Properties

Label 370.2.h.e.117.10
Level $370$
Weight $2$
Character 370.117
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 117.10
Root \(2.41612 - 2.41612i\) of defining polynomial
Character \(\chi\) \(=\) 370.117
Dual form 370.2.h.e.253.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(2.41612 + 2.41612i) q^{3} +1.00000 q^{4} +(0.667560 - 2.13410i) q^{5} +(-2.41612 - 2.41612i) q^{6} +(-0.875609 - 0.875609i) q^{7} -1.00000 q^{8} +8.67529i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(2.41612 + 2.41612i) q^{3} +1.00000 q^{4} +(0.667560 - 2.13410i) q^{5} +(-2.41612 - 2.41612i) q^{6} +(-0.875609 - 0.875609i) q^{7} -1.00000 q^{8} +8.67529i q^{9} +(-0.667560 + 2.13410i) q^{10} +1.92497i q^{11} +(2.41612 + 2.41612i) q^{12} +3.05698 q^{13} +(0.875609 + 0.875609i) q^{14} +(6.76914 - 3.54333i) q^{15} +1.00000 q^{16} +3.63520i q^{17} -8.67529i q^{18} +(3.22623 - 3.22623i) q^{19} +(0.667560 - 2.13410i) q^{20} -4.23116i q^{21} -1.92497i q^{22} -2.01378 q^{23} +(-2.41612 - 2.41612i) q^{24} +(-4.10873 - 2.84927i) q^{25} -3.05698 q^{26} +(-13.7122 + 13.7122i) q^{27} +(-0.875609 - 0.875609i) q^{28} +(4.81913 + 4.81913i) q^{29} +(-6.76914 + 3.54333i) q^{30} +(0.936472 - 0.936472i) q^{31} -1.00000 q^{32} +(-4.65096 + 4.65096i) q^{33} -3.63520i q^{34} +(-2.45316 + 1.28411i) q^{35} +8.67529i q^{36} +(-0.586931 - 6.05438i) q^{37} +(-3.22623 + 3.22623i) q^{38} +(7.38603 + 7.38603i) q^{39} +(-0.667560 + 2.13410i) q^{40} -12.7650i q^{41} +4.23116i q^{42} -4.81157 q^{43} +1.92497i q^{44} +(18.5139 + 5.79128i) q^{45} +2.01378 q^{46} +(-5.85922 - 5.85922i) q^{47} +(2.41612 + 2.41612i) q^{48} -5.46662i q^{49} +(4.10873 + 2.84927i) q^{50} +(-8.78310 + 8.78310i) q^{51} +3.05698 q^{52} +(-3.89480 + 3.89480i) q^{53} +(13.7122 - 13.7122i) q^{54} +(4.10806 + 1.28503i) q^{55} +(0.875609 + 0.875609i) q^{56} +15.5899 q^{57} +(-4.81913 - 4.81913i) q^{58} +(-3.25043 + 3.25043i) q^{59} +(6.76914 - 3.54333i) q^{60} +(3.16695 - 3.16695i) q^{61} +(-0.936472 + 0.936472i) q^{62} +(7.59617 - 7.59617i) q^{63} +1.00000 q^{64} +(2.04072 - 6.52388i) q^{65} +(4.65096 - 4.65096i) q^{66} +(-3.71697 + 3.71697i) q^{67} +3.63520i q^{68} +(-4.86553 - 4.86553i) q^{69} +(2.45316 - 1.28411i) q^{70} -3.90508 q^{71} -8.67529i q^{72} +(8.57777 + 8.57777i) q^{73} +(0.586931 + 6.05438i) q^{74} +(-3.04299 - 16.8114i) q^{75} +(3.22623 - 3.22623i) q^{76} +(1.68552 - 1.68552i) q^{77} +(-7.38603 - 7.38603i) q^{78} +(4.19139 - 4.19139i) q^{79} +(0.667560 - 2.13410i) q^{80} -40.2348 q^{81} +12.7650i q^{82} +(-7.79493 + 7.79493i) q^{83} -4.23116i q^{84} +(7.75787 + 2.42672i) q^{85} +4.81157 q^{86} +23.2872i q^{87} -1.92497i q^{88} +(-7.79425 - 7.79425i) q^{89} +(-18.5139 - 5.79128i) q^{90} +(-2.67672 - 2.67672i) q^{91} -2.01378 q^{92} +4.52526 q^{93} +(5.85922 + 5.85922i) q^{94} +(-4.73138 - 9.03878i) q^{95} +(-2.41612 - 2.41612i) q^{96} -14.8936i q^{97} +5.46662i q^{98} -16.6997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10}) \) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.41612 + 2.41612i 1.39495 + 1.39495i 0.813791 + 0.581158i \(0.197400\pi\)
0.581158 + 0.813791i \(0.302600\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.667560 2.13410i 0.298542 0.954397i
\(6\) −2.41612 2.41612i −0.986378 0.986378i
\(7\) −0.875609 0.875609i −0.330949 0.330949i 0.521998 0.852947i \(-0.325187\pi\)
−0.852947 + 0.521998i \(0.825187\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.67529i 2.89176i
\(10\) −0.667560 + 2.13410i −0.211101 + 0.674860i
\(11\) 1.92497i 0.580400i 0.956966 + 0.290200i \(0.0937218\pi\)
−0.956966 + 0.290200i \(0.906278\pi\)
\(12\) 2.41612 + 2.41612i 0.697474 + 0.697474i
\(13\) 3.05698 0.847853 0.423927 0.905697i \(-0.360651\pi\)
0.423927 + 0.905697i \(0.360651\pi\)
\(14\) 0.875609 + 0.875609i 0.234016 + 0.234016i
\(15\) 6.76914 3.54333i 1.74778 0.914884i
\(16\) 1.00000 0.250000
\(17\) 3.63520i 0.881667i 0.897589 + 0.440833i \(0.145317\pi\)
−0.897589 + 0.440833i \(0.854683\pi\)
\(18\) 8.67529i 2.04479i
\(19\) 3.22623 3.22623i 0.740148 0.740148i −0.232459 0.972606i \(-0.574677\pi\)
0.972606 + 0.232459i \(0.0746770\pi\)
\(20\) 0.667560 2.13410i 0.149271 0.477198i
\(21\) 4.23116i 0.923314i
\(22\) 1.92497i 0.410404i
\(23\) −2.01378 −0.419902 −0.209951 0.977712i \(-0.567330\pi\)
−0.209951 + 0.977712i \(0.567330\pi\)
\(24\) −2.41612 2.41612i −0.493189 0.493189i
\(25\) −4.10873 2.84927i −0.821745 0.569855i
\(26\) −3.05698 −0.599523
\(27\) −13.7122 + 13.7122i −2.63891 + 2.63891i
\(28\) −0.875609 0.875609i −0.165475 0.165475i
\(29\) 4.81913 + 4.81913i 0.894890 + 0.894890i 0.994979 0.100089i \(-0.0319127\pi\)
−0.100089 + 0.994979i \(0.531913\pi\)
\(30\) −6.76914 + 3.54333i −1.23587 + 0.646920i
\(31\) 0.936472 0.936472i 0.168195 0.168195i −0.617990 0.786186i \(-0.712053\pi\)
0.786186 + 0.617990i \(0.212053\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.65096 + 4.65096i −0.809628 + 0.809628i
\(34\) 3.63520i 0.623432i
\(35\) −2.45316 + 1.28411i −0.414659 + 0.217055i
\(36\) 8.67529i 1.44588i
\(37\) −0.586931 6.05438i −0.0964908 0.995334i
\(38\) −3.22623 + 3.22623i −0.523363 + 0.523363i
\(39\) 7.38603 + 7.38603i 1.18271 + 1.18271i
\(40\) −0.667560 + 2.13410i −0.105551 + 0.337430i
\(41\) 12.7650i 1.99356i −0.0801960 0.996779i \(-0.525555\pi\)
0.0801960 0.996779i \(-0.474445\pi\)
\(42\) 4.23116i 0.652882i
\(43\) −4.81157 −0.733757 −0.366879 0.930269i \(-0.619574\pi\)
−0.366879 + 0.930269i \(0.619574\pi\)
\(44\) 1.92497i 0.290200i
\(45\) 18.5139 + 5.79128i 2.75989 + 0.863313i
\(46\) 2.01378 0.296915
\(47\) −5.85922 5.85922i −0.854654 0.854654i 0.136048 0.990702i \(-0.456560\pi\)
−0.990702 + 0.136048i \(0.956560\pi\)
\(48\) 2.41612 + 2.41612i 0.348737 + 0.348737i
\(49\) 5.46662i 0.780945i
\(50\) 4.10873 + 2.84927i 0.581062 + 0.402948i
\(51\) −8.78310 + 8.78310i −1.22988 + 1.22988i
\(52\) 3.05698 0.423927
\(53\) −3.89480 + 3.89480i −0.534991 + 0.534991i −0.922054 0.387062i \(-0.873490\pi\)
0.387062 + 0.922054i \(0.373490\pi\)
\(54\) 13.7122 13.7122i 1.86599 1.86599i
\(55\) 4.10806 + 1.28503i 0.553931 + 0.173274i
\(56\) 0.875609 + 0.875609i 0.117008 + 0.117008i
\(57\) 15.5899 2.06494
\(58\) −4.81913 4.81913i −0.632783 0.632783i
\(59\) −3.25043 + 3.25043i −0.423170 + 0.423170i −0.886294 0.463124i \(-0.846729\pi\)
0.463124 + 0.886294i \(0.346729\pi\)
\(60\) 6.76914 3.54333i 0.873892 0.457442i
\(61\) 3.16695 3.16695i 0.405486 0.405486i −0.474675 0.880161i \(-0.657434\pi\)
0.880161 + 0.474675i \(0.157434\pi\)
\(62\) −0.936472 + 0.936472i −0.118932 + 0.118932i
\(63\) 7.59617 7.59617i 0.957027 0.957027i
\(64\) 1.00000 0.125000
\(65\) 2.04072 6.52388i 0.253120 0.809188i
\(66\) 4.65096 4.65096i 0.572493 0.572493i
\(67\) −3.71697 + 3.71697i −0.454100 + 0.454100i −0.896713 0.442613i \(-0.854052\pi\)
0.442613 + 0.896713i \(0.354052\pi\)
\(68\) 3.63520i 0.440833i
\(69\) −4.86553 4.86553i −0.585741 0.585741i
\(70\) 2.45316 1.28411i 0.293208 0.153481i
\(71\) −3.90508 −0.463448 −0.231724 0.972782i \(-0.574437\pi\)
−0.231724 + 0.972782i \(0.574437\pi\)
\(72\) 8.67529i 1.02239i
\(73\) 8.57777 + 8.57777i 1.00395 + 1.00395i 0.999992 + 0.00396036i \(0.00126063\pi\)
0.00396036 + 0.999992i \(0.498739\pi\)
\(74\) 0.586931 + 6.05438i 0.0682293 + 0.703807i
\(75\) −3.04299 16.8114i −0.351375 1.94121i
\(76\) 3.22623 3.22623i 0.370074 0.370074i
\(77\) 1.68552 1.68552i 0.192083 0.192083i
\(78\) −7.38603 7.38603i −0.836303 0.836303i
\(79\) 4.19139 4.19139i 0.471568 0.471568i −0.430854 0.902422i \(-0.641788\pi\)
0.902422 + 0.430854i \(0.141788\pi\)
\(80\) 0.667560 2.13410i 0.0746355 0.238599i
\(81\) −40.2348 −4.47053
\(82\) 12.7650i 1.40966i
\(83\) −7.79493 + 7.79493i −0.855604 + 0.855604i −0.990817 0.135212i \(-0.956828\pi\)
0.135212 + 0.990817i \(0.456828\pi\)
\(84\) 4.23116i 0.461657i
\(85\) 7.75787 + 2.42672i 0.841460 + 0.263214i
\(86\) 4.81157 0.518845
\(87\) 23.2872i 2.49665i
\(88\) 1.92497i 0.205202i
\(89\) −7.79425 7.79425i −0.826188 0.826188i 0.160799 0.986987i \(-0.448593\pi\)
−0.986987 + 0.160799i \(0.948593\pi\)
\(90\) −18.5139 5.79128i −1.95154 0.610454i
\(91\) −2.67672 2.67672i −0.280596 0.280596i
\(92\) −2.01378 −0.209951
\(93\) 4.52526 0.469248
\(94\) 5.85922 + 5.85922i 0.604332 + 0.604332i
\(95\) −4.73138 9.03878i −0.485429 0.927360i
\(96\) −2.41612 2.41612i −0.246594 0.246594i
\(97\) 14.8936i 1.51221i −0.654449 0.756106i \(-0.727099\pi\)
0.654449 0.756106i \(-0.272901\pi\)
\(98\) 5.46662i 0.552212i
\(99\) −16.6997 −1.67838
\(100\) −4.10873 2.84927i −0.410873 0.284927i
\(101\) 0.977455i 0.0972604i −0.998817 0.0486302i \(-0.984514\pi\)
0.998817 0.0486302i \(-0.0154856\pi\)
\(102\) 8.78310 8.78310i 0.869656 0.869656i
\(103\) 11.3553i 1.11887i −0.828873 0.559437i \(-0.811018\pi\)
0.828873 0.559437i \(-0.188982\pi\)
\(104\) −3.05698 −0.299761
\(105\) −9.02969 2.82455i −0.881208 0.275648i
\(106\) 3.89480 3.89480i 0.378296 0.378296i
\(107\) −4.47857 4.47857i −0.432960 0.432960i 0.456674 0.889634i \(-0.349041\pi\)
−0.889634 + 0.456674i \(0.849041\pi\)
\(108\) −13.7122 + 13.7122i −1.31946 + 1.31946i
\(109\) 7.18760 7.18760i 0.688447 0.688447i −0.273442 0.961889i \(-0.588162\pi\)
0.961889 + 0.273442i \(0.0881621\pi\)
\(110\) −4.10806 1.28503i −0.391689 0.122523i
\(111\) 13.2100 16.0462i 1.25384 1.52304i
\(112\) −0.875609 0.875609i −0.0827373 0.0827373i
\(113\) 3.47531i 0.326930i 0.986549 + 0.163465i \(0.0522671\pi\)
−0.986549 + 0.163465i \(0.947733\pi\)
\(114\) −15.5899 −1.46013
\(115\) −1.34432 + 4.29759i −0.125358 + 0.400753i
\(116\) 4.81913 + 4.81913i 0.447445 + 0.447445i
\(117\) 26.5202i 2.45179i
\(118\) 3.25043 3.25043i 0.299227 0.299227i
\(119\) 3.18302 3.18302i 0.291787 0.291787i
\(120\) −6.76914 + 3.54333i −0.617935 + 0.323460i
\(121\) 7.29450 0.663136
\(122\) −3.16695 + 3.16695i −0.286722 + 0.286722i
\(123\) 30.8418 30.8418i 2.78091 2.78091i
\(124\) 0.936472 0.936472i 0.0840976 0.0840976i
\(125\) −8.82344 + 6.86635i −0.789193 + 0.614145i
\(126\) −7.59617 + 7.59617i −0.676720 + 0.676720i
\(127\) 5.75444 + 5.75444i 0.510624 + 0.510624i 0.914718 0.404093i \(-0.132413\pi\)
−0.404093 + 0.914718i \(0.632413\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −11.6253 11.6253i −1.02355 1.02355i
\(130\) −2.04072 + 6.52388i −0.178983 + 0.572182i
\(131\) 1.96912 1.96912i 0.172043 0.172043i −0.615833 0.787876i \(-0.711181\pi\)
0.787876 + 0.615833i \(0.211181\pi\)
\(132\) −4.65096 + 4.65096i −0.404814 + 0.404814i
\(133\) −5.64983 −0.489903
\(134\) 3.71697 3.71697i 0.321097 0.321097i
\(135\) 20.1094 + 38.4169i 1.73074 + 3.30640i
\(136\) 3.63520i 0.311716i
\(137\) 7.83311 + 7.83311i 0.669228 + 0.669228i 0.957537 0.288309i \(-0.0930932\pi\)
−0.288309 + 0.957537i \(0.593093\pi\)
\(138\) 4.86553 + 4.86553i 0.414182 + 0.414182i
\(139\) 0.678086 0.0575145 0.0287572 0.999586i \(-0.490845\pi\)
0.0287572 + 0.999586i \(0.490845\pi\)
\(140\) −2.45316 + 1.28411i −0.207329 + 0.108527i
\(141\) 28.3132i 2.38440i
\(142\) 3.90508 0.327707
\(143\) 5.88458i 0.492094i
\(144\) 8.67529i 0.722941i
\(145\) 13.5015 7.06742i 1.12124 0.586918i
\(146\) −8.57777 8.57777i −0.709902 0.709902i
\(147\) 13.2080 13.2080i 1.08938 1.08938i
\(148\) −0.586931 6.05438i −0.0482454 0.497667i
\(149\) 5.12261i 0.419660i 0.977738 + 0.209830i \(0.0672911\pi\)
−0.977738 + 0.209830i \(0.932709\pi\)
\(150\) 3.04299 + 16.8114i 0.248459 + 1.37264i
\(151\) 20.3046i 1.65236i 0.563405 + 0.826181i \(0.309491\pi\)
−0.563405 + 0.826181i \(0.690509\pi\)
\(152\) −3.22623 + 3.22623i −0.261682 + 0.261682i
\(153\) −31.5365 −2.54957
\(154\) −1.68552 + 1.68552i −0.135823 + 0.135823i
\(155\) −1.37337 2.62367i −0.110312 0.210738i
\(156\) 7.38603 + 7.38603i 0.591356 + 0.591356i
\(157\) −9.36950 9.36950i −0.747767 0.747767i 0.226292 0.974059i \(-0.427340\pi\)
−0.974059 + 0.226292i \(0.927340\pi\)
\(158\) −4.19139 + 4.19139i −0.333449 + 0.333449i
\(159\) −18.8206 −1.49257
\(160\) −0.667560 + 2.13410i −0.0527753 + 0.168715i
\(161\) 1.76328 + 1.76328i 0.138966 + 0.138966i
\(162\) 40.2348 3.16115
\(163\) 21.6389i 1.69489i 0.530884 + 0.847445i \(0.321860\pi\)
−0.530884 + 0.847445i \(0.678140\pi\)
\(164\) 12.7650i 0.996779i
\(165\) 6.82079 + 13.0304i 0.530998 + 1.01441i
\(166\) 7.79493 7.79493i 0.605004 0.605004i
\(167\) 15.0063i 1.16122i −0.814181 0.580611i \(-0.802814\pi\)
0.814181 0.580611i \(-0.197186\pi\)
\(168\) 4.23116i 0.326441i
\(169\) −3.65489 −0.281145
\(170\) −7.75787 2.42672i −0.595002 0.186121i
\(171\) 27.9885 + 27.9885i 2.14033 + 2.14033i
\(172\) −4.81157 −0.366879
\(173\) −3.27813 3.27813i −0.249231 0.249231i 0.571424 0.820655i \(-0.306391\pi\)
−0.820655 + 0.571424i \(0.806391\pi\)
\(174\) 23.2872i 1.76540i
\(175\) 1.10279 + 6.09249i 0.0833630 + 0.460549i
\(176\) 1.92497i 0.145100i
\(177\) −15.7069 −1.18060
\(178\) 7.79425 + 7.79425i 0.584203 + 0.584203i
\(179\) 15.3991 + 15.3991i 1.15098 + 1.15098i 0.986357 + 0.164623i \(0.0526406\pi\)
0.164623 + 0.986357i \(0.447359\pi\)
\(180\) 18.5139 + 5.79128i 1.37994 + 0.431656i
\(181\) 8.69492 0.646288 0.323144 0.946350i \(-0.395260\pi\)
0.323144 + 0.946350i \(0.395260\pi\)
\(182\) 2.67672 + 2.67672i 0.198412 + 0.198412i
\(183\) 15.3035 1.13126
\(184\) 2.01378 0.148458
\(185\) −13.3124 2.78910i −0.978750 0.205058i
\(186\) −4.52526 −0.331808
\(187\) −6.99765 −0.511719
\(188\) −5.85922 5.85922i −0.427327 0.427327i
\(189\) 24.0131 1.74669
\(190\) 4.73138 + 9.03878i 0.343250 + 0.655742i
\(191\) 2.73993 + 2.73993i 0.198255 + 0.198255i 0.799251 0.600997i \(-0.205230\pi\)
−0.600997 + 0.799251i \(0.705230\pi\)
\(192\) 2.41612 + 2.41612i 0.174369 + 0.174369i
\(193\) −12.4758 −0.898030 −0.449015 0.893524i \(-0.648225\pi\)
−0.449015 + 0.893524i \(0.648225\pi\)
\(194\) 14.8936i 1.06930i
\(195\) 20.6931 10.8319i 1.48186 0.775687i
\(196\) 5.46662i 0.390473i
\(197\) 2.72212 + 2.72212i 0.193943 + 0.193943i 0.797398 0.603454i \(-0.206209\pi\)
−0.603454 + 0.797398i \(0.706209\pi\)
\(198\) 16.6997 1.18679
\(199\) −5.62070 5.62070i −0.398441 0.398441i 0.479242 0.877683i \(-0.340912\pi\)
−0.877683 + 0.479242i \(0.840912\pi\)
\(200\) 4.10873 + 2.84927i 0.290531 + 0.201474i
\(201\) −17.9613 −1.26689
\(202\) 0.977455i 0.0687735i
\(203\) 8.43935i 0.592326i
\(204\) −8.78310 + 8.78310i −0.614940 + 0.614940i
\(205\) −27.2417 8.52140i −1.90265 0.595161i
\(206\) 11.3553i 0.791163i
\(207\) 17.4701i 1.21426i
\(208\) 3.05698 0.211963
\(209\) 6.21039 + 6.21039i 0.429581 + 0.429581i
\(210\) 9.02969 + 2.82455i 0.623108 + 0.194913i
\(211\) 25.2888 1.74095 0.870477 0.492210i \(-0.163811\pi\)
0.870477 + 0.492210i \(0.163811\pi\)
\(212\) −3.89480 + 3.89480i −0.267496 + 0.267496i
\(213\) −9.43516 9.43516i −0.646486 0.646486i
\(214\) 4.47857 + 4.47857i 0.306149 + 0.306149i
\(215\) −3.21201 + 10.2683i −0.219057 + 0.700295i
\(216\) 13.7122 13.7122i 0.932997 0.932997i
\(217\) −1.63997 −0.111328
\(218\) −7.18760 + 7.18760i −0.486805 + 0.486805i
\(219\) 41.4499i 2.80092i
\(220\) 4.10806 + 1.28503i 0.276966 + 0.0866368i
\(221\) 11.1127i 0.747524i
\(222\) −13.2100 + 16.0462i −0.886599 + 1.07695i
\(223\) −16.8265 + 16.8265i −1.12679 + 1.12679i −0.136090 + 0.990696i \(0.543454\pi\)
−0.990696 + 0.136090i \(0.956546\pi\)
\(224\) 0.875609 + 0.875609i 0.0585041 + 0.0585041i
\(225\) 24.7183 35.6444i 1.64789 2.37629i
\(226\) 3.47531i 0.231174i
\(227\) 13.3976i 0.889233i −0.895721 0.444616i \(-0.853340\pi\)
0.895721 0.444616i \(-0.146660\pi\)
\(228\) 15.5899 1.03247
\(229\) 12.4697i 0.824019i 0.911180 + 0.412010i \(0.135173\pi\)
−0.911180 + 0.412010i \(0.864827\pi\)
\(230\) 1.34432 4.29759i 0.0886417 0.283375i
\(231\) 8.14484 0.535891
\(232\) −4.81913 4.81913i −0.316391 0.316391i
\(233\) 11.3131 + 11.3131i 0.741144 + 0.741144i 0.972798 0.231655i \(-0.0744139\pi\)
−0.231655 + 0.972798i \(0.574414\pi\)
\(234\) 26.5202i 1.73368i
\(235\) −16.4155 + 8.59275i −1.07083 + 0.560529i
\(236\) −3.25043 + 3.25043i −0.211585 + 0.211585i
\(237\) 20.2538 1.31563
\(238\) −3.18302 + 3.18302i −0.206324 + 0.206324i
\(239\) 9.77163 9.77163i 0.632074 0.632074i −0.316514 0.948588i \(-0.602512\pi\)
0.948588 + 0.316514i \(0.102512\pi\)
\(240\) 6.76914 3.54333i 0.436946 0.228721i
\(241\) 2.61835 + 2.61835i 0.168663 + 0.168663i 0.786391 0.617729i \(-0.211947\pi\)
−0.617729 + 0.786391i \(0.711947\pi\)
\(242\) −7.29450 −0.468908
\(243\) −56.0756 56.0756i −3.59725 3.59725i
\(244\) 3.16695 3.16695i 0.202743 0.202743i
\(245\) −11.6663 3.64929i −0.745331 0.233145i
\(246\) −30.8418 + 30.8418i −1.96640 + 1.96640i
\(247\) 9.86251 9.86251i 0.627536 0.627536i
\(248\) −0.936472 + 0.936472i −0.0594660 + 0.0594660i
\(249\) −37.6670 −2.38705
\(250\) 8.82344 6.86635i 0.558044 0.434266i
\(251\) −1.40191 + 1.40191i −0.0884879 + 0.0884879i −0.749965 0.661477i \(-0.769930\pi\)
0.661477 + 0.749965i \(0.269930\pi\)
\(252\) 7.59617 7.59617i 0.478513 0.478513i
\(253\) 3.87646i 0.243711i
\(254\) −5.75444 5.75444i −0.361066 0.361066i
\(255\) 12.8807 + 24.6072i 0.806622 + 1.54096i
\(256\) 1.00000 0.0625000
\(257\) 26.1658i 1.63218i 0.577925 + 0.816090i \(0.303862\pi\)
−0.577925 + 0.816090i \(0.696138\pi\)
\(258\) 11.6253 + 11.6253i 0.723762 + 0.723762i
\(259\) −4.78735 + 5.81519i −0.297471 + 0.361338i
\(260\) 2.04072 6.52388i 0.126560 0.404594i
\(261\) −41.8074 + 41.8074i −2.58781 + 2.58781i
\(262\) −1.96912 + 1.96912i −0.121653 + 0.121653i
\(263\) 11.7781 + 11.7781i 0.726266 + 0.726266i 0.969874 0.243608i \(-0.0783310\pi\)
−0.243608 + 0.969874i \(0.578331\pi\)
\(264\) 4.65096 4.65096i 0.286247 0.286247i
\(265\) 5.71186 + 10.9119i 0.350877 + 0.670311i
\(266\) 5.64983 0.346413
\(267\) 37.6637i 2.30498i
\(268\) −3.71697 + 3.71697i −0.227050 + 0.227050i
\(269\) 0.0307805i 0.00187672i 1.00000 0.000938361i \(0.000298690\pi\)
−1.00000 0.000938361i \(0.999701\pi\)
\(270\) −20.1094 38.4169i −1.22382 2.33798i
\(271\) −29.5640 −1.79588 −0.897941 0.440115i \(-0.854938\pi\)
−0.897941 + 0.440115i \(0.854938\pi\)
\(272\) 3.63520i 0.220417i
\(273\) 12.9346i 0.782835i
\(274\) −7.83311 7.83311i −0.473216 0.473216i
\(275\) 5.48476 7.90917i 0.330743 0.476941i
\(276\) −4.86553 4.86553i −0.292871 0.292871i
\(277\) −4.25124 −0.255432 −0.127716 0.991811i \(-0.540765\pi\)
−0.127716 + 0.991811i \(0.540765\pi\)
\(278\) −0.678086 −0.0406689
\(279\) 8.12416 + 8.12416i 0.486381 + 0.486381i
\(280\) 2.45316 1.28411i 0.146604 0.0767404i
\(281\) −18.2679 18.2679i −1.08977 1.08977i −0.995552 0.0942188i \(-0.969965\pi\)
−0.0942188 0.995552i \(-0.530035\pi\)
\(282\) 28.3132i 1.68602i
\(283\) 2.36072i 0.140330i 0.997535 + 0.0701650i \(0.0223526\pi\)
−0.997535 + 0.0701650i \(0.977647\pi\)
\(284\) −3.90508 −0.231724
\(285\) 10.4072 33.2704i 0.616470 1.97077i
\(286\) 5.88458i 0.347963i
\(287\) −11.1772 + 11.1772i −0.659766 + 0.659766i
\(288\) 8.67529i 0.511196i
\(289\) 3.78529 0.222664
\(290\) −13.5015 + 7.06742i −0.792838 + 0.415013i
\(291\) 35.9847 35.9847i 2.10946 2.10946i
\(292\) 8.57777 + 8.57777i 0.501976 + 0.501976i
\(293\) 10.6576 10.6576i 0.622625 0.622625i −0.323577 0.946202i \(-0.604885\pi\)
0.946202 + 0.323577i \(0.104885\pi\)
\(294\) −13.2080 + 13.2080i −0.770307 + 0.770307i
\(295\) 4.76687 + 9.10659i 0.277538 + 0.530206i
\(296\) 0.586931 + 6.05438i 0.0341146 + 0.351904i
\(297\) −26.3955 26.3955i −1.53162 1.53162i
\(298\) 5.12261i 0.296745i
\(299\) −6.15607 −0.356015
\(300\) −3.04299 16.8114i −0.175687 0.970605i
\(301\) 4.21305 + 4.21305i 0.242836 + 0.242836i
\(302\) 20.3046i 1.16840i
\(303\) 2.36165 2.36165i 0.135673 0.135673i
\(304\) 3.22623 3.22623i 0.185037 0.185037i
\(305\) −4.64444 8.87270i −0.265940 0.508049i
\(306\) 31.5365 1.80282
\(307\) −12.4671 + 12.4671i −0.711533 + 0.711533i −0.966856 0.255323i \(-0.917818\pi\)
0.255323 + 0.966856i \(0.417818\pi\)
\(308\) 1.68552 1.68552i 0.0960414 0.0960414i
\(309\) 27.4358 27.4358i 1.56077 1.56077i
\(310\) 1.37337 + 2.62367i 0.0780021 + 0.149014i
\(311\) −16.0489 + 16.0489i −0.910048 + 0.910048i −0.996275 0.0862278i \(-0.972519\pi\)
0.0862278 + 0.996275i \(0.472519\pi\)
\(312\) −7.38603 7.38603i −0.418152 0.418152i
\(313\) 16.5993 0.938246 0.469123 0.883133i \(-0.344570\pi\)
0.469123 + 0.883133i \(0.344570\pi\)
\(314\) 9.36950 + 9.36950i 0.528751 + 0.528751i
\(315\) −11.1400 21.2818i −0.627671 1.19910i
\(316\) 4.19139 4.19139i 0.235784 0.235784i
\(317\) −2.57082 + 2.57082i −0.144391 + 0.144391i −0.775607 0.631216i \(-0.782556\pi\)
0.631216 + 0.775607i \(0.282556\pi\)
\(318\) 18.8206 1.05541
\(319\) −9.27667 + 9.27667i −0.519394 + 0.519394i
\(320\) 0.667560 2.13410i 0.0373177 0.119300i
\(321\) 21.6416i 1.20791i
\(322\) −1.76328 1.76328i −0.0982639 0.0982639i
\(323\) 11.7280 + 11.7280i 0.652564 + 0.652564i
\(324\) −40.2348 −2.23527
\(325\) −12.5603 8.71017i −0.696719 0.483153i
\(326\) 21.6389i 1.19847i
\(327\) 34.7322 1.92070
\(328\) 12.7650i 0.704829i
\(329\) 10.2608i 0.565694i
\(330\) −6.82079 13.0304i −0.375472 0.717299i
\(331\) 4.43217 + 4.43217i 0.243614 + 0.243614i 0.818344 0.574729i \(-0.194893\pi\)
−0.574729 + 0.818344i \(0.694893\pi\)
\(332\) −7.79493 + 7.79493i −0.427802 + 0.427802i
\(333\) 52.5235 5.09179i 2.87827 0.279029i
\(334\) 15.0063i 0.821108i
\(335\) 5.45106 + 10.4137i 0.297823 + 0.568959i
\(336\) 4.23116i 0.230829i
\(337\) −15.7372 + 15.7372i −0.857261 + 0.857261i −0.991015 0.133753i \(-0.957297\pi\)
0.133753 + 0.991015i \(0.457297\pi\)
\(338\) 3.65489 0.198800
\(339\) −8.39678 + 8.39678i −0.456050 + 0.456050i
\(340\) 7.75787 + 2.42672i 0.420730 + 0.131607i
\(341\) 1.80268 + 1.80268i 0.0976205 + 0.0976205i
\(342\) −27.9885 27.9885i −1.51344 1.51344i
\(343\) −10.9159 + 10.9159i −0.589402 + 0.589402i
\(344\) 4.81157 0.259422
\(345\) −13.6315 + 7.13548i −0.733898 + 0.384161i
\(346\) 3.27813 + 3.27813i 0.176233 + 0.176233i
\(347\) −8.61447 −0.462449 −0.231225 0.972900i \(-0.574273\pi\)
−0.231225 + 0.972900i \(0.574273\pi\)
\(348\) 23.2872i 1.24833i
\(349\) 6.48449i 0.347107i −0.984824 0.173553i \(-0.944475\pi\)
0.984824 0.173553i \(-0.0555249\pi\)
\(350\) −1.10279 6.09249i −0.0589466 0.325657i
\(351\) −41.9179 + 41.9179i −2.23741 + 2.23741i
\(352\) 1.92497i 0.102601i
\(353\) 7.88401i 0.419624i 0.977742 + 0.209812i \(0.0672851\pi\)
−0.977742 + 0.209812i \(0.932715\pi\)
\(354\) 15.7069 0.834811
\(355\) −2.60688 + 8.33382i −0.138359 + 0.442313i
\(356\) −7.79425 7.79425i −0.413094 0.413094i
\(357\) 15.3811 0.814055
\(358\) −15.3991 15.3991i −0.813865 0.813865i
\(359\) 22.1603i 1.16958i 0.811186 + 0.584789i \(0.198823\pi\)
−0.811186 + 0.584789i \(0.801177\pi\)
\(360\) −18.5139 5.79128i −0.975768 0.305227i
\(361\) 1.81711i 0.0956373i
\(362\) −8.69492 −0.456995
\(363\) 17.6244 + 17.6244i 0.925041 + 0.925041i
\(364\) −2.67672 2.67672i −0.140298 0.140298i
\(365\) 24.0320 12.5796i 1.25789 0.658447i
\(366\) −15.3035 −0.799925
\(367\) −24.3406 24.3406i −1.27057 1.27057i −0.945791 0.324776i \(-0.894711\pi\)
−0.324776 0.945791i \(-0.605289\pi\)
\(368\) −2.01378 −0.104975
\(369\) 110.740 5.76490
\(370\) 13.3124 + 2.78910i 0.692081 + 0.144998i
\(371\) 6.82064 0.354110
\(372\) 4.52526 0.234624
\(373\) −10.9227 10.9227i −0.565556 0.565556i 0.365324 0.930880i \(-0.380958\pi\)
−0.930880 + 0.365324i \(0.880958\pi\)
\(374\) 6.99765 0.361840
\(375\) −37.9085 4.72857i −1.95758 0.244182i
\(376\) 5.85922 + 5.85922i 0.302166 + 0.302166i
\(377\) 14.7320 + 14.7320i 0.758735 + 0.758735i
\(378\) −24.0131 −1.23510
\(379\) 0.495224i 0.0254380i −0.999919 0.0127190i \(-0.995951\pi\)
0.999919 0.0127190i \(-0.00404869\pi\)
\(380\) −4.73138 9.03878i −0.242715 0.463680i
\(381\) 27.8069i 1.42459i
\(382\) −2.73993 2.73993i −0.140187 0.140187i
\(383\) 14.8669 0.759661 0.379831 0.925056i \(-0.375982\pi\)
0.379831 + 0.925056i \(0.375982\pi\)
\(384\) −2.41612 2.41612i −0.123297 0.123297i
\(385\) −2.47187 4.72224i −0.125978 0.240668i
\(386\) 12.4758 0.635003
\(387\) 41.7417i 2.12185i
\(388\) 14.8936i 0.756106i
\(389\) 16.3839 16.3839i 0.830695 0.830695i −0.156917 0.987612i \(-0.550155\pi\)
0.987612 + 0.156917i \(0.0501555\pi\)
\(390\) −20.6931 + 10.8319i −1.04784 + 0.548493i
\(391\) 7.32049i 0.370213i
\(392\) 5.46662i 0.276106i
\(393\) 9.51529 0.479983
\(394\) −2.72212 2.72212i −0.137139 0.137139i
\(395\) −6.14682 11.7428i −0.309280 0.590846i
\(396\) −16.6997 −0.839189
\(397\) 16.3508 16.3508i 0.820621 0.820621i −0.165576 0.986197i \(-0.552948\pi\)
0.986197 + 0.165576i \(0.0529483\pi\)
\(398\) 5.62070 + 5.62070i 0.281740 + 0.281740i
\(399\) −13.6507 13.6507i −0.683389 0.683389i
\(400\) −4.10873 2.84927i −0.205436 0.142464i
\(401\) 1.61742 1.61742i 0.0807703 0.0807703i −0.665567 0.746338i \(-0.731810\pi\)
0.746338 + 0.665567i \(0.231810\pi\)
\(402\) 17.9613 0.895828
\(403\) 2.86277 2.86277i 0.142605 0.142605i
\(404\) 0.977455i 0.0486302i
\(405\) −26.8592 + 85.8649i −1.33464 + 4.26666i
\(406\) 8.43935i 0.418838i
\(407\) 11.6545 1.12982i 0.577691 0.0560032i
\(408\) 8.78310 8.78310i 0.434828 0.434828i
\(409\) 4.96548 + 4.96548i 0.245527 + 0.245527i 0.819132 0.573605i \(-0.194456\pi\)
−0.573605 + 0.819132i \(0.694456\pi\)
\(410\) 27.2417 + 8.52140i 1.34537 + 0.420842i
\(411\) 37.8515i 1.86708i
\(412\) 11.3553i 0.559437i
\(413\) 5.69222 0.280096
\(414\) 17.4701i 0.858609i
\(415\) 11.4315 + 21.8387i 0.561152 + 1.07202i
\(416\) −3.05698 −0.149881
\(417\) 1.63834 + 1.63834i 0.0802298 + 0.0802298i
\(418\) −6.21039 6.21039i −0.303760 0.303760i
\(419\) 5.39563i 0.263594i −0.991277 0.131797i \(-0.957925\pi\)
0.991277 0.131797i \(-0.0420747\pi\)
\(420\) −9.02969 2.82455i −0.440604 0.137824i
\(421\) 1.76092 1.76092i 0.0858222 0.0858222i −0.662892 0.748715i \(-0.730671\pi\)
0.748715 + 0.662892i \(0.230671\pi\)
\(422\) −25.2888 −1.23104
\(423\) 50.8304 50.8304i 2.47146 2.47146i
\(424\) 3.89480 3.89480i 0.189148 0.189148i
\(425\) 10.3577 14.9361i 0.502422 0.724506i
\(426\) 9.43516 + 9.43516i 0.457135 + 0.457135i
\(427\) −5.54602 −0.268391
\(428\) −4.47857 4.47857i −0.216480 0.216480i
\(429\) −14.2179 + 14.2179i −0.686445 + 0.686445i
\(430\) 3.21201 10.2683i 0.154897 0.495183i
\(431\) −7.96389 + 7.96389i −0.383607 + 0.383607i −0.872400 0.488793i \(-0.837437\pi\)
0.488793 + 0.872400i \(0.337437\pi\)
\(432\) −13.7122 + 13.7122i −0.659728 + 0.659728i
\(433\) 3.23648 3.23648i 0.155535 0.155535i −0.625050 0.780585i \(-0.714921\pi\)
0.780585 + 0.625050i \(0.214921\pi\)
\(434\) 1.63997 0.0787209
\(435\) 49.6971 + 15.5456i 2.38279 + 0.745355i
\(436\) 7.18760 7.18760i 0.344223 0.344223i
\(437\) −6.49691 + 6.49691i −0.310789 + 0.310789i
\(438\) 41.4499i 1.98055i
\(439\) 1.43898 + 1.43898i 0.0686789 + 0.0686789i 0.740612 0.671933i \(-0.234536\pi\)
−0.671933 + 0.740612i \(0.734536\pi\)
\(440\) −4.10806 1.28503i −0.195844 0.0612615i
\(441\) 47.4245 2.25831
\(442\) 11.1127i 0.528579i
\(443\) −19.8400 19.8400i −0.942626 0.942626i 0.0558147 0.998441i \(-0.482224\pi\)
−0.998441 + 0.0558147i \(0.982224\pi\)
\(444\) 13.2100 16.0462i 0.626920 0.761520i
\(445\) −21.8368 + 11.4305i −1.03516 + 0.541859i
\(446\) 16.8265 16.8265i 0.796758 0.796758i
\(447\) −12.3768 + 12.3768i −0.585404 + 0.585404i
\(448\) −0.875609 0.875609i −0.0413686 0.0413686i
\(449\) −13.4394 + 13.4394i −0.634247 + 0.634247i −0.949130 0.314884i \(-0.898034\pi\)
0.314884 + 0.949130i \(0.398034\pi\)
\(450\) −24.7183 + 35.6444i −1.16523 + 1.68029i
\(451\) 24.5722 1.15706
\(452\) 3.47531i 0.163465i
\(453\) −49.0583 + 49.0583i −2.30496 + 2.30496i
\(454\) 13.3976i 0.628782i
\(455\) −7.49924 + 3.92550i −0.351570 + 0.184030i
\(456\) −15.5899 −0.730065
\(457\) 0.134698i 0.00630090i −0.999995 0.00315045i \(-0.998997\pi\)
0.999995 0.00315045i \(-0.00100282\pi\)
\(458\) 12.4697i 0.582669i
\(459\) −49.8466 49.8466i −2.32664 2.32664i
\(460\) −1.34432 + 4.29759i −0.0626791 + 0.200376i
\(461\) 7.52644 + 7.52644i 0.350541 + 0.350541i 0.860311 0.509770i \(-0.170269\pi\)
−0.509770 + 0.860311i \(0.670269\pi\)
\(462\) −8.14484 −0.378932
\(463\) −19.4799 −0.905306 −0.452653 0.891687i \(-0.649522\pi\)
−0.452653 + 0.891687i \(0.649522\pi\)
\(464\) 4.81913 + 4.81913i 0.223722 + 0.223722i
\(465\) 3.02088 9.65734i 0.140090 0.447848i
\(466\) −11.3131 11.3131i −0.524068 0.524068i
\(467\) 4.43682i 0.205312i −0.994717 0.102656i \(-0.967266\pi\)
0.994717 0.102656i \(-0.0327340\pi\)
\(468\) 26.5202i 1.22590i
\(469\) 6.50922 0.300568
\(470\) 16.4155 8.59275i 0.757191 0.396354i
\(471\) 45.2757i 2.08619i
\(472\) 3.25043 3.25043i 0.149613 0.149613i
\(473\) 9.26211i 0.425872i
\(474\) −20.2538 −0.930288
\(475\) −22.4481 + 4.06329i −1.02999 + 0.186436i
\(476\) 3.18302 3.18302i 0.145893 0.145893i
\(477\) −33.7885 33.7885i −1.54707 1.54707i
\(478\) −9.77163 + 9.77163i −0.446944 + 0.446944i
\(479\) 10.5292 10.5292i 0.481093 0.481093i −0.424387 0.905481i \(-0.639510\pi\)
0.905481 + 0.424387i \(0.139510\pi\)
\(480\) −6.76914 + 3.54333i −0.308968 + 0.161730i
\(481\) −1.79423 18.5081i −0.0818100 0.843897i
\(482\) −2.61835 2.61835i −0.119262 0.119262i
\(483\) 8.52061i 0.387701i
\(484\) 7.29450 0.331568
\(485\) −31.7843 9.94235i −1.44325 0.451459i
\(486\) 56.0756 + 56.0756i 2.54364 + 2.54364i
\(487\) 9.78190i 0.443260i −0.975131 0.221630i \(-0.928862\pi\)
0.975131 0.221630i \(-0.0711377\pi\)
\(488\) −3.16695 + 3.16695i −0.143361 + 0.143361i
\(489\) −52.2822 + 52.2822i −2.36428 + 2.36428i
\(490\) 11.6663 + 3.64929i 0.527029 + 0.164858i
\(491\) −9.56888 −0.431837 −0.215919 0.976411i \(-0.569275\pi\)
−0.215919 + 0.976411i \(0.569275\pi\)
\(492\) 30.8418 30.8418i 1.39046 1.39046i
\(493\) −17.5185 + 17.5185i −0.788995 + 0.788995i
\(494\) −9.86251 + 9.86251i −0.443735 + 0.443735i
\(495\) −11.1480 + 35.6387i −0.501066 + 1.60184i
\(496\) 0.936472 0.936472i 0.0420488 0.0420488i
\(497\) 3.41933 + 3.41933i 0.153378 + 0.153378i
\(498\) 37.6670 1.68790
\(499\) 13.9261 + 13.9261i 0.623418 + 0.623418i 0.946404 0.322986i \(-0.104687\pi\)
−0.322986 + 0.946404i \(0.604687\pi\)
\(500\) −8.82344 + 6.86635i −0.394596 + 0.307073i
\(501\) 36.2570 36.2570i 1.61984 1.61984i
\(502\) 1.40191 1.40191i 0.0625704 0.0625704i
\(503\) −0.0190379 −0.000848857 −0.000424428 1.00000i \(-0.500135\pi\)
−0.000424428 1.00000i \(0.500135\pi\)
\(504\) −7.59617 + 7.59617i −0.338360 + 0.338360i
\(505\) −2.08598 0.652510i −0.0928250 0.0290363i
\(506\) 3.87646i 0.172330i
\(507\) −8.83066 8.83066i −0.392183 0.392183i
\(508\) 5.75444 + 5.75444i 0.255312 + 0.255312i
\(509\) −13.1961 −0.584908 −0.292454 0.956280i \(-0.594472\pi\)
−0.292454 + 0.956280i \(0.594472\pi\)
\(510\) −12.8807 24.6072i −0.570368 1.08963i
\(511\) 15.0216i 0.664515i
\(512\) −1.00000 −0.0441942
\(513\) 88.4774i 3.90637i
\(514\) 26.1658i 1.15413i
\(515\) −24.2333 7.58036i −1.06785 0.334031i
\(516\) −11.6253 11.6253i −0.511777 0.511777i
\(517\) 11.2788 11.2788i 0.496041 0.496041i
\(518\) 4.78735 5.81519i 0.210344 0.255505i
\(519\) 15.8407i 0.695330i
\(520\) −2.04072 + 6.52388i −0.0894913 + 0.286091i
\(521\) 15.1816i 0.665117i 0.943083 + 0.332559i \(0.107912\pi\)
−0.943083 + 0.332559i \(0.892088\pi\)
\(522\) 41.8074 41.8074i 1.82986 1.82986i
\(523\) −6.40480 −0.280062 −0.140031 0.990147i \(-0.544720\pi\)
−0.140031 + 0.990147i \(0.544720\pi\)
\(524\) 1.96912 1.96912i 0.0860216 0.0860216i
\(525\) −12.0557 + 17.3847i −0.526155 + 0.758729i
\(526\) −11.7781 11.7781i −0.513547 0.513547i
\(527\) 3.40427 + 3.40427i 0.148292 + 0.148292i
\(528\) −4.65096 + 4.65096i −0.202407 + 0.202407i
\(529\) −18.9447 −0.823683
\(530\) −5.71186 10.9119i −0.248107 0.473982i
\(531\) −28.1984 28.1984i −1.22371 1.22371i
\(532\) −5.64983 −0.244951
\(533\) 39.0223i 1.69024i
\(534\) 37.6637i 1.62987i
\(535\) −12.5474 + 6.56798i −0.542472 + 0.283959i
\(536\) 3.71697 3.71697i 0.160549 0.160549i
\(537\) 74.4120i 3.21111i
\(538\) 0.0307805i 0.00132704i
\(539\) 10.5231 0.453260
\(540\) 20.1094 + 38.4169i 0.865372 + 1.65320i
\(541\) 2.84624 + 2.84624i 0.122369 + 0.122369i 0.765639 0.643270i \(-0.222423\pi\)
−0.643270 + 0.765639i \(0.722423\pi\)
\(542\) 29.5640 1.26988
\(543\) 21.0080 + 21.0080i 0.901539 + 0.901539i
\(544\) 3.63520i 0.155858i
\(545\) −10.5409 20.1372i −0.451521 0.862582i
\(546\) 12.9346i 0.553548i
\(547\) 11.8169 0.505253 0.252627 0.967564i \(-0.418706\pi\)
0.252627 + 0.967564i \(0.418706\pi\)
\(548\) 7.83311 + 7.83311i 0.334614 + 0.334614i
\(549\) 27.4742 + 27.4742i 1.17257 + 1.17257i
\(550\) −5.48476 + 7.90917i −0.233871 + 0.337248i
\(551\) 31.0952 1.32470
\(552\) 4.86553 + 4.86553i 0.207091 + 0.207091i
\(553\) −7.34004 −0.312130
\(554\) 4.25124 0.180618
\(555\) −25.4257 38.9033i −1.07926 1.65135i
\(556\) 0.678086 0.0287572
\(557\) 46.6368 1.97607 0.988033 0.154245i \(-0.0492944\pi\)
0.988033 + 0.154245i \(0.0492944\pi\)
\(558\) −8.12416 8.12416i −0.343923 0.343923i
\(559\) −14.7089 −0.622118
\(560\) −2.45316 + 1.28411i −0.103665 + 0.0542636i
\(561\) −16.9072 16.9072i −0.713822 0.713822i
\(562\) 18.2679 + 18.2679i 0.770584 + 0.770584i
\(563\) 18.5082 0.780030 0.390015 0.920809i \(-0.372470\pi\)
0.390015 + 0.920809i \(0.372470\pi\)
\(564\) 28.3132i 1.19220i
\(565\) 7.41665 + 2.31998i 0.312021 + 0.0976023i
\(566\) 2.36072i 0.0992283i
\(567\) 35.2300 + 35.2300i 1.47952 + 1.47952i
\(568\) 3.90508 0.163854
\(569\) −10.7292 10.7292i −0.449790 0.449790i 0.445495 0.895285i \(-0.353028\pi\)
−0.895285 + 0.445495i \(0.853028\pi\)
\(570\) −10.4072 + 33.2704i −0.435910 + 1.39354i
\(571\) 0.731150 0.0305977 0.0152988 0.999883i \(-0.495130\pi\)
0.0152988 + 0.999883i \(0.495130\pi\)
\(572\) 5.88458i 0.246047i
\(573\) 13.2400i 0.553110i
\(574\) 11.1772 11.1772i 0.466525 0.466525i
\(575\) 8.27406 + 5.73780i 0.345052 + 0.239283i
\(576\) 8.67529i 0.361470i
\(577\) 9.84843i 0.409995i −0.978762 0.204998i \(-0.934281\pi\)
0.978762 0.204998i \(-0.0657187\pi\)
\(578\) −3.78529 −0.157447
\(579\) −30.1431 30.1431i −1.25271 1.25271i
\(580\) 13.5015 7.06742i 0.560621 0.293459i
\(581\) 13.6506 0.566323
\(582\) −35.9847 + 35.9847i −1.49161 + 1.49161i
\(583\) −7.49736 7.49736i −0.310509 0.310509i
\(584\) −8.57777 8.57777i −0.354951 0.354951i
\(585\) 56.5966 + 17.7038i 2.33998 + 0.731962i
\(586\) −10.6576 + 10.6576i −0.440263 + 0.440263i
\(587\) 3.62231 0.149509 0.0747544 0.997202i \(-0.476183\pi\)
0.0747544 + 0.997202i \(0.476183\pi\)
\(588\) 13.2080 13.2080i 0.544689 0.544689i
\(589\) 6.04254i 0.248979i
\(590\) −4.76687 9.10659i −0.196249 0.374912i
\(591\) 13.1540i 0.541082i
\(592\) −0.586931 6.05438i −0.0241227 0.248833i
\(593\) 24.4083 24.4083i 1.00233 1.00233i 0.00233126 0.999997i \(-0.499258\pi\)
0.999997 0.00233126i \(-0.000742064\pi\)
\(594\) 26.3955 + 26.3955i 1.08302 + 1.08302i
\(595\) −4.66801 8.91772i −0.191370 0.365591i
\(596\) 5.12261i 0.209830i
\(597\) 27.1606i 1.11161i
\(598\) 6.15607 0.251741
\(599\) 10.0741i 0.411615i 0.978592 + 0.205808i \(0.0659821\pi\)
−0.978592 + 0.205808i \(0.934018\pi\)
\(600\) 3.04299 + 16.8114i 0.124230 + 0.686322i
\(601\) 16.4771 0.672116 0.336058 0.941841i \(-0.390906\pi\)
0.336058 + 0.941841i \(0.390906\pi\)
\(602\) −4.21305 4.21305i −0.171711 0.171711i
\(603\) −32.2458 32.2458i −1.31315 1.31315i
\(604\) 20.3046i 0.826181i
\(605\) 4.86952 15.5672i 0.197974 0.632895i
\(606\) −2.36165 + 2.36165i −0.0959355 + 0.0959355i
\(607\) 45.5231 1.84772 0.923862 0.382726i \(-0.125015\pi\)
0.923862 + 0.382726i \(0.125015\pi\)
\(608\) −3.22623 + 3.22623i −0.130841 + 0.130841i
\(609\) 20.3905 20.3905i 0.826265 0.826265i
\(610\) 4.64444 + 8.87270i 0.188048 + 0.359245i
\(611\) −17.9115 17.9115i −0.724621 0.724621i
\(612\) −31.5365 −1.27479
\(613\) 17.4896 + 17.4896i 0.706398 + 0.706398i 0.965776 0.259378i \(-0.0835176\pi\)
−0.259378 + 0.965776i \(0.583518\pi\)
\(614\) 12.4671 12.4671i 0.503130 0.503130i
\(615\) −45.2306 86.4081i −1.82387 3.48431i
\(616\) −1.68552 + 1.68552i −0.0679115 + 0.0679115i
\(617\) 4.01386 4.01386i 0.161592 0.161592i −0.621680 0.783272i \(-0.713549\pi\)
0.783272 + 0.621680i \(0.213549\pi\)
\(618\) −27.4358 + 27.4358i −1.10363 + 1.10363i
\(619\) −4.28932 −0.172402 −0.0862012 0.996278i \(-0.527473\pi\)
−0.0862012 + 0.996278i \(0.527473\pi\)
\(620\) −1.37337 2.62367i −0.0551558 0.105369i
\(621\) 27.6133 27.6133i 1.10808 1.10808i
\(622\) 16.0489 16.0489i 0.643501 0.643501i
\(623\) 13.6494i 0.546853i
\(624\) 7.38603 + 7.38603i 0.295678 + 0.295678i
\(625\) 8.76328 + 23.4138i 0.350531 + 0.936551i
\(626\) −16.5993 −0.663440
\(627\) 30.0101i 1.19849i
\(628\) −9.36950 9.36950i −0.373884 0.373884i
\(629\) 22.0089 2.13361i 0.877553 0.0850727i
\(630\) 11.1400 + 21.2818i 0.443830 + 0.847889i
\(631\) 7.95854 7.95854i 0.316825 0.316825i −0.530722 0.847546i \(-0.678079\pi\)
0.847546 + 0.530722i \(0.178079\pi\)
\(632\) −4.19139 + 4.19139i −0.166724 + 0.166724i
\(633\) 61.1008 + 61.1008i 2.42854 + 2.42854i
\(634\) 2.57082 2.57082i 0.102100 0.102100i
\(635\) 16.1220 8.43910i 0.639781 0.334895i
\(636\) −18.8206 −0.746285
\(637\) 16.7113i 0.662127i
\(638\) 9.27667 9.27667i 0.367267 0.367267i
\(639\) 33.8777i 1.34018i
\(640\) −0.667560 + 2.13410i −0.0263876 + 0.0843575i
\(641\) 20.2510 0.799866 0.399933 0.916544i \(-0.369033\pi\)
0.399933 + 0.916544i \(0.369033\pi\)
\(642\) 21.6416i 0.854124i
\(643\) 27.6440i 1.09017i 0.838379 + 0.545087i \(0.183503\pi\)
−0.838379 + 0.545087i \(0.816497\pi\)
\(644\) 1.76328 + 1.76328i 0.0694831 + 0.0694831i
\(645\) −32.5702 + 17.0490i −1.28245 + 0.671302i
\(646\) −11.7280 11.7280i −0.461432 0.461432i
\(647\) 21.7566 0.855342 0.427671 0.903934i \(-0.359334\pi\)
0.427671 + 0.903934i \(0.359334\pi\)
\(648\) 40.2348 1.58057
\(649\) −6.25698 6.25698i −0.245608 0.245608i
\(650\) 12.5603 + 8.71017i 0.492655 + 0.341641i
\(651\) −3.96236 3.96236i −0.155297 0.155297i
\(652\) 21.6389i 0.847445i
\(653\) 15.8716i 0.621105i −0.950556 0.310553i \(-0.899486\pi\)
0.950556 0.310553i \(-0.100514\pi\)
\(654\) −34.7322 −1.35814
\(655\) −2.88779 5.51681i −0.112835 0.215559i
\(656\) 12.7650i 0.498390i
\(657\) −74.4147 + 74.4147i −2.90319 + 2.90319i
\(658\) 10.2608i 0.400006i
\(659\) −33.4745 −1.30398 −0.651990 0.758227i \(-0.726066\pi\)
−0.651990 + 0.758227i \(0.726066\pi\)
\(660\) 6.82079 + 13.0304i 0.265499 + 0.507207i
\(661\) −33.1517 + 33.1517i −1.28945 + 1.28945i −0.354333 + 0.935119i \(0.615292\pi\)
−0.935119 + 0.354333i \(0.884708\pi\)
\(662\) −4.43217 4.43217i −0.172261 0.172261i
\(663\) −26.8497 + 26.8497i −1.04276 + 1.04276i
\(664\) 7.79493 7.79493i 0.302502 0.302502i
\(665\) −3.77160 + 12.0573i −0.146256 + 0.467561i
\(666\) −52.5235 + 5.09179i −2.03524 + 0.197303i
\(667\) −9.70465 9.70465i −0.375766 0.375766i
\(668\) 15.0063i 0.580611i
\(669\) −81.3098 −3.14362
\(670\) −5.45106 10.4137i −0.210593 0.402315i
\(671\) 6.09627 + 6.09627i 0.235344 + 0.235344i
\(672\) 4.23116i 0.163220i
\(673\) 8.36499 8.36499i 0.322447 0.322447i −0.527258 0.849705i \(-0.676780\pi\)
0.849705 + 0.527258i \(0.176780\pi\)
\(674\) 15.7372 15.7372i 0.606175 0.606175i
\(675\) 95.4095 17.2699i 3.67231 0.664718i
\(676\) −3.65489 −0.140573
\(677\) −27.0712 + 27.0712i −1.04043 + 1.04043i −0.0412815 + 0.999148i \(0.513144\pi\)
−0.999148 + 0.0412815i \(0.986856\pi\)
\(678\) 8.39678 8.39678i 0.322476 0.322476i
\(679\) −13.0409 + 13.0409i −0.500466 + 0.500466i
\(680\) −7.75787 2.42672i −0.297501 0.0930604i
\(681\) 32.3703 32.3703i 1.24043 1.24043i
\(682\) −1.80268 1.80268i −0.0690281 0.0690281i
\(683\) 12.1368 0.464403 0.232202 0.972668i \(-0.425407\pi\)
0.232202 + 0.972668i \(0.425407\pi\)
\(684\) 27.9885 + 27.9885i 1.07017 + 1.07017i
\(685\) 21.9457 11.4875i 0.838501 0.438916i
\(686\) 10.9159 10.9159i 0.416770 0.416770i
\(687\) −30.1282 + 30.1282i −1.14946 + 1.14946i
\(688\) −4.81157 −0.183439
\(689\) −11.9063 + 11.9063i −0.453594 + 0.453594i
\(690\) 13.6315 7.13548i 0.518944 0.271643i
\(691\) 16.8996i 0.642892i 0.946928 + 0.321446i \(0.104169\pi\)
−0.946928 + 0.321446i \(0.895831\pi\)
\(692\) −3.27813 3.27813i −0.124616 0.124616i
\(693\) 14.6224 + 14.6224i 0.555458 + 0.555458i
\(694\) 8.61447 0.327001
\(695\) 0.452663 1.44710i 0.0171705 0.0548916i
\(696\) 23.2872i 0.882699i
\(697\) 46.4034 1.75765
\(698\) 6.48449i 0.245441i
\(699\) 54.6675i 2.06771i
\(700\) 1.10279 + 6.09249i 0.0416815 + 0.230274i
\(701\) −29.5313 29.5313i −1.11538 1.11538i −0.992410 0.122973i \(-0.960757\pi\)
−0.122973 0.992410i \(-0.539243\pi\)
\(702\) 41.9179 41.9179i 1.58209 1.58209i
\(703\) −21.4264 17.6392i −0.808112 0.665277i
\(704\) 1.92497i 0.0725499i
\(705\) −60.4230 18.9007i −2.27566 0.711843i
\(706\) 7.88401i 0.296719i
\(707\) −0.855869 + 0.855869i −0.0321882 + 0.0321882i
\(708\) −15.7069 −0.590301
\(709\) 11.8999 11.8999i 0.446910 0.446910i −0.447416 0.894326i \(-0.647656\pi\)
0.894326 + 0.447416i \(0.147656\pi\)
\(710\) 2.60688 8.33382i 0.0978344 0.312763i
\(711\) 36.3615 + 36.3615i 1.36366 + 1.36366i
\(712\) 7.79425 + 7.79425i 0.292102 + 0.292102i
\(713\) −1.88585 + 1.88585i −0.0706255 + 0.0706255i
\(714\) −15.3811 −0.575624
\(715\) 12.5583 + 3.92831i 0.469652 + 0.146911i
\(716\) 15.3991 + 15.3991i 0.575490 + 0.575490i
\(717\) 47.2189 1.76342
\(718\) 22.1603i 0.827016i
\(719\) 27.9313i 1.04166i −0.853660 0.520831i \(-0.825622\pi\)
0.853660 0.520831i \(-0.174378\pi\)
\(720\) 18.5139 + 5.79128i 0.689972 + 0.215828i
\(721\) −9.94282 + 9.94282i −0.370290 + 0.370290i
\(722\) 1.81711i 0.0676258i
\(723\) 12.6525i 0.470551i
\(724\) 8.69492 0.323144
\(725\) −6.06947 33.5315i −0.225414 1.24533i
\(726\) −17.6244 17.6244i −0.654103 0.654103i
\(727\) 9.97158 0.369825 0.184913 0.982755i \(-0.440800\pi\)
0.184913 + 0.982755i \(0.440800\pi\)
\(728\) 2.67672 + 2.67672i 0.0992058 + 0.0992058i
\(729\) 150.267i 5.56543i
\(730\) −24.0320 + 12.5796i −0.889463 + 0.465592i
\(731\) 17.4910i 0.646929i
\(732\) 15.3035 0.565632
\(733\) 13.0344 + 13.0344i 0.481437 + 0.481437i 0.905590 0.424154i \(-0.139428\pi\)
−0.424154 + 0.905590i \(0.639428\pi\)
\(734\) 24.3406 + 24.3406i 0.898426 + 0.898426i
\(735\) −19.3700 37.0043i −0.714474 1.36492i
\(736\) 2.01378 0.0742288
\(737\) −7.15504 7.15504i −0.263559 0.263559i
\(738\) −110.740 −4.07640
\(739\) 18.8384 0.692982 0.346491 0.938053i \(-0.387373\pi\)
0.346491 + 0.938053i \(0.387373\pi\)
\(740\) −13.3124 2.78910i −0.489375 0.102529i
\(741\) 47.6581 1.75076
\(742\) −6.82064 −0.250394
\(743\) 12.7095 + 12.7095i 0.466266 + 0.466266i 0.900703 0.434436i \(-0.143052\pi\)
−0.434436 + 0.900703i \(0.643052\pi\)
\(744\) −4.52526 −0.165904
\(745\) 10.9321 + 3.41965i 0.400522 + 0.125286i
\(746\) 10.9227 + 10.9227i 0.399909 + 0.399909i
\(747\) −67.6233 67.6233i −2.47421 2.47421i
\(748\) −6.99765 −0.255859
\(749\) 7.84296i 0.286575i
\(750\) 37.9085 + 4.72857i 1.38422 + 0.172663i
\(751\) 37.9745i 1.38571i 0.721077 + 0.692855i \(0.243647\pi\)
−0.721077 + 0.692855i \(0.756353\pi\)
\(752\) −5.85922 5.85922i −0.213664 0.213664i
\(753\) −6.77438 −0.246872
\(754\) −14.7320 14.7320i −0.536507 0.536507i
\(755\) 43.3319 + 13.5545i 1.57701 + 0.493299i
\(756\) 24.0131 0.873346
\(757\) 11.5922i 0.421326i −0.977559 0.210663i \(-0.932438\pi\)
0.977559 0.210663i \(-0.0675623\pi\)
\(758\) 0.495224i 0.0179874i
\(759\) 9.36599 9.36599i 0.339964 0.339964i
\(760\) 4.73138 + 9.03878i 0.171625 + 0.327871i
\(761\) 12.7639i 0.462692i 0.972871 + 0.231346i \(0.0743130\pi\)
−0.972871 + 0.231346i \(0.925687\pi\)
\(762\) 27.8069i 1.00734i
\(763\) −12.5871 −0.455682
\(764\) 2.73993 + 2.73993i 0.0991274 + 0.0991274i
\(765\) −21.0525 + 67.3018i −0.761154 + 2.43330i
\(766\) −14.8669 −0.537162
\(767\) −9.93650 + 9.93650i −0.358786 + 0.358786i
\(768\) 2.41612 + 2.41612i 0.0871843 + 0.0871843i
\(769\) 12.7912 + 12.7912i 0.461263 + 0.461263i 0.899069 0.437806i \(-0.144244\pi\)
−0.437806 + 0.899069i \(0.644244\pi\)
\(770\) 2.47187 + 4.72224i 0.0890802 + 0.170178i
\(771\) −63.2198 + 63.2198i −2.27681 + 2.27681i
\(772\) −12.4758 −0.449015
\(773\) 38.5353 38.5353i 1.38602 1.38602i 0.552511 0.833505i \(-0.313670\pi\)
0.833505 0.552511i \(-0.186330\pi\)
\(774\) 41.7417i 1.50038i
\(775\) −6.51597 + 1.17944i −0.234061 + 0.0423668i
\(776\) 14.8936i 0.534648i
\(777\) −25.6170 + 2.48340i −0.919006 + 0.0890913i
\(778\) −16.3839 + 16.3839i