Properties

Label 287.2.n.a.64.12
Level $287$
Weight $2$
Character 287.64
Analytic conductor $2.292$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,2,Mod(64,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.n (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 64.12
Character \(\chi\) \(=\) 287.64
Dual form 287.2.n.a.148.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0458641 + 0.141155i) q^{2} +2.46220i q^{3} +(1.60021 - 1.16262i) q^{4} +(1.41155 - 1.02555i) q^{5} +(-0.347553 + 0.112927i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.477650 + 0.347033i) q^{8} -3.06244 q^{9} +O(q^{10})\) \(q+(0.0458641 + 0.141155i) q^{2} +2.46220i q^{3} +(1.60021 - 1.16262i) q^{4} +(1.41155 - 1.02555i) q^{5} +(-0.347553 + 0.112927i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.477650 + 0.347033i) q^{8} -3.06244 q^{9} +(0.209501 + 0.152212i) q^{10} +(2.65267 - 3.65109i) q^{11} +(2.86261 + 3.94005i) q^{12} +(-0.388673 + 0.126288i) q^{13} +0.148419i q^{14} +(2.52511 + 3.47552i) q^{15} +(1.19538 - 3.67899i) q^{16} +(-3.71653 + 5.11537i) q^{17} +(-0.140456 - 0.432279i) q^{18} +(-7.93559 - 2.57843i) q^{19} +(1.06645 - 3.28220i) q^{20} +(-0.760862 + 2.34169i) q^{21} +(0.637032 + 0.206984i) q^{22} +(1.02240 + 3.14664i) q^{23} +(-0.854466 + 1.17607i) q^{24} +(-0.604367 + 1.86005i) q^{25} +(-0.0356523 - 0.0490712i) q^{26} -0.153735i q^{27} +(1.88116 - 0.611227i) q^{28} +(1.11576 + 1.53571i) q^{29} +(-0.374776 + 0.515835i) q^{30} +(-0.484807 - 0.352233i) q^{31} +1.75495 q^{32} +(8.98971 + 6.53141i) q^{33} +(-0.892516 - 0.289996i) q^{34} +(1.65938 - 0.539164i) q^{35} +(-4.90055 + 3.56046i) q^{36} +(-4.63436 + 3.36706i) q^{37} -1.23841i q^{38} +(-0.310945 - 0.956992i) q^{39} +1.03013 q^{40} +(5.47571 - 3.31912i) q^{41} -0.365439 q^{42} +(-3.89490 - 11.9873i) q^{43} -8.92657i q^{44} +(-4.32278 + 3.14069i) q^{45} +(-0.397273 + 0.288636i) q^{46} +(-9.00883 + 2.92715i) q^{47} +(9.05841 + 2.94326i) q^{48} +(0.809017 + 0.587785i) q^{49} -0.290275 q^{50} +(-12.5951 - 9.15085i) q^{51} +(-0.475135 + 0.653967i) q^{52} +(-0.250762 - 0.345144i) q^{53} +(0.0217006 - 0.00705094i) q^{54} -7.87414i q^{55} +(0.347033 + 0.477650i) q^{56} +(6.34861 - 19.5390i) q^{57} +(-0.165601 + 0.227930i) q^{58} +(2.03785 + 6.27186i) q^{59} +(8.08144 + 2.62582i) q^{60} +(4.35730 - 13.4104i) q^{61} +(0.0274842 - 0.0845878i) q^{62} +(-2.91255 - 0.946345i) q^{63} +(-2.31026 - 7.11025i) q^{64} +(-0.419117 + 0.576865i) q^{65} +(-0.509637 + 1.56850i) q^{66} +(2.21422 + 3.04761i) q^{67} +12.5066i q^{68} +(-7.74766 + 2.51737i) q^{69} +(0.152212 + 0.209501i) q^{70} +(-2.97773 + 4.09850i) q^{71} +(-1.46277 - 1.06277i) q^{72} +6.69702 q^{73} +(-0.687828 - 0.499737i) q^{74} +(-4.57982 - 1.48807i) q^{75} +(-15.6964 + 5.10006i) q^{76} +(3.65109 - 2.65267i) q^{77} +(0.120823 - 0.0877832i) q^{78} -7.43419i q^{79} +(-2.08566 - 6.41899i) q^{80} -8.80879 q^{81} +(0.719650 + 0.620697i) q^{82} -7.24229 q^{83} +(1.50496 + 4.63180i) q^{84} +11.0321i q^{85} +(1.51343 - 1.09957i) q^{86} +(-3.78124 + 2.74723i) q^{87} +(2.53410 - 0.823378i) q^{88} +(13.3884 + 4.35014i) q^{89} +(-0.641585 - 0.466139i) q^{90} -0.408675 q^{91} +(5.29442 + 3.84662i) q^{92} +(0.867268 - 1.19369i) q^{93} +(-0.826364 - 1.13739i) q^{94} +(-13.8458 + 4.49877i) q^{95} +4.32104i q^{96} +(-4.83995 - 6.66162i) q^{97} +(-0.0458641 + 0.141155i) q^{98} +(-8.12364 + 11.1812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0458641 + 0.141155i 0.0324308 + 0.0998118i 0.965962 0.258685i \(-0.0832893\pi\)
−0.933531 + 0.358497i \(0.883289\pi\)
\(3\) 2.46220i 1.42155i 0.703418 + 0.710776i \(0.251656\pi\)
−0.703418 + 0.710776i \(0.748344\pi\)
\(4\) 1.60021 1.16262i 0.800106 0.581311i
\(5\) 1.41155 1.02555i 0.631264 0.458640i −0.225574 0.974226i \(-0.572426\pi\)
0.856838 + 0.515586i \(0.172426\pi\)
\(6\) −0.347553 + 0.112927i −0.141888 + 0.0461021i
\(7\) 0.951057 + 0.309017i 0.359466 + 0.116797i
\(8\) 0.477650 + 0.347033i 0.168875 + 0.122695i
\(9\) −3.06244 −1.02081
\(10\) 0.209501 + 0.152212i 0.0662501 + 0.0481335i
\(11\) 2.65267 3.65109i 0.799810 1.10084i −0.193007 0.981197i \(-0.561824\pi\)
0.992817 0.119646i \(-0.0381761\pi\)
\(12\) 2.86261 + 3.94005i 0.826365 + 1.13739i
\(13\) −0.388673 + 0.126288i −0.107799 + 0.0350259i −0.362420 0.932015i \(-0.618049\pi\)
0.254621 + 0.967041i \(0.418049\pi\)
\(14\) 0.148419i 0.0396668i
\(15\) 2.52511 + 3.47552i 0.651981 + 0.897376i
\(16\) 1.19538 3.67899i 0.298844 0.919747i
\(17\) −3.71653 + 5.11537i −0.901391 + 1.24066i 0.0686309 + 0.997642i \(0.478137\pi\)
−0.970022 + 0.243017i \(0.921863\pi\)
\(18\) −0.140456 0.432279i −0.0331058 0.101889i
\(19\) −7.93559 2.57843i −1.82055 0.591532i −0.999795 0.0202495i \(-0.993554\pi\)
−0.820753 0.571283i \(-0.806446\pi\)
\(20\) 1.06645 3.28220i 0.238466 0.733922i
\(21\) −0.760862 + 2.34169i −0.166034 + 0.510999i
\(22\) 0.637032 + 0.206984i 0.135816 + 0.0441292i
\(23\) 1.02240 + 3.14664i 0.213186 + 0.656119i 0.999277 + 0.0380089i \(0.0121015\pi\)
−0.786091 + 0.618110i \(0.787898\pi\)
\(24\) −0.854466 + 1.17607i −0.174417 + 0.240065i
\(25\) −0.604367 + 1.86005i −0.120873 + 0.372010i
\(26\) −0.0356523 0.0490712i −0.00699199 0.00962365i
\(27\) 0.153735i 0.0295864i
\(28\) 1.88116 0.611227i 0.355506 0.115511i
\(29\) 1.11576 + 1.53571i 0.207192 + 0.285175i 0.899948 0.435997i \(-0.143604\pi\)
−0.692757 + 0.721171i \(0.743604\pi\)
\(30\) −0.374776 + 0.515835i −0.0684244 + 0.0941781i
\(31\) −0.484807 0.352233i −0.0870738 0.0632628i 0.543397 0.839476i \(-0.317138\pi\)
−0.630470 + 0.776213i \(0.717138\pi\)
\(32\) 1.75495 0.310234
\(33\) 8.98971 + 6.53141i 1.56491 + 1.13697i
\(34\) −0.892516 0.289996i −0.153065 0.0497339i
\(35\) 1.65938 0.539164i 0.280486 0.0911354i
\(36\) −4.90055 + 3.56046i −0.816759 + 0.593410i
\(37\) −4.63436 + 3.36706i −0.761884 + 0.553541i −0.899488 0.436946i \(-0.856060\pi\)
0.137604 + 0.990487i \(0.456060\pi\)
\(38\) 1.23841i 0.200896i
\(39\) −0.310945 0.956992i −0.0497911 0.153241i
\(40\) 1.03013 0.162877
\(41\) 5.47571 3.31912i 0.855163 0.518360i
\(42\) −0.365439 −0.0563884
\(43\) −3.89490 11.9873i −0.593967 1.82804i −0.559804 0.828625i \(-0.689124\pi\)
−0.0341628 0.999416i \(-0.510876\pi\)
\(44\) 8.92657i 1.34573i
\(45\) −4.32278 + 3.14069i −0.644403 + 0.468186i
\(46\) −0.397273 + 0.288636i −0.0585747 + 0.0425570i
\(47\) −9.00883 + 2.92715i −1.31407 + 0.426968i −0.880455 0.474129i \(-0.842763\pi\)
−0.433617 + 0.901097i \(0.642763\pi\)
\(48\) 9.05841 + 2.94326i 1.30747 + 0.424822i
\(49\) 0.809017 + 0.587785i 0.115574 + 0.0839693i
\(50\) −0.290275 −0.0410510
\(51\) −12.5951 9.15085i −1.76366 1.28138i
\(52\) −0.475135 + 0.653967i −0.0658894 + 0.0906889i
\(53\) −0.250762 0.345144i −0.0344448 0.0474092i 0.791447 0.611237i \(-0.209328\pi\)
−0.825892 + 0.563828i \(0.809328\pi\)
\(54\) 0.0217006 0.00705094i 0.00295307 0.000959511i
\(55\) 7.87414i 1.06175i
\(56\) 0.347033 + 0.477650i 0.0463743 + 0.0638287i
\(57\) 6.34861 19.5390i 0.840894 2.58801i
\(58\) −0.165601 + 0.227930i −0.0217444 + 0.0299286i
\(59\) 2.03785 + 6.27186i 0.265306 + 0.816527i 0.991623 + 0.129167i \(0.0412303\pi\)
−0.726317 + 0.687360i \(0.758770\pi\)
\(60\) 8.08144 + 2.62582i 1.04331 + 0.338992i
\(61\) 4.35730 13.4104i 0.557895 1.71702i −0.130278 0.991478i \(-0.541587\pi\)
0.688173 0.725547i \(-0.258413\pi\)
\(62\) 0.0274842 0.0845878i 0.00349050 0.0107427i
\(63\) −2.91255 0.946345i −0.366947 0.119228i
\(64\) −2.31026 7.11025i −0.288783 0.888782i
\(65\) −0.419117 + 0.576865i −0.0519851 + 0.0715513i
\(66\) −0.509637 + 1.56850i −0.0627320 + 0.193069i
\(67\) 2.21422 + 3.04761i 0.270510 + 0.372325i 0.922562 0.385850i \(-0.126092\pi\)
−0.652052 + 0.758174i \(0.726092\pi\)
\(68\) 12.5066i 1.51665i
\(69\) −7.74766 + 2.51737i −0.932708 + 0.303055i
\(70\) 0.152212 + 0.209501i 0.0181928 + 0.0250402i
\(71\) −2.97773 + 4.09850i −0.353392 + 0.486402i −0.948293 0.317397i \(-0.897191\pi\)
0.594901 + 0.803799i \(0.297191\pi\)
\(72\) −1.46277 1.06277i −0.172390 0.125248i
\(73\) 6.69702 0.783827 0.391914 0.920002i \(-0.371813\pi\)
0.391914 + 0.920002i \(0.371813\pi\)
\(74\) −0.687828 0.499737i −0.0799584 0.0580932i
\(75\) −4.57982 1.48807i −0.528832 0.171828i
\(76\) −15.6964 + 5.10006i −1.80050 + 0.585017i
\(77\) 3.65109 2.65267i 0.416080 0.302300i
\(78\) 0.120823 0.0877832i 0.0136805 0.00993949i
\(79\) 7.43419i 0.836411i −0.908352 0.418206i \(-0.862659\pi\)
0.908352 0.418206i \(-0.137341\pi\)
\(80\) −2.08566 6.41899i −0.233183 0.717665i
\(81\) −8.80879 −0.978754
\(82\) 0.719650 + 0.620697i 0.0794721 + 0.0685445i
\(83\) −7.24229 −0.794945 −0.397473 0.917614i \(-0.630113\pi\)
−0.397473 + 0.917614i \(0.630113\pi\)
\(84\) 1.50496 + 4.63180i 0.164205 + 0.505371i
\(85\) 11.0321i 1.19660i
\(86\) 1.51343 1.09957i 0.163197 0.118570i
\(87\) −3.78124 + 2.74723i −0.405391 + 0.294534i
\(88\) 2.53410 0.823378i 0.270136 0.0877724i
\(89\) 13.3884 + 4.35014i 1.41916 + 0.461114i 0.915336 0.402690i \(-0.131925\pi\)
0.503827 + 0.863804i \(0.331925\pi\)
\(90\) −0.641585 0.466139i −0.0676290 0.0491353i
\(91\) −0.408675 −0.0428408
\(92\) 5.29442 + 3.84662i 0.551981 + 0.401038i
\(93\) 0.867268 1.19369i 0.0899315 0.123780i
\(94\) −0.826364 1.13739i −0.0852329 0.117313i
\(95\) −13.8458 + 4.49877i −1.42055 + 0.461564i
\(96\) 4.32104i 0.441014i
\(97\) −4.83995 6.66162i −0.491422 0.676385i 0.489227 0.872156i \(-0.337279\pi\)
−0.980649 + 0.195772i \(0.937279\pi\)
\(98\) −0.0458641 + 0.141155i −0.00463298 + 0.0142588i
\(99\) −8.12364 + 11.1812i −0.816456 + 1.12376i
\(100\) 1.19542 + 3.67913i 0.119542 + 0.367913i
\(101\) 10.0720 + 3.27260i 1.00220 + 0.325636i 0.763746 0.645517i \(-0.223358\pi\)
0.238458 + 0.971153i \(0.423358\pi\)
\(102\) 0.714029 2.19756i 0.0706994 0.217590i
\(103\) 0.355165 1.09309i 0.0349955 0.107705i −0.932033 0.362374i \(-0.881966\pi\)
0.967028 + 0.254669i \(0.0819664\pi\)
\(104\) −0.229476 0.0745612i −0.0225020 0.00731133i
\(105\) 1.32753 + 4.08572i 0.129554 + 0.398725i
\(106\) 0.0372179 0.0512261i 0.00361493 0.00497552i
\(107\) 4.83935 14.8940i 0.467838 1.43986i −0.387540 0.921853i \(-0.626675\pi\)
0.855378 0.518005i \(-0.173325\pi\)
\(108\) −0.178736 0.246009i −0.0171989 0.0236723i
\(109\) 17.4674i 1.67307i 0.547910 + 0.836537i \(0.315424\pi\)
−0.547910 + 0.836537i \(0.684576\pi\)
\(110\) 1.11148 0.361140i 0.105975 0.0344334i
\(111\) −8.29038 11.4107i −0.786888 1.08306i
\(112\) 2.27374 3.12953i 0.214848 0.295713i
\(113\) 0.417663 + 0.303450i 0.0392904 + 0.0285461i 0.607257 0.794505i \(-0.292270\pi\)
−0.567967 + 0.823052i \(0.692270\pi\)
\(114\) 3.04921 0.285584
\(115\) 4.67021 + 3.39311i 0.435500 + 0.316409i
\(116\) 3.57091 + 1.16026i 0.331551 + 0.107727i
\(117\) 1.19029 0.386748i 0.110042 0.0357549i
\(118\) −0.791842 + 0.575307i −0.0728949 + 0.0529613i
\(119\) −5.11537 + 3.71653i −0.468925 + 0.340694i
\(120\) 2.53638i 0.231539i
\(121\) −2.89459 8.90862i −0.263144 0.809875i
\(122\) 2.09279 0.189472
\(123\) 8.17235 + 13.4823i 0.736876 + 1.21566i
\(124\) −1.18531 −0.106444
\(125\) 3.75030 + 11.5422i 0.335437 + 1.03237i
\(126\) 0.454525i 0.0404923i
\(127\) 0.327794 0.238156i 0.0290870 0.0211329i −0.573147 0.819453i \(-0.694278\pi\)
0.602234 + 0.798320i \(0.294278\pi\)
\(128\) 3.73726 2.71528i 0.330330 0.239999i
\(129\) 29.5151 9.59003i 2.59866 0.844355i
\(130\) −0.100650 0.0327032i −0.00882759 0.00286826i
\(131\) 0.978821 + 0.711155i 0.0855200 + 0.0621339i 0.629724 0.776819i \(-0.283168\pi\)
−0.544204 + 0.838953i \(0.683168\pi\)
\(132\) 21.9790 1.91303
\(133\) −6.75041 4.90446i −0.585335 0.425271i
\(134\) −0.328633 + 0.452324i −0.0283895 + 0.0390748i
\(135\) −0.157664 0.217005i −0.0135695 0.0186768i
\(136\) −3.55040 + 1.15360i −0.304445 + 0.0989201i
\(137\) 0.698319i 0.0596614i 0.999555 + 0.0298307i \(0.00949682\pi\)
−0.999555 + 0.0298307i \(0.990503\pi\)
\(138\) −0.710679 0.978166i −0.0604970 0.0832670i
\(139\) −1.32991 + 4.09304i −0.112801 + 0.347167i −0.991482 0.130243i \(-0.958424\pi\)
0.878681 + 0.477410i \(0.158424\pi\)
\(140\) 2.02851 2.79201i 0.171440 0.235968i
\(141\) −7.20722 22.1816i −0.606958 1.86802i
\(142\) −0.715095 0.232349i −0.0600095 0.0194983i
\(143\) −0.569935 + 1.75408i −0.0476603 + 0.146683i
\(144\) −3.66076 + 11.2667i −0.305064 + 0.938889i
\(145\) 3.14991 + 1.02347i 0.261585 + 0.0849943i
\(146\) 0.307153 + 0.945320i 0.0254202 + 0.0782352i
\(147\) −1.44725 + 1.99196i −0.119367 + 0.164294i
\(148\) −3.50134 + 10.7760i −0.287808 + 0.885783i
\(149\) −0.136573 0.187977i −0.0111885 0.0153996i 0.803386 0.595458i \(-0.203030\pi\)
−0.814575 + 0.580059i \(0.803030\pi\)
\(150\) 0.714715i 0.0583562i
\(151\) −5.35187 + 1.73893i −0.435529 + 0.141512i −0.518572 0.855034i \(-0.673536\pi\)
0.0830427 + 0.996546i \(0.473536\pi\)
\(152\) −2.89563 3.98550i −0.234867 0.323267i
\(153\) 11.3816 15.6655i 0.920152 1.26648i
\(154\) 0.541892 + 0.393708i 0.0436669 + 0.0317259i
\(155\) −1.04556 −0.0839815
\(156\) −1.61020 1.16988i −0.128919 0.0936652i
\(157\) −10.6532 3.46145i −0.850221 0.276253i −0.148682 0.988885i \(-0.547503\pi\)
−0.701538 + 0.712632i \(0.747503\pi\)
\(158\) 1.04937 0.340962i 0.0834837 0.0271255i
\(159\) 0.849815 0.617427i 0.0673947 0.0489651i
\(160\) 2.47720 1.79979i 0.195840 0.142286i
\(161\) 3.30857i 0.260752i
\(162\) −0.404007 1.24341i −0.0317418 0.0976912i
\(163\) 3.36654 0.263688 0.131844 0.991270i \(-0.457910\pi\)
0.131844 + 0.991270i \(0.457910\pi\)
\(164\) 4.90342 11.6775i 0.382893 0.911859i
\(165\) 19.3877 1.50933
\(166\) −0.332161 1.02229i −0.0257807 0.0793449i
\(167\) 6.40260i 0.495448i −0.968831 0.247724i \(-0.920317\pi\)
0.968831 0.247724i \(-0.0796826\pi\)
\(168\) −1.17607 + 0.854466i −0.0907359 + 0.0659235i
\(169\) −10.3821 + 7.54304i −0.798623 + 0.580234i
\(170\) −1.55724 + 0.505977i −0.119435 + 0.0388067i
\(171\) 24.3022 + 7.89628i 1.85844 + 0.603843i
\(172\) −20.1693 14.6539i −1.53790 1.11735i
\(173\) 10.5470 0.801873 0.400937 0.916106i \(-0.368685\pi\)
0.400937 + 0.916106i \(0.368685\pi\)
\(174\) −0.561209 0.407742i −0.0425451 0.0309109i
\(175\) −1.14957 + 1.58225i −0.0868996 + 0.119607i
\(176\) −10.2614 14.1236i −0.773479 1.06460i
\(177\) −15.4426 + 5.01760i −1.16074 + 0.377146i
\(178\) 2.08935i 0.156604i
\(179\) 0.471877 + 0.649482i 0.0352697 + 0.0485446i 0.826288 0.563248i \(-0.190449\pi\)
−0.791018 + 0.611793i \(0.790449\pi\)
\(180\) −3.26594 + 10.0515i −0.243429 + 0.749197i
\(181\) 3.36751 4.63498i 0.250305 0.344515i −0.665313 0.746565i \(-0.731702\pi\)
0.915618 + 0.402049i \(0.131702\pi\)
\(182\) −0.0187435 0.0576866i −0.00138936 0.00427602i
\(183\) 33.0191 + 10.7286i 2.44084 + 0.793077i
\(184\) −0.603636 + 1.85780i −0.0445006 + 0.136959i
\(185\) −3.08854 + 9.50554i −0.227074 + 0.698861i
\(186\) 0.208272 + 0.0676718i 0.0152713 + 0.00496193i
\(187\) 8.81791 + 27.1388i 0.644830 + 1.98458i
\(188\) −11.0129 + 15.1579i −0.803197 + 1.10551i
\(189\) 0.0475069 0.146211i 0.00345562 0.0106353i
\(190\) −1.27005 1.74807i −0.0921391 0.126819i
\(191\) 16.7463i 1.21172i 0.795571 + 0.605860i \(0.207171\pi\)
−0.795571 + 0.605860i \(0.792829\pi\)
\(192\) 17.5069 5.68833i 1.26345 0.410520i
\(193\) 10.3421 + 14.2347i 0.744441 + 1.02463i 0.998351 + 0.0574069i \(0.0182832\pi\)
−0.253910 + 0.967228i \(0.581717\pi\)
\(194\) 0.718342 0.988713i 0.0515739 0.0709854i
\(195\) −1.42036 1.03195i −0.101714 0.0738995i
\(196\) 1.97797 0.141284
\(197\) 9.45257 + 6.86770i 0.673468 + 0.489303i 0.871184 0.490956i \(-0.163353\pi\)
−0.197716 + 0.980259i \(0.563353\pi\)
\(198\) −1.95087 0.633877i −0.138642 0.0450477i
\(199\) −5.12674 + 1.66578i −0.363425 + 0.118084i −0.485037 0.874494i \(-0.661194\pi\)
0.121612 + 0.992578i \(0.461194\pi\)
\(200\) −0.934175 + 0.678718i −0.0660562 + 0.0479926i
\(201\) −7.50383 + 5.45185i −0.529279 + 0.384544i
\(202\) 1.57181i 0.110593i
\(203\) 0.586591 + 1.80534i 0.0411706 + 0.126710i
\(204\) −30.7938 −2.15600
\(205\) 4.32531 10.3007i 0.302093 0.719434i
\(206\) 0.170584 0.0118852
\(207\) −3.13105 9.63638i −0.217623 0.669775i
\(208\) 1.58088i 0.109615i
\(209\) −30.4646 + 22.1338i −2.10728 + 1.53103i
\(210\) −0.515835 + 0.374776i −0.0355960 + 0.0258620i
\(211\) 12.9454 4.20622i 0.891198 0.289568i 0.172599 0.984992i \(-0.444784\pi\)
0.718599 + 0.695424i \(0.244784\pi\)
\(212\) −0.802545 0.260763i −0.0551190 0.0179093i
\(213\) −10.0913 7.33178i −0.691446 0.502365i
\(214\) 2.32432 0.158887
\(215\) −17.7914 12.9262i −1.21336 0.881560i
\(216\) 0.0533513 0.0734318i 0.00363010 0.00499640i
\(217\) −0.352233 0.484807i −0.0239111 0.0329108i
\(218\) −2.46562 + 0.801128i −0.166993 + 0.0542592i
\(219\) 16.4894i 1.11425i
\(220\) −9.15465 12.6003i −0.617206 0.849512i
\(221\) 0.798509 2.45756i 0.0537135 0.165313i
\(222\) 1.23045 1.69357i 0.0825826 0.113665i
\(223\) −3.71895 11.4458i −0.249039 0.766465i −0.994946 0.100414i \(-0.967983\pi\)
0.745906 0.666051i \(-0.232017\pi\)
\(224\) 1.66906 + 0.542309i 0.111518 + 0.0362346i
\(225\) 1.85084 5.69629i 0.123389 0.379753i
\(226\) −0.0236778 + 0.0728727i −0.00157502 + 0.00484742i
\(227\) 9.15723 + 2.97536i 0.607787 + 0.197482i 0.596710 0.802457i \(-0.296474\pi\)
0.0110765 + 0.999939i \(0.496474\pi\)
\(228\) −12.5574 38.6476i −0.831632 2.55950i
\(229\) −1.49052 + 2.05152i −0.0984962 + 0.135568i −0.855420 0.517934i \(-0.826701\pi\)
0.756924 + 0.653503i \(0.226701\pi\)
\(230\) −0.264760 + 0.814847i −0.0174577 + 0.0537294i
\(231\) 6.53141 + 8.98971i 0.429735 + 0.591480i
\(232\) 1.12074i 0.0735802i
\(233\) 5.84545 1.89930i 0.382948 0.124427i −0.111216 0.993796i \(-0.535474\pi\)
0.494163 + 0.869369i \(0.335474\pi\)
\(234\) 0.109183 + 0.150277i 0.00713751 + 0.00982394i
\(235\) −9.71447 + 13.3708i −0.633702 + 0.872216i
\(236\) 10.5528 + 7.66706i 0.686929 + 0.499083i
\(237\) 18.3045 1.18900
\(238\) −0.759220 0.551605i −0.0492129 0.0357553i
\(239\) −13.3331 4.33218i −0.862446 0.280226i −0.155796 0.987789i \(-0.549794\pi\)
−0.706650 + 0.707564i \(0.749794\pi\)
\(240\) 15.8049 5.13531i 1.02020 0.331483i
\(241\) −15.2284 + 11.0641i −0.980949 + 0.712701i −0.957921 0.287034i \(-0.907331\pi\)
−0.0230285 + 0.999735i \(0.507331\pi\)
\(242\) 1.12474 0.817172i 0.0723011 0.0525298i
\(243\) 22.1502i 1.42094i
\(244\) −8.61862 26.5254i −0.551750 1.69811i
\(245\) 1.74477 0.111469
\(246\) −1.52828 + 1.77192i −0.0974396 + 0.112974i
\(247\) 3.40997 0.216971
\(248\) −0.109332 0.336488i −0.00694256 0.0213670i
\(249\) 17.8320i 1.13006i
\(250\) −1.45724 + 1.05875i −0.0921642 + 0.0669612i
\(251\) 1.40162 1.01834i 0.0884695 0.0642769i −0.542671 0.839945i \(-0.682587\pi\)
0.631141 + 0.775668i \(0.282587\pi\)
\(252\) −5.76094 + 1.87184i −0.362905 + 0.117915i
\(253\) 14.2007 + 4.61410i 0.892793 + 0.290086i
\(254\) 0.0486510 + 0.0353470i 0.00305263 + 0.00221787i
\(255\) −27.1632 −1.70103
\(256\) −11.5420 8.38576i −0.721375 0.524110i
\(257\) −3.09778 + 4.26373i −0.193234 + 0.265964i −0.894630 0.446808i \(-0.852561\pi\)
0.701396 + 0.712772i \(0.252561\pi\)
\(258\) 2.70737 + 3.72637i 0.168553 + 0.231994i
\(259\) −5.44801 + 1.77017i −0.338523 + 0.109993i
\(260\) 1.41038i 0.0874682i
\(261\) −3.41695 4.70303i −0.211504 0.291110i
\(262\) −0.0554905 + 0.170782i −0.00342821 + 0.0105510i
\(263\) 9.38596 12.9187i 0.578763 0.796599i −0.414796 0.909914i \(-0.636147\pi\)
0.993559 + 0.113315i \(0.0361470\pi\)
\(264\) 2.02732 + 6.23946i 0.124773 + 0.384012i
\(265\) −0.707926 0.230019i −0.0434876 0.0141300i
\(266\) 0.382689 1.17779i 0.0234642 0.0722152i
\(267\) −10.7109 + 32.9649i −0.655498 + 2.01742i
\(268\) 7.08644 + 2.30252i 0.432873 + 0.140649i
\(269\) −7.66906 23.6030i −0.467591 1.43910i −0.855694 0.517481i \(-0.826870\pi\)
0.388103 0.921616i \(-0.373130\pi\)
\(270\) 0.0234003 0.0322078i 0.00142410 0.00196010i
\(271\) 9.71436 29.8977i 0.590105 1.81616i 0.0123832 0.999923i \(-0.496058\pi\)
0.577722 0.816234i \(-0.303942\pi\)
\(272\) 14.3767 + 19.7879i 0.871716 + 1.19981i
\(273\) 1.00624i 0.0609005i
\(274\) −0.0985714 + 0.0320278i −0.00595492 + 0.00193487i
\(275\) 5.18802 + 7.14069i 0.312849 + 0.430600i
\(276\) −9.47115 + 13.0359i −0.570096 + 0.784670i
\(277\) 1.96843 + 1.43015i 0.118272 + 0.0859293i 0.645349 0.763888i \(-0.276712\pi\)
−0.527077 + 0.849817i \(0.676712\pi\)
\(278\) −0.638749 −0.0383096
\(279\) 1.48469 + 1.07869i 0.0888861 + 0.0645795i
\(280\) 0.979709 + 0.318327i 0.0585488 + 0.0190237i
\(281\) 18.0626 5.86889i 1.07752 0.350109i 0.284110 0.958792i \(-0.408302\pi\)
0.793414 + 0.608683i \(0.208302\pi\)
\(282\) 2.80049 2.03467i 0.166767 0.121163i
\(283\) 9.41737 6.84212i 0.559805 0.406722i −0.271583 0.962415i \(-0.587547\pi\)
0.831387 + 0.555693i \(0.187547\pi\)
\(284\) 10.0204i 0.594604i
\(285\) −11.0769 34.0911i −0.656137 2.01938i
\(286\) −0.273737 −0.0161864
\(287\) 6.23338 1.46458i 0.367945 0.0864517i
\(288\) −5.37442 −0.316691
\(289\) −7.10108 21.8549i −0.417711 1.28558i
\(290\) 0.491566i 0.0288658i
\(291\) 16.4022 11.9169i 0.961516 0.698583i
\(292\) 10.7167 7.78611i 0.627145 0.455648i
\(293\) −26.2187 + 8.51898i −1.53171 + 0.497684i −0.949076 0.315048i \(-0.897980\pi\)
−0.582638 + 0.812732i \(0.697980\pi\)
\(294\) −0.347553 0.112927i −0.0202697 0.00658602i
\(295\) 9.30864 + 6.76312i 0.541970 + 0.393764i
\(296\) −3.38208 −0.196580
\(297\) −0.561301 0.407809i −0.0325700 0.0236635i
\(298\) 0.0202701 0.0278994i 0.00117421 0.00161617i
\(299\) −0.794762 1.09390i −0.0459623 0.0632617i
\(300\) −9.05875 + 2.94337i −0.523007 + 0.169935i
\(301\) 12.6042i 0.726492i
\(302\) −0.490918 0.675691i −0.0282492 0.0388816i
\(303\) −8.05781 + 24.7994i −0.462909 + 1.42469i
\(304\) −18.9720 + 26.1127i −1.08812 + 1.49767i
\(305\) −7.60249 23.3981i −0.435317 1.33977i
\(306\) 2.73328 + 0.888095i 0.156251 + 0.0507690i
\(307\) 0.954824 2.93865i 0.0544947 0.167717i −0.920105 0.391672i \(-0.871897\pi\)
0.974600 + 0.223955i \(0.0718968\pi\)
\(308\) 2.75846 8.48967i 0.157178 0.483744i
\(309\) 2.69140 + 0.874488i 0.153108 + 0.0497479i
\(310\) −0.0479537 0.147586i −0.00272359 0.00838234i
\(311\) −2.90953 + 4.00463i −0.164985 + 0.227082i −0.883502 0.468427i \(-0.844821\pi\)
0.718518 + 0.695509i \(0.244821\pi\)
\(312\) 0.183585 0.565016i 0.0103934 0.0319877i
\(313\) −2.48882 3.42557i −0.140676 0.193624i 0.732865 0.680374i \(-0.238183\pi\)
−0.873542 + 0.486749i \(0.838183\pi\)
\(314\) 1.66252i 0.0938212i
\(315\) −5.08174 + 1.65116i −0.286323 + 0.0930321i
\(316\) −8.64315 11.8963i −0.486215 0.669218i
\(317\) 15.7177 21.6336i 0.882796 1.21506i −0.0928426 0.995681i \(-0.529595\pi\)
0.975639 0.219384i \(-0.0704047\pi\)
\(318\) 0.126129 + 0.0916381i 0.00707296 + 0.00513881i
\(319\) 8.56677 0.479647
\(320\) −10.5530 7.66719i −0.589929 0.428609i
\(321\) 36.6720 + 11.9155i 2.04683 + 0.665057i
\(322\) −0.467022 + 0.151745i −0.0260261 + 0.00845640i
\(323\) 42.6825 31.0106i 2.37492 1.72548i
\(324\) −14.0959 + 10.2413i −0.783107 + 0.568961i
\(325\) 0.799276i 0.0443358i
\(326\) 0.154403 + 0.475205i 0.00855162 + 0.0263192i
\(327\) −43.0083 −2.37836
\(328\) 3.76732 + 0.314875i 0.208015 + 0.0173861i
\(329\) −9.47244 −0.522233
\(330\) 0.889200 + 2.73668i 0.0489489 + 0.150649i
\(331\) 33.2092i 1.82534i 0.408696 + 0.912671i \(0.365984\pi\)
−0.408696 + 0.912671i \(0.634016\pi\)
\(332\) −11.5892 + 8.42006i −0.636041 + 0.462111i
\(333\) 14.1924 10.3114i 0.777741 0.565062i
\(334\) 0.903760 0.293649i 0.0494515 0.0160678i
\(335\) 6.25095 + 2.03106i 0.341526 + 0.110969i
\(336\) 7.70554 + 5.59840i 0.420372 + 0.305418i
\(337\) −23.9198 −1.30299 −0.651496 0.758652i \(-0.725858\pi\)
−0.651496 + 0.758652i \(0.725858\pi\)
\(338\) −1.54091 1.11953i −0.0838142 0.0608946i
\(339\) −0.747154 + 1.02837i −0.0405798 + 0.0558534i
\(340\) 12.8262 + 17.6537i 0.695596 + 0.957406i
\(341\) −2.57206 + 0.835714i −0.139285 + 0.0452564i
\(342\) 3.79254i 0.205077i
\(343\) 0.587785 + 0.809017i 0.0317374 + 0.0436828i
\(344\) 2.29958 7.07738i 0.123985 0.381587i
\(345\) −8.35452 + 11.4990i −0.449792 + 0.619086i
\(346\) 0.483729 + 1.48876i 0.0260054 + 0.0800364i
\(347\) −28.4743 9.25186i −1.52858 0.496666i −0.580381 0.814345i \(-0.697097\pi\)
−0.948198 + 0.317679i \(0.897097\pi\)
\(348\) −2.85679 + 8.79230i −0.153140 + 0.471317i
\(349\) −5.30629 + 16.3311i −0.284039 + 0.874183i 0.702646 + 0.711540i \(0.252002\pi\)
−0.986685 + 0.162643i \(0.947998\pi\)
\(350\) −0.276068 0.0896998i −0.0147564 0.00479465i
\(351\) 0.0194149 + 0.0597528i 0.00103629 + 0.00318937i
\(352\) 4.65530 6.40747i 0.248128 0.341519i
\(353\) −6.90952 + 21.2653i −0.367757 + 1.13184i 0.580480 + 0.814275i \(0.302865\pi\)
−0.948237 + 0.317564i \(0.897135\pi\)
\(354\) −1.41652 1.94967i −0.0752872 0.103624i
\(355\) 8.83905i 0.469128i
\(356\) 26.4818 8.60446i 1.40353 0.456035i
\(357\) −9.15085 12.5951i −0.484314 0.666602i
\(358\) −0.0700356 + 0.0963958i −0.00370150 + 0.00509467i
\(359\) −22.6526 16.4581i −1.19556 0.868623i −0.201717 0.979444i \(-0.564652\pi\)
−0.993840 + 0.110821i \(0.964652\pi\)
\(360\) −3.15470 −0.166267
\(361\) 40.9539 + 29.7548i 2.15547 + 1.56604i
\(362\) 0.808700 + 0.262762i 0.0425043 + 0.0138105i
\(363\) 21.9348 7.12706i 1.15128 0.374074i
\(364\) −0.653967 + 0.475135i −0.0342772 + 0.0249038i
\(365\) 9.45318 6.86814i 0.494802 0.359495i
\(366\) 5.15287i 0.269345i
\(367\) −3.22819 9.93535i −0.168510 0.518621i 0.830768 0.556619i \(-0.187902\pi\)
−0.999278 + 0.0379984i \(0.987902\pi\)
\(368\) 12.7986 0.667173
\(369\) −16.7690 + 10.1646i −0.872961 + 0.529148i
\(370\) −1.48341 −0.0771188
\(371\) −0.131833 0.405741i −0.00684445 0.0210650i
\(372\) 2.91847i 0.151315i
\(373\) −0.953000 + 0.692395i −0.0493445 + 0.0358509i −0.612184 0.790715i \(-0.709709\pi\)
0.562840 + 0.826566i \(0.309709\pi\)
\(374\) −3.42635 + 2.48939i −0.177172 + 0.128723i
\(375\) −28.4193 + 9.23400i −1.46757 + 0.476842i
\(376\) −5.31889 1.72821i −0.274301 0.0891257i
\(377\) −0.627608 0.455984i −0.0323235 0.0234844i
\(378\) 0.0228173 0.00117360
\(379\) 16.6597 + 12.1040i 0.855754 + 0.621742i 0.926726 0.375737i \(-0.122610\pi\)
−0.0709727 + 0.997478i \(0.522610\pi\)
\(380\) −16.9258 + 23.2964i −0.868277 + 1.19508i
\(381\) 0.586388 + 0.807095i 0.0300416 + 0.0413487i
\(382\) −2.36383 + 0.768055i −0.120944 + 0.0392971i
\(383\) 23.2667i 1.18887i 0.804143 + 0.594436i \(0.202625\pi\)
−0.804143 + 0.594436i \(0.797375\pi\)
\(384\) 6.68556 + 9.20189i 0.341171 + 0.469582i
\(385\) 2.43324 7.48875i 0.124009 0.381662i
\(386\) −1.53497 + 2.11270i −0.0781278 + 0.107534i
\(387\) 11.9279 + 36.7103i 0.606329 + 1.86609i
\(388\) −15.4899 5.03297i −0.786380 0.255510i
\(389\) 2.94063 9.05033i 0.149096 0.458870i −0.848419 0.529325i \(-0.822445\pi\)
0.997515 + 0.0704553i \(0.0224452\pi\)
\(390\) 0.0805218 0.247821i 0.00407738 0.0125489i
\(391\) −19.8960 6.46460i −1.00618 0.326929i
\(392\) 0.182446 + 0.561512i 0.00921492 + 0.0283606i
\(393\) −1.75101 + 2.41006i −0.0883266 + 0.121571i
\(394\) −0.535877 + 1.64926i −0.0269971 + 0.0830886i
\(395\) −7.62414 10.4937i −0.383612 0.527996i
\(396\) 27.3371i 1.37374i
\(397\) 21.5764 7.01059i 1.08289 0.351851i 0.287393 0.957813i \(-0.407212\pi\)
0.795494 + 0.605962i \(0.207212\pi\)
\(398\) −0.470267 0.647266i −0.0235723 0.0324445i
\(399\) 12.0758 16.6209i 0.604545 0.832085i
\(400\) 6.12065 + 4.44692i 0.306033 + 0.222346i
\(401\) 16.7973 0.838815 0.419407 0.907798i \(-0.362238\pi\)
0.419407 + 0.907798i \(0.362238\pi\)
\(402\) −1.11371 0.809160i −0.0555470 0.0403572i
\(403\) 0.232914 + 0.0756783i 0.0116023 + 0.00376980i
\(404\) 19.9222 6.47311i 0.991166 0.322049i
\(405\) −12.4340 + 9.03386i −0.617852 + 0.448896i
\(406\) −0.227930 + 0.165601i −0.0113120 + 0.00821862i
\(407\) 25.8521i 1.28144i
\(408\) −2.84039 8.74181i −0.140620 0.432784i
\(409\) 31.7140 1.56815 0.784077 0.620663i \(-0.213137\pi\)
0.784077 + 0.620663i \(0.213137\pi\)
\(410\) 1.65238 + 0.138107i 0.0816051 + 0.00682061i
\(411\) −1.71940 −0.0848119
\(412\) −0.702506 2.16209i −0.0346100 0.106519i
\(413\) 6.59462i 0.324500i
\(414\) 1.21662 0.883928i 0.0597938 0.0434427i
\(415\) −10.2229 + 7.42734i −0.501820 + 0.364594i
\(416\) −0.682102 + 0.221628i −0.0334428 + 0.0108662i
\(417\) −10.0779 3.27450i −0.493516 0.160353i
\(418\) −4.52153 3.28508i −0.221155 0.160679i
\(419\) −4.25477 −0.207859 −0.103930 0.994585i \(-0.533142\pi\)
−0.103930 + 0.994585i \(0.533142\pi\)
\(420\) 6.87448 + 4.99460i 0.335440 + 0.243712i
\(421\) 10.6519 14.6611i 0.519144 0.714540i −0.466284 0.884635i \(-0.654407\pi\)
0.985428 + 0.170095i \(0.0544074\pi\)
\(422\) 1.18746 + 1.63440i 0.0578046 + 0.0795612i
\(423\) 27.5890 8.96420i 1.34142 0.435854i
\(424\) 0.251881i 0.0122324i
\(425\) −7.26869 10.0045i −0.352583 0.485289i
\(426\) 0.572089 1.76071i 0.0277178 0.0853066i
\(427\) 8.28808 11.4076i 0.401088 0.552050i
\(428\) −9.57211 29.4599i −0.462685 1.42400i
\(429\) −4.31889 1.40329i −0.208518 0.0677517i
\(430\) 1.00862 3.10420i 0.0486397 0.149698i
\(431\) −2.85803 + 8.79612i −0.137667 + 0.423694i −0.995995 0.0894060i \(-0.971503\pi\)
0.858329 + 0.513100i \(0.171503\pi\)
\(432\) −0.565591 0.183772i −0.0272120 0.00884171i
\(433\) −0.870429 2.67890i −0.0418301 0.128740i 0.927961 0.372678i \(-0.121561\pi\)
−0.969791 + 0.243938i \(0.921561\pi\)
\(434\) 0.0522781 0.0719547i 0.00250943 0.00345394i
\(435\) −2.51998 + 7.75570i −0.120824 + 0.371858i
\(436\) 20.3080 + 27.9516i 0.972577 + 1.33864i
\(437\) 27.6066i 1.32060i
\(438\) −2.32757 + 0.756273i −0.111216 + 0.0361361i
\(439\) 12.4389 + 17.1206i 0.593674 + 0.817122i 0.995111 0.0987644i \(-0.0314890\pi\)
−0.401437 + 0.915887i \(0.631489\pi\)
\(440\) 2.73259 3.76108i 0.130271 0.179303i
\(441\) −2.47756 1.80006i −0.117979 0.0857170i
\(442\) 0.383520 0.0182422
\(443\) 29.0303 + 21.0917i 1.37927 + 1.00210i 0.996948 + 0.0780683i \(0.0248752\pi\)
0.382321 + 0.924029i \(0.375125\pi\)
\(444\) −26.5327 8.62101i −1.25919 0.409135i
\(445\) 23.3596 7.59000i 1.10735 0.359801i
\(446\) 1.44506 1.04990i 0.0684257 0.0497142i
\(447\) 0.462836 0.336270i 0.0218914 0.0159050i
\(448\) 7.47616i 0.353215i
\(449\) 11.1919 + 34.4450i 0.528177 + 1.62556i 0.757947 + 0.652317i \(0.226203\pi\)
−0.229770 + 0.973245i \(0.573797\pi\)
\(450\) 0.888948 0.0419054
\(451\) 2.40686 28.7968i 0.113334 1.35599i
\(452\) 1.02115 0.0480307
\(453\) −4.28160 13.1774i −0.201167 0.619128i
\(454\) 1.42905i 0.0670688i
\(455\) −0.576865 + 0.419117i −0.0270439 + 0.0196485i
\(456\) 9.81310 7.12964i 0.459541 0.333876i
\(457\) 19.8413 6.44683i 0.928137 0.301570i 0.194336 0.980935i \(-0.437745\pi\)
0.733800 + 0.679365i \(0.237745\pi\)
\(458\) −0.357944 0.116303i −0.0167256 0.00543449i
\(459\) 0.786413 + 0.571363i 0.0367066 + 0.0266689i
\(460\) 11.4182 0.532378
\(461\) 25.3406 + 18.4110i 1.18023 + 0.857486i 0.992197 0.124677i \(-0.0397893\pi\)
0.188031 + 0.982163i \(0.439789\pi\)
\(462\) −0.969387 + 1.33425i −0.0451000 + 0.0620748i
\(463\) −13.8032 18.9985i −0.641491 0.882936i 0.357204 0.934027i \(-0.383730\pi\)
−0.998694 + 0.0510906i \(0.983730\pi\)
\(464\) 6.98362 2.26912i 0.324207 0.105341i
\(465\) 2.57438i 0.119384i
\(466\) 0.536192 + 0.738005i 0.0248386 + 0.0341874i
\(467\) −5.06354 + 15.5840i −0.234313 + 0.721140i 0.762899 + 0.646517i \(0.223775\pi\)
−0.997212 + 0.0746226i \(0.976225\pi\)
\(468\) 1.45507 2.00273i 0.0672607 0.0925764i
\(469\) 1.16408 + 3.58268i 0.0537523 + 0.165433i
\(470\) −2.33291 0.758008i −0.107609 0.0349643i
\(471\) 8.52278 26.2304i 0.392709 1.20863i
\(472\) −1.20316 + 3.70296i −0.0553801 + 0.170442i
\(473\) −54.0984 17.5776i −2.48745 0.808221i
\(474\) 0.839518 + 2.58377i 0.0385603 + 0.118677i
\(475\) 9.59201 13.2023i 0.440112 0.605762i
\(476\) −3.86475 + 11.8945i −0.177141 + 0.545183i
\(477\) 0.767943 + 1.05698i 0.0351617 + 0.0483959i
\(478\) 2.08073i 0.0951702i
\(479\) −29.7738 + 9.67409i −1.36040 + 0.442020i −0.896176 0.443698i \(-0.853666\pi\)
−0.464223 + 0.885718i \(0.653666\pi\)
\(480\) 4.43145 + 6.09936i 0.202267 + 0.278397i
\(481\) 1.37603 1.89395i 0.0627417 0.0863565i
\(482\) −2.26019 1.64213i −0.102949 0.0747968i
\(483\) −8.14637 −0.370673
\(484\) −14.9893 10.8904i −0.681333 0.495017i
\(485\) −13.6637 4.43959i −0.620434 0.201591i
\(486\) 3.12662 1.01590i 0.141826 0.0460822i
\(487\) −26.0489 + 18.9256i −1.18039 + 0.857602i −0.992215 0.124534i \(-0.960256\pi\)
−0.188172 + 0.982136i \(0.560256\pi\)
\(488\) 6.73512 4.89335i 0.304884 0.221511i
\(489\) 8.28910i 0.374846i
\(490\) 0.0800224 + 0.246284i 0.00361504 + 0.0111260i
\(491\) −7.75796 −0.350112 −0.175056 0.984558i \(-0.556011\pi\)
−0.175056 + 0.984558i \(0.556011\pi\)
\(492\) 28.7523 + 12.0732i 1.29626 + 0.544302i
\(493\) −12.0025 −0.540566
\(494\) 0.156395 + 0.481336i 0.00703656 + 0.0216563i
\(495\) 24.1141i 1.08385i
\(496\) −1.87538 + 1.36255i −0.0842072 + 0.0611801i
\(497\) −4.09850 + 2.97773i −0.183843 + 0.133570i
\(498\) 2.51708 0.817849i 0.112793 0.0366487i
\(499\) 21.5054 + 6.98754i 0.962716 + 0.312805i 0.747872 0.663843i \(-0.231076\pi\)
0.214844 + 0.976648i \(0.431076\pi\)
\(500\) 19.4206 + 14.1099i 0.868514 + 0.631012i
\(501\) 15.7645 0.704305
\(502\) 0.208028 + 0.151141i 0.00928473 + 0.00674575i
\(503\) 6.94214 9.55504i 0.309535 0.426038i −0.625701 0.780063i \(-0.715187\pi\)
0.935236 + 0.354025i \(0.115187\pi\)
\(504\) −1.06277 1.46277i −0.0473394 0.0651571i
\(505\) 17.5734 5.70994i 0.782006 0.254089i
\(506\) 2.21613i 0.0985191i
\(507\) −18.5725 25.5628i −0.824833 1.13529i
\(508\) 0.247654 0.762201i 0.0109879 0.0338172i
\(509\) 1.89379 2.60658i 0.0839408 0.115535i −0.764982 0.644052i \(-0.777252\pi\)
0.848922 + 0.528518i \(0.177252\pi\)
\(510\) −1.24582 3.83423i −0.0551657 0.169783i
\(511\) 6.36925 + 2.06949i 0.281759 + 0.0915490i
\(512\) 3.50934 10.8006i 0.155092 0.477325i
\(513\) −0.396396 + 1.21998i −0.0175013 + 0.0538635i
\(514\) −0.743925 0.241716i −0.0328131 0.0106616i
\(515\) −0.619682 1.90718i −0.0273064 0.0840406i
\(516\) 36.0808 49.6610i 1.58837 2.18620i
\(517\) −13.2102 + 40.6568i −0.580983 + 1.78808i
\(518\) −0.499737 0.687828i −0.0219572 0.0302214i
\(519\) 25.9688i 1.13991i
\(520\) −0.400383 + 0.130092i −0.0175579 + 0.00570492i
\(521\) 1.92886 + 2.65485i 0.0845049 + 0.116311i 0.849177 0.528109i \(-0.177099\pi\)
−0.764672 + 0.644420i \(0.777099\pi\)
\(522\) 0.507142 0.698021i 0.0221970 0.0305515i
\(523\) −22.4531 16.3131i −0.981805 0.713323i −0.0236939 0.999719i \(-0.507543\pi\)
−0.958111 + 0.286396i \(0.907543\pi\)
\(524\) 2.39313 0.104544
\(525\) −3.89583 2.83048i −0.170028 0.123532i
\(526\) 2.25402 + 0.732374i 0.0982798 + 0.0319330i
\(527\) 3.60360 1.17088i 0.156975 0.0510043i
\(528\) 34.7750 25.2655i 1.51339 1.09954i
\(529\) 9.75137 7.08479i 0.423973 0.308034i
\(530\) 0.110477i 0.00479882i
\(531\) −6.24079 19.2072i −0.270827 0.833521i
\(532\) −16.5041 −0.715545
\(533\) −1.70910 + 1.98157i −0.0740293 + 0.0858312i
\(534\) −5.14441 −0.222620
\(535\) −8.44357 25.9866i −0.365047 1.12350i
\(536\) 2.22410i 0.0960664i
\(537\) −1.59916 + 1.16186i −0.0690087 + 0.0501378i
\(538\) 2.97995 2.16506i 0.128475 0.0933422i
\(539\) 4.29211 1.39459i 0.184874 0.0600693i
\(540\) −0.504590 0.163951i −0.0217141 0.00705534i
\(541\) 22.0942 + 16.0524i 0.949905 + 0.690146i 0.950784 0.309853i \(-0.100280\pi\)
−0.000879402 1.00000i \(0.500280\pi\)
\(542\) 4.66576 0.200412
\(543\) 11.4123 + 8.29149i 0.489747 + 0.355822i
\(544\) −6.52232 + 8.97721i −0.279642 + 0.384895i
\(545\) 17.9137 + 24.6561i 0.767340 + 1.05615i
\(546\) 0.142036 0.0461503i 0.00607859 0.00197505i
\(547\) 15.7693i 0.674248i 0.941460 + 0.337124i \(0.109454\pi\)
−0.941460 + 0.337124i \(0.890546\pi\)
\(548\) 0.811882 + 1.11746i 0.0346819 + 0.0477355i
\(549\) −13.3440 + 41.0685i −0.569506 + 1.75276i
\(550\) −0.770002 + 1.05982i −0.0328330 + 0.0451908i
\(551\) −4.89449 15.0637i −0.208512 0.641735i
\(552\) −4.57428 1.48627i −0.194694 0.0632600i
\(553\) 2.29729 7.07033i 0.0976907 0.300661i
\(554\) −0.111593 + 0.343447i −0.00474112 + 0.0145917i
\(555\) −23.4046 7.60460i −0.993468 0.322797i
\(556\) 2.63052 + 8.09592i 0.111559 + 0.343343i
\(557\) 6.97882 9.60553i 0.295702 0.406999i −0.635154 0.772386i \(-0.719063\pi\)
0.930856 + 0.365387i \(0.119063\pi\)
\(558\) −0.0841688 + 0.259045i −0.00356315 + 0.0109662i
\(559\) 3.02769 + 4.16725i 0.128057 + 0.176256i
\(560\) 6.74933i 0.285211i
\(561\) −66.8211 + 21.7115i −2.82119 + 0.916660i
\(562\) 1.65685 + 2.28046i 0.0698900 + 0.0961953i
\(563\) 18.8782 25.9836i 0.795620 1.09508i −0.197766 0.980249i \(-0.563369\pi\)
0.993385 0.114827i \(-0.0366314\pi\)
\(564\) −37.3219 27.1159i −1.57153 1.14179i
\(565\) 0.900755 0.0378950
\(566\) 1.39772 + 1.01550i 0.0587506 + 0.0426848i
\(567\) −8.37765 2.72206i −0.351828 0.114316i
\(568\) −2.84463 + 0.924276i −0.119358 + 0.0387818i
\(569\) −29.7357 + 21.6043i −1.24659 + 0.905698i −0.998019 0.0629162i \(-0.979960\pi\)
−0.248568 + 0.968614i \(0.579960\pi\)
\(570\) 4.30411 3.12712i 0.180279 0.130981i
\(571\) 9.03659i 0.378170i 0.981961 + 0.189085i \(0.0605521\pi\)
−0.981961 + 0.189085i \(0.939448\pi\)
\(572\) 1.12731 + 3.46952i 0.0471354 + 0.145068i
\(573\) −41.2328 −1.72252
\(574\) 0.492622 + 0.812702i 0.0205616 + 0.0339215i
\(575\) −6.47081 −0.269852
\(576\) 7.07503 + 21.7747i 0.294793 + 0.907280i
\(577\) 10.2230i 0.425588i 0.977097 + 0.212794i \(0.0682564\pi\)
−0.977097 + 0.212794i \(0.931744\pi\)
\(578\) 2.75925 2.00471i 0.114770 0.0833849i
\(579\) −35.0487 + 25.4643i −1.45657 + 1.05826i
\(580\) 6.23042 2.02439i 0.258704 0.0840581i
\(581\) −6.88783 2.23799i −0.285755 0.0928476i
\(582\) 2.43441 + 1.76870i 0.100910 + 0.0733151i
\(583\) −1.92534 −0.0797394
\(584\) 3.19883 + 2.32409i 0.132369 + 0.0961715i
\(585\) 1.28352 1.76661i 0.0530670 0.0730405i
\(586\) −2.40500 3.31019i −0.0993495 0.136743i
\(587\) −5.29875 + 1.72167i −0.218703 + 0.0710608i −0.416319 0.909219i \(-0.636680\pi\)
0.197616 + 0.980279i \(0.436680\pi\)
\(588\) 4.87017i 0.200842i
\(589\) 2.93902 + 4.04521i 0.121100 + 0.166680i
\(590\) −0.527718 + 1.62415i −0.0217258 + 0.0668651i
\(591\) −16.9097 + 23.2741i −0.695570 + 0.957370i
\(592\) 6.84756 + 21.0746i 0.281433 + 0.866162i
\(593\) −37.6239 12.2248i −1.54503 0.502011i −0.592271 0.805739i \(-0.701769\pi\)
−0.952759 + 0.303728i \(0.901769\pi\)
\(594\) 0.0318208 0.0979344i 0.00130562 0.00401830i
\(595\) −3.40910 + 10.4921i −0.139760 + 0.430136i
\(596\) −0.437092 0.142020i −0.0179040 0.00581735i
\(597\) −4.10148 12.6231i −0.167862 0.516628i
\(598\) 0.117958 0.162355i 0.00482367 0.00663921i
\(599\) 5.24310 16.1366i 0.214227 0.659324i −0.784980 0.619521i \(-0.787327\pi\)
0.999208 0.0398031i \(-0.0126731\pi\)
\(600\) −1.67114 2.30013i −0.0682240 0.0939023i
\(601\) 17.4002i 0.709769i −0.934910 0.354885i \(-0.884520\pi\)
0.934910 0.354885i \(-0.115480\pi\)
\(602\) 1.77914 0.578079i 0.0725125 0.0235607i
\(603\) −6.78090 9.33311i −0.276140 0.380074i
\(604\) −6.54242 + 9.00487i −0.266207 + 0.366403i
\(605\) −13.2221 9.60642i −0.537555 0.390557i
\(606\) −3.87013 −0.157213
\(607\) 28.9842 + 21.0582i 1.17643 + 0.854727i 0.991765 0.128074i \(-0.0408795\pi\)
0.184666 + 0.982801i \(0.440880\pi\)
\(608\) −13.9266 4.52501i −0.564796 0.183513i
\(609\) −4.44511 + 1.44430i −0.180125 + 0.0585262i
\(610\) 2.95408 2.14626i 0.119607 0.0868997i
\(611\) 3.13183 2.27541i 0.126700 0.0920531i
\(612\) 38.3007i 1.54821i
\(613\) 6.17039 + 18.9905i 0.249220 + 0.767019i 0.994914 + 0.100731i \(0.0321181\pi\)
−0.745694 + 0.666288i \(0.767882\pi\)
\(614\) 0.458597 0.0185075
\(615\) 25.3625 + 10.6498i 1.02271 + 0.429441i
\(616\) 2.66451 0.107356
\(617\) 5.80834 + 17.8762i 0.233835 + 0.719670i 0.997274 + 0.0737897i \(0.0235094\pi\)
−0.763439 + 0.645880i \(0.776491\pi\)
\(618\) 0.420012i 0.0168954i
\(619\) 15.2525 11.0816i 0.613051 0.445407i −0.237437 0.971403i \(-0.576307\pi\)
0.850487 + 0.525996i \(0.176307\pi\)
\(620\) −1.67312 + 1.21559i −0.0671941 + 0.0488194i
\(621\) 0.483750 0.157180i 0.0194122 0.00630741i
\(622\) −0.698718 0.227027i −0.0280160 0.00910296i
\(623\) 11.3888 + 8.27446i 0.456283 + 0.331509i
\(624\) −3.89246 −0.155823
\(625\) 9.21963 + 6.69845i 0.368785 + 0.267938i
\(626\) 0.369389 0.508420i 0.0147638 0.0203206i
\(627\) −54.4979 75.0099i −2.17644 2.99561i
\(628\) −21.0718 + 6.84664i −0.840856 + 0.273211i
\(629\) 36.2202i 1.44419i
\(630\) −0.466139 0.641585i −0.0185714 0.0255614i
\(631\) −7.97911 + 24.5572i −0.317643 + 0.977605i 0.657009 + 0.753882i \(0.271821\pi\)
−0.974653 + 0.223723i \(0.928179\pi\)
\(632\) 2.57991 3.55094i 0.102623 0.141249i
\(633\) 10.3566 + 31.8742i 0.411636 + 1.26689i
\(634\) 3.77458 + 1.22643i 0.149908 + 0.0487079i
\(635\) 0.218456 0.672338i 0.00866916 0.0266809i
\(636\) 0.642050 1.97603i 0.0254590 0.0783546i
\(637\) −0.388673 0.126288i −0.0153998 0.00500370i
\(638\) 0.392907 + 1.20924i 0.0155553 + 0.0478744i
\(639\) 9.11912 12.5514i 0.360747 0.496525i
\(640\) 2.49067 7.66550i 0.0984524 0.303005i
\(641\) −7.30570 10.0554i −0.288558 0.397166i 0.639987 0.768386i \(-0.278940\pi\)
−0.928545 + 0.371220i \(0.878940\pi\)
\(642\) 5.72294i 0.225867i
\(643\) −15.0389 + 4.88643i −0.593075 + 0.192702i −0.590150 0.807294i \(-0.700931\pi\)
−0.00292560 + 0.999996i \(0.500931\pi\)
\(644\) 3.84662 + 5.29442i 0.151578 + 0.208629i
\(645\) 31.8269 43.8060i 1.25318 1.72486i
\(646\) 6.33491 + 4.60258i 0.249244 + 0.181086i
\(647\) 12.8414 0.504848 0.252424 0.967617i \(-0.418772\pi\)
0.252424 + 0.967617i \(0.418772\pi\)
\(648\) −4.20752 3.05694i −0.165287 0.120088i
\(649\) 28.3048 + 9.19680i 1.11106 + 0.361006i
\(650\) 0.112822 0.0366581i 0.00442524 0.00143785i
\(651\) 1.19369 0.867268i 0.0467845 0.0339909i
\(652\) 5.38718 3.91402i 0.210978 0.153285i
\(653\) 39.6975i 1.55348i −0.629819 0.776742i \(-0.716871\pi\)
0.629819 0.776742i \(-0.283129\pi\)
\(654\) −1.97254 6.07085i −0.0771323 0.237389i
\(655\) 2.11098 0.0824828
\(656\) −5.66547 24.1127i −0.221200 0.941442i
\(657\) −20.5092 −0.800141
\(658\) −0.434445 1.33708i −0.0169364 0.0521250i
\(659\) 10.6503i 0.414875i −0.978248 0.207438i \(-0.933488\pi\)
0.978248 0.207438i \(-0.0665124\pi\)
\(660\) 31.0245 22.5406i 1.20763 0.877391i
\(661\) 22.5817 16.4066i 0.878327 0.638142i −0.0544813 0.998515i \(-0.517351\pi\)
0.932808 + 0.360373i \(0.117351\pi\)
\(662\) −4.68765 + 1.52311i −0.182191 + 0.0591973i
\(663\) 6.05100 + 1.96609i 0.235001 + 0.0763566i
\(664\) −3.45928 2.51332i −0.134246 0.0975356i
\(665\) −14.5583 −0.564547
\(666\) 2.10643 + 1.53041i 0.0816226 + 0.0593023i
\(667\) −3.69158 + 5.08102i −0.142938 + 0.196738i
\(668\) −7.44380 10.2455i −0.288009 0.396411i
\(669\) 28.1818 9.15681i 1.08957 0.354023i
\(670\) 0.975508i 0.0376871i
\(671\) −37.4040 51.4822i −1.44397 1.98745i
\(672\) −1.33527 + 4.10955i −0.0515093 + 0.158529i
\(673\) −11.2776 + 15.5223i −0.434721 + 0.598342i −0.969029 0.246948i \(-0.920572\pi\)
0.534308 + 0.845290i \(0.320572\pi\)
\(674\) −1.09706 3.37640i −0.0422571 0.130054i
\(675\) 0.285956 + 0.0929126i 0.0110064 + 0.00357621i
\(676\) −7.84386 + 24.1409i −0.301687 + 0.928497i
\(677\) 10.8853 33.5014i 0.418355 1.28756i −0.490861 0.871238i \(-0.663318\pi\)
0.909216 0.416326i \(-0.136682\pi\)
\(678\) −0.179427 0.0582995i −0.00689086 0.00223898i
\(679\) −2.54451 7.83120i −0.0976494 0.300534i
\(680\) −3.82850 + 5.26948i −0.146816 + 0.202075i
\(681\) −7.32595 + 22.5470i −0.280731 + 0.864001i
\(682\) −0.235931 0.324731i −0.00903426 0.0124346i
\(683\) 14.5389i 0.556317i 0.960535 + 0.278158i \(0.0897240\pi\)
−0.960535 + 0.278158i \(0.910276\pi\)
\(684\) 48.0691 15.6186i 1.83797 0.597193i
\(685\) 0.716162 + 0.985712i 0.0273631 + 0.0376621i
\(686\) −0.0872387 + 0.120074i −0.00333079 + 0.00458444i
\(687\) −5.05126 3.66996i −0.192718 0.140018i
\(688\) −48.7569 −1.85884
\(689\) 0.141052 + 0.102480i 0.00537365 + 0.00390418i
\(690\) −2.00632 0.651892i −0.0763792 0.0248171i
\(691\) −10.0120 + 3.25308i −0.380873 + 0.123753i −0.493195 0.869919i \(-0.664171\pi\)
0.112322 + 0.993672i \(0.464171\pi\)
\(692\) 16.8774 12.2622i 0.641584 0.466138i
\(693\) −11.1812 + 8.12364i −0.424740 + 0.308591i
\(694\) 4.44362i 0.168678i
\(695\) 2.32039 + 7.14142i 0.0880173 + 0.270889i
\(696\) −2.75949 −0.104598
\(697\) −3.37213 + 40.3459i −0.127729 + 1.52821i
\(698\) −2.54859 −0.0964655
\(699\) 4.67646 + 14.3927i 0.176880 + 0.544381i
\(700\) 3.86846i 0.146214i
\(701\) −41.4224 + 30.0951i −1.56450 + 1.13668i −0.632308 + 0.774717i \(0.717892\pi\)
−0.932194 + 0.361960i \(0.882108\pi\)
\(702\) −0.00754398 + 0.00548102i −0.000284729 + 0.000206868i
\(703\) 45.4581 14.7702i 1.71448 0.557069i
\(704\) −32.0885 10.4262i −1.20938 0.392952i
\(705\) −32.9217 23.9190i −1.23990 0.900841i
\(706\) −3.31861 −0.124898
\(707\) 8.56778 + 6.22486i 0.322225 + 0.234110i
\(708\) −18.8778 + 25.9831i −0.709473 + 0.976506i
\(709\) −19.6617 27.0620i −0.738410 1.01633i −0.998709 0.0508057i \(-0.983821\pi\)
0.260299 0.965528i \(-0.416179\pi\)
\(710\) −1.24768 + 0.405395i −0.0468245 + 0.0152142i
\(711\) 22.7667i 0.853819i
\(712\) 4.88531 + 6.72405i 0.183085 + 0.251995i
\(713\) 0.612680 1.88563i 0.0229450 0.0706176i
\(714\) 1.35816 1.86935i 0.0508280 0.0699587i
\(715\) 0.994406 + 3.06047i 0.0371887 + 0.114455i
\(716\) 1.51021 + 0.490696i 0.0564390 + 0.0183382i
\(717\) 10.6667 32.8287i 0.398355 1.22601i
\(718\) 1.28420 3.95236i 0.0479260 0.147501i
\(719\) −12.8021 4.15967i −0.477439 0.155129i 0.0604046 0.998174i \(-0.480761\pi\)
−0.537844 + 0.843045i \(0.680761\pi\)
\(720\) 6.38719 + 19.6578i 0.238037 + 0.732602i
\(721\) 0.675564 0.929834i 0.0251593 0.0346288i
\(722\) −2.32173 + 7.14554i −0.0864057 + 0.265929i
\(723\) −27.2420 37.4955i −1.01314 1.39447i
\(724\) 11.3321i 0.421154i
\(725\) −3.53083 + 1.14724i −0.131132 + 0.0426073i
\(726\) 2.01204 + 2.76934i 0.0746739 + 0.102780i
\(727\) 6.89928 9.49604i 0.255880 0.352189i −0.661680 0.749787i \(-0.730156\pi\)
0.917560 + 0.397598i \(0.130156\pi\)
\(728\) −0.195204 0.141824i −0.00723473 0.00525634i
\(729\) 28.1119 1.04118
\(730\) 1.40304 + 1.01936i 0.0519287 + 0.0377284i
\(731\) 75.7948 + 24.6272i 2.80337 + 0.910871i
\(732\) 65.3108 21.2208i 2.41396 0.784342i
\(733\) −12.3523 + 8.97446i −0.456242 + 0.331479i −0.792055 0.610449i \(-0.790989\pi\)
0.335813 + 0.941929i \(0.390989\pi\)
\(734\) 1.25437 0.911352i 0.0462996 0.0336386i
\(735\) 4.29598i 0.158460i
\(736\) 1.79427 + 5.52219i 0.0661376 + 0.203551i
\(737\) 17.0007 0.626227
\(738\) −2.20388 1.90085i −0.0811261 0.0699711i
\(739\) 10.7844 0.396710 0.198355 0.980130i \(-0.436440\pi\)
0.198355 + 0.980130i \(0.436440\pi\)
\(740\) 6.10904 + 18.8017i 0.224573 + 0.691164i
\(741\) 8.39604i 0.308436i
\(742\) 0.0512261 0.0372179i 0.00188057 0.00136631i
\(743\) 8.96750 6.51527i 0.328986 0.239022i −0.411015 0.911629i \(-0.634825\pi\)
0.740000 + 0.672607i \(0.234825\pi\)
\(744\) 0.828501 0.269196i 0.0303743 0.00986922i
\(745\) −0.385559 0.125276i −0.0141258 0.00458975i
\(746\) −0.141444 0.102765i −0.00517862 0.00376249i
\(747\) 22.1791 0.811490
\(748\) 45.6627 + 33.1759i 1.66959 + 1.21303i
\(749\) 9.20500 12.6696i 0.336343 0.462937i
\(750\) −2.60686 3.58803i −0.0951889 0.131016i
\(751\) 11.7401 3.81459i 0.428402 0.139196i −0.0868763 0.996219i \(-0.527688\pi\)
0.515279 + 0.857023i \(0.327688\pi\)
\(752\) 36.6424i 1.33621i
\(753\) 2.50735 + 3.45107i 0.0913730 + 0.125764i
\(754\) 0.0355798 0.109503i 0.00129574 0.00398788i
\(755\) −5.77108 + 7.94321i −0.210031 + 0.289083i
\(756\) −0.0939672 0.289201i −0.00341755 0.0105182i
\(757\) −36.5007 11.8598i −1.32664 0.431051i −0.441870 0.897079i \(-0.645685\pi\)
−0.884770 + 0.466028i \(0.845685\pi\)
\(758\) −0.944461 + 2.90675i −0.0343044 + 0.105578i
\(759\) −11.3609 + 34.9651i −0.412373 + 1.26915i
\(760\) −8.17466 2.65611i −0.296526 0.0963472i
\(761\) −13.9965 43.0767i −0.507371 1.56153i −0.796748 0.604312i \(-0.793448\pi\)
0.289377 0.957215i \(-0.406552\pi\)
\(762\) −0.0870314 + 0.119788i −0.00315282 + 0.00433948i
\(763\) −5.39773 + 16.6125i −0.195411 + 0.601413i
\(764\) 19.4696 + 26.7977i 0.704387 + 0.969505i
\(765\) 33.7851i 1.22150i
\(766\) −3.28421 + 1.06711i −0.118663 + 0.0385561i
\(767\) −1.58412 2.18035i −0.0571991 0.0787278i
\(768\) 20.6474 28.4187i 0.745050 1.02547i
\(769\) 14.8088 + 10.7592i 0.534020 + 0.387988i 0.821859 0.569690i \(-0.192937\pi\)
−0.287839 + 0.957679i \(0.592937\pi\)
\(770\) 1.16867 0.0421161
\(771\) −10.4982 7.62736i −0.378082 0.274693i
\(772\) 33.0991 + 10.7546i 1.19126 + 0.387065i
\(773\) −21.5383 + 6.99822i −0.774679 + 0.251709i −0.669567 0.742752i \(-0.733520\pi\)
−0.105112 + 0.994460i \(0.533520\pi\)
\(774\) −4.63478 + 3.36737i −0.166594 + 0.121038i
\(775\) 0.948171 0.688887i 0.0340593 0.0247455i
\(776\) 4.86154i 0.174519i
\(777\) −4.35851 13.4141i −0.156361 0.481229i
\(778\) 1.41237 0.0506359
\(779\) −52.0111 + 12.2204i −1.86349 + 0.437843i
\(780\) −3.47265 −0.124341
\(781\) 7.06502 + 21.7439i 0.252806 + 0.778058i
\(782\) 3.10492i 0.111032i
\(783\) 0.236094 0.171532i 0.00843730 0.00613006i
\(784\) 3.12953 2.27374i 0.111769 0.0812050i
\(785\) −18.5875 + 6.03943i −0.663415 + 0.215557i
\(786\) −0.420500 0.136629i −0.0149987 0.00487339i
\(787\) 0.307199 + 0.223193i 0.0109505 + 0.00795597i 0.593247 0.805020i \(-0.297846\pi\)
−0.582297 + 0.812976i \(0.697846\pi\)
\(788\) 23.1107 0.823283
\(789\) 31.8084 + 23.1101i 1.13241 + 0.822743i
\(790\) 1.13157 1.55747i 0.0402594 0.0554124i
\(791\) 0.303450 + 0.417663i 0.0107894 + 0.0148504i
\(792\) −7.76051 + 2.52154i −0.275758 + 0.0895991i
\(793\) 5.76253i 0.204633i
\(794\) 1.97916 + 2.72408i 0.0702378 + 0.0966741i
\(795\) 0.566354 1.74306i 0.0200865 0.0618199i
\(796\) −6.26720 + 8.62606i −0.222135 + 0.305743i
\(797\) 15.3944 + 47.3791i 0.545297 + 1.67825i 0.720282 + 0.693681i \(0.244012\pi\)
−0.174985 + 0.984571i \(0.555988\pi\)
\(798\) 2.89997 + 0.942257i 0.102658 + 0.0333555i
\(799\) 18.5082 56.9623i 0.654772 2.01518i
\(800\) −1.06063 + 3.26429i −0.0374991 + 0.115410i
\(801\) −41.0010 13.3220i −1.44870 0.470711i
\(802\) 0.770391 + 2.37102i 0.0272035 + 0.0837236i
\(803\) 17.7650 24.4514i 0.626913 0.862871i
\(804\) −5.66927 + 17.4482i −0.199940 + 0.615352i
\(805\) 3.39311 + 4.67021i 0.119591 + 0.164603i
\(806\) 0.0363479i 0.00128030i
\(807\) 58.1152 18.8828i 2.04575 0.664705i
\(808\) 3.67521 + 5.05849i 0.129293 + 0.177957i
\(809\) −23.5997 + 32.4822i −0.829722 + 1.14201i 0.158252 + 0.987399i \(0.449414\pi\)
−0.987975 + 0.154616i \(0.950586\pi\)
\(810\) −1.84545 1.34080i −0.0648426 0.0471109i
\(811\) −46.9546 −1.64880 −0.824399 0.566009i \(-0.808487\pi\)
−0.824399 + 0.566009i \(0.808487\pi\)
\(812\) 3.03760 + 2.20694i 0.106599 + 0.0774486i
\(813\) 73.6142 + 23.9187i 2.58176 + 0.838866i
\(814\) −3.64916 + 1.18568i −0.127903 + 0.0415582i
\(815\) 4.75204 3.45256i 0.166457 0.120938i
\(816\) −48.7217 + 35.3984i −1.70560 + 1.23919i
\(817\) 105.169i 3.67939i
\(818\) 1.45453 + 4.47659i 0.0508565 + 0.156520i
\(819\) 1.25154 0.0437324
\(820\) −5.05444 21.5121i −0.176509 0.751234i
\(821\) 34.2975 1.19699 0.598495 0.801126i \(-0.295766\pi\)
0.598495 + 0.801126i \(0.295766\pi\)
\(822\) −0.0788589 0.242703i −0.00275052 0.00846523i
\(823\) 38.3663i 1.33737i −0.743548 0.668683i \(-0.766858\pi\)
0.743548 0.668683i \(-0.233142\pi\)
\(824\) 0.548982 0.398859i 0.0191247 0.0138949i
\(825\) −17.5818 + 12.7739i −0.612121 + 0.444732i
\(826\) −0.930866 + 0.302457i −0.0323890 + 0.0105238i
\(827\) −9.62807 3.12835i −0.334801 0.108783i 0.136792 0.990600i \(-0.456321\pi\)
−0.471593 + 0.881816i \(0.656321\pi\)
\(828\) −16.2138 11.7800i −0.563469 0.409384i
\(829\) −30.9763 −1.07585 −0.537925 0.842993i \(-0.680792\pi\)
−0.537925 + 0.842993i \(0.680792\pi\)
\(830\) −1.51727 1.10236i −0.0526652 0.0382635i
\(831\) −3.52131 + 4.84667i −0.122153 + 0.168129i
\(832\) 1.79587 + 2.47181i 0.0622607 + 0.0856945i
\(833\) −6.01347 + 1.95390i −0.208355 + 0.0676985i
\(834\) 1.57273i 0.0544592i
\(835\) −6.56619 9.03758i −0.227232 0.312758i
\(836\) −23.0165 + 70.8375i −0.796043 + 2.44997i
\(837\) −0.0541506 + 0.0745319i −0.00187172 + 0.00257620i
\(838\) −0.195141 0.600584i −0.00674105 0.0207468i
\(839\) 12.0183 + 3.90500i 0.414919 + 0.134815i 0.509035 0.860746i \(-0.330002\pi\)
−0.0941157 + 0.995561i \(0.530002\pi\)
\(840\) −0.783785 + 2.41224i −0.0270431 + 0.0832303i
\(841\) 7.84800 24.1537i 0.270621 0.832885i
\(842\) 2.55804 + 0.831157i 0.0881558 + 0.0286436i
\(843\) 14.4504 + 44.4738i 0.497698 + 1.53176i
\(844\) 15.8252 21.7815i 0.544724 0.749749i
\(845\) −6.91908 + 21.2947i −0.238024 + 0.732562i
\(846\) 2.53069 + 3.48319i 0.0870069 + 0.119755i
\(847\) 9.36708i 0.321857i
\(848\) −1.56954 + 0.509973i −0.0538981 + 0.0175125i
\(849\) 16.8467 + 23.1875i 0.578177 + 0.795792i
\(850\) 1.07881 1.48486i 0.0370030 0.0509303i
\(851\) −15.3331 11.1401i −0.525612 0.381879i
\(852\) −24.6724 −0.845261
\(853\) −44.8109 32.5570i −1.53430 1.11473i −0.953790 0.300475i \(-0.902855\pi\)
−0.580506 0.814256i \(-0.697145\pi\)
\(854\) 1.99036 + 0.646708i 0.0681088 + 0.0221299i
\(855\) 42.4019 13.7772i 1.45011 0.471170i
\(856\) 7.48023 5.43471i 0.255669 0.185754i
\(857\) 0.586268 0.425948i 0.0200265 0.0145501i −0.577727 0.816230i \(-0.696060\pi\)
0.597753 + 0.801680i \(0.296060\pi\)
\(858\) 0.673995i 0.0230098i
\(859\) 5.70210 + 17.5493i 0.194553 + 0.598773i 0.999982 + 0.00607985i \(0.00193529\pi\)
−0.805428 + 0.592693i \(0.798065\pi\)
\(860\) −43.4983 −1.48328
\(861\) 3.60610 + 15.3478i 0.122896 + 0.523053i
\(862\) −1.37270 −0.0467544
\(863\) −6.47239 19.9200i −0.220323 0.678084i −0.998733 0.0503275i \(-0.983974\pi\)
0.778410 0.627756i \(-0.216026\pi\)
\(864\) 0.269798i 0.00917871i
\(865\) 14.8876 10.8165i 0.506194 0.367771i
\(866\) 0.338220 0.245731i 0.0114932 0.00835029i
\(867\) 53.8111 17.4843i 1.82752 0.593798i
\(868\) −1.12729 0.366280i −0.0382629 0.0124324i
\(869\) −27.1429 19.7204i −0.920758 0.668970i
\(870\) −1.21033 −0.0410342
\(871\) −1.24548 0.904895i −0.0422015 0.0306612i
\(872\) −6.06177 + 8.34331i −0.205278 + 0.282540i
\(873\) 14.8220 + 20.4008i 0.501650 + 0.690462i
\(874\) 3.89682 1.26615i 0.131812 0.0428283i
\(875\) 12.1362i 0.410280i
\(876\) 19.1710 + 26.3866i 0.647727 + 0.891520i
\(877\) −8.90969 + 27.4212i −0.300859 + 0.925948i 0.680331 + 0.732905i \(0.261836\pi\)
−0.981190 + 0.193044i \(0.938164\pi\)
\(878\) −1.84617 + 2.54103i −0.0623051 + 0.0857557i
\(879\) −20.9754 64.5558i −0.707484 2.17741i
\(880\) −28.9688 9.41255i −0.976540 0.317297i
\(881\) −1.06773 + 3.28612i −0.0359726 + 0.110712i −0.967430 0.253137i \(-0.918538\pi\)
0.931458 + 0.363849i \(0.118538\pi\)
\(882\) 0.140456 0.432279i 0.00472940 0.0145556i
\(883\) 2.89843 + 0.941756i 0.0975399 + 0.0316926i 0.357380 0.933959i \(-0.383670\pi\)
−0.259841 + 0.965652i \(0.583670\pi\)
\(884\) −1.57943 4.86098i −0.0531219 0.163492i
\(885\) −16.6522 + 22.9197i −0.559757 + 0.770439i
\(886\) −1.64576 + 5.06513i −0.0552904 + 0.170166i
\(887\) −27.7698 38.2218i −0.932418 1.28336i −0.958909 0.283714i \(-0.908433\pi\)
0.0264913 0.999649i \(-0.491567\pi\)
\(888\) 8.32737i 0.279448i
\(889\) 0.385345 0.125206i 0.0129240 0.00419928i
\(890\) 2.14274 + 2.94923i 0.0718247 + 0.0988583i
\(891\) −23.3668 + 32.1616i −0.782817 + 1.07746i
\(892\) −19.2582 13.9919i −0.644813 0.468484i
\(893\) 79.0378 2.64490
\(894\) 0.0686939 + 0.0499090i 0.00229747 + 0.00166921i
\(895\) 1.33215 + 0.432843i 0.0445290 + 0.0144684i
\(896\) 4.39341 1.42751i 0.146774 0.0476896i
\(897\) 2.69339 1.95687i 0.0899298 0.0653378i
\(898\) −4.34879 + 3.15958i −0.145121 + 0.105437i
\(899\) 1.13753i 0.0379388i
\(900\) −3.66090 11.2671i −0.122030 0.375570i
\(901\) 2.69750 0.0898669
\(902\) 4.17521 0.981001i 0.139019 0.0326638i
\(903\) 31.0340 1.03275
\(904\) 0.0941895 + 0.289886i 0.00313270 + 0.00964145i
\(905\) 9.99606i 0.332280i
\(906\) 1.66369 1.20874i 0.0552723 0.0401577i
\(907\) 40.8711 29.6946i 1.35710 0.985992i 0.358478 0.933538i \(-0.383296\pi\)
0.998623 0.0524541i \(-0.0167043\pi\)
\(908\) 18.1127 5.88519i 0.601093 0.195307i
\(909\) −30.8450 10.0221i −1.02306 0.332413i
\(910\) −0.0856180 0.0622051i −0.00283821 0.00206208i
\(911\) −48.1146 −1.59411 −0.797054 0.603908i \(-0.793609\pi\)
−0.797054 + 0.603908i \(0.793609\pi\)
\(912\) −64.2948 46.7129i −2.12901 1.54682i
\(913\) −19.2114 + 26.4422i −0.635805 + 0.875110i
\(914\) 1.82001 + 2.50503i 0.0602005 + 0.0828589i
\(915\) 57.6108 18.7189i 1.90455 0.618827i
\(916\) 5.01578i 0.165726i
\(917\) 0.711155 + 0.978821i 0.0234844 + 0.0323235i
\(918\) −0.0445827 + 0.137211i −0.00147145 + 0.00452865i
\(919\) 22.3458 30.7564i 0.737121 1.01456i −0.261658 0.965161i \(-0.584269\pi\)
0.998779 0.0493993i \(-0.0157307\pi\)
\(920\) 1.05321 + 3.24144i 0.0347232 + 0.106867i
\(921\) 7.23554 + 2.35097i 0.238419 + 0.0774671i
\(922\) −1.43659 + 4.42136i −0.0473115 + 0.145610i
\(923\) 0.639775 1.96903i 0.0210585 0.0648113i
\(924\) 20.9033 + 6.79189i 0.687667 + 0.223437i
\(925\) −3.46204 10.6551i −0.113831 0.350337i
\(926\) 2.04867 2.81975i 0.0673234 0.0926627i
\(927\) −1.08767 + 3.34751i −0.0357238 + 0.109947i
\(928\) 1.95810 + 2.69510i 0.0642779 + 0.0884710i
\(929\) 13.3863i 0.439189i 0.975591 + 0.219594i \(0.0704734\pi\)
−0.975591 + 0.219594i \(0.929527\pi\)
\(930\) 0.363387 0.118072i 0.0119159 0.00387173i
\(931\) −4.90446 6.75041i −0.160737 0.221236i
\(932\) 7.14579 9.83533i 0.234068 0.322167i
\(933\) −9.86021 7.16386i −0.322809 0.234534i
\(934\) −2.43199 −0.0795773
\(935\) 40.2791 + 29.2645i 1.31727 + 0.957051i
\(936\) 0.702755 + 0.228339i 0.0229703 + 0.00746350i
\(937\) −30.4187 + 9.88363i −0.993735 + 0.322884i −0.760360 0.649502i \(-0.774977\pi\)
−0.233376 + 0.972387i \(0.574977\pi\)
\(938\) −0.452324 + 0.328633i −0.0147689 + 0.0107302i
\(939\) 8.43443 6.12797i 0.275247 0.199979i
\(940\) 32.6904i 1.06624i
\(941\) −6.35211 19.5498i −0.207073 0.637304i −0.999622 0.0274964i \(-0.991247\pi\)
0.792549 0.609808i \(-0.208753\pi\)
\(942\) 4.09345 0.133372
\(943\) 16.0425 + 13.8366i 0.522415 + 0.450582i
\(944\) 25.5101 0.830283
\(945\) −0.0828886 0.255105i −0.00269637 0.00829856i
\(946\) 8.44246i 0.274488i
\(947\) −16.1336 + 11.7217i −0.524271 + 0.380905i −0.818210 0.574919i \(-0.805034\pi\)
0.293939 + 0.955824i \(0.405034\pi\)
\(948\) 29.2910 21.2812i 0.951329 0.691181i
\(949\) −2.60295 + 0.845751i −0.0844954 + 0.0274542i
\(950\) 2.30350 + 0.748452i 0.0747354 + 0.0242830i
\(951\) 53.2663 + 38.7002i 1.72728 + 1.25494i
\(952\) −3.73312 −0.120991
\(953\) 18.2617 + 13.2679i 0.591556 + 0.429791i 0.842872 0.538115i \(-0.180863\pi\)
−0.251316 + 0.967905i \(0.580863\pi\)
\(954\) −0.113978 + 0.156877i −0.00369016 + 0.00507907i
\(955\) 17.1742 + 23.6382i 0.555744 + 0.764916i
\(956\) −26.3725 + 8.56893i −0.852946 + 0.277139i
\(957\) 21.0931i 0.681844i
\(958\) −2.73110 3.75903i −0.0882377 0.121449i
\(959\) −0.215793 + 0.664141i −0.00696830 + 0.0214462i
\(960\) 18.8782 25.9836i 0.609290 0.838616i
\(961\) −9.46856 29.1412i −0.305437 0.940039i
\(962\) 0.330451 + 0.107370i 0.0106542 + 0.00346175i
\(963\) −14.8202 + 45.6120i −0.477575 + 1.46982i
\(964\) −11.5053 + 35.4098i −0.370562 + 1.14047i
\(965\) 29.1968 + 9.48661i 0.939878 + 0.305385i
\(966\) −0.373626 1.14990i −0.0120212 0.0369975i
\(967\) −0.592611 + 0.815659i −0.0190571 + 0.0262298i −0.818439 0.574593i \(-0.805160\pi\)
0.799382 + 0.600823i \(0.205160\pi\)
\(968\) 1.70899 5.25972i 0.0549290 0.169054i
\(969\) 76.3544 + 105.093i 2.45286 + 3.37607i
\(970\) 2.13231i 0.0684645i
\(971\) −11.9917 + 3.89634i −0.384832 + 0.125040i −0.495043 0.868869i \(-0.664848\pi\)
0.110210 + 0.993908i \(0.464848\pi\)
\(972\) −25.7523 35.4451i −0.826007 1.13690i
\(973\) −2.52964 + 3.48175i −0.0810965 + 0.111620i
\(974\) −3.86616 2.80893i −0.123880 0.0900039i
\(975\) 1.96798 0.0630257
\(976\) −44.1280 32.0609i −1.41250 1.02624i
\(977\) −6.94519 2.25663i −0.222196 0.0721960i 0.195803 0.980643i \(-0.437269\pi\)
−0.418000 + 0.908447i \(0.637269\pi\)
\(978\) −1.17005 + 0.380172i −0.0374141 + 0.0121566i
\(979\) 51.3976 37.3426i 1.64268 1.19347i
\(980\) 2.79201 2.02851i 0.0891873 0.0647984i
\(981\) 53.4929i 1.70790i
\(982\) −0.355812 1.09508i −0.0113544 0.0349453i
\(983\) −10.3462 −0.329991 −0.164996 0.986294i \(-0.552761\pi\)
−0.164996 + 0.986294i \(0.552761\pi\)
\(984\) −0.775286 + 9.27590i −0.0247152 + 0.295705i
\(985\) 20.3859 0.649550
\(986\) −0.550484 1.69422i −0.0175310 0.0539548i
\(987\) 23.3231i 0.742381i
\(988\) 5.45668 3.96451i 0.173600 0.126128i
\(989\) 33.7374 24.5117i 1.07279 0.779426i
\(990\) −3.40383 + 1.10597i −0.108181 + 0.0351500i
\(991\) 43.4075 + 14.1039i 1.37888 + 0.448027i 0.902302 0.431103i \(-0.141876\pi\)
0.476582 + 0.879130i \(0.341876\pi\)
\(992\) −0.850811 0.618150i −0.0270133 0.0196263i
\(993\) −81.7677 −2.59482
\(994\) −0.608296 0.441953i −0.0192940 0.0140179i
\(995\) −5.52831 + 7.60906i −0.175259 + 0.241223i
\(996\) −20.7319 28.5350i −0.656915 0.904165i
\(997\) −41.3372 + 13.4313i −1.30916 + 0.425372i −0.878760 0.477265i \(-0.841628\pi\)
−0.430402 + 0.902637i \(0.641628\pi\)
\(998\) 3.35608i 0.106235i
\(999\) 0.517636 + 0.712465i 0.0163773 + 0.0225414i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 287.2.n.a.64.12 88
41.25 even 10 inner 287.2.n.a.148.12 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.n.a.64.12 88 1.1 even 1 trivial
287.2.n.a.148.12 yes 88 41.25 even 10 inner