Properties

Label 403.2.s.a.160.3
Level $403$
Weight $2$
Character 403.160
Analytic conductor $3.218$
Analytic rank $0$
Dimension $70$
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] = [403,2,Mod(160,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.160");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.s (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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(35\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 160.3
Character \(\chi\) \(=\) 403.160
Dual form 403.2.s.a.335.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.12624 - 1.22758i) q^{2} +(0.398773 + 0.690696i) q^{3} +(2.01392 + 3.48821i) q^{4} +(-3.14114 + 1.81354i) q^{5} -1.95811i q^{6} +4.93931i q^{7} -4.97868i q^{8} +(1.18196 - 2.04721i) q^{9} +O(q^{10})\) \(q+(-2.12624 - 1.22758i) q^{2} +(0.398773 + 0.690696i) q^{3} +(2.01392 + 3.48821i) q^{4} +(-3.14114 + 1.81354i) q^{5} -1.95811i q^{6} +4.93931i q^{7} -4.97868i q^{8} +(1.18196 - 2.04721i) q^{9} +8.90508 q^{10} -1.53473i q^{11} +(-1.60619 + 2.78201i) q^{12} +(-2.13237 + 2.90740i) q^{13} +(6.06341 - 10.5021i) q^{14} +(-2.50521 - 1.44638i) q^{15} +(-2.08390 + 3.60943i) q^{16} -5.88743 q^{17} +(-5.02625 + 2.90191i) q^{18} -4.36041i q^{19} +(-12.6520 - 7.30464i) q^{20} +(-3.41156 + 1.96967i) q^{21} +(-1.88401 + 3.26319i) q^{22} +(1.48885 - 2.57877i) q^{23} +(3.43875 - 1.98536i) q^{24} +(4.07785 - 7.06304i) q^{25} +(8.10300 - 3.56417i) q^{26} +4.27798 q^{27} +(-17.2294 + 9.94737i) q^{28} +(0.886250 - 1.53503i) q^{29} +(3.55111 + 6.15070i) q^{30} +(-5.54265 - 0.528277i) q^{31} +(0.238413 - 0.137648i) q^{32} +(1.06003 - 0.612009i) q^{33} +(12.5181 + 7.22731i) q^{34} +(-8.95763 - 15.5151i) q^{35} +9.52149 q^{36} +(6.00938 - 3.46951i) q^{37} +(-5.35276 + 9.27126i) q^{38} +(-2.85846 - 0.313423i) q^{39} +(9.02903 + 15.6387i) q^{40} +7.63343i q^{41} +9.67171 q^{42} -9.04601 q^{43} +(5.35346 - 3.09082i) q^{44} +8.57412i q^{45} +(-6.33130 + 3.65538i) q^{46} -4.38154i q^{47} -3.32402 q^{48} -17.3968 q^{49} +(-17.3409 + 10.0118i) q^{50} +(-2.34775 - 4.06642i) q^{51} +(-14.4361 - 1.58287i) q^{52} +(3.98870 + 6.90863i) q^{53} +(-9.09599 - 5.25157i) q^{54} +(2.78329 + 4.82080i) q^{55} +24.5912 q^{56} +(3.01171 - 1.73881i) q^{57} +(-3.76875 + 2.17589i) q^{58} +6.54753i q^{59} -11.6516i q^{60} +(-0.474064 - 0.821103i) q^{61} +(11.1365 + 7.92730i) q^{62} +(10.1118 + 5.83807i) q^{63} +7.65972 q^{64} +(1.42538 - 12.9997i) q^{65} -3.00517 q^{66} -2.88244i q^{67} +(-11.8568 - 20.5366i) q^{68} +2.37486 q^{69} +43.9849i q^{70} +(-7.82584 - 4.51825i) q^{71} +(-10.1924 - 5.88460i) q^{72} +(-3.41873 + 1.97381i) q^{73} -17.0365 q^{74} +6.50455 q^{75} +(15.2100 - 8.78151i) q^{76} +7.58050 q^{77} +(5.69302 + 4.17541i) q^{78} +(-1.84710 + 3.19928i) q^{79} -15.1170i q^{80} +(-1.83994 - 3.18686i) q^{81} +(9.37067 - 16.2305i) q^{82} +(1.91225 - 1.10404i) q^{83} +(-13.7412 - 7.93350i) q^{84} +(18.4933 - 10.6771i) q^{85} +(19.2339 + 11.1047i) q^{86} +1.41365 q^{87} -7.64092 q^{88} +(-13.9315 - 8.04337i) q^{89} +(10.5254 - 18.2306i) q^{90} +(-14.3606 - 10.5324i) q^{91} +11.9937 q^{92} +(-1.84538 - 4.03894i) q^{93} +(-5.37871 + 9.31620i) q^{94} +(7.90777 + 13.6967i) q^{95} +(0.190145 + 0.109780i) q^{96} +(1.72108 - 0.993664i) q^{97} +(36.9897 + 21.3560i) q^{98} +(-3.14192 - 1.81399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9} + 2 q^{10} + 13 q^{12} + q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} - 12 q^{17} - 3 q^{20} - 9 q^{21} + 4 q^{22} + 10 q^{23} + 18 q^{24} + 19 q^{25} + 6 q^{26} + 34 q^{27} - 33 q^{28} - 18 q^{29} - 31 q^{30} - 2 q^{31} + 36 q^{32} - 12 q^{33} + 9 q^{34} - 12 q^{35} - 16 q^{36} - 18 q^{37} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 98 q^{42} - 38 q^{43} + 42 q^{44} - 6 q^{46} + 54 q^{48} - 18 q^{49} - 51 q^{50} - 7 q^{51} + 41 q^{52} - 22 q^{53} + 18 q^{54} - 15 q^{55} - 50 q^{56} + 15 q^{57} - 12 q^{58} - 13 q^{61} - 23 q^{62} - 6 q^{63} - 38 q^{64} - 12 q^{65} - 52 q^{66} - 44 q^{68} + 32 q^{69} + 27 q^{71} - 15 q^{72} - 9 q^{73} + 38 q^{74} - 50 q^{75} + 126 q^{76} + 34 q^{77} + 14 q^{78} + 6 q^{79} - 11 q^{81} + 39 q^{82} - 54 q^{83} + 15 q^{84} - 33 q^{85} - 24 q^{86} + 28 q^{87} - 32 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 14 q^{93} - 43 q^{94} + 25 q^{95} + 36 q^{96} - 75 q^{97} + 93 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12624 1.22758i −1.50348 0.868032i −0.999992 0.00402754i \(-0.998718\pi\)
−0.503484 0.864005i \(-0.667949\pi\)
\(3\) 0.398773 + 0.690696i 0.230232 + 0.398773i 0.957876 0.287181i \(-0.0927182\pi\)
−0.727644 + 0.685955i \(0.759385\pi\)
\(4\) 2.01392 + 3.48821i 1.00696 + 1.74411i
\(5\) −3.14114 + 1.81354i −1.40476 + 0.811039i −0.994876 0.101098i \(-0.967764\pi\)
−0.409885 + 0.912137i \(0.634431\pi\)
\(6\) 1.95811i 0.799395i
\(7\) 4.93931i 1.86688i 0.358728 + 0.933442i \(0.383211\pi\)
−0.358728 + 0.933442i \(0.616789\pi\)
\(8\) 4.97868i 1.76023i
\(9\) 1.18196 2.04721i 0.393987 0.682405i
\(10\) 8.90508 2.81603
\(11\) 1.53473i 0.462738i −0.972866 0.231369i \(-0.925680\pi\)
0.972866 0.231369i \(-0.0743205\pi\)
\(12\) −1.60619 + 2.78201i −0.463668 + 0.803097i
\(13\) −2.13237 + 2.90740i −0.591413 + 0.806369i
\(14\) 6.06341 10.5021i 1.62052 2.80682i
\(15\) −2.50521 1.44638i −0.646842 0.373454i
\(16\) −2.08390 + 3.60943i −0.520976 + 0.902356i
\(17\) −5.88743 −1.42791 −0.713956 0.700190i \(-0.753098\pi\)
−0.713956 + 0.700190i \(0.753098\pi\)
\(18\) −5.02625 + 2.90191i −1.18470 + 0.683986i
\(19\) 4.36041i 1.00035i −0.865925 0.500173i \(-0.833270\pi\)
0.865925 0.500173i \(-0.166730\pi\)
\(20\) −12.6520 7.30464i −2.82908 1.63337i
\(21\) −3.41156 + 1.96967i −0.744464 + 0.429816i
\(22\) −1.88401 + 3.26319i −0.401671 + 0.695715i
\(23\) 1.48885 2.57877i 0.310447 0.537710i −0.668012 0.744150i \(-0.732855\pi\)
0.978459 + 0.206440i \(0.0661879\pi\)
\(24\) 3.43875 1.98536i 0.701932 0.405261i
\(25\) 4.07785 7.06304i 0.815569 1.41261i
\(26\) 8.10300 3.56417i 1.58913 0.698991i
\(27\) 4.27798 0.823297
\(28\) −17.2294 + 9.94737i −3.25604 + 1.87988i
\(29\) 0.886250 1.53503i 0.164572 0.285048i −0.771931 0.635706i \(-0.780709\pi\)
0.936503 + 0.350659i \(0.114042\pi\)
\(30\) 3.55111 + 6.15070i 0.648341 + 1.12296i
\(31\) −5.54265 0.528277i −0.995489 0.0948814i
\(32\) 0.238413 0.137648i 0.0421458 0.0243329i
\(33\) 1.06003 0.612009i 0.184528 0.106537i
\(34\) 12.5181 + 7.22731i 2.14683 + 1.23947i
\(35\) −8.95763 15.5151i −1.51412 2.62253i
\(36\) 9.52149 1.58691
\(37\) 6.00938 3.46951i 0.987935 0.570385i 0.0832788 0.996526i \(-0.473461\pi\)
0.904656 + 0.426142i \(0.140127\pi\)
\(38\) −5.35276 + 9.27126i −0.868333 + 1.50400i
\(39\) −2.85846 0.313423i −0.457721 0.0501878i
\(40\) 9.02903 + 15.6387i 1.42761 + 2.47270i
\(41\) 7.63343i 1.19214i 0.802932 + 0.596071i \(0.203272\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(42\) 9.67171 1.49238
\(43\) −9.04601 −1.37950 −0.689752 0.724046i \(-0.742280\pi\)
−0.689752 + 0.724046i \(0.742280\pi\)
\(44\) 5.35346 3.09082i 0.807064 0.465959i
\(45\) 8.57412i 1.27815i
\(46\) −6.33130 + 3.65538i −0.933499 + 0.538956i
\(47\) 4.38154i 0.639114i −0.947567 0.319557i \(-0.896466\pi\)
0.947567 0.319557i \(-0.103534\pi\)
\(48\) −3.32402 −0.479781
\(49\) −17.3968 −2.48526
\(50\) −17.3409 + 10.0118i −2.45238 + 1.41588i
\(51\) −2.34775 4.06642i −0.328751 0.569413i
\(52\) −14.4361 1.58287i −2.00192 0.219505i
\(53\) 3.98870 + 6.90863i 0.547890 + 0.948974i 0.998419 + 0.0562119i \(0.0179022\pi\)
−0.450529 + 0.892762i \(0.648764\pi\)
\(54\) −9.09599 5.25157i −1.23781 0.714648i
\(55\) 2.78329 + 4.82080i 0.375299 + 0.650036i
\(56\) 24.5912 3.28614
\(57\) 3.01171 1.73881i 0.398911 0.230312i
\(58\) −3.76875 + 2.17589i −0.494862 + 0.285708i
\(59\) 6.54753i 0.852416i 0.904625 + 0.426208i \(0.140151\pi\)
−0.904625 + 0.426208i \(0.859849\pi\)
\(60\) 11.6516i 1.50421i
\(61\) −0.474064 0.821103i −0.0606977 0.105131i 0.834080 0.551644i \(-0.185999\pi\)
−0.894777 + 0.446512i \(0.852666\pi\)
\(62\) 11.1365 + 7.92730i 1.41433 + 1.00677i
\(63\) 10.1118 + 5.83807i 1.27397 + 0.735527i
\(64\) 7.65972 0.957465
\(65\) 1.42538 12.9997i 0.176797 1.61241i
\(66\) −3.00517 −0.369910
\(67\) 2.88244i 0.352146i −0.984377 0.176073i \(-0.943660\pi\)
0.984377 0.176073i \(-0.0563395\pi\)
\(68\) −11.8568 20.5366i −1.43785 2.49043i
\(69\) 2.37486 0.285899
\(70\) 43.9849i 5.25721i
\(71\) −7.82584 4.51825i −0.928756 0.536218i −0.0423383 0.999103i \(-0.513481\pi\)
−0.886418 + 0.462886i \(0.846814\pi\)
\(72\) −10.1924 5.88460i −1.20119 0.693507i
\(73\) −3.41873 + 1.97381i −0.400133 + 0.231017i −0.686541 0.727091i \(-0.740872\pi\)
0.286409 + 0.958108i \(0.407539\pi\)
\(74\) −17.0365 −1.98045
\(75\) 6.50455 0.751080
\(76\) 15.2100 8.78151i 1.74471 1.00731i
\(77\) 7.58050 0.863878
\(78\) 5.69302 + 4.17541i 0.644607 + 0.472772i
\(79\) −1.84710 + 3.19928i −0.207816 + 0.359947i −0.951026 0.309110i \(-0.899969\pi\)
0.743211 + 0.669058i \(0.233302\pi\)
\(80\) 15.1170i 1.69013i
\(81\) −1.83994 3.18686i −0.204437 0.354096i
\(82\) 9.37067 16.2305i 1.03482 1.79236i
\(83\) 1.91225 1.10404i 0.209896 0.121184i −0.391367 0.920235i \(-0.627998\pi\)
0.601263 + 0.799051i \(0.294664\pi\)
\(84\) −13.7412 7.93350i −1.49929 0.865615i
\(85\) 18.4933 10.6771i 2.00588 1.15809i
\(86\) 19.2339 + 11.1047i 2.07405 + 1.19745i
\(87\) 1.41365 0.151559
\(88\) −7.64092 −0.814525
\(89\) −13.9315 8.04337i −1.47674 0.852596i −0.477084 0.878857i \(-0.658306\pi\)
−0.999655 + 0.0262614i \(0.991640\pi\)
\(90\) 10.5254 18.2306i 1.10948 1.92167i
\(91\) −14.3606 10.5324i −1.50540 1.10410i
\(92\) 11.9937 1.25043
\(93\) −1.84538 4.03894i −0.191357 0.418819i
\(94\) −5.37871 + 9.31620i −0.554771 + 0.960892i
\(95\) 7.90777 + 13.6967i 0.811320 + 1.40525i
\(96\) 0.190145 + 0.109780i 0.0194066 + 0.0112044i
\(97\) 1.72108 0.993664i 0.174749 0.100891i −0.410074 0.912052i \(-0.634497\pi\)
0.584823 + 0.811161i \(0.301164\pi\)
\(98\) 36.9897 + 21.3560i 3.73652 + 2.15728i
\(99\) −3.14192 1.81399i −0.315775 0.182313i
\(100\) 32.8498 3.28498
\(101\) 3.63150 6.28994i 0.361348 0.625873i −0.626835 0.779152i \(-0.715650\pi\)
0.988183 + 0.153279i \(0.0489834\pi\)
\(102\) 11.5282i 1.14147i
\(103\) 0.616571 + 1.06793i 0.0607525 + 0.105226i 0.894802 0.446463i \(-0.147317\pi\)
−0.834049 + 0.551690i \(0.813983\pi\)
\(104\) 14.4750 + 10.6164i 1.41939 + 1.04102i
\(105\) 7.14413 12.3740i 0.697196 1.20758i
\(106\) 19.5858i 1.90235i
\(107\) 1.98589 + 3.43966i 0.191983 + 0.332525i 0.945907 0.324437i \(-0.105175\pi\)
−0.753924 + 0.656961i \(0.771841\pi\)
\(108\) 8.61550 + 14.9225i 0.829027 + 1.43592i
\(109\) 0.960300i 0.0919800i −0.998942 0.0459900i \(-0.985356\pi\)
0.998942 0.0459900i \(-0.0146442\pi\)
\(110\) 13.6669i 1.30309i
\(111\) 4.79276 + 2.76710i 0.454908 + 0.262641i
\(112\) −17.8281 10.2930i −1.68460 0.972601i
\(113\) −4.64270 + 8.04139i −0.436748 + 0.756470i −0.997437 0.0715569i \(-0.977203\pi\)
0.560688 + 0.828027i \(0.310537\pi\)
\(114\) −8.53815 −0.799671
\(115\) 10.8004i 1.00714i
\(116\) 7.13934 0.662871
\(117\) 3.43171 + 7.80185i 0.317261 + 0.721281i
\(118\) 8.03764 13.9216i 0.739924 1.28159i
\(119\) 29.0799i 2.66575i
\(120\) −7.20107 + 12.4726i −0.657365 + 1.13859i
\(121\) 8.64461 0.785874
\(122\) 2.32781i 0.210750i
\(123\) −5.27238 + 3.04401i −0.475394 + 0.274469i
\(124\) −9.31970 20.3978i −0.836934 1.83178i
\(125\) 11.4459i 1.02376i
\(126\) −14.3334 24.8262i −1.27692 2.21169i
\(127\) −2.79891 4.84785i −0.248363 0.430177i 0.714709 0.699422i \(-0.246559\pi\)
−0.963072 + 0.269245i \(0.913226\pi\)
\(128\) −16.7632 9.67823i −1.48167 0.855443i
\(129\) −3.60731 6.24804i −0.317606 0.550109i
\(130\) −18.9889 + 25.8907i −1.66544 + 2.27076i
\(131\) −4.25828 + 7.37556i −0.372048 + 0.644406i −0.989880 0.141904i \(-0.954678\pi\)
0.617833 + 0.786310i \(0.288011\pi\)
\(132\) 4.26963 + 2.46507i 0.371624 + 0.214557i
\(133\) 21.5374 1.86753
\(134\) −3.53843 + 6.12875i −0.305674 + 0.529443i
\(135\) −13.4377 + 7.75828i −1.15654 + 0.667726i
\(136\) 29.3116i 2.51345i
\(137\) −16.0060 9.24109i −1.36749 0.789520i −0.376881 0.926262i \(-0.623004\pi\)
−0.990607 + 0.136742i \(0.956337\pi\)
\(138\) −5.04951 2.91533i −0.429843 0.248170i
\(139\) 6.91482 + 11.9768i 0.586508 + 1.01586i 0.994686 + 0.102959i \(0.0328309\pi\)
−0.408178 + 0.912902i \(0.633836\pi\)
\(140\) 36.0799 62.4922i 3.04931 5.28156i
\(141\) 3.02631 1.74724i 0.254862 0.147144i
\(142\) 11.0931 + 19.2137i 0.930908 + 1.61238i
\(143\) 4.46208 + 3.27261i 0.373138 + 0.273669i
\(144\) 4.92618 + 8.53239i 0.410515 + 0.711033i
\(145\) 6.42900i 0.533899i
\(146\) 9.69205 0.802120
\(147\) −6.93738 12.0159i −0.572185 0.991054i
\(148\) 24.2048 + 13.9746i 1.98962 + 1.14871i
\(149\) 8.10887i 0.664304i 0.943226 + 0.332152i \(0.107775\pi\)
−0.943226 + 0.332152i \(0.892225\pi\)
\(150\) −13.8302 7.98487i −1.12923 0.651962i
\(151\) 8.90676i 0.724822i 0.932018 + 0.362411i \(0.118046\pi\)
−0.932018 + 0.362411i \(0.881954\pi\)
\(152\) −21.7091 −1.76084
\(153\) −6.95871 + 12.0528i −0.562578 + 0.974414i
\(154\) −16.1179 9.30569i −1.29882 0.749874i
\(155\) 18.3683 8.39241i 1.47538 0.674095i
\(156\) −4.66343 10.6021i −0.373373 0.848850i
\(157\) −14.8634 −1.18623 −0.593116 0.805117i \(-0.702102\pi\)
−0.593116 + 0.805117i \(0.702102\pi\)
\(158\) 7.85476 4.53495i 0.624891 0.360781i
\(159\) −3.18118 + 5.50996i −0.252284 + 0.436968i
\(160\) −0.499258 + 0.864741i −0.0394698 + 0.0683638i
\(161\) 12.7373 + 7.35390i 1.00384 + 0.579569i
\(162\) 9.03470i 0.709833i
\(163\) −2.14032 + 1.23572i −0.167643 + 0.0967887i −0.581474 0.813565i \(-0.697524\pi\)
0.413831 + 0.910354i \(0.364190\pi\)
\(164\) −26.6270 + 15.3731i −2.07922 + 1.20044i
\(165\) −2.21980 + 3.84481i −0.172811 + 0.299318i
\(166\) −5.42119 −0.420766
\(167\) −4.17246 + 2.40897i −0.322874 + 0.186412i −0.652673 0.757640i \(-0.726352\pi\)
0.329799 + 0.944051i \(0.393019\pi\)
\(168\) 9.80633 + 16.9851i 0.756575 + 1.31043i
\(169\) −3.90600 12.3993i −0.300462 0.953794i
\(170\) −52.4280 −4.02105
\(171\) −8.92669 5.15383i −0.682641 0.394123i
\(172\) −18.2179 31.5544i −1.38910 2.40600i
\(173\) −5.01013 + 8.67780i −0.380913 + 0.659761i −0.991193 0.132425i \(-0.957724\pi\)
0.610280 + 0.792186i \(0.291057\pi\)
\(174\) −3.00576 1.73537i −0.227866 0.131558i
\(175\) 34.8865 + 20.1418i 2.63717 + 1.52257i
\(176\) 5.53949 + 3.19823i 0.417555 + 0.241075i
\(177\) −4.52235 + 2.61098i −0.339921 + 0.196253i
\(178\) 19.7478 + 34.2042i 1.48016 + 2.56371i
\(179\) −2.02587 3.50890i −0.151420 0.262268i 0.780329 0.625369i \(-0.215051\pi\)
−0.931750 + 0.363101i \(0.881718\pi\)
\(180\) −29.9083 + 17.2676i −2.22924 + 1.28705i
\(181\) 4.37524 + 7.57814i 0.325209 + 0.563278i 0.981555 0.191182i \(-0.0612320\pi\)
−0.656346 + 0.754460i \(0.727899\pi\)
\(182\) 17.6045 + 40.0232i 1.30494 + 2.96672i
\(183\) 0.378088 0.654868i 0.0279491 0.0484092i
\(184\) −12.8389 7.41251i −0.946493 0.546458i
\(185\) −12.5842 + 21.7965i −0.925209 + 1.60251i
\(186\) −1.03442 + 10.8531i −0.0758477 + 0.795788i
\(187\) 9.03561i 0.660749i
\(188\) 15.2837 8.82408i 1.11468 0.643562i
\(189\) 21.1303i 1.53700i
\(190\) 38.8298i 2.81701i
\(191\) −10.6273 + 18.4070i −0.768962 + 1.33188i 0.169165 + 0.985588i \(0.445893\pi\)
−0.938126 + 0.346293i \(0.887440\pi\)
\(192\) 3.05449 + 5.29053i 0.220439 + 0.381811i
\(193\) 1.63268 0.942629i 0.117523 0.0678519i −0.440086 0.897956i \(-0.645052\pi\)
0.557609 + 0.830104i \(0.311719\pi\)
\(194\) −4.87922 −0.350308
\(195\) 9.54724 4.19943i 0.683692 0.300727i
\(196\) −35.0357 60.6837i −2.50255 4.33455i
\(197\) 4.27574i 0.304634i −0.988332 0.152317i \(-0.951327\pi\)
0.988332 0.152317i \(-0.0486734\pi\)
\(198\) 4.45364 + 7.71393i 0.316506 + 0.548205i
\(199\) −1.26983 + 2.19941i −0.0900159 + 0.155912i −0.907518 0.420014i \(-0.862025\pi\)
0.817502 + 0.575926i \(0.195358\pi\)
\(200\) −35.1646 20.3023i −2.48651 1.43559i
\(201\) 1.99089 1.14944i 0.140427 0.0810753i
\(202\) −15.4429 + 8.91594i −1.08656 + 0.627323i
\(203\) 7.58199 + 4.37746i 0.532151 + 0.307238i
\(204\) 9.45636 16.3789i 0.662078 1.14675i
\(205\) −13.8435 23.9777i −0.966873 1.67467i
\(206\) 3.02757i 0.210941i
\(207\) −3.51952 6.09600i −0.244624 0.423701i
\(208\) −6.05041 13.7554i −0.419521 0.953764i
\(209\) −6.69204 −0.462898
\(210\) −30.3802 + 17.5400i −2.09643 + 1.21038i
\(211\) 0.901731 + 1.56184i 0.0620778 + 0.107522i 0.895394 0.445275i \(-0.146894\pi\)
−0.833316 + 0.552797i \(0.813561\pi\)
\(212\) −16.0658 + 27.8269i −1.10341 + 1.91116i
\(213\) 7.20703i 0.493818i
\(214\) 9.75137i 0.666590i
\(215\) 28.4148 16.4053i 1.93787 1.11883i
\(216\) 21.2987i 1.44919i
\(217\) 2.60933 27.3769i 0.177133 1.85846i
\(218\) −1.17885 + 2.04182i −0.0798416 + 0.138290i
\(219\) −2.72660 1.57420i −0.184247 0.106375i
\(220\) −11.2106 + 19.4174i −0.755821 + 1.30912i
\(221\) 12.5542 17.1172i 0.844486 1.15142i
\(222\) −6.79369 11.7670i −0.455963 0.789750i
\(223\) −12.7421 + 7.35666i −0.853275 + 0.492638i −0.861754 0.507326i \(-0.830634\pi\)
0.00847962 + 0.999964i \(0.497301\pi\)
\(224\) 0.679884 + 1.17759i 0.0454267 + 0.0786813i
\(225\) −9.63970 16.6965i −0.642647 1.11310i
\(226\) 19.7429 11.3986i 1.31328 0.758223i
\(227\) 15.0133 + 8.66795i 0.996470 + 0.575312i 0.907202 0.420696i \(-0.138214\pi\)
0.0892678 + 0.996008i \(0.471547\pi\)
\(228\) 12.1307 + 7.00366i 0.803375 + 0.463829i
\(229\) 18.1120 + 10.4570i 1.19688 + 0.691017i 0.959858 0.280488i \(-0.0904961\pi\)
0.237020 + 0.971505i \(0.423829\pi\)
\(230\) 13.2583 22.9641i 0.874229 1.51421i
\(231\) 3.02290 + 5.23582i 0.198892 + 0.344492i
\(232\) −7.64242 4.41235i −0.501750 0.289685i
\(233\) −2.59043 −0.169705 −0.0848524 0.996394i \(-0.527042\pi\)
−0.0848524 + 0.996394i \(0.527042\pi\)
\(234\) 2.28080 20.8013i 0.149101 1.35982i
\(235\) 7.94610 + 13.7631i 0.518346 + 0.897802i
\(236\) −22.8392 + 13.1862i −1.48670 + 0.858348i
\(237\) −2.94630 −0.191383
\(238\) −35.6979 + 61.8307i −2.31395 + 4.00789i
\(239\) −4.16744 + 2.40607i −0.269569 + 0.155636i −0.628692 0.777655i \(-0.716409\pi\)
0.359123 + 0.933290i \(0.383076\pi\)
\(240\) 10.4412 6.02824i 0.673978 0.389121i
\(241\) 14.4654i 0.931799i −0.884838 0.465899i \(-0.845731\pi\)
0.884838 0.465899i \(-0.154269\pi\)
\(242\) −18.3805 10.6120i −1.18154 0.682163i
\(243\) 7.88440 13.6562i 0.505784 0.876044i
\(244\) 1.90945 3.30727i 0.122240 0.211726i
\(245\) 54.6458 31.5498i 3.49119 2.01564i
\(246\) 14.9471 0.952991
\(247\) 12.6775 + 9.29800i 0.806648 + 0.591618i
\(248\) −2.63012 + 27.5951i −0.167013 + 1.75229i
\(249\) 1.52511 + 0.880521i 0.0966497 + 0.0558007i
\(250\) 14.0508 24.3368i 0.888653 1.53919i
\(251\) 9.00164 0.568179 0.284089 0.958798i \(-0.408309\pi\)
0.284089 + 0.958798i \(0.408309\pi\)
\(252\) 47.0296i 2.96259i
\(253\) −3.95771 2.28498i −0.248819 0.143656i
\(254\) 13.7436i 0.862348i
\(255\) 14.7492 + 8.51548i 0.923633 + 0.533260i
\(256\) 16.1019 + 27.8894i 1.00637 + 1.74309i
\(257\) 19.5375 1.21872 0.609358 0.792895i \(-0.291427\pi\)
0.609358 + 0.792895i \(0.291427\pi\)
\(258\) 17.7131i 1.10277i
\(259\) 17.1370 + 29.6822i 1.06484 + 1.84436i
\(260\) 48.2163 21.2083i 2.99025 1.31528i
\(261\) −2.09502 3.62869i −0.129679 0.224610i
\(262\) 18.1082 10.4548i 1.11873 0.645899i
\(263\) −13.1603 + 22.7942i −0.811496 + 1.40555i 0.100321 + 0.994955i \(0.468013\pi\)
−0.911817 + 0.410597i \(0.865320\pi\)
\(264\) −3.04700 5.27755i −0.187530 0.324811i
\(265\) −25.0582 14.4673i −1.53931 0.888721i
\(266\) −45.7936 26.4390i −2.80779 1.62108i
\(267\) 12.8299i 0.785179i
\(268\) 10.0546 5.80500i 0.614180 0.354597i
\(269\) −8.44498 + 14.6271i −0.514900 + 0.891832i 0.484951 + 0.874541i \(0.338837\pi\)
−0.999851 + 0.0172909i \(0.994496\pi\)
\(270\) 38.0957 2.31843
\(271\) 10.0033 + 5.77541i 0.607657 + 0.350831i 0.772048 0.635564i \(-0.219232\pi\)
−0.164391 + 0.986395i \(0.552566\pi\)
\(272\) 12.2688 21.2503i 0.743908 1.28849i
\(273\) 1.54809 14.1188i 0.0936948 0.854511i
\(274\) 22.6884 + 39.2975i 1.37066 + 2.37405i
\(275\) −10.8398 6.25839i −0.653667 0.377395i
\(276\) 4.78277 + 8.28400i 0.287889 + 0.498638i
\(277\) −8.13062 14.0826i −0.488521 0.846144i 0.511391 0.859348i \(-0.329130\pi\)
−0.999913 + 0.0132041i \(0.995797\pi\)
\(278\) 33.9541i 2.03643i
\(279\) −7.63268 + 10.7226i −0.456957 + 0.641944i
\(280\) −77.2446 + 44.5972i −4.61625 + 2.66519i
\(281\) 0.767274i 0.0457717i 0.999738 + 0.0228859i \(0.00728543\pi\)
−0.999738 + 0.0228859i \(0.992715\pi\)
\(282\) −8.57954 −0.510904
\(283\) −13.3783 + 23.1719i −0.795259 + 1.37743i 0.127415 + 0.991849i \(0.459332\pi\)
−0.922675 + 0.385580i \(0.874001\pi\)
\(284\) 36.3976i 2.15980i
\(285\) −6.30681 + 10.9237i −0.373583 + 0.647066i
\(286\) −5.47003 12.4359i −0.323450 0.735350i
\(287\) −37.7039 −2.22559
\(288\) 0.650775i 0.0383473i
\(289\) 17.6619 1.03893
\(290\) 7.89212 13.6696i 0.463441 0.802704i
\(291\) 1.37264 + 0.792494i 0.0804656 + 0.0464568i
\(292\) −13.7701 7.95018i −0.805835 0.465249i
\(293\) 7.32664i 0.428027i 0.976831 + 0.214013i \(0.0686537\pi\)
−0.976831 + 0.214013i \(0.931346\pi\)
\(294\) 34.0648i 1.98670i
\(295\) −11.8742 20.5667i −0.691343 1.19744i
\(296\) −17.2736 29.9188i −1.00401 1.73899i
\(297\) 6.56553i 0.380971i
\(298\) 9.95431 17.2414i 0.576638 0.998766i
\(299\) 4.32274 + 9.82758i 0.249990 + 0.568343i
\(300\) 13.0996 + 22.6892i 0.756307 + 1.30996i
\(301\) 44.6811i 2.57537i
\(302\) 10.9338 18.9379i 0.629169 1.08975i
\(303\) 5.79258 0.332775
\(304\) 15.7386 + 9.08667i 0.902669 + 0.521156i
\(305\) 2.97820 + 1.71947i 0.170531 + 0.0984564i
\(306\) 29.5917 17.0848i 1.69165 0.976672i
\(307\) −15.4430 8.91601i −0.881378 0.508864i −0.0102654 0.999947i \(-0.503268\pi\)
−0.871112 + 0.491084i \(0.836601\pi\)
\(308\) 15.2665 + 26.4424i 0.869891 + 1.50669i
\(309\) −0.491744 + 0.851726i −0.0279743 + 0.0484530i
\(310\) −49.3577 4.70435i −2.80333 0.267189i
\(311\) −11.0665 −0.627525 −0.313762 0.949502i \(-0.601590\pi\)
−0.313762 + 0.949502i \(0.601590\pi\)
\(312\) −1.56043 + 14.2314i −0.0883420 + 0.805693i
\(313\) −8.90128 + 15.4175i −0.503130 + 0.871446i 0.496864 + 0.867829i \(0.334485\pi\)
−0.999993 + 0.00361777i \(0.998848\pi\)
\(314\) 31.6032 + 18.2461i 1.78347 + 1.02969i
\(315\) −42.3502 −2.38617
\(316\) −14.8797 −0.837047
\(317\) 27.4362 + 15.8403i 1.54097 + 0.889678i 0.998778 + 0.0494223i \(0.0157380\pi\)
0.542190 + 0.840256i \(0.317595\pi\)
\(318\) 13.5279 7.81031i 0.758605 0.437981i
\(319\) −2.35585 1.36015i −0.131903 0.0761540i
\(320\) −24.0603 + 13.8912i −1.34501 + 0.776541i
\(321\) −1.58384 + 2.74329i −0.0884013 + 0.153116i
\(322\) −18.0550 31.2723i −1.00617 1.74273i
\(323\) 25.6716i 1.42841i
\(324\) 7.41097 12.8362i 0.411720 0.713121i
\(325\) 11.8396 + 26.9170i 0.656745 + 1.49308i
\(326\) 6.06777 0.336063
\(327\) 0.663275 0.382942i 0.0366792 0.0211767i
\(328\) 38.0044 2.09844
\(329\) 21.6418 1.19315
\(330\) 9.43965 5.44999i 0.519636 0.300012i
\(331\) −23.4880 13.5608i −1.29102 0.745370i −0.312184 0.950022i \(-0.601061\pi\)
−0.978835 + 0.204652i \(0.934394\pi\)
\(332\) 7.70223 + 4.44688i 0.422715 + 0.244054i
\(333\) 16.4033i 0.898896i
\(334\) 11.8288 0.647245
\(335\) 5.22742 + 9.05415i 0.285604 + 0.494681i
\(336\) 16.4184i 0.895695i
\(337\) 0.382064 0.0208124 0.0104062 0.999946i \(-0.496688\pi\)
0.0104062 + 0.999946i \(0.496688\pi\)
\(338\) −6.91611 + 31.1588i −0.376187 + 1.69482i
\(339\) −7.40553 −0.402213
\(340\) 74.4879 + 43.0056i 4.03967 + 2.33231i
\(341\) −0.810762 + 8.50646i −0.0439052 + 0.460650i
\(342\) 12.6535 + 21.9165i 0.684223 + 1.18511i
\(343\) 51.3530i 2.77280i
\(344\) 45.0372i 2.42824i
\(345\) −7.45976 + 4.30690i −0.401620 + 0.231875i
\(346\) 21.3054 12.3007i 1.14539 0.661290i
\(347\) 14.0482 0.754148 0.377074 0.926183i \(-0.376930\pi\)
0.377074 + 0.926183i \(0.376930\pi\)
\(348\) 2.84698 + 4.93111i 0.152614 + 0.264335i
\(349\) 5.51745 + 3.18550i 0.295342 + 0.170516i 0.640349 0.768084i \(-0.278790\pi\)
−0.345006 + 0.938600i \(0.612123\pi\)
\(350\) −49.4513 85.6522i −2.64329 4.57830i
\(351\) −9.12222 + 12.4378i −0.486908 + 0.663881i
\(352\) −0.211252 0.365899i −0.0112597 0.0195025i
\(353\) −7.77461 + 4.48867i −0.413801 + 0.238908i −0.692422 0.721493i \(-0.743456\pi\)
0.278621 + 0.960401i \(0.410123\pi\)
\(354\) 12.8208 0.681417
\(355\) 32.7761 1.73957
\(356\) 64.7948i 3.43412i
\(357\) 20.0853 11.5963i 1.06303 0.613740i
\(358\) 9.94768i 0.525751i
\(359\) −11.3769 + 6.56844i −0.600448 + 0.346669i −0.769218 0.638986i \(-0.779354\pi\)
0.168770 + 0.985656i \(0.446021\pi\)
\(360\) 42.6878 2.24984
\(361\) −0.0131565 −0.000692446
\(362\) 21.4839i 1.12917i
\(363\) 3.44724 + 5.97079i 0.180933 + 0.313385i
\(364\) 7.81831 71.3042i 0.409791 3.73736i
\(365\) 7.15915 12.4000i 0.374727 0.649047i
\(366\) −1.60781 + 0.928269i −0.0840415 + 0.0485214i
\(367\) −34.3691 −1.79406 −0.897028 0.441975i \(-0.854278\pi\)
−0.897028 + 0.441975i \(0.854278\pi\)
\(368\) 6.20524 + 10.7478i 0.323471 + 0.560268i
\(369\) 15.6273 + 9.02240i 0.813523 + 0.469688i
\(370\) 53.5140 30.8963i 2.78206 1.60622i
\(371\) −34.1239 + 19.7014i −1.77162 + 1.02285i
\(372\) 10.3722 14.5712i 0.537776 0.755481i
\(373\) −13.2569 22.9616i −0.686415 1.18891i −0.972990 0.230848i \(-0.925850\pi\)
0.286574 0.958058i \(-0.407483\pi\)
\(374\) 11.0920 19.2118i 0.573552 0.993421i
\(375\) −7.90566 + 4.56434i −0.408247 + 0.235701i
\(376\) −21.8143 −1.12499
\(377\) 2.57314 + 5.84994i 0.132524 + 0.301287i
\(378\) 25.9391 44.9279i 1.33417 2.31084i
\(379\) −1.89002 + 1.09120i −0.0970836 + 0.0560513i −0.547756 0.836638i \(-0.684518\pi\)
0.450672 + 0.892690i \(0.351184\pi\)
\(380\) −31.8512 + 55.1679i −1.63393 + 2.83005i
\(381\) 2.23226 3.86639i 0.114362 0.198081i
\(382\) 45.1921 26.0917i 2.31223 1.33497i
\(383\) −9.64561 5.56890i −0.492868 0.284557i 0.232896 0.972502i \(-0.425180\pi\)
−0.725763 + 0.687944i \(0.758513\pi\)
\(384\) 15.4377i 0.787801i
\(385\) −23.8114 + 13.7475i −1.21354 + 0.700639i
\(386\) −4.62862 −0.235591
\(387\) −10.6920 + 18.5191i −0.543506 + 0.941380i
\(388\) 6.93222 + 4.00232i 0.351930 + 0.203187i
\(389\) −5.81542 + 10.0726i −0.294853 + 0.510701i −0.974951 0.222421i \(-0.928604\pi\)
0.680097 + 0.733122i \(0.261937\pi\)
\(390\) −25.4548 2.79105i −1.28896 0.141330i
\(391\) −8.76551 + 15.1823i −0.443291 + 0.767803i
\(392\) 86.6131i 4.37462i
\(393\) −6.79236 −0.342629
\(394\) −5.24882 + 9.09123i −0.264432 + 0.458009i
\(395\) 13.3992i 0.674186i
\(396\) 14.6129i 0.734326i
\(397\) 10.8654i 0.545320i −0.962110 0.272660i \(-0.912097\pi\)
0.962110 0.272660i \(-0.0879035\pi\)
\(398\) 5.39992 3.11764i 0.270673 0.156273i
\(399\) 8.58855 + 14.8758i 0.429965 + 0.744721i
\(400\) 16.9957 + 29.4374i 0.849784 + 1.47187i
\(401\) −0.281911 0.162761i −0.0140780 0.00812791i 0.492945 0.870061i \(-0.335921\pi\)
−0.507022 + 0.861933i \(0.669254\pi\)
\(402\) −5.64413 −0.281504
\(403\) 13.3549 14.9882i 0.665254 0.746617i
\(404\) 29.2542 1.45545
\(405\) 11.5590 + 6.67359i 0.574371 + 0.331613i
\(406\) −10.7474 18.6150i −0.533385 0.923849i
\(407\) −5.32476 9.22276i −0.263939 0.457155i
\(408\) −20.2454 + 11.6887i −1.00230 + 0.578677i
\(409\) 22.4371i 1.10944i −0.832035 0.554722i \(-0.812824\pi\)
0.832035 0.554722i \(-0.187176\pi\)
\(410\) 67.9763i 3.35711i
\(411\) 14.7404i 0.727090i
\(412\) −2.48345 + 4.30146i −0.122351 + 0.211918i
\(413\) −32.3403 −1.59136
\(414\) 17.2820i 0.849366i
\(415\) −4.00443 + 6.93587i −0.196570 + 0.340469i
\(416\) −0.108186 + 0.986677i −0.00530428 + 0.0483758i
\(417\) −5.51489 + 9.55208i −0.270066 + 0.467767i
\(418\) 14.2289 + 8.21504i 0.695956 + 0.401811i
\(419\) 18.4900 32.0256i 0.903296 1.56456i 0.0801086 0.996786i \(-0.474473\pi\)
0.823188 0.567769i \(-0.192193\pi\)
\(420\) 57.5508 2.80819
\(421\) 7.45593 4.30468i 0.363380 0.209797i −0.307183 0.951651i \(-0.599386\pi\)
0.670562 + 0.741853i \(0.266053\pi\)
\(422\) 4.42780i 0.215542i
\(423\) −8.96996 5.17881i −0.436134 0.251802i
\(424\) 34.3959 19.8585i 1.67041 0.964412i
\(425\) −24.0080 + 41.5832i −1.16456 + 2.01708i
\(426\) −8.84723 + 15.3238i −0.428650 + 0.742443i
\(427\) 4.05568 2.34155i 0.196268 0.113316i
\(428\) −7.99884 + 13.8544i −0.386639 + 0.669678i
\(429\) −0.481019 + 4.38697i −0.0232238 + 0.211805i
\(430\) −80.5554 −3.88473
\(431\) −18.4769 + 10.6677i −0.890003 + 0.513843i −0.873943 0.486028i \(-0.838445\pi\)
−0.0160592 + 0.999871i \(0.505112\pi\)
\(432\) −8.91489 + 15.4410i −0.428918 + 0.742907i
\(433\) −20.5856 35.6553i −0.989280 1.71348i −0.621109 0.783724i \(-0.713318\pi\)
−0.368171 0.929758i \(-0.620016\pi\)
\(434\) −39.1554 + 55.0065i −1.87952 + 2.64040i
\(435\) −4.44048 + 2.56371i −0.212905 + 0.122921i
\(436\) 3.34973 1.93397i 0.160423 0.0926202i
\(437\) −11.2445 6.49200i −0.537896 0.310554i
\(438\) 3.86493 + 6.69426i 0.184674 + 0.319864i
\(439\) 17.9590 0.857136 0.428568 0.903509i \(-0.359018\pi\)
0.428568 + 0.903509i \(0.359018\pi\)
\(440\) 24.0012 13.8571i 1.14421 0.660612i
\(441\) −20.5623 + 35.6150i −0.979158 + 1.69595i
\(442\) −47.7059 + 20.9838i −2.26914 + 0.998098i
\(443\) 8.10825 + 14.0439i 0.385235 + 0.667246i 0.991802 0.127786i \(-0.0407872\pi\)
−0.606567 + 0.795032i \(0.707454\pi\)
\(444\) 22.2909i 1.05788i
\(445\) 58.3479 2.76596
\(446\) 36.1236 1.71050
\(447\) −5.60076 + 3.23360i −0.264907 + 0.152944i
\(448\) 37.8337i 1.78748i
\(449\) 33.2956 19.2232i 1.57131 0.907199i 0.575306 0.817938i \(-0.304883\pi\)
0.996008 0.0892605i \(-0.0284504\pi\)
\(450\) 47.3341i 2.23135i
\(451\) 11.7152 0.551649
\(452\) −37.4001 −1.75915
\(453\) −6.15186 + 3.55178i −0.289040 + 0.166877i
\(454\) −21.2813 36.8602i −0.998779 1.72994i
\(455\) 64.2096 + 7.04040i 3.01019 + 0.330059i
\(456\) −8.65700 14.9944i −0.405401 0.702175i
\(457\) −6.59766 3.80916i −0.308626 0.178185i 0.337686 0.941259i \(-0.390356\pi\)
−0.646311 + 0.763074i \(0.723689\pi\)
\(458\) −25.6736 44.4681i −1.19965 2.07786i
\(459\) −25.1863 −1.17560
\(460\) −37.6739 + 21.7511i −1.75656 + 1.01415i
\(461\) 28.1627 16.2597i 1.31167 0.757291i 0.329295 0.944227i \(-0.393189\pi\)
0.982372 + 0.186936i \(0.0598557\pi\)
\(462\) 14.8435i 0.690580i
\(463\) 25.7935i 1.19873i 0.800477 + 0.599363i \(0.204579\pi\)
−0.800477 + 0.599363i \(0.795421\pi\)
\(464\) 3.69372 + 6.39771i 0.171477 + 0.297006i
\(465\) 13.1214 + 9.34023i 0.608490 + 0.433143i
\(466\) 5.50787 + 3.17997i 0.255147 + 0.147309i
\(467\) −3.62846 −0.167905 −0.0839525 0.996470i \(-0.526754\pi\)
−0.0839525 + 0.996470i \(0.526754\pi\)
\(468\) −20.3033 + 27.6828i −0.938521 + 1.27964i
\(469\) 14.2373 0.657416
\(470\) 39.0180i 1.79977i
\(471\) −5.92714 10.2661i −0.273108 0.473038i
\(472\) 32.5981 1.50045
\(473\) 13.8832i 0.638349i
\(474\) 6.26454 + 3.61683i 0.287740 + 0.166127i
\(475\) −30.7977 17.7811i −1.41310 0.815852i
\(476\) 101.437 58.5645i 4.64934 2.68430i
\(477\) 18.8579 0.863446
\(478\) 11.8146 0.540388
\(479\) −15.8080 + 9.12675i −0.722286 + 0.417012i −0.815593 0.578625i \(-0.803589\pi\)
0.0933076 + 0.995637i \(0.470256\pi\)
\(480\) −0.796364 −0.0363489
\(481\) −2.72692 + 24.8700i −0.124337 + 1.13397i
\(482\) −17.7575 + 30.7569i −0.808831 + 1.40094i
\(483\) 11.7302i 0.533741i
\(484\) 17.4095 + 30.1542i 0.791343 + 1.37065i
\(485\) −3.60410 + 6.24248i −0.163654 + 0.283456i
\(486\) −33.5282 + 19.3575i −1.52087 + 0.878074i
\(487\) 13.0341 + 7.52527i 0.590633 + 0.341002i 0.765348 0.643617i \(-0.222567\pi\)
−0.174714 + 0.984619i \(0.555900\pi\)
\(488\) −4.08801 + 2.36021i −0.185055 + 0.106842i
\(489\) −1.70701 0.985541i −0.0771935 0.0445677i
\(490\) −154.920 −6.99856
\(491\) −12.3527 −0.557470 −0.278735 0.960368i \(-0.589915\pi\)
−0.278735 + 0.960368i \(0.589915\pi\)
\(492\) −21.2363 12.2608i −0.957405 0.552758i
\(493\) −5.21774 + 9.03739i −0.234995 + 0.407023i
\(494\) −15.5412 35.3324i −0.699233 1.58968i
\(495\) 13.1589 0.591451
\(496\) 13.4571 18.9049i 0.604242 0.848855i
\(497\) 22.3170 38.6543i 1.00106 1.73388i
\(498\) −2.16182 3.74439i −0.0968737 0.167790i
\(499\) −8.44899 4.87803i −0.378229 0.218370i 0.298819 0.954310i \(-0.403407\pi\)
−0.677047 + 0.735939i \(0.736741\pi\)
\(500\) −39.9259 + 23.0512i −1.78554 + 1.03088i
\(501\) −3.32773 1.92126i −0.148672 0.0858358i
\(502\) −19.1396 11.0503i −0.854243 0.493197i
\(503\) 25.1551 1.12161 0.560806 0.827947i \(-0.310491\pi\)
0.560806 + 0.827947i \(0.310491\pi\)
\(504\) 29.0659 50.3436i 1.29470 2.24248i
\(505\) 26.3435i 1.17227i
\(506\) 5.61001 + 9.71682i 0.249395 + 0.431966i
\(507\) 7.00655 7.64238i 0.311172 0.339410i
\(508\) 11.2735 19.5264i 0.500183 0.866342i
\(509\) 19.1356i 0.848171i −0.905622 0.424086i \(-0.860596\pi\)
0.905622 0.424086i \(-0.139404\pi\)
\(510\) −20.9069 36.2118i −0.925773 1.60349i
\(511\) −9.74925 16.8862i −0.431281 0.747001i
\(512\) 40.3530i 1.78337i
\(513\) 18.6537i 0.823582i
\(514\) −41.5413 23.9839i −1.83231 1.05788i
\(515\) −3.87347 2.23635i −0.170686 0.0985454i
\(516\) 14.5297 25.1661i 0.639632 1.10788i
\(517\) −6.72448 −0.295742
\(518\) 84.1484i 3.69727i
\(519\) −7.99163 −0.350793
\(520\) −64.7214 7.09652i −2.83822 0.311203i
\(521\) 4.63805 8.03334i 0.203197 0.351947i −0.746360 0.665543i \(-0.768200\pi\)
0.949557 + 0.313595i \(0.101534\pi\)
\(522\) 10.2873i 0.450261i
\(523\) −15.1155 + 26.1808i −0.660954 + 1.14481i 0.319411 + 0.947616i \(0.396515\pi\)
−0.980365 + 0.197190i \(0.936818\pi\)
\(524\) −34.3033 −1.49855
\(525\) 32.1280i 1.40218i
\(526\) 55.9636 32.3106i 2.44013 1.40881i
\(527\) 32.6320 + 3.11020i 1.42147 + 0.135482i
\(528\) 5.10147i 0.222013i
\(529\) 7.06664 + 12.2398i 0.307245 + 0.532164i
\(530\) 35.5197 + 61.5219i 1.54288 + 2.67234i
\(531\) 13.4042 + 7.73892i 0.581693 + 0.335840i
\(532\) 43.3746 + 75.1270i 1.88053 + 3.25717i
\(533\) −22.1935 16.2773i −0.961306 0.705048i
\(534\) −15.7498 + 27.2795i −0.681561 + 1.18050i
\(535\) −12.4759 7.20298i −0.539381 0.311412i
\(536\) −14.3507 −0.619858
\(537\) 1.61572 2.79851i 0.0697236 0.120765i
\(538\) 35.9120 20.7338i 1.54828 0.893899i
\(539\) 26.6994i 1.15002i
\(540\) −54.1250 31.2491i −2.32917 1.34475i
\(541\) 31.4261 + 18.1439i 1.35111 + 0.780065i 0.988405 0.151838i \(-0.0485191\pi\)
0.362707 + 0.931903i \(0.381852\pi\)
\(542\) −14.1796 24.5598i −0.609065 1.05493i
\(543\) −3.48946 + 6.04392i −0.149747 + 0.259369i
\(544\) −1.40364 + 0.810391i −0.0601805 + 0.0347452i
\(545\) 1.74154 + 3.01644i 0.0745994 + 0.129210i
\(546\) −20.6237 + 28.1196i −0.882611 + 1.20341i
\(547\) −3.33533 5.77696i −0.142608 0.247005i 0.785870 0.618392i \(-0.212216\pi\)
−0.928478 + 0.371387i \(0.878882\pi\)
\(548\) 74.4432i 3.18006i
\(549\) −2.24130 −0.0956563
\(550\) 15.3654 + 26.6136i 0.655182 + 1.13481i
\(551\) −6.69336 3.86441i −0.285147 0.164629i
\(552\) 11.8237i 0.503248i
\(553\) −15.8022 9.12343i −0.671980 0.387968i
\(554\) 39.9240i 1.69621i
\(555\) −20.0730 −0.852050
\(556\) −27.8518 + 48.2407i −1.18118 + 2.04586i
\(557\) 2.27566 + 1.31385i 0.0964228 + 0.0556697i 0.547436 0.836848i \(-0.315604\pi\)
−0.451013 + 0.892517i \(0.648937\pi\)
\(558\) 29.3917 13.4290i 1.24425 0.568494i
\(559\) 19.2894 26.3004i 0.815856 1.11239i
\(560\) 74.6674 3.15527
\(561\) −6.24086 + 3.60316i −0.263489 + 0.152126i
\(562\) 0.941892 1.63140i 0.0397313 0.0688167i
\(563\) −9.14493 + 15.8395i −0.385413 + 0.667555i −0.991826 0.127595i \(-0.959274\pi\)
0.606413 + 0.795150i \(0.292608\pi\)
\(564\) 12.1895 + 7.03761i 0.513271 + 0.296337i
\(565\) 33.6788i 1.41688i
\(566\) 56.8910 32.8460i 2.39131 1.38062i
\(567\) 15.7409 9.08802i 0.661056 0.381661i
\(568\) −22.4949 + 38.9623i −0.943866 + 1.63482i
\(569\) −29.9439 −1.25531 −0.627656 0.778491i \(-0.715985\pi\)
−0.627656 + 0.778491i \(0.715985\pi\)
\(570\) 26.8196 15.4843i 1.12335 0.648565i
\(571\) −3.79275 6.56924i −0.158722 0.274914i 0.775686 0.631119i \(-0.217404\pi\)
−0.934408 + 0.356205i \(0.884071\pi\)
\(572\) −2.42928 + 22.1554i −0.101573 + 0.926365i
\(573\) −16.9515 −0.708158
\(574\) 80.1673 + 46.2846i 3.34612 + 1.93188i
\(575\) −12.1426 21.0316i −0.506382 0.877080i
\(576\) 9.05348 15.6811i 0.377228 0.653378i
\(577\) 21.3145 + 12.3059i 0.887335 + 0.512303i 0.873070 0.487595i \(-0.162126\pi\)
0.0142653 + 0.999898i \(0.495459\pi\)
\(578\) −37.5533 21.6814i −1.56201 0.901828i
\(579\) 1.30214 + 0.751791i 0.0541151 + 0.0312433i
\(580\) −22.4257 + 12.9475i −0.931176 + 0.537615i
\(581\) 5.45318 + 9.44519i 0.226236 + 0.391852i
\(582\) −1.94570 3.37006i −0.0806520 0.139693i
\(583\) 10.6029 6.12157i 0.439126 0.253530i
\(584\) 9.82695 + 17.0208i 0.406642 + 0.704325i
\(585\) −24.9284 18.2832i −1.03066 0.755917i
\(586\) 8.99406 15.5782i 0.371541 0.643528i
\(587\) 10.2847 + 5.93790i 0.424497 + 0.245083i 0.696999 0.717072i \(-0.254518\pi\)
−0.272503 + 0.962155i \(0.587851\pi\)
\(588\) 27.9426 48.3981i 1.15234 1.99590i
\(589\) −2.30350 + 24.1682i −0.0949142 + 0.995833i
\(590\) 58.3063i 2.40043i
\(591\) 2.95323 1.70505i 0.121480 0.0701364i
\(592\) 28.9205i 1.18863i
\(593\) 5.46819i 0.224552i 0.993677 + 0.112276i \(0.0358140\pi\)
−0.993677 + 0.112276i \(0.964186\pi\)
\(594\) −8.05973 + 13.9599i −0.330695 + 0.572780i
\(595\) 52.7375 + 91.3440i 2.16203 + 3.74474i
\(596\) −28.2854 + 16.3306i −1.15862 + 0.668928i
\(597\) −2.02550 −0.0828981
\(598\) 2.87301 26.2023i 0.117486 1.07149i
\(599\) −10.7832 18.6771i −0.440591 0.763126i 0.557142 0.830417i \(-0.311898\pi\)
−0.997733 + 0.0672910i \(0.978564\pi\)
\(600\) 32.3840i 1.32207i
\(601\) −16.8015 29.1011i −0.685348 1.18706i −0.973327 0.229421i \(-0.926317\pi\)
0.287979 0.957637i \(-0.407017\pi\)
\(602\) −54.8497 + 95.0025i −2.23551 + 3.87201i
\(603\) −5.90097 3.40693i −0.240306 0.138741i
\(604\) −31.0687 + 17.9375i −1.26417 + 0.729867i
\(605\) −27.1539 + 15.6773i −1.10396 + 0.637374i
\(606\) −12.3164 7.11087i −0.500319 0.288860i
\(607\) 12.0922 20.9443i 0.490806 0.850102i −0.509138 0.860685i \(-0.670036\pi\)
0.999944 + 0.0105836i \(0.00336891\pi\)
\(608\) −0.600199 1.03958i −0.0243413 0.0421604i
\(609\) 6.98246i 0.282944i
\(610\) −4.22158 7.31199i −0.170927 0.296054i
\(611\) 12.7389 + 9.34307i 0.515362 + 0.377980i
\(612\) −56.0571 −2.26597
\(613\) 8.14382 4.70184i 0.328926 0.189905i −0.326438 0.945219i \(-0.605849\pi\)
0.655364 + 0.755313i \(0.272515\pi\)
\(614\) 21.8903 + 37.9151i 0.883420 + 1.53013i
\(615\) 11.0409 19.1233i 0.445210 0.771127i
\(616\) 37.7409i 1.52062i
\(617\) 21.9186i 0.882411i −0.897406 0.441206i \(-0.854551\pi\)
0.897406 0.441206i \(-0.145449\pi\)
\(618\) 2.09113 1.20731i 0.0841175 0.0485652i
\(619\) 15.8020i 0.635138i −0.948235 0.317569i \(-0.897134\pi\)
0.948235 0.317569i \(-0.102866\pi\)
\(620\) 66.2667 + 47.1708i 2.66134 + 1.89443i
\(621\) 6.36927 11.0319i 0.255590 0.442695i
\(622\) 23.5300 + 13.5851i 0.943468 + 0.544711i
\(623\) 39.7287 68.8122i 1.59170 2.75690i
\(624\) 7.08804 9.66427i 0.283749 0.386880i
\(625\) −0.368432 0.638142i −0.0147373 0.0255257i
\(626\) 37.8524 21.8541i 1.51289 0.873466i
\(627\) −2.66861 4.62216i −0.106574 0.184591i
\(628\) −29.9338 51.8468i −1.19449 2.06891i
\(629\) −35.3798 + 20.4265i −1.41068 + 0.814459i
\(630\) 90.0466 + 51.9884i 3.58754 + 2.07127i
\(631\) −13.8442 7.99297i −0.551130 0.318195i 0.198448 0.980111i \(-0.436410\pi\)
−0.749578 + 0.661917i \(0.769743\pi\)
\(632\) 15.9282 + 9.19614i 0.633589 + 0.365803i
\(633\) −0.719173 + 1.24564i −0.0285846 + 0.0495099i
\(634\) −38.8905 67.3603i −1.54454 2.67522i
\(635\) 17.5835 + 10.1519i 0.697781 + 0.402864i
\(636\) −25.6265 −1.01616
\(637\) 37.0964 50.5795i 1.46981 2.00403i
\(638\) 3.33940 + 5.78401i 0.132208 + 0.228991i
\(639\) −18.4997 + 10.6808i −0.731835 + 0.422525i
\(640\) 70.2074 2.77519
\(641\) 23.7831 41.1935i 0.939376 1.62705i 0.172738 0.984968i \(-0.444739\pi\)
0.766638 0.642079i \(-0.221928\pi\)
\(642\) 6.73523 3.88859i 0.265818 0.153470i
\(643\) −35.9651 + 20.7644i −1.41832 + 0.818869i −0.996152 0.0876467i \(-0.972065\pi\)
−0.422172 + 0.906516i \(0.638732\pi\)
\(644\) 59.2407i 2.33441i
\(645\) 22.6621 + 13.0840i 0.892320 + 0.515181i
\(646\) 31.5140 54.5839i 1.23990 2.14757i
\(647\) 5.89610 10.2123i 0.231799 0.401488i −0.726538 0.687126i \(-0.758872\pi\)
0.958338 + 0.285638i \(0.0922053\pi\)
\(648\) −15.8664 + 9.16045i −0.623290 + 0.359857i
\(649\) 10.0487 0.394445
\(650\) 7.86894 71.7659i 0.308645 2.81489i
\(651\) 19.9496 9.11491i 0.781887 0.357241i
\(652\) −8.62087 4.97726i −0.337619 0.194925i
\(653\) −13.5770 + 23.5161i −0.531310 + 0.920255i 0.468023 + 0.883717i \(0.344967\pi\)
−0.999332 + 0.0365389i \(0.988367\pi\)
\(654\) −1.88037 −0.0735283
\(655\) 30.8902i 1.20698i
\(656\) −27.5523 15.9073i −1.07574 0.621077i
\(657\) 9.33184i 0.364070i
\(658\) −46.0156 26.5671i −1.79387 1.03569i
\(659\) −18.6463 32.2963i −0.726355 1.25808i −0.958414 0.285382i \(-0.907880\pi\)
0.232059 0.972702i \(-0.425454\pi\)
\(660\) −17.8820 −0.696057
\(661\) 27.3238i 1.06277i 0.847130 + 0.531386i \(0.178328\pi\)
−0.847130 + 0.531386i \(0.821672\pi\)
\(662\) 33.2941 + 57.6670i 1.29401 + 2.24129i
\(663\) 16.8290 + 1.84526i 0.653585 + 0.0716638i
\(664\) −5.49665 9.52047i −0.213311 0.369466i
\(665\) −67.6521 + 39.0589i −2.62343 + 1.51464i
\(666\) −20.1364 + 34.8773i −0.780270 + 1.35147i
\(667\) −2.63899 4.57086i −0.102182 0.176985i
\(668\) −16.8060 9.70294i −0.650243 0.375418i
\(669\) −10.1624 5.86728i −0.392902 0.226842i
\(670\) 25.6684i 0.991655i
\(671\) −1.26017 + 0.727560i −0.0486483 + 0.0280871i
\(672\) −0.542239 + 0.939186i −0.0209173 + 0.0362299i
\(673\) −15.1827 −0.585249 −0.292625 0.956227i \(-0.594529\pi\)
−0.292625 + 0.956227i \(0.594529\pi\)
\(674\) −0.812358 0.469015i −0.0312909 0.0180658i
\(675\) 17.4449 30.2155i 0.671456 1.16300i
\(676\) 35.3851 38.5962i 1.36096 1.48447i
\(677\) −5.68598 9.84840i −0.218530 0.378505i 0.735829 0.677168i \(-0.236793\pi\)
−0.954359 + 0.298663i \(0.903459\pi\)
\(678\) 15.7459 + 9.09091i 0.604718 + 0.349134i
\(679\) 4.90802 + 8.50094i 0.188352 + 0.326236i
\(680\) −53.1578 92.0720i −2.03851 3.53080i
\(681\) 13.8262i 0.529821i
\(682\) 12.1663 17.0915i 0.465870 0.654466i
\(683\) −0.164547 + 0.0950015i −0.00629623 + 0.00363513i −0.503145 0.864202i \(-0.667824\pi\)
0.496849 + 0.867837i \(0.334490\pi\)
\(684\) 41.5176i 1.58746i
\(685\) 67.0363 2.56133
\(686\) −63.0401 + 109.189i −2.40688 + 4.16884i
\(687\) 16.6799i 0.636377i
\(688\) 18.8510 32.6509i 0.718688 1.24480i
\(689\) −28.5916 3.13499i −1.08925 0.119434i
\(690\) 21.1483 0.805101
\(691\) 37.0335i 1.40882i 0.709793 + 0.704410i \(0.248788\pi\)
−0.709793 + 0.704410i \(0.751212\pi\)
\(692\) −40.3600 −1.53426
\(693\) 8.95985 15.5189i 0.340356 0.589515i
\(694\) −29.8698 17.2454i −1.13384 0.654625i
\(695\) −43.4409 25.0806i −1.64781 0.951361i
\(696\) 7.03812i 0.266779i
\(697\) 44.9413i 1.70227i
\(698\) −7.82093 13.5463i −0.296027 0.512733i
\(699\) −1.03299 1.78920i −0.0390715 0.0676737i
\(700\) 162.255i 6.13268i
\(701\) −14.4685 + 25.0601i −0.546466 + 0.946507i 0.452047 + 0.891994i \(0.350694\pi\)
−0.998513 + 0.0545126i \(0.982639\pi\)
\(702\) 34.6644 15.2474i 1.30832 0.575477i
\(703\) −15.1285 26.2033i −0.570582 0.988277i
\(704\) 11.7556i 0.443055i
\(705\) −6.33739 + 10.9767i −0.238680 + 0.413406i
\(706\) 22.0409 0.829519
\(707\) 31.0680 + 17.9371i 1.16843 + 0.674595i
\(708\) −18.2153 10.5166i −0.684573 0.395238i
\(709\) 7.58835 4.38114i 0.284986 0.164537i −0.350692 0.936491i \(-0.614054\pi\)
0.635679 + 0.771954i \(0.280720\pi\)
\(710\) −69.6897 40.2354i −2.61541 1.51001i
\(711\) 4.36641 + 7.56284i 0.163753 + 0.283629i
\(712\) −40.0454 + 69.3606i −1.50076 + 2.59940i
\(713\) −9.61448 + 13.5067i −0.360065 + 0.505829i
\(714\) −56.9416 −2.13098
\(715\) −19.9510 2.18757i −0.746126 0.0818106i
\(716\) 8.15986 14.1333i 0.304948 0.528186i
\(717\) −3.32373 1.91895i −0.124127 0.0716647i
\(718\) 32.2532 1.20368
\(719\) −26.1879 −0.976644 −0.488322 0.872664i \(-0.662391\pi\)
−0.488322 + 0.872664i \(0.662391\pi\)
\(720\) −30.9476 17.8676i −1.15335 0.665887i
\(721\) −5.27485 + 3.04544i −0.196446 + 0.113418i
\(722\) 0.0279738 + 0.0161507i 0.00104108 + 0.000601065i
\(723\) 9.99119 5.76842i 0.371576 0.214530i
\(724\) −17.6228 + 30.5235i −0.654945 + 1.13440i
\(725\) −7.22798 12.5192i −0.268441 0.464953i
\(726\) 16.9271i 0.628223i
\(727\) 8.35776 14.4761i 0.309972 0.536888i −0.668384 0.743817i \(-0.733014\pi\)
0.978356 + 0.206929i \(0.0663469\pi\)
\(728\) −52.4376 + 71.4967i −1.94347 + 2.64984i
\(729\) 1.53674 0.0569161
\(730\) −30.4441 + 17.5769i −1.12679 + 0.650551i
\(731\) 53.2578 1.96981
\(732\) 3.04576 0.112574
\(733\) −34.8785 + 20.1371i −1.28827 + 0.743781i −0.978345 0.206982i \(-0.933636\pi\)
−0.309921 + 0.950762i \(0.600303\pi\)
\(734\) 73.0769 + 42.1910i 2.69732 + 1.55730i
\(735\) 43.5826 + 25.1624i 1.60757 + 0.928130i
\(736\) 0.819747i 0.0302163i
\(737\) −4.42376 −0.162951
\(738\) −22.1515 38.3675i −0.815408 1.41233i
\(739\) 1.13910i 0.0419023i 0.999781 + 0.0209512i \(0.00666945\pi\)
−0.999781 + 0.0209512i \(0.993331\pi\)
\(740\) −101.374 −3.72659
\(741\) −1.36665 + 12.4641i −0.0502052 + 0.457879i
\(742\) 96.7406 3.55146
\(743\) 25.6749 + 14.8234i 0.941920 + 0.543818i 0.890562 0.454863i \(-0.150312\pi\)
0.0513583 + 0.998680i \(0.483645\pi\)
\(744\) −20.1086 + 9.18756i −0.737217 + 0.336832i
\(745\) −14.7057 25.4711i −0.538777 0.933189i
\(746\) 65.0957i 2.38332i
\(747\) 5.21971i 0.190979i
\(748\) −31.5181 + 18.1970i −1.15242 + 0.665348i
\(749\) −16.9896 + 9.80893i −0.620785 + 0.358410i
\(750\) 22.4124 0.818385
\(751\) 2.68173 + 4.64490i 0.0978578 + 0.169495i 0.910798 0.412853i \(-0.135468\pi\)
−0.812940 + 0.582348i \(0.802134\pi\)
\(752\) 15.8149 + 9.13071i 0.576709 + 0.332963i
\(753\) 3.58961 + 6.21739i 0.130813 + 0.226574i
\(754\) 1.71018 15.5971i 0.0622810 0.568013i
\(755\) −16.1528 27.9774i −0.587859 1.01820i
\(756\) −73.7068 + 42.5546i −2.68069 + 1.54770i
\(757\) 27.5993 1.00311 0.501557 0.865125i \(-0.332761\pi\)
0.501557 + 0.865125i \(0.332761\pi\)
\(758\) 5.35816 0.194617
\(759\) 3.64476i 0.132296i
\(760\) 68.1913 39.3702i 2.47356 1.42811i
\(761\) 28.8240i 1.04487i 0.852680 + 0.522434i \(0.174976\pi\)
−0.852680 + 0.522434i \(0.825024\pi\)
\(762\) −9.49262 + 5.48057i −0.343881 + 0.198540i
\(763\) 4.74322 0.171716
\(764\) −85.6098 −3.09725
\(765\) 50.4796i 1.82509i
\(766\) 13.6726 + 23.6816i 0.494010 + 0.855650i
\(767\) −19.0363 13.9618i −0.687362 0.504130i
\(768\) −12.8421 + 22.2431i −0.463398 + 0.802628i
\(769\) 13.8390 7.98997i 0.499048 0.288126i −0.229272 0.973362i \(-0.573635\pi\)
0.728320 + 0.685237i \(0.240301\pi\)
\(770\) 67.5049 2.43271
\(771\) 7.79104 + 13.4945i 0.280587 + 0.485991i
\(772\) 6.57618 + 3.79676i 0.236682 + 0.136648i
\(773\) −10.3747 + 5.98981i −0.373151 + 0.215439i −0.674834 0.737970i \(-0.735785\pi\)
0.301683 + 0.953408i \(0.402451\pi\)
\(774\) 45.4675 26.2507i 1.63430 0.943561i
\(775\) −26.3333 + 36.9937i −0.945920 + 1.32885i
\(776\) −4.94714 8.56869i −0.177592 0.307598i
\(777\) −13.6676 + 23.6729i −0.490321 + 0.849261i
\(778\) 24.7299 14.2778i 0.886609 0.511884i
\(779\) 33.2849 1.19255
\(780\) 33.8759 + 24.8455i 1.21295 + 0.889611i
\(781\) −6.93429 + 12.0105i −0.248128 + 0.429771i
\(782\) 37.2751 21.5208i 1.33295 0.769582i
\(783\) 3.79136 6.56682i 0.135492 0.234679i
\(784\) 36.2532 62.7924i 1.29476 2.24259i
\(785\) 46.6882 26.9554i 1.66637 0.962080i
\(786\) 14.4421 + 8.33818i 0.515134 + 0.297413i
\(787\) 48.1330i 1.71576i 0.513853 + 0.857878i \(0.328218\pi\)
−0.513853 + 0.857878i \(0.671782\pi\)
\(788\) 14.9147 8.61099i 0.531313 0.306754i
\(789\) −20.9918 −0.747329
\(790\) −16.4486 + 28.4898i −0.585215 + 1.01362i
\(791\) −39.7189 22.9317i −1.41224 0.815358i
\(792\) −9.03126 + 15.6426i −0.320912 + 0.555836i
\(793\) 3.39816 + 0.372599i 0.120672 + 0.0132314i
\(794\) −13.3382 + 23.1025i −0.473356 + 0.819876i
\(795\) 23.0767i 0.818448i
\(796\) −10.2293 −0.362569
\(797\) −1.36424 + 2.36293i −0.0483238 + 0.0836993i −0.889176 0.457566i \(-0.848721\pi\)
0.840852 + 0.541265i \(0.182055\pi\)
\(798\) 42.1726i 1.49289i
\(799\) 25.7960i 0.912599i
\(800\) 2.24522i 0.0793806i
\(801\) −32.9330 + 19.0139i −1.16363 + 0.671823i
\(802\) 0.399606 + 0.692138i 0.0141106 + 0.0244402i
\(803\) 3.02926 + 5.24683i 0.106900 + 0.185157i
\(804\) 8.01898 + 4.62976i 0.282808 + 0.163279i
\(805\) −53.3463 −1.88021
\(806\) −46.7949 + 15.4743i −1.64828 + 0.545059i
\(807\) −13.4705 −0.474185
\(808\) −31.3156 18.0801i −1.10168 0.636055i
\(809\) 16.1096 + 27.9027i 0.566385 + 0.981007i 0.996919 + 0.0784332i \(0.0249917\pi\)
−0.430535 + 0.902574i \(0.641675\pi\)
\(810\) −16.3848 28.3793i −0.575702 0.997146i
\(811\) 10.3835 5.99489i 0.364613 0.210509i −0.306490 0.951874i \(-0.599154\pi\)
0.671102 + 0.741365i \(0.265821\pi\)
\(812\) 35.2634i 1.23750i
\(813\) 9.21232i 0.323090i
\(814\) 26.1463i 0.916429i
\(815\) 4.48204 7.76311i 0.156999 0.271930i
\(816\) 19.5699 0.685085
\(817\) 39.4443i 1.37998i
\(818\) −27.5434 + 47.7066i −0.963034 + 1.66802i
\(819\) −38.5358 + 16.9503i −1.34655 + 0.592290i
\(820\) 55.7595 96.5782i 1.94720 3.37266i
\(821\) −2.24651 1.29702i −0.0784036 0.0452664i 0.460286 0.887771i \(-0.347747\pi\)
−0.538689 + 0.842505i \(0.681080\pi\)
\(822\) −18.0951 + 31.3416i −0.631138 + 1.09316i
\(823\) 30.2286 1.05370 0.526852 0.849957i \(-0.323372\pi\)
0.526852 + 0.849957i \(0.323372\pi\)
\(824\) 5.31689 3.06971i 0.185223 0.106938i
\(825\) 9.98271i 0.347553i
\(826\) 68.7631 + 39.7004i 2.39257 + 1.38135i
\(827\) 31.3850 18.1201i 1.09136 0.630098i 0.157424 0.987531i \(-0.449681\pi\)
0.933939 + 0.357433i \(0.116348\pi\)
\(828\) 14.1761 24.5537i 0.492653 0.853300i
\(829\) −17.3372 + 30.0289i −0.602146 + 1.04295i 0.390349 + 0.920667i \(0.372354\pi\)
−0.992496 + 0.122281i \(0.960979\pi\)
\(830\) 17.0287 9.83153i 0.591075 0.341257i
\(831\) 6.48455 11.2316i 0.224946 0.389619i
\(832\) −16.3333 + 22.2699i −0.566257 + 0.772070i
\(833\) 102.422 3.54873
\(834\) 23.4519 13.5400i 0.812074 0.468851i
\(835\) 8.73752 15.1338i 0.302374 0.523728i
\(836\) −13.4772 23.3433i −0.466120 0.807343i
\(837\) −23.7113 2.25996i −0.819583 0.0781155i
\(838\) −78.6283 + 45.3961i −2.71617 + 1.56818i
\(839\) −29.2180 + 16.8690i −1.00872 + 0.582382i −0.910815 0.412814i \(-0.864546\pi\)
−0.0979003 + 0.995196i \(0.531213\pi\)
\(840\) −61.6062 35.5683i −2.12561 1.22722i
\(841\) 12.9291 + 22.3939i 0.445832 + 0.772203i
\(842\) −21.1374 −0.728444
\(843\) −0.529953 + 0.305968i −0.0182525 + 0.0105381i
\(844\) −3.63203 + 6.29086i −0.125020 + 0.216540i
\(845\) 34.7560 + 31.8643i 1.19564 + 1.09617i
\(846\) 12.7148 + 22.0227i 0.437145 + 0.757157i
\(847\) 42.6984i 1.46713i
\(848\) −33.2483 −1.14175
\(849\) −21.3397 −0.732376
\(850\) 102.094 58.9437i 3.50178 2.02175i
\(851\) 20.6624i 0.708297i
\(852\) 25.1396 14.5144i 0.861270 0.497254i
\(853\) 36.2443i 1.24098i −0.784214 0.620490i \(-0.786934\pi\)
0.784214 0.620490i \(-0.213066\pi\)
\(854\) −11.4978 −0.393446
\(855\) 37.3867 1.27860
\(856\) 17.1250 9.88711i 0.585319 0.337934i
\(857\) 16.0843 + 27.8589i 0.549430 + 0.951641i 0.998314 + 0.0580508i \(0.0184885\pi\)
−0.448883 + 0.893590i \(0.648178\pi\)
\(858\) 6.40812 8.73723i 0.218770 0.298284i
\(859\) 5.10558 + 8.84312i 0.174200 + 0.301723i 0.939884 0.341494i \(-0.110933\pi\)
−0.765684 + 0.643217i \(0.777599\pi\)
\(860\) 114.450 + 66.0779i 3.90272 + 2.25324i
\(861\) −15.0353 26.0419i −0.512402 0.887506i
\(862\) 52.3818 1.78413
\(863\) −44.2327 + 25.5377i −1.50570 + 0.869315i −0.505719 + 0.862698i \(0.668773\pi\)
−0.999978 + 0.00661651i \(0.997894\pi\)
\(864\) 1.01992 0.588853i 0.0346985 0.0200332i
\(865\) 36.3443i 1.23574i
\(866\) 101.082i 3.43491i
\(867\) 7.04308 + 12.1990i 0.239196 + 0.414299i
\(868\) 100.751 46.0329i 3.41972 1.56246i
\(869\) 4.91003 + 2.83480i 0.166561 + 0.0961642i
\(870\) 12.5887 0.426796
\(871\) 8.38042 + 6.14643i 0.283960 + 0.208264i
\(872\) −4.78102 −0.161906
\(873\) 4.69789i 0.158999i
\(874\) 15.9389 + 27.6070i 0.539143 + 0.933822i
\(875\) −56.5351 −1.91123
\(876\) 12.6813i 0.428461i
\(877\) 6.35177 + 3.66719i 0.214484 + 0.123832i 0.603394 0.797444i \(-0.293815\pi\)
−0.388910 + 0.921276i \(0.627148\pi\)
\(878\) −38.1851 22.0462i −1.28868 0.744022i
\(879\) −5.06048 + 2.92167i −0.170686 + 0.0985455i
\(880\) −23.2004 −0.782086
\(881\) −4.36666 −0.147117 −0.0735583 0.997291i \(-0.523435\pi\)
−0.0735583 + 0.997291i \(0.523435\pi\)
\(882\) 87.4407 50.4839i 2.94428 1.69988i
\(883\) 36.5899 1.23135 0.615674 0.788001i \(-0.288884\pi\)
0.615674 + 0.788001i \(0.288884\pi\)
\(884\) 84.9913 + 9.31907i 2.85857 + 0.313434i
\(885\) 9.47023 16.4029i 0.318338 0.551378i
\(886\) 39.8142i 1.33758i
\(887\) 4.09896 + 7.09961i 0.137630 + 0.238382i 0.926599 0.376051i \(-0.122718\pi\)
−0.788969 + 0.614433i \(0.789385\pi\)
\(888\) 13.7765 23.8616i 0.462309 0.800743i
\(889\) 23.9450 13.8247i 0.803091 0.463665i
\(890\) −124.061 71.6269i −4.15855 2.40094i
\(891\) −4.89097 + 2.82380i −0.163854 + 0.0946009i
\(892\) −51.3232 29.6314i −1.71843 0.992134i
\(893\) −19.1053 −0.639335
\(894\) 15.8781 0.531041
\(895\) 12.7271 + 7.34797i 0.425419 + 0.245616i
\(896\) 47.8038 82.7986i 1.59701 2.76611i
\(897\) −5.06407 + 6.90467i −0.169084 + 0.230540i
\(898\) −94.3923 −3.14991
\(899\) −5.72309 + 8.03994i −0.190876 + 0.268147i
\(900\) 38.8272 67.2506i 1.29424 2.24169i
\(901\) −23.4832 40.6741i −0.782339 1.35505i
\(902\) −24.9094 14.3814i −0.829391 0.478849i
\(903\) 30.8610 17.8176i 1.02699 0.592933i
\(904\) 40.0355 + 23.1145i 1.33156 + 0.768777i
\(905\) −27.4865 15.8693i −0.913682 0.527514i
\(906\) 17.4404 0.579419
\(907\) 1.86674 3.23330i 0.0619842 0.107360i −0.833368 0.552718i \(-0.813590\pi\)
0.895352 + 0.445359i \(0.146924\pi\)
\(908\) 69.8262i 2.31726i
\(909\) −8.58457 14.8689i −0.284732 0.493171i
\(910\) −127.882 93.7921i −4.23925 3.10918i
\(911\) 23.5123 40.7246i 0.778999 1.34927i −0.153520 0.988145i \(-0.549061\pi\)
0.932519 0.361120i \(-0.117606\pi\)
\(912\) 14.4941i 0.479947i
\(913\) −1.69440 2.93478i −0.0560763 0.0971271i
\(914\) 9.35213 + 16.1984i 0.309341 + 0.535794i
\(915\) 2.74271i 0.0906712i
\(916\) 84.2381i 2.78331i
\(917\) −36.4302 21.0330i −1.20303 0.694570i
\(918\) 53.5520 + 30.9183i 1.76748 + 1.02045i
\(919\) 21.6439 37.4884i 0.713967 1.23663i −0.249390 0.968403i \(-0.580230\pi\)
0.963357 0.268224i \(-0.0864367\pi\)
\(920\) 53.7715 1.77280
\(921\) 14.2219i 0.468627i
\(922\) −79.8407 −2.62941
\(923\) 29.8240 13.1183i 0.981668 0.431794i
\(924\) −12.1758 + 21.0890i −0.400553 + 0.693778i
\(925\) 56.5926i 1.86075i
\(926\) 31.6637 54.8431i 1.04053 1.80226i
\(927\) 2.91505 0.0957427
\(928\) 0.487961i 0.0160181i
\(929\) −16.0551 + 9.26944i −0.526752 + 0.304120i −0.739693 0.672945i \(-0.765029\pi\)
0.212941 + 0.977065i \(0.431696\pi\)
\(930\) −16.4333 35.9671i −0.538868 1.17941i
\(931\) 75.8571i 2.48612i
\(932\) −5.21692 9.03597i −0.170886 0.295983i
\(933\) −4.41303 7.64360i −0.144476 0.250240i
\(934\) 7.71496 + 4.45423i 0.252441 + 0.145747i
\(935\) −16.3864 28.3821i −0.535894 0.928195i
\(936\) 38.8429 17.0854i 1.26962 0.558453i
\(937\) −18.4008 + 31.8712i −0.601129 + 1.04119i 0.391522 + 0.920169i \(0.371949\pi\)
−0.992650 + 0.121017i \(0.961385\pi\)
\(938\) −30.2718 17.4774i −0.988409 0.570658i
\(939\) −14.1984 −0.463346
\(940\) −32.0056 + 55.4353i −1.04391 + 1.80810i
\(941\) 6.16790 3.56104i 0.201068 0.116087i −0.396086 0.918214i \(-0.629632\pi\)
0.597154 + 0.802127i \(0.296298\pi\)
\(942\) 29.1042i 0.948267i
\(943\) 19.6848 + 11.3650i 0.641026 + 0.370097i
\(944\) −23.6328 13.6444i −0.769183 0.444088i
\(945\) −38.3205 66.3731i −1.24657 2.15912i
\(946\) 17.0427 29.5189i 0.554107 0.959742i
\(947\) 35.2724 20.3645i 1.14620 0.661759i 0.198241 0.980153i \(-0.436477\pi\)
0.947958 + 0.318395i \(0.103144\pi\)
\(948\) −5.93362 10.2773i −0.192715 0.333792i
\(949\) 1.55135 14.1485i 0.0503589 0.459281i
\(950\) 43.6555 + 75.6135i 1.41637 + 2.45323i
\(951\) 25.2667i 0.819329i
\(952\) −144.779 −4.69232
\(953\) 22.3361 + 38.6872i 0.723536 + 1.25320i 0.959574 + 0.281458i \(0.0908180\pi\)
−0.236037 + 0.971744i \(0.575849\pi\)
\(954\) −40.0964 23.1497i −1.29817 0.749499i
\(955\) 77.0918i 2.49463i
\(956\) −16.7858 9.69127i −0.542891 0.313438i
\(957\) 2.16957i 0.0701323i
\(958\) 44.8154 1.44792
\(959\) 45.6446 79.0588i 1.47394 2.55294i
\(960\) −19.1892 11.0789i −0.619328 0.357569i
\(961\) 30.4418 + 5.85611i 0.981995 + 0.188907i
\(962\) 36.3280 49.5319i 1.17126 1.59697i
\(963\) 9.38896 0.302555
\(964\) 50.4584 29.1322i 1.62515 0.938283i
\(965\) −3.41899 + 5.92186i −0.110061 + 0.190631i
\(966\) 14.3997 24.9411i 0.463304 0.802466i
\(967\) −10.7429 6.20241i −0.345468 0.199456i 0.317220 0.948352i \(-0.397251\pi\)
−0.662687 + 0.748896i \(0.730584\pi\)
\(968\) 43.0387i 1.38332i
\(969\) −17.7313 + 10.2372i −0.569610 + 0.328865i
\(970\) 15.3263 8.84866i 0.492099 0.284113i
\(971\) −10.5498 + 18.2728i −0.338559 + 0.586401i −0.984162 0.177272i \(-0.943273\pi\)
0.645603 + 0.763673i \(0.276606\pi\)
\(972\) 63.5142 2.03722
\(973\) −59.1573 + 34.1545i −1.89649 + 1.09494i
\(974\) −18.4758 32.0010i −0.592002 1.02538i
\(975\) −13.8701 + 18.9113i −0.444198 + 0.605648i
\(976\) 3.95161 0.126488
\(977\) −41.7936 24.1296i −1.33710 0.771973i −0.350721 0.936480i \(-0.614063\pi\)
−0.986376 + 0.164507i \(0.947397\pi\)
\(978\) 2.41967 + 4.19098i 0.0773724 + 0.134013i
\(979\) −12.3444 + 21.3811i −0.394529 + 0.683344i
\(980\) 220.104 + 127.077i 7.03098 + 4.05934i
\(981\) −1.96594 1.13504i −0.0627676 0.0362389i
\(982\) 26.2648 + 15.1640i 0.838142 + 0.483902i
\(983\) 18.9832 10.9600i 0.605470 0.349568i −0.165720 0.986173i \(-0.552995\pi\)
0.771191 + 0.636604i \(0.219662\pi\)
\(984\) 15.1551 + 26.2495i 0.483128 + 0.836803i
\(985\) 7.75422 + 13.4307i 0.247070 + 0.427938i
\(986\) 22.1883 12.8104i 0.706619 0.407967i
\(987\) 8.63018 + 14.9479i 0.274702 + 0.475797i
\(988\) −6.90198 + 62.9471i −0.219581 + 2.00261i
\(989\) −13.4682 + 23.3275i −0.428263 + 0.741773i
\(990\) −27.9790 16.1537i −0.889232 0.513398i
\(991\) −9.31430 + 16.1328i −0.295878 + 0.512477i −0.975189 0.221375i \(-0.928946\pi\)
0.679310 + 0.733851i \(0.262279\pi\)
\(992\) −1.39415 + 0.636984i −0.0442644 + 0.0202243i
\(993\) 21.6308i 0.686432i
\(994\) −94.9026 + 54.7921i −3.01013 + 1.73790i
\(995\) 9.21154i 0.292026i
\(996\) 7.09319i 0.224756i
\(997\) −5.15687 + 8.93196i −0.163320 + 0.282878i −0.936057 0.351848i \(-0.885554\pi\)
0.772738 + 0.634726i \(0.218887\pi\)
\(998\) 11.9764 + 20.7437i 0.379105 + 0.656629i
\(999\) 25.7080 14.8425i 0.813364 0.469596i
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 403.2.s.a.160.3 70
13.10 even 6 403.2.v.a.36.3 yes 70
31.25 even 3 403.2.v.a.56.3 yes 70
403.335 even 6 inner 403.2.s.a.335.3 yes 70
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.s.a.160.3 70 1.1 even 1 trivial
403.2.s.a.335.3 yes 70 403.335 even 6 inner
403.2.v.a.36.3 yes 70 13.10 even 6
403.2.v.a.56.3 yes 70 31.25 even 3