Properties

Label 201.2.e.b.37.4
Level $201$
Weight $2$
Character 201.37
Analytic conductor $1.605$
Analytic rank $0$
Dimension $10$
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] = [201,2,Mod(37,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.e (of order \(3\), 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: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 49x^{6} - 39x^{5} + 128x^{4} - 14x^{3} + 119x^{2} - 49x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.4
Root \(-0.527336 - 0.913372i\) of defining polynomial
Character \(\chi\) \(=\) 201.37
Dual form 201.2.e.b.163.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.527336 + 0.913372i) q^{2} -1.00000 q^{3} +(0.443834 - 0.768743i) q^{4} +0.832996 q^{5} +(-0.527336 - 0.913372i) q^{6} +(1.13029 - 1.95772i) q^{7} +3.04554 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.527336 + 0.913372i) q^{2} -1.00000 q^{3} +(0.443834 - 0.768743i) q^{4} +0.832996 q^{5} +(-0.527336 - 0.913372i) q^{6} +(1.13029 - 1.95772i) q^{7} +3.04554 q^{8} +1.00000 q^{9} +(0.439269 + 0.760836i) q^{10} +(-0.713790 + 1.23632i) q^{11} +(-0.443834 + 0.768743i) q^{12} +(0.308980 + 0.535170i) q^{13} +2.38417 q^{14} -0.832996 q^{15} +(0.718355 + 1.24423i) q^{16} +(2.57744 + 4.46426i) q^{17} +(0.527336 + 0.913372i) q^{18} +(-0.939269 - 1.62686i) q^{19} +(0.369712 - 0.640360i) q^{20} +(-1.13029 + 1.95772i) q^{21} -1.50563 q^{22} +(-1.55467 - 2.69277i) q^{23} -3.04554 q^{24} -4.30612 q^{25} +(-0.325873 + 0.564428i) q^{26} -1.00000 q^{27} +(-1.00332 - 1.73780i) q^{28} +(-0.962039 + 1.66630i) q^{29} +(-0.439269 - 0.760836i) q^{30} +(-0.286210 + 0.495730i) q^{31} +(2.28791 - 3.96278i) q^{32} +(0.713790 - 1.23632i) q^{33} +(-2.71836 + 4.70833i) q^{34} +(0.941526 - 1.63077i) q^{35} +(0.443834 - 0.768743i) q^{36} +(-2.67890 - 4.63999i) q^{37} +(0.990620 - 1.71580i) q^{38} +(-0.308980 - 0.535170i) q^{39} +2.53692 q^{40} +(-4.25132 + 7.36350i) q^{41} -2.38417 q^{42} -7.16863 q^{43} +(0.633608 + 1.09744i) q^{44} +0.832996 q^{45} +(1.63967 - 2.83999i) q^{46} +(0.624228 - 1.08120i) q^{47} +(-0.718355 - 1.24423i) q^{48} +(0.944897 + 1.63661i) q^{49} +(-2.27077 - 3.93309i) q^{50} +(-2.57744 - 4.46426i) q^{51} +0.548544 q^{52} -4.80713 q^{53} +(-0.527336 - 0.913372i) q^{54} +(-0.594584 + 1.02985i) q^{55} +(3.44234 - 5.96231i) q^{56} +(0.939269 + 1.62686i) q^{57} -2.02927 q^{58} +7.75196 q^{59} +(-0.369712 + 0.640360i) q^{60} +(-1.96992 - 3.41201i) q^{61} -0.603715 q^{62} +(1.13029 - 1.95772i) q^{63} +7.69941 q^{64} +(0.257379 + 0.445794i) q^{65} +1.50563 q^{66} +(-7.67540 - 2.84399i) q^{67} +4.57582 q^{68} +(1.55467 + 2.69277i) q^{69} +1.98600 q^{70} +(-4.64824 + 8.05099i) q^{71} +3.04554 q^{72} +(7.88356 + 13.6547i) q^{73} +(2.82536 - 4.89367i) q^{74} +4.30612 q^{75} -1.66752 q^{76} +(1.61358 + 2.79480i) q^{77} +(0.325873 - 0.564428i) q^{78} +(-0.745691 + 1.29158i) q^{79} +(0.598387 + 1.03644i) q^{80} +1.00000 q^{81} -8.96749 q^{82} +(-0.355767 - 0.616206i) q^{83} +(1.00332 + 1.73780i) q^{84} +(2.14700 + 3.71871i) q^{85} +(-3.78028 - 6.54763i) q^{86} +(0.962039 - 1.66630i) q^{87} +(-2.17388 + 3.76527i) q^{88} -0.514759 q^{89} +(0.439269 + 0.760836i) q^{90} +1.39695 q^{91} -2.76006 q^{92} +(0.286210 - 0.495730i) q^{93} +1.31671 q^{94} +(-0.782407 - 1.35517i) q^{95} +(-2.28791 + 3.96278i) q^{96} +(0.590375 + 1.02256i) q^{97} +(-0.996556 + 1.72609i) q^{98} +(-0.713790 + 1.23632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + 3 q^{13} - 22 q^{14} - 2 q^{15} + 2 q^{17} - 2 q^{18} + 3 q^{19} + 16 q^{20} + q^{21} + 6 q^{22} - q^{23} - 12 q^{24} + 7 q^{26} - 10 q^{27} - 9 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 9 q^{32} - 2 q^{33} - 20 q^{34} + 19 q^{35} - 6 q^{36} + 27 q^{37} - 16 q^{38} - 3 q^{39} - 22 q^{40} - 7 q^{41} + 22 q^{42} + 12 q^{43} - 7 q^{44} + 2 q^{45} + 30 q^{46} - 33 q^{47} - 24 q^{49} + 21 q^{50} - 2 q^{51} - 32 q^{52} - 24 q^{53} + 2 q^{54} + 6 q^{55} - q^{56} - 3 q^{57} + 44 q^{58} + 24 q^{59} - 16 q^{60} + q^{61} + 2 q^{62} - q^{63} - 8 q^{64} - 6 q^{65} - 6 q^{66} + 2 q^{67} - 18 q^{68} + q^{69} + 42 q^{70} - q^{71} + 12 q^{72} + 12 q^{73} + 43 q^{74} + 2 q^{76} + 40 q^{77} - 7 q^{78} + 7 q^{79} - q^{80} + 10 q^{81} - 74 q^{82} + 12 q^{83} + 9 q^{84} - 27 q^{85} - 27 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} - 80 q^{91} - 28 q^{92} + 12 q^{93} + 30 q^{94} - 12 q^{95} + 9 q^{96} - 9 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.527336 + 0.913372i 0.372883 + 0.645852i 0.990008 0.141013i \(-0.0450360\pi\)
−0.617125 + 0.786865i \(0.711703\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.443834 0.768743i 0.221917 0.384371i
\(5\) 0.832996 0.372527 0.186264 0.982500i \(-0.440362\pi\)
0.186264 + 0.982500i \(0.440362\pi\)
\(6\) −0.527336 0.913372i −0.215284 0.372883i
\(7\) 1.13029 1.95772i 0.427209 0.739947i −0.569415 0.822050i \(-0.692830\pi\)
0.996624 + 0.0821028i \(0.0261636\pi\)
\(8\) 3.04554 1.07676
\(9\) 1.00000 0.333333
\(10\) 0.439269 + 0.760836i 0.138909 + 0.240597i
\(11\) −0.713790 + 1.23632i −0.215216 + 0.372765i −0.953339 0.301901i \(-0.902379\pi\)
0.738123 + 0.674666i \(0.235712\pi\)
\(12\) −0.443834 + 0.768743i −0.128124 + 0.221917i
\(13\) 0.308980 + 0.535170i 0.0856958 + 0.148429i 0.905687 0.423946i \(-0.139355\pi\)
−0.819992 + 0.572375i \(0.806022\pi\)
\(14\) 2.38417 0.637195
\(15\) −0.832996 −0.215079
\(16\) 0.718355 + 1.24423i 0.179589 + 0.311057i
\(17\) 2.57744 + 4.46426i 0.625122 + 1.08274i 0.988517 + 0.151107i \(0.0482840\pi\)
−0.363396 + 0.931635i \(0.618383\pi\)
\(18\) 0.527336 + 0.913372i 0.124294 + 0.215284i
\(19\) −0.939269 1.62686i −0.215483 0.373228i 0.737939 0.674868i \(-0.235799\pi\)
−0.953422 + 0.301640i \(0.902466\pi\)
\(20\) 0.369712 0.640360i 0.0826701 0.143189i
\(21\) −1.13029 + 1.95772i −0.246649 + 0.427209i
\(22\) −1.50563 −0.321001
\(23\) −1.55467 2.69277i −0.324171 0.561481i 0.657173 0.753740i \(-0.271752\pi\)
−0.981344 + 0.192258i \(0.938419\pi\)
\(24\) −3.04554 −0.621669
\(25\) −4.30612 −0.861224
\(26\) −0.325873 + 0.564428i −0.0639089 + 0.110694i
\(27\) −1.00000 −0.192450
\(28\) −1.00332 1.73780i −0.189610 0.328414i
\(29\) −0.962039 + 1.66630i −0.178646 + 0.309424i −0.941417 0.337245i \(-0.890505\pi\)
0.762771 + 0.646669i \(0.223838\pi\)
\(30\) −0.439269 0.760836i −0.0801991 0.138909i
\(31\) −0.286210 + 0.495730i −0.0514048 + 0.0890357i −0.890583 0.454821i \(-0.849703\pi\)
0.839178 + 0.543857i \(0.183037\pi\)
\(32\) 2.28791 3.96278i 0.404450 0.700527i
\(33\) 0.713790 1.23632i 0.124255 0.215216i
\(34\) −2.71836 + 4.70833i −0.466194 + 0.807472i
\(35\) 0.941526 1.63077i 0.159147 0.275650i
\(36\) 0.443834 0.768743i 0.0739723 0.128124i
\(37\) −2.67890 4.63999i −0.440408 0.762810i 0.557311 0.830304i \(-0.311833\pi\)
−0.997720 + 0.0674938i \(0.978500\pi\)
\(38\) 0.990620 1.71580i 0.160700 0.278340i
\(39\) −0.308980 0.535170i −0.0494765 0.0856958i
\(40\) 2.53692 0.401123
\(41\) −4.25132 + 7.36350i −0.663945 + 1.14999i 0.315626 + 0.948884i \(0.397786\pi\)
−0.979570 + 0.201102i \(0.935548\pi\)
\(42\) −2.38417 −0.367885
\(43\) −7.16863 −1.09321 −0.546603 0.837392i \(-0.684079\pi\)
−0.546603 + 0.837392i \(0.684079\pi\)
\(44\) 0.633608 + 1.09744i 0.0955201 + 0.165446i
\(45\) 0.832996 0.124176
\(46\) 1.63967 2.83999i 0.241756 0.418733i
\(47\) 0.624228 1.08120i 0.0910531 0.157709i −0.816901 0.576777i \(-0.804310\pi\)
0.907955 + 0.419069i \(0.137643\pi\)
\(48\) −0.718355 1.24423i −0.103686 0.179589i
\(49\) 0.944897 + 1.63661i 0.134985 + 0.233801i
\(50\) −2.27077 3.93309i −0.321135 0.556223i
\(51\) −2.57744 4.46426i −0.360914 0.625122i
\(52\) 0.548544 0.0760694
\(53\) −4.80713 −0.660310 −0.330155 0.943927i \(-0.607101\pi\)
−0.330155 + 0.943927i \(0.607101\pi\)
\(54\) −0.527336 0.913372i −0.0717613 0.124294i
\(55\) −0.594584 + 1.02985i −0.0801737 + 0.138865i
\(56\) 3.44234 5.96231i 0.460002 0.796747i
\(57\) 0.939269 + 1.62686i 0.124409 + 0.215483i
\(58\) −2.02927 −0.266456
\(59\) 7.75196 1.00922 0.504610 0.863348i \(-0.331636\pi\)
0.504610 + 0.863348i \(0.331636\pi\)
\(60\) −0.369712 + 0.640360i −0.0477296 + 0.0826701i
\(61\) −1.96992 3.41201i −0.252223 0.436863i 0.711915 0.702266i \(-0.247828\pi\)
−0.964138 + 0.265403i \(0.914495\pi\)
\(62\) −0.603715 −0.0766719
\(63\) 1.13029 1.95772i 0.142403 0.246649i
\(64\) 7.69941 0.962427
\(65\) 0.257379 + 0.445794i 0.0319240 + 0.0552940i
\(66\) 1.50563 0.185330
\(67\) −7.67540 2.84399i −0.937699 0.347448i
\(68\) 4.57582 0.554900
\(69\) 1.55467 + 2.69277i 0.187160 + 0.324171i
\(70\) 1.98600 0.237372
\(71\) −4.64824 + 8.05099i −0.551645 + 0.955477i 0.446511 + 0.894778i \(0.352666\pi\)
−0.998156 + 0.0606992i \(0.980667\pi\)
\(72\) 3.04554 0.358920
\(73\) 7.88356 + 13.6547i 0.922701 + 1.59816i 0.795218 + 0.606324i \(0.207357\pi\)
0.127483 + 0.991841i \(0.459310\pi\)
\(74\) 2.82536 4.89367i 0.328441 0.568877i
\(75\) 4.30612 0.497228
\(76\) −1.66752 −0.191277
\(77\) 1.61358 + 2.79480i 0.183884 + 0.318497i
\(78\) 0.325873 0.564428i 0.0368978 0.0639089i
\(79\) −0.745691 + 1.29158i −0.0838968 + 0.145314i −0.904921 0.425580i \(-0.860070\pi\)
0.821024 + 0.570894i \(0.193403\pi\)
\(80\) 0.598387 + 1.03644i 0.0669017 + 0.115877i
\(81\) 1.00000 0.111111
\(82\) −8.96749 −0.990294
\(83\) −0.355767 0.616206i −0.0390505 0.0676374i 0.845840 0.533437i \(-0.179100\pi\)
−0.884890 + 0.465800i \(0.845767\pi\)
\(84\) 1.00332 + 1.73780i 0.109471 + 0.189610i
\(85\) 2.14700 + 3.71871i 0.232875 + 0.403351i
\(86\) −3.78028 6.54763i −0.407638 0.706049i
\(87\) 0.962039 1.66630i 0.103141 0.178646i
\(88\) −2.17388 + 3.76527i −0.231736 + 0.401379i
\(89\) −0.514759 −0.0545643 −0.0272822 0.999628i \(-0.508685\pi\)
−0.0272822 + 0.999628i \(0.508685\pi\)
\(90\) 0.439269 + 0.760836i 0.0463030 + 0.0801991i
\(91\) 1.39695 0.146440
\(92\) −2.76006 −0.287757
\(93\) 0.286210 0.495730i 0.0296786 0.0514048i
\(94\) 1.31671 0.135808
\(95\) −0.782407 1.35517i −0.0802733 0.139037i
\(96\) −2.28791 + 3.96278i −0.233509 + 0.404450i
\(97\) 0.590375 + 1.02256i 0.0599435 + 0.103825i 0.894440 0.447188i \(-0.147575\pi\)
−0.834496 + 0.551014i \(0.814241\pi\)
\(98\) −0.996556 + 1.72609i −0.100667 + 0.174361i
\(99\) −0.713790 + 1.23632i −0.0717386 + 0.124255i
\(100\) −1.91120 + 3.31030i −0.191120 + 0.331030i
\(101\) −5.28898 + 9.16077i −0.526273 + 0.911531i 0.473259 + 0.880923i \(0.343078\pi\)
−0.999531 + 0.0306077i \(0.990256\pi\)
\(102\) 2.71836 4.70833i 0.269157 0.466194i
\(103\) 6.21562 10.7658i 0.612443 1.06078i −0.378385 0.925648i \(-0.623520\pi\)
0.990827 0.135134i \(-0.0431464\pi\)
\(104\) 0.941013 + 1.62988i 0.0922739 + 0.159823i
\(105\) −0.941526 + 1.63077i −0.0918835 + 0.159147i
\(106\) −2.53497 4.39070i −0.246218 0.426462i
\(107\) −13.4452 −1.29980 −0.649900 0.760020i \(-0.725189\pi\)
−0.649900 + 0.760020i \(0.725189\pi\)
\(108\) −0.443834 + 0.768743i −0.0427079 + 0.0739723i
\(109\) 17.6159 1.68730 0.843648 0.536897i \(-0.180404\pi\)
0.843648 + 0.536897i \(0.180404\pi\)
\(110\) −1.25418 −0.119582
\(111\) 2.67890 + 4.63999i 0.254270 + 0.440408i
\(112\) 3.24779 0.306888
\(113\) 2.90861 5.03786i 0.273619 0.473922i −0.696167 0.717880i \(-0.745113\pi\)
0.969786 + 0.243958i \(0.0784458\pi\)
\(114\) −0.990620 + 1.71580i −0.0927801 + 0.160700i
\(115\) −1.29504 2.24307i −0.120763 0.209167i
\(116\) 0.853971 + 1.47912i 0.0792892 + 0.137333i
\(117\) 0.308980 + 0.535170i 0.0285653 + 0.0494765i
\(118\) 4.08789 + 7.08043i 0.376320 + 0.651806i
\(119\) 11.6530 1.06823
\(120\) −2.53692 −0.231588
\(121\) 4.48101 + 7.76133i 0.407364 + 0.705576i
\(122\) 2.07762 3.59855i 0.188099 0.325797i
\(123\) 4.25132 7.36350i 0.383329 0.663945i
\(124\) 0.254059 + 0.440043i 0.0228152 + 0.0395171i
\(125\) −7.75196 −0.693356
\(126\) 2.38417 0.212398
\(127\) 8.35473 14.4708i 0.741362 1.28408i −0.210513 0.977591i \(-0.567513\pi\)
0.951875 0.306486i \(-0.0991533\pi\)
\(128\) −0.515648 0.893128i −0.0455772 0.0789421i
\(129\) 7.16863 0.631163
\(130\) −0.271451 + 0.470167i −0.0238078 + 0.0412363i
\(131\) −6.06892 −0.530244 −0.265122 0.964215i \(-0.585412\pi\)
−0.265122 + 0.964215i \(0.585412\pi\)
\(132\) −0.633608 1.09744i −0.0551485 0.0955201i
\(133\) −4.24658 −0.368225
\(134\) −1.44989 8.51023i −0.125252 0.735172i
\(135\) −0.832996 −0.0716929
\(136\) 7.84971 + 13.5961i 0.673107 + 1.16586i
\(137\) 5.12537 0.437890 0.218945 0.975737i \(-0.429739\pi\)
0.218945 + 0.975737i \(0.429739\pi\)
\(138\) −1.63967 + 2.83999i −0.139578 + 0.241756i
\(139\) 20.9364 1.77580 0.887899 0.460037i \(-0.152164\pi\)
0.887899 + 0.460037i \(0.152164\pi\)
\(140\) −0.835762 1.44758i −0.0706348 0.122343i
\(141\) −0.624228 + 1.08120i −0.0525695 + 0.0910531i
\(142\) −9.80474 −0.822796
\(143\) −0.882189 −0.0737723
\(144\) 0.718355 + 1.24423i 0.0598629 + 0.103686i
\(145\) −0.801375 + 1.38802i −0.0665506 + 0.115269i
\(146\) −8.31457 + 14.4013i −0.688118 + 1.19186i
\(147\) −0.944897 1.63661i −0.0779338 0.134985i
\(148\) −4.75595 −0.390936
\(149\) 1.46100 0.119690 0.0598450 0.998208i \(-0.480939\pi\)
0.0598450 + 0.998208i \(0.480939\pi\)
\(150\) 2.27077 + 3.93309i 0.185408 + 0.321135i
\(151\) −4.04073 6.99874i −0.328830 0.569550i 0.653450 0.756969i \(-0.273321\pi\)
−0.982280 + 0.187420i \(0.939988\pi\)
\(152\) −2.86058 4.95467i −0.232024 0.401877i
\(153\) 2.57744 + 4.46426i 0.208374 + 0.360914i
\(154\) −1.70179 + 2.94759i −0.137134 + 0.237524i
\(155\) −0.238412 + 0.412941i −0.0191497 + 0.0331682i
\(156\) −0.548544 −0.0439187
\(157\) −7.92335 13.7236i −0.632352 1.09527i −0.987070 0.160292i \(-0.948756\pi\)
0.354718 0.934973i \(-0.384577\pi\)
\(158\) −1.57292 −0.125135
\(159\) 4.80713 0.381230
\(160\) 1.90582 3.30098i 0.150668 0.260965i
\(161\) −7.02891 −0.553956
\(162\) 0.527336 + 0.913372i 0.0414314 + 0.0717613i
\(163\) 7.13366 12.3559i 0.558751 0.967786i −0.438850 0.898560i \(-0.644614\pi\)
0.997601 0.0692253i \(-0.0220527\pi\)
\(164\) 3.77376 + 6.53634i 0.294681 + 0.510403i
\(165\) 0.594584 1.02985i 0.0462883 0.0801737i
\(166\) 0.375217 0.649895i 0.0291225 0.0504416i
\(167\) 1.47723 2.55864i 0.114311 0.197993i −0.803193 0.595719i \(-0.796867\pi\)
0.917504 + 0.397726i \(0.130200\pi\)
\(168\) −3.44234 + 5.96231i −0.265582 + 0.460002i
\(169\) 6.30906 10.9276i 0.485312 0.840586i
\(170\) −2.26438 + 3.92202i −0.173670 + 0.300805i
\(171\) −0.939269 1.62686i −0.0718277 0.124409i
\(172\) −3.18168 + 5.51083i −0.242601 + 0.420197i
\(173\) −11.5206 19.9543i −0.875895 1.51709i −0.855807 0.517296i \(-0.826939\pi\)
−0.0200880 0.999798i \(-0.506395\pi\)
\(174\) 2.02927 0.153839
\(175\) −4.86715 + 8.43016i −0.367922 + 0.637260i
\(176\) −2.05102 −0.154601
\(177\) −7.75196 −0.582673
\(178\) −0.271451 0.470167i −0.0203461 0.0352405i
\(179\) −10.6867 −0.798761 −0.399380 0.916785i \(-0.630775\pi\)
−0.399380 + 0.916785i \(0.630775\pi\)
\(180\) 0.369712 0.640360i 0.0275567 0.0477296i
\(181\) −4.37430 + 7.57652i −0.325139 + 0.563158i −0.981541 0.191254i \(-0.938745\pi\)
0.656401 + 0.754412i \(0.272078\pi\)
\(182\) 0.736661 + 1.27593i 0.0546049 + 0.0945785i
\(183\) 1.96992 + 3.41201i 0.145621 + 0.252223i
\(184\) −4.73482 8.20094i −0.349055 0.604582i
\(185\) −2.23151 3.86509i −0.164064 0.284167i
\(186\) 0.603715 0.0442665
\(187\) −7.35901 −0.538144
\(188\) −0.554107 0.959742i −0.0404124 0.0699964i
\(189\) −1.13029 + 1.95772i −0.0822164 + 0.142403i
\(190\) 0.825183 1.42926i 0.0598650 0.103689i
\(191\) −8.08452 14.0028i −0.584976 1.01321i −0.994878 0.101078i \(-0.967771\pi\)
0.409903 0.912129i \(-0.365563\pi\)
\(192\) −7.69941 −0.555657
\(193\) 7.15854 0.515283 0.257641 0.966241i \(-0.417055\pi\)
0.257641 + 0.966241i \(0.417055\pi\)
\(194\) −0.622652 + 1.07847i −0.0447038 + 0.0774293i
\(195\) −0.257379 0.445794i −0.0184313 0.0319240i
\(196\) 1.67751 0.119822
\(197\) 0.218605 0.378635i 0.0155750 0.0269766i −0.858133 0.513428i \(-0.828375\pi\)
0.873708 + 0.486451i \(0.161709\pi\)
\(198\) −1.50563 −0.107000
\(199\) 8.10268 + 14.0342i 0.574384 + 0.994862i 0.996108 + 0.0881377i \(0.0280915\pi\)
−0.421725 + 0.906724i \(0.638575\pi\)
\(200\) −13.1145 −0.927332
\(201\) 7.67540 + 2.84399i 0.541381 + 0.200599i
\(202\) −11.1563 −0.784952
\(203\) 2.17476 + 3.76680i 0.152638 + 0.264378i
\(204\) −4.57582 −0.320372
\(205\) −3.54133 + 6.13377i −0.247337 + 0.428401i
\(206\) 13.1109 0.913477
\(207\) −1.55467 2.69277i −0.108057 0.187160i
\(208\) −0.443916 + 0.768884i −0.0307800 + 0.0533125i
\(209\) 2.68176 0.185501
\(210\) −1.98600 −0.137047
\(211\) −2.15714 3.73628i −0.148504 0.257216i 0.782171 0.623064i \(-0.214112\pi\)
−0.930675 + 0.365848i \(0.880779\pi\)
\(212\) −2.13357 + 3.69545i −0.146534 + 0.253804i
\(213\) 4.64824 8.05099i 0.318492 0.551645i
\(214\) −7.09015 12.2805i −0.484673 0.839478i
\(215\) −5.97144 −0.407249
\(216\) −3.04554 −0.207223
\(217\) 0.646999 + 1.12064i 0.0439212 + 0.0760737i
\(218\) 9.28949 + 16.0899i 0.629164 + 1.08974i
\(219\) −7.88356 13.6547i −0.532722 0.922701i
\(220\) 0.527793 + 0.914165i 0.0355838 + 0.0616330i
\(221\) −1.59276 + 2.75874i −0.107141 + 0.185573i
\(222\) −2.82536 + 4.89367i −0.189626 + 0.328441i
\(223\) −18.9649 −1.26998 −0.634992 0.772518i \(-0.718997\pi\)
−0.634992 + 0.772518i \(0.718997\pi\)
\(224\) −5.17200 8.95817i −0.345569 0.598543i
\(225\) −4.30612 −0.287075
\(226\) 6.13526 0.408112
\(227\) −1.90313 + 3.29632i −0.126315 + 0.218785i −0.922246 0.386603i \(-0.873648\pi\)
0.795931 + 0.605387i \(0.206982\pi\)
\(228\) 1.66752 0.110434
\(229\) 6.42081 + 11.1212i 0.424299 + 0.734908i 0.996355 0.0853070i \(-0.0271871\pi\)
−0.572055 + 0.820215i \(0.693854\pi\)
\(230\) 1.36584 2.36570i 0.0900606 0.155990i
\(231\) −1.61358 2.79480i −0.106166 0.183884i
\(232\) −2.92993 + 5.07479i −0.192359 + 0.333176i
\(233\) −4.61173 + 7.98774i −0.302124 + 0.523295i −0.976617 0.214987i \(-0.931029\pi\)
0.674493 + 0.738282i \(0.264362\pi\)
\(234\) −0.325873 + 0.564428i −0.0213030 + 0.0368978i
\(235\) 0.519980 0.900632i 0.0339197 0.0587507i
\(236\) 3.44058 5.95926i 0.223963 0.387915i
\(237\) 0.745691 1.29158i 0.0484378 0.0838968i
\(238\) 6.14505 + 10.6435i 0.398324 + 0.689918i
\(239\) −9.01312 + 15.6112i −0.583010 + 1.00980i 0.412110 + 0.911134i \(0.364792\pi\)
−0.995120 + 0.0986690i \(0.968541\pi\)
\(240\) −0.598387 1.03644i −0.0386257 0.0669017i
\(241\) −3.90380 −0.251466 −0.125733 0.992064i \(-0.540128\pi\)
−0.125733 + 0.992064i \(0.540128\pi\)
\(242\) −4.72599 + 8.18566i −0.303798 + 0.526194i
\(243\) −1.00000 −0.0641500
\(244\) −3.49728 −0.223890
\(245\) 0.787096 + 1.36329i 0.0502857 + 0.0870974i
\(246\) 8.96749 0.571746
\(247\) 0.580431 1.00534i 0.0369320 0.0639680i
\(248\) −0.871664 + 1.50977i −0.0553507 + 0.0958702i
\(249\) 0.355767 + 0.616206i 0.0225458 + 0.0390505i
\(250\) −4.08789 7.08043i −0.258541 0.447805i
\(251\) 9.53385 + 16.5131i 0.601771 + 1.04230i 0.992553 + 0.121815i \(0.0388715\pi\)
−0.390781 + 0.920484i \(0.627795\pi\)
\(252\) −1.00332 1.73780i −0.0632032 0.109471i
\(253\) 4.43884 0.279067
\(254\) 17.6230 1.10576
\(255\) −2.14700 3.71871i −0.134450 0.232875i
\(256\) 8.24325 14.2777i 0.515203 0.892358i
\(257\) 14.3517 24.8579i 0.895237 1.55060i 0.0617259 0.998093i \(-0.480340\pi\)
0.833511 0.552503i \(-0.186327\pi\)
\(258\) 3.78028 + 6.54763i 0.235350 + 0.407638i
\(259\) −12.1117 −0.752585
\(260\) 0.456935 0.0283379
\(261\) −0.962039 + 1.66630i −0.0595487 + 0.103141i
\(262\) −3.20036 5.54318i −0.197719 0.342459i
\(263\) 28.5607 1.76113 0.880565 0.473926i \(-0.157164\pi\)
0.880565 + 0.473926i \(0.157164\pi\)
\(264\) 2.17388 3.76527i 0.133793 0.231736i
\(265\) −4.00432 −0.245983
\(266\) −2.23937 3.87871i −0.137305 0.237819i
\(267\) 0.514759 0.0315027
\(268\) −5.59290 + 4.63815i −0.341640 + 0.283320i
\(269\) 32.3731 1.97382 0.986912 0.161259i \(-0.0515554\pi\)
0.986912 + 0.161259i \(0.0515554\pi\)
\(270\) −0.439269 0.760836i −0.0267330 0.0463030i
\(271\) 21.0856 1.28086 0.640429 0.768018i \(-0.278757\pi\)
0.640429 + 0.768018i \(0.278757\pi\)
\(272\) −3.70304 + 6.41385i −0.224530 + 0.388897i
\(273\) −1.39695 −0.0845471
\(274\) 2.70279 + 4.68137i 0.163281 + 0.282812i
\(275\) 3.07366 5.32374i 0.185349 0.321034i
\(276\) 2.76006 0.166136
\(277\) −12.7228 −0.764438 −0.382219 0.924072i \(-0.624840\pi\)
−0.382219 + 0.924072i \(0.624840\pi\)
\(278\) 11.0405 + 19.1227i 0.662165 + 1.14690i
\(279\) −0.286210 + 0.495730i −0.0171349 + 0.0296786i
\(280\) 2.86745 4.96658i 0.171363 0.296810i
\(281\) −7.58597 13.1393i −0.452541 0.783824i 0.546002 0.837784i \(-0.316149\pi\)
−0.998543 + 0.0539600i \(0.982816\pi\)
\(282\) −1.31671 −0.0784091
\(283\) −18.9563 −1.12684 −0.563419 0.826172i \(-0.690514\pi\)
−0.563419 + 0.826172i \(0.690514\pi\)
\(284\) 4.12610 + 7.14661i 0.244839 + 0.424073i
\(285\) 0.782407 + 1.35517i 0.0463458 + 0.0802733i
\(286\) −0.465210 0.805767i −0.0275084 0.0476460i
\(287\) 9.61043 + 16.6458i 0.567286 + 0.982568i
\(288\) 2.28791 3.96278i 0.134817 0.233509i
\(289\) −4.78642 + 8.29032i −0.281554 + 0.487666i
\(290\) −1.69037 −0.0992622
\(291\) −0.590375 1.02256i −0.0346084 0.0599435i
\(292\) 13.9960 0.819052
\(293\) 31.2734 1.82701 0.913506 0.406825i \(-0.133364\pi\)
0.913506 + 0.406825i \(0.133364\pi\)
\(294\) 0.996556 1.72609i 0.0581203 0.100667i
\(295\) 6.45735 0.375961
\(296\) −8.15870 14.1313i −0.474215 0.821364i
\(297\) 0.713790 1.23632i 0.0414183 0.0717386i
\(298\) 0.770439 + 1.33444i 0.0446303 + 0.0773020i
\(299\) 0.960726 1.66403i 0.0555602 0.0962332i
\(300\) 1.91120 3.31030i 0.110343 0.191120i
\(301\) −8.10262 + 14.0341i −0.467027 + 0.808915i
\(302\) 4.26164 7.38138i 0.245230 0.424750i
\(303\) 5.28898 9.16077i 0.303844 0.526273i
\(304\) 1.34946 2.33733i 0.0773967 0.134055i
\(305\) −1.64094 2.84219i −0.0939599 0.162743i
\(306\) −2.71836 + 4.70833i −0.155398 + 0.269157i
\(307\) −5.85184 10.1357i −0.333982 0.578474i 0.649307 0.760527i \(-0.275059\pi\)
−0.983289 + 0.182053i \(0.941726\pi\)
\(308\) 2.86464 0.163228
\(309\) −6.21562 + 10.7658i −0.353594 + 0.612443i
\(310\) −0.502892 −0.0285623
\(311\) −0.574859 −0.0325973 −0.0162986 0.999867i \(-0.505188\pi\)
−0.0162986 + 0.999867i \(0.505188\pi\)
\(312\) −0.941013 1.62988i −0.0532744 0.0922739i
\(313\) 6.04001 0.341402 0.170701 0.985323i \(-0.445397\pi\)
0.170701 + 0.985323i \(0.445397\pi\)
\(314\) 8.35653 14.4739i 0.471586 0.816811i
\(315\) 0.941526 1.63077i 0.0530490 0.0918835i
\(316\) 0.661926 + 1.14649i 0.0372362 + 0.0644951i
\(317\) −3.10752 5.38238i −0.174536 0.302304i 0.765465 0.643478i \(-0.222509\pi\)
−0.940000 + 0.341173i \(0.889176\pi\)
\(318\) 2.53497 + 4.39070i 0.142154 + 0.246218i
\(319\) −1.37339 2.37878i −0.0768950 0.133186i
\(320\) 6.41358 0.358530
\(321\) 13.4452 0.750440
\(322\) −3.70660 6.42001i −0.206560 0.357773i
\(323\) 4.84182 8.38628i 0.269406 0.466625i
\(324\) 0.443834 0.768743i 0.0246574 0.0427079i
\(325\) −1.33051 2.30450i −0.0738032 0.127831i
\(326\) 15.0473 0.833395
\(327\) −17.6159 −0.974161
\(328\) −12.9476 + 22.4258i −0.714910 + 1.23826i
\(329\) −1.41112 2.44412i −0.0777974 0.134749i
\(330\) 1.25418 0.0690405
\(331\) 1.65108 2.85976i 0.0907517 0.157186i −0.817076 0.576530i \(-0.804406\pi\)
0.907828 + 0.419344i \(0.137740\pi\)
\(332\) −0.631605 −0.0346638
\(333\) −2.67890 4.63999i −0.146803 0.254270i
\(334\) 3.11598 0.170499
\(335\) −6.39358 2.36903i −0.349318 0.129434i
\(336\) −3.24779 −0.177182
\(337\) 15.2528 + 26.4186i 0.830871 + 1.43911i 0.897348 + 0.441324i \(0.145491\pi\)
−0.0664766 + 0.997788i \(0.521176\pi\)
\(338\) 13.3080 0.723859
\(339\) −2.90861 + 5.03786i −0.157974 + 0.273619i
\(340\) 3.81164 0.206715
\(341\) −0.408588 0.707694i −0.0221263 0.0383238i
\(342\) 0.990620 1.71580i 0.0535666 0.0927801i
\(343\) 20.0961 1.08509
\(344\) −21.8324 −1.17712
\(345\) 1.29504 + 2.24307i 0.0697224 + 0.120763i
\(346\) 12.1504 21.0452i 0.653212 1.13140i
\(347\) −7.38767 + 12.7958i −0.396591 + 0.686915i −0.993303 0.115540i \(-0.963140\pi\)
0.596712 + 0.802455i \(0.296473\pi\)
\(348\) −0.853971 1.47912i −0.0457777 0.0792892i
\(349\) −29.0181 −1.55330 −0.776651 0.629931i \(-0.783083\pi\)
−0.776651 + 0.629931i \(0.783083\pi\)
\(350\) −10.2665 −0.548767
\(351\) −0.308980 0.535170i −0.0164922 0.0285653i
\(352\) 3.26618 + 5.65719i 0.174088 + 0.301529i
\(353\) −3.46490 6.00139i −0.184418 0.319422i 0.758962 0.651135i \(-0.225707\pi\)
−0.943380 + 0.331713i \(0.892373\pi\)
\(354\) −4.08789 7.08043i −0.217269 0.376320i
\(355\) −3.87197 + 6.70645i −0.205503 + 0.355941i
\(356\) −0.228467 + 0.395717i −0.0121088 + 0.0209730i
\(357\) −11.6530 −0.616743
\(358\) −5.63548 9.76093i −0.297844 0.515881i
\(359\) 10.4060 0.549206 0.274603 0.961558i \(-0.411454\pi\)
0.274603 + 0.961558i \(0.411454\pi\)
\(360\) 2.53692 0.133708
\(361\) 7.73555 13.3984i 0.407134 0.705177i
\(362\) −9.22691 −0.484956
\(363\) −4.48101 7.76133i −0.235192 0.407364i
\(364\) 0.620013 1.07389i 0.0324975 0.0562873i
\(365\) 6.56697 + 11.3743i 0.343731 + 0.595360i
\(366\) −2.07762 + 3.59855i −0.108599 + 0.188099i
\(367\) −16.3874 + 28.3839i −0.855418 + 1.48163i 0.0208394 + 0.999783i \(0.493366\pi\)
−0.876257 + 0.481844i \(0.839967\pi\)
\(368\) 2.23361 3.86873i 0.116435 0.201672i
\(369\) −4.25132 + 7.36350i −0.221315 + 0.383329i
\(370\) 2.35351 4.07641i 0.122353 0.211922i
\(371\) −5.43344 + 9.41100i −0.282090 + 0.488595i
\(372\) −0.254059 0.440043i −0.0131724 0.0228152i
\(373\) −7.05241 + 12.2151i −0.365160 + 0.632476i −0.988802 0.149234i \(-0.952319\pi\)
0.623642 + 0.781710i \(0.285652\pi\)
\(374\) −3.88067 6.72152i −0.200665 0.347561i
\(375\) 7.75196 0.400309
\(376\) 1.90111 3.29283i 0.0980425 0.169815i
\(377\) −1.18901 −0.0612369
\(378\) −2.38417 −0.122628
\(379\) −4.53066 7.84733i −0.232724 0.403090i 0.725885 0.687816i \(-0.241431\pi\)
−0.958609 + 0.284726i \(0.908097\pi\)
\(380\) −1.38903 −0.0712560
\(381\) −8.35473 + 14.4708i −0.428026 + 0.741362i
\(382\) 8.52652 14.7684i 0.436255 0.755615i
\(383\) 10.2326 + 17.7233i 0.522859 + 0.905619i 0.999646 + 0.0266000i \(0.00846805\pi\)
−0.476787 + 0.879019i \(0.658199\pi\)
\(384\) 0.515648 + 0.893128i 0.0263140 + 0.0455772i
\(385\) 1.34410 + 2.32806i 0.0685019 + 0.118649i
\(386\) 3.77495 + 6.53841i 0.192140 + 0.332796i
\(387\) −7.16863 −0.364402
\(388\) 1.04811 0.0532100
\(389\) −6.13345 10.6235i −0.310978 0.538630i 0.667596 0.744524i \(-0.267323\pi\)
−0.978574 + 0.205893i \(0.933990\pi\)
\(390\) 0.271451 0.470167i 0.0137454 0.0238078i
\(391\) 8.01415 13.8809i 0.405293 0.701988i
\(392\) 2.87772 + 4.98436i 0.145347 + 0.251748i
\(393\) 6.06892 0.306136
\(394\) 0.461113 0.0232305
\(395\) −0.621158 + 1.07588i −0.0312538 + 0.0541332i
\(396\) 0.633608 + 1.09744i 0.0318400 + 0.0551485i
\(397\) 9.35080 0.469303 0.234652 0.972080i \(-0.424605\pi\)
0.234652 + 0.972080i \(0.424605\pi\)
\(398\) −8.54566 + 14.8015i −0.428355 + 0.741933i
\(399\) 4.24658 0.212595
\(400\) −3.09332 5.35779i −0.154666 0.267890i
\(401\) −37.4643 −1.87088 −0.935438 0.353491i \(-0.884994\pi\)
−0.935438 + 0.353491i \(0.884994\pi\)
\(402\) 1.44989 + 8.51023i 0.0723141 + 0.424452i
\(403\) −0.353733 −0.0176207
\(404\) 4.69485 + 8.13172i 0.233578 + 0.404568i
\(405\) 0.832996 0.0413919
\(406\) −2.29366 + 3.97274i −0.113832 + 0.197164i
\(407\) 7.64869 0.379132
\(408\) −7.84971 13.5961i −0.388618 0.673107i
\(409\) −10.5166 + 18.2153i −0.520013 + 0.900689i 0.479716 + 0.877424i \(0.340740\pi\)
−0.999729 + 0.0232654i \(0.992594\pi\)
\(410\) −7.46989 −0.368911
\(411\) −5.12537 −0.252816
\(412\) −5.51740 9.55642i −0.271823 0.470811i
\(413\) 8.76195 15.1761i 0.431147 0.746769i
\(414\) 1.63967 2.83999i 0.0805853 0.139578i
\(415\) −0.296352 0.513297i −0.0145474 0.0251968i
\(416\) 2.82768 0.138638
\(417\) −20.9364 −1.02526
\(418\) 1.41419 + 2.44945i 0.0691703 + 0.119806i
\(419\) 15.2100 + 26.3445i 0.743057 + 1.28701i 0.951097 + 0.308892i \(0.0999582\pi\)
−0.208040 + 0.978120i \(0.566708\pi\)
\(420\) 0.835762 + 1.44758i 0.0407810 + 0.0706348i
\(421\) 0.300281 + 0.520102i 0.0146348 + 0.0253482i 0.873250 0.487272i \(-0.162008\pi\)
−0.858615 + 0.512621i \(0.828675\pi\)
\(422\) 2.27508 3.94055i 0.110749 0.191823i
\(423\) 0.624228 1.08120i 0.0303510 0.0525695i
\(424\) −14.6403 −0.710996
\(425\) −11.0988 19.2236i −0.538369 0.932483i
\(426\) 9.80474 0.475041
\(427\) −8.90633 −0.431008
\(428\) −5.96745 + 10.3359i −0.288448 + 0.499606i
\(429\) 0.882189 0.0425925
\(430\) −3.14896 5.45415i −0.151856 0.263022i
\(431\) 9.37537 16.2386i 0.451596 0.782187i −0.546890 0.837205i \(-0.684188\pi\)
0.998485 + 0.0550178i \(0.0175216\pi\)
\(432\) −0.718355 1.24423i −0.0345619 0.0598629i
\(433\) 0.462064 0.800319i 0.0222054 0.0384609i −0.854709 0.519107i \(-0.826265\pi\)
0.876915 + 0.480646i \(0.159598\pi\)
\(434\) −0.682372 + 1.18190i −0.0327549 + 0.0567331i
\(435\) 0.801375 1.38802i 0.0384230 0.0665506i
\(436\) 7.81853 13.5421i 0.374440 0.648548i
\(437\) −2.92051 + 5.05847i −0.139707 + 0.241979i
\(438\) 8.31457 14.4013i 0.397285 0.688118i
\(439\) −4.46070 7.72616i −0.212898 0.368750i 0.739723 0.672912i \(-0.234957\pi\)
−0.952620 + 0.304162i \(0.901623\pi\)
\(440\) −1.81083 + 3.13645i −0.0863280 + 0.149524i
\(441\) 0.944897 + 1.63661i 0.0449951 + 0.0779338i
\(442\) −3.35967 −0.159803
\(443\) −17.5449 + 30.3886i −0.833583 + 1.44381i 0.0615964 + 0.998101i \(0.480381\pi\)
−0.895179 + 0.445707i \(0.852952\pi\)
\(444\) 4.75595 0.225707
\(445\) −0.428792 −0.0203267
\(446\) −10.0009 17.3220i −0.473555 0.820222i
\(447\) −1.46100 −0.0691030
\(448\) 8.70256 15.0733i 0.411157 0.712145i
\(449\) −3.18088 + 5.50945i −0.150115 + 0.260007i −0.931270 0.364331i \(-0.881298\pi\)
0.781155 + 0.624338i \(0.214631\pi\)
\(450\) −2.27077 3.93309i −0.107045 0.185408i
\(451\) −6.06910 10.5120i −0.285783 0.494990i
\(452\) −2.58188 4.47195i −0.121441 0.210343i
\(453\) 4.04073 + 6.99874i 0.189850 + 0.328830i
\(454\) −4.01436 −0.188403
\(455\) 1.16365 0.0545528
\(456\) 2.86058 + 4.95467i 0.133959 + 0.232024i
\(457\) 17.1029 29.6231i 0.800039 1.38571i −0.119550 0.992828i \(-0.538145\pi\)
0.919590 0.392880i \(-0.128521\pi\)
\(458\) −6.77185 + 11.7292i −0.316428 + 0.548069i
\(459\) −2.57744 4.46426i −0.120305 0.208374i
\(460\) −2.29912 −0.107197
\(461\) −1.67330 −0.0779331 −0.0389666 0.999241i \(-0.512407\pi\)
−0.0389666 + 0.999241i \(0.512407\pi\)
\(462\) 1.70179 2.94759i 0.0791746 0.137134i
\(463\) 4.92715 + 8.53407i 0.228984 + 0.396612i 0.957507 0.288409i \(-0.0931263\pi\)
−0.728523 + 0.685021i \(0.759793\pi\)
\(464\) −2.76434 −0.128331
\(465\) 0.238412 0.412941i 0.0110561 0.0191497i
\(466\) −9.72771 −0.450628
\(467\) −13.6240 23.5975i −0.630444 1.09196i −0.987461 0.157863i \(-0.949540\pi\)
0.357017 0.934098i \(-0.383794\pi\)
\(468\) 0.548544 0.0253565
\(469\) −14.2431 + 11.8117i −0.657687 + 0.545415i
\(470\) 1.09682 0.0505924
\(471\) 7.92335 + 13.7236i 0.365089 + 0.632352i
\(472\) 23.6089 1.08669
\(473\) 5.11690 8.86273i 0.235275 0.407509i
\(474\) 1.57292 0.0722466
\(475\) 4.04460 + 7.00545i 0.185579 + 0.321432i
\(476\) 5.17200 8.95817i 0.237058 0.410597i
\(477\) −4.80713 −0.220103
\(478\) −19.0118 −0.869577
\(479\) 3.40234 + 5.89303i 0.155457 + 0.269260i 0.933225 0.359292i \(-0.116982\pi\)
−0.777768 + 0.628551i \(0.783648\pi\)
\(480\) −1.90582 + 3.30098i −0.0869885 + 0.150668i
\(481\) 1.65546 2.86733i 0.0754823 0.130739i
\(482\) −2.05861 3.56562i −0.0937673 0.162410i
\(483\) 7.02891 0.319826
\(484\) 7.95529 0.361604
\(485\) 0.491780 + 0.851789i 0.0223306 + 0.0386777i
\(486\) −0.527336 0.913372i −0.0239204 0.0414314i
\(487\) −8.21278 14.2249i −0.372157 0.644594i 0.617741 0.786382i \(-0.288048\pi\)
−0.989897 + 0.141788i \(0.954715\pi\)
\(488\) −5.99949 10.3914i −0.271584 0.470397i
\(489\) −7.13366 + 12.3559i −0.322595 + 0.558751i
\(490\) −0.830127 + 1.43782i −0.0375013 + 0.0649542i
\(491\) −35.8410 −1.61748 −0.808740 0.588166i \(-0.799850\pi\)
−0.808740 + 0.588166i \(0.799850\pi\)
\(492\) −3.77376 6.53634i −0.170134 0.294681i
\(493\) −9.91840 −0.446702
\(494\) 1.22433 0.0550852
\(495\) −0.594584 + 1.02985i −0.0267246 + 0.0462883i
\(496\) −0.822401 −0.0369269
\(497\) 10.5077 + 18.1999i 0.471335 + 0.816377i
\(498\) −0.375217 + 0.649895i −0.0168139 + 0.0291225i
\(499\) −11.2462 19.4790i −0.503449 0.871999i −0.999992 0.00398722i \(-0.998731\pi\)
0.496543 0.868012i \(-0.334603\pi\)
\(500\) −3.44058 + 5.95926i −0.153867 + 0.266506i
\(501\) −1.47723 + 2.55864i −0.0659977 + 0.114311i
\(502\) −10.0551 + 17.4159i −0.448780 + 0.777310i
\(503\) 13.6267 23.6021i 0.607583 1.05236i −0.384054 0.923310i \(-0.625472\pi\)
0.991638 0.129054i \(-0.0411942\pi\)
\(504\) 3.44234 5.96231i 0.153334 0.265582i
\(505\) −4.40570 + 7.63089i −0.196051 + 0.339570i
\(506\) 2.34076 + 4.05431i 0.104059 + 0.180236i
\(507\) −6.30906 + 10.9276i −0.280195 + 0.485312i
\(508\) −7.41622 12.8453i −0.329042 0.569917i
\(509\) −12.9035 −0.571939 −0.285970 0.958239i \(-0.592316\pi\)
−0.285970 + 0.958239i \(0.592316\pi\)
\(510\) 2.26438 3.92202i 0.100268 0.173670i
\(511\) 35.6428 1.57674
\(512\) 15.3253 0.677287
\(513\) 0.939269 + 1.62686i 0.0414697 + 0.0718277i
\(514\) 30.2727 1.33527
\(515\) 5.17758 8.96784i 0.228152 0.395170i
\(516\) 3.18168 5.51083i 0.140066 0.242601i
\(517\) 0.891136 + 1.54349i 0.0391921 + 0.0678828i
\(518\) −6.38694 11.0625i −0.280626 0.486059i
\(519\) 11.5206 + 19.9543i 0.505698 + 0.875895i
\(520\) 0.783860 + 1.35769i 0.0343745 + 0.0595384i
\(521\) −27.9102 −1.22277 −0.611385 0.791333i \(-0.709387\pi\)
−0.611385 + 0.791333i \(0.709387\pi\)
\(522\) −2.02927 −0.0888188
\(523\) −3.12709 5.41628i −0.136738 0.236837i 0.789522 0.613722i \(-0.210329\pi\)
−0.926260 + 0.376885i \(0.876995\pi\)
\(524\) −2.69359 + 4.66544i −0.117670 + 0.203811i
\(525\) 4.86715 8.43016i 0.212420 0.367922i
\(526\) 15.0611 + 26.0866i 0.656695 + 1.13743i
\(527\) −2.95076 −0.128537
\(528\) 2.05102 0.0892592
\(529\) 6.66599 11.5458i 0.289826 0.501993i
\(530\) −2.11162 3.65744i −0.0917230 0.158869i
\(531\) 7.75196 0.336406
\(532\) −1.88477 + 3.26453i −0.0817153 + 0.141535i
\(533\) −5.25430 −0.227589
\(534\) 0.271451 + 0.470167i 0.0117468 + 0.0203461i
\(535\) −11.1998 −0.484211
\(536\) −23.3757 8.66148i −1.00968 0.374119i
\(537\) 10.6867 0.461165
\(538\) 17.0715 + 29.5687i 0.736005 + 1.27480i
\(539\) −2.69783 −0.116204
\(540\) −0.369712 + 0.640360i −0.0159099 + 0.0275567i
\(541\) 38.8177 1.66890 0.834451 0.551082i \(-0.185785\pi\)
0.834451 + 0.551082i \(0.185785\pi\)
\(542\) 11.1192 + 19.2590i 0.477610 + 0.827244i
\(543\) 4.37430 7.57652i 0.187719 0.325139i
\(544\) 23.5878 1.01132
\(545\) 14.6740 0.628564
\(546\) −0.736661 1.27593i −0.0315262 0.0546049i
\(547\) −15.9091 + 27.5553i −0.680222 + 1.17818i 0.294691 + 0.955593i \(0.404783\pi\)
−0.974913 + 0.222586i \(0.928550\pi\)
\(548\) 2.27481 3.94009i 0.0971751 0.168312i
\(549\) −1.96992 3.41201i −0.0840743 0.145621i
\(550\) 6.48341 0.276454
\(551\) 3.61445 0.153981
\(552\) 4.73482 + 8.20094i 0.201527 + 0.349055i
\(553\) 1.68569 + 2.91970i 0.0716829 + 0.124158i
\(554\) −6.70918 11.6206i −0.285046 0.493714i
\(555\) 2.23151 + 3.86509i 0.0947225 + 0.164064i
\(556\) 9.29227 16.0947i 0.394080 0.682566i
\(557\) 4.56572 7.90806i 0.193456 0.335075i −0.752937 0.658092i \(-0.771364\pi\)
0.946393 + 0.323017i \(0.104697\pi\)
\(558\) −0.603715 −0.0255573
\(559\) −2.21497 3.83644i −0.0936831 0.162264i
\(560\) 2.70540 0.114324
\(561\) 7.35901 0.310698
\(562\) 8.00070 13.8576i 0.337489 0.584549i
\(563\) −0.692468 −0.0291841 −0.0145920 0.999894i \(-0.504645\pi\)
−0.0145920 + 0.999894i \(0.504645\pi\)
\(564\) 0.554107 + 0.959742i 0.0233321 + 0.0404124i
\(565\) 2.42286 4.19652i 0.101931 0.176549i
\(566\) −9.99636 17.3142i −0.420178 0.727770i
\(567\) 1.13029 1.95772i 0.0474676 0.0822164i
\(568\) −14.1564 + 24.5196i −0.593990 + 1.02882i
\(569\) 14.2321 24.6508i 0.596642 1.03341i −0.396671 0.917961i \(-0.629835\pi\)
0.993313 0.115453i \(-0.0368320\pi\)
\(570\) −0.825183 + 1.42926i −0.0345631 + 0.0598650i
\(571\) 4.17007 7.22278i 0.174512 0.302264i −0.765480 0.643460i \(-0.777498\pi\)
0.939992 + 0.341196i \(0.110832\pi\)
\(572\) −0.391545 + 0.678176i −0.0163713 + 0.0283560i
\(573\) 8.08452 + 14.0028i 0.337736 + 0.584976i
\(574\) −10.1359 + 17.5558i −0.423062 + 0.732765i
\(575\) 6.69460 + 11.5954i 0.279184 + 0.483561i
\(576\) 7.69941 0.320809
\(577\) 8.79468 15.2328i 0.366127 0.634151i −0.622829 0.782358i \(-0.714017\pi\)
0.988956 + 0.148207i \(0.0473502\pi\)
\(578\) −10.0962 −0.419946
\(579\) −7.15854 −0.297499
\(580\) 0.711355 + 1.23210i 0.0295374 + 0.0511603i
\(581\) −1.60848 −0.0667308
\(582\) 0.622652 1.07847i 0.0258098 0.0447038i
\(583\) 3.43128 5.94315i 0.142109 0.246140i
\(584\) 24.0097 + 41.5860i 0.993529 + 1.72084i
\(585\) 0.257379 + 0.445794i 0.0106413 + 0.0184313i
\(586\) 16.4916 + 28.5643i 0.681261 + 1.17998i
\(587\) 9.13198 + 15.8171i 0.376917 + 0.652840i 0.990612 0.136703i \(-0.0436508\pi\)
−0.613695 + 0.789543i \(0.710317\pi\)
\(588\) −1.67751 −0.0691793
\(589\) 1.07531 0.0443074
\(590\) 3.40519 + 5.89797i 0.140190 + 0.242815i
\(591\) −0.218605 + 0.378635i −0.00899221 + 0.0155750i
\(592\) 3.84880 6.66633i 0.158185 0.273984i
\(593\) −21.3179 36.9237i −0.875422 1.51628i −0.856312 0.516458i \(-0.827250\pi\)
−0.0191096 0.999817i \(-0.506083\pi\)
\(594\) 1.50563 0.0617767
\(595\) 9.70691 0.397945
\(596\) 0.648442 1.12313i 0.0265612 0.0460054i
\(597\) −8.10268 14.0342i −0.331621 0.574384i
\(598\) 2.02650 0.0828698
\(599\) −6.13494 + 10.6260i −0.250667 + 0.434168i −0.963710 0.266953i \(-0.913983\pi\)
0.713043 + 0.701121i \(0.247317\pi\)
\(600\) 13.1145 0.535396
\(601\) 8.80483 + 15.2504i 0.359156 + 0.622077i 0.987820 0.155600i \(-0.0497311\pi\)
−0.628664 + 0.777677i \(0.716398\pi\)
\(602\) −17.0912 −0.696586
\(603\) −7.67540 2.84399i −0.312566 0.115816i
\(604\) −7.17364 −0.291891
\(605\) 3.73266 + 6.46516i 0.151754 + 0.262846i
\(606\) 11.1563 0.453192
\(607\) −11.8160 + 20.4658i −0.479595 + 0.830683i −0.999726 0.0234037i \(-0.992550\pi\)
0.520131 + 0.854086i \(0.325883\pi\)
\(608\) −8.59586 −0.348608
\(609\) −2.17476 3.76680i −0.0881259 0.152638i
\(610\) 1.73065 2.99758i 0.0700721 0.121368i
\(611\) 0.771498 0.0312115
\(612\) 4.57582 0.184967
\(613\) −6.80455 11.7858i −0.274833 0.476025i 0.695260 0.718758i \(-0.255289\pi\)
−0.970093 + 0.242734i \(0.921956\pi\)
\(614\) 6.17177 10.6898i 0.249072 0.431406i
\(615\) 3.54133 6.13377i 0.142800 0.247337i
\(616\) 4.91422 + 8.51167i 0.197999 + 0.342945i
\(617\) −40.7431 −1.64026 −0.820128 0.572181i \(-0.806098\pi\)
−0.820128 + 0.572181i \(0.806098\pi\)
\(618\) −13.1109 −0.527396
\(619\) −1.21800 2.10964i −0.0489555 0.0847934i 0.840509 0.541797i \(-0.182256\pi\)
−0.889465 + 0.457004i \(0.848923\pi\)
\(620\) 0.211630 + 0.366554i 0.00849928 + 0.0147212i
\(621\) 1.55467 + 2.69277i 0.0623868 + 0.108057i
\(622\) −0.303144 0.525061i −0.0121550 0.0210530i
\(623\) −0.581826 + 1.00775i −0.0233104 + 0.0403747i
\(624\) 0.443916 0.768884i 0.0177708 0.0307800i
\(625\) 15.0732 0.602930
\(626\) 3.18511 + 5.51678i 0.127303 + 0.220495i
\(627\) −2.68176 −0.107099
\(628\) −14.0666 −0.561318
\(629\) 13.8094 23.9186i 0.550618 0.953698i
\(630\) 1.98600 0.0791242
\(631\) 18.1408 + 31.4208i 0.722173 + 1.25084i 0.960127 + 0.279564i \(0.0901901\pi\)
−0.237954 + 0.971277i \(0.576477\pi\)
\(632\) −2.27103 + 3.93355i −0.0903369 + 0.156468i
\(633\) 2.15714 + 3.73628i 0.0857387 + 0.148504i
\(634\) 3.27741 5.67664i 0.130163 0.225448i
\(635\) 6.95946 12.0541i 0.276178 0.478354i
\(636\) 2.13357 3.69545i 0.0846014 0.146534i
\(637\) −0.583910 + 1.01136i −0.0231353 + 0.0400716i
\(638\) 1.44847 2.50883i 0.0573456 0.0993255i
\(639\) −4.64824 + 8.05099i −0.183882 + 0.318492i
\(640\) −0.429532 0.743972i −0.0169788 0.0294081i
\(641\) −4.46785 + 7.73854i −0.176469 + 0.305654i −0.940669 0.339326i \(-0.889801\pi\)
0.764199 + 0.644980i \(0.223134\pi\)
\(642\) 7.09015 + 12.2805i 0.279826 + 0.484673i
\(643\) −26.1480 −1.03118 −0.515589 0.856836i \(-0.672427\pi\)
−0.515589 + 0.856836i \(0.672427\pi\)
\(644\) −3.11967 + 5.40342i −0.122932 + 0.212925i
\(645\) 5.97144 0.235125
\(646\) 10.2131 0.401828
\(647\) 20.3952 + 35.3256i 0.801819 + 1.38879i 0.918418 + 0.395612i \(0.129468\pi\)
−0.116599 + 0.993179i \(0.537199\pi\)
\(648\) 3.04554 0.119640
\(649\) −5.53327 + 9.58391i −0.217200 + 0.376201i
\(650\) 1.40325 2.43050i 0.0550399 0.0953319i
\(651\) −0.646999 1.12064i −0.0253579 0.0439212i
\(652\) −6.33232 10.9679i −0.247993 0.429536i
\(653\) 12.4495 + 21.5632i 0.487188 + 0.843835i 0.999891 0.0147309i \(-0.00468916\pi\)
−0.512703 + 0.858566i \(0.671356\pi\)
\(654\) −9.28949 16.0899i −0.363248 0.629164i
\(655\) −5.05538 −0.197530
\(656\) −12.2158 −0.476948
\(657\) 7.88356 + 13.6547i 0.307567 + 0.532722i
\(658\) 1.48826 2.57775i 0.0580186 0.100491i
\(659\) 11.1988 19.3970i 0.436245 0.755599i −0.561151 0.827713i \(-0.689641\pi\)
0.997396 + 0.0721146i \(0.0229747\pi\)
\(660\) −0.527793 0.914165i −0.0205443 0.0355838i
\(661\) −38.7373 −1.50671 −0.753354 0.657616i \(-0.771565\pi\)
−0.753354 + 0.657616i \(0.771565\pi\)
\(662\) 3.48270 0.135359
\(663\) 1.59276 2.75874i 0.0618576 0.107141i
\(664\) −1.08350 1.87668i −0.0420480 0.0728293i
\(665\) −3.53738 −0.137174
\(666\) 2.82536 4.89367i 0.109480 0.189626i
\(667\) 5.98262 0.231648
\(668\) −1.31129 2.27122i −0.0507353 0.0878761i
\(669\) 18.9649 0.733226
\(670\) −1.20776 7.08899i −0.0466597 0.273872i
\(671\) 5.62445 0.217130
\(672\) 5.17200 + 8.95817i 0.199514 + 0.345569i
\(673\) 23.4903 0.905483 0.452741 0.891642i \(-0.350446\pi\)
0.452741 + 0.891642i \(0.350446\pi\)
\(674\) −16.0867 + 27.8629i −0.619635 + 1.07324i
\(675\) 4.30612 0.165743
\(676\) −5.60035 9.70009i −0.215398 0.373080i
\(677\) 20.6440 35.7564i 0.793413 1.37423i −0.130429 0.991458i \(-0.541635\pi\)
0.923842 0.382774i \(-0.125031\pi\)
\(678\) −6.13526 −0.235623
\(679\) 2.66918 0.102434
\(680\) 6.53877 + 11.3255i 0.250751 + 0.434313i
\(681\) 1.90313 3.29632i 0.0729282 0.126315i
\(682\) 0.430926 0.746385i 0.0165010 0.0285806i
\(683\) −4.97437 8.61586i −0.190339 0.329677i 0.755024 0.655698i \(-0.227625\pi\)
−0.945363 + 0.326021i \(0.894292\pi\)
\(684\) −1.66752 −0.0637591
\(685\) 4.26941 0.163126
\(686\) 10.5974 + 18.3552i 0.404610 + 0.700804i
\(687\) −6.42081 11.1212i −0.244969 0.424299i
\(688\) −5.14963 8.91941i −0.196328 0.340049i
\(689\) −1.48531 2.57263i −0.0565858 0.0980094i
\(690\) −1.36584 + 2.36570i −0.0519965 + 0.0900606i
\(691\) −12.3699 + 21.4252i −0.470572 + 0.815054i −0.999434 0.0336538i \(-0.989286\pi\)
0.528862 + 0.848708i \(0.322619\pi\)
\(692\) −20.4529 −0.777503
\(693\) 1.61358 + 2.79480i 0.0612947 + 0.106166i
\(694\) −15.5831 −0.591527
\(695\) 17.4399 0.661533
\(696\) 2.92993 5.07479i 0.111059 0.192359i
\(697\) −43.8301 −1.66018
\(698\) −15.3023 26.5043i −0.579199 1.00320i
\(699\) 4.61173 7.98774i 0.174432 0.302124i
\(700\) 4.32042 + 7.48318i 0.163296 + 0.282838i
\(701\) 25.7172 44.5435i 0.971326 1.68239i 0.279763 0.960069i \(-0.409744\pi\)
0.691563 0.722317i \(-0.256923\pi\)
\(702\) 0.325873 0.564428i 0.0122993 0.0213030i
\(703\) −5.03241 + 8.71640i −0.189801 + 0.328745i
\(704\) −5.49577 + 9.51895i −0.207129 + 0.358759i
\(705\) −0.519980 + 0.900632i −0.0195836 + 0.0339197i
\(706\) 3.65433 6.32949i 0.137533 0.238214i
\(707\) 11.9561 + 20.7086i 0.449657 + 0.778828i
\(708\) −3.44058 + 5.95926i −0.129305 + 0.223963i
\(709\) −8.33267 14.4326i −0.312940 0.542028i 0.666058 0.745900i \(-0.267980\pi\)
−0.978997 + 0.203873i \(0.934647\pi\)
\(710\) −8.16731 −0.306514
\(711\) −0.745691 + 1.29158i −0.0279656 + 0.0484378i
\(712\) −1.56772 −0.0587528
\(713\) 1.77985 0.0666559
\(714\) −6.14505 10.6435i −0.229973 0.398324i
\(715\) −0.734860 −0.0274822
\(716\) −4.74312 + 8.21532i −0.177259 + 0.307021i
\(717\) 9.01312 15.6112i 0.336601 0.583010i
\(718\) 5.48744 + 9.50452i 0.204789 + 0.354706i
\(719\) 3.97866 + 6.89124i 0.148379 + 0.257000i 0.930628 0.365965i \(-0.119261\pi\)
−0.782250 + 0.622965i \(0.785928\pi\)
\(720\) 0.598387 + 1.03644i 0.0223006 + 0.0386257i
\(721\) −14.0509 24.3368i −0.523282 0.906351i
\(722\) 16.3169 0.607253
\(723\) 3.90380 0.145184
\(724\) 3.88293 + 6.72543i 0.144308 + 0.249949i
\(725\) 4.14265 7.17529i 0.153854 0.266483i
\(726\) 4.72599 8.18566i 0.175398 0.303798i
\(727\) 18.4741 + 31.9981i 0.685167 + 1.18674i 0.973384 + 0.229179i \(0.0736042\pi\)
−0.288217 + 0.957565i \(0.593062\pi\)
\(728\) 4.25446 0.157681
\(729\) 1.00000 0.0370370
\(730\) −6.92600 + 11.9962i −0.256343 + 0.443999i
\(731\) −18.4767 32.0026i −0.683387 1.18366i
\(732\) 3.49728 0.129263
\(733\) 17.7298 30.7089i 0.654864 1.13426i −0.327064 0.945002i \(-0.606059\pi\)
0.981928 0.189255i \(-0.0606074\pi\)
\(734\) −34.5667 −1.27588
\(735\) −0.787096 1.36329i −0.0290325 0.0502857i
\(736\) −14.2278 −0.524444
\(737\) 8.99470 7.45925i 0.331324 0.274765i
\(738\) −8.96749 −0.330098
\(739\) −12.8612 22.2763i −0.473107 0.819445i 0.526419 0.850225i \(-0.323534\pi\)
−0.999526 + 0.0307797i \(0.990201\pi\)
\(740\) −3.96168 −0.145634
\(741\) −0.580431 + 1.00534i −0.0213227 + 0.0369320i
\(742\) −11.4610 −0.420746
\(743\) 12.2309 + 21.1846i 0.448709 + 0.777187i 0.998302 0.0582451i \(-0.0185505\pi\)
−0.549593 + 0.835433i \(0.685217\pi\)
\(744\) 0.871664 1.50977i 0.0319567 0.0553507i
\(745\) 1.21701 0.0445878
\(746\) −14.8760 −0.544648
\(747\) −0.355767 0.616206i −0.0130168 0.0225458i
\(748\) −3.26618 + 5.65719i −0.119423 + 0.206847i
\(749\) −15.1970 + 26.3220i −0.555286 + 0.961783i
\(750\) 4.08789 + 7.08043i 0.149268 + 0.258541i
\(751\) 11.0637 0.403720 0.201860 0.979414i \(-0.435301\pi\)
0.201860 + 0.979414i \(0.435301\pi\)
\(752\) 1.79367 0.0654085
\(753\) −9.53385 16.5131i −0.347433 0.601771i
\(754\) −0.627005 1.08600i −0.0228342 0.0395500i
\(755\) −3.36591 5.82993i −0.122498 0.212173i
\(756\) 1.00332 + 1.73780i 0.0364904 + 0.0632032i
\(757\) −10.4668 + 18.1290i −0.380422 + 0.658910i −0.991123 0.132952i \(-0.957554\pi\)
0.610701 + 0.791861i \(0.290888\pi\)
\(758\) 4.77835 8.27635i 0.173558 0.300611i
\(759\) −4.43884 −0.161120
\(760\) −2.38285 4.12722i −0.0864352 0.149710i
\(761\) −12.1681 −0.441093 −0.220547 0.975376i \(-0.570784\pi\)
−0.220547 + 0.975376i \(0.570784\pi\)
\(762\) −17.6230 −0.638414
\(763\) 19.9110 34.4869i 0.720828 1.24851i
\(764\) −14.3527 −0.519264
\(765\) 2.14700 + 3.71871i 0.0776249 + 0.134450i
\(766\) −10.7920 + 18.6923i −0.389930 + 0.675379i
\(767\) 2.39520 + 4.14861i 0.0864858 + 0.149798i
\(768\) −8.24325 + 14.2777i −0.297453 + 0.515203i
\(769\) 13.1071 22.7022i 0.472655 0.818662i −0.526855 0.849955i \(-0.676629\pi\)
0.999510 + 0.0312927i \(0.00996242\pi\)
\(770\) −1.41759 + 2.45533i −0.0510863 + 0.0884841i
\(771\) −14.3517 + 24.8579i −0.516865 + 0.895237i
\(772\) 3.17720 5.50307i 0.114350 0.198060i
\(773\) −4.49338 + 7.78277i −0.161616 + 0.279927i −0.935448 0.353464i \(-0.885004\pi\)
0.773833 + 0.633390i \(0.218337\pi\)
\(774\) −3.78028 6.54763i −0.135879 0.235350i
\(775\) 1.23245 2.13467i 0.0442710 0.0766797i
\(776\) 1.79801 + 3.11425i 0.0645449 + 0.111795i
\(777\) 12.1117 0.434505
\(778\) 6.46878 11.2043i 0.231917 0.401692i
\(779\) 15.9725 0.572275
\(780\) −0.456935 −0.0163609
\(781\) −6.63574 11.4934i −0.237446 0.411268i
\(782\) 16.9046 0.604507
\(783\) 0.962039 1.66630i 0.0343805 0.0595487i
\(784\) −1.35754 + 2.35134i −0.0484837 + 0.0839763i
\(785\) −6.60012 11.4317i −0.235568 0.408016i
\(786\) 3.20036 + 5.54318i 0.114153 + 0.197719i
\(787\) 4.82133 + 8.35079i 0.171862 + 0.297674i 0.939071 0.343724i \(-0.111688\pi\)
−0.767209 + 0.641397i \(0.778355\pi\)
\(788\) −0.194049 0.336102i −0.00691269 0.0119731i
\(789\) −28.5607 −1.01679
\(790\) −1.31024 −0.0466161
\(791\) −6.57514 11.3885i −0.233785 0.404928i
\(792\) −2.17388 + 3.76527i −0.0772454 + 0.133793i
\(793\) 1.21734 2.10849i 0.0432289 0.0748746i
\(794\) 4.93101 + 8.54076i 0.174995 + 0.303100i
\(795\) 4.00432 0.142019
\(796\) 14.3850 0.509862
\(797\) 22.8239 39.5322i 0.808466 1.40030i −0.105461 0.994423i \(-0.533632\pi\)
0.913926 0.405880i \(-0.133035\pi\)
\(798\) 2.23937 + 3.87871i 0.0792729 + 0.137305i
\(799\) 6.43565 0.227677
\(800\) −9.85202 + 17.0642i −0.348321 + 0.603310i
\(801\) −0.514759 −0.0181881
\(802\) −19.7562 34.2188i −0.697617 1.20831i
\(803\) −22.5088 −0.794319
\(804\) 5.59290 4.63815i 0.197246 0.163575i
\(805\) −5.85505 −0.206363
\(806\) −0.186536 0.323090i −0.00657045 0.0113804i
\(807\) −32.3731 −1.13959
\(808\) −16.1078 + 27.8995i −0.566670 + 0.981502i
\(809\) 20.7668 0.730121 0.365060 0.930984i \(-0.381048\pi\)
0.365060 + 0.930984i \(0.381048\pi\)
\(810\) 0.439269 + 0.760836i 0.0154343 + 0.0267330i
\(811\) 7.02612 12.1696i 0.246720 0.427332i −0.715894 0.698209i \(-0.753980\pi\)
0.962614 + 0.270877i \(0.0873138\pi\)
\(812\) 3.86093 0.135492
\(813\) −21.0856 −0.739503
\(814\) 4.03343 + 6.98610i 0.141372 + 0.244863i
\(815\) 5.94231 10.2924i 0.208150 0.360526i
\(816\) 3.70304 6.41385i 0.129632 0.224530i
\(817\) 6.73327 + 11.6624i 0.235567 + 0.408015i
\(818\) −22.1831 −0.775616
\(819\) 1.39695 0.0488133
\(820\) 3.14353 + 5.44475i 0.109777 + 0.190139i
\(821\) 15.2618 + 26.4341i 0.532639 + 0.922558i 0.999274 + 0.0381079i \(0.0121331\pi\)
−0.466634 + 0.884450i \(0.654534\pi\)
\(822\) −2.70279 4.68137i −0.0942706 0.163281i
\(823\) −23.9634 41.5058i −0.835311 1.44680i −0.893777 0.448511i \(-0.851954\pi\)
0.0584667 0.998289i \(-0.481379\pi\)
\(824\) 18.9299 32.7876i 0.659455 1.14221i
\(825\) −3.07366 + 5.32374i −0.107011 + 0.185349i
\(826\) 18.4820 0.643069
\(827\) 10.9411 + 18.9506i 0.380461 + 0.658978i 0.991128 0.132910i \(-0.0424320\pi\)
−0.610667 + 0.791887i \(0.709099\pi\)
\(828\) −2.76006 −0.0959188
\(829\) −0.363130 −0.0126120 −0.00630600 0.999980i \(-0.502007\pi\)
−0.00630600 + 0.999980i \(0.502007\pi\)
\(830\) 0.312554 0.541360i 0.0108489 0.0187909i
\(831\) 12.7228 0.441349
\(832\) 2.37897 + 4.12049i 0.0824759 + 0.142852i
\(833\) −4.87084 + 8.43654i −0.168764 + 0.292309i
\(834\) −11.0405 19.1227i −0.382301 0.662165i
\(835\) 1.23053 2.13133i 0.0425841 0.0737578i
\(836\) 1.19026 2.06159i 0.0411659 0.0713014i
\(837\) 0.286210 0.495730i 0.00989286 0.0171349i
\(838\) −16.0416 + 27.7848i −0.554146 + 0.959809i
\(839\) −11.2480 + 19.4822i −0.388326 + 0.672600i −0.992224 0.124461i \(-0.960280\pi\)
0.603899 + 0.797061i \(0.293613\pi\)
\(840\) −2.86745 + 4.96658i −0.0989366 + 0.171363i
\(841\) 12.6490 + 21.9086i 0.436171 + 0.755470i
\(842\) −0.316698 + 0.548537i −0.0109141 + 0.0189038i
\(843\) 7.58597 + 13.1393i 0.261275 + 0.452541i
\(844\) −3.82965 −0.131822
\(845\) 5.25542 9.10266i 0.180792 0.313141i
\(846\) 1.31671 0.0452695
\(847\) 20.2593 0.696118
\(848\) −3.45323 5.98117i −0.118584 0.205394i
\(849\) 18.9563 0.650580
\(850\) 11.7056 20.2746i 0.401497 0.695414i
\(851\) −8.32962 + 14.4273i −0.285536 + 0.494562i
\(852\) −4.12610 7.14661i −0.141358 0.244839i
\(853\) −2.83112 4.90365i −0.0969358 0.167898i 0.813479 0.581594i \(-0.197571\pi\)
−0.910415 + 0.413696i \(0.864237\pi\)
\(854\) −4.69663 8.13480i −0.160715 0.278367i
\(855\) −0.782407 1.35517i −0.0267578 0.0463458i
\(856\) −40.9480 −1.39957
\(857\) −14.8633 −0.507721 −0.253861 0.967241i \(-0.581700\pi\)
−0.253861 + 0.967241i \(0.581700\pi\)
\(858\) 0.465210 + 0.805767i 0.0158820 + 0.0275084i
\(859\) −21.4760 + 37.1975i −0.732751 + 1.26916i 0.222953 + 0.974829i \(0.428430\pi\)
−0.955703 + 0.294332i \(0.904903\pi\)
\(860\) −2.65033 + 4.59050i −0.0903754 + 0.156535i
\(861\) −9.61043 16.6458i −0.327523 0.567286i
\(862\) 19.7759 0.673569
\(863\) 22.5825 0.768716 0.384358 0.923184i \(-0.374423\pi\)
0.384358 + 0.923184i \(0.374423\pi\)
\(864\) −2.28791 + 3.96278i −0.0778364 + 0.134817i
\(865\) −9.59661 16.6218i −0.326295 0.565159i
\(866\) 0.974652 0.0331200
\(867\) 4.78642 8.29032i 0.162555 0.281554i
\(868\) 1.14864 0.0389874
\(869\) −1.06453 1.84383i −0.0361118 0.0625476i
\(870\) 1.69037 0.0573091
\(871\) −0.849532 4.98638i −0.0287853 0.168957i
\(872\) 53.6499 1.81682
\(873\) 0.590375 + 1.02256i 0.0199812 + 0.0346084i
\(874\) −6.16036 −0.208377
\(875\) −8.76195 + 15.1761i −0.296208 + 0.513047i
\(876\) −13.9960 −0.472880
\(877\) −0.732725 1.26912i −0.0247424 0.0428550i 0.853389 0.521274i \(-0.174543\pi\)
−0.878131 + 0.478419i \(0.841210\pi\)
\(878\) 4.70458 8.14856i 0.158772 0.275001i
\(879\) −31.2734 −1.05483
\(880\) −1.70849 −0.0575932
\(881\) 17.4077 + 30.1509i 0.586479 + 1.01581i 0.994689 + 0.102923i \(0.0328196\pi\)
−0.408210 + 0.912888i \(0.633847\pi\)
\(882\) −0.996556 + 1.72609i −0.0335558 + 0.0581203i
\(883\) 8.29415 14.3659i 0.279120 0.483451i −0.692046 0.721853i \(-0.743290\pi\)
0.971166 + 0.238403i \(0.0766238\pi\)
\(884\) 1.41384 + 2.44884i 0.0475526 + 0.0823635i
\(885\) −6.45735 −0.217061
\(886\) −37.0082 −1.24331
\(887\) 22.9646 + 39.7758i 0.771075 + 1.33554i 0.936974 + 0.349399i \(0.113614\pi\)
−0.165899 + 0.986143i \(0.553053\pi\)
\(888\) 8.15870 + 14.1313i 0.273788 + 0.474215i
\(889\) −18.8865 32.7124i −0.633433 1.09714i
\(890\) −0.226117 0.391647i −0.00757947 0.0131280i
\(891\) −0.713790 + 1.23632i −0.0239129 + 0.0414183i
\(892\) −8.41727 + 14.5791i −0.281831 + 0.488146i
\(893\) −2.34527 −0.0784816
\(894\) −0.770439 1.33444i −0.0257673 0.0446303i
\(895\) −8.90197 −0.297560
\(896\) −2.33132 −0.0778840
\(897\) −0.960726 + 1.66403i −0.0320777 + 0.0555602i
\(898\) −6.70957 −0.223901
\(899\) −0.550690 0.953823i −0.0183665 0.0318118i
\(900\) −1.91120 + 3.31030i −0.0637067 + 0.110343i
\(901\) −12.3901 21.4603i −0.412774 0.714946i
\(902\) 6.40091 11.0867i 0.213127 0.369147i
\(903\) 8.10262 14.0341i 0.269638 0.467027i
\(904\) 8.85830 15.3430i 0.294623 0.510301i
\(905\) −3.64378 + 6.31121i −0.121123 + 0.209792i
\(906\) −4.26164 + 7.38138i −0.141583 + 0.245230i
\(907\) −13.8915 + 24.0607i −0.461259 + 0.798924i −0.999024 0.0441708i \(-0.985935\pi\)
0.537765 + 0.843095i \(0.319269\pi\)
\(908\) 1.68935 + 2.92604i 0.0560631 + 0.0971041i
\(909\) −5.28898 + 9.16077i −0.175424 + 0.303844i
\(910\) 0.613635 + 1.06285i 0.0203418 + 0.0352331i
\(911\) −26.1508 −0.866416 −0.433208 0.901294i \(-0.642618\pi\)
−0.433208 + 0.901294i \(0.642618\pi\)
\(912\) −1.34946 + 2.33733i −0.0446850 + 0.0773967i
\(913\) 1.01577 0.0336171
\(914\) 36.0759 1.19328
\(915\) 1.64094 + 2.84219i 0.0542478 + 0.0939599i
\(916\) 11.3991 0.376637
\(917\) −6.85963 + 11.8812i −0.226525 + 0.392352i
\(918\) 2.71836 4.70833i 0.0897191 0.155398i
\(919\) 23.3286 + 40.4063i 0.769539 + 1.33288i 0.937813 + 0.347140i \(0.112847\pi\)
−0.168275 + 0.985740i \(0.553820\pi\)
\(920\) −3.94408 6.83135i −0.130033 0.225223i
\(921\) 5.85184 + 10.1357i 0.192825 + 0.333982i
\(922\) −0.882388 1.52834i −0.0290599 0.0503333i
\(923\) −5.74487 −0.189095
\(924\) −2.86464 −0.0942398
\(925\) 11.5357 + 19.9803i 0.379290 + 0.656950i
\(926\) −5.19652 + 9.00064i −0.170768 + 0.295780i
\(927\) 6.21562 10.7658i 0.204148 0.353594i
\(928\) 4.40212 + 7.62470i 0.144507 + 0.250293i
\(929\) −33.2073 −1.08950 −0.544748 0.838600i \(-0.683375\pi\)
−0.544748 + 0.838600i \(0.683375\pi\)
\(930\) 0.502892 0.0164905
\(931\) 1.77502 3.07443i 0.0581741 0.100760i
\(932\) 4.09368 + 7.09046i 0.134093 + 0.232256i
\(933\) 0.574859 0.0188201
\(934\) 14.3689 24.8876i 0.470163 0.814347i
\(935\) −6.13003 −0.200473
\(936\) 0.941013 + 1.62988i 0.0307580 + 0.0532744i
\(937\) −27.4424 −0.896505 −0.448253 0.893907i \(-0.647954\pi\)
−0.448253 + 0.893907i \(0.647954\pi\)
\(938\) −18.2994 6.78054i −0.597497 0.221392i
\(939\) −6.04001 −0.197108
\(940\) −0.461569 0.799461i −0.0150547 0.0260756i
\(941\) −21.4206 −0.698293 −0.349147 0.937068i \(-0.613528\pi\)
−0.349147 + 0.937068i \(0.613528\pi\)
\(942\) −8.35653 + 14.4739i −0.272270 + 0.471586i
\(943\) 26.4376 0.860928
\(944\) 5.56866 + 9.64520i 0.181244 + 0.313925i
\(945\) −0.941526 + 1.63077i −0.0306278 + 0.0530490i
\(946\) 10.7933 0.350920
\(947\) 53.6910 1.74472 0.872361 0.488862i \(-0.162588\pi\)
0.872361 + 0.488862i \(0.162588\pi\)
\(948\) −0.661926 1.14649i −0.0214984 0.0372362i
\(949\) −4.87173 + 8.43809i −0.158143 + 0.273912i
\(950\) −4.26573 + 7.38845i −0.138398 + 0.239713i
\(951\) 3.10752 + 5.38238i 0.100768 + 0.174536i
\(952\) 35.4897 1.15023
\(953\) −0.108986 −0.00353040 −0.00176520 0.999998i \(-0.500562\pi\)
−0.00176520 + 0.999998i \(0.500562\pi\)
\(954\) −2.53497 4.39070i −0.0820727 0.142154i
\(955\) −6.73438 11.6643i −0.217919 0.377447i
\(956\) 8.00065 + 13.8575i 0.258760 + 0.448185i
\(957\) 1.37339 + 2.37878i 0.0443953 + 0.0768950i
\(958\) −3.58836 + 6.21522i −0.115935 + 0.200805i
\(959\) 5.79314 10.0340i 0.187070 0.324015i
\(960\) −6.41358 −0.206997
\(961\) 15.3362 + 26.5630i 0.494715 + 0.856872i
\(962\) 3.49192 0.112584
\(963\) −13.4452 −0.433267
\(964\) −1.73264 + 3.00102i −0.0558046 + 0.0966563i
\(965\) 5.96303 0.191957
\(966\) 3.70660 + 6.42001i 0.119258 + 0.206560i
\(967\) 22.1707 38.4007i 0.712961 1.23488i −0.250780 0.968044i \(-0.580687\pi\)
0.963741 0.266840i \(-0.0859795\pi\)
\(968\) 13.6471 + 23.6375i 0.438634 + 0.759737i
\(969\) −4.84182 + 8.38628i −0.155542 + 0.269406i
\(970\) −0.518667 + 0.898357i −0.0166534 + 0.0288445i
\(971\) 11.8519 20.5281i 0.380345 0.658778i −0.610766 0.791811i \(-0.709138\pi\)
0.991112 + 0.133033i \(0.0424718\pi\)
\(972\) −0.443834 + 0.768743i −0.0142360 + 0.0246574i
\(973\) 23.6641 40.9875i 0.758637 1.31400i
\(974\) 8.66178 15.0027i 0.277541 0.480716i
\(975\) 1.33051 + 2.30450i 0.0426103 + 0.0738032i
\(976\) 2.83021 4.90207i 0.0905929 0.156911i
\(977\) 13.1525 + 22.7808i 0.420785 + 0.728821i 0.996016 0.0891697i \(-0.0284213\pi\)
−0.575231 + 0.817991i \(0.695088\pi\)
\(978\) −15.0473 −0.481161
\(979\) 0.367430 0.636407i 0.0117431 0.0203397i
\(980\) 1.39736 0.0446370
\(981\) 17.6159 0.562432
\(982\) −18.9002 32.7362i −0.603130 1.04465i
\(983\) 9.50229 0.303076 0.151538 0.988451i \(-0.451577\pi\)
0.151538 + 0.988451i \(0.451577\pi\)
\(984\) 12.9476 22.4258i 0.412753 0.714910i
\(985\) 0.182097 0.315401i 0.00580209 0.0100495i
\(986\) −5.23033 9.05920i −0.166568 0.288504i
\(987\) 1.41112 + 2.44412i 0.0449163 + 0.0777974i
\(988\) −0.515230 0.892405i −0.0163917 0.0283912i
\(989\) 11.1449 + 19.3035i 0.354386 + 0.613815i
\(990\) −1.25418 −0.0398605
\(991\) −10.2654 −0.326090 −0.163045 0.986619i \(-0.552132\pi\)
−0.163045 + 0.986619i \(0.552132\pi\)
\(992\) 1.30965 + 2.26837i 0.0415813 + 0.0720209i
\(993\) −1.65108 + 2.85976i −0.0523955 + 0.0907517i
\(994\) −11.0822 + 19.1949i −0.351506 + 0.608825i
\(995\) 6.74950 + 11.6905i 0.213973 + 0.370613i
\(996\) 0.631605 0.0200132
\(997\) 32.6943 1.03544 0.517719 0.855551i \(-0.326781\pi\)
0.517719 + 0.855551i \(0.326781\pi\)
\(998\) 11.8610 20.5439i 0.375455 0.650307i
\(999\) 2.67890 + 4.63999i 0.0847567 + 0.146803i
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 201.2.e.b.37.4 10
3.2 odd 2 603.2.g.g.37.2 10
67.29 even 3 inner 201.2.e.b.163.4 yes 10
201.29 odd 6 603.2.g.g.163.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.e.b.37.4 10 1.1 even 1 trivial
201.2.e.b.163.4 yes 10 67.29 even 3 inner
603.2.g.g.37.2 10 3.2 odd 2
603.2.g.g.163.2 10 201.29 odd 6