Properties

Label 273.2.bf.b.185.18
Level $273$
Weight $2$
Character 273.185
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(152,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.152");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bf (of order \(6\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 185.18
Character \(\chi\) \(=\) 273.185
Dual form 273.2.bf.b.152.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.473030 + 0.273104i) q^{2} +(-0.966120 - 1.43757i) q^{3} +(-0.850828 - 1.47368i) q^{4} +(1.25657 + 2.17644i) q^{5} +(-0.0643970 - 0.943866i) q^{6} +(2.53535 - 0.756296i) q^{7} -2.02188i q^{8} +(-1.13323 + 2.77773i) q^{9} +1.37270i q^{10} -6.02763i q^{11} +(-1.29652 + 2.64688i) q^{12} +(-1.89716 - 3.06607i) q^{13} +(1.40585 + 0.334664i) q^{14} +(1.91480 - 3.90911i) q^{15} +(-1.14947 + 1.99095i) q^{16} +(0.323651 + 0.560581i) q^{17} +(-1.29466 + 1.00446i) q^{18} -2.29555i q^{19} +(2.13825 - 3.70356i) q^{20} +(-3.53668 - 2.91408i) q^{21} +(1.64617 - 2.85125i) q^{22} +(0.894874 + 0.516656i) q^{23} +(-2.90659 + 1.95337i) q^{24} +(-0.657937 + 1.13958i) q^{25} +(-0.0600548 - 1.96847i) q^{26} +(5.08802 - 1.05453i) q^{27} +(-3.27169 - 3.09282i) q^{28} +(-4.46255 + 2.57646i) q^{29} +(1.97335 - 1.32619i) q^{30} +(9.25745 + 5.34479i) q^{31} +(-4.58946 + 2.64973i) q^{32} +(-8.66515 + 5.82341i) q^{33} +0.353562i q^{34} +(4.83188 + 4.56771i) q^{35} +(5.05766 - 0.693365i) q^{36} +(1.97766 - 3.42541i) q^{37} +(0.626924 - 1.08587i) q^{38} +(-2.57482 + 5.68949i) q^{39} +(4.40050 - 2.54063i) q^{40} +(4.48689 + 7.77153i) q^{41} +(-0.877112 - 2.34433i) q^{42} +(-4.09951 + 7.10056i) q^{43} +(-8.88279 + 5.12848i) q^{44} +(-7.46955 + 1.02402i) q^{45} +(0.282202 + 0.488787i) q^{46} +(2.09646 + 3.63118i) q^{47} +(3.97266 - 0.271042i) q^{48} +(5.85603 - 3.83496i) q^{49} +(-0.622448 + 0.359370i) q^{50} +(0.493189 - 1.00686i) q^{51} +(-2.90425 + 5.40450i) q^{52} +(0.0406517 + 0.0234703i) q^{53} +(2.69478 + 0.890735i) q^{54} +(13.1188 - 7.57414i) q^{55} +(-1.52914 - 5.12617i) q^{56} +(-3.30002 + 2.21778i) q^{57} -2.81456 q^{58} +(0.831148 + 1.43959i) q^{59} +(-7.38994 + 0.504192i) q^{60} +3.59276i q^{61} +(2.91937 + 5.05650i) q^{62} +(-0.772338 + 7.89959i) q^{63} +1.70329 q^{64} +(4.28922 - 7.98179i) q^{65} +(-5.68928 + 0.388162i) q^{66} +1.52251 q^{67} +(0.550743 - 0.953916i) q^{68} +(-0.121826 - 1.78560i) q^{69} +(1.03817 + 3.48027i) q^{70} +(-11.4729 - 6.62389i) q^{71} +(5.61623 + 2.29124i) q^{72} +(4.76835 + 2.75301i) q^{73} +(1.87099 - 1.08022i) q^{74} +(2.27387 - 0.155139i) q^{75} +(-3.38290 + 1.95312i) q^{76} +(-4.55868 - 15.2822i) q^{77} +(-2.77179 + 1.98811i) q^{78} +(-2.14796 - 3.72038i) q^{79} -5.77758 q^{80} +(-6.43160 - 6.29559i) q^{81} +4.90156i q^{82} -11.8816 q^{83} +(-1.28530 + 7.69132i) q^{84} +(-0.813381 + 1.40882i) q^{85} +(-3.87838 + 2.23919i) q^{86} +(8.01520 + 3.92608i) q^{87} -12.1871 q^{88} +(-0.507769 + 0.879481i) q^{89} +(-3.81299 - 1.55558i) q^{90} +(-7.12882 - 6.33877i) q^{91} -1.75834i q^{92} +(-1.26028 - 18.4720i) q^{93} +2.29021i q^{94} +(4.99614 - 2.88452i) q^{95} +(8.24314 + 4.03773i) q^{96} +(8.58147 + 4.95452i) q^{97} +(3.81742 - 0.214744i) q^{98} +(16.7432 + 6.83067i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.473030 + 0.273104i 0.334483 + 0.193114i 0.657830 0.753167i \(-0.271475\pi\)
−0.323347 + 0.946281i \(0.604808\pi\)
\(3\) −0.966120 1.43757i −0.557789 0.829982i
\(4\) −0.850828 1.47368i −0.425414 0.736839i
\(5\) 1.25657 + 2.17644i 0.561955 + 0.973335i 0.997326 + 0.0730836i \(0.0232840\pi\)
−0.435371 + 0.900251i \(0.643383\pi\)
\(6\) −0.0643970 0.943866i −0.0262900 0.385332i
\(7\) 2.53535 0.756296i 0.958273 0.285853i
\(8\) 2.02188i 0.714841i
\(9\) −1.13323 + 2.77773i −0.377742 + 0.925911i
\(10\) 1.37270i 0.434085i
\(11\) 6.02763i 1.81740i −0.417450 0.908700i \(-0.637076\pi\)
0.417450 0.908700i \(-0.362924\pi\)
\(12\) −1.29652 + 2.64688i −0.374272 + 0.764087i
\(13\) −1.89716 3.06607i −0.526176 0.850376i
\(14\) 1.40585 + 0.334664i 0.375728 + 0.0894428i
\(15\) 1.91480 3.90911i 0.494398 1.00933i
\(16\) −1.14947 + 1.99095i −0.287369 + 0.497737i
\(17\) 0.323651 + 0.560581i 0.0784970 + 0.135961i 0.902602 0.430477i \(-0.141655\pi\)
−0.824105 + 0.566438i \(0.808321\pi\)
\(18\) −1.29466 + 1.00446i −0.305154 + 0.236754i
\(19\) 2.29555i 0.526636i −0.964709 0.263318i \(-0.915183\pi\)
0.964709 0.263318i \(-0.0848168\pi\)
\(20\) 2.13825 3.70356i 0.478127 0.828141i
\(21\) −3.53668 2.91408i −0.771768 0.635904i
\(22\) 1.64617 2.85125i 0.350965 0.607889i
\(23\) 0.894874 + 0.516656i 0.186594 + 0.107730i 0.590387 0.807120i \(-0.298975\pi\)
−0.403793 + 0.914850i \(0.632308\pi\)
\(24\) −2.90659 + 1.95337i −0.593305 + 0.398731i
\(25\) −0.657937 + 1.13958i −0.131587 + 0.227916i
\(26\) −0.0600548 1.96847i −0.0117777 0.386048i
\(27\) 5.08802 1.05453i 0.979190 0.202944i
\(28\) −3.27169 3.09282i −0.618291 0.584487i
\(29\) −4.46255 + 2.57646i −0.828676 + 0.478436i −0.853399 0.521258i \(-0.825463\pi\)
0.0247234 + 0.999694i \(0.492129\pi\)
\(30\) 1.97335 1.32619i 0.360283 0.242128i
\(31\) 9.25745 + 5.34479i 1.66269 + 0.959953i 0.971424 + 0.237351i \(0.0762792\pi\)
0.691264 + 0.722602i \(0.257054\pi\)
\(32\) −4.58946 + 2.64973i −0.811310 + 0.468410i
\(33\) −8.66515 + 5.82341i −1.50841 + 1.01373i
\(34\) 0.353562i 0.0606354i
\(35\) 4.83188 + 4.56771i 0.816738 + 0.772084i
\(36\) 5.05766 0.693365i 0.842944 0.115561i
\(37\) 1.97766 3.42541i 0.325126 0.563134i −0.656412 0.754402i \(-0.727927\pi\)
0.981538 + 0.191268i \(0.0612601\pi\)
\(38\) 0.626924 1.08587i 0.101701 0.176151i
\(39\) −2.57482 + 5.68949i −0.412301 + 0.911048i
\(40\) 4.40050 2.54063i 0.695780 0.401709i
\(41\) 4.48689 + 7.77153i 0.700735 + 1.21371i 0.968209 + 0.250143i \(0.0804778\pi\)
−0.267474 + 0.963565i \(0.586189\pi\)
\(42\) −0.877112 2.34433i −0.135341 0.361738i
\(43\) −4.09951 + 7.10056i −0.625169 + 1.08282i 0.363339 + 0.931657i \(0.381637\pi\)
−0.988508 + 0.151168i \(0.951697\pi\)
\(44\) −8.88279 + 5.12848i −1.33913 + 0.773147i
\(45\) −7.46955 + 1.02402i −1.11350 + 0.152651i
\(46\) 0.282202 + 0.488787i 0.0416084 + 0.0720678i
\(47\) 2.09646 + 3.63118i 0.305800 + 0.529662i 0.977439 0.211217i \(-0.0677426\pi\)
−0.671639 + 0.740879i \(0.734409\pi\)
\(48\) 3.97266 0.271042i 0.573404 0.0391216i
\(49\) 5.85603 3.83496i 0.836576 0.547851i
\(50\) −0.622448 + 0.359370i −0.0880274 + 0.0508226i
\(51\) 0.493189 1.00686i 0.0690603 0.140989i
\(52\) −2.90425 + 5.40450i −0.402747 + 0.749469i
\(53\) 0.0406517 + 0.0234703i 0.00558394 + 0.00322389i 0.502789 0.864409i \(-0.332307\pi\)
−0.497205 + 0.867633i \(0.665640\pi\)
\(54\) 2.69478 + 0.890735i 0.366714 + 0.121214i
\(55\) 13.1188 7.57414i 1.76894 1.02130i
\(56\) −1.52914 5.12617i −0.204339 0.685013i
\(57\) −3.30002 + 2.21778i −0.437098 + 0.293752i
\(58\) −2.81456 −0.369570
\(59\) 0.831148 + 1.43959i 0.108206 + 0.187419i 0.915044 0.403355i \(-0.132156\pi\)
−0.806837 + 0.590774i \(0.798823\pi\)
\(60\) −7.38994 + 0.504192i −0.954037 + 0.0650909i
\(61\) 3.59276i 0.460006i 0.973190 + 0.230003i \(0.0738736\pi\)
−0.973190 + 0.230003i \(0.926126\pi\)
\(62\) 2.91937 + 5.05650i 0.370760 + 0.642176i
\(63\) −0.772338 + 7.89959i −0.0973054 + 0.995255i
\(64\) 1.70329 0.212911
\(65\) 4.28922 7.98179i 0.532013 0.990019i
\(66\) −5.68928 + 0.388162i −0.700302 + 0.0477794i
\(67\) 1.52251 0.186004 0.0930020 0.995666i \(-0.470354\pi\)
0.0930020 + 0.995666i \(0.470354\pi\)
\(68\) 0.550743 0.953916i 0.0667875 0.115679i
\(69\) −0.121826 1.78560i −0.0146661 0.214961i
\(70\) 1.03817 + 3.48027i 0.124085 + 0.415972i
\(71\) −11.4729 6.62389i −1.36158 0.786111i −0.371749 0.928333i \(-0.621242\pi\)
−0.989835 + 0.142222i \(0.954575\pi\)
\(72\) 5.61623 + 2.29124i 0.661879 + 0.270025i
\(73\) 4.76835 + 2.75301i 0.558093 + 0.322215i 0.752380 0.658730i \(-0.228906\pi\)
−0.194287 + 0.980945i \(0.562239\pi\)
\(74\) 1.87099 1.08022i 0.217498 0.125572i
\(75\) 2.27387 0.155139i 0.262564 0.0179139i
\(76\) −3.38290 + 1.95312i −0.388046 + 0.224038i
\(77\) −4.55868 15.2822i −0.519509 1.74157i
\(78\) −2.77179 + 1.98811i −0.313844 + 0.225109i
\(79\) −2.14796 3.72038i −0.241665 0.418575i 0.719524 0.694468i \(-0.244360\pi\)
−0.961189 + 0.275892i \(0.911027\pi\)
\(80\) −5.77758 −0.645953
\(81\) −6.43160 6.29559i −0.714622 0.699511i
\(82\) 4.90156i 0.541286i
\(83\) −11.8816 −1.30417 −0.652085 0.758146i \(-0.726106\pi\)
−0.652085 + 0.758146i \(0.726106\pi\)
\(84\) −1.28530 + 7.69132i −0.140238 + 0.839191i
\(85\) −0.813381 + 1.40882i −0.0882236 + 0.152808i
\(86\) −3.87838 + 2.23919i −0.418217 + 0.241458i
\(87\) 8.01520 + 3.92608i 0.859320 + 0.420920i
\(88\) −12.1871 −1.29915
\(89\) −0.507769 + 0.879481i −0.0538234 + 0.0932248i −0.891682 0.452663i \(-0.850474\pi\)
0.837858 + 0.545888i \(0.183807\pi\)
\(90\) −3.81299 1.55558i −0.401924 0.163972i
\(91\) −7.12882 6.33877i −0.747303 0.664483i
\(92\) 1.75834i 0.183320i
\(93\) −1.26028 18.4720i −0.130685 1.91545i
\(94\) 2.29021i 0.236217i
\(95\) 4.99614 2.88452i 0.512593 0.295946i
\(96\) 8.24314 + 4.03773i 0.841312 + 0.412099i
\(97\) 8.58147 + 4.95452i 0.871317 + 0.503055i 0.867786 0.496939i \(-0.165543\pi\)
0.00353111 + 0.999994i \(0.498876\pi\)
\(98\) 3.81742 0.214744i 0.385618 0.0216924i
\(99\) 16.7432 + 6.83067i 1.68275 + 0.686508i
\(100\) 2.23916 0.223916
\(101\) −5.31728 −0.529089 −0.264545 0.964373i \(-0.585222\pi\)
−0.264545 + 0.964373i \(0.585222\pi\)
\(102\) 0.508271 0.341583i 0.0503263 0.0338218i
\(103\) 2.41439 1.39395i 0.237897 0.137350i −0.376313 0.926493i \(-0.622808\pi\)
0.614210 + 0.789143i \(0.289475\pi\)
\(104\) −6.19922 + 3.83581i −0.607883 + 0.376132i
\(105\) 1.89824 11.3591i 0.185249 1.10854i
\(106\) 0.0128197 + 0.0222043i 0.00124515 + 0.00215667i
\(107\) 16.6485 + 9.61203i 1.60947 + 0.929230i 0.989488 + 0.144617i \(0.0461949\pi\)
0.619986 + 0.784613i \(0.287138\pi\)
\(108\) −5.88307 6.60088i −0.566099 0.635170i
\(109\) −3.02537 + 5.24009i −0.289778 + 0.501910i −0.973757 0.227592i \(-0.926915\pi\)
0.683979 + 0.729502i \(0.260248\pi\)
\(110\) 8.27412 0.788906
\(111\) −6.83493 + 0.466326i −0.648743 + 0.0442617i
\(112\) −1.40858 + 5.91710i −0.133098 + 0.559113i
\(113\) 7.42599 + 4.28740i 0.698578 + 0.403324i 0.806818 0.590800i \(-0.201188\pi\)
−0.108239 + 0.994125i \(0.534521\pi\)
\(114\) −2.16669 + 0.147827i −0.202929 + 0.0138452i
\(115\) 2.59686i 0.242158i
\(116\) 7.59374 + 4.38425i 0.705061 + 0.407067i
\(117\) 10.6666 1.79524i 0.986131 0.165970i
\(118\) 0.907960i 0.0835845i
\(119\) 1.24454 + 1.17649i 0.114086 + 0.107849i
\(120\) −7.90374 3.87148i −0.721510 0.353416i
\(121\) −25.3324 −2.30294
\(122\) −0.981198 + 1.69949i −0.0888335 + 0.153864i
\(123\) 6.83725 13.9585i 0.616494 1.25859i
\(124\) 18.1900i 1.63351i
\(125\) 9.25873 0.828126
\(126\) −2.52275 + 3.52582i −0.224744 + 0.314105i
\(127\) 1.59609 + 2.76452i 0.141630 + 0.245311i 0.928111 0.372304i \(-0.121432\pi\)
−0.786480 + 0.617615i \(0.788099\pi\)
\(128\) 9.98463 + 5.76463i 0.882525 + 0.509526i
\(129\) 14.1682 0.966650i 1.24744 0.0851088i
\(130\) 4.20879 2.60422i 0.369135 0.228405i
\(131\) −1.65182 2.86103i −0.144320 0.249969i 0.784799 0.619750i \(-0.212766\pi\)
−0.929119 + 0.369781i \(0.879433\pi\)
\(132\) 15.9544 + 7.81492i 1.38865 + 0.680202i
\(133\) −1.73612 5.82003i −0.150540 0.504661i
\(134\) 0.720192 + 0.415803i 0.0622151 + 0.0359199i
\(135\) 8.68858 + 9.74870i 0.747794 + 0.839035i
\(136\) 1.13342 0.654383i 0.0971903 0.0561129i
\(137\) −7.14564 + 4.12554i −0.610493 + 0.352468i −0.773158 0.634213i \(-0.781324\pi\)
0.162665 + 0.986681i \(0.447991\pi\)
\(138\) 0.430027 0.877912i 0.0366063 0.0747329i
\(139\) 7.50372 + 4.33228i 0.636457 + 0.367459i 0.783249 0.621709i \(-0.213561\pi\)
−0.146791 + 0.989168i \(0.546895\pi\)
\(140\) 2.62023 11.0070i 0.221450 0.930260i
\(141\) 3.19465 6.52197i 0.269038 0.549249i
\(142\) −3.61802 6.26660i −0.303618 0.525881i
\(143\) −18.4812 + 11.4354i −1.54547 + 0.956273i
\(144\) −4.22771 5.44912i −0.352309 0.454094i
\(145\) −11.2150 6.47500i −0.931357 0.537719i
\(146\) 1.50371 + 2.60451i 0.124448 + 0.215551i
\(147\) −11.1707 4.71344i −0.921340 0.388758i
\(148\) −6.73060 −0.553252
\(149\) 13.8118i 1.13151i −0.824574 0.565753i \(-0.808585\pi\)
0.824574 0.565753i \(-0.191415\pi\)
\(150\) 1.11798 + 0.547619i 0.0912827 + 0.0447129i
\(151\) −3.90858 + 6.76986i −0.318076 + 0.550924i −0.980087 0.198571i \(-0.936370\pi\)
0.662011 + 0.749494i \(0.269703\pi\)
\(152\) −4.64132 −0.376461
\(153\) −1.92391 + 0.263753i −0.155539 + 0.0213232i
\(154\) 2.01723 8.47393i 0.162553 0.682848i
\(155\) 26.8644i 2.15780i
\(156\) 10.5752 1.04632i 0.846694 0.0837730i
\(157\) −7.63926 4.41053i −0.609679 0.351999i 0.163161 0.986600i \(-0.447831\pi\)
−0.772840 + 0.634601i \(0.781164\pi\)
\(158\) 2.34647i 0.186675i
\(159\) −0.00553421 0.0811148i −0.000438891 0.00643282i
\(160\) −11.5340 6.65914i −0.911840 0.526451i
\(161\) 2.65957 + 0.633115i 0.209603 + 0.0498964i
\(162\) −1.32299 4.73450i −0.103944 0.371978i
\(163\) 12.5765 0.985066 0.492533 0.870294i \(-0.336071\pi\)
0.492533 + 0.870294i \(0.336071\pi\)
\(164\) 7.63515 13.2245i 0.596205 1.03266i
\(165\) −23.5627 11.5417i −1.83435 0.898519i
\(166\) −5.62034 3.24490i −0.436223 0.251853i
\(167\) −6.71323 11.6277i −0.519486 0.899775i −0.999743 0.0226481i \(-0.992790\pi\)
0.480258 0.877127i \(-0.340543\pi\)
\(168\) −5.89191 + 7.15074i −0.454570 + 0.551691i
\(169\) −5.80160 + 11.6336i −0.446277 + 0.894895i
\(170\) −0.769508 + 0.444276i −0.0590186 + 0.0340744i
\(171\) 6.37643 + 2.60138i 0.487618 + 0.198932i
\(172\) 13.9519 1.06382
\(173\) −8.44726 −0.642233 −0.321116 0.947040i \(-0.604058\pi\)
−0.321116 + 0.947040i \(0.604058\pi\)
\(174\) 2.71921 + 4.04614i 0.206142 + 0.306737i
\(175\) −0.806242 + 3.38683i −0.0609462 + 0.256020i
\(176\) 12.0007 + 6.92861i 0.904587 + 0.522263i
\(177\) 1.26653 2.58565i 0.0951980 0.194350i
\(178\) −0.480380 + 0.277347i −0.0360060 + 0.0207881i
\(179\) 12.9185i 0.965577i −0.875737 0.482788i \(-0.839624\pi\)
0.875737 0.482788i \(-0.160376\pi\)
\(180\) 7.86438 + 10.1365i 0.586176 + 0.755527i
\(181\) 1.36110i 0.101170i 0.998720 + 0.0505848i \(0.0161085\pi\)
−0.998720 + 0.0505848i \(0.983891\pi\)
\(182\) −1.64100 4.94534i −0.121639 0.366573i
\(183\) 5.16485 3.47104i 0.381797 0.256587i
\(184\) 1.04461 1.80932i 0.0770099 0.133385i
\(185\) 9.94028 0.730824
\(186\) 4.44862 9.08199i 0.326188 0.665924i
\(187\) 3.37897 1.95085i 0.247095 0.142660i
\(188\) 3.56746 6.17902i 0.260184 0.450651i
\(189\) 12.1024 6.52166i 0.880320 0.474381i
\(190\) 3.15110 0.228605
\(191\) 10.3102i 0.746020i −0.927827 0.373010i \(-0.878326\pi\)
0.927827 0.373010i \(-0.121674\pi\)
\(192\) −1.64558 2.44860i −0.118760 0.176713i
\(193\) 3.23962 0.233193 0.116597 0.993179i \(-0.462802\pi\)
0.116597 + 0.993179i \(0.462802\pi\)
\(194\) 2.70620 + 4.68727i 0.194294 + 0.336527i
\(195\) −15.6183 + 1.54529i −1.11845 + 0.110661i
\(196\) −10.6340 5.36702i −0.759569 0.383358i
\(197\) 11.8813 6.85965i 0.846505 0.488730i −0.0129653 0.999916i \(-0.504127\pi\)
0.859470 + 0.511186i \(0.170794\pi\)
\(198\) 6.05453 + 7.80374i 0.430277 + 0.554587i
\(199\) 2.88404 1.66510i 0.204444 0.118036i −0.394283 0.918989i \(-0.629007\pi\)
0.598727 + 0.800953i \(0.295674\pi\)
\(200\) 2.30409 + 1.33027i 0.162924 + 0.0940640i
\(201\) −1.47092 2.18871i −0.103751 0.154380i
\(202\) −2.51524 1.45217i −0.176971 0.102174i
\(203\) −9.36559 + 9.90724i −0.657335 + 0.695352i
\(204\) −1.90341 + 0.129863i −0.133265 + 0.00909226i
\(205\) −11.2762 + 19.5309i −0.787563 + 1.36410i
\(206\) 1.52277 0.106096
\(207\) −2.44923 + 1.90023i −0.170233 + 0.132075i
\(208\) 8.28512 0.252766i 0.574470 0.0175262i
\(209\) −13.8367 −0.957107
\(210\) 4.00015 4.85480i 0.276037 0.335013i
\(211\) −4.67281 8.09355i −0.321690 0.557183i 0.659147 0.752014i \(-0.270917\pi\)
−0.980837 + 0.194831i \(0.937584\pi\)
\(212\) 0.0798766i 0.00548595i
\(213\) 1.56189 + 22.8926i 0.107019 + 1.56858i
\(214\) 5.25017 + 9.09356i 0.358894 + 0.621623i
\(215\) −20.6053 −1.40527
\(216\) −2.13213 10.2873i −0.145073 0.699965i
\(217\) 27.5132 + 6.54956i 1.86772 + 0.444613i
\(218\) −2.86218 + 1.65248i −0.193851 + 0.111920i
\(219\) −0.649150 9.51457i −0.0438655 0.642935i
\(220\) −22.3237 12.8886i −1.50506 0.868949i
\(221\) 1.10476 2.05585i 0.0743145 0.138291i
\(222\) −3.36049 1.64606i −0.225541 0.110476i
\(223\) 4.72711 2.72920i 0.316550 0.182760i −0.333304 0.942820i \(-0.608163\pi\)
0.649854 + 0.760059i \(0.274830\pi\)
\(224\) −9.63193 + 10.1890i −0.643560 + 0.680780i
\(225\) −2.41986 3.11897i −0.161324 0.207931i
\(226\) 2.34181 + 4.05614i 0.155775 + 0.269810i
\(227\) 11.3923 + 19.7320i 0.756132 + 1.30966i 0.944809 + 0.327620i \(0.106247\pi\)
−0.188677 + 0.982039i \(0.560420\pi\)
\(228\) 6.07604 + 2.97622i 0.402396 + 0.197105i
\(229\) −15.1066 + 8.72181i −0.998273 + 0.576353i −0.907737 0.419540i \(-0.862191\pi\)
−0.0905364 + 0.995893i \(0.528858\pi\)
\(230\) −0.709212 + 1.22839i −0.0467641 + 0.0809977i
\(231\) −17.5650 + 21.3178i −1.15569 + 1.40261i
\(232\) 5.20928 + 9.02273i 0.342006 + 0.592371i
\(233\) −1.62211 + 0.936526i −0.106268 + 0.0613538i −0.552192 0.833717i \(-0.686208\pi\)
0.445924 + 0.895071i \(0.352875\pi\)
\(234\) 5.53593 + 2.06390i 0.361895 + 0.134921i
\(235\) −5.26870 + 9.12566i −0.343692 + 0.595292i
\(236\) 1.41433 2.44969i 0.0920650 0.159461i
\(237\) −3.27312 + 6.68218i −0.212612 + 0.434054i
\(238\) 0.267398 + 0.896405i 0.0173328 + 0.0581053i
\(239\) 23.7791i 1.53814i −0.639164 0.769071i \(-0.720719\pi\)
0.639164 0.769071i \(-0.279281\pi\)
\(240\) 5.58183 + 8.30568i 0.360306 + 0.536130i
\(241\) −18.0905 + 10.4446i −1.16531 + 0.672795i −0.952572 0.304314i \(-0.901573\pi\)
−0.212743 + 0.977108i \(0.568240\pi\)
\(242\) −11.9830 6.91837i −0.770295 0.444730i
\(243\) −2.83667 + 15.3282i −0.181973 + 0.983304i
\(244\) 5.29457 3.05682i 0.338950 0.195693i
\(245\) 15.7051 + 7.92643i 1.00336 + 0.506401i
\(246\) 7.04634 4.73549i 0.449258 0.301924i
\(247\) −7.03833 + 4.35502i −0.447838 + 0.277103i
\(248\) 10.8065 18.7174i 0.686214 1.18856i
\(249\) 11.4790 + 17.0806i 0.727453 + 1.08244i
\(250\) 4.37966 + 2.52860i 0.276994 + 0.159922i
\(251\) 10.1622 17.6015i 0.641433 1.11100i −0.343680 0.939087i \(-0.611673\pi\)
0.985113 0.171908i \(-0.0549932\pi\)
\(252\) 12.2986 5.58302i 0.774737 0.351697i
\(253\) 3.11421 5.39397i 0.195789 0.339116i
\(254\) 1.74360i 0.109403i
\(255\) 2.81110 0.191793i 0.176038 0.0120105i
\(256\) 1.44540 + 2.50350i 0.0903374 + 0.156469i
\(257\) −11.9462 + 20.6914i −0.745183 + 1.29069i 0.204926 + 0.978777i \(0.434304\pi\)
−0.950109 + 0.311917i \(0.899029\pi\)
\(258\) 6.96597 + 3.41213i 0.433683 + 0.212430i
\(259\) 2.42345 10.1803i 0.150586 0.632575i
\(260\) −15.4120 + 0.470195i −0.955810 + 0.0291603i
\(261\) −2.09963 15.3155i −0.129964 0.948005i
\(262\) 1.80447i 0.111481i
\(263\) 1.61574i 0.0996308i 0.998758 + 0.0498154i \(0.0158633\pi\)
−0.998758 + 0.0498154i \(0.984137\pi\)
\(264\) 11.7742 + 17.5199i 0.724653 + 1.07827i
\(265\) 0.117968i 0.00724672i
\(266\) 0.768239 3.22719i 0.0471038 0.197872i
\(267\) 1.75488 0.119730i 0.107397 0.00732736i
\(268\) −1.29539 2.24369i −0.0791287 0.137055i
\(269\) −8.22623 14.2482i −0.501562 0.868731i −0.999998 0.00180469i \(-0.999426\pi\)
0.498436 0.866926i \(-0.333908\pi\)
\(270\) 1.44755 + 6.98432i 0.0880951 + 0.425052i
\(271\) −0.531956 0.307125i −0.0323140 0.0186565i 0.483756 0.875203i \(-0.339272\pi\)
−0.516070 + 0.856546i \(0.672606\pi\)
\(272\) −1.48812 −0.0902302
\(273\) −2.22514 + 16.3722i −0.134672 + 0.990890i
\(274\) −4.50681 −0.272266
\(275\) 6.86897 + 3.96580i 0.414214 + 0.239147i
\(276\) −2.52774 + 1.69877i −0.152152 + 0.102254i
\(277\) 4.83367 + 8.37217i 0.290427 + 0.503035i 0.973911 0.226931i \(-0.0728692\pi\)
−0.683484 + 0.729966i \(0.739536\pi\)
\(278\) 2.36633 + 4.09860i 0.141923 + 0.245817i
\(279\) −25.3372 + 19.6579i −1.51690 + 1.17689i
\(280\) 9.23535 9.76947i 0.551918 0.583837i
\(281\) 4.25154i 0.253625i −0.991927 0.126813i \(-0.959525\pi\)
0.991927 0.126813i \(-0.0404747\pi\)
\(282\) 3.29234 2.21262i 0.196056 0.131759i
\(283\) 13.4666i 0.800506i 0.916405 + 0.400253i \(0.131078\pi\)
−0.916405 + 0.400253i \(0.868922\pi\)
\(284\) 22.5432i 1.33769i
\(285\) −8.97357 4.39551i −0.531549 0.260368i
\(286\) −11.8652 + 0.361988i −0.701603 + 0.0214048i
\(287\) 17.2534 + 16.3101i 1.01844 + 0.962757i
\(288\) −2.15934 15.7510i −0.127240 0.928139i
\(289\) 8.29050 14.3596i 0.487676 0.844680i
\(290\) −3.53670 6.12574i −0.207682 0.359716i
\(291\) −1.16826 17.1231i −0.0684845 1.00378i
\(292\) 9.36934i 0.548299i
\(293\) 6.93842 12.0177i 0.405347 0.702081i −0.589015 0.808122i \(-0.700484\pi\)
0.994362 + 0.106041i \(0.0338174\pi\)
\(294\) −3.99680 5.28035i −0.233098 0.307956i
\(295\) −2.08879 + 3.61789i −0.121614 + 0.210642i
\(296\) −6.92575 3.99859i −0.402551 0.232413i
\(297\) −6.35632 30.6687i −0.368831 1.77958i
\(298\) 3.77206 6.53340i 0.218510 0.378470i
\(299\) −0.113611 3.72392i −0.00657030 0.215360i
\(300\) −2.16330 3.21896i −0.124898 0.185847i
\(301\) −5.02358 + 21.1029i −0.289554 + 1.21635i
\(302\) −3.69776 + 2.13490i −0.212782 + 0.122850i
\(303\) 5.13713 + 7.64397i 0.295120 + 0.439135i
\(304\) 4.57032 + 2.63868i 0.262126 + 0.151338i
\(305\) −7.81944 + 4.51456i −0.447740 + 0.258503i
\(306\) −0.982101 0.400666i −0.0561430 0.0229045i
\(307\) 19.0928i 1.08969i 0.838538 + 0.544843i \(0.183411\pi\)
−0.838538 + 0.544843i \(0.816589\pi\)
\(308\) −18.6424 + 19.7205i −1.06225 + 1.12368i
\(309\) −4.33649 2.12414i −0.246694 0.120838i
\(310\) −7.33679 + 12.7077i −0.416702 + 0.721748i
\(311\) −1.31104 + 2.27079i −0.0743423 + 0.128765i −0.900800 0.434234i \(-0.857019\pi\)
0.826458 + 0.562999i \(0.190352\pi\)
\(312\) 11.5034 + 5.20597i 0.651254 + 0.294730i
\(313\) 3.15245 1.82007i 0.178187 0.102876i −0.408253 0.912869i \(-0.633862\pi\)
0.586441 + 0.809992i \(0.300529\pi\)
\(314\) −2.40907 4.17263i −0.135952 0.235475i
\(315\) −18.1635 + 8.24544i −1.02340 + 0.464578i
\(316\) −3.65509 + 6.33081i −0.205615 + 0.356136i
\(317\) −14.6674 + 8.46825i −0.823805 + 0.475624i −0.851727 0.523986i \(-0.824444\pi\)
0.0279217 + 0.999610i \(0.491111\pi\)
\(318\) 0.0195349 0.0398812i 0.00109546 0.00223642i
\(319\) 15.5299 + 26.8986i 0.869510 + 1.50603i
\(320\) 2.14030 + 3.70711i 0.119647 + 0.207234i
\(321\) −2.26648 33.2198i −0.126503 1.85415i
\(322\) 1.08515 + 1.02582i 0.0604730 + 0.0571668i
\(323\) 1.28684 0.742958i 0.0716018 0.0413393i
\(324\) −3.80549 + 14.8346i −0.211416 + 0.824143i
\(325\) 4.74224 0.144678i 0.263052 0.00802531i
\(326\) 5.94905 + 3.43469i 0.329488 + 0.190230i
\(327\) 10.4559 0.713372i 0.578211 0.0394496i
\(328\) 15.7131 9.07194i 0.867608 0.500914i
\(329\) 8.06152 + 7.62077i 0.444446 + 0.420147i
\(330\) −7.99379 11.8946i −0.440044 0.654778i
\(331\) −10.4278 −0.573166 −0.286583 0.958055i \(-0.592519\pi\)
−0.286583 + 0.958055i \(0.592519\pi\)
\(332\) 10.1092 + 17.5096i 0.554813 + 0.960964i
\(333\) 7.27374 + 9.37518i 0.398599 + 0.513757i
\(334\) 7.33365i 0.401279i
\(335\) 1.91314 + 3.31365i 0.104526 + 0.181044i
\(336\) 9.86711 3.69169i 0.538295 0.201398i
\(337\) 18.5940 1.01288 0.506440 0.862275i \(-0.330961\pi\)
0.506440 + 0.862275i \(0.330961\pi\)
\(338\) −5.92153 + 3.91862i −0.322089 + 0.213145i
\(339\) −1.01095 14.8175i −0.0549075 0.804778i
\(340\) 2.76819 0.150126
\(341\) 32.2165 55.8005i 1.74462 3.02177i
\(342\) 2.30580 + 2.97196i 0.124683 + 0.160705i
\(343\) 11.9467 14.1519i 0.645064 0.764129i
\(344\) 14.3564 + 8.28870i 0.774048 + 0.446897i
\(345\) 3.73317 2.50887i 0.200987 0.135073i
\(346\) −3.99581 2.30698i −0.214816 0.124024i
\(347\) 6.55263 3.78316i 0.351763 0.203091i −0.313698 0.949523i \(-0.601568\pi\)
0.665462 + 0.746432i \(0.268235\pi\)
\(348\) −1.03379 15.1522i −0.0554170 0.812246i
\(349\) −23.2338 + 13.4141i −1.24368 + 0.718038i −0.969841 0.243738i \(-0.921626\pi\)
−0.273837 + 0.961776i \(0.588293\pi\)
\(350\) −1.30633 + 1.38189i −0.0698265 + 0.0738649i
\(351\) −12.8860 13.5996i −0.687806 0.725895i
\(352\) 15.9716 + 27.6636i 0.851288 + 1.47447i
\(353\) −12.8501 −0.683940 −0.341970 0.939711i \(-0.611094\pi\)
−0.341970 + 0.939711i \(0.611094\pi\)
\(354\) 1.30526 0.877198i 0.0693737 0.0466226i
\(355\) 33.2935i 1.76704i
\(356\) 1.72810 0.0915889
\(357\) 0.488924 2.92574i 0.0258766 0.154847i
\(358\) 3.52811 6.11086i 0.186466 0.322969i
\(359\) −14.4330 + 8.33290i −0.761745 + 0.439794i −0.829922 0.557880i \(-0.811615\pi\)
0.0681770 + 0.997673i \(0.478282\pi\)
\(360\) 2.07043 + 15.1025i 0.109121 + 0.795972i
\(361\) 13.7304 0.722655
\(362\) −0.371722 + 0.643841i −0.0195373 + 0.0338395i
\(363\) 24.4741 + 36.4171i 1.28456 + 1.91140i
\(364\) −3.27590 + 15.8988i −0.171704 + 0.833323i
\(365\) 13.8374i 0.724282i
\(366\) 3.39109 0.231363i 0.177255 0.0120936i
\(367\) 27.1720i 1.41837i −0.705023 0.709184i \(-0.749063\pi\)
0.705023 0.709184i \(-0.250937\pi\)
\(368\) −2.05727 + 1.18776i −0.107243 + 0.0619165i
\(369\) −26.6719 + 3.65650i −1.38848 + 0.190350i
\(370\) 4.70205 + 2.71473i 0.244448 + 0.141132i
\(371\) 0.120817 + 0.0287607i 0.00627250 + 0.00149318i
\(372\) −26.1494 + 17.5737i −1.35579 + 0.911155i
\(373\) −17.0879 −0.884780 −0.442390 0.896823i \(-0.645869\pi\)
−0.442390 + 0.896823i \(0.645869\pi\)
\(374\) 2.13114 0.110199
\(375\) −8.94504 13.3101i −0.461920 0.687330i
\(376\) 7.34179 4.23879i 0.378624 0.218599i
\(377\) 16.3658 + 8.79458i 0.842880 + 0.452944i
\(378\) 7.50589 + 0.220273i 0.386061 + 0.0113296i
\(379\) −11.4321 19.8010i −0.587229 1.01711i −0.994594 0.103845i \(-0.966886\pi\)
0.407365 0.913266i \(-0.366448\pi\)
\(380\) −8.50171 4.90846i −0.436128 0.251799i
\(381\) 2.43217 4.96535i 0.124604 0.254383i
\(382\) 2.81576 4.87703i 0.144067 0.249531i
\(383\) −8.52108 −0.435407 −0.217703 0.976015i \(-0.569857\pi\)
−0.217703 + 0.976015i \(0.569857\pi\)
\(384\) −1.35928 19.9230i −0.0693655 1.01669i
\(385\) 27.5325 29.1248i 1.40319 1.48434i
\(386\) 1.53244 + 0.884754i 0.0779991 + 0.0450328i
\(387\) −15.0778 19.4339i −0.766447 0.987879i
\(388\) 16.8618i 0.856027i
\(389\) −11.0480 6.37855i −0.560155 0.323406i 0.193053 0.981188i \(-0.438161\pi\)
−0.753208 + 0.657783i \(0.771494\pi\)
\(390\) −7.80995 3.53445i −0.395472 0.178974i
\(391\) 0.668865i 0.0338260i
\(392\) −7.75380 11.8402i −0.391626 0.598019i
\(393\) −2.51708 + 5.13870i −0.126970 + 0.259213i
\(394\) 7.49359 0.377522
\(395\) 5.39813 9.34983i 0.271609 0.470441i
\(396\) −4.17935 30.4857i −0.210020 1.53197i
\(397\) 3.89299i 0.195384i 0.995217 + 0.0976918i \(0.0311459\pi\)
−0.995217 + 0.0976918i \(0.968854\pi\)
\(398\) 1.81898 0.0911773
\(399\) −6.68942 + 8.11864i −0.334890 + 0.406440i
\(400\) −1.51256 2.61983i −0.0756281 0.130992i
\(401\) −19.1034 11.0293i −0.953977 0.550779i −0.0596628 0.998219i \(-0.519003\pi\)
−0.894314 + 0.447440i \(0.852336\pi\)
\(402\) −0.0980450 1.43704i −0.00489004 0.0716732i
\(403\) −1.17530 38.5239i −0.0585461 1.91901i
\(404\) 4.52409 + 7.83596i 0.225082 + 0.389854i
\(405\) 5.62025 21.9089i 0.279272 1.08866i
\(406\) −7.13591 + 2.12864i −0.354150 + 0.105643i
\(407\) −20.6471 11.9206i −1.02344 0.590883i
\(408\) −2.03575 0.997167i −0.100784 0.0493671i
\(409\) 7.43125 4.29044i 0.367452 0.212148i −0.304893 0.952387i \(-0.598621\pi\)
0.672345 + 0.740238i \(0.265287\pi\)
\(410\) −10.6680 + 6.15915i −0.526853 + 0.304179i
\(411\) 12.8343 + 6.28661i 0.633069 + 0.310096i
\(412\) −4.10846 2.37202i −0.202409 0.116861i
\(413\) 3.19601 + 3.02128i 0.157265 + 0.148667i
\(414\) −1.67752 + 0.229974i −0.0824456 + 0.0113026i
\(415\) −14.9300 25.8595i −0.732886 1.26940i
\(416\) 16.8312 + 9.04468i 0.825217 + 0.443452i
\(417\) −1.02154 14.9726i −0.0500248 0.733213i
\(418\) −6.54520 3.77887i −0.320136 0.184831i
\(419\) 12.5477 + 21.7332i 0.612994 + 1.06174i 0.990733 + 0.135825i \(0.0433684\pi\)
−0.377739 + 0.925912i \(0.623298\pi\)
\(420\) −18.3548 + 6.86729i −0.895622 + 0.335089i
\(421\) −11.9143 −0.580668 −0.290334 0.956925i \(-0.593766\pi\)
−0.290334 + 0.956925i \(0.593766\pi\)
\(422\) 5.10466i 0.248491i
\(423\) −12.4622 + 1.70847i −0.605933 + 0.0830685i
\(424\) 0.0474539 0.0821926i 0.00230457 0.00399163i
\(425\) −0.851768 −0.0413168
\(426\) −5.51324 + 11.2555i −0.267117 + 0.545328i
\(427\) 2.71719 + 9.10892i 0.131494 + 0.440812i
\(428\) 32.7127i 1.58123i
\(429\) 34.2942 + 15.5201i 1.65574 + 0.749316i
\(430\) −9.74692 5.62739i −0.470038 0.271377i
\(431\) 28.8820i 1.39119i 0.718432 + 0.695597i \(0.244860\pi\)
−0.718432 + 0.695597i \(0.755140\pi\)
\(432\) −3.74904 + 11.3421i −0.180376 + 0.545699i
\(433\) −6.48299 3.74296i −0.311553 0.179875i 0.336068 0.941838i \(-0.390903\pi\)
−0.647621 + 0.761963i \(0.724236\pi\)
\(434\) 11.2258 + 10.6121i 0.538858 + 0.509397i
\(435\) 1.52678 + 22.3780i 0.0732036 + 1.07294i
\(436\) 10.2963 0.493102
\(437\) 1.18601 2.05423i 0.0567345 0.0982671i
\(438\) 2.29140 4.67797i 0.109487 0.223522i
\(439\) −8.85143 5.11037i −0.422456 0.243905i 0.273672 0.961823i \(-0.411762\pi\)
−0.696127 + 0.717918i \(0.745095\pi\)
\(440\) −15.3140 26.5246i −0.730065 1.26451i
\(441\) 4.01628 + 20.6124i 0.191251 + 0.981541i
\(442\) 1.08405 0.670762i 0.0515629 0.0319049i
\(443\) 26.2992 15.1839i 1.24951 0.721407i 0.278501 0.960436i \(-0.410162\pi\)
0.971012 + 0.239029i \(0.0768291\pi\)
\(444\) 6.50257 + 9.67572i 0.308598 + 0.459190i
\(445\) −2.55219 −0.120985
\(446\) 2.98142 0.141174
\(447\) −19.8555 + 13.3439i −0.939131 + 0.631143i
\(448\) 4.31844 1.28819i 0.204027 0.0608613i
\(449\) 19.0172 + 10.9796i 0.897478 + 0.518159i 0.876381 0.481618i \(-0.159951\pi\)
0.0210967 + 0.999777i \(0.493284\pi\)
\(450\) −0.292861 2.13624i −0.0138056 0.100703i
\(451\) 46.8439 27.0453i 2.20579 1.27352i
\(452\) 14.5914i 0.686320i
\(453\) 13.5083 0.921631i 0.634676 0.0433020i
\(454\) 12.4451i 0.584078i
\(455\) 4.83810 23.4806i 0.226814 1.10079i
\(456\) 4.48407 + 6.67223i 0.209986 + 0.312456i
\(457\) −18.0285 + 31.2263i −0.843338 + 1.46070i 0.0437182 + 0.999044i \(0.486080\pi\)
−0.887057 + 0.461661i \(0.847254\pi\)
\(458\) −9.52785 −0.445207
\(459\) 2.23789 + 2.51095i 0.104456 + 0.117201i
\(460\) 3.82693 2.20948i 0.178431 0.103017i
\(461\) −4.57076 + 7.91680i −0.212882 + 0.368722i −0.952615 0.304178i \(-0.901618\pi\)
0.739734 + 0.672900i \(0.234952\pi\)
\(462\) −14.1308 + 5.28691i −0.657423 + 0.245969i
\(463\) 22.1372 1.02880 0.514401 0.857550i \(-0.328014\pi\)
0.514401 + 0.857550i \(0.328014\pi\)
\(464\) 11.8463i 0.549950i
\(465\) 38.6195 25.9543i 1.79094 1.20360i
\(466\) −1.02308 −0.0473931
\(467\) 0.315959 + 0.547257i 0.0146208 + 0.0253240i 0.873243 0.487285i \(-0.162013\pi\)
−0.858622 + 0.512609i \(0.828679\pi\)
\(468\) −11.7211 14.1917i −0.541807 0.656014i
\(469\) 3.86009 1.15147i 0.178243 0.0531698i
\(470\) −4.98451 + 2.87781i −0.229918 + 0.132743i
\(471\) 1.03999 + 15.2431i 0.0479201 + 0.702364i
\(472\) 2.91067 1.68048i 0.133975 0.0773503i
\(473\) 42.7996 + 24.7103i 1.96793 + 1.13618i
\(474\) −3.37322 + 2.26697i −0.154937 + 0.104125i
\(475\) 2.61596 + 1.51033i 0.120029 + 0.0692986i
\(476\) 0.674886 2.83504i 0.0309334 0.129944i
\(477\) −0.111262 + 0.0863224i −0.00509432 + 0.00395243i
\(478\) 6.49417 11.2482i 0.297036 0.514482i
\(479\) 22.3302 1.02029 0.510146 0.860088i \(-0.329591\pi\)
0.510146 + 0.860088i \(0.329591\pi\)
\(480\) 1.57020 + 23.0144i 0.0716696 + 1.05046i
\(481\) −14.2545 + 0.434882i −0.649949 + 0.0198289i
\(482\) −11.4098 −0.519704
\(483\) −1.65931 4.43498i −0.0755013 0.201799i
\(484\) 21.5535 + 37.3317i 0.979704 + 1.69690i
\(485\) 24.9028i 1.13078i
\(486\) −5.52802 + 6.47599i −0.250756 + 0.293757i
\(487\) 20.1441 + 34.8907i 0.912817 + 1.58105i 0.810066 + 0.586339i \(0.199431\pi\)
0.102752 + 0.994707i \(0.467235\pi\)
\(488\) 7.26412 0.328831
\(489\) −12.1504 18.0796i −0.549459 0.817587i
\(490\) 5.26424 + 8.03856i 0.237814 + 0.363145i
\(491\) −6.70526 + 3.87128i −0.302604 + 0.174709i −0.643612 0.765352i \(-0.722565\pi\)
0.341008 + 0.940060i \(0.389232\pi\)
\(492\) −26.3876 + 1.80034i −1.18964 + 0.0811657i
\(493\) −2.88862 1.66775i −0.130097 0.0751116i
\(494\) −4.51871 + 0.137859i −0.203307 + 0.00620256i
\(495\) 6.17239 + 45.0237i 0.277428 + 2.02367i
\(496\) −21.2824 + 12.2874i −0.955608 + 0.551721i
\(497\) −34.0975 8.11698i −1.52948 0.364096i
\(498\) 0.765137 + 11.2146i 0.0342866 + 0.502538i
\(499\) −7.94320 13.7580i −0.355587 0.615894i 0.631632 0.775269i \(-0.282386\pi\)
−0.987218 + 0.159375i \(0.949052\pi\)
\(500\) −7.87759 13.6444i −0.352296 0.610195i
\(501\) −10.2298 + 20.8845i −0.457034 + 0.933049i
\(502\) 9.61407 5.55069i 0.429097 0.247739i
\(503\) −14.9743 + 25.9362i −0.667671 + 1.15644i 0.310883 + 0.950448i \(0.399375\pi\)
−0.978554 + 0.205992i \(0.933958\pi\)
\(504\) 15.9720 + 1.56157i 0.711449 + 0.0695579i
\(505\) −6.68154 11.5728i −0.297325 0.514981i
\(506\) 2.94623 1.70101i 0.130976 0.0756190i
\(507\) 22.3292 2.89926i 0.991676 0.128761i
\(508\) 2.71600 4.70426i 0.120503 0.208718i
\(509\) 3.30037 5.71641i 0.146286 0.253376i −0.783566 0.621309i \(-0.786601\pi\)
0.929852 + 0.367933i \(0.119935\pi\)
\(510\) 1.38211 + 0.676999i 0.0612011 + 0.0299780i
\(511\) 14.1715 + 3.37356i 0.626912 + 0.149238i
\(512\) 21.4795i 0.949271i
\(513\) −2.42073 11.6798i −0.106878 0.515676i
\(514\) −11.3018 + 6.52511i −0.498502 + 0.287810i
\(515\) 6.06769 + 3.50318i 0.267375 + 0.154369i
\(516\) −13.4792 20.0569i −0.593389 0.882955i
\(517\) 21.8874 12.6367i 0.962607 0.555762i
\(518\) 3.92665 4.15375i 0.172527 0.182505i
\(519\) 8.16106 + 12.1435i 0.358231 + 0.533042i
\(520\) −16.1382 8.67228i −0.707706 0.380304i
\(521\) −11.1062 + 19.2365i −0.486570 + 0.842764i −0.999881 0.0154387i \(-0.995086\pi\)
0.513311 + 0.858203i \(0.328419\pi\)
\(522\) 3.18954 7.81811i 0.139602 0.342189i
\(523\) −22.8268 13.1791i −0.998147 0.576280i −0.0904472 0.995901i \(-0.528830\pi\)
−0.907699 + 0.419621i \(0.862163\pi\)
\(524\) −2.81082 + 4.86849i −0.122791 + 0.212681i
\(525\) 5.64774 2.11305i 0.246488 0.0922212i
\(526\) −0.441265 + 0.764294i −0.0192401 + 0.0333248i
\(527\) 6.91940i 0.301414i
\(528\) −1.63374 23.9457i −0.0710995 1.04210i
\(529\) −10.9661 18.9939i −0.476788 0.825822i
\(530\) −0.0322176 + 0.0558025i −0.00139944 + 0.00242390i
\(531\) −4.94068 + 0.677327i −0.214407 + 0.0293935i
\(532\) −7.09972 + 7.51033i −0.307812 + 0.325614i
\(533\) 15.3157 28.5009i 0.663398 1.23451i
\(534\) 0.862811 + 0.422630i 0.0373375 + 0.0182890i
\(535\) 48.3127i 2.08874i
\(536\) 3.07832i 0.132963i
\(537\) −18.5713 + 12.4809i −0.801412 + 0.538588i
\(538\) 8.98647i 0.387434i
\(539\) −23.1157 35.2980i −0.995664 1.52039i
\(540\) 6.97395 21.0986i 0.300111 0.907941i
\(541\) 7.27566 + 12.6018i 0.312805 + 0.541794i 0.978968 0.204012i \(-0.0653981\pi\)
−0.666164 + 0.745806i \(0.732065\pi\)
\(542\) −0.167754 0.290559i −0.00720566 0.0124806i
\(543\) 1.95668 1.31498i 0.0839691 0.0564314i
\(544\) −2.97077 1.71518i −0.127371 0.0735376i
\(545\) −15.2064 −0.651369
\(546\) −5.52387 + 7.13685i −0.236400 + 0.305429i
\(547\) 13.3560 0.571060 0.285530 0.958370i \(-0.407830\pi\)
0.285530 + 0.958370i \(0.407830\pi\)
\(548\) 12.1594 + 7.02025i 0.519425 + 0.299890i
\(549\) −9.97973 4.07141i −0.425925 0.173764i
\(550\) 2.16615 + 3.75189i 0.0923651 + 0.159981i
\(551\) 5.91439 + 10.2440i 0.251961 + 0.436410i
\(552\) −3.61025 + 0.246316i −0.153663 + 0.0104839i
\(553\) −8.25955 7.80798i −0.351232 0.332029i
\(554\) 5.28038i 0.224342i
\(555\) −9.60350 14.2899i −0.407646 0.606571i
\(556\) 14.7441i 0.625289i
\(557\) 21.4071i 0.907046i 0.891245 + 0.453523i \(0.149833\pi\)
−0.891245 + 0.453523i \(0.850167\pi\)
\(558\) −17.3539 + 2.37908i −0.734649 + 0.100714i
\(559\) 29.5482 0.901470i 1.24976 0.0381281i
\(560\) −14.6482 + 4.36956i −0.619000 + 0.184648i
\(561\) −6.06898 2.97276i −0.256233 0.125510i
\(562\) 1.16111 2.01111i 0.0489786 0.0848334i
\(563\) 14.7814 + 25.6022i 0.622963 + 1.07900i 0.988931 + 0.148376i \(0.0474045\pi\)
−0.365969 + 0.930627i \(0.619262\pi\)
\(564\) −12.3294 + 0.841195i −0.519160 + 0.0354207i
\(565\) 21.5497i 0.906601i
\(566\) −3.67778 + 6.37011i −0.154589 + 0.267756i
\(567\) −21.0677 11.0974i −0.884761 0.466045i
\(568\) −13.3927 + 23.1968i −0.561944 + 0.973316i
\(569\) 23.8838 + 13.7893i 1.00126 + 0.578078i 0.908621 0.417622i \(-0.137136\pi\)
0.0926389 + 0.995700i \(0.470470\pi\)
\(570\) −3.04434 4.52993i −0.127513 0.189738i
\(571\) 17.4312 30.1918i 0.729475 1.26349i −0.227630 0.973748i \(-0.573098\pi\)
0.957105 0.289740i \(-0.0935689\pi\)
\(572\) 32.5763 + 17.5057i 1.36208 + 0.731952i
\(573\) −14.8216 + 9.96088i −0.619183 + 0.416122i
\(574\) 3.70703 + 12.4272i 0.154728 + 0.518700i
\(575\) −1.17754 + 0.679853i −0.0491068 + 0.0283518i
\(576\) −1.93021 + 4.73128i −0.0804255 + 0.197137i
\(577\) −9.56438 5.52200i −0.398170 0.229884i 0.287524 0.957773i \(-0.407168\pi\)
−0.685694 + 0.727890i \(0.740501\pi\)
\(578\) 7.84331 4.52834i 0.326239 0.188354i
\(579\) −3.12986 4.65719i −0.130073 0.193546i
\(580\) 22.0364i 0.915014i
\(581\) −30.1240 + 8.98598i −1.24975 + 0.372801i
\(582\) 4.12378 8.41882i 0.170936 0.348971i
\(583\) 0.141470 0.245033i 0.00585909 0.0101482i
\(584\) 5.56624 9.64100i 0.230332 0.398948i
\(585\) 17.3106 + 20.9595i 0.715706 + 0.866568i
\(586\) 6.56417 3.78982i 0.271163 0.156556i
\(587\) −12.6832 21.9680i −0.523493 0.906717i −0.999626 0.0273434i \(-0.991295\pi\)
0.476133 0.879373i \(-0.342038\pi\)
\(588\) 2.55822 + 20.4723i 0.105499 + 0.844262i
\(589\) 12.2692 21.2510i 0.505546 0.875631i
\(590\) −1.97612 + 1.14092i −0.0813557 + 0.0469707i
\(591\) −21.3400 10.4529i −0.877808 0.429976i
\(592\) 4.54654 + 7.87484i 0.186862 + 0.323654i
\(593\) −5.88143 10.1869i −0.241521 0.418327i 0.719627 0.694361i \(-0.244313\pi\)
−0.961148 + 0.276034i \(0.910980\pi\)
\(594\) 5.36903 16.2432i 0.220294 0.666465i
\(595\) −0.996725 + 4.18701i −0.0408618 + 0.171651i
\(596\) −20.3541 + 11.7515i −0.833738 + 0.481359i
\(597\) −5.18002 2.53732i −0.212004 0.103846i
\(598\) 0.963278 1.79256i 0.0393913 0.0733031i
\(599\) −39.8531 23.0092i −1.62835 0.940131i −0.984584 0.174911i \(-0.944036\pi\)
−0.643770 0.765219i \(-0.722631\pi\)
\(600\) −0.313672 4.59749i −0.0128056 0.187692i
\(601\) −26.1034 + 15.0708i −1.06478 + 0.614751i −0.926751 0.375677i \(-0.877410\pi\)
−0.138030 + 0.990428i \(0.544077\pi\)
\(602\) −8.13958 + 8.61033i −0.331745 + 0.350931i
\(603\) −1.72534 + 4.22912i −0.0702614 + 0.172223i
\(604\) 13.3021 0.541256
\(605\) −31.8319 55.1344i −1.29415 2.24153i
\(606\) 0.342417 + 5.01880i 0.0139097 + 0.203875i
\(607\) 36.2573i 1.47164i 0.677179 + 0.735818i \(0.263202\pi\)
−0.677179 + 0.735818i \(0.736798\pi\)
\(608\) 6.08259 + 10.5353i 0.246681 + 0.427265i
\(609\) 23.2907 + 3.89212i 0.943785 + 0.157717i
\(610\) −4.93178 −0.199682
\(611\) 7.15614 13.3168i 0.289507 0.538741i
\(612\) 2.02561 + 2.61082i 0.0818803 + 0.105536i
\(613\) 33.6982 1.36106 0.680530 0.732721i \(-0.261750\pi\)
0.680530 + 0.732721i \(0.261750\pi\)
\(614\) −5.21433 + 9.03149i −0.210433 + 0.364481i
\(615\) 38.9713 2.65889i 1.57147 0.107217i
\(616\) −30.8987 + 9.21707i −1.24494 + 0.371367i
\(617\) 6.51889 + 3.76368i 0.262441 + 0.151520i 0.625447 0.780266i \(-0.284916\pi\)
−0.363007 + 0.931786i \(0.618250\pi\)
\(618\) −1.47118 2.18909i −0.0591795 0.0880582i
\(619\) −39.6473 22.8904i −1.59356 0.920043i −0.992689 0.120697i \(-0.961487\pi\)
−0.600871 0.799346i \(-0.705179\pi\)
\(620\) 39.5895 22.8570i 1.58995 0.917960i
\(621\) 5.09797 + 1.68508i 0.204574 + 0.0676201i
\(622\) −1.24032 + 0.716101i −0.0497325 + 0.0287130i
\(623\) −0.622225 + 2.61382i −0.0249289 + 0.104720i
\(624\) −8.36779 11.6663i −0.334980 0.467024i
\(625\) 14.9239 + 25.8490i 0.596957 + 1.03396i
\(626\) 1.98828 0.0794675
\(627\) 13.3679 + 19.8913i 0.533864 + 0.794382i
\(628\) 15.0104i 0.598981i
\(629\) 2.56029 0.102086
\(630\) −10.8437 1.06019i −0.432025 0.0422388i
\(631\) −14.0226 + 24.2878i −0.558230 + 0.966882i 0.439415 + 0.898284i \(0.355186\pi\)
−0.997644 + 0.0685980i \(0.978147\pi\)
\(632\) −7.52214 + 4.34291i −0.299215 + 0.172752i
\(633\) −7.12056 + 14.5368i −0.283017 + 0.577788i
\(634\) −9.25085 −0.367398
\(635\) −4.01121 + 6.94761i −0.159180 + 0.275708i
\(636\) −0.114828 + 0.0771704i −0.00455324 + 0.00306001i
\(637\) −22.8681 10.6795i −0.906065 0.423138i
\(638\) 16.9652i 0.671657i
\(639\) 31.4008 24.3623i 1.24220 0.963759i
\(640\) 28.9746i 1.14532i
\(641\) −0.799986 + 0.461872i −0.0315975 + 0.0182428i −0.515716 0.856760i \(-0.672474\pi\)
0.484118 + 0.875003i \(0.339141\pi\)
\(642\) 8.00035 16.3330i 0.315749 0.644611i
\(643\) 6.72532 + 3.88286i 0.265221 + 0.153125i 0.626714 0.779250i \(-0.284400\pi\)
−0.361493 + 0.932375i \(0.617733\pi\)
\(644\) −1.32983 4.45802i −0.0524025 0.175670i
\(645\) 19.9072 + 29.6216i 0.783844 + 1.16635i
\(646\) 0.811620 0.0319328
\(647\) 24.2168 0.952061 0.476030 0.879429i \(-0.342075\pi\)
0.476030 + 0.879429i \(0.342075\pi\)
\(648\) −12.7289 + 13.0039i −0.500039 + 0.510841i
\(649\) 8.67733 5.00986i 0.340615 0.196654i
\(650\) 2.28274 + 1.22669i 0.0895363 + 0.0481147i
\(651\) −17.1655 45.8798i −0.672771 1.79817i
\(652\) −10.7004 18.5337i −0.419061 0.725835i
\(653\) −31.2511 18.0428i −1.22295 0.706070i −0.257404 0.966304i \(-0.582867\pi\)
−0.965546 + 0.260234i \(0.916200\pi\)
\(654\) 5.14077 + 2.51810i 0.201020 + 0.0984654i
\(655\) 4.15124 7.19017i 0.162203 0.280943i
\(656\) −20.6303 −0.805477
\(657\) −13.0507 + 10.1254i −0.509157 + 0.395030i
\(658\) 1.73208 + 5.80649i 0.0675234 + 0.226361i
\(659\) 10.7491 + 6.20598i 0.418724 + 0.241751i 0.694531 0.719462i \(-0.255612\pi\)
−0.275807 + 0.961213i \(0.588945\pi\)
\(660\) 3.03909 + 44.5438i 0.118296 + 1.73387i
\(661\) 28.4702i 1.10736i 0.832728 + 0.553682i \(0.186778\pi\)
−0.832728 + 0.553682i \(0.813222\pi\)
\(662\) −4.93268 2.84789i −0.191714 0.110686i
\(663\) −4.02276 + 0.398017i −0.156231 + 0.0154577i
\(664\) 24.0230i 0.932275i
\(665\) 10.4854 11.0918i 0.406607 0.430123i
\(666\) 0.880299 + 6.42123i 0.0341109 + 0.248818i
\(667\) −5.32456 −0.206168
\(668\) −11.4236 + 19.7863i −0.441993 + 0.765554i
\(669\) −8.49036 4.15882i −0.328256 0.160789i
\(670\) 2.08994i 0.0807415i
\(671\) 21.6559 0.836015
\(672\) 23.9530 + 4.00281i 0.924007 + 0.154412i
\(673\) 5.65042 + 9.78682i 0.217808 + 0.377254i 0.954137 0.299369i \(-0.0967761\pi\)
−0.736330 + 0.676623i \(0.763443\pi\)
\(674\) 8.79553 + 5.07810i 0.338791 + 0.195601i
\(675\) −2.14588 + 6.49202i −0.0825948 + 0.249878i
\(676\) 22.0804 1.34853i 0.849246 0.0518666i
\(677\) 6.45592 + 11.1820i 0.248121 + 0.429758i 0.963004 0.269485i \(-0.0868536\pi\)
−0.714883 + 0.699244i \(0.753520\pi\)
\(678\) 3.56852 7.28524i 0.137048 0.279788i
\(679\) 25.5041 + 6.07131i 0.978759 + 0.232996i
\(680\) 2.84845 + 1.64456i 0.109233 + 0.0630658i
\(681\) 17.3599 35.4407i 0.665232 1.35809i
\(682\) 30.4787 17.5969i 1.16709 0.673820i
\(683\) 7.62396 4.40170i 0.291723 0.168426i −0.346996 0.937867i \(-0.612798\pi\)
0.638719 + 0.769440i \(0.279465\pi\)
\(684\) −1.59165 11.6101i −0.0608584 0.443924i
\(685\) −17.9580 10.3681i −0.686140 0.396143i
\(686\) 9.51610 3.43155i 0.363327 0.131017i
\(687\) 27.1330 + 13.2905i 1.03519 + 0.507066i
\(688\) −9.42456 16.3238i −0.359308 0.622340i
\(689\) −0.00516104 0.169168i −0.000196620 0.00644478i
\(690\) 2.45108 0.167230i 0.0933112 0.00636633i
\(691\) −18.3482 10.5934i −0.698000 0.402990i 0.108602 0.994085i \(-0.465363\pi\)
−0.806602 + 0.591095i \(0.798696\pi\)
\(692\) 7.18716 + 12.4485i 0.273215 + 0.473222i
\(693\) 47.6158 + 4.65537i 1.80878 + 0.176843i
\(694\) 4.13279 0.156878
\(695\) 21.7752i 0.825982i
\(696\) 7.93804 16.2057i 0.300891 0.614277i
\(697\) −2.90438 + 5.03053i −0.110011 + 0.190545i
\(698\) −14.6537 −0.554652
\(699\) 2.91348 + 1.42710i 0.110198 + 0.0539780i
\(700\) 5.67707 1.69347i 0.214573 0.0640072i
\(701\) 39.6954i 1.49927i 0.661849 + 0.749637i \(0.269772\pi\)
−0.661849 + 0.749637i \(0.730228\pi\)
\(702\) −2.38137 9.95227i −0.0898789 0.375624i
\(703\) −7.86321 4.53982i −0.296566 0.171223i
\(704\) 10.2668i 0.386945i
\(705\) 18.2090 1.24234i 0.685790 0.0467893i
\(706\) −6.07847 3.50941i −0.228766 0.132078i
\(707\) −13.4812 + 4.02144i −0.507012 + 0.151242i
\(708\) −4.88802 + 0.333494i −0.183703 + 0.0125335i
\(709\) −9.11397 −0.342282 −0.171141 0.985247i \(-0.554745\pi\)
−0.171141 + 0.985247i \(0.554745\pi\)
\(710\) 9.09260 15.7488i 0.341239 0.591043i
\(711\) 12.7683 1.75044i 0.478850 0.0656465i
\(712\) 1.77820 + 1.02664i 0.0666409 + 0.0384751i
\(713\) 5.52284 + 9.56583i 0.206832 + 0.358243i
\(714\) 1.03031 1.25044i 0.0385583 0.0467965i
\(715\) −48.1113 25.8539i −1.79926 0.966880i
\(716\) −19.0378 + 10.9915i −0.711474 + 0.410770i
\(717\) −34.1841 + 22.9734i −1.27663 + 0.857959i
\(718\) −9.10300 −0.339721
\(719\) 10.9246 0.407418 0.203709 0.979032i \(-0.434700\pi\)
0.203709 + 0.979032i \(0.434700\pi\)
\(720\) 6.54730 16.0486i 0.244003 0.598095i
\(721\) 5.06709 5.36014i 0.188708 0.199622i
\(722\) 6.49492 + 3.74984i 0.241716 + 0.139555i
\(723\) 32.4925 + 15.9157i 1.20841 + 0.591913i
\(724\) 2.00582 1.15806i 0.0745458 0.0430390i
\(725\) 6.78058i 0.251824i
\(726\) 1.63133 + 23.9104i 0.0605443 + 0.887397i
\(727\) 45.7930i 1.69837i −0.528098 0.849183i \(-0.677095\pi\)
0.528098 0.849183i \(-0.322905\pi\)
\(728\) −12.8162 + 14.4136i −0.475000 + 0.534203i
\(729\) 24.7759 10.7309i 0.917627 0.397442i
\(730\) −3.77905 + 6.54550i −0.139869 + 0.242260i
\(731\) −5.30725 −0.196296
\(732\) −9.50960 4.65807i −0.351485 0.172167i
\(733\) 17.4750 10.0892i 0.645455 0.372654i −0.141258 0.989973i \(-0.545115\pi\)
0.786713 + 0.617319i \(0.211781\pi\)
\(734\) 7.42079 12.8532i 0.273906 0.474420i
\(735\) −3.77817 30.2351i −0.139360 1.11524i
\(736\) −5.47599 −0.201848
\(737\) 9.17712i 0.338043i
\(738\) −13.6152 5.55457i −0.501183 0.204466i
\(739\) −48.5659 −1.78652 −0.893262 0.449536i \(-0.851589\pi\)
−0.893262 + 0.449536i \(0.851589\pi\)
\(740\) −8.45747 14.6488i −0.310903 0.538500i
\(741\) 13.0605 + 5.91063i 0.479790 + 0.217132i
\(742\) 0.0492954 + 0.0466003i 0.00180969 + 0.00171075i
\(743\) −6.39543 + 3.69241i −0.234626 + 0.135461i −0.612704 0.790312i \(-0.709918\pi\)
0.378078 + 0.925774i \(0.376585\pi\)
\(744\) −37.3480 + 2.54814i −1.36924 + 0.0934193i
\(745\) 30.0606 17.3555i 1.10134 0.635856i
\(746\) −8.08311 4.66678i −0.295944 0.170863i
\(747\) 13.4645 33.0038i 0.492640 1.20755i
\(748\) −5.74985 3.31968i −0.210235 0.121380i
\(749\) 49.4794 + 11.7787i 1.80794 + 0.430383i
\(750\) −0.596235 8.73900i −0.0217714 0.319103i
\(751\) 11.5832 20.0627i 0.422676 0.732097i −0.573524 0.819189i \(-0.694424\pi\)
0.996200 + 0.0870918i \(0.0277573\pi\)
\(752\) −9.63931 −0.351510
\(753\) −35.1213 + 2.39622i −1.27989 + 0.0873230i
\(754\) 5.33967 + 8.62966i 0.194459 + 0.314274i
\(755\) −19.6456 −0.714978
\(756\) −19.9079 12.2862i −0.724043 0.446846i
\(757\) −19.9604 34.5725i −0.725475 1.25656i −0.958778 0.284155i \(-0.908287\pi\)
0.233304 0.972404i \(-0.425046\pi\)
\(758\) 12.4886i 0.453608i
\(759\) −10.7629 + 0.734320i −0.390669 + 0.0266541i
\(760\) −5.83214 10.1016i −0.211554 0.366422i
\(761\) −7.97685 −0.289161 −0.144580 0.989493i \(-0.546183\pi\)
−0.144580 + 0.989493i \(0.546183\pi\)
\(762\) 2.50655 1.68453i 0.0908027 0.0610239i
\(763\) −3.70732 + 15.5736i −0.134214 + 0.563801i
\(764\) −15.1939 + 8.77221i −0.549696 + 0.317367i
\(765\) −2.99157 3.85586i −0.108161 0.139409i
\(766\) −4.03073 2.32714i −0.145636 0.0840830i
\(767\) 2.83707 5.27949i 0.102441 0.190631i
\(768\) 2.20254 4.49655i 0.0794773 0.162255i
\(769\) −8.79268 + 5.07646i −0.317072 + 0.183062i −0.650087 0.759860i \(-0.725267\pi\)
0.333015 + 0.942922i \(0.391934\pi\)
\(770\) 20.9778 6.25768i 0.755988 0.225511i
\(771\) 41.2868 2.81687i 1.48691 0.101447i
\(772\) −2.75636 4.77416i −0.0992036 0.171826i
\(773\) 8.69927 + 15.0676i 0.312891 + 0.541943i 0.978987 0.203923i \(-0.0653692\pi\)
−0.666096 + 0.745866i \(0.732036\pi\)
\(774\) −1.82478 13.3106i −0.0655903 0.478440i
\(775\) −12.1816 + 7.03307i −0.437577 + 0.252635i
\(776\) 10.0174 17.3507i 0.359604 0.622853i
\(777\) −16.9763 + 6.35153i −0.609021 + 0.227860i
\(778\) −3.48402 6.03450i −0.124908 0.216347i
\(779\) 17.8399 10.2999i 0.639182 0.369032i
\(780\) 15.5658 + 21.7016i 0.557343 + 0.777040i
\(781\) −39.9264 + 69.1545i −1.42868 + 2.47454i
\(782\) −0.182670 + 0.316393i −0.00653226 + 0.0113142i
\(783\) −19.9886 + 17.8150i −0.714335 + 0.636655i
\(784\) 0.903839 + 16.0672i 0.0322800 + 0.573830i
\(785\) 22.1686i 0.791230i
\(786\) −2.59406 + 1.74333i −0.0925269 + 0.0621827i
\(787\) −14.0025 + 8.08436i −0.499136 + 0.288176i −0.728357 0.685198i \(-0.759716\pi\)
0.229221 + 0.973374i \(0.426382\pi\)
\(788\) −20.2178 11.6728i −0.720230 0.415825i
\(789\) 2.32274 1.56100i 0.0826918 0.0555730i
\(790\) 5.10696 2.94850i 0.181697 0.104903i
\(791\) 22.0701 + 5.25382i 0.784721 + 0.186804i
\(792\) 13.8108 33.8526i 0.490744 1.20290i
\(793\) 11.0157 6.81603i 0.391178 0.242044i
\(794\) −1.06319 + 1.84150i −0.0377313 + 0.0653525i
\(795\) 0.169588 0.113971i 0.00601465 0.00404215i
\(796\) −4.90764 2.83343i −0.173947 0.100428i
\(797\) −7.83061 + 13.5630i −0.277374 + 0.480426i −0.970731 0.240168i \(-0.922798\pi\)
0.693357 + 0.720594i \(0.256131\pi\)
\(798\) −5.38153 + 2.01345i −0.190504 + 0.0712755i
\(799\) −1.35705 + 2.35047i −0.0480088 + 0.0831537i
\(800\) 6.97341i 0.246547i
\(801\) −1.86755 2.40710i −0.0659865 0.0850505i
\(802\) −6.02431 10.4344i −0.212726 0.368452i
\(803\) 16.5941 28.7418i 0.585593 1.01428i
\(804\) −1.97395 + 4.02989i −0.0696160 + 0.142123i
\(805\) 1.96399 + 6.58395i 0.0692216 + 0.232054i
\(806\) 9.96509 18.5440i 0.351005 0.653183i
\(807\) −12.5354 + 25.5913i −0.441265 + 0.900857i
\(808\) 10.7509i 0.378215i
\(809\) 7.94208i 0.279229i −0.990206 0.139614i \(-0.955414\pi\)
0.990206 0.139614i \(-0.0445863\pi\)
\(810\) 8.64195 8.82864i 0.303647 0.310207i
\(811\) 27.8689i 0.978608i −0.872113 0.489304i \(-0.837251\pi\)
0.872113 0.489304i \(-0.162749\pi\)
\(812\) 22.5686 + 5.37250i 0.792002 + 0.188538i
\(813\) 0.0724190 + 1.06144i 0.00253984 + 0.0372265i
\(814\) −6.51114 11.2776i −0.228215 0.395281i
\(815\) 15.8032 + 27.3720i 0.553563 + 0.958799i
\(816\) 1.43770 + 2.13927i 0.0503295 + 0.0748895i
\(817\) 16.2997 + 9.41063i 0.570254 + 0.329236i
\(818\) 4.68694 0.163875
\(819\) 25.6860 12.6187i 0.897540 0.440933i
\(820\) 38.3764 1.34016
\(821\) −18.3241 10.5794i −0.639515 0.369224i 0.144912 0.989444i \(-0.453710\pi\)
−0.784428 + 0.620220i \(0.787043\pi\)
\(822\) 4.35411 + 6.47886i 0.151867 + 0.225976i
\(823\) −23.3711 40.4800i −0.814666 1.41104i −0.909567 0.415556i \(-0.863587\pi\)
0.0949015 0.995487i \(-0.469746\pi\)
\(824\) −2.81839 4.88159i −0.0981832 0.170058i
\(825\) −0.935122 13.7061i −0.0325568 0.477184i
\(826\) 0.686687 + 2.30200i 0.0238929 + 0.0800968i
\(827\) 19.8390i 0.689871i −0.938626 0.344935i \(-0.887901\pi\)
0.938626 0.344935i \(-0.112099\pi\)
\(828\) 4.88420 + 1.99260i 0.169738 + 0.0692475i
\(829\) 22.9829i 0.798231i 0.916901 + 0.399115i \(0.130683\pi\)
−0.916901 + 0.399115i \(0.869317\pi\)
\(830\) 16.3098i 0.566121i
\(831\) 7.36568 15.0373i 0.255513 0.521637i
\(832\) −3.23141 5.22241i −0.112029 0.181054i
\(833\) 4.04511 + 2.04159i 0.140155 + 0.0707369i
\(834\) 3.60587 7.36150i 0.124861 0.254908i
\(835\) 16.8713 29.2219i 0.583855 1.01127i
\(836\) 11.7727 + 20.3909i 0.407167 + 0.705234i
\(837\) 52.7384 + 17.4322i 1.82290 + 0.602544i
\(838\) 13.7073i 0.473510i
\(839\) 3.02970 5.24760i 0.104597 0.181167i −0.808977 0.587841i \(-0.799978\pi\)
0.913573 + 0.406674i \(0.133311\pi\)
\(840\) −22.9668 3.83800i −0.792429 0.132423i
\(841\) −1.22374 + 2.11958i −0.0421979 + 0.0730888i
\(842\) −5.63583 3.25385i −0.194224 0.112135i
\(843\) −6.11189 + 4.10749i −0.210505 + 0.141470i
\(844\) −7.95152 + 13.7724i −0.273703 + 0.474067i
\(845\) −32.6101 + 1.99162i −1.12182 + 0.0685137i
\(846\) −6.36159 2.59532i −0.218716 0.0892291i
\(847\) −64.2265 + 19.1588i −2.20685 + 0.658303i
\(848\) −0.0934561 + 0.0539569i −0.00320930 + 0.00185289i
\(849\) 19.3592 13.0103i 0.664406 0.446514i
\(850\) −0.402912 0.232621i −0.0138198 0.00797885i
\(851\) 3.53952 2.04354i 0.121333 0.0700517i
\(852\) 32.4074 21.7794i 1.11026 0.746150i
\(853\) 26.7903i 0.917284i −0.888621 0.458642i \(-0.848336\pi\)
0.888621 0.458642i \(-0.151664\pi\)
\(854\) −1.20237 + 5.05087i −0.0411443 + 0.172837i
\(855\) 2.35068 + 17.1467i 0.0803915 + 0.586406i
\(856\) 19.4343 33.6612i 0.664252 1.15052i
\(857\) 4.19504 7.26603i 0.143300 0.248203i −0.785437 0.618941i \(-0.787562\pi\)
0.928737 + 0.370738i \(0.120895\pi\)
\(858\) 11.9836 + 16.7073i 0.409113 + 0.570379i
\(859\) 10.3636 5.98343i 0.353601 0.204152i −0.312669 0.949862i \(-0.601223\pi\)
0.666270 + 0.745710i \(0.267890\pi\)
\(860\) 17.5316 + 30.3655i 0.597821 + 1.03546i
\(861\) 6.77812 40.5606i 0.230998 1.38230i
\(862\) −7.88778 + 13.6620i −0.268659 + 0.465331i
\(863\) 16.9737 9.79980i 0.577793 0.333589i −0.182463 0.983213i \(-0.558407\pi\)
0.760256 + 0.649624i \(0.225074\pi\)
\(864\) −20.5571 + 18.3216i −0.699366 + 0.623313i
\(865\) −10.6146 18.3850i −0.360906 0.625108i
\(866\) −2.04443 3.54106i −0.0694727 0.120330i
\(867\) −28.6525 + 1.95487i −0.973091 + 0.0663909i
\(868\) −13.7570 46.1181i −0.466944 1.56535i
\(869\) −22.4251 + 12.9471i −0.760719 + 0.439201i
\(870\) −5.38932 + 11.0025i −0.182715 + 0.373018i
\(871\) −2.88843 4.66812i −0.0978708 0.158173i
\(872\) 10.5948 + 6.11692i 0.358786 + 0.207145i
\(873\) −23.4871 + 18.2225i −0.794917 + 0.616737i
\(874\) 1.12204 0.647808i 0.0379535 0.0219124i
\(875\) 23.4741 7.00234i 0.793571 0.236722i
\(876\) −13.4691 + 9.05191i −0.455079 + 0.305836i
\(877\) −11.4236 −0.385748 −0.192874 0.981224i \(-0.561781\pi\)
−0.192874 + 0.981224i \(0.561781\pi\)
\(878\) −2.79133 4.83472i −0.0942028 0.163164i
\(879\) −23.9797 + 1.63606i −0.808814 + 0.0551828i
\(880\) 34.8251i 1.17395i
\(881\) −22.1811 38.4188i −0.747300 1.29436i −0.949113 0.314937i \(-0.898017\pi\)
0.201813 0.979424i \(-0.435317\pi\)
\(882\) −3.72950 + 10.8471i −0.125579 + 0.365242i
\(883\) −12.9921 −0.437220 −0.218610 0.975812i \(-0.570152\pi\)
−0.218610 + 0.975812i \(0.570152\pi\)
\(884\) −3.96962 + 0.121107i −0.133513 + 0.00407327i
\(885\) 7.21901 0.492530i 0.242664 0.0165562i
\(886\) 16.5871 0.557254
\(887\) −20.8583 + 36.1277i −0.700354 + 1.21305i 0.267989 + 0.963422i \(0.413641\pi\)
−0.968342 + 0.249626i \(0.919692\pi\)
\(888\) 0.942853 + 13.8194i 0.0316401 + 0.463748i
\(889\) 6.13745 + 5.80190i 0.205844 + 0.194590i
\(890\) −1.20726 0.697013i −0.0404675 0.0233639i
\(891\) −37.9475 + 38.7673i −1.27129 + 1.29875i
\(892\) −8.04391 4.64415i −0.269330 0.155498i
\(893\) 8.33556 4.81254i 0.278939 0.161045i
\(894\) −13.0365 + 0.889439i −0.436006 + 0.0297473i
\(895\) 28.1165 16.2330i 0.939829 0.542611i
\(896\) 29.6743 + 7.06403i 0.991350 + 0.235993i
\(897\) −5.24365 + 3.76108i −0.175080 + 0.125579i
\(898\) 5.99714 + 10.3874i 0.200127 + 0.346631i
\(899\) −55.0825 −1.83711
\(900\) −2.53748 + 6.21980i −0.0845826 + 0.207327i
\(901\) 0.0303847i 0.00101226i
\(902\) 29.5448 0.983734
\(903\) 35.1903 13.1661i 1.17106 0.438142i
\(904\) 8.66858 15.0144i 0.288313 0.499372i
\(905\) −2.96235 + 1.71032i −0.0984720 + 0.0568528i
\(906\) 6.64155 + 3.25322i 0.220651 + 0.108081i
\(907\) −58.0241 −1.92666 −0.963329 0.268324i \(-0.913530\pi\)
−0.963329 + 0.268324i \(0.913530\pi\)
\(908\) 19.3858 33.5771i 0.643339 1.11430i
\(909\) 6.02568 14.7700i 0.199859 0.489890i
\(910\) 8.70121 9.78571i 0.288442 0.324393i
\(911\) 41.9642i 1.39034i −0.718847 0.695168i \(-0.755330\pi\)
0.718847 0.695168i \(-0.244670\pi\)
\(912\) −0.622191 9.11944i −0.0206028 0.301975i
\(913\) 71.6177i 2.37020i
\(914\) −17.0561 + 9.84732i −0.564164 + 0.325720i
\(915\) 14.0445 + 6.87941i 0.464297 + 0.227426i
\(916\) 25.7063 + 14.8415i 0.849359 + 0.490378i
\(917\) −6.35172 6.00446i −0.209752 0.198285i
\(918\) 0.372842 + 1.79893i 0.0123056 + 0.0593736i
\(919\) −10.7537 −0.354732 −0.177366 0.984145i \(-0.556758\pi\)
−0.177366 + 0.984145i \(0.556758\pi\)
\(920\) 5.25052 0.173104
\(921\) 27.4473 18.4460i 0.904420 0.607815i
\(922\) −4.32422 + 2.49659i −0.142411 + 0.0822208i
\(923\) 1.45657 + 47.7433i 0.0479437 + 1.57149i
\(924\) 46.3604 + 7.74733i 1.52515 + 0.254869i
\(925\) 2.60235 + 4.50741i 0.0855648 + 0.148203i
\(926\) 10.4716 + 6.04576i 0.344117 + 0.198676i
\(927\) 1.13597 + 8.28618i 0.0373101 + 0.272154i
\(928\) 13.6538 23.6491i 0.448209 0.776320i
\(929\) 31.6451 1.03824 0.519121 0.854701i \(-0.326259\pi\)
0.519121 + 0.854701i \(0.326259\pi\)
\(930\) 25.3564 1.72999i 0.831470 0.0567286i
\(931\) −8.80334 13.4428i −0.288518 0.440571i
\(932\) 2.76027 + 1.59364i 0.0904158 + 0.0522016i
\(933\) 4.53105 0.309139i 0.148340 0.0101208i
\(934\) 0.345159i 0.0112939i
\(935\) 8.49184 + 4.90276i 0.277713 + 0.160338i
\(936\) −3.62975 21.5666i −0.118642 0.704927i
\(937\) 2.52593i 0.0825185i −0.999148 0.0412593i \(-0.986863\pi\)
0.999148 0.0412593i \(-0.0131370\pi\)
\(938\) 2.14041 + 0.509529i 0.0698869 + 0.0166367i
\(939\) −5.66213 2.77347i −0.184777 0.0905089i
\(940\) 17.9310 0.584846
\(941\) 0.833591 1.44382i 0.0271743 0.0470672i −0.852118 0.523349i \(-0.824682\pi\)
0.879293 + 0.476282i \(0.158016\pi\)
\(942\) −3.67100 + 7.49447i −0.119608 + 0.244183i
\(943\) 9.27271i 0.301961i
\(944\) −3.82153 −0.124380
\(945\) 29.4015 + 18.1453i 0.956432 + 0.590265i
\(946\) 13.4970 + 23.3775i 0.438825 + 0.760067i
\(947\) −17.3559 10.0204i −0.563991 0.325620i 0.190755 0.981638i \(-0.438906\pi\)
−0.754746 + 0.656017i \(0.772240\pi\)
\(948\) 12.6322 0.861858i 0.410276 0.0279919i
\(949\) −0.605378 19.8430i −0.0196514 0.644130i
\(950\) 0.824953 + 1.42886i 0.0267650 + 0.0463584i
\(951\) 26.3442 + 12.9042i 0.854270 + 0.418446i
\(952\) 2.37872 2.51630i 0.0770949 0.0815536i
\(953\) 6.14947 + 3.55040i 0.199201 + 0.115009i 0.596283 0.802774i \(-0.296644\pi\)
−0.397082 + 0.917783i \(0.629977\pi\)
\(954\) −0.0762051 + 0.0104471i −0.00246723 + 0.000338237i
\(955\) 22.4396 12.9555i 0.726127 0.419230i
\(956\) −35.0427 + 20.2319i −1.13336 + 0.654347i
\(957\) 23.6649 48.3127i 0.764979 1.56173i
\(958\) 10.5628 + 6.09846i 0.341270 + 0.197032i
\(959\) −14.9966 + 15.8639i −0.484265 + 0.512273i
\(960\) 3.26145 6.65835i 0.105263 0.214897i
\(961\) 41.6336 + 72.1116i 1.34302 + 2.32618i
\(962\) −6.86157 3.68725i −0.221226 0.118882i
\(963\) −45.5662 + 35.3526i −1.46835 + 1.13922i
\(964\) 30.7839 + 17.7731i 0.991483 + 0.572433i
\(965\) 4.07081 + 7.05085i 0.131044 + 0.226975i
\(966\) 0.426308 2.55105i 0.0137162 0.0820785i
\(967\) −57.1582 −1.83808 −0.919041 0.394161i \(-0.871035\pi\)
−0.919041 + 0.394161i \(0.871035\pi\)
\(968\) 51.2189i 1.64624i
\(969\) −2.31130 1.13214i −0.0742496 0.0363696i
\(970\) −6.80105 + 11.7798i −0.218369 + 0.378226i
\(971\) 2.08912 0.0670431 0.0335216 0.999438i \(-0.489328\pi\)
0.0335216 + 0.999438i \(0.489328\pi\)
\(972\) 25.0023 8.86131i 0.801950 0.284227i
\(973\) 22.3011 + 5.30881i 0.714940 + 0.170193i
\(974\) 22.0058i 0.705111i
\(975\) −4.78956 6.67754i −0.153389 0.213852i
\(976\) −7.15300 4.12979i −0.228962 0.132191i
\(977\) 21.3475i 0.682968i 0.939888 + 0.341484i \(0.110929\pi\)
−0.939888 + 0.341484i \(0.889071\pi\)
\(978\) −0.809888 11.8705i −0.0258974 0.379577i
\(979\) 5.30119 + 3.06064i 0.169427 + 0.0978186i
\(980\) −1.68132 29.8883i −0.0537078 0.954745i
\(981\) −11.1272 14.3419i −0.355263 0.457901i
\(982\) −4.22905 −0.134955
\(983\) −26.2192 + 45.4129i −0.836261 + 1.44845i 0.0567381 + 0.998389i \(0.481930\pi\)
−0.892999 + 0.450058i \(0.851403\pi\)
\(984\) −28.2223 13.8241i −0.899693 0.440695i
\(985\) 29.8593 + 17.2393i 0.951395 + 0.549288i
\(986\) −0.910938 1.57779i −0.0290102 0.0502471i
\(987\) 3.16702 18.9516i 0.100807 0.603236i
\(988\) 12.4063 + 6.66685i 0.394697 + 0.212101i
\(989\) −7.33709 + 4.23607i −0.233306 + 0.134699i
\(990\) −9.37644 + 22.9833i −0.298003 + 0.730457i
\(991\) −7.60585 −0.241608 −0.120804 0.992676i \(-0.538547\pi\)
−0.120804 + 0.992676i \(0.538547\pi\)
\(992\) −56.6490 −1.79861
\(993\) 10.0745 + 14.9908i 0.319706 + 0.475718i
\(994\) −13.9124 13.1517i −0.441274 0.417148i
\(995\) 7.24798 + 4.18463i 0.229777 + 0.132662i
\(996\) 15.4046 31.4490i 0.488114 0.996500i
\(997\) 24.5233 14.1586i 0.776662 0.448406i −0.0585841 0.998282i \(-0.518659\pi\)
0.835246 + 0.549877i \(0.185325\pi\)
\(998\) 8.67729i 0.274675i
\(999\) 6.45019 19.5141i 0.204075 0.617398i
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 273.2.bf.b.185.18 yes 64
3.2 odd 2 inner 273.2.bf.b.185.15 yes 64
7.5 odd 6 273.2.r.b.68.15 64
13.9 even 3 273.2.r.b.269.15 yes 64
21.5 even 6 273.2.r.b.68.18 yes 64
39.35 odd 6 273.2.r.b.269.18 yes 64
91.61 odd 6 inner 273.2.bf.b.152.15 yes 64
273.152 even 6 inner 273.2.bf.b.152.18 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.r.b.68.15 64 7.5 odd 6
273.2.r.b.68.18 yes 64 21.5 even 6
273.2.r.b.269.15 yes 64 13.9 even 3
273.2.r.b.269.18 yes 64 39.35 odd 6
273.2.bf.b.152.15 yes 64 91.61 odd 6 inner
273.2.bf.b.152.18 yes 64 273.152 even 6 inner
273.2.bf.b.185.15 yes 64 3.2 odd 2 inner
273.2.bf.b.185.18 yes 64 1.1 even 1 trivial