
\(682\) 1.00000 0.0382920
\(683\) −9.19098 + 6.67764i −0.351683 + 0.255513i −0.749575 0.661920i \(-0.769742\pi\)
0.397892 + 0.917432i \(0.369742\pi\)
\(684\) 0 0
\(685\) −3.51722 + 10.8249i −0.134386 + 0.413598i
\(686\) 4.63525 14.2658i 0.176975 0.544673i
\(687\) 0 0
\(688\) −1.92705 5.93085i −0.0734681 0.226112i
\(689\) −3.23607 + 9.95959i −0.123284 + 0.379430i
\(690\) 0 0
\(691\) −9.97214 30.6911i −0.379358 1.16754i −0.940491 0.339818i \(-0.889634\pi\)
0.561133 0.827725i \(-0.310366\pi\)
\(692\) −1.00000 + 0.726543i −0.0380143 + 0.0276190i
\(693\) 0 0
\(694\) −17.0623 + 12.3965i −0.647676 + 0.470564i
\(695\) 9.63525 7.00042i 0.365486 0.265541i
\(696\) 0 0
\(697\) −1.36475 0.991545i −0.0516934 0.0375575i
\(698\) −5.48936 + 16.8945i −0.207775 + 0.639466i
\(699\) 0 0
\(700\) −4.63525 + 14.2658i −0.175196 + 0.539198i
\(701\) −18.1803 −0.686662 −0.343331 0.939214i \(-0.611555\pi\)
−0.343331 + 0.939214i \(0.611555\pi\)
\(702\) 0 0
\(703\) 39.4336 + 28.6502i 1.48727 + 1.08056i
\(704\) 3.42705 + 2.48990i 0.129162 + 0.0938416i
\(705\) 0 0
\(706\) −17.1803 + 12.4822i −0.646591 + 0.469776i
\(707\) 1.85410 0.0697307
\(708\) 0 0
\(709\) 3.78115 + 11.6372i 0.142004 + 0.437044i 0.996614 0.0822274i \(-0.0262034\pi\)
−0.854609 + 0.519271i \(0.826203\pi\)
\(710\) 6.70820 0.251754
\(711\) 0 0
\(712\) −1.38197 4.25325i −0.0517914 0.159397i
\(713\) −0.128677 0.396027i −0.00481900 0.0148313i
\(714\) 0 0
\(715\) 7.66312 + 5.56758i 0.286584 + 0.208216i
\(716\) −3.45492 10.6331i −0.129116 0.397379i
\(717\) 0 0
\(718\) 8.09017 0.301922
\(719\) 9.30902 6.76340i 0.347168 0.252232i −0.400512 0.916291i \(-0.631168\pi\)
0.747680 + 0.664059i \(0.231168\pi\)
\(720\) 0 0
\(721\) −31.9058 23.1809i −1.18823 0.863302i
\(722\) −12.3541 8.97578i −0.459772 0.334044i
\(723\) 0 0
\(724\) 5.41641 0.201299
\(725\) 14.6353 45.0427i 0.543540 1.67284i
\(726\) 0 0
\(727\) 0.819660 2.52265i 0.0303995 0.0935601i −0.934706 0.355423i \(-0.884337\pi\)
0.965105 + 0.261863i \(0.0843368\pi\)
\(728\) 2.42705 + 1.76336i 0.0899525 + 0.0653543i
\(729\) 0 0
\(730\) 5.32624 + 16.3925i 0.197133 + 0.606713i
\(731\) −5.78115 + 4.20025i −0.213824 + 0.155352i
\(732\) 0 0
\(733\) −25.7082 + 18.6781i −0.949554 + 0.689891i −0.950701 0.310108i \(-0.899635\pi\)
0.00114721 + 0.999999i \(0.499635\pi\)
\(734\) 10.9828 + 33.8015i 0.405382 + 1.24764i
\(735\) 0 0
\(736\) 0.545085 1.67760i 0.0200921 0.0618371i
\(737\) 13.3992 + 41.2385i 0.493565 + 1.51904i
\(738\) 0 0
\(739\) 9.27051 28.5317i 0.341021 1.04956i −0.622658 0.782494i \(-0.713947\pi\)
0.963679 0.267062i \(-0.0860527\pi\)
\(740\) 15.0623 10.9434i 0.553701 0.402288i
\(741\) 0 0
\(742\) −25.4164 + 18.4661i −0.933066 + 0.677912i
\(743\) −15.2705 −0.560221 −0.280110 0.959968i \(-0.590371\pi\)
−0.280110 + 0.959968i \(0.590371\pi\)
\(744\) 0 0
\(745\) 4.04508 + 2.93893i 0.148200 + 0.107674i
\(746\) 9.51722 + 6.91467i 0.348450 + 0.253164i
\(747\) 0 0
\(748\) 1.50000 4.61653i 0.0548454 0.168797i
\(749\) −3.27051 −0.119502
\(750\) 0 0
\(751\) 7.85410 0.286600 0.143300 0.989679i \(-0.454229\pi\)
0.143300 + 0.989679i \(0.454229\pi\)
\(752\) 3.69098 11.3597i 0.134596 0.414245i
\(753\) 0 0
\(754\) −7.66312 5.56758i −0.279074 0.202759i
\(755\) 17.5623 + 12.7598i 0.639158 + 0.464375i
\(756\) 0 0
\(757\) −16.4164 −0.596664 −0.298332 0.954462i \(-0.596430\pi\)
−0.298332 + 0.954462i \(0.596430\pi\)
\(758\) −7.66312 + 5.56758i −0.278337 + 0.202224i
\(759\) 0 0
\(760\) −10.5902 + 7.69421i −0.384146 + 0.279098i
\(761\) −8.31966 + 25.6053i −0.301587 + 0.928191i 0.679341 + 0.733823i \(0.262266\pi\)
−0.980929 + 0.194368i \(0.937734\pi\)
\(762\) 0 0
\(763\) 13.9058 + 42.7975i 0.503422 + 1.54938i
\(764\) 4.21885 12.9843i 0.152633 0.469755i
\(765\) 0 0
\(766\) −3.50000 10.7719i −0.126460 0.389204i
\(767\) −3.61803 + 2.62866i −0.130640 + 0.0949153i
\(768\) 0 0
\(769\) −2.76393 + 2.00811i −0.0996699 + 0.0724144i −0.636504 0.771273i \(-0.719620\pi\)
0.536834 + 0.843688i \(0.319620\pi\)
\(770\) 8.78115 + 27.0256i 0.316451 + 0.973935i
\(771\) 0 0
\(772\) 11.8541 + 8.61251i 0.426638 + 0.309971i
\(773\) −9.51722 + 29.2910i −0.342311 + 1.05352i 0.620697 + 0.784050i \(0.286850\pi\)
−0.963008 + 0.269473i \(0.913150\pi\)
\(774\) 0 0
\(775\) 0.954915 + 0.693786i 0.0343016 + 0.0249215i
\(776\) 9.56231 0.343267
\(777\) 0 0
\(778\) 14.7361 + 10.7064i 0.528314 + 0.383842i
\(779\) 6.97214 + 5.06555i 0.249803 + 0.181492i
\(780\) 0 0
\(781\) 10.2812 7.46969i 0.367889 0.267287i
\(782\) −2.02129 −0.0722810
\(783\) 0 0
\(784\) 0.618034 + 1.90211i 0.0220726 + 0.0679326i
\(785\) −8.25329 5.99637i −0.294573 0.214019i
\(786\) 0 0
\(787\) −3.52786 10.8576i −0.125755 0.387033i 0.868283 0.496069i \(-0.165224\pi\)
−0.994038 + 0.109036i