Properties

Label 847.2.f.z.148.4
Level $847$
Weight $2$
Character 847.148
Analytic conductor $6.763$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 148.4
Character \(\chi\) \(=\) 847.148
Dual form 847.2.f.z.372.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0371933 - 0.114469i) q^{2} +(-2.23923 - 1.62690i) q^{3} +(1.60631 - 1.16706i) q^{4} +(-0.867882 + 2.67107i) q^{5} +(-0.102945 + 0.316832i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.388082 - 0.281958i) q^{8} +(1.44031 + 4.43281i) q^{9} +O(q^{10})\) \(q+(-0.0371933 - 0.114469i) q^{2} +(-2.23923 - 1.62690i) q^{3} +(1.60631 - 1.16706i) q^{4} +(-0.867882 + 2.67107i) q^{5} +(-0.102945 + 0.316832i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.388082 - 0.281958i) q^{8} +(1.44031 + 4.43281i) q^{9} +0.338034 q^{10} -5.49558 q^{12} +(-0.333638 - 1.02683i) q^{13} +(-0.0973732 - 0.0707458i) q^{14} +(6.28893 - 4.56918i) q^{15} +(1.20927 - 3.72176i) q^{16} +(-2.15023 + 6.61772i) q^{17} +(0.453850 - 0.329741i) q^{18} +(6.10332 + 4.43432i) q^{19} +(1.72319 + 5.30344i) q^{20} -2.76784 q^{21} +4.82552 q^{23} +(0.410289 + 1.26274i) q^{24} +(-2.33629 - 1.69741i) q^{25} +(-0.105131 + 0.0763824i) q^{26} +(1.42061 - 4.37220i) q^{27} +(0.613557 - 1.88834i) q^{28} +(0.992877 - 0.721367i) q^{29} +(-0.756935 - 0.549946i) q^{30} +(-2.49503 - 7.67891i) q^{31} -1.43040 q^{32} +0.837498 q^{34} +(0.867882 + 2.67107i) q^{35} +(7.48693 + 5.43957i) q^{36} +(-1.24205 + 0.902399i) q^{37} +(0.280590 - 0.863568i) q^{38} +(-0.923456 + 2.84210i) q^{39} +(1.08994 - 0.791887i) q^{40} +(7.52374 + 5.46632i) q^{41} +(0.102945 + 0.316832i) q^{42} +5.23402 q^{43} -13.0904 q^{45} +(-0.179477 - 0.552373i) q^{46} +(1.53217 + 1.11319i) q^{47} +(-8.76276 + 6.36651i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.107407 + 0.330565i) q^{50} +(15.5812 - 11.3204i) q^{51} +(-1.73430 - 1.26004i) q^{52} +(-1.18215 - 3.63829i) q^{53} -0.553319 q^{54} -0.479696 q^{56} +(-6.45255 - 19.8589i) q^{57} +(-0.119503 - 0.0868237i) q^{58} +(5.39088 - 3.91670i) q^{59} +(4.76952 - 14.6791i) q^{60} +(3.02822 - 9.31990i) q^{61} +(-0.786200 + 0.571207i) q^{62} +(3.77078 + 2.73963i) q^{63} +(-2.36535 - 7.27979i) q^{64} +3.03229 q^{65} -2.06100 q^{67} +(4.26931 + 13.1396i) q^{68} +(-10.8054 - 7.85062i) q^{69} +(0.273475 - 0.198691i) q^{70} +(3.86926 - 11.9084i) q^{71} +(0.690910 - 2.12640i) q^{72} +(2.07681 - 1.50889i) q^{73} +(0.149493 + 0.108613i) q^{74} +(2.46997 + 7.60180i) q^{75} +14.9789 q^{76} +0.359679 q^{78} +(4.73672 + 14.5781i) q^{79} +(8.89156 + 6.46010i) q^{80} +(1.01813 - 0.739718i) q^{81} +(0.345892 - 1.06455i) q^{82} +(-0.632256 + 1.94588i) q^{83} +(-4.44602 + 3.23022i) q^{84} +(-15.8102 - 11.4868i) q^{85} +(-0.194670 - 0.599134i) q^{86} -3.39687 q^{87} +4.76119 q^{89} +(0.486873 + 1.49844i) q^{90} +(-0.873475 - 0.634617i) q^{91} +(7.75130 - 5.63165i) q^{92} +(-6.90584 + 21.2540i) q^{93} +(0.0704390 - 0.216789i) q^{94} +(-17.1413 + 12.4539i) q^{95} +(3.20298 + 2.32710i) q^{96} +(2.81673 + 8.66899i) q^{97} -0.120360 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0371933 0.114469i −0.0262996 0.0809418i 0.937045 0.349208i \(-0.113549\pi\)
−0.963345 + 0.268266i \(0.913549\pi\)
\(3\) −2.23923 1.62690i −1.29282 0.939288i −0.292961 0.956124i \(-0.594641\pi\)
−0.999858 + 0.0168358i \(0.994641\pi\)
\(4\) 1.60631 1.16706i 0.803157 0.583528i
\(5\) −0.867882 + 2.67107i −0.388129 + 1.19454i 0.546056 + 0.837748i \(0.316128\pi\)
−0.934185 + 0.356789i \(0.883872\pi\)
\(6\) −0.102945 + 0.316832i −0.0420271 + 0.129346i
\(7\) 0.809017 0.587785i 0.305780 0.222162i
\(8\) −0.388082 0.281958i −0.137208 0.0996873i
\(9\) 1.44031 + 4.43281i 0.480103 + 1.47760i
\(10\) 0.338034 0.106896
\(11\) 0 0
\(12\) −5.49558 −1.58644
\(13\) −0.333638 1.02683i −0.0925344 0.284792i 0.894069 0.447930i \(-0.147838\pi\)
−0.986603 + 0.163138i \(0.947838\pi\)
\(14\) −0.0973732 0.0707458i −0.0260241 0.0189076i
\(15\) 6.28893 4.56918i 1.62380 1.17976i
\(16\) 1.20927 3.72176i 0.302318 0.930440i
\(17\) −2.15023 + 6.61772i −0.521507 + 1.60503i 0.249615 + 0.968345i \(0.419696\pi\)
−0.771122 + 0.636688i \(0.780304\pi\)
\(18\) 0.453850 0.329741i 0.106974 0.0777208i
\(19\) 6.10332 + 4.43432i 1.40020 + 1.01730i 0.994658 + 0.103225i \(0.0329161\pi\)
0.405539 + 0.914078i \(0.367084\pi\)
\(20\) 1.72319 + 5.30344i 0.385317 + 1.18588i
\(21\) −2.76784 −0.603992
\(22\) 0 0
\(23\) 4.82552 1.00619 0.503095 0.864231i \(-0.332194\pi\)
0.503095 + 0.864231i \(0.332194\pi\)
\(24\) 0.410289 + 1.26274i 0.0837498 + 0.257755i
\(25\) −2.33629 1.69741i −0.467258 0.339483i
\(26\) −0.105131 + 0.0763824i −0.0206179 + 0.0149798i
\(27\) 1.42061 4.37220i 0.273397 0.841431i
\(28\) 0.613557 1.88834i 0.115951 0.356862i
\(29\) 0.992877 0.721367i 0.184373 0.133955i −0.491770 0.870725i \(-0.663650\pi\)
0.676143 + 0.736770i \(0.263650\pi\)
\(30\) −0.756935 0.549946i −0.138197 0.100406i
\(31\) −2.49503 7.67891i −0.448121 1.37917i −0.879025 0.476776i \(-0.841805\pi\)
0.430904 0.902398i \(-0.358195\pi\)
\(32\) −1.43040 −0.252861
\(33\) 0 0
\(34\) 0.837498 0.143630
\(35\) 0.867882 + 2.67107i 0.146699 + 0.451493i
\(36\) 7.48693 + 5.43957i 1.24782 + 0.906595i
\(37\) −1.24205 + 0.902399i −0.204191 + 0.148354i −0.685182 0.728372i \(-0.740277\pi\)
0.480990 + 0.876726i \(0.340277\pi\)
\(38\) 0.280590 0.863568i 0.0455177 0.140089i
\(39\) −0.923456 + 2.84210i −0.147871 + 0.455101i
\(40\) 1.08994 0.791887i 0.172334 0.125208i
\(41\) 7.52374 + 5.46632i 1.17501 + 0.853696i 0.991600 0.129341i \(-0.0412861\pi\)
0.183411 + 0.983036i \(0.441286\pi\)
\(42\) 0.102945 + 0.316832i 0.0158848 + 0.0488882i
\(43\) 5.23402 0.798181 0.399091 0.916912i \(-0.369326\pi\)
0.399091 + 0.916912i \(0.369326\pi\)
\(44\) 0 0
\(45\) −13.0904 −1.95140
\(46\) −0.179477 0.552373i −0.0264624 0.0814429i
\(47\) 1.53217 + 1.11319i 0.223490 + 0.162375i 0.693896 0.720075i \(-0.255893\pi\)
−0.470406 + 0.882450i \(0.655893\pi\)
\(48\) −8.76276 + 6.36651i −1.26479 + 0.918927i
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) −0.107407 + 0.330565i −0.0151897 + 0.0467490i
\(51\) 15.5812 11.3204i 2.18180 1.58517i
\(52\) −1.73430 1.26004i −0.240504 0.174736i
\(53\) −1.18215 3.63829i −0.162381 0.499757i 0.836453 0.548039i \(-0.184625\pi\)
−0.998834 + 0.0482819i \(0.984625\pi\)
\(54\) −0.553319 −0.0752972
\(55\) 0 0
\(56\) −0.479696 −0.0641021
\(57\) −6.45255 19.8589i −0.854661 2.63038i
\(58\) −0.119503 0.0868237i −0.0156915 0.0114005i
\(59\) 5.39088 3.91670i 0.701832 0.509911i −0.178696 0.983904i \(-0.557188\pi\)
0.880528 + 0.473993i \(0.157188\pi\)
\(60\) 4.76952 14.6791i 0.615742 1.89506i
\(61\) 3.02822 9.31990i 0.387724 1.19329i −0.546761 0.837289i \(-0.684139\pi\)
0.934485 0.356002i \(-0.115861\pi\)
\(62\) −0.786200 + 0.571207i −0.0998474 + 0.0725434i
\(63\) 3.77078 + 2.73963i 0.475073 + 0.345161i
\(64\) −2.36535 7.27979i −0.295668 0.909973i
\(65\) 3.03229 0.376110
\(66\) 0 0
\(67\) −2.06100 −0.251792 −0.125896 0.992043i \(-0.540181\pi\)
−0.125896 + 0.992043i \(0.540181\pi\)
\(68\) 4.26931 + 13.1396i 0.517729 + 1.59341i
\(69\) −10.8054 7.85062i −1.30082 0.945103i
\(70\) 0.273475 0.198691i 0.0326865 0.0237482i
\(71\) 3.86926 11.9084i 0.459197 1.41326i −0.406940 0.913455i \(-0.633404\pi\)
0.866137 0.499808i \(-0.166596\pi\)
\(72\) 0.690910 2.12640i 0.0814245 0.250599i
\(73\) 2.07681 1.50889i 0.243073 0.176603i −0.459579 0.888137i \(-0.652000\pi\)
0.702651 + 0.711535i \(0.252000\pi\)
\(74\) 0.149493 + 0.108613i 0.0173782 + 0.0126260i
\(75\) 2.46997 + 7.60180i 0.285208 + 0.877780i
\(76\) 14.9789 1.71820
\(77\) 0 0
\(78\) 0.359679 0.0407257
\(79\) 4.73672 + 14.5781i 0.532923 + 1.64017i 0.748095 + 0.663591i \(0.230969\pi\)
−0.215173 + 0.976576i \(0.569031\pi\)
\(80\) 8.89156 + 6.46010i 0.994107 + 0.722261i
\(81\) 1.01813 0.739718i 0.113126 0.0821909i
\(82\) 0.345892 1.06455i 0.0381974 0.117559i
\(83\) −0.632256 + 1.94588i −0.0693991 + 0.213589i −0.979741 0.200268i \(-0.935819\pi\)
0.910342 + 0.413857i \(0.135819\pi\)
\(84\) −4.44602 + 3.23022i −0.485101 + 0.352446i
\(85\) −15.8102 11.4868i −1.71486 1.24592i
\(86\) −0.194670 0.599134i −0.0209918 0.0646063i
\(87\) −3.39687 −0.364183
\(88\) 0 0
\(89\) 4.76119 0.504685 0.252342 0.967638i \(-0.418799\pi\)
0.252342 + 0.967638i \(0.418799\pi\)
\(90\) 0.486873 + 1.49844i 0.0513209 + 0.157950i
\(91\) −0.873475 0.634617i −0.0915650 0.0665259i
\(92\) 7.75130 5.63165i 0.808129 0.587140i
\(93\) −6.90584 + 21.2540i −0.716102 + 2.20394i
\(94\) 0.0704390 0.216789i 0.00726523 0.0223601i
\(95\) −17.1413 + 12.4539i −1.75866 + 1.27774i
\(96\) 3.20298 + 2.32710i 0.326903 + 0.237509i
\(97\) 2.81673 + 8.66899i 0.285995 + 0.880203i 0.986099 + 0.166161i \(0.0531373\pi\)
−0.700103 + 0.714042i \(0.746863\pi\)
\(98\) −0.120360 −0.0121582
\(99\) 0 0
\(100\) −5.73379 −0.573379
\(101\) 1.46593 + 4.51167i 0.145866 + 0.448928i 0.997121 0.0758231i \(-0.0241584\pi\)
−0.851256 + 0.524751i \(0.824158\pi\)
\(102\) −1.87535 1.36252i −0.185687 0.134910i
\(103\) −0.283885 + 0.206254i −0.0279720 + 0.0203228i −0.601683 0.798735i \(-0.705503\pi\)
0.573711 + 0.819058i \(0.305503\pi\)
\(104\) −0.160045 + 0.492567i −0.0156937 + 0.0483001i
\(105\) 2.40216 7.39308i 0.234427 0.721491i
\(106\) −0.372503 + 0.270639i −0.0361807 + 0.0262868i
\(107\) 2.06116 + 1.49752i 0.199260 + 0.144771i 0.682941 0.730473i \(-0.260701\pi\)
−0.483681 + 0.875244i \(0.660701\pi\)
\(108\) −2.82065 8.68106i −0.271417 0.835336i
\(109\) 3.81522 0.365432 0.182716 0.983166i \(-0.441511\pi\)
0.182716 + 0.983166i \(0.441511\pi\)
\(110\) 0 0
\(111\) 4.24933 0.403329
\(112\) −1.20927 3.72176i −0.114266 0.351673i
\(113\) −1.87262 1.36054i −0.176161 0.127988i 0.496211 0.868202i \(-0.334724\pi\)
−0.672372 + 0.740214i \(0.734724\pi\)
\(114\) −2.03324 + 1.47724i −0.190430 + 0.138356i
\(115\) −4.18798 + 12.8893i −0.390531 + 1.20193i
\(116\) 0.752997 2.31749i 0.0699140 0.215173i
\(117\) 4.07121 2.95791i 0.376383 0.273459i
\(118\) −0.648845 0.471414i −0.0597311 0.0433972i
\(119\) 2.15023 + 6.61772i 0.197111 + 0.606646i
\(120\) −3.72894 −0.340404
\(121\) 0 0
\(122\) −1.17947 −0.106784
\(123\) −7.95426 24.4807i −0.717211 2.20735i
\(124\) −12.9695 9.42291i −1.16470 0.846202i
\(125\) −4.79919 + 3.48682i −0.429253 + 0.311870i
\(126\) 0.173355 0.533533i 0.0154437 0.0475309i
\(127\) −3.04272 + 9.36452i −0.269997 + 0.830967i 0.720502 + 0.693453i \(0.243911\pi\)
−0.990500 + 0.137514i \(0.956089\pi\)
\(128\) −3.05976 + 2.22305i −0.270447 + 0.196492i
\(129\) −11.7202 8.51521i −1.03190 0.749722i
\(130\) −0.112781 0.347104i −0.00989153 0.0304430i
\(131\) −16.3782 −1.43097 −0.715484 0.698629i \(-0.753794\pi\)
−0.715484 + 0.698629i \(0.753794\pi\)
\(132\) 0 0
\(133\) 7.54411 0.654158
\(134\) 0.0766554 + 0.235921i 0.00662202 + 0.0203805i
\(135\) 10.4455 + 7.58911i 0.899007 + 0.653167i
\(136\) 2.70039 1.96195i 0.231556 0.168235i
\(137\) −4.39242 + 13.5185i −0.375270 + 1.15496i 0.568027 + 0.823010i \(0.307707\pi\)
−0.943297 + 0.331951i \(0.892293\pi\)
\(138\) −0.496763 + 1.52888i −0.0422873 + 0.130147i
\(139\) −7.42631 + 5.39553i −0.629891 + 0.457643i −0.856362 0.516375i \(-0.827281\pi\)
0.226471 + 0.974018i \(0.427281\pi\)
\(140\) 4.51137 + 3.27771i 0.381281 + 0.277017i
\(141\) −1.61984 4.98536i −0.136415 0.419843i
\(142\) −1.50705 −0.126469
\(143\) 0 0
\(144\) 18.2396 1.51997
\(145\) 1.06512 + 3.27810i 0.0884534 + 0.272232i
\(146\) −0.249965 0.181610i −0.0206872 0.0150302i
\(147\) −2.23923 + 1.62690i −0.184689 + 0.134184i
\(148\) −0.941966 + 2.89907i −0.0774291 + 0.238302i
\(149\) −3.59077 + 11.0513i −0.294168 + 0.905355i 0.689332 + 0.724446i \(0.257904\pi\)
−0.983500 + 0.180910i \(0.942096\pi\)
\(150\) 0.778305 0.565471i 0.0635483 0.0461705i
\(151\) 14.4935 + 10.5302i 1.17947 + 0.856934i 0.992112 0.125358i \(-0.0400080\pi\)
0.187357 + 0.982292i \(0.440008\pi\)
\(152\) −1.11830 3.44176i −0.0907058 0.279164i
\(153\) −32.4321 −2.62198
\(154\) 0 0
\(155\) 22.6763 1.82140
\(156\) 1.83353 + 5.64304i 0.146800 + 0.451804i
\(157\) −6.00942 4.36610i −0.479604 0.348453i 0.321568 0.946886i \(-0.395790\pi\)
−0.801172 + 0.598434i \(0.795790\pi\)
\(158\) 1.49257 1.08442i 0.118743 0.0862715i
\(159\) −3.27200 + 10.0702i −0.259487 + 0.798618i
\(160\) 1.24141 3.82068i 0.0981424 0.302051i
\(161\) 3.90393 2.83637i 0.307673 0.223537i
\(162\) −0.122543 0.0890324i −0.00962785 0.00699505i
\(163\) 2.42670 + 7.46861i 0.190074 + 0.584987i 0.999999 0.00154665i \(-0.000492315\pi\)
−0.809925 + 0.586533i \(0.800492\pi\)
\(164\) 18.4650 1.44187
\(165\) 0 0
\(166\) 0.246259 0.0191134
\(167\) 1.66949 + 5.13817i 0.129189 + 0.397603i 0.994641 0.103389i \(-0.0329686\pi\)
−0.865452 + 0.500992i \(0.832969\pi\)
\(168\) 1.07415 + 0.780415i 0.0828724 + 0.0602103i
\(169\) 9.57415 6.95603i 0.736473 0.535079i
\(170\) −0.726850 + 2.23701i −0.0557468 + 0.171571i
\(171\) −10.8659 + 33.4417i −0.830932 + 2.55735i
\(172\) 8.40749 6.10840i 0.641065 0.465761i
\(173\) −15.9547 11.5918i −1.21302 0.881307i −0.217515 0.976057i \(-0.569795\pi\)
−0.995501 + 0.0947496i \(0.969795\pi\)
\(174\) 0.126341 + 0.388836i 0.00957785 + 0.0294776i
\(175\) −2.88781 −0.218298
\(176\) 0 0
\(177\) −18.4435 −1.38630
\(178\) −0.177084 0.545009i −0.0132730 0.0408501i
\(179\) 18.8737 + 13.7125i 1.41069 + 1.02492i 0.993222 + 0.116229i \(0.0370806\pi\)
0.417463 + 0.908694i \(0.362919\pi\)
\(180\) −21.0272 + 15.2772i −1.56728 + 1.13869i
\(181\) 0.953318 2.93401i 0.0708596 0.218083i −0.909355 0.416021i \(-0.863424\pi\)
0.980215 + 0.197938i \(0.0634243\pi\)
\(182\) −0.0401566 + 0.123589i −0.00297660 + 0.00916105i
\(183\) −21.9434 + 15.9428i −1.62210 + 1.17853i
\(184\) −1.87270 1.36060i −0.138057 0.100304i
\(185\) −1.33242 4.10076i −0.0979614 0.301494i
\(186\) 2.68978 0.197224
\(187\) 0 0
\(188\) 3.76030 0.274248
\(189\) −1.42061 4.37220i −0.103334 0.318031i
\(190\) 2.06313 + 1.49895i 0.149675 + 0.108745i
\(191\) −10.1705 + 7.38933i −0.735914 + 0.534673i −0.891429 0.453161i \(-0.850296\pi\)
0.155515 + 0.987834i \(0.450296\pi\)
\(192\) −6.54690 + 20.1493i −0.472482 + 1.45415i
\(193\) 6.38693 19.6569i 0.459741 1.41494i −0.405737 0.913990i \(-0.632985\pi\)
0.865478 0.500947i \(-0.167015\pi\)
\(194\) 0.887568 0.644856i 0.0637237 0.0462980i
\(195\) −6.79000 4.93322i −0.486242 0.353275i
\(196\) −0.613557 1.88834i −0.0438255 0.134881i
\(197\) −6.27954 −0.447399 −0.223699 0.974658i \(-0.571813\pi\)
−0.223699 + 0.974658i \(0.571813\pi\)
\(198\) 0 0
\(199\) −6.86896 −0.486927 −0.243464 0.969910i \(-0.578284\pi\)
−0.243464 + 0.969910i \(0.578284\pi\)
\(200\) 0.428073 + 1.31747i 0.0302693 + 0.0931594i
\(201\) 4.61506 + 3.35304i 0.325521 + 0.236505i
\(202\) 0.461924 0.335607i 0.0325009 0.0236133i
\(203\) 0.379245 1.16720i 0.0266178 0.0819212i
\(204\) 11.8168 36.3682i 0.827338 2.54629i
\(205\) −21.1306 + 15.3523i −1.47583 + 1.07225i
\(206\) 0.0341683 + 0.0248247i 0.00238062 + 0.00172962i
\(207\) 6.95024 + 21.3906i 0.483075 + 1.48675i
\(208\) −4.22508 −0.292957
\(209\) 0 0
\(210\) −0.935623 −0.0645641
\(211\) −3.17009 9.75652i −0.218238 0.671667i −0.998908 0.0467233i \(-0.985122\pi\)
0.780670 0.624943i \(-0.214878\pi\)
\(212\) −6.14499 4.46459i −0.422039 0.306630i
\(213\) −28.0378 + 20.3707i −1.92112 + 1.39578i
\(214\) 0.0947586 0.291637i 0.00647756 0.0199359i
\(215\) −4.54252 + 13.9804i −0.309797 + 0.953457i
\(216\) −1.78409 + 1.29622i −0.121392 + 0.0881966i
\(217\) −6.53207 4.74583i −0.443426 0.322168i
\(218\) −0.141900 0.436724i −0.00961070 0.0295787i
\(219\) −7.10527 −0.480130
\(220\) 0 0
\(221\) 7.51268 0.505358
\(222\) −0.158047 0.486417i −0.0106074 0.0326462i
\(223\) 10.9396 + 7.94808i 0.732570 + 0.532243i 0.890375 0.455227i \(-0.150442\pi\)
−0.157806 + 0.987470i \(0.550442\pi\)
\(224\) −1.15721 + 0.840765i −0.0773196 + 0.0561760i
\(225\) 4.15934 12.8011i 0.277290 0.853410i
\(226\) −0.0860905 + 0.264959i −0.00572666 + 0.0176248i
\(227\) 10.9836 7.98003i 0.729005 0.529653i −0.160243 0.987078i \(-0.551228\pi\)
0.889249 + 0.457424i \(0.151228\pi\)
\(228\) −33.5413 24.3692i −2.22133 1.61389i
\(229\) −0.448988 1.38184i −0.0296700 0.0913148i 0.935125 0.354318i \(-0.115287\pi\)
−0.964795 + 0.263003i \(0.915287\pi\)
\(230\) 1.63119 0.107557
\(231\) 0 0
\(232\) −0.588713 −0.0386509
\(233\) −2.53514 7.80234i −0.166082 0.511149i 0.833032 0.553225i \(-0.186603\pi\)
−0.999114 + 0.0420760i \(0.986603\pi\)
\(234\) −0.490010 0.356013i −0.0320330 0.0232733i
\(235\) −4.30314 + 3.12641i −0.280706 + 0.203945i
\(236\) 4.08843 12.5829i 0.266134 0.819077i
\(237\) 13.1105 40.3499i 0.851617 2.62101i
\(238\) 0.677550 0.492269i 0.0439191 0.0319091i
\(239\) 8.40045 + 6.10329i 0.543380 + 0.394789i 0.825339 0.564638i \(-0.190984\pi\)
−0.281959 + 0.959427i \(0.590984\pi\)
\(240\) −9.40034 28.9313i −0.606790 1.86751i
\(241\) 8.20445 0.528495 0.264248 0.964455i \(-0.414876\pi\)
0.264248 + 0.964455i \(0.414876\pi\)
\(242\) 0 0
\(243\) −17.2749 −1.10818
\(244\) −6.01257 18.5048i −0.384915 1.18465i
\(245\) 2.27214 + 1.65081i 0.145162 + 0.105466i
\(246\) −2.50644 + 1.82103i −0.159805 + 0.116105i
\(247\) 2.51700 7.74653i 0.160153 0.492900i
\(248\) −1.19686 + 3.68354i −0.0760004 + 0.233905i
\(249\) 4.58152 3.32867i 0.290342 0.210946i
\(250\) 0.577630 + 0.419673i 0.0365325 + 0.0265424i
\(251\) −5.08184 15.6403i −0.320763 0.987207i −0.973317 0.229465i \(-0.926302\pi\)
0.652554 0.757742i \(-0.273698\pi\)
\(252\) 9.25435 0.582969
\(253\) 0 0
\(254\) 1.18512 0.0743608
\(255\) 16.7149 + 51.4432i 1.04673 + 3.22150i
\(256\) −12.0168 8.73074i −0.751052 0.545671i
\(257\) 9.74377 7.07926i 0.607800 0.441592i −0.240839 0.970565i \(-0.577423\pi\)
0.848639 + 0.528973i \(0.177423\pi\)
\(258\) −0.538816 + 1.65831i −0.0335452 + 0.103242i
\(259\) −0.474419 + 1.46011i −0.0294790 + 0.0907270i
\(260\) 4.87081 3.53885i 0.302075 0.219470i
\(261\) 4.62774 + 3.36225i 0.286450 + 0.208118i
\(262\) 0.609157 + 1.87479i 0.0376339 + 0.115825i
\(263\) −1.87602 −0.115681 −0.0578403 0.998326i \(-0.518421\pi\)
−0.0578403 + 0.998326i \(0.518421\pi\)
\(264\) 0 0
\(265\) 10.7441 0.660003
\(266\) −0.280590 0.863568i −0.0172041 0.0529487i
\(267\) −10.6614 7.74596i −0.652467 0.474045i
\(268\) −3.31062 + 2.40531i −0.202228 + 0.146927i
\(269\) −4.33520 + 13.3424i −0.264322 + 0.813498i 0.727527 + 0.686079i \(0.240669\pi\)
−0.991849 + 0.127419i \(0.959331\pi\)
\(270\) 0.480216 1.47795i 0.0292250 0.0899453i
\(271\) 1.09482 0.795435i 0.0665058 0.0483193i −0.554036 0.832493i \(-0.686913\pi\)
0.620541 + 0.784174i \(0.286913\pi\)
\(272\) 22.0294 + 16.0053i 1.33573 + 0.970462i
\(273\) 0.923456 + 2.84210i 0.0558901 + 0.172012i
\(274\) 1.71081 0.103354
\(275\) 0 0
\(276\) −26.5190 −1.59626
\(277\) 4.13573 + 12.7285i 0.248492 + 0.764780i 0.995042 + 0.0994513i \(0.0317087\pi\)
−0.746550 + 0.665329i \(0.768291\pi\)
\(278\) 0.893829 + 0.649405i 0.0536083 + 0.0389487i
\(279\) 30.4456 22.1200i 1.82273 1.32429i
\(280\) 0.416320 1.28130i 0.0248798 0.0765723i
\(281\) −0.716570 + 2.20538i −0.0427470 + 0.131562i −0.970152 0.242496i \(-0.922034\pi\)
0.927405 + 0.374058i \(0.122034\pi\)
\(282\) −0.510422 + 0.370843i −0.0303952 + 0.0220834i
\(283\) −18.0151 13.0887i −1.07089 0.778045i −0.0948154 0.995495i \(-0.530226\pi\)
−0.976071 + 0.217450i \(0.930226\pi\)
\(284\) −7.68247 23.6442i −0.455871 1.40303i
\(285\) 58.6445 3.47380
\(286\) 0 0
\(287\) 9.29986 0.548953
\(288\) −2.06021 6.34068i −0.121399 0.373628i
\(289\) −25.4175 18.4669i −1.49515 1.08629i
\(290\) 0.335626 0.243847i 0.0197086 0.0143192i
\(291\) 7.79625 23.9944i 0.457024 1.40658i
\(292\) 1.57505 4.84751i 0.0921729 0.283679i
\(293\) −1.97384 + 1.43408i −0.115313 + 0.0837800i −0.643947 0.765070i \(-0.722704\pi\)
0.528634 + 0.848850i \(0.322704\pi\)
\(294\) 0.269513 + 0.195813i 0.0157183 + 0.0114200i
\(295\) 5.78312 + 17.7986i 0.336706 + 1.03628i
\(296\) 0.736455 0.0428056
\(297\) 0 0
\(298\) 1.39858 0.0810176
\(299\) −1.60998 4.95499i −0.0931073 0.286555i
\(300\) 12.8393 + 9.32828i 0.741276 + 0.538569i
\(301\) 4.23441 3.07648i 0.244068 0.177325i
\(302\) 0.666318 2.05071i 0.0383423 0.118005i
\(303\) 4.05746 12.4876i 0.233095 0.717393i
\(304\) 23.8841 17.3528i 1.36984 0.995250i
\(305\) 22.2659 + 16.1771i 1.27494 + 0.926301i
\(306\) 1.20626 + 3.71247i 0.0689571 + 0.212228i
\(307\) 8.89055 0.507410 0.253705 0.967282i \(-0.418351\pi\)
0.253705 + 0.967282i \(0.418351\pi\)
\(308\) 0 0
\(309\) 0.971237 0.0552517
\(310\) −0.843404 2.59573i −0.0479021 0.147428i
\(311\) 9.57449 + 6.95627i 0.542919 + 0.394454i 0.825168 0.564887i \(-0.191080\pi\)
−0.282249 + 0.959341i \(0.591080\pi\)
\(312\) 1.15973 0.842594i 0.0656569 0.0477025i
\(313\) −9.12853 + 28.0947i −0.515975 + 1.58801i 0.265525 + 0.964104i \(0.414455\pi\)
−0.781501 + 0.623905i \(0.785545\pi\)
\(314\) −0.276273 + 0.850282i −0.0155910 + 0.0479842i
\(315\) −10.5903 + 7.69432i −0.596697 + 0.433526i
\(316\) 24.6221 + 17.8890i 1.38510 + 1.00634i
\(317\) −7.77317 23.9233i −0.436585 1.34367i −0.891454 0.453111i \(-0.850314\pi\)
0.454870 0.890558i \(-0.349686\pi\)
\(318\) 1.27442 0.0714660
\(319\) 0 0
\(320\) 21.4976 1.20175
\(321\) −2.17910 6.70659i −0.121626 0.374325i
\(322\) −0.469876 0.341385i −0.0261852 0.0190246i
\(323\) −42.4686 + 30.8553i −2.36302 + 1.71683i
\(324\) 0.772152 2.37644i 0.0428973 0.132024i
\(325\) −0.963484 + 2.96530i −0.0534445 + 0.164485i
\(326\) 0.764668 0.555564i 0.0423510 0.0307698i
\(327\) −8.54315 6.20696i −0.472437 0.343246i
\(328\) −1.37856 4.24276i −0.0761181 0.234267i
\(329\) 1.89387 0.104412
\(330\) 0 0
\(331\) −9.46333 −0.520152 −0.260076 0.965588i \(-0.583748\pi\)
−0.260076 + 0.965588i \(0.583748\pi\)
\(332\) 1.25535 + 3.86358i 0.0688964 + 0.212041i
\(333\) −5.78910 4.20603i −0.317241 0.230489i
\(334\) 0.526067 0.382210i 0.0287851 0.0209136i
\(335\) 1.78871 5.50508i 0.0977276 0.300775i
\(336\) −3.34707 + 10.3012i −0.182598 + 0.561979i
\(337\) −13.9352 + 10.1245i −0.759098 + 0.551517i −0.898634 0.438700i \(-0.855439\pi\)
0.139535 + 0.990217i \(0.455439\pi\)
\(338\) −1.15234 0.837227i −0.0626792 0.0455391i
\(339\) 1.97977 + 6.09310i 0.107526 + 0.330932i
\(340\) −38.8019 −2.10433
\(341\) 0 0
\(342\) 4.23217 0.228850
\(343\) −0.309017 0.951057i −0.0166853 0.0513522i
\(344\) −2.03123 1.47578i −0.109517 0.0795685i
\(345\) 30.3474 22.0487i 1.63385 1.18706i
\(346\) −0.733493 + 2.25746i −0.0394328 + 0.121362i
\(347\) 2.69922 8.30733i 0.144902 0.445961i −0.852097 0.523384i \(-0.824669\pi\)
0.996998 + 0.0774232i \(0.0246693\pi\)
\(348\) −5.45644 + 3.96433i −0.292496 + 0.212511i
\(349\) −24.2584 17.6248i −1.29852 0.943433i −0.298584 0.954383i \(-0.596514\pi\)
−0.999940 + 0.0109508i \(0.996514\pi\)
\(350\) 0.107407 + 0.330565i 0.00574116 + 0.0176695i
\(351\) −4.96348 −0.264931
\(352\) 0 0
\(353\) 7.31999 0.389604 0.194802 0.980843i \(-0.437594\pi\)
0.194802 + 0.980843i \(0.437594\pi\)
\(354\) 0.685973 + 2.11121i 0.0364590 + 0.112209i
\(355\) 28.4500 + 20.6701i 1.50997 + 1.09706i
\(356\) 7.64796 5.55657i 0.405341 0.294498i
\(357\) 5.95149 18.3168i 0.314986 0.969427i
\(358\) 0.867687 2.67047i 0.0458587 0.141139i
\(359\) 4.02078 2.92127i 0.212209 0.154179i −0.476604 0.879118i \(-0.658132\pi\)
0.688812 + 0.724940i \(0.258132\pi\)
\(360\) 5.08013 + 3.69093i 0.267747 + 0.194529i
\(361\) 11.7160 + 36.0580i 0.616630 + 1.89779i
\(362\) −0.371311 −0.0195156
\(363\) 0 0
\(364\) −2.14371 −0.112361
\(365\) 2.22792 + 6.85685i 0.116615 + 0.358904i
\(366\) 2.64110 + 1.91887i 0.138053 + 0.100301i
\(367\) 11.4915 8.34904i 0.599850 0.435816i −0.245976 0.969276i \(-0.579108\pi\)
0.845825 + 0.533460i \(0.179108\pi\)
\(368\) 5.83537 17.9594i 0.304190 0.936200i
\(369\) −13.3947 + 41.2245i −0.697298 + 2.14606i
\(370\) −0.419854 + 0.305041i −0.0218271 + 0.0158583i
\(371\) −3.09491 2.24858i −0.160680 0.116741i
\(372\) 13.7116 + 42.2001i 0.710916 + 2.18797i
\(373\) −8.97781 −0.464853 −0.232427 0.972614i \(-0.574667\pi\)
−0.232427 + 0.972614i \(0.574667\pi\)
\(374\) 0 0
\(375\) 16.4192 0.847883
\(376\) −0.280736 0.864015i −0.0144778 0.0445582i
\(377\) −1.07198 0.778842i −0.0552100 0.0401124i
\(378\) −0.447644 + 0.325233i −0.0230243 + 0.0167282i
\(379\) 3.33416 10.2615i 0.171264 0.527097i −0.828179 0.560464i \(-0.810623\pi\)
0.999443 + 0.0333665i \(0.0106228\pi\)
\(380\) −13.0000 + 40.0097i −0.666884 + 2.05246i
\(381\) 22.0484 16.0191i 1.12958 0.820685i
\(382\) 1.22412 + 0.889379i 0.0626317 + 0.0455046i
\(383\) −7.26498 22.3593i −0.371223 1.14251i −0.945991 0.324192i \(-0.894908\pi\)
0.574768 0.818316i \(-0.305092\pi\)
\(384\) 10.4682 0.534202
\(385\) 0 0
\(386\) −2.48766 −0.126619
\(387\) 7.53861 + 23.2015i 0.383209 + 1.17940i
\(388\) 14.6417 + 10.6379i 0.743322 + 0.540055i
\(389\) 9.60671 6.97968i 0.487079 0.353884i −0.316981 0.948432i \(-0.602669\pi\)
0.804060 + 0.594548i \(0.202669\pi\)
\(390\) −0.312159 + 0.960727i −0.0158068 + 0.0486483i
\(391\) −10.3760 + 31.9339i −0.524735 + 1.61497i
\(392\) −0.388082 + 0.281958i −0.0196011 + 0.0142410i
\(393\) 36.6745 + 26.6456i 1.84998 + 1.34409i
\(394\) 0.233556 + 0.718813i 0.0117664 + 0.0362133i
\(395\) −43.0501 −2.16608
\(396\) 0 0
\(397\) −23.7264 −1.19079 −0.595397 0.803431i \(-0.703005\pi\)
−0.595397 + 0.803431i \(0.703005\pi\)
\(398\) 0.255479 + 0.786283i 0.0128060 + 0.0394128i
\(399\) −16.8930 12.2735i −0.845708 0.614443i
\(400\) −9.14259 + 6.64248i −0.457129 + 0.332124i
\(401\) −1.17464 + 3.61517i −0.0586587 + 0.180533i −0.976092 0.217356i \(-0.930257\pi\)
0.917434 + 0.397888i \(0.130257\pi\)
\(402\) 0.212170 0.652992i 0.0105821 0.0325683i
\(403\) −7.05251 + 5.12395i −0.351311 + 0.255242i
\(404\) 7.62011 + 5.53634i 0.379115 + 0.275443i
\(405\) 1.09222 + 3.36149i 0.0542726 + 0.167034i
\(406\) −0.147713 −0.00733089
\(407\) 0 0
\(408\) −9.23866 −0.457382
\(409\) 1.84882 + 5.69009i 0.0914183 + 0.281357i 0.986304 0.164939i \(-0.0527428\pi\)
−0.894885 + 0.446296i \(0.852743\pi\)
\(410\) 2.54328 + 1.84780i 0.125604 + 0.0912564i
\(411\) 31.8288 23.1249i 1.57000 1.14067i
\(412\) −0.215298 + 0.662618i −0.0106070 + 0.0326449i
\(413\) 2.05913 6.33736i 0.101323 0.311841i
\(414\) 2.19006 1.59117i 0.107636 0.0782019i
\(415\) −4.64886 3.37760i −0.228204 0.165800i
\(416\) 0.477234 + 1.46877i 0.0233983 + 0.0720126i
\(417\) 25.4072 1.24419
\(418\) 0 0
\(419\) −4.16889 −0.203664 −0.101832 0.994802i \(-0.532470\pi\)
−0.101832 + 0.994802i \(0.532470\pi\)
\(420\) −4.76952 14.6791i −0.232729 0.716265i
\(421\) −18.9759 13.7868i −0.924828 0.671927i 0.0198933 0.999802i \(-0.493667\pi\)
−0.944721 + 0.327875i \(0.893667\pi\)
\(422\) −0.998914 + 0.725753i −0.0486264 + 0.0353291i
\(423\) −2.72775 + 8.39515i −0.132628 + 0.408186i
\(424\) −0.567073 + 1.74527i −0.0275395 + 0.0847579i
\(425\) 16.2566 11.8111i 0.788560 0.572922i
\(426\) 3.37463 + 2.45181i 0.163501 + 0.118791i
\(427\) −3.02822 9.31990i −0.146546 0.451022i
\(428\) 5.05856 0.244515
\(429\) 0 0
\(430\) 1.76928 0.0853221
\(431\) −11.5180 35.4487i −0.554802 1.70751i −0.696465 0.717591i \(-0.745245\pi\)
0.141663 0.989915i \(-0.454755\pi\)
\(432\) −14.5544 10.5744i −0.700248 0.508760i
\(433\) 18.4345 13.3935i 0.885906 0.643648i −0.0489013 0.998804i \(-0.515572\pi\)
0.934807 + 0.355155i \(0.115572\pi\)
\(434\) −0.300302 + 0.924233i −0.0144149 + 0.0443646i
\(435\) 2.94808 9.07326i 0.141350 0.435030i
\(436\) 6.12844 4.45257i 0.293499 0.213239i
\(437\) 29.4517 + 21.3979i 1.40886 + 1.02360i
\(438\) 0.264268 + 0.813334i 0.0126272 + 0.0388626i
\(439\) 1.42974 0.0682379 0.0341189 0.999418i \(-0.489137\pi\)
0.0341189 + 0.999418i \(0.489137\pi\)
\(440\) 0 0
\(441\) 4.66094 0.221949
\(442\) −0.279421 0.859969i −0.0132907 0.0409046i
\(443\) 21.3824 + 15.5352i 1.01591 + 0.738101i 0.965440 0.260624i \(-0.0839284\pi\)
0.0504690 + 0.998726i \(0.483928\pi\)
\(444\) 6.82577 4.95921i 0.323937 0.235354i
\(445\) −4.13215 + 12.7175i −0.195883 + 0.602865i
\(446\) 0.502930 1.54786i 0.0238144 0.0732933i
\(447\) 26.0198 18.9045i 1.23070 0.894152i
\(448\) −6.19256 4.49915i −0.292571 0.212565i
\(449\) 4.35312 + 13.3975i 0.205436 + 0.632268i 0.999695 + 0.0246886i \(0.00785943\pi\)
−0.794259 + 0.607580i \(0.792141\pi\)
\(450\) −1.62003 −0.0763691
\(451\) 0 0
\(452\) −4.59583 −0.216170
\(453\) −15.3229 47.1590i −0.719932 2.21572i
\(454\) −1.32198 0.960476i −0.0620437 0.0450774i
\(455\) 2.45318 1.78234i 0.115007 0.0835572i
\(456\) −3.09526 + 9.52624i −0.144949 + 0.446107i
\(457\) −9.11071 + 28.0399i −0.426181 + 1.31165i 0.475678 + 0.879620i \(0.342203\pi\)
−0.901859 + 0.432031i \(0.857797\pi\)
\(458\) −0.141479 + 0.102791i −0.00661088 + 0.00480309i
\(459\) 25.8794 + 18.8025i 1.20795 + 0.877624i
\(460\) 8.31530 + 25.5918i 0.387703 + 1.19323i
\(461\) −31.7282 −1.47773 −0.738866 0.673853i \(-0.764638\pi\)
−0.738866 + 0.673853i \(0.764638\pi\)
\(462\) 0 0
\(463\) −12.7839 −0.594117 −0.297059 0.954859i \(-0.596006\pi\)
−0.297059 + 0.954859i \(0.596006\pi\)
\(464\) −1.48410 4.56758i −0.0688975 0.212045i
\(465\) −50.7774 36.8919i −2.35474 1.71082i
\(466\) −0.798837 + 0.580389i −0.0370054 + 0.0268860i
\(467\) 9.13972 28.1292i 0.422936 1.30166i −0.482021 0.876160i \(-0.660097\pi\)
0.904957 0.425503i \(-0.139903\pi\)
\(468\) 3.08760 9.50266i 0.142724 0.439260i
\(469\) −1.66739 + 1.21143i −0.0769928 + 0.0559385i
\(470\) 0.517925 + 0.376295i 0.0238901 + 0.0173572i
\(471\) 6.35328 + 19.5534i 0.292744 + 0.900973i
\(472\) −3.19645 −0.147129
\(473\) 0 0
\(474\) −5.10644 −0.234546
\(475\) −6.73224 20.7197i −0.308897 0.950686i
\(476\) 11.1772 + 8.12070i 0.512306 + 0.372212i
\(477\) 14.4252 10.4805i 0.660484 0.479869i
\(478\) 0.386197 1.18859i 0.0176643 0.0543650i
\(479\) 8.82473 27.1597i 0.403212 1.24096i −0.519167 0.854673i \(-0.673758\pi\)
0.922379 0.386286i \(-0.126242\pi\)
\(480\) −8.99566 + 6.53573i −0.410594 + 0.298314i
\(481\) 1.34101 + 0.974297i 0.0611446 + 0.0444241i
\(482\) −0.305150 0.939156i −0.0138992 0.0427774i
\(483\) −13.3563 −0.607731
\(484\) 0 0
\(485\) −25.6000 −1.16244
\(486\) 0.642509 + 1.97744i 0.0291448 + 0.0896985i
\(487\) −0.856166 0.622041i −0.0387966 0.0281874i 0.568218 0.822878i \(-0.307633\pi\)
−0.607015 + 0.794691i \(0.707633\pi\)
\(488\) −3.80302 + 2.76306i −0.172155 + 0.125078i
\(489\) 6.71671 20.6719i 0.303740 0.934816i
\(490\) 0.104458 0.321489i 0.00471894 0.0145234i
\(491\) 14.9255 10.8440i 0.673577 0.489382i −0.197644 0.980274i \(-0.563329\pi\)
0.871221 + 0.490892i \(0.163329\pi\)
\(492\) −41.3473 30.0406i −1.86408 1.35434i
\(493\) 2.63890 + 8.12169i 0.118850 + 0.365782i
\(494\) −0.980354 −0.0441082
\(495\) 0 0
\(496\) −31.5962 −1.41871
\(497\) −3.86926 11.9084i −0.173560 0.534163i
\(498\) −0.551431 0.400638i −0.0247102 0.0179530i
\(499\) −25.6695 + 18.6500i −1.14913 + 0.834889i −0.988365 0.152104i \(-0.951395\pi\)
−0.160762 + 0.986993i \(0.551395\pi\)
\(500\) −3.63970 + 11.2018i −0.162772 + 0.500962i
\(501\) 4.62088 14.2216i 0.206446 0.635375i
\(502\) −1.60132 + 1.16343i −0.0714704 + 0.0519263i
\(503\) −23.4844 17.0624i −1.04712 0.760775i −0.0754549 0.997149i \(-0.524041\pi\)
−0.971662 + 0.236374i \(0.924041\pi\)
\(504\) −0.690910 2.12640i −0.0307756 0.0947175i
\(505\) −13.3232 −0.592876
\(506\) 0 0
\(507\) −32.7555 −1.45472
\(508\) 6.04136 + 18.5934i 0.268042 + 0.824948i
\(509\) −2.33669 1.69770i −0.103572 0.0752494i 0.534794 0.844983i \(-0.320389\pi\)
−0.638366 + 0.769733i \(0.720389\pi\)
\(510\) 5.26697 3.82668i 0.233225 0.169448i
\(511\) 0.793272 2.44144i 0.0350923 0.108003i
\(512\) −2.88991 + 8.89422i −0.127717 + 0.393073i
\(513\) 28.0582 20.3855i 1.23880 0.900041i
\(514\) −1.17276 0.852059i −0.0517282 0.0375827i
\(515\) −0.304540 0.937279i −0.0134197 0.0413014i
\(516\) −28.7640 −1.26626
\(517\) 0 0
\(518\) 0.184783 0.00811890
\(519\) 16.8677 + 51.9134i 0.740409 + 2.27874i
\(520\) −1.17678 0.854980i −0.0516052 0.0374933i
\(521\) −25.6222 + 18.6157i −1.12253 + 0.815567i −0.984591 0.174874i \(-0.944048\pi\)
−0.137940 + 0.990441i \(0.544048\pi\)
\(522\) 0.212753 0.654786i 0.00931193 0.0286592i
\(523\) 4.95603 15.2531i 0.216712 0.666971i −0.782316 0.622882i \(-0.785962\pi\)
0.999028 0.0440888i \(-0.0140384\pi\)
\(524\) −26.3085 + 19.1142i −1.14929 + 0.835009i
\(525\) 6.46648 + 4.69817i 0.282220 + 0.205045i
\(526\) 0.0697754 + 0.214747i 0.00304235 + 0.00936340i
\(527\) 56.1818 2.44732
\(528\) 0 0
\(529\) 0.285644 0.0124193
\(530\) −0.399607 1.22986i −0.0173578 0.0534219i
\(531\) 25.1265 + 18.2555i 1.09040 + 0.792221i
\(532\) 12.1182 8.80440i 0.525391 0.381719i
\(533\) 3.10278 9.54938i 0.134396 0.413630i
\(534\) −0.490140 + 1.50850i −0.0212104 + 0.0652790i
\(535\) −5.78882 + 4.20583i −0.250273 + 0.181834i
\(536\) 0.799839 + 0.581117i 0.0345478 + 0.0251004i
\(537\) −19.9536 61.4110i −0.861063 2.65008i
\(538\) 1.68853 0.0727976
\(539\) 0 0
\(540\) 25.6357 1.10318
\(541\) −4.20098 12.9293i −0.180614 0.555873i 0.819231 0.573463i \(-0.194401\pi\)
−0.999845 + 0.0175903i \(0.994401\pi\)
\(542\) −0.131773 0.0957385i −0.00566013 0.00411232i
\(543\) −6.90803 + 5.01898i −0.296452 + 0.215385i
\(544\) 3.07568 9.46596i 0.131869 0.405850i
\(545\) −3.31116 + 10.1907i −0.141834 + 0.436522i
\(546\) 0.290987 0.211414i 0.0124531 0.00904769i
\(547\) −7.13946 5.18712i −0.305261 0.221785i 0.424599 0.905381i \(-0.360415\pi\)
−0.729861 + 0.683596i \(0.760415\pi\)
\(548\) 8.72120 + 26.8411i 0.372551 + 1.14660i
\(549\) 45.6749 1.94936
\(550\) 0 0
\(551\) 9.25862 0.394430
\(552\) 1.97986 + 6.09337i 0.0842682 + 0.259351i
\(553\) 12.4009 + 9.00978i 0.527340 + 0.383135i
\(554\) 1.30320 0.946827i 0.0553675 0.0402268i
\(555\) −3.68792 + 11.3503i −0.156544 + 0.481791i
\(556\) −5.63210 + 17.3338i −0.238854 + 0.735118i
\(557\) 27.5001 19.9800i 1.16522 0.846581i 0.174790 0.984606i \(-0.444075\pi\)
0.990429 + 0.138025i \(0.0440755\pi\)
\(558\) −3.66443 2.66236i −0.155128 0.112707i
\(559\) −1.74627 5.37446i −0.0738592 0.227315i
\(560\) 10.9906 0.464437
\(561\) 0 0
\(562\) 0.279099 0.0117731
\(563\) 6.25004 + 19.2357i 0.263408 + 0.810686i 0.992056 + 0.125798i \(0.0401491\pi\)
−0.728648 + 0.684888i \(0.759851\pi\)
\(564\) −8.42016 6.11761i −0.354553 0.257598i
\(565\) 5.25929 3.82110i 0.221260 0.160755i
\(566\) −0.828215 + 2.54899i −0.0348125 + 0.107142i
\(567\) 0.388893 1.19689i 0.0163320 0.0502646i
\(568\) −4.85925 + 3.53045i −0.203890 + 0.148135i
\(569\) 23.4073 + 17.0064i 0.981284 + 0.712944i 0.957995 0.286784i \(-0.0925864\pi\)
0.0232885 + 0.999729i \(0.492586\pi\)
\(570\) −2.18118 6.71298i −0.0913596 0.281176i
\(571\) 7.51312 0.314414 0.157207 0.987566i \(-0.449751\pi\)
0.157207 + 0.987566i \(0.449751\pi\)
\(572\) 0 0
\(573\) 34.7958 1.45362
\(574\) −0.345892 1.06455i −0.0144372 0.0444333i
\(575\) −11.2738 8.19091i −0.470151 0.341585i
\(576\) 28.8631 20.9703i 1.20263 0.873761i
\(577\) 10.6224 32.6924i 0.442216 1.36100i −0.443292 0.896377i \(-0.646190\pi\)
0.885508 0.464624i \(-0.153810\pi\)
\(578\) −1.16853 + 3.59636i −0.0486043 + 0.149589i
\(579\) −46.2816 + 33.6255i −1.92340 + 1.39743i
\(580\) 5.53664 + 4.02261i 0.229897 + 0.167030i
\(581\) 0.632256 + 1.94588i 0.0262304 + 0.0807289i
\(582\) −3.03658 −0.125870
\(583\) 0 0
\(584\) −1.23142 −0.0509565
\(585\) 4.36744 + 13.4416i 0.180571 + 0.555741i
\(586\) 0.237572 + 0.172606i 0.00981400 + 0.00713029i
\(587\) −34.0104 + 24.7100i −1.40376 + 1.01989i −0.409566 + 0.912280i \(0.634320\pi\)
−0.994193 + 0.107611i \(0.965680\pi\)
\(588\) −1.69823 + 5.22661i −0.0700338 + 0.215542i
\(589\) 18.8228 57.9306i 0.775580 2.38699i
\(590\) 1.82230 1.32398i 0.0750228 0.0545073i
\(591\) 14.0613 + 10.2162i 0.578406 + 0.420236i
\(592\) 1.85654 + 5.71385i 0.0763034 + 0.234838i
\(593\) −29.2867 −1.20266 −0.601331 0.799000i \(-0.705363\pi\)
−0.601331 + 0.799000i \(0.705363\pi\)
\(594\) 0 0
\(595\) −19.5425 −0.801165
\(596\) 7.12953 + 21.9424i 0.292037 + 0.898797i
\(597\) 15.3812 + 11.1751i 0.629509 + 0.457365i
\(598\) −0.507313 + 0.368585i −0.0207456 + 0.0150725i
\(599\) −4.68399 + 14.4158i −0.191383 + 0.589015i 0.808617 + 0.588335i \(0.200216\pi\)
−1.00000 0.000679814i \(0.999784\pi\)
\(600\) 1.18484 3.64655i 0.0483708 0.148870i
\(601\) 25.7862 18.7348i 1.05184 0.764207i 0.0792785 0.996853i \(-0.474738\pi\)
0.972561 + 0.232646i \(0.0747384\pi\)
\(602\) −0.509654 0.370285i −0.0207719 0.0150917i
\(603\) −2.96848 9.13605i −0.120886 0.372049i
\(604\) 35.5705 1.44734
\(605\) 0 0
\(606\) −1.58035 −0.0641974
\(607\) 6.22556 + 19.1603i 0.252688 + 0.777693i 0.994276 + 0.106838i \(0.0340726\pi\)
−0.741589 + 0.670855i \(0.765927\pi\)
\(608\) −8.73016 6.34283i −0.354055 0.257236i
\(609\) −2.74812 + 1.99663i −0.111360 + 0.0809075i
\(610\) 1.02364 3.15044i 0.0414460 0.127558i
\(611\) 0.631865 1.94468i 0.0255625 0.0786733i
\(612\) −52.0962 + 37.8501i −2.10586 + 1.53000i
\(613\) −3.14814 2.28726i −0.127152 0.0923815i 0.522391 0.852706i \(-0.325040\pi\)
−0.649544 + 0.760324i \(0.725040\pi\)
\(614\) −0.330668 1.01769i −0.0133447 0.0410707i
\(615\) 72.2929 2.91513
\(616\) 0 0
\(617\) 28.6122 1.15189 0.575943 0.817490i \(-0.304635\pi\)
0.575943 + 0.817490i \(0.304635\pi\)
\(618\) −0.0361235 0.111177i −0.00145310 0.00447218i
\(619\) 21.1595 + 15.3733i 0.850473 + 0.617905i 0.925276 0.379293i \(-0.123833\pi\)
−0.0748032 + 0.997198i \(0.523833\pi\)
\(620\) 36.4252 26.4645i 1.46287 1.06284i
\(621\) 6.85520 21.0981i 0.275090 0.846639i
\(622\) 0.440172 1.35471i 0.0176493 0.0543189i
\(623\) 3.85188 2.79856i 0.154322 0.112122i
\(624\) 9.46092 + 6.87376i 0.378740 + 0.275171i
\(625\) −9.61030 29.5775i −0.384412 1.18310i
\(626\) 3.55550 0.142106
\(627\) 0 0
\(628\) −14.7485 −0.588529
\(629\) −3.30114 10.1599i −0.131625 0.405101i
\(630\) 1.27465 + 0.926087i 0.0507833 + 0.0368962i
\(631\) 4.59742 3.34022i 0.183020 0.132972i −0.492503 0.870311i \(-0.663918\pi\)
0.675523 + 0.737339i \(0.263918\pi\)
\(632\) 2.27219 6.99307i 0.0903827 0.278169i
\(633\) −8.77429 + 27.0045i −0.348747 + 1.07333i
\(634\) −2.44937 + 1.77957i −0.0972771 + 0.0706759i
\(635\) −22.3725 16.2546i −0.887827 0.645044i
\(636\) 6.49661 + 19.9945i 0.257607 + 0.792834i
\(637\) −1.07967 −0.0427782
\(638\) 0 0
\(639\) 58.3605 2.30870
\(640\) −3.28240 10.1022i −0.129748 0.399324i
\(641\) 16.7703 + 12.1843i 0.662387 + 0.481252i 0.867468 0.497493i \(-0.165746\pi\)
−0.205081 + 0.978745i \(0.565746\pi\)
\(642\) −0.686649 + 0.498879i −0.0270999 + 0.0196892i
\(643\) 6.57453 20.2343i 0.259274 0.797964i −0.733683 0.679492i \(-0.762200\pi\)
0.992957 0.118472i \(-0.0377997\pi\)
\(644\) 2.96073 9.11220i 0.116669 0.359071i
\(645\) 32.9164 23.9152i 1.29608 0.941659i
\(646\) 5.11152 + 3.71373i 0.201110 + 0.146115i
\(647\) −5.33727 16.4264i −0.209830 0.645790i −0.999480 0.0322329i \(-0.989738\pi\)
0.789651 0.613557i \(-0.210262\pi\)
\(648\) −0.603690 −0.0237152
\(649\) 0 0
\(650\) 0.375270 0.0147193
\(651\) 6.90584 + 21.2540i 0.270661 + 0.833010i
\(652\) 12.6143 + 9.16484i 0.494015 + 0.358923i
\(653\) −33.2334 + 24.1455i −1.30052 + 0.944886i −0.999961 0.00887528i \(-0.997175\pi\)
−0.300564 + 0.953762i \(0.597175\pi\)
\(654\) −0.392757 + 1.20878i −0.0153580 + 0.0472671i
\(655\) 14.2143 43.7472i 0.555399 1.70934i
\(656\) 29.4426 21.3913i 1.14954 0.835190i
\(657\) 9.67989 + 7.03285i 0.377649 + 0.274378i
\(658\) −0.0704390 0.216789i −0.00274600 0.00845132i
\(659\) −6.00410 −0.233887 −0.116943 0.993139i \(-0.537310\pi\)
−0.116943 + 0.993139i \(0.537310\pi\)
\(660\) 0 0
\(661\) −1.83502 −0.0713739 −0.0356870 0.999363i \(-0.511362\pi\)
−0.0356870 + 0.999363i \(0.511362\pi\)
\(662\) 0.351972 + 1.08326i 0.0136798 + 0.0421020i
\(663\) −16.8226 12.2223i −0.653336 0.474676i
\(664\) 0.794025 0.576893i 0.0308142 0.0223878i
\(665\) −6.54740 + 20.1508i −0.253897 + 0.781416i
\(666\) −0.266144 + 0.819108i −0.0103129 + 0.0317398i
\(667\) 4.79115 3.48097i 0.185514 0.134784i
\(668\) 8.67825 + 6.30512i 0.335772 + 0.243952i
\(669\) −11.5656 35.5952i −0.447151 1.37619i
\(670\) −0.696689 −0.0269154
\(671\) 0 0
\(672\) 3.95910 0.152726
\(673\) −13.7328 42.2653i −0.529361 1.62921i −0.755527 0.655117i \(-0.772619\pi\)
0.226166 0.974089i \(-0.427381\pi\)
\(674\) 1.67724 + 1.21858i 0.0646048 + 0.0469381i
\(675\) −10.7404 + 7.80336i −0.413398 + 0.300352i
\(676\) 7.26102 22.3471i 0.279270 0.859505i
\(677\) −4.80433 + 14.7862i −0.184645 + 0.568280i −0.999942 0.0107634i \(-0.996574\pi\)
0.815297 + 0.579043i \(0.196574\pi\)
\(678\) 0.623838 0.453245i 0.0239583 0.0174068i
\(679\) 7.37429 + 5.35773i 0.282999 + 0.205611i
\(680\) 2.89687 + 8.91565i 0.111090 + 0.341899i
\(681\) −37.5774 −1.43997
\(682\) 0 0
\(683\) −36.8979 −1.41186 −0.705930 0.708282i \(-0.749471\pi\)
−0.705930 + 0.708282i \(0.749471\pi\)
\(684\) 21.5743 + 66.3989i 0.824914 + 2.53882i
\(685\) −32.2966 23.4649i −1.23399 0.896547i
\(686\) −0.0973732 + 0.0707458i −0.00371773 + 0.00270109i
\(687\) −1.24273 + 3.82472i −0.0474130 + 0.145922i
\(688\) 6.32937 19.4798i 0.241305 0.742660i
\(689\) −3.34150 + 2.42774i −0.127301 + 0.0924895i
\(690\) −3.65261 2.65377i −0.139052 0.101027i
\(691\) −5.77015 17.7587i −0.219507 0.675572i −0.998803 0.0489163i \(-0.984423\pi\)
0.779296 0.626656i \(-0.215577\pi\)
\(692\) −39.1566 −1.48851
\(693\) 0 0
\(694\) −1.05133 −0.0399078
\(695\) −7.96665 24.5188i −0.302192 0.930052i
\(696\) 1.31826 + 0.957775i 0.0499687 + 0.0363044i
\(697\) −52.3523 + 38.0362i −1.98299 + 1.44072i
\(698\) −1.11524 + 3.43236i −0.0422125 + 0.129917i
\(699\) −7.01685 + 21.5956i −0.265402 + 0.816822i
\(700\) −4.63874 + 3.37024i −0.175328 + 0.127383i
\(701\) −21.1419 15.3605i −0.798518 0.580157i 0.111961 0.993713i \(-0.464287\pi\)
−0.910479 + 0.413555i \(0.864287\pi\)
\(702\) 0.184608 + 0.568165i 0.00696758 + 0.0214440i
\(703\) −11.5821 −0.436828
\(704\) 0 0
\(705\) 14.7221 0.554465
\(706\) −0.272254 0.837913i −0.0102464 0.0315353i
\(707\) 3.83786 + 2.78837i 0.144337 + 0.104867i
\(708\) −29.6260 + 21.5246i −1.11341 + 0.808942i
\(709\) −5.08176 + 15.6401i −0.190850 + 0.587375i −1.00000 0.000226975i \(-0.999928\pi\)
0.809150 + 0.587602i \(0.199928\pi\)
\(710\) 1.30794 4.02543i 0.0490862 0.151072i
\(711\) −57.7998 + 41.9940i −2.16766 + 1.57490i
\(712\) −1.84773 1.34246i −0.0692467 0.0503107i
\(713\) −12.0398 37.0547i −0.450895 1.38771i
\(714\) −2.31806 −0.0867513
\(715\) 0 0
\(716\) 46.3204 1.73107
\(717\) −8.88113 27.3333i −0.331672 1.02078i
\(718\) −0.483941 0.351604i −0.0180605 0.0131217i
\(719\) 7.56360 5.49528i 0.282075 0.204939i −0.437747 0.899098i \(-0.644223\pi\)
0.719822 + 0.694159i \(0.244223\pi\)
\(720\) −15.8298 + 48.7192i −0.589943 + 1.81566i
\(721\) −0.108434 + 0.333726i −0.00403830 + 0.0124286i
\(722\) 3.69177 2.68223i 0.137394 0.0998223i
\(723\) −18.3716 13.3478i −0.683249 0.496409i
\(724\) −1.89283 5.82552i −0.0703463 0.216504i
\(725\) −3.54411 −0.131625
\(726\) 0 0
\(727\) 27.7523 1.02928 0.514638 0.857408i \(-0.327927\pi\)
0.514638 + 0.857408i \(0.327927\pi\)
\(728\) 0.160045 + 0.492567i 0.00593165 + 0.0182557i
\(729\) 35.6280 + 25.8853i 1.31956 + 0.958714i
\(730\) 0.702033 0.510057i 0.0259834 0.0188780i
\(731\) −11.2543 + 34.6373i −0.416257 + 1.28111i
\(732\) −16.6418 + 51.2183i −0.615100 + 1.89308i
\(733\) 1.17817 0.855990i 0.0435167 0.0316167i −0.565814 0.824533i \(-0.691438\pi\)
0.609331 + 0.792916i \(0.291438\pi\)
\(734\) −1.38311 1.00489i −0.0510516 0.0370911i
\(735\) −2.40216 7.39308i −0.0886049 0.272698i
\(736\) −6.90240 −0.254426
\(737\) 0 0
\(738\) 5.21712 0.192045
\(739\) 8.52782 + 26.2459i 0.313701 + 0.965472i 0.976286 + 0.216485i \(0.0694594\pi\)
−0.662585 + 0.748987i \(0.730541\pi\)
\(740\) −6.92610 5.03211i −0.254609 0.184984i
\(741\) −18.2389 + 13.2514i −0.670024 + 0.486801i
\(742\) −0.142284 + 0.437904i −0.00522339 + 0.0160759i
\(743\) −8.64546 + 26.6080i −0.317171 + 0.976153i 0.657680 + 0.753297i \(0.271538\pi\)
−0.974851 + 0.222855i \(0.928462\pi\)
\(744\) 8.67277 6.30114i 0.317959 0.231011i
\(745\) −26.4023 19.1824i −0.967305 0.702788i
\(746\) 0.333914 + 1.02768i 0.0122255 + 0.0376261i
\(747\) −9.53638 −0.348918
\(748\) 0 0
\(749\) 2.54774 0.0930922
\(750\) −0.610683 1.87949i −0.0222990 0.0686292i
\(751\) −27.5840 20.0409i −1.00655 0.731304i −0.0430704 0.999072i \(-0.513714\pi\)
−0.963483 + 0.267768i \(0.913714\pi\)
\(752\) 5.99582 4.35622i 0.218645 0.158855i
\(753\) −14.0657 + 43.2898i −0.512583 + 1.57757i
\(754\) −0.0492827 + 0.151677i −0.00179477 + 0.00552374i
\(755\) −40.7055 + 29.5743i −1.48142 + 1.07632i
\(756\) −7.38455 5.36519i −0.268574 0.195130i
\(757\) −12.2874 37.8168i −0.446594 1.37447i −0.880727 0.473625i \(-0.842945\pi\)
0.434133 0.900849i \(-0.357055\pi\)
\(758\) −1.29863 −0.0471684
\(759\) 0 0
\(760\) 10.1637 0.368677
\(761\) 1.18173 + 3.63699i 0.0428376 + 0.131841i 0.970188 0.242353i \(-0.0779194\pi\)
−0.927350 + 0.374194i \(0.877919\pi\)
\(762\) −2.65375 1.92806i −0.0961351 0.0698462i
\(763\) 3.08658 2.24253i 0.111742 0.0811850i
\(764\) −7.71332 + 23.7392i −0.279058 + 0.858853i
\(765\) 28.1473 86.6283i 1.01767 3.13205i
\(766\) −2.28924 + 1.66323i −0.0827137 + 0.0600950i
\(767\) −5.82039 4.22876i −0.210162 0.152692i
\(768\) 12.7044 + 39.1003i 0.458432 + 1.41091i
\(769\) 19.6583 0.708897 0.354449 0.935075i \(-0.384669\pi\)
0.354449 + 0.935075i \(0.384669\pi\)
\(770\) 0 0
\(771\) −33.3358 −1.20056
\(772\) −12.6813 39.0291i −0.456411 1.40469i
\(773\) 14.2359 + 10.3430i 0.512031 + 0.372012i 0.813593 0.581434i \(-0.197508\pi\)
−0.301563 + 0.953446i \(0.597508\pi\)
\(774\) 2.37546 1.72587i 0.0853842 0.0620353i
\(775\) −7.20518 + 22.1753i −0.258818 + 0.796559i
\(776\) 1.35117 4.15848i 0.0485043 0.149281i
\(777\) 3.43778 2.49770i 0.123330 0.0896044i
\(778\) −1.15626 0.840074i −0.0414540 0.0301181i
\(779\) 21.6804 + 66.7253i 0.776780 + 2.39068i
\(780\) −16.6642 −0.596675
\(781\) 0 0
\(782\) 4.04136 0.144519
\(783\) −1.74347 5.36584i −0.0623065 0.191760i
\(784\) −3.16592 2.30017i −0.113069 0.0821491i
\(785\) 16.8776 12.2623i 0.602388 0.437660i
\(786\) 1.68605 5.18913i 0.0601394 0.185090i
\(787\) 16.7168 51.4490i 0.595890 1.83396i 0.0456418 0.998958i \(-0.485467\pi\)
0.550248 0.835001i \(-0.314533\pi\)
\(788\) −10.0869 + 7.32857i −0.359331 + 0.261069i
\(789\) 4.20085 + 3.05209i 0.149554 + 0.108657i
\(790\) 1.60117 + 4.92790i 0.0569671 + 0.175327i
\(791\) −2.31468 −0.0823006
\(792\) 0 0
\(793\) −10.5803 −0.375717
\(794\) 0.882462 + 2.71594i 0.0313174 + 0.0963851i
\(795\) −24.0584 17.4795i −0.853265 0.619933i
\(796\) −11.0337 + 8.01646i −0.391079 + 0.284136i
\(797\) 11.2867 34.7368i 0.399794 1.23044i −0.525370 0.850874i \(-0.676073\pi\)
0.925164 0.379566i \(-0.123927\pi\)
\(798\) −0.776629 + 2.39022i −0.0274924 + 0.0846128i
\(799\) −10.6613 + 7.74587i −0.377169 + 0.274029i
\(800\) 3.34182 + 2.42797i 0.118151 + 0.0858418i
\(801\) 6.85758 + 21.1055i 0.242301 + 0.745725i
\(802\) 0.457513 0.0161554
\(803\) 0 0
\(804\) 11.3264 0.399452
\(805\) 4.18798 + 12.8893i 0.147607 + 0.454288i
\(806\) 0.848839 + 0.616718i 0.0298991 + 0.0217230i
\(807\) 31.4141 22.8237i 1.10583 0.803432i
\(808\) 0.703201 2.16423i 0.0247385 0.0761373i
\(809\) −14.5038 + 44.6382i −0.509928 + 1.56940i 0.282397 + 0.959298i \(0.408870\pi\)
−0.792325 + 0.610099i \(0.791130\pi\)
\(810\) 0.344164 0.250050i 0.0120927 0.00878585i
\(811\) −10.2434 7.44224i −0.359693 0.261332i 0.393231 0.919440i \(-0.371357\pi\)
−0.752924 + 0.658107i \(0.771357\pi\)
\(812\) −0.752997 2.31749i −0.0264250 0.0813278i
\(813\) −3.74565 −0.131366
\(814\) 0 0
\(815\) −22.0552 −0.772561
\(816\) −23.2899 71.6789i −0.815309 2.50926i
\(817\) 31.9449 + 23.2093i 1.11761 + 0.811992i
\(818\) 0.582575 0.423266i 0.0203693 0.0147991i
\(819\) 1.55506 4.78599i 0.0543383 0.167236i
\(820\) −16.0254 + 49.3212i −0.559632 + 1.72237i
\(821\) −39.8795 + 28.9742i −1.39180 + 1.01121i −0.396140 + 0.918190i \(0.629651\pi\)
−0.995665 + 0.0930154i \(0.970349\pi\)
\(822\) −3.83091 2.78332i −0.133618 0.0970793i
\(823\) 5.94113 + 18.2849i 0.207095 + 0.637373i 0.999621 + 0.0275344i \(0.00876559\pi\)
−0.792526 + 0.609838i \(0.791234\pi\)
\(824\) 0.168326 0.00586390
\(825\) 0 0
\(826\) −0.802017 −0.0279057
\(827\) −13.4861 41.5059i −0.468957 1.44330i −0.853937 0.520377i \(-0.825792\pi\)
0.384980 0.922925i \(-0.374208\pi\)
\(828\) 36.1283 + 26.2488i 1.25555 + 0.912207i
\(829\) 29.6968 21.5760i 1.03141 0.749364i 0.0628205 0.998025i \(-0.479990\pi\)
0.968591 + 0.248661i \(0.0799904\pi\)
\(830\) −0.213724 + 0.657775i −0.00741846 + 0.0228317i
\(831\) 11.4470 35.2304i 0.397094 1.22213i
\(832\) −6.68594 + 4.85762i −0.231793 + 0.168408i
\(833\) 5.62937 + 4.08998i 0.195046 + 0.141709i
\(834\) −0.944975 2.90833i −0.0327218 0.100707i
\(835\) −15.1733 −0.525094
\(836\) 0 0
\(837\) −37.1182 −1.28299
\(838\) 0.155055 + 0.477209i 0.00535628 + 0.0164849i
\(839\) −32.7284 23.7786i −1.12991 0.820928i −0.144228 0.989544i \(-0.546070\pi\)
−0.985682 + 0.168617i \(0.946070\pi\)
\(840\) −3.01678 + 2.19182i −0.104089 + 0.0756248i
\(841\) −8.49606 + 26.1482i −0.292968 + 0.901661i
\(842\) −0.872385 + 2.68493i −0.0300644 + 0.0925287i
\(843\) 5.19248 3.77256i 0.178839 0.129934i
\(844\) −16.4786 11.9724i −0.567215 0.412106i
\(845\) 10.2708 + 31.6102i 0.353326 + 1.08742i
\(846\) 1.06244 0.0365274
\(847\) 0 0
\(848\) −14.9704 −0.514085
\(849\) 19.0459 + 58.6174i 0.653655 + 2.01174i
\(850\) −1.95664 1.42158i −0.0671122 0.0487599i
\(851\) −5.99352 + 4.35455i −0.205455 + 0.149272i
\(852\) −21.2638 + 65.4434i −0.728487 + 2.24205i
\(853\) −7.87834 + 24.2470i −0.269749 + 0.830203i 0.720812 + 0.693131i \(0.243769\pi\)
−0.990561 + 0.137072i \(0.956231\pi\)
\(854\) −0.954211 + 0.693275i −0.0326524 + 0.0237234i
\(855\) −79.8946 58.0468i −2.73234 1.98516i
\(856\) −0.377661 1.16232i −0.0129082 0.0397274i
\(857\) −49.4756 −1.69005 −0.845027 0.534723i \(-0.820416\pi\)
−0.845027 + 0.534723i \(0.820416\pi\)
\(858\) 0 0
\(859\) 21.6779 0.739641 0.369821 0.929103i \(-0.379419\pi\)
0.369821 + 0.929103i \(0.379419\pi\)
\(860\) 9.01923 + 27.7583i 0.307553 + 0.946551i
\(861\) −20.8245 15.1299i −0.709697 0.515625i
\(862\) −3.62939 + 2.63691i −0.123618 + 0.0898134i
\(863\) 4.21494 12.9723i 0.143478 0.441581i −0.853334 0.521365i \(-0.825423\pi\)
0.996812 + 0.0797840i \(0.0254231\pi\)
\(864\) −2.03204 + 6.25398i −0.0691314 + 0.212765i
\(865\) 44.8093 32.5558i 1.52356 1.10693i
\(866\) −2.21878 1.61203i −0.0753971 0.0547792i
\(867\) 26.8719 + 82.7031i 0.912617 + 2.80875i
\(868\) −16.0312 −0.544135
\(869\) 0 0
\(870\) −1.14826 −0.0389295
\(871\) 0.687629 + 2.11630i 0.0232994 + 0.0717082i
\(872\) −1.48062 1.07573i −0.0501400 0.0364289i
\(873\) −34.3711 + 24.9721i −1.16328 + 0.845176i
\(874\) 1.35399 4.16716i 0.0457995 0.140956i
\(875\) −1.83313 + 5.64179i −0.0619710 + 0.190727i
\(876\) −11.4133 + 8.29225i −0.385620 + 0.280169i
\(877\) 23.5659 + 17.1216i 0.795763 + 0.578156i 0.909668 0.415336i \(-0.136336\pi\)
−0.113905 + 0.993492i \(0.536336\pi\)
\(878\) −0.0531768 0.163661i −0.00179463 0.00552330i
\(879\) 6.75299 0.227773
\(880\) 0 0
\(881\) −48.8256 −1.64498 −0.822488 0.568783i \(-0.807414\pi\)
−0.822488 + 0.568783i \(0.807414\pi\)
\(882\) −0.173355 0.533533i −0.00583718 0.0179650i
\(883\) 19.5888 + 14.2321i 0.659217 + 0.478949i 0.866398 0.499353i \(-0.166429\pi\)
−0.207181 + 0.978303i \(0.566429\pi\)
\(884\) 12.0677 8.76771i 0.405881 0.294890i
\(885\) 16.0068 49.2637i 0.538061 1.65598i
\(886\) 0.983022 3.02543i 0.0330253 0.101641i
\(887\) 5.37793 3.90730i 0.180573 0.131194i −0.493827 0.869560i \(-0.664402\pi\)
0.674400 + 0.738366i \(0.264402\pi\)
\(888\) −1.64909 1.19813i −0.0553399 0.0402068i
\(889\) 3.04272 + 9.36452i 0.102049 + 0.314076i
\(890\) 1.60944 0.0539486
\(891\) 0 0
\(892\) 26.8483 0.898947
\(893\) 4.41509 + 13.5883i 0.147745 + 0.454714i
\(894\) −3.13174 2.27534i −0.104741 0.0760989i
\(895\) −53.0072 + 38.5120i −1.77184 + 1.28731i
\(896\) −1.16873 + 3.59697i −0.0390444 + 0.120166i
\(897\) −4.45615 + 13.7146i −0.148787 + 0.457918i
\(898\) 1.37170 0.996595i 0.0457741 0.0332568i
\(899\) −8.01657 5.82438i −0.267368 0.194254i
\(900\) −8.25843 25.4168i −0.275281 0.847228i
\(901\) 26.6191 0.886809
\(902\) 0 0
\(903\) −14.4869 −0.482095
\(904\) 0.343115 + 1.05600i 0.0114118 + 0.0351220i
\(905\) 7.00957 + 5.09275i 0.233006 + 0.169289i
\(906\) −4.82834 + 3.50799i −0.160411 + 0.116545i
\(907\) −2.58896 + 7.96801i −0.0859651 + 0.264573i −0.984794 0.173726i \(-0.944419\pi\)
0.898829 + 0.438300i \(0.144419\pi\)
\(908\) 8.32992 25.6369i 0.276438 0.850789i
\(909\) −17.8880 + 12.9964i −0.593308 + 0.431063i
\(910\) −0.295264 0.214522i −0.00978791 0.00711133i
\(911\) −5.80543 17.8673i −0.192343 0.591970i −0.999997 0.00231392i \(-0.999263\pi\)
0.807655 0.589656i \(-0.200737\pi\)
\(912\) −81.7130 −2.70579
\(913\) 0 0
\(914\) 3.54856 0.117376
\(915\) −23.5400 72.4487i −0.778209 2.39508i
\(916\) −2.33390 1.69568i −0.0771144 0.0560269i
\(917\) −13.2502 + 9.62685i −0.437561 + 0.317907i
\(918\) 1.18976 3.66171i 0.0392680 0.120854i
\(919\) −5.56351 + 17.1227i −0.183523 + 0.564827i −0.999920 0.0126652i \(-0.995968\pi\)
0.816397 + 0.577492i \(0.195968\pi\)
\(920\) 5.25952 3.82127i 0.173401 0.125983i
\(921\) −19.9080 14.4640i −0.655990 0.476605i
\(922\) 1.18008 + 3.63190i 0.0388637 + 0.119610i
\(923\) −13.5188 −0.444977
\(924\) 0 0
\(925\) 4.43353 0.145773
\(926\) 0.475474 + 1.46336i 0.0156250 + 0.0480890i
\(927\) −1.32317 0.961338i −0.0434585 0.0315745i
\(928\) −1.42021 + 1.03184i −0.0466206 + 0.0338718i
\(929\) −3.12803 + 9.62708i −0.102627 + 0.315854i −0.989166 0.146800i \(-0.953103\pi\)
0.886539 + 0.462654i \(0.153103\pi\)
\(930\) −2.33441 + 7.18457i −0.0765483 + 0.235591i
\(931\) 6.10332 4.43432i 0.200028 0.145329i
\(932\) −13.1780 9.57437i −0.431659 0.313619i
\(933\) −10.1223 31.1534i −0.331391 1.01992i
\(934\) −3.55986 −0.116482
\(935\) 0 0
\(936\) −2.41397 −0.0789031
\(937\) 8.71776 + 26.8305i 0.284797 + 0.876515i 0.986459 + 0.164005i \(0.0524414\pi\)
−0.701663 + 0.712509i \(0.747559\pi\)
\(938\) 0.200687 + 0.145807i 0.00655265 + 0.00476078i
\(939\) 66.1481 48.0594i 2.15866 1.56836i
\(940\) −3.26349 + 10.0440i −0.106443 + 0.327599i
\(941\) 6.22672 19.1639i 0.202985 0.624725i −0.796805 0.604237i \(-0.793478\pi\)
0.999790 0.0204879i \(-0.00652195\pi\)
\(942\) 2.00196 1.45451i 0.0652274 0.0473905i
\(943\) 36.3060 + 26.3778i 1.18228 + 0.858980i
\(944\) −8.05798 24.7999i −0.262265 0.807169i
\(945\) 12.9114 0.420007
\(946\) 0 0
\(947\) 0.125141 0.00406653 0.00203326 0.999998i \(-0.499353\pi\)
0.00203326 + 0.999998i \(0.499353\pi\)
\(948\) −26.0310 80.1153i −0.845449 2.60202i
\(949\) −2.24228 1.62911i −0.0727875 0.0528832i
\(950\) −2.12137 + 1.54127i −0.0688264 + 0.0500053i
\(951\) −21.5149 + 66.2160i −0.697668 + 2.14720i
\(952\) 1.03146 3.17449i 0.0334297 0.102886i
\(953\) −23.7442 + 17.2512i −0.769151 + 0.558821i −0.901704 0.432355i \(-0.857683\pi\)
0.132552 + 0.991176i \(0.457683\pi\)
\(954\) −1.73621 1.26143i −0.0562120 0.0408404i
\(955\) −10.9106 33.5792i −0.353057 1.08660i
\(956\) 20.6166 0.666790
\(957\) 0 0
\(958\) −3.43717 −0.111050
\(959\) 4.39242 + 13.5185i 0.141839 + 0.436534i
\(960\) −48.1381 34.9744i −1.55365 1.12879i
\(961\) −27.6610 + 20.0969i −0.892290 + 0.648287i
\(962\) 0.0616505 0.189741i 0.00198769 0.00611749i
\(963\) −3.66952 + 11.2936i −0.118249 + 0.363932i
\(964\) 13.1789 9.57505i 0.424465 0.308392i
\(965\) 46.9619 + 34.1198i 1.51176 + 1.09836i
\(966\) 0.496763 + 1.52888i 0.0159831 + 0.0491909i
\(967\) 51.9463 1.67048 0.835240 0.549885i \(-0.185328\pi\)
0.835240 + 0.549885i \(0.185328\pi\)
\(968\) 0 0
\(969\) 145.295 4.66756
\(970\) 0.952149 + 2.93041i 0.0305717 + 0.0940899i
\(971\) 20.2308 + 14.6985i 0.649236 + 0.471697i 0.863011 0.505185i \(-0.168576\pi\)
−0.213775 + 0.976883i \(0.568576\pi\)
\(972\) −27.7489 + 20.1608i −0.890047 + 0.646657i
\(973\) −2.83660 + 8.73015i −0.0909371 + 0.279876i
\(974\) −0.0393608 + 0.121140i −0.00126120 + 0.00388158i
\(975\) 6.98169 5.07249i 0.223593 0.162450i
\(976\) −31.0245 22.5406i −0.993070 0.721507i
\(977\) −5.38173 16.5633i −0.172177 0.529906i 0.827316 0.561736i \(-0.189866\pi\)
−0.999493 + 0.0318303i \(0.989866\pi\)
\(978\) −2.61611 −0.0836540
\(979\) 0 0
\(980\) 5.57636 0.178130
\(981\) 5.49509 + 16.9121i 0.175445 + 0.539963i
\(982\) −1.79643 1.30518i −0.0573263 0.0416500i
\(983\) 34.2497 24.8839i 1.09240 0.793672i 0.112593 0.993641i \(-0.464084\pi\)
0.979802 + 0.199969i \(0.0640843\pi\)
\(984\) −3.81562 + 11.7433i −0.121638 + 0.374362i
\(985\) 5.44990 16.7731i 0.173648 0.534434i
\(986\) 0.831533 0.604144i 0.0264814 0.0192399i
\(987\) −4.24080 3.08112i −0.134986 0.0980732i
\(988\) −4.99754 15.3808i −0.158993 0.489330i
\(989\) 25.2569 0.803122
\(990\) 0 0
\(991\) 55.6263 1.76703 0.883513 0.468406i \(-0.155172\pi\)
0.883513 + 0.468406i \(0.155172\pi\)
\(992\) 3.56888 + 10.9839i 0.113312 + 0.348738i
\(993\) 21.1906 + 15.3958i 0.672462 + 0.488573i
\(994\) −1.21923 + 0.885821i −0.0386716 + 0.0280965i
\(995\) 5.96144 18.3474i 0.188991 0.581653i
\(996\) 3.47462 10.6938i 0.110097 0.338845i
\(997\) −13.2895 + 9.65540i −0.420883 + 0.305790i −0.777993 0.628273i \(-0.783762\pi\)
0.357110 + 0.934062i \(0.383762\pi\)
\(998\) 3.08958 + 2.24471i 0.0977991 + 0.0710552i
\(999\) 2.18100 + 6.71244i 0.0690039 + 0.212372i
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 847.2.f.z.148.4 24
11.2 odd 10 847.2.f.y.372.3 24
11.3 even 5 847.2.a.m.1.4 6
11.4 even 5 inner 847.2.f.z.729.3 24
11.5 even 5 inner 847.2.f.z.323.3 24
11.6 odd 10 847.2.f.y.323.4 24
11.7 odd 10 847.2.f.y.729.4 24
11.8 odd 10 847.2.a.n.1.3 yes 6
11.9 even 5 inner 847.2.f.z.372.4 24
11.10 odd 2 847.2.f.y.148.3 24
33.8 even 10 7623.2.a.cp.1.4 6
33.14 odd 10 7623.2.a.cs.1.3 6
77.41 even 10 5929.2.a.bm.1.3 6
77.69 odd 10 5929.2.a.bj.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.m.1.4 6 11.3 even 5
847.2.a.n.1.3 yes 6 11.8 odd 10
847.2.f.y.148.3 24 11.10 odd 2
847.2.f.y.323.4 24 11.6 odd 10
847.2.f.y.372.3 24 11.2 odd 10
847.2.f.y.729.4 24 11.7 odd 10
847.2.f.z.148.4 24 1.1 even 1 trivial
847.2.f.z.323.3 24 11.5 even 5 inner
847.2.f.z.372.4 24 11.9 even 5 inner
847.2.f.z.729.3 24 11.4 even 5 inner
5929.2.a.bj.1.4 6 77.69 odd 10
5929.2.a.bm.1.3 6 77.41 even 10
7623.2.a.cp.1.4 6 33.8 even 10
7623.2.a.cs.1.3 6 33.14 odd 10