Properties

Label 165.2.k.c.122.3
Level $165$
Weight $2$
Character 165.122
Analytic conductor $1.318$
Analytic rank $0$
Dimension $16$
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] = [165,2,Mod(23,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.k (of order \(4\), degree \(2\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 8 x^{14} + 19 x^{12} - 80 x^{11} + 168 x^{10} + 28 x^{9} + 119 x^{8} - 432 x^{7} + 784 x^{6} + 84 x^{5} + 169 x^{4} - 420 x^{3} + 392 x^{2} - 112 x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 122.3
Root \(1.05652 + 1.05652i\) of defining polynomial
Character \(\chi\) \(=\) 165.122
Dual form 165.2.k.c.23.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.05652 + 1.05652i) q^{2} +(-1.71860 + 0.215468i) q^{3} -0.232479i q^{4} +(-0.158945 - 2.23041i) q^{5} +(1.58809 - 2.04338i) q^{6} +(-1.04338 - 1.04338i) q^{7} +(-1.86743 - 1.86743i) q^{8} +(2.90715 - 0.740604i) q^{9} +O(q^{10})\) \(q+(-1.05652 + 1.05652i) q^{2} +(-1.71860 + 0.215468i) q^{3} -0.232479i q^{4} +(-0.158945 - 2.23041i) q^{5} +(1.58809 - 2.04338i) q^{6} +(-1.04338 - 1.04338i) q^{7} +(-1.86743 - 1.86743i) q^{8} +(2.90715 - 0.740604i) q^{9} +(2.52441 + 2.18855i) q^{10} +1.00000i q^{11} +(0.0500918 + 0.399538i) q^{12} +(3.37924 - 3.37924i) q^{13} +2.20471 q^{14} +(0.753744 + 3.79893i) q^{15} +4.41091 q^{16} +(-0.138459 + 0.138459i) q^{17} +(-2.28900 + 3.85393i) q^{18} -6.97457i q^{19} +(-0.518525 + 0.0369515i) q^{20} +(2.01797 + 1.56834i) q^{21} +(-1.05652 - 1.05652i) q^{22} +(-2.64775 - 2.64775i) q^{23} +(3.61172 + 2.80698i) q^{24} +(-4.94947 + 0.709026i) q^{25} +7.14049i q^{26} +(-4.83664 + 1.89920i) q^{27} +(-0.242565 + 0.242565i) q^{28} -0.161760 q^{29} +(-4.81000 - 3.21731i) q^{30} -7.53000 q^{31} +(-0.925378 + 0.925378i) q^{32} +(-0.215468 - 1.71860i) q^{33} -0.292570i q^{34} +(-2.16133 + 2.49301i) q^{35} +(-0.172175 - 0.675852i) q^{36} +(3.94032 + 3.94032i) q^{37} +(7.36879 + 7.36879i) q^{38} +(-5.07943 + 6.53567i) q^{39} +(-3.86831 + 4.46195i) q^{40} -8.21214i q^{41} +(-3.78901 + 0.475044i) q^{42} +(-1.14357 + 1.14357i) q^{43} +0.232479 q^{44} +(-2.11393 - 6.36642i) q^{45} +5.59482 q^{46} +(-0.797409 + 0.797409i) q^{47} +(-7.58058 + 0.950409i) q^{48} -4.82271i q^{49} +(4.48013 - 5.97833i) q^{50} +(0.208122 - 0.267789i) q^{51} +(-0.785604 - 0.785604i) q^{52} +(-0.0372189 - 0.0372189i) q^{53} +(3.10347 - 7.11656i) q^{54} +(2.23041 - 0.158945i) q^{55} +3.89688i q^{56} +(1.50279 + 11.9865i) q^{57} +(0.170903 - 0.170903i) q^{58} +10.3955 q^{59} +(0.883173 - 0.175230i) q^{60} -8.33669 q^{61} +(7.95562 - 7.95562i) q^{62} +(-3.80600 - 2.26053i) q^{63} +6.86646i q^{64} +(-8.07421 - 6.99998i) q^{65} +(2.04338 + 1.58809i) q^{66} +(5.41037 + 5.41037i) q^{67} +(0.0321889 + 0.0321889i) q^{68} +(5.12092 + 3.97991i) q^{69} +(-0.350429 - 4.91742i) q^{70} +15.1518i q^{71} +(-6.81190 - 4.04586i) q^{72} +(3.98389 - 3.98389i) q^{73} -8.32608 q^{74} +(8.35337 - 2.28498i) q^{75} -1.62144 q^{76} +(1.04338 - 1.04338i) q^{77} +(-1.53854 - 12.2716i) q^{78} -13.5518i q^{79} +(-0.701093 - 9.83815i) q^{80} +(7.90301 - 4.30609i) q^{81} +(8.67631 + 8.67631i) q^{82} +(5.92343 + 5.92343i) q^{83} +(0.364606 - 0.469136i) q^{84} +(0.330828 + 0.286814i) q^{85} -2.41641i q^{86} +(0.278000 - 0.0348540i) q^{87} +(1.86743 - 1.86743i) q^{88} +2.98552 q^{89} +(8.95968 + 4.49285i) q^{90} -7.05168 q^{91} +(-0.615548 + 0.615548i) q^{92} +(12.9410 - 1.62247i) q^{93} -1.68496i q^{94} +(-15.5562 + 1.10857i) q^{95} +(1.39096 - 1.78974i) q^{96} +(7.94941 + 7.94941i) q^{97} +(5.09530 + 5.09530i) q^{98} +(0.740604 + 2.90715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24} - 18 q^{25} - 20 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{30} + 8 q^{31} + 28 q^{32} + 4 q^{33} + 44 q^{36} - 6 q^{37} + 24 q^{38} + 24 q^{39} + 16 q^{40} - 60 q^{42} + 16 q^{43} + 12 q^{44} + 24 q^{45} - 32 q^{46} + 48 q^{47} - 48 q^{48} - 12 q^{50} - 8 q^{51} + 36 q^{52} - 4 q^{53} + 4 q^{54} + 2 q^{55} - 8 q^{57} - 12 q^{58} - 68 q^{59} - 28 q^{60} - 8 q^{61} + 48 q^{62} - 12 q^{63} - 48 q^{65} + 8 q^{66} + 6 q^{67} + 24 q^{68} + 12 q^{69} - 4 q^{70} - 8 q^{72} + 8 q^{74} + 8 q^{75} + 16 q^{76} - 8 q^{77} - 48 q^{78} - 24 q^{80} + 2 q^{81} + 12 q^{82} - 8 q^{83} + 52 q^{84} - 4 q^{85} - 36 q^{87} - 16 q^{88} + 32 q^{89} + 44 q^{90} - 56 q^{91} + 20 q^{92} + 28 q^{93} - 48 q^{95} + 80 q^{96} + 18 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.05652 + 1.05652i −0.747074 + 0.747074i −0.973929 0.226854i \(-0.927156\pi\)
0.226854 + 0.973929i \(0.427156\pi\)
\(3\) −1.71860 + 0.215468i −0.992232 + 0.124400i
\(4\) 0.232479i 0.116240i
\(5\) −0.158945 2.23041i −0.0710824 0.997470i
\(6\) 1.58809 2.04338i 0.648335 0.834207i
\(7\) −1.04338 1.04338i −0.394361 0.394361i 0.481877 0.876239i \(-0.339955\pi\)
−0.876239 + 0.481877i \(0.839955\pi\)
\(8\) −1.86743 1.86743i −0.660234 0.660234i
\(9\) 2.90715 0.740604i 0.969049 0.246868i
\(10\) 2.52441 + 2.18855i 0.798288 + 0.692081i
\(11\) 1.00000i 0.301511i
\(12\) 0.0500918 + 0.399538i 0.0144603 + 0.115337i
\(13\) 3.37924 3.37924i 0.937233 0.937233i −0.0609106 0.998143i \(-0.519400\pi\)
0.998143 + 0.0609106i \(0.0194004\pi\)
\(14\) 2.20471 0.589234
\(15\) 0.753744 + 3.79893i 0.194616 + 0.980880i
\(16\) 4.41091 1.10273
\(17\) −0.138459 + 0.138459i −0.0335813 + 0.0335813i −0.723698 0.690117i \(-0.757559\pi\)
0.690117 + 0.723698i \(0.257559\pi\)
\(18\) −2.28900 + 3.85393i −0.539523 + 0.908380i
\(19\) 6.97457i 1.60008i −0.599949 0.800038i \(-0.704813\pi\)
0.599949 0.800038i \(-0.295187\pi\)
\(20\) −0.518525 + 0.0369515i −0.115946 + 0.00826260i
\(21\) 2.01797 + 1.56834i 0.440357 + 0.342239i
\(22\) −1.05652 1.05652i −0.225251 0.225251i
\(23\) −2.64775 2.64775i −0.552094 0.552094i 0.374951 0.927045i \(-0.377660\pi\)
−0.927045 + 0.374951i \(0.877660\pi\)
\(24\) 3.61172 + 2.80698i 0.737239 + 0.572972i
\(25\) −4.94947 + 0.709026i −0.989895 + 0.141805i
\(26\) 7.14049i 1.40036i
\(27\) −4.83664 + 1.89920i −0.930811 + 0.365500i
\(28\) −0.242565 + 0.242565i −0.0458405 + 0.0458405i
\(29\) −0.161760 −0.0300381 −0.0150190 0.999887i \(-0.504781\pi\)
−0.0150190 + 0.999887i \(0.504781\pi\)
\(30\) −4.81000 3.21731i −0.878182 0.587397i
\(31\) −7.53000 −1.35243 −0.676214 0.736705i \(-0.736381\pi\)
−0.676214 + 0.736705i \(0.736381\pi\)
\(32\) −0.925378 + 0.925378i −0.163585 + 0.163585i
\(33\) −0.215468 1.71860i −0.0375081 0.299169i
\(34\) 0.292570i 0.0501754i
\(35\) −2.16133 + 2.49301i −0.365332 + 0.421396i
\(36\) −0.172175 0.675852i −0.0286959 0.112642i
\(37\) 3.94032 + 3.94032i 0.647785 + 0.647785i 0.952457 0.304672i \(-0.0985470\pi\)
−0.304672 + 0.952457i \(0.598547\pi\)
\(38\) 7.36879 + 7.36879i 1.19538 + 1.19538i
\(39\) −5.07943 + 6.53567i −0.813360 + 1.04654i
\(40\) −3.86831 + 4.46195i −0.611633 + 0.705495i
\(41\) 8.21214i 1.28252i −0.767324 0.641260i \(-0.778412\pi\)
0.767324 0.641260i \(-0.221588\pi\)
\(42\) −3.78901 + 0.475044i −0.584657 + 0.0733009i
\(43\) −1.14357 + 1.14357i −0.174392 + 0.174392i −0.788906 0.614514i \(-0.789352\pi\)
0.614514 + 0.788906i \(0.289352\pi\)
\(44\) 0.232479 0.0350476
\(45\) −2.11393 6.36642i −0.315126 0.949050i
\(46\) 5.59482 0.824911
\(47\) −0.797409 + 0.797409i −0.116314 + 0.116314i −0.762868 0.646554i \(-0.776209\pi\)
0.646554 + 0.762868i \(0.276209\pi\)
\(48\) −7.58058 + 0.950409i −1.09416 + 0.137180i
\(49\) 4.82271i 0.688958i
\(50\) 4.48013 5.97833i 0.633586 0.845464i
\(51\) 0.208122 0.267789i 0.0291429 0.0374979i
\(52\) −0.785604 0.785604i −0.108944 0.108944i
\(53\) −0.0372189 0.0372189i −0.00511240 0.00511240i 0.704546 0.709658i \(-0.251151\pi\)
−0.709658 + 0.704546i \(0.751151\pi\)
\(54\) 3.10347 7.11656i 0.422329 0.968441i
\(55\) 2.23041 0.158945i 0.300749 0.0214322i
\(56\) 3.89688i 0.520742i
\(57\) 1.50279 + 11.9865i 0.199050 + 1.58765i
\(58\) 0.170903 0.170903i 0.0224407 0.0224407i
\(59\) 10.3955 1.35338 0.676688 0.736270i \(-0.263414\pi\)
0.676688 + 0.736270i \(0.263414\pi\)
\(60\) 0.883173 0.175230i 0.114017 0.0226221i
\(61\) −8.33669 −1.06740 −0.533702 0.845673i \(-0.679200\pi\)
−0.533702 + 0.845673i \(0.679200\pi\)
\(62\) 7.95562 7.95562i 1.01036 1.01036i
\(63\) −3.80600 2.26053i −0.479511 0.284800i
\(64\) 6.86646i 0.858308i
\(65\) −8.07421 6.99998i −1.00148 0.868241i
\(66\) 2.04338 + 1.58809i 0.251523 + 0.195480i
\(67\) 5.41037 + 5.41037i 0.660982 + 0.660982i 0.955611 0.294630i \(-0.0951963\pi\)
−0.294630 + 0.955611i \(0.595196\pi\)
\(68\) 0.0321889 + 0.0321889i 0.00390348 + 0.00390348i
\(69\) 5.12092 + 3.97991i 0.616486 + 0.479125i
\(70\) −0.350429 4.91742i −0.0418842 0.587744i
\(71\) 15.1518i 1.79819i 0.437755 + 0.899095i \(0.355774\pi\)
−0.437755 + 0.899095i \(0.644226\pi\)
\(72\) −6.81190 4.04586i −0.802790 0.476809i
\(73\) 3.98389 3.98389i 0.466279 0.466279i −0.434428 0.900707i \(-0.643049\pi\)
0.900707 + 0.434428i \(0.143049\pi\)
\(74\) −8.32608 −0.967887
\(75\) 8.35337 2.28498i 0.964565 0.263847i
\(76\) −1.62144 −0.185992
\(77\) 1.04338 1.04338i 0.118904 0.118904i
\(78\) −1.53854 12.2716i −0.174206 1.38949i
\(79\) 13.5518i 1.52470i −0.647165 0.762350i \(-0.724046\pi\)
0.647165 0.762350i \(-0.275954\pi\)
\(80\) −0.701093 9.83815i −0.0783846 1.09994i
\(81\) 7.90301 4.30609i 0.878112 0.478454i
\(82\) 8.67631 + 8.67631i 0.958138 + 0.958138i
\(83\) 5.92343 + 5.92343i 0.650181 + 0.650181i 0.953036 0.302856i \(-0.0979400\pi\)
−0.302856 + 0.953036i \(0.597940\pi\)
\(84\) 0.364606 0.469136i 0.0397818 0.0511869i
\(85\) 0.330828 + 0.286814i 0.0358834 + 0.0311093i
\(86\) 2.41641i 0.260568i
\(87\) 0.278000 0.0348540i 0.0298047 0.00373675i
\(88\) 1.86743 1.86743i 0.199068 0.199068i
\(89\) 2.98552 0.316464 0.158232 0.987402i \(-0.449421\pi\)
0.158232 + 0.987402i \(0.449421\pi\)
\(90\) 8.95968 + 4.49285i 0.944433 + 0.473588i
\(91\) −7.05168 −0.739217
\(92\) −0.615548 + 0.615548i −0.0641753 + 0.0641753i
\(93\) 12.9410 1.62247i 1.34192 0.168243i
\(94\) 1.68496i 0.173790i
\(95\) −15.5562 + 1.10857i −1.59603 + 0.113737i
\(96\) 1.39096 1.78974i 0.141964 0.182665i
\(97\) 7.94941 + 7.94941i 0.807141 + 0.807141i 0.984200 0.177060i \(-0.0566585\pi\)
−0.177060 + 0.984200i \(0.556659\pi\)
\(98\) 5.09530 + 5.09530i 0.514703 + 0.514703i
\(99\) 0.740604 + 2.90715i 0.0744335 + 0.292179i
\(100\) 0.164834 + 1.15065i 0.0164834 + 0.115065i
\(101\) 2.33132i 0.231975i −0.993251 0.115987i \(-0.962997\pi\)
0.993251 0.115987i \(-0.0370032\pi\)
\(102\) 0.0630395 + 0.502810i 0.00624184 + 0.0497857i
\(103\) −1.95903 + 1.95903i −0.193029 + 0.193029i −0.797003 0.603975i \(-0.793583\pi\)
0.603975 + 0.797003i \(0.293583\pi\)
\(104\) −12.6210 −1.23759
\(105\) 3.17729 4.75018i 0.310072 0.463570i
\(106\) 0.0786451 0.00763869
\(107\) 6.57276 6.57276i 0.635413 0.635413i −0.314008 0.949420i \(-0.601672\pi\)
0.949420 + 0.314008i \(0.101672\pi\)
\(108\) 0.441524 + 1.12442i 0.0424857 + 0.108197i
\(109\) 18.5815i 1.77979i 0.456170 + 0.889893i \(0.349221\pi\)
−0.456170 + 0.889893i \(0.650779\pi\)
\(110\) −2.18855 + 2.52441i −0.208670 + 0.240693i
\(111\) −7.62083 5.92281i −0.723338 0.562168i
\(112\) −4.60227 4.60227i −0.434873 0.434873i
\(113\) −8.98496 8.98496i −0.845234 0.845234i 0.144300 0.989534i \(-0.453907\pi\)
−0.989534 + 0.144300i \(0.953907\pi\)
\(114\) −14.2517 11.0762i −1.33479 1.03738i
\(115\) −5.48473 + 6.32642i −0.511454 + 0.589942i
\(116\) 0.0376059i 0.00349162i
\(117\) 7.32127 12.3266i 0.676852 1.13960i
\(118\) −10.9831 + 10.9831i −1.01107 + 1.01107i
\(119\) 0.288932 0.0264863
\(120\) 5.68666 8.50178i 0.519118 0.776103i
\(121\) −1.00000 −0.0909091
\(122\) 8.80791 8.80791i 0.797430 0.797430i
\(123\) 1.76945 + 14.1133i 0.159546 + 1.27256i
\(124\) 1.75057i 0.157206i
\(125\) 2.36812 + 10.9267i 0.211811 + 0.977311i
\(126\) 6.40943 1.63282i 0.570997 0.145463i
\(127\) −5.97520 5.97520i −0.530213 0.530213i 0.390422 0.920636i \(-0.372329\pi\)
−0.920636 + 0.390422i \(0.872329\pi\)
\(128\) −9.10532 9.10532i −0.804805 0.804805i
\(129\) 1.71893 2.21173i 0.151343 0.194732i
\(130\) 15.9262 1.13495i 1.39682 0.0995413i
\(131\) 2.56196i 0.223839i −0.993717 0.111920i \(-0.964300\pi\)
0.993717 0.111920i \(-0.0357000\pi\)
\(132\) −0.399538 + 0.0500918i −0.0347754 + 0.00435993i
\(133\) −7.27714 + 7.27714i −0.631008 + 0.631008i
\(134\) −11.4323 −0.987605
\(135\) 5.00475 + 10.4858i 0.430740 + 0.902476i
\(136\) 0.517124 0.0443430
\(137\) 6.89566 6.89566i 0.589136 0.589136i −0.348261 0.937397i \(-0.613228\pi\)
0.937397 + 0.348261i \(0.113228\pi\)
\(138\) −9.61523 + 1.20550i −0.818503 + 0.102619i
\(139\) 4.80305i 0.407389i 0.979034 + 0.203695i \(0.0652950\pi\)
−0.979034 + 0.203695i \(0.934705\pi\)
\(140\) 0.579574 + 0.502465i 0.0489830 + 0.0424661i
\(141\) 1.19861 1.54224i 0.100941 0.129880i
\(142\) −16.0082 16.0082i −1.34338 1.34338i
\(143\) 3.37924 + 3.37924i 0.282586 + 0.282586i
\(144\) 12.8232 3.26674i 1.06860 0.272228i
\(145\) 0.0257110 + 0.360791i 0.00213518 + 0.0299621i
\(146\) 8.41813i 0.696689i
\(147\) 1.03914 + 8.28829i 0.0857066 + 0.683606i
\(148\) 0.916044 0.916044i 0.0752983 0.0752983i
\(149\) −9.35238 −0.766177 −0.383088 0.923712i \(-0.625140\pi\)
−0.383088 + 0.923712i \(0.625140\pi\)
\(150\) −6.41139 + 11.2397i −0.523488 + 0.917715i
\(151\) −2.84779 −0.231750 −0.115875 0.993264i \(-0.536967\pi\)
−0.115875 + 0.993264i \(0.536967\pi\)
\(152\) −13.0245 + 13.0245i −1.05643 + 1.05643i
\(153\) −0.299978 + 0.505065i −0.0242518 + 0.0408320i
\(154\) 2.20471i 0.177661i
\(155\) 1.19686 + 16.7950i 0.0961339 + 1.34901i
\(156\) 1.51941 + 1.18086i 0.121650 + 0.0945448i
\(157\) −11.7887 11.7887i −0.940838 0.940838i 0.0575074 0.998345i \(-0.481685\pi\)
−0.998345 + 0.0575074i \(0.981685\pi\)
\(158\) 14.3178 + 14.3178i 1.13906 + 1.13906i
\(159\) 0.0719837 + 0.0559447i 0.00570868 + 0.00443671i
\(160\) 2.21106 + 1.91689i 0.174799 + 0.151543i
\(161\) 5.52523i 0.435449i
\(162\) −3.80023 + 12.8992i −0.298574 + 1.01346i
\(163\) −1.02307 + 1.02307i −0.0801327 + 0.0801327i −0.746037 0.665904i \(-0.768046\pi\)
0.665904 + 0.746037i \(0.268046\pi\)
\(164\) −1.90915 −0.149080
\(165\) −3.79893 + 0.753744i −0.295746 + 0.0586789i
\(166\) −12.5165 −0.971467
\(167\) −0.279986 + 0.279986i −0.0216660 + 0.0216660i −0.717857 0.696191i \(-0.754877\pi\)
0.696191 + 0.717857i \(0.254877\pi\)
\(168\) −0.839651 6.69716i −0.0647805 0.516697i
\(169\) 9.83853i 0.756810i
\(170\) −0.652552 + 0.0465027i −0.0500485 + 0.00356659i
\(171\) −5.16539 20.2761i −0.395007 1.55055i
\(172\) 0.265856 + 0.265856i 0.0202713 + 0.0202713i
\(173\) 13.8099 + 13.8099i 1.04995 + 1.04995i 0.998685 + 0.0512647i \(0.0163252\pi\)
0.0512647 + 0.998685i \(0.483675\pi\)
\(174\) −0.256889 + 0.330537i −0.0194747 + 0.0250580i
\(175\) 5.90398 + 4.42441i 0.446299 + 0.334454i
\(176\) 4.41091i 0.332485i
\(177\) −17.8656 + 2.23989i −1.34286 + 0.168360i
\(178\) −3.15427 + 3.15427i −0.236422 + 0.236422i
\(179\) 8.00740 0.598501 0.299250 0.954175i \(-0.403263\pi\)
0.299250 + 0.954175i \(0.403263\pi\)
\(180\) −1.48006 + 0.491445i −0.110317 + 0.0366301i
\(181\) 16.9227 1.25785 0.628927 0.777464i \(-0.283494\pi\)
0.628927 + 0.777464i \(0.283494\pi\)
\(182\) 7.45026 7.45026i 0.552250 0.552250i
\(183\) 14.3274 1.79629i 1.05911 0.132785i
\(184\) 9.88895i 0.729023i
\(185\) 8.16224 9.41483i 0.600100 0.692192i
\(186\) −11.9583 + 15.3867i −0.876827 + 1.12821i
\(187\) −0.138459 0.138459i −0.0101251 0.0101251i
\(188\) 0.185381 + 0.185381i 0.0135203 + 0.0135203i
\(189\) 7.02805 + 3.06487i 0.511215 + 0.222937i
\(190\) 15.2642 17.6067i 1.10738 1.27732i
\(191\) 21.2773i 1.53957i −0.638301 0.769787i \(-0.720362\pi\)
0.638301 0.769787i \(-0.279638\pi\)
\(192\) −1.47950 11.8007i −0.106774 0.851640i
\(193\) 6.92019 6.92019i 0.498126 0.498126i −0.412728 0.910854i \(-0.635424\pi\)
0.910854 + 0.412728i \(0.135424\pi\)
\(194\) −16.7975 −1.20599
\(195\) 15.3846 + 10.2904i 1.10171 + 0.736912i
\(196\) −1.12118 −0.0800843
\(197\) −1.80376 + 1.80376i −0.128513 + 0.128513i −0.768438 0.639925i \(-0.778966\pi\)
0.639925 + 0.768438i \(0.278966\pi\)
\(198\) −3.85393 2.28900i −0.273887 0.162672i
\(199\) 14.5849i 1.03390i 0.856016 + 0.516949i \(0.172932\pi\)
−0.856016 + 0.516949i \(0.827068\pi\)
\(200\) 10.5668 + 7.91872i 0.747187 + 0.559938i
\(201\) −10.4640 8.13248i −0.738073 0.573621i
\(202\) 2.46309 + 2.46309i 0.173302 + 0.173302i
\(203\) 0.168777 + 0.168777i 0.0118459 + 0.0118459i
\(204\) −0.0622554 0.0483841i −0.00435875 0.00338756i
\(205\) −18.3164 + 1.30528i −1.27928 + 0.0911647i
\(206\) 4.13951i 0.288414i
\(207\) −9.65834 5.73647i −0.671301 0.398712i
\(208\) 14.9055 14.9055i 1.03351 1.03351i
\(209\) 6.97457 0.482441
\(210\) 1.66179 + 8.37555i 0.114674 + 0.577968i
\(211\) −5.42436 −0.373428 −0.186714 0.982414i \(-0.559784\pi\)
−0.186714 + 0.982414i \(0.559784\pi\)
\(212\) −0.00865262 + 0.00865262i −0.000594265 + 0.000594265i
\(213\) −3.26472 26.0398i −0.223695 1.78422i
\(214\) 13.8885i 0.949401i
\(215\) 2.73239 + 2.36886i 0.186347 + 0.161555i
\(216\) 12.5787 + 5.48545i 0.855870 + 0.373238i
\(217\) 7.85667 + 7.85667i 0.533346 + 0.533346i
\(218\) −19.6318 19.6318i −1.32963 1.32963i
\(219\) −5.98829 + 7.70509i −0.404651 + 0.520662i
\(220\) −0.0369515 0.518525i −0.00249127 0.0349589i
\(221\) 0.935774i 0.0629469i
\(222\) 14.3092 1.79400i 0.960368 0.120405i
\(223\) 10.3117 10.3117i 0.690525 0.690525i −0.271823 0.962347i \(-0.587626\pi\)
0.962347 + 0.271823i \(0.0876264\pi\)
\(224\) 1.93104 0.129023
\(225\) −13.8637 + 5.72684i −0.924249 + 0.381790i
\(226\) 18.9856 1.26291
\(227\) 18.3744 18.3744i 1.21955 1.21955i 0.251766 0.967788i \(-0.418989\pi\)
0.967788 0.251766i \(-0.0810113\pi\)
\(228\) 2.78661 0.349369i 0.184548 0.0231375i
\(229\) 14.3877i 0.950765i −0.879779 0.475382i \(-0.842310\pi\)
0.879779 0.475382i \(-0.157690\pi\)
\(230\) −0.889269 12.4787i −0.0586367 0.822824i
\(231\) −1.56834 + 2.01797i −0.103189 + 0.132773i
\(232\) 0.302075 + 0.302075i 0.0198322 + 0.0198322i
\(233\) −12.8401 12.8401i −0.841181 0.841181i 0.147832 0.989012i \(-0.452771\pi\)
−0.989012 + 0.147832i \(0.952771\pi\)
\(234\) 5.28827 + 20.7584i 0.345705 + 1.35702i
\(235\) 1.90529 + 1.65181i 0.124288 + 0.107752i
\(236\) 2.41674i 0.157316i
\(237\) 2.91998 + 23.2901i 0.189673 + 1.51286i
\(238\) −0.305263 + 0.305263i −0.0197872 + 0.0197872i
\(239\) −6.03008 −0.390054 −0.195027 0.980798i \(-0.562479\pi\)
−0.195027 + 0.980798i \(0.562479\pi\)
\(240\) 3.32470 + 16.7567i 0.214608 + 1.08164i
\(241\) 8.19817 0.528091 0.264045 0.964510i \(-0.414943\pi\)
0.264045 + 0.964510i \(0.414943\pi\)
\(242\) 1.05652 1.05652i 0.0679158 0.0679158i
\(243\) −12.6543 + 9.10327i −0.811771 + 0.583975i
\(244\) 1.93811i 0.124075i
\(245\) −10.7566 + 0.766546i −0.687215 + 0.0489728i
\(246\) −16.7805 13.0416i −1.06989 0.831502i
\(247\) −23.5687 23.5687i −1.49964 1.49964i
\(248\) 14.0617 + 14.0617i 0.892920 + 0.892920i
\(249\) −11.4563 8.90368i −0.726013 0.564248i
\(250\) −14.0462 9.04230i −0.888362 0.571885i
\(251\) 9.14311i 0.577108i −0.957464 0.288554i \(-0.906825\pi\)
0.957464 0.288554i \(-0.0931745\pi\)
\(252\) −0.525527 + 0.884817i −0.0331051 + 0.0557382i
\(253\) 2.64775 2.64775i 0.166463 0.166463i
\(254\) 12.6259 0.792218
\(255\) −0.630359 0.421634i −0.0394746 0.0264037i
\(256\) 5.50704 0.344190
\(257\) −8.53152 + 8.53152i −0.532182 + 0.532182i −0.921221 0.389039i \(-0.872807\pi\)
0.389039 + 0.921221i \(0.372807\pi\)
\(258\) 0.520657 + 4.15283i 0.0324147 + 0.258544i
\(259\) 8.22252i 0.510923i
\(260\) −1.62735 + 1.87709i −0.100924 + 0.116412i
\(261\) −0.470260 + 0.119800i −0.0291084 + 0.00741544i
\(262\) 2.70677 + 2.70677i 0.167225 + 0.167225i
\(263\) 1.80302 + 1.80302i 0.111179 + 0.111179i 0.760508 0.649329i \(-0.224950\pi\)
−0.649329 + 0.760508i \(0.724950\pi\)
\(264\) −2.80698 + 3.61172i −0.172758 + 0.222286i
\(265\) −0.0770976 + 0.0889292i −0.00473607 + 0.00546287i
\(266\) 15.3769i 0.942820i
\(267\) −5.13090 + 0.643283i −0.314006 + 0.0393683i
\(268\) 1.25780 1.25780i 0.0768323 0.0768323i
\(269\) 3.78908 0.231024 0.115512 0.993306i \(-0.463149\pi\)
0.115512 + 0.993306i \(0.463149\pi\)
\(270\) −16.3661 5.79088i −0.996011 0.352422i
\(271\) 28.8342 1.75155 0.875776 0.482718i \(-0.160350\pi\)
0.875776 + 0.482718i \(0.160350\pi\)
\(272\) −0.610731 + 0.610731i −0.0370310 + 0.0370310i
\(273\) 12.1190 1.51941i 0.733475 0.0919588i
\(274\) 14.5708i 0.880257i
\(275\) −0.709026 4.94947i −0.0427559 0.298464i
\(276\) 0.925248 1.19051i 0.0556934 0.0716602i
\(277\) 14.3716 + 14.3716i 0.863507 + 0.863507i 0.991744 0.128236i \(-0.0409316\pi\)
−0.128236 + 0.991744i \(0.540932\pi\)
\(278\) −5.07453 5.07453i −0.304350 0.304350i
\(279\) −21.8908 + 5.57675i −1.31057 + 0.333871i
\(280\) 8.69164 0.619390i 0.519425 0.0370156i
\(281\) 21.9763i 1.31099i 0.755197 + 0.655497i \(0.227541\pi\)
−0.755197 + 0.655497i \(0.772459\pi\)
\(282\) 0.363054 + 2.89577i 0.0216196 + 0.172440i
\(283\) 5.65151 5.65151i 0.335947 0.335947i −0.518892 0.854840i \(-0.673655\pi\)
0.854840 + 0.518892i \(0.173655\pi\)
\(284\) 3.52248 0.209021
\(285\) 26.4959 5.25704i 1.56948 0.311400i
\(286\) −7.14049 −0.422226
\(287\) −8.56840 + 8.56840i −0.505776 + 0.505776i
\(288\) −2.00487 + 3.37555i −0.118138 + 0.198906i
\(289\) 16.9617i 0.997745i
\(290\) −0.408348 0.354020i −0.0239790 0.0207888i
\(291\) −15.3747 11.9490i −0.901279 0.700462i
\(292\) −0.926172 0.926172i −0.0542001 0.0542001i
\(293\) 13.8329 + 13.8329i 0.808128 + 0.808128i 0.984350 0.176223i \(-0.0563878\pi\)
−0.176223 + 0.984350i \(0.556388\pi\)
\(294\) −9.85463 7.65889i −0.574734 0.446676i
\(295\) −1.65231 23.1862i −0.0962013 1.34995i
\(296\) 14.7165i 0.855380i
\(297\) −1.89920 4.83664i −0.110202 0.280650i
\(298\) 9.88100 9.88100i 0.572391 0.572391i
\(299\) −17.8948 −1.03488
\(300\) −0.531211 1.94199i −0.0306695 0.112121i
\(301\) 2.38635 0.137547
\(302\) 3.00876 3.00876i 0.173134 0.173134i
\(303\) 0.502323 + 4.00659i 0.0288577 + 0.230173i
\(304\) 30.7642i 1.76445i
\(305\) 1.32508 + 18.5943i 0.0758737 + 1.06470i
\(306\) −0.216679 0.850545i −0.0123867 0.0486224i
\(307\) 2.68221 + 2.68221i 0.153082 + 0.153082i 0.779493 0.626411i \(-0.215477\pi\)
−0.626411 + 0.779493i \(0.715477\pi\)
\(308\) −0.242565 0.242565i −0.0138214 0.0138214i
\(309\) 2.94467 3.78889i 0.167516 0.215542i
\(310\) −19.0088 16.4798i −1.07963 0.935990i
\(311\) 27.6326i 1.56690i 0.621453 + 0.783452i \(0.286543\pi\)
−0.621453 + 0.783452i \(0.713457\pi\)
\(312\) 21.6903 2.71941i 1.22797 0.153956i
\(313\) −12.8540 + 12.8540i −0.726549 + 0.726549i −0.969931 0.243382i \(-0.921743\pi\)
0.243382 + 0.969931i \(0.421743\pi\)
\(314\) 24.9100 1.40575
\(315\) −4.43697 + 8.84824i −0.249995 + 0.498542i
\(316\) −3.15052 −0.177231
\(317\) −3.24834 + 3.24834i −0.182445 + 0.182445i −0.792420 0.609975i \(-0.791179\pi\)
0.609975 + 0.792420i \(0.291179\pi\)
\(318\) −0.135159 + 0.0169455i −0.00757935 + 0.000950255i
\(319\) 0.161760i 0.00905682i
\(320\) 15.3150 1.09139i 0.856136 0.0610106i
\(321\) −9.87971 + 12.7121i −0.551431 + 0.709522i
\(322\) −5.83753 5.83753i −0.325313 0.325313i
\(323\) 0.965693 + 0.965693i 0.0537326 + 0.0537326i
\(324\) −1.00108 1.83729i −0.0556154 0.102072i
\(325\) −14.3295 + 19.1214i −0.794857 + 1.06067i
\(326\) 2.16178i 0.119730i
\(327\) −4.00371 31.9341i −0.221406 1.76596i
\(328\) −15.3355 + 15.3355i −0.846764 + 0.846764i
\(329\) 1.66400 0.0917395
\(330\) 3.21731 4.81000i 0.177107 0.264782i
\(331\) 33.0142 1.81463 0.907314 0.420455i \(-0.138129\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(332\) 1.37708 1.37708i 0.0755769 0.0755769i
\(333\) 14.3733 + 8.53688i 0.787653 + 0.467818i
\(334\) 0.591624i 0.0323722i
\(335\) 11.2074 12.9273i 0.612325 0.706294i
\(336\) 8.90108 + 6.91780i 0.485594 + 0.377397i
\(337\) 7.43583 + 7.43583i 0.405055 + 0.405055i 0.880010 0.474955i \(-0.157536\pi\)
−0.474955 + 0.880010i \(0.657536\pi\)
\(338\) 10.3946 + 10.3946i 0.565393 + 0.565393i
\(339\) 17.3775 + 13.5056i 0.943816 + 0.733521i
\(340\) 0.0666783 0.0769108i 0.00361614 0.00417107i
\(341\) 7.53000i 0.407773i
\(342\) 26.8795 + 15.9648i 1.45348 + 0.863278i
\(343\) −12.3356 + 12.3356i −0.666060 + 0.666060i
\(344\) 4.27105 0.230279
\(345\) 8.06289 12.0543i 0.434092 0.648984i
\(346\) −29.1810 −1.56878
\(347\) −12.6263 + 12.6263i −0.677815 + 0.677815i −0.959505 0.281690i \(-0.909105\pi\)
0.281690 + 0.959505i \(0.409105\pi\)
\(348\) −0.00810285 0.0646293i −0.000434358 0.00346450i
\(349\) 22.9188i 1.22682i −0.789766 0.613408i \(-0.789798\pi\)
0.789766 0.613408i \(-0.210202\pi\)
\(350\) −10.9122 + 1.56320i −0.583280 + 0.0835565i
\(351\) −9.92632 + 22.7620i −0.529828 + 1.21495i
\(352\) −0.925378 0.925378i −0.0493228 0.0493228i
\(353\) −12.5661 12.5661i −0.668826 0.668826i 0.288618 0.957444i \(-0.406804\pi\)
−0.957444 + 0.288618i \(0.906804\pi\)
\(354\) 16.5090 21.2419i 0.877441 1.12900i
\(355\) 33.7948 2.40831i 1.79364 0.127820i
\(356\) 0.694072i 0.0367857i
\(357\) −0.496557 + 0.0622554i −0.0262806 + 0.00329491i
\(358\) −8.45999 + 8.45999i −0.447125 + 0.447125i
\(359\) −18.3875 −0.970455 −0.485227 0.874388i \(-0.661263\pi\)
−0.485227 + 0.874388i \(0.661263\pi\)
\(360\) −7.94121 + 15.8364i −0.418539 + 0.834652i
\(361\) −29.6446 −1.56024
\(362\) −17.8792 + 17.8792i −0.939710 + 0.939710i
\(363\) 1.71860 0.215468i 0.0902029 0.0113091i
\(364\) 1.63937i 0.0859264i
\(365\) −9.51893 8.25249i −0.498243 0.431955i
\(366\) −13.2394 + 17.0351i −0.692035 + 0.890436i
\(367\) −2.00228 2.00228i −0.104518 0.104518i 0.652914 0.757432i \(-0.273546\pi\)
−0.757432 + 0.652914i \(0.773546\pi\)
\(368\) −11.6790 11.6790i −0.608810 0.608810i
\(369\) −6.08194 23.8739i −0.316613 1.24283i
\(370\) 1.32339 + 18.5706i 0.0687998 + 0.965438i
\(371\) 0.0776670i 0.00403227i
\(372\) −0.377192 3.00853i −0.0195565 0.155985i
\(373\) 1.42819 1.42819i 0.0739491 0.0739491i −0.669165 0.743114i \(-0.733348\pi\)
0.743114 + 0.669165i \(0.233348\pi\)
\(374\) 0.292570 0.0151285
\(375\) −6.42418 18.2683i −0.331743 0.943370i
\(376\) 2.97820 0.153589
\(377\) −0.546626 + 0.546626i −0.0281527 + 0.0281527i
\(378\) −10.6634 + 4.18718i −0.548466 + 0.215365i
\(379\) 7.51540i 0.386040i −0.981195 0.193020i \(-0.938172\pi\)
0.981195 0.193020i \(-0.0618282\pi\)
\(380\) 0.257721 + 3.61649i 0.0132208 + 0.185522i
\(381\) 11.5564 + 8.98150i 0.592054 + 0.460136i
\(382\) 22.4800 + 22.4800i 1.15018 + 1.15018i
\(383\) 0.239638 + 0.239638i 0.0122450 + 0.0122450i 0.713203 0.700958i \(-0.247244\pi\)
−0.700958 + 0.713203i \(0.747244\pi\)
\(384\) 17.6103 + 13.6865i 0.898671 + 0.698435i
\(385\) −2.49301 2.16133i −0.127056 0.110152i
\(386\) 14.6227i 0.744275i
\(387\) −2.47759 + 4.17144i −0.125943 + 0.212046i
\(388\) 1.84808 1.84808i 0.0938218 0.0938218i
\(389\) 28.0738 1.42340 0.711699 0.702485i \(-0.247926\pi\)
0.711699 + 0.702485i \(0.247926\pi\)
\(390\) −27.1262 + 5.38210i −1.37359 + 0.272533i
\(391\) 0.733211 0.0370801
\(392\) −9.00605 + 9.00605i −0.454874 + 0.454874i
\(393\) 0.552019 + 4.40298i 0.0278457 + 0.222101i
\(394\) 3.81143i 0.192017i
\(395\) −30.2262 + 2.15400i −1.52084 + 0.108379i
\(396\) 0.675852 0.172175i 0.0339628 0.00865213i
\(397\) −13.0553 13.0553i −0.655226 0.655226i 0.299021 0.954247i \(-0.403340\pi\)
−0.954247 + 0.299021i \(0.903340\pi\)
\(398\) −15.4093 15.4093i −0.772398 0.772398i
\(399\) 10.9385 14.0745i 0.547609 0.704604i
\(400\) −21.8317 + 3.12745i −1.09158 + 0.156373i
\(401\) 2.07860i 0.103800i 0.998652 + 0.0519001i \(0.0165277\pi\)
−0.998652 + 0.0519001i \(0.983472\pi\)
\(402\) 19.6476 2.46330i 0.979933 0.122858i
\(403\) −25.4457 + 25.4457i −1.26754 + 1.26754i
\(404\) −0.541983 −0.0269647
\(405\) −10.8605 16.9425i −0.539662 0.841881i
\(406\) −0.356634 −0.0176995
\(407\) −3.94032 + 3.94032i −0.195314 + 0.195314i
\(408\) −0.888728 + 0.111424i −0.0439986 + 0.00551629i
\(409\) 1.39211i 0.0688354i 0.999408 + 0.0344177i \(0.0109577\pi\)
−0.999408 + 0.0344177i \(0.989042\pi\)
\(410\) 17.9727 20.7308i 0.887607 1.02382i
\(411\) −10.3651 + 13.3366i −0.511271 + 0.657848i
\(412\) 0.455434 + 0.455434i 0.0224376 + 0.0224376i
\(413\) −10.8465 10.8465i −0.533719 0.533719i
\(414\) 16.2650 4.14354i 0.799379 0.203644i
\(415\) 12.2702 14.1532i 0.602320 0.694753i
\(416\) 6.25415i 0.306635i
\(417\) −1.03490 8.25450i −0.0506794 0.404225i
\(418\) −7.36879 + 7.36879i −0.360419 + 0.360419i
\(419\) −8.51722 −0.416093 −0.208047 0.978119i \(-0.566711\pi\)
−0.208047 + 0.978119i \(0.566711\pi\)
\(420\) −1.10432 0.738655i −0.0538853 0.0360427i
\(421\) −19.3495 −0.943039 −0.471519 0.881856i \(-0.656294\pi\)
−0.471519 + 0.881856i \(0.656294\pi\)
\(422\) 5.73095 5.73095i 0.278979 0.278979i
\(423\) −1.72762 + 2.90875i −0.0839998 + 0.141428i
\(424\) 0.139007i 0.00675077i
\(425\) 0.587129 0.783471i 0.0284799 0.0380039i
\(426\) 30.9609 + 24.0624i 1.50006 + 1.16583i
\(427\) 8.69836 + 8.69836i 0.420943 + 0.420943i
\(428\) −1.52803 1.52803i −0.0738602 0.0738602i
\(429\) −6.53567 5.07943i −0.315545 0.245237i
\(430\) −5.38958 + 0.384076i −0.259909 + 0.0185218i
\(431\) 28.5298i 1.37423i −0.726548 0.687116i \(-0.758876\pi\)
0.726548 0.687116i \(-0.241124\pi\)
\(432\) −21.3340 + 8.37718i −1.02643 + 0.403047i
\(433\) −29.2496 + 29.2496i −1.40564 + 1.40564i −0.625099 + 0.780545i \(0.714941\pi\)
−0.780545 + 0.625099i \(0.785059\pi\)
\(434\) −16.6015 −0.796898
\(435\) −0.121926 0.614515i −0.00584589 0.0294637i
\(436\) 4.31982 0.206882
\(437\) −18.4669 + 18.4669i −0.883393 + 0.883393i
\(438\) −1.81383 14.4674i −0.0866684 0.691278i
\(439\) 5.90310i 0.281740i −0.990028 0.140870i \(-0.955010\pi\)
0.990028 0.140870i \(-0.0449899\pi\)
\(440\) −4.46195 3.86831i −0.212715 0.184414i
\(441\) −3.57172 14.0203i −0.170082 0.667634i
\(442\) −0.988666 0.988666i −0.0470260 0.0470260i
\(443\) −0.198416 0.198416i −0.00942704 0.00942704i 0.702378 0.711805i \(-0.252122\pi\)
−0.711805 + 0.702378i \(0.752122\pi\)
\(444\) −1.37693 + 1.77169i −0.0653463 + 0.0840806i
\(445\) −0.474534 6.65894i −0.0224951 0.315664i
\(446\) 21.7892i 1.03175i
\(447\) 16.0730 2.01513i 0.760225 0.0953126i
\(448\) 7.16434 7.16434i 0.338483 0.338483i
\(449\) 24.8090 1.17081 0.585404 0.810741i \(-0.300936\pi\)
0.585404 + 0.810741i \(0.300936\pi\)
\(450\) 8.59681 20.6979i 0.405258 0.975708i
\(451\) 8.21214 0.386694
\(452\) −2.08882 + 2.08882i −0.0982498 + 0.0982498i
\(453\) 4.89420 0.613607i 0.229950 0.0288298i
\(454\) 38.8260i 1.82219i
\(455\) 1.12083 + 15.7281i 0.0525453 + 0.737347i
\(456\) 19.5775 25.1902i 0.916800 1.17964i
\(457\) 13.7125 + 13.7125i 0.641443 + 0.641443i 0.950910 0.309467i \(-0.100151\pi\)
−0.309467 + 0.950910i \(0.600151\pi\)
\(458\) 15.2009 + 15.2009i 0.710292 + 0.710292i
\(459\) 0.406716 0.932638i 0.0189839 0.0435318i
\(460\) 1.47076 + 1.27509i 0.0685747 + 0.0594512i
\(461\) 8.41541i 0.391945i 0.980609 + 0.195972i \(0.0627863\pi\)
−0.980609 + 0.195972i \(0.937214\pi\)
\(462\) −0.475044 3.78901i −0.0221011 0.176281i
\(463\) 23.8342 23.8342i 1.10767 1.10767i 0.114212 0.993456i \(-0.463566\pi\)
0.993456 0.114212i \(-0.0364342\pi\)
\(464\) −0.713509 −0.0331238
\(465\) −5.67570 28.6060i −0.263204 1.32657i
\(466\) 27.1316 1.25685
\(467\) 27.3489 27.3489i 1.26556 1.26556i 0.317196 0.948360i \(-0.397259\pi\)
0.948360 0.317196i \(-0.102741\pi\)
\(468\) −2.86569 1.70205i −0.132466 0.0786771i
\(469\) 11.2902i 0.521331i
\(470\) −3.75816 + 0.267816i −0.173351 + 0.0123534i
\(471\) 22.8000 + 17.7199i 1.05057 + 0.816489i
\(472\) −19.4128 19.4128i −0.893546 0.893546i
\(473\) −1.14357 1.14357i −0.0525812 0.0525812i
\(474\) −27.6916 21.5215i −1.27192 0.988516i
\(475\) 4.94515 + 34.5204i 0.226899 + 1.58391i
\(476\) 0.0671707i 0.00307876i
\(477\) −0.135765 0.0806363i −0.00621626 0.00369208i
\(478\) 6.37092 6.37092i 0.291399 0.291399i
\(479\) −4.45179 −0.203407 −0.101704 0.994815i \(-0.532429\pi\)
−0.101704 + 0.994815i \(0.532429\pi\)
\(480\) −4.21294 2.81795i −0.192294 0.128621i
\(481\) 26.6306 1.21425
\(482\) −8.66155 + 8.66155i −0.394523 + 0.394523i
\(483\) −1.19051 9.49565i −0.0541700 0.432067i
\(484\) 0.232479i 0.0105672i
\(485\) 16.4669 18.9940i 0.747725 0.862472i
\(486\) 3.75170 22.9873i 0.170181 1.04273i
\(487\) 3.97415 + 3.97415i 0.180086 + 0.180086i 0.791393 0.611307i \(-0.209356\pi\)
−0.611307 + 0.791393i \(0.709356\pi\)
\(488\) 15.5682 + 15.5682i 0.704737 + 0.704737i
\(489\) 1.53780 1.97867i 0.0695417 0.0894788i
\(490\) 10.5547 12.1745i 0.476815 0.549987i
\(491\) 17.5760i 0.793192i −0.917993 0.396596i \(-0.870191\pi\)
0.917993 0.396596i \(-0.129809\pi\)
\(492\) 3.28106 0.411361i 0.147922 0.0185456i
\(493\) 0.0223972 0.0223972i 0.00100872 0.00100872i
\(494\) 49.8018 2.24069
\(495\) 6.36642 2.11393i 0.286149 0.0950140i
\(496\) −33.2142 −1.49136
\(497\) 15.8091 15.8091i 0.709136 0.709136i
\(498\) 21.5108 2.69690i 0.963921 0.120851i
\(499\) 8.21295i 0.367662i −0.982958 0.183831i \(-0.941150\pi\)
0.982958 0.183831i \(-0.0588499\pi\)
\(500\) 2.54023 0.550538i 0.113602 0.0246208i
\(501\) 0.420855 0.541511i 0.0188024 0.0241929i
\(502\) 9.65991 + 9.65991i 0.431143 + 0.431143i
\(503\) −18.7472 18.7472i −0.835895 0.835895i 0.152420 0.988316i \(-0.451293\pi\)
−0.988316 + 0.152420i \(0.951293\pi\)
\(504\) 2.88604 + 11.3288i 0.128555 + 0.504625i
\(505\) −5.19980 + 0.370551i −0.231388 + 0.0164893i
\(506\) 5.59482i 0.248720i
\(507\) 2.11989 + 16.9085i 0.0941474 + 0.750931i
\(508\) −1.38911 + 1.38911i −0.0616319 + 0.0616319i
\(509\) 24.0212 1.06472 0.532361 0.846518i \(-0.321305\pi\)
0.532361 + 0.846518i \(0.321305\pi\)
\(510\) 1.11145 0.220523i 0.0492160 0.00976493i
\(511\) −8.31343 −0.367765
\(512\) 12.3923 12.3923i 0.547669 0.547669i
\(513\) 13.2461 + 33.7335i 0.584828 + 1.48937i
\(514\) 18.0275i 0.795159i
\(515\) 4.68082 + 4.05806i 0.206261 + 0.178820i
\(516\) −0.514182 0.399615i −0.0226356 0.0175921i
\(517\) −0.797409 0.797409i −0.0350700 0.0350700i
\(518\) 8.68728 + 8.68728i 0.381697 + 0.381697i
\(519\) −26.7093 20.7581i −1.17241 0.911180i
\(520\) 2.00604 + 28.1499i 0.0879707 + 1.23446i
\(521\) 12.0705i 0.528817i −0.964411 0.264408i \(-0.914823\pi\)
0.964411 0.264408i \(-0.0851767\pi\)
\(522\) 0.370269 0.623412i 0.0162062 0.0272860i
\(523\) 22.4783 22.4783i 0.982908 0.982908i −0.0169486 0.999856i \(-0.505395\pi\)
0.999856 + 0.0169486i \(0.00539517\pi\)
\(524\) −0.595603 −0.0260190
\(525\) −11.0999 6.33165i −0.484438 0.276336i
\(526\) −3.80986 −0.166118
\(527\) 1.04260 1.04260i 0.0454163 0.0454163i
\(528\) −0.950409 7.58058i −0.0413612 0.329902i
\(529\) 8.97883i 0.390384i
\(530\) −0.0125003 0.175411i −0.000542977 0.00761937i
\(531\) 30.2212 7.69893i 1.31149 0.334105i
\(532\) 1.69179 + 1.69179i 0.0733482 + 0.0733482i
\(533\) −27.7508 27.7508i −1.20202 1.20202i
\(534\) 4.74127 6.10056i 0.205175 0.263997i
\(535\) −15.7047 13.6153i −0.678972 0.588639i
\(536\) 20.2069i 0.872806i
\(537\) −13.7615 + 1.72533i −0.593852 + 0.0744537i
\(538\) −4.00325 + 4.00325i −0.172592 + 0.172592i
\(539\) 4.82271 0.207729
\(540\) 2.43774 1.16350i 0.104904 0.0500691i
\(541\) 4.15229 0.178521 0.0892605 0.996008i \(-0.471550\pi\)
0.0892605 + 0.996008i \(0.471550\pi\)
\(542\) −30.4640 + 30.4640i −1.30854 + 1.30854i
\(543\) −29.0833 + 3.64629i −1.24808 + 0.156477i
\(544\) 0.256254i 0.0109868i
\(545\) 41.4444 2.95344i 1.77528 0.126511i
\(546\) −11.1987 + 14.4093i −0.479260 + 0.616660i
\(547\) 13.9478 + 13.9478i 0.596365 + 0.596365i 0.939343 0.342978i \(-0.111436\pi\)
−0.342978 + 0.939343i \(0.611436\pi\)
\(548\) −1.60310 1.60310i −0.0684810 0.0684810i
\(549\) −24.2360 + 6.17419i −1.03437 + 0.263508i
\(550\) 5.97833 + 4.48013i 0.254917 + 0.191033i
\(551\) 1.12821i 0.0480632i
\(552\) −2.13075 16.9951i −0.0906907 0.723360i
\(553\) −14.1397 + 14.1397i −0.601283 + 0.601283i
\(554\) −30.3679 −1.29021
\(555\) −11.9990 + 17.9390i −0.509330 + 0.761468i
\(556\) 1.11661 0.0473548
\(557\) −32.3534 + 32.3534i −1.37086 + 1.37086i −0.511682 + 0.859175i \(0.670977\pi\)
−0.859175 + 0.511682i \(0.829023\pi\)
\(558\) 17.2362 29.0201i 0.729666 1.22852i
\(559\) 7.72877i 0.326892i
\(560\) −9.53344 + 10.9965i −0.402861 + 0.464685i
\(561\) 0.267789 + 0.208122i 0.0113061 + 0.00878692i
\(562\) −23.2184 23.2184i −0.979410 0.979410i
\(563\) 15.8283 + 15.8283i 0.667083 + 0.667083i 0.957040 0.289957i \(-0.0936410\pi\)
−0.289957 + 0.957040i \(0.593641\pi\)
\(564\) −0.358539 0.278652i −0.0150972 0.0117334i
\(565\) −18.6121 + 21.4683i −0.783015 + 0.903177i
\(566\) 11.9419i 0.501955i
\(567\) −12.7388 3.75297i −0.534978 0.157610i
\(568\) 28.2949 28.2949i 1.18723 1.18723i
\(569\) 23.3745 0.979912 0.489956 0.871747i \(-0.337013\pi\)
0.489956 + 0.871747i \(0.337013\pi\)
\(570\) −22.4393 + 33.5477i −0.939880 + 1.40516i
\(571\) −14.3694 −0.601339 −0.300669 0.953728i \(-0.597210\pi\)
−0.300669 + 0.953728i \(0.597210\pi\)
\(572\) 0.785604 0.785604i 0.0328478 0.0328478i
\(573\) 4.58458 + 36.5672i 0.191524 + 1.52762i
\(574\) 18.1054i 0.755705i
\(575\) 14.9823 + 11.2276i 0.624805 + 0.468225i
\(576\) 5.08533 + 19.9618i 0.211889 + 0.831742i
\(577\) 27.3648 + 27.3648i 1.13921 + 1.13921i 0.988592 + 0.150621i \(0.0481272\pi\)
0.150621 + 0.988592i \(0.451873\pi\)
\(578\) −17.9204 17.9204i −0.745389 0.745389i
\(579\) −10.4019 + 13.3841i −0.432290 + 0.556224i
\(580\) 0.0838766 0.00597727i 0.00348279 0.000248193i
\(581\) 12.3608i 0.512813i
\(582\) 28.8681 3.61931i 1.19662 0.150025i
\(583\) 0.0372189 0.0372189i 0.00154145 0.00154145i
\(584\) −14.8792 −0.615706
\(585\) −28.6571 14.3702i −1.18483 0.594134i
\(586\) −29.2296 −1.20746
\(587\) 10.8344 10.8344i 0.447183 0.447183i −0.447234 0.894417i \(-0.647591\pi\)
0.894417 + 0.447234i \(0.147591\pi\)
\(588\) 1.92686 0.241578i 0.0794622 0.00996251i
\(589\) 52.5185i 2.16399i
\(590\) 26.2425 + 22.7510i 1.08038 + 0.936646i
\(591\) 2.71129 3.48860i 0.111528 0.143502i
\(592\) 17.3804 + 17.3804i 0.714331 + 0.714331i
\(593\) −29.3036 29.3036i −1.20335 1.20335i −0.973140 0.230214i \(-0.926057\pi\)
−0.230214 0.973140i \(-0.573943\pi\)
\(594\) 7.11656 + 3.10347i 0.291996 + 0.127337i
\(595\) −0.0459243 0.644436i −0.00188271 0.0264193i
\(596\) 2.17424i 0.0890602i
\(597\) −3.14258 25.0656i −0.128617 1.02587i
\(598\) 18.9062 18.9062i 0.773133 0.773133i
\(599\) −3.87877 −0.158482 −0.0792411 0.996855i \(-0.525250\pi\)
−0.0792411 + 0.996855i \(0.525250\pi\)
\(600\) −19.8663 11.3323i −0.811040 0.462638i
\(601\) −5.52177 −0.225238 −0.112619 0.993638i \(-0.535924\pi\)
−0.112619 + 0.993638i \(0.535924\pi\)
\(602\) −2.52123 + 2.52123i −0.102758 + 0.102758i
\(603\) 19.7357 + 11.7218i 0.803699 + 0.477348i
\(604\) 0.662053i 0.0269386i
\(605\) 0.158945 + 2.23041i 0.00646204 + 0.0906791i
\(606\) −4.76377 3.70234i −0.193515 0.150397i
\(607\) −8.91423 8.91423i −0.361817 0.361817i 0.502664 0.864482i \(-0.332353\pi\)
−0.864482 + 0.502664i \(0.832353\pi\)
\(608\) 6.45411 + 6.45411i 0.261749 + 0.261749i
\(609\) −0.326426 0.253694i −0.0132275 0.0102802i
\(610\) −21.0452 18.2453i −0.852096 0.738730i
\(611\) 5.38927i 0.218027i
\(612\) 0.117417 + 0.0697387i 0.00474631 + 0.00281902i
\(613\) −11.8416 + 11.8416i −0.478277 + 0.478277i −0.904580 0.426303i \(-0.859816\pi\)
0.426303 + 0.904580i \(0.359816\pi\)
\(614\) −5.66764 −0.228727
\(615\) 31.1973 6.18985i 1.25800 0.249599i
\(616\) −3.89688 −0.157010
\(617\) −12.9487 + 12.9487i −0.521295 + 0.521295i −0.917962 0.396668i \(-0.870167\pi\)
0.396668 + 0.917962i \(0.370167\pi\)
\(618\) 0.891931 + 7.11415i 0.0358787 + 0.286173i
\(619\) 22.4360i 0.901777i 0.892580 + 0.450889i \(0.148893\pi\)
−0.892580 + 0.450889i \(0.851107\pi\)
\(620\) 3.90450 0.278245i 0.156808 0.0111746i
\(621\) 17.8348 + 7.77761i 0.715686 + 0.312105i
\(622\) −29.1945 29.1945i −1.17059 1.17059i
\(623\) −3.11504 3.11504i −0.124801 0.124801i
\(624\) −22.4049 + 28.8283i −0.896915 + 1.15405i
\(625\) 23.9946 7.01861i 0.959783 0.280745i
\(626\) 27.1610i 1.08557i
\(627\) −11.9865 + 1.50279i −0.478694 + 0.0600158i
\(628\) −2.74062 + 2.74062i −0.109363 + 0.109363i
\(629\) −1.09115 −0.0435069
\(630\) −4.66061 14.0361i −0.185683 0.559213i
\(631\) −18.3686 −0.731243 −0.365622 0.930764i \(-0.619144\pi\)
−0.365622 + 0.930764i \(0.619144\pi\)
\(632\) −25.3070 + 25.3070i −1.00666 + 1.00666i
\(633\) 9.32228 1.16877i 0.370527 0.0464546i
\(634\) 6.86389i 0.272600i
\(635\) −12.3774 + 14.2769i −0.491183 + 0.566561i
\(636\) 0.0130060 0.0167347i 0.000515722 0.000663575i
\(637\) −16.2971 16.2971i −0.645714 0.645714i
\(638\) 0.170903 + 0.170903i 0.00676612 + 0.00676612i
\(639\) 11.2215 + 44.0485i 0.443915 + 1.74253i
\(640\) −18.8614 + 21.7559i −0.745561 + 0.859976i
\(641\) 12.9593i 0.511860i 0.966695 + 0.255930i \(0.0823817\pi\)
−0.966695 + 0.255930i \(0.917618\pi\)
\(642\) −2.99253 23.8688i −0.118106 0.942026i
\(643\) 5.94169 5.94169i 0.234317 0.234317i −0.580175 0.814492i \(-0.697016\pi\)
0.814492 + 0.580175i \(0.197016\pi\)
\(644\) 1.28450 0.0506165
\(645\) −5.20628 3.48237i −0.204997 0.137118i
\(646\) −2.04055 −0.0802845
\(647\) 20.3903 20.3903i 0.801625 0.801625i −0.181724 0.983350i \(-0.558168\pi\)
0.983350 + 0.181724i \(0.0581678\pi\)
\(648\) −22.7996 6.71698i −0.895652 0.263868i
\(649\) 10.3955i 0.408058i
\(650\) −5.06279 35.3416i −0.198579 1.38621i
\(651\) −15.1953 11.8096i −0.595551 0.462854i
\(652\) 0.237842 + 0.237842i 0.00931460 + 0.00931460i
\(653\) 0.357485 + 0.357485i 0.0139895 + 0.0139895i 0.714067 0.700077i \(-0.246851\pi\)
−0.700077 + 0.714067i \(0.746851\pi\)
\(654\) 37.9691 + 29.5091i 1.48471 + 1.15390i
\(655\) −5.71423 + 0.407211i −0.223273 + 0.0159111i
\(656\) 36.2230i 1.41427i
\(657\) 8.63126 14.5322i 0.336738 0.566956i
\(658\) −1.75806 + 1.75806i −0.0685362 + 0.0685362i
\(659\) 27.8465 1.08474 0.542372 0.840138i \(-0.317526\pi\)
0.542372 + 0.840138i \(0.317526\pi\)
\(660\) 0.175230 + 0.883173i 0.00682082 + 0.0343775i
\(661\) 16.1467 0.628034 0.314017 0.949417i \(-0.398325\pi\)
0.314017 + 0.949417i \(0.398325\pi\)
\(662\) −34.8803 + 34.8803i −1.35566 + 1.35566i
\(663\) −0.201629 1.60822i −0.00783062 0.0624580i
\(664\) 22.1231i 0.858544i
\(665\) 17.3877 + 15.0744i 0.674266 + 0.584558i
\(666\) −24.2051 + 6.16632i −0.937930 + 0.238940i
\(667\) 0.428300 + 0.428300i 0.0165839 + 0.0165839i
\(668\) 0.0650911 + 0.0650911i 0.00251845 + 0.00251845i
\(669\) −15.4999 + 19.9435i −0.599259 + 0.771062i
\(670\) 1.81712 + 25.4988i 0.0702013 + 0.985106i
\(671\) 8.33669i 0.321835i
\(672\) −3.31869 + 0.416078i −0.128021 + 0.0160505i
\(673\) 15.9975 15.9975i 0.616658 0.616658i −0.328015 0.944673i \(-0.606380\pi\)
0.944673 + 0.328015i \(0.106380\pi\)
\(674\) −15.7122 −0.605213
\(675\) 22.5922 12.8293i 0.869575 0.493801i
\(676\) −2.28726 −0.0879714
\(677\) −3.58130 + 3.58130i −0.137641 + 0.137641i −0.772570 0.634929i \(-0.781029\pi\)
0.634929 + 0.772570i \(0.281029\pi\)
\(678\) −32.6286 + 4.09079i −1.25310 + 0.157106i
\(679\) 16.5885i 0.636610i
\(680\) −0.0821944 1.15340i −0.00315201 0.0442309i
\(681\) −27.6191 + 35.5373i −1.05837 + 1.36179i
\(682\) 7.95562 + 7.95562i 0.304636 + 0.304636i
\(683\) 15.0743 + 15.0743i 0.576802 + 0.576802i 0.934021 0.357219i \(-0.116275\pi\)
−0.357219 + 0.934021i \(0.616275\pi\)
\(684\) −4.71378 + 1.20085i −0.180236 + 0.0459156i
\(685\) −16.4762 14.2841i −0.629523 0.545768i
\(686\) 26.0657i 0.995192i
\(687\) 3.10008 + 24.7266i 0.118275 + 0.943379i
\(688\) −5.04417 + 5.04417i −0.192307 + 0.192307i
\(689\) −0.251543 −0.00958302
\(690\) 4.21706 + 21.2543i 0.160541 + 0.809138i
\(691\) 4.01842 0.152868 0.0764340 0.997075i \(-0.475647\pi\)
0.0764340 + 0.997075i \(0.475647\pi\)
\(692\) 3.21053 3.21053i 0.122046 0.122046i
\(693\) 2.26053 3.80600i 0.0858705 0.144578i
\(694\) 26.6799i 1.01276i
\(695\) 10.7128 0.763421i 0.406359 0.0289582i
\(696\) −0.584232 0.454057i −0.0221452 0.0172110i
\(697\) 1.13705 + 1.13705i 0.0430687 + 0.0430687i
\(698\) 24.2143 + 24.2143i 0.916523 + 0.916523i
\(699\) 24.8335 + 19.3003i 0.939289 + 0.730003i
\(700\) 1.02858 1.37255i 0.0388768 0.0518776i
\(701\) 36.2944i 1.37082i 0.728157 + 0.685410i \(0.240377\pi\)
−0.728157 + 0.685410i \(0.759623\pi\)
\(702\) −13.5612 34.5359i −0.511834 1.30348i
\(703\) 27.4820 27.4820i 1.03651 1.03651i
\(704\) −6.86646 −0.258789
\(705\) −3.63034 2.42826i −0.136727 0.0914535i
\(706\) 26.5527 0.999325
\(707\) −2.43245 + 2.43245i −0.0914818 + 0.0914818i
\(708\) 0.520728 + 4.15339i 0.0195702 + 0.156094i
\(709\) 17.0221i 0.639277i −0.947540 0.319639i \(-0.896438\pi\)
0.947540 0.319639i \(-0.103562\pi\)
\(710\) −33.1605 + 38.2494i −1.24449 + 1.43547i
\(711\) −10.0365 39.3972i −0.376399 1.47751i
\(712\) −5.57523 5.57523i −0.208941 0.208941i
\(713\) 19.9376 + 19.9376i 0.746668 + 0.746668i
\(714\) 0.458849 0.590398i 0.0171720 0.0220951i
\(715\) 6.99998 8.07421i 0.261785 0.301958i
\(716\) 1.86156i 0.0695696i
\(717\) 10.3633 1.29929i 0.387024 0.0485228i
\(718\) 19.4268 19.4268i 0.725002 0.725002i
\(719\) −20.9403 −0.780940 −0.390470 0.920616i \(-0.627688\pi\)
−0.390470 + 0.920616i \(0.627688\pi\)
\(720\) −9.32435 28.0817i −0.347498 1.04654i
\(721\) 4.08803 0.152246
\(722\) 31.3202 31.3202i 1.16562 1.16562i
\(723\) −14.0893 + 1.76644i −0.523989 + 0.0656946i
\(724\) 3.93418i 0.146213i
\(725\) 0.800627 0.114692i 0.0297345 0.00425956i
\(726\) −1.58809 + 2.04338i −0.0589395 + 0.0758370i
\(727\) −7.72035 7.72035i −0.286332 0.286332i 0.549296 0.835628i \(-0.314896\pi\)
−0.835628 + 0.549296i \(0.814896\pi\)
\(728\) 13.1685 + 13.1685i 0.488056 + 0.488056i
\(729\) 19.7861 18.3714i 0.732819 0.680424i
\(730\) 18.7759 1.33802i 0.694927 0.0495224i
\(731\) 0.316674i 0.0117126i
\(732\) −0.417600 3.33083i −0.0154349 0.123111i
\(733\) −0.579034 + 0.579034i −0.0213871 + 0.0213871i −0.717719 0.696332i \(-0.754814\pi\)
0.696332 + 0.717719i \(0.254814\pi\)
\(734\) 4.23091 0.156166
\(735\) 18.3211 3.63509i 0.675785 0.134082i
\(736\) 4.90034 0.180629
\(737\) −5.41037 + 5.41037i −0.199293 + 0.199293i
\(738\) 31.6490 + 18.7976i 1.16502 + 0.691949i
\(739\) 40.7534i 1.49914i 0.661925 + 0.749570i \(0.269740\pi\)
−0.661925 + 0.749570i \(0.730260\pi\)
\(740\) −2.18876 1.89755i −0.0804603 0.0697555i
\(741\) 45.5835 + 35.4269i 1.67455 + 1.30144i
\(742\) −0.0820569 0.0820569i −0.00301240 0.00301240i
\(743\) −24.8882 24.8882i −0.913060 0.913060i 0.0834523 0.996512i \(-0.473405\pi\)
−0.996512 + 0.0834523i \(0.973405\pi\)
\(744\) −27.1963 21.1366i −0.997064 0.774905i
\(745\) 1.48652 + 20.8597i 0.0544617 + 0.764239i
\(746\) 3.01784i 0.110491i
\(747\) 21.6072 + 12.8334i 0.790566 + 0.469548i
\(748\) −0.0321889 + 0.0321889i −0.00117694 + 0.00117694i
\(749\) −13.7158 −0.501165
\(750\) 26.0881 + 12.5136i 0.952604 + 0.456930i
\(751\) 18.0268 0.657805 0.328903 0.944364i \(-0.393321\pi\)
0.328903 + 0.944364i \(0.393321\pi\)
\(752\) −3.51730 + 3.51730i −0.128263 + 0.128263i
\(753\) 1.97005 + 15.7133i 0.0717924 + 0.572625i
\(754\) 1.15505i 0.0420643i
\(755\) 0.452643 + 6.35175i 0.0164734 + 0.231164i
\(756\) 0.712520 1.63388i 0.0259141 0.0594235i
\(757\) −33.3360 33.3360i −1.21162 1.21162i −0.970494 0.241123i \(-0.922484\pi\)
−0.241123 0.970494i \(-0.577516\pi\)
\(758\) 7.94019 + 7.94019i 0.288401 + 0.288401i
\(759\) −3.97991 + 5.12092i −0.144462 + 0.185878i
\(760\) 31.1201 + 26.9798i 1.12885 + 0.978660i
\(761\) 45.3776i 1.64494i 0.568811 + 0.822468i \(0.307404\pi\)
−0.568811 + 0.822468i \(0.692596\pi\)
\(762\) −21.6988 + 2.72047i −0.786064 + 0.0985521i
\(763\) 19.3876 19.3876i 0.701879 0.701879i
\(764\) −4.94654 −0.178960
\(765\) 1.17418 + 0.588796i 0.0424526 + 0.0212880i
\(766\) −0.506367 −0.0182958
\(767\) 35.1288 35.1288i 1.26843 1.26843i
\(768\) −9.46438 + 1.18659i −0.341516 + 0.0428173i
\(769\) 8.85728i 0.319402i −0.987165 0.159701i \(-0.948947\pi\)
0.987165 0.159701i \(-0.0510530\pi\)
\(770\) 4.91742 0.350429i 0.177211 0.0126286i
\(771\) 12.8240 16.5005i 0.461844 0.594251i
\(772\) −1.60880 1.60880i −0.0579021 0.0579021i
\(773\) −25.8567 25.8567i −0.930001 0.930001i 0.0677042 0.997705i \(-0.478433\pi\)
−0.997705 + 0.0677042i \(0.978433\pi\)
\(774\) −1.78960 7.02485i −0.0643258 0.252503i
\(775\) 37.2696 5.33897i 1.33876 0.191782i
\(776\) 29.6899i 1.06580i
\(777\) 1.77169 + 14.1312i 0.0635589 + 0.506954i
\(778\) −29.6606 + 29.6606i −1.06338 + 1.06338i
\(779\) −57.2761 −2.05213
\(780\) 2.39231 3.57660i 0.0856584 0.128063i
\(781\) −15.1518 −0.542174
\(782\) −0.774654 + 0.774654i −0.0277016 + 0.0277016i
\(783\) 0.782374 0.307214i 0.0279598 0.0109789i
\(784\) 21.2725i 0.759734i
\(785\) −24.4198 + 28.1673i −0.871581 + 1.00533i
\(786\) −5.23506 4.06862i −0.186729 0.145123i
\(787\) 2.52646 + 2.52646i 0.0900586 + 0.0900586i 0.750701 0.660642i \(-0.229716\pi\)
−0.660642 + 0.750701i \(0.729716\pi\)
\(788\) 0.419338 + 0.419338i 0.0149383 + 0.0149383i
\(789\) −3.48715 2.71017i −0.124146 0.0964845i
\(790\) 29.6589 34.2104i 1.05522 1.21715i
\(791\) 18.7495i 0.666655i
\(792\) 4.04586 6.81190i 0.143763 0.242050i
\(793\) −28.1717 + 28.1717i −1.00041 + 1.00041i
\(794\) 27.5864 0.979004
\(795\) 0.113338 0.169445i 0.00401970 0.00600961i
\(796\) 3.39069 0.120180
\(797\) 6.73965 6.73965i 0.238731 0.238731i −0.577594 0.816324i \(-0.696008\pi\)
0.816324 + 0.577594i \(0.196008\pi\)
\(798\) 3.31323 + 26.4267i 0.117287 + 0.935496i
\(799\) 0.220817i 0.00781195i
\(800\) 3.92401 5.23625i 0.138735 0.185129i
\(801\) 8.67934 2.21109i 0.306669 0.0781249i
\(802\) −2.19608 2.19608i −0.0775464 0.0775464i
\(803\) 3.98389 + 3.98389i 0.140588 + 0.140588i
\(804\) −1.89063 + 2.43266i −0.0666775 + 0.0857935i
\(805\) 12.3235 0.878209i 0.434348 0.0309528i
\(806\) 53.7679i 1.89389i
\(807\) −6.51190 + 0.816424i −0.229230 + 0.0287395i
\(808\) −4.35356 + 4.35356i −0.153158 + 0.153158i
\(809\) −26.6054 −0.935397 −0.467698 0.883888i \(-0.654917\pi\)
−0.467698 + 0.883888i \(0.654917\pi\)
\(810\) 29.3745 + 6.42581i 1.03212 + 0.225780i
\(811\) −49.2615 −1.72980 −0.864902 0.501941i \(-0.832620\pi\)
−0.864902 + 0.501941i \(0.832620\pi\)
\(812\) 0.0392373 0.0392373i 0.00137696 0.00137696i
\(813\) −49.5543 + 6.21283i −1.73795 + 0.217894i
\(814\) 8.32608i 0.291829i
\(815\) 2.44447 + 2.11925i 0.0856260 + 0.0742340i
\(816\) 0.918008 1.18119i 0.0321367 0.0413500i
\(817\) 7.97588 + 7.97588i 0.279041 + 0.279041i
\(818\) −1.47079 1.47079i −0.0514251 0.0514251i
\(819\) −20.5003 + 5.22250i −0.716337 + 0.182489i
\(820\) 0.303451 + 4.25820i 0.0105970 + 0.148703i
\(821\) 12.0560i 0.420756i −0.977620 0.210378i \(-0.932531\pi\)
0.977620 0.210378i \(-0.0674695\pi\)
\(822\) −3.13954 25.0414i −0.109504 0.873419i
\(823\) 24.7646 24.7646i 0.863241 0.863241i −0.128472 0.991713i \(-0.541007\pi\)
0.991713 + 0.128472i \(0.0410072\pi\)
\(824\) 7.31668 0.254888
\(825\) 2.28498 + 8.35337i 0.0795528 + 0.290827i
\(826\) 22.9191 0.797456
\(827\) 29.8690 29.8690i 1.03865 1.03865i 0.0394242 0.999223i \(-0.487448\pi\)
0.999223 0.0394242i \(-0.0125524\pi\)
\(828\) −1.33361 + 2.24537i −0.0463462 + 0.0780318i
\(829\) 13.4176i 0.466013i −0.972475 0.233006i \(-0.925144\pi\)
0.972475 0.233006i \(-0.0748563\pi\)
\(830\) 1.98943 + 27.9169i 0.0690542 + 0.969009i
\(831\) −27.7956 21.6024i −0.964220 0.749379i
\(832\) 23.2034 + 23.2034i 0.804434 + 0.804434i
\(833\) 0.667748 + 0.667748i 0.0231361 + 0.0231361i
\(834\) 9.81446 + 7.62767i 0.339847 + 0.264125i
\(835\) 0.668987 + 0.579982i 0.0231513 + 0.0200711i
\(836\) 1.62144i 0.0560788i
\(837\) 36.4199 14.3010i 1.25886 0.494313i
\(838\) 8.99863 8.99863i 0.310853 0.310853i
\(839\) −32.2680 −1.11401 −0.557007 0.830508i \(-0.688050\pi\)
−0.557007 + 0.830508i \(0.688050\pi\)
\(840\) −14.8040 + 2.93725i −0.510785 + 0.101345i
\(841\) −28.9738 −0.999098
\(842\) 20.4432 20.4432i 0.704520 0.704520i
\(843\) −4.73518 37.7684i −0.163088 1.30081i
\(844\) 1.26105i 0.0434072i
\(845\) −21.9440 + 1.56379i −0.754896 + 0.0537959i
\(846\) −1.24789 4.89843i −0.0429033 0.168411i
\(847\) 1.04338 + 1.04338i 0.0358510 + 0.0358510i
\(848\) −0.164169 0.164169i −0.00563759 0.00563759i
\(849\) −8.49494 + 10.9304i −0.291546 + 0.375129i
\(850\) 0.207440 + 1.44807i 0.00711514 + 0.0496684i
\(851\) 20.8660i 0.715277i
\(852\) −6.05373 + 0.758982i −0.207397 + 0.0260023i
\(853\) 11.1082 11.1082i 0.380338 0.380338i −0.490886 0.871224i \(-0.663327\pi\)
0.871224 + 0.490886i \(0.163327\pi\)
\(854\) −18.3800 −0.628951
\(855\) −44.4030 + 14.7437i −1.51855 + 0.504225i
\(856\) −24.5483 −0.839043
\(857\) −25.3044 + 25.3044i −0.864382 + 0.864382i −0.991843 0.127462i \(-0.959317\pi\)
0.127462 + 0.991843i \(0.459317\pi\)
\(858\) 12.2716 1.53854i 0.418946 0.0525250i
\(859\) 14.5610i 0.496814i 0.968656 + 0.248407i \(0.0799071\pi\)
−0.968656 + 0.248407i \(0.920093\pi\)
\(860\) 0.550711 0.635224i 0.0187791 0.0216610i
\(861\) 12.8794 16.5718i 0.438929 0.564766i
\(862\) 30.1424 + 30.1424i 1.02665 + 1.02665i
\(863\) −31.1659 31.1659i −1.06090 1.06090i −0.998021 0.0628778i \(-0.979972\pi\)
−0.0628778 0.998021i \(-0.520028\pi\)
\(864\) 2.71824 6.23319i 0.0924765 0.212057i
\(865\) 28.6068 32.9969i 0.972661 1.12193i
\(866\) 61.8056i 2.10024i
\(867\) −3.65469 29.1502i −0.124120 0.989994i
\(868\) 1.82652 1.82652i 0.0619960 0.0619960i
\(869\) 13.5518 0.459714
\(870\) 0.778066 + 0.520432i 0.0263789 + 0.0176443i
\(871\) 36.5659 1.23899
\(872\) 34.6996 34.6996i 1.17508 1.17508i
\(873\) 28.9975 + 17.2227i 0.981416 + 0.582902i
\(874\) 39.0214i 1.31992i
\(875\) 8.92984 13.8715i 0.301884 0.468944i
\(876\) 1.79128 + 1.39216i 0.0605216 + 0.0470366i
\(877\) 5.05706 + 5.05706i 0.170765 + 0.170765i 0.787315 0.616551i \(-0.211470\pi\)
−0.616551 + 0.787315i \(0.711470\pi\)
\(878\) 6.23676 + 6.23676i 0.210481 + 0.210481i
\(879\) −26.7538 20.7927i −0.902382 0.701319i
\(880\) 9.83815 0.701093i 0.331644 0.0236338i
\(881\) 0.249716i 0.00841316i 0.999991 + 0.00420658i \(0.00133900\pi\)
−0.999991 + 0.00420658i \(0.998661\pi\)
\(882\) 18.5864 + 11.0392i 0.625836 + 0.371709i
\(883\) −4.25796 + 4.25796i −0.143292 + 0.143292i −0.775114 0.631822i \(-0.782307\pi\)
0.631822 + 0.775114i \(0.282307\pi\)
\(884\) 0.217548 0.00731694
\(885\) 7.83553 + 39.4917i 0.263389 + 1.32750i
\(886\) 0.419263 0.0140854
\(887\) −17.6949 + 17.6949i −0.594137 + 0.594137i −0.938746 0.344609i \(-0.888011\pi\)
0.344609 + 0.938746i \(0.388011\pi\)
\(888\) 3.17093 + 25.2917i 0.106410 + 0.848735i
\(889\) 12.4688i 0.418191i
\(890\) 7.53667 + 6.53396i 0.252630 + 0.219019i
\(891\) 4.30609 + 7.90301i 0.144259 + 0.264761i
\(892\) −2.39727 2.39727i −0.0802664 0.0802664i
\(893\) 5.56158 + 5.56158i 0.186111 + 0.186111i
\(894\) −14.8524 + 19.1105i −0.496739 + 0.639150i
\(895\) −1.27274 17.8598i −0.0425429 0.596987i
\(896\) 19.0007i 0.634768i
\(897\) 30.7539 3.85575i 1.02684 0.128740i
\(898\) −26.2113 + 26.2113i −0.874681 + 0.874681i
\(899\) 1.21805 0.0406244
\(900\) 1.33137 + 3.22303i 0.0443791 + 0.107434i
\(901\) 0.0103066 0.000343362
\(902\) −8.67631 + 8.67631i −0.288889 + 0.288889i
\(903\) −4.10118 + 0.514182i −0.136479 + 0.0171109i
\(904\) 33.5575i 1.11611i
\(905\) −2.68978 37.7446i −0.0894113 1.25467i
\(906\) −4.52255 + 5.81913i −0.150252 + 0.193328i
\(907\) 20.7669 + 20.7669i 0.689555 + 0.689555i 0.962134 0.272578i \(-0.0878764\pi\)
−0.272578 + 0.962134i \(0.587876\pi\)
\(908\) −4.27168 4.27168i −0.141761 0.141761i
\(909\) −1.72658 6.77748i −0.0572671 0.224795i
\(910\) −17.8013 15.4330i −0.590108 0.511598i
\(911\) 51.3966i 1.70285i 0.524479 + 0.851423i \(0.324260\pi\)
−0.524479 + 0.851423i \(0.675740\pi\)
\(912\) 6.62869 + 52.8713i 0.219498 + 1.75074i
\(913\) −5.92343 + 5.92343i −0.196037 + 0.196037i
\(914\) −28.9751 −0.958411
\(915\) −6.28373 31.6705i −0.207734 1.04700i
\(916\) −3.34484 −0.110517
\(917\) −2.67310 + 2.67310i −0.0882736 + 0.0882736i
\(918\) 0.555648 + 1.41506i 0.0183391 + 0.0467038i
\(919\) 8.13299i 0.268283i 0.990962 + 0.134141i \(0.0428276\pi\)
−0.990962 + 0.134141i \(0.957172\pi\)
\(920\) 22.0564 1.57180i 0.727179 0.0518208i
\(921\) −5.18757 4.03171i −0.170936 0.132849i
\(922\) −8.89107 8.89107i −0.292812 0.292812i
\(923\) 51.2016 + 51.2016i 1.68532 + 1.68532i
\(924\) 0.469136 + 0.364606i 0.0154334 + 0.0119947i
\(925\) −22.2963 16.7087i −0.733098 0.549379i
\(926\) 50.3627i 1.65502i
\(927\) −4.24432 + 7.14605i −0.139402 + 0.234707i
\(928\) 0.149689 0.149689i 0.00491378 0.00491378i
\(929\) 58.9243 1.93324 0.966622 0.256208i \(-0.0824733\pi\)
0.966622 + 0.256208i \(0.0824733\pi\)
\(930\) 36.2193 + 24.2263i 1.18768 + 0.794413i
\(931\) −33.6363 −1.10239
\(932\) −2.98505 + 2.98505i −0.0977786 + 0.0977786i
\(933\) −5.95394 47.4894i −0.194923 1.55473i
\(934\) 57.7895i 1.89093i
\(935\) −0.286814 + 0.330828i −0.00937980 + 0.0108192i
\(936\) −36.6910 + 9.34713i −1.19928 + 0.305520i
\(937\) −25.4166 25.4166i −0.830325 0.830325i 0.157236 0.987561i \(-0.449742\pi\)
−0.987561 + 0.157236i \(0.949742\pi\)
\(938\) 11.9283 + 11.9283i 0.389473 + 0.389473i
\(939\) 19.3212 24.8604i 0.630522 0.811288i
\(940\) 0.384011 0.442942i 0.0125251 0.0144472i
\(941\) 13.9714i 0.455454i −0.973725 0.227727i \(-0.926871\pi\)
0.973725 0.227727i \(-0.0731294\pi\)
\(942\) −42.8102 + 5.36729i −1.39483 + 0.174876i
\(943\) −21.7437 + 21.7437i −0.708072 + 0.708072i
\(944\) 45.8536 1.49241
\(945\) 5.71886 16.1626i 0.186034 0.525769i
\(946\) 2.41641 0.0785641
\(947\) 16.9086 16.9086i 0.549455 0.549455i −0.376828 0.926283i \(-0.622985\pi\)
0.926283 + 0.376828i \(0.122985\pi\)
\(948\) 5.41447 0.678835i 0.175854 0.0220476i
\(949\) 26.9250i 0.874023i
\(950\) −41.6963 31.2470i −1.35281 1.01379i
\(951\) 4.88268 6.28250i 0.158332 0.203724i
\(952\) −0.539558 0.539558i −0.0174872 0.0174872i
\(953\) −1.08828 1.08828i −0.0352529 0.0352529i 0.689261 0.724513i \(-0.257936\pi\)
−0.724513 + 0.689261i \(0.757936\pi\)
\(954\) 0.228633 0.0582449i 0.00740227 0.00188575i
\(955\) −47.4572 + 3.38193i −1.53568 + 0.109437i
\(956\) 1.40187i 0.0453397i
\(957\) 0.0348540 + 0.278000i 0.00112667 + 0.00898647i
\(958\) 4.70341 4.70341i 0.151960 0.151960i
\(959\) −14.3896 −0.464665
\(960\) −26.0852 + 5.17555i −0.841896 + 0.167040i
\(961\) 25.7010 0.829064
\(962\) −28.1358 + 28.1358i −0.907135 + 0.907135i
\(963\) 14.2402 23.9758i 0.458883 0.772609i
\(964\) 1.90591i 0.0613851i
\(965\) −16.5348 14.3350i −0.532275 0.461458i
\(966\) 11.2902 + 8.77456i 0.363255 + 0.282317i
\(967\) −8.46891 8.46891i −0.272342 0.272342i 0.557701 0.830042i \(-0.311684\pi\)
−0.830042 + 0.557701i \(0.811684\pi\)
\(968\) 1.86743 + 1.86743i 0.0600213 + 0.0600213i
\(969\) −1.86771 1.45156i −0.0599996 0.0466309i
\(970\) 2.66988 + 37.4653i 0.0857246 + 1.20294i
\(971\) 23.1322i 0.742347i 0.928564 + 0.371173i \(0.121044\pi\)
−0.928564 + 0.371173i \(0.878956\pi\)
\(972\) 2.11632 + 2.94186i 0.0678811 + 0.0943601i
\(973\) 5.01142 5.01142i 0.160659 0.160659i
\(974\) −8.39756 −0.269075
\(975\) 20.5066 35.9496i 0.656735 1.15131i
\(976\) −36.7724 −1.17706
\(977\) 26.7706 26.7706i 0.856468 0.856468i −0.134452 0.990920i \(-0.542927\pi\)
0.990920 + 0.134452i \(0.0429273\pi\)
\(978\) 0.465795 + 3.71523i 0.0148945 + 0.118800i
\(979\) 2.98552i 0.0954176i
\(980\) 0.178206 + 2.50069i 0.00569259 + 0.0798817i
\(981\) 13.7615 + 54.0192i 0.439372 + 1.72470i
\(982\) 18.5694 + 18.5694i 0.592573 + 0.592573i
\(983\) 2.19423 + 2.19423i 0.0699849 + 0.0699849i 0.741233 0.671248i \(-0.234241\pi\)
−0.671248 + 0.741233i \(0.734241\pi\)
\(984\) 23.0513 29.6599i 0.734849 0.945524i
\(985\) 4.30984 + 3.73644i 0.137323 + 0.119053i
\(986\) 0.0473262i 0.00150717i
\(987\) −2.85975 + 0.358539i −0.0910269 + 0.0114124i
\(988\) −5.47925 + 5.47925i −0.174318 + 0.174318i
\(989\) 6.05576 0.192562
\(990\) −4.49285 + 8.95968i −0.142792 + 0.284757i
\(991\) −5.63682 −0.179059 −0.0895297 0.995984i \(-0.528536\pi\)
−0.0895297 + 0.995984i \(0.528536\pi\)
\(992\) 6.96810 6.96810i 0.221237 0.221237i
\(993\) −56.7382 + 7.11350i −1.80053 + 0.225740i
\(994\) 33.4054i 1.05955i
\(995\) 32.5304 2.31820i 1.03128 0.0734920i
\(996\) −2.06992 + 2.66335i −0.0655880 + 0.0843916i
\(997\) −30.3894 30.3894i −0.962443 0.962443i 0.0368765 0.999320i \(-0.488259\pi\)
−0.999320 + 0.0368765i \(0.988259\pi\)
\(998\) 8.67716 + 8.67716i 0.274671 + 0.274671i
\(999\) −26.5413 11.5745i −0.839731 0.366200i
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 165.2.k.c.122.3 yes 16
3.2 odd 2 165.2.k.d.122.6 yes 16
5.2 odd 4 825.2.k.i.518.3 16
5.3 odd 4 165.2.k.d.23.6 yes 16
5.4 even 2 825.2.k.j.782.6 16
15.2 even 4 825.2.k.j.518.6 16
15.8 even 4 inner 165.2.k.c.23.3 16
15.14 odd 2 825.2.k.i.782.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.k.c.23.3 16 15.8 even 4 inner
165.2.k.c.122.3 yes 16 1.1 even 1 trivial
165.2.k.d.23.6 yes 16 5.3 odd 4
165.2.k.d.122.6 yes 16 3.2 odd 2
825.2.k.i.518.3 16 5.2 odd 4
825.2.k.i.782.3 16 15.14 odd 2
825.2.k.j.518.6 16 15.2 even 4
825.2.k.j.782.6 16 5.4 even 2