Properties

Label 273.2.br.b.17.7
Level $273$
Weight $2$
Character 273.17
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(17,273)]
 
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, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.br (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 17.7
Character \(\chi\) \(=\) 273.17
Dual form 273.2.br.b.257.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.76950 q^{2} +(0.796103 + 1.53825i) q^{3} +1.13114 q^{4} +(-1.27320 + 0.735080i) q^{5} +(-1.40871 - 2.72194i) q^{6} +(1.84076 - 1.90042i) q^{7} +1.53745 q^{8} +(-1.73244 + 2.44921i) q^{9} +O(q^{10})\) \(q-1.76950 q^{2} +(0.796103 + 1.53825i) q^{3} +1.13114 q^{4} +(-1.27320 + 0.735080i) q^{5} +(-1.40871 - 2.72194i) q^{6} +(1.84076 - 1.90042i) q^{7} +1.53745 q^{8} +(-1.73244 + 2.44921i) q^{9} +(2.25292 - 1.30072i) q^{10} +(2.02394 + 3.50557i) q^{11} +(0.900501 + 1.73997i) q^{12} +(3.05379 + 1.91686i) q^{13} +(-3.25723 + 3.36280i) q^{14} +(-2.14433 - 1.37330i) q^{15} -4.98280 q^{16} -6.22727 q^{17} +(3.06556 - 4.33389i) q^{18} +(-2.02595 + 3.50905i) q^{19} +(-1.44016 + 0.831476i) q^{20} +(4.38876 + 1.31863i) q^{21} +(-3.58137 - 6.20311i) q^{22} -0.654380i q^{23} +(1.22397 + 2.36499i) q^{24} +(-1.41932 + 2.45833i) q^{25} +(-5.40370 - 3.39188i) q^{26} +(-5.14671 - 0.715107i) q^{27} +(2.08215 - 2.14964i) q^{28} +(-0.812171 - 0.468907i) q^{29} +(3.79440 + 2.43005i) q^{30} +(1.65710 - 2.87019i) q^{31} +5.74217 q^{32} +(-3.78118 + 5.90412i) q^{33} +11.0192 q^{34} +(-0.946690 + 3.77271i) q^{35} +(-1.95963 + 2.77040i) q^{36} +10.0086i q^{37} +(3.58492 - 6.20926i) q^{38} +(-0.517475 + 6.22352i) q^{39} +(-1.95748 + 1.13015i) q^{40} +(2.97494 + 1.71758i) q^{41} +(-7.76592 - 2.33331i) q^{42} +(3.47167 + 6.01311i) q^{43} +(2.28935 + 3.96528i) q^{44} +(0.405369 - 4.39181i) q^{45} +1.15793i q^{46} +(7.24756 - 4.18438i) q^{47} +(-3.96682 - 7.66481i) q^{48} +(-0.223190 - 6.99644i) q^{49} +(2.51148 - 4.35002i) q^{50} +(-4.95755 - 9.57911i) q^{51} +(3.45426 + 2.16823i) q^{52} +(1.08605 + 0.627033i) q^{53} +(9.10711 + 1.26538i) q^{54} +(-5.15374 - 2.97551i) q^{55} +(2.83009 - 2.92181i) q^{56} +(-7.01066 - 0.322860i) q^{57} +(1.43714 + 0.829732i) q^{58} -11.2914i q^{59} +(-2.42553 - 1.55339i) q^{60} +(3.60157 + 2.07937i) q^{61} +(-2.93225 + 5.07881i) q^{62} +(1.46552 + 7.80078i) q^{63} -0.195178 q^{64} +(-5.29712 - 0.195750i) q^{65} +(6.69081 - 10.4474i) q^{66} +(-0.435969 + 0.251707i) q^{67} -7.04390 q^{68} +(1.00660 - 0.520953i) q^{69} +(1.67517 - 6.67582i) q^{70} +(2.60070 + 4.50455i) q^{71} +(-2.66355 + 3.76555i) q^{72} +(6.11936 - 10.5990i) q^{73} -17.7102i q^{74} +(-4.91145 - 0.226185i) q^{75} +(-2.29163 + 3.96921i) q^{76} +(10.3876 + 2.60658i) q^{77} +(0.915673 - 11.0125i) q^{78} +(-6.00957 - 10.4089i) q^{79} +(6.34408 - 3.66276i) q^{80} +(-2.99729 - 8.48624i) q^{81} +(-5.26416 - 3.03927i) q^{82} +14.7126i q^{83} +(4.96429 + 1.49155i) q^{84} +(7.92853 - 4.57754i) q^{85} +(-6.14312 - 10.6402i) q^{86} +(0.0747261 - 1.62262i) q^{87} +(3.11171 + 5.38965i) q^{88} -2.56014i q^{89} +(-0.717301 + 7.77131i) q^{90} +(9.26414 - 2.27502i) q^{91} -0.740193i q^{92} +(5.73430 + 0.264080i) q^{93} +(-12.8246 + 7.40427i) q^{94} -5.95693i q^{95} +(4.57136 + 8.83291i) q^{96} +(-7.00912 - 12.1402i) q^{97} +(0.394935 + 12.3802i) q^{98} +(-12.0922 - 1.11613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 6 q^{3} + 56 q^{4} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 6 q^{3} + 56 q^{4} - 6 q^{7} - 6 q^{10} - 6 q^{12} - 12 q^{13} - 9 q^{15} + 16 q^{16} - 36 q^{18} - 12 q^{21} - 18 q^{22} - 12 q^{24} + 16 q^{25} + 18 q^{28} - 22 q^{30} + 36 q^{31} - 15 q^{33} - 24 q^{34} - 4 q^{36} - 9 q^{39} - 54 q^{40} + 39 q^{42} - 12 q^{43} - 6 q^{45} - 54 q^{48} + 2 q^{49} - 14 q^{51} - 48 q^{52} + 18 q^{54} + 42 q^{55} + 30 q^{58} - 9 q^{60} + 6 q^{61} + 3 q^{63} - 28 q^{64} - 9 q^{66} + 48 q^{67} - 39 q^{69} - 84 q^{70} - 123 q^{72} - 12 q^{73} + 18 q^{76} - 11 q^{78} + 4 q^{79} - 66 q^{82} + 27 q^{84} - 30 q^{85} - 30 q^{88} + 130 q^{91} + 84 q^{94} - 24 q^{96} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76950 −1.25123 −0.625613 0.780133i \(-0.715151\pi\)
−0.625613 + 0.780133i \(0.715151\pi\)
\(3\) 0.796103 + 1.53825i 0.459630 + 0.888110i
\(4\) 1.13114 0.565569
\(5\) −1.27320 + 0.735080i −0.569390 + 0.328738i −0.756906 0.653524i \(-0.773290\pi\)
0.187516 + 0.982262i \(0.439956\pi\)
\(6\) −1.40871 2.72194i −0.575101 1.11123i
\(7\) 1.84076 1.90042i 0.695743 0.718291i
\(8\) 1.53745 0.543572
\(9\) −1.73244 + 2.44921i −0.577480 + 0.816405i
\(10\) 2.25292 1.30072i 0.712436 0.411325i
\(11\) 2.02394 + 3.50557i 0.610241 + 1.05697i 0.991200 + 0.132376i \(0.0422606\pi\)
−0.380959 + 0.924592i \(0.624406\pi\)
\(12\) 0.900501 + 1.73997i 0.259952 + 0.502287i
\(13\) 3.05379 + 1.91686i 0.846970 + 0.531640i
\(14\) −3.25723 + 3.36280i −0.870532 + 0.898745i
\(15\) −2.14433 1.37330i −0.553664 0.354584i
\(16\) −4.98280 −1.24570
\(17\) −6.22727 −1.51033 −0.755167 0.655532i \(-0.772444\pi\)
−0.755167 + 0.655532i \(0.772444\pi\)
\(18\) 3.06556 4.33389i 0.722559 1.02151i
\(19\) −2.02595 + 3.50905i −0.464784 + 0.805030i −0.999192 0.0401968i \(-0.987202\pi\)
0.534407 + 0.845227i \(0.320535\pi\)
\(20\) −1.44016 + 0.831476i −0.322029 + 0.185924i
\(21\) 4.38876 + 1.31863i 0.957706 + 0.287748i
\(22\) −3.58137 6.20311i −0.763550 1.32251i
\(23\) 0.654380i 0.136448i −0.997670 0.0682238i \(-0.978267\pi\)
0.997670 0.0682238i \(-0.0217332\pi\)
\(24\) 1.22397 + 2.36499i 0.249842 + 0.482752i
\(25\) −1.41932 + 2.45833i −0.283863 + 0.491666i
\(26\) −5.40370 3.39188i −1.05975 0.665203i
\(27\) −5.14671 0.715107i −0.990485 0.137622i
\(28\) 2.08215 2.14964i 0.393490 0.406243i
\(29\) −0.812171 0.468907i −0.150816 0.0870738i 0.422693 0.906273i \(-0.361085\pi\)
−0.573509 + 0.819199i \(0.694418\pi\)
\(30\) 3.79440 + 2.43005i 0.692759 + 0.443665i
\(31\) 1.65710 2.87019i 0.297625 0.515501i −0.677967 0.735092i \(-0.737139\pi\)
0.975592 + 0.219591i \(0.0704722\pi\)
\(32\) 5.74217 1.01508
\(33\) −3.78118 + 5.90412i −0.658219 + 1.02778i
\(34\) 11.0192 1.88977
\(35\) −0.946690 + 3.77271i −0.160020 + 0.637705i
\(36\) −1.95963 + 2.77040i −0.326605 + 0.461733i
\(37\) 10.0086i 1.64540i 0.568475 + 0.822701i \(0.307534\pi\)
−0.568475 + 0.822701i \(0.692466\pi\)
\(38\) 3.58492 6.20926i 0.581551 1.00728i
\(39\) −0.517475 + 6.22352i −0.0828623 + 0.996561i
\(40\) −1.95748 + 1.13015i −0.309505 + 0.178693i
\(41\) 2.97494 + 1.71758i 0.464608 + 0.268241i 0.713980 0.700166i \(-0.246891\pi\)
−0.249372 + 0.968408i \(0.580224\pi\)
\(42\) −7.76592 2.33331i −1.19831 0.360038i
\(43\) 3.47167 + 6.01311i 0.529424 + 0.916990i 0.999411 + 0.0343164i \(0.0109254\pi\)
−0.469987 + 0.882674i \(0.655741\pi\)
\(44\) 2.28935 + 3.96528i 0.345133 + 0.597788i
\(45\) 0.405369 4.39181i 0.0604288 0.654692i
\(46\) 1.15793i 0.170727i
\(47\) 7.24756 4.18438i 1.05717 0.610355i 0.132519 0.991181i \(-0.457694\pi\)
0.924647 + 0.380826i \(0.124360\pi\)
\(48\) −3.96682 7.66481i −0.572562 1.10632i
\(49\) −0.223190 6.99644i −0.0318843 0.999492i
\(50\) 2.51148 4.35002i 0.355177 0.615185i
\(51\) −4.95755 9.57911i −0.694195 1.34134i
\(52\) 3.45426 + 2.16823i 0.479020 + 0.300679i
\(53\) 1.08605 + 0.627033i 0.149181 + 0.0861296i 0.572732 0.819742i \(-0.305883\pi\)
−0.423552 + 0.905872i \(0.639217\pi\)
\(54\) 9.10711 + 1.26538i 1.23932 + 0.172197i
\(55\) −5.15374 2.97551i −0.694930 0.401218i
\(56\) 2.83009 2.92181i 0.378186 0.390443i
\(57\) −7.01066 0.322860i −0.928585 0.0427638i
\(58\) 1.43714 + 0.829732i 0.188705 + 0.108949i
\(59\) 11.2914i 1.47001i −0.678062 0.735005i \(-0.737180\pi\)
0.678062 0.735005i \(-0.262820\pi\)
\(60\) −2.42553 1.55339i −0.313135 0.200541i
\(61\) 3.60157 + 2.07937i 0.461134 + 0.266236i 0.712521 0.701651i \(-0.247553\pi\)
−0.251387 + 0.967887i \(0.580887\pi\)
\(62\) −2.93225 + 5.07881i −0.372396 + 0.645009i
\(63\) 1.46552 + 7.80078i 0.184638 + 0.982807i
\(64\) −0.195178 −0.0243972
\(65\) −5.29712 0.195750i −0.657027 0.0242798i
\(66\) 6.69081 10.4474i 0.823582 1.28598i
\(67\) −0.435969 + 0.251707i −0.0532622 + 0.0307509i −0.526395 0.850240i \(-0.676457\pi\)
0.473132 + 0.880991i \(0.343123\pi\)
\(68\) −7.04390 −0.854198
\(69\) 1.00660 0.520953i 0.121181 0.0627154i
\(70\) 1.67517 6.67582i 0.200221 0.797913i
\(71\) 2.60070 + 4.50455i 0.308647 + 0.534592i 0.978067 0.208293i \(-0.0667906\pi\)
−0.669420 + 0.742884i \(0.733457\pi\)
\(72\) −2.66355 + 3.76555i −0.313902 + 0.443775i
\(73\) 6.11936 10.5990i 0.716217 1.24052i −0.246272 0.969201i \(-0.579206\pi\)
0.962488 0.271323i \(-0.0874610\pi\)
\(74\) 17.7102i 2.05877i
\(75\) −4.91145 0.226185i −0.567125 0.0261176i
\(76\) −2.29163 + 3.96921i −0.262868 + 0.455300i
\(77\) 10.3876 + 2.60658i 1.18378 + 0.297047i
\(78\) 0.915673 11.0125i 0.103680 1.24692i
\(79\) −6.00957 10.4089i −0.676130 1.17109i −0.976137 0.217154i \(-0.930323\pi\)
0.300007 0.953937i \(-0.403011\pi\)
\(80\) 6.34408 3.66276i 0.709290 0.409509i
\(81\) −2.99729 8.48624i −0.333033 0.942915i
\(82\) −5.26416 3.03927i −0.581330 0.335631i
\(83\) 14.7126i 1.61492i 0.589923 + 0.807460i \(0.299158\pi\)
−0.589923 + 0.807460i \(0.700842\pi\)
\(84\) 4.96429 + 1.49155i 0.541649 + 0.162741i
\(85\) 7.92853 4.57754i 0.859970 0.496504i
\(86\) −6.14312 10.6402i −0.662430 1.14736i
\(87\) 0.0747261 1.62262i 0.00801148 0.173963i
\(88\) 3.11171 + 5.38965i 0.331710 + 0.574538i
\(89\) 2.56014i 0.271374i −0.990752 0.135687i \(-0.956676\pi\)
0.990752 0.135687i \(-0.0433242\pi\)
\(90\) −0.717301 + 7.77131i −0.0756102 + 0.819169i
\(91\) 9.26414 2.27502i 0.971146 0.238486i
\(92\) 0.740193i 0.0771705i
\(93\) 5.73430 + 0.264080i 0.594619 + 0.0273838i
\(94\) −12.8246 + 7.40427i −1.32275 + 0.763692i
\(95\) 5.95693i 0.611168i
\(96\) 4.57136 + 8.83291i 0.466562 + 0.901505i
\(97\) −7.00912 12.1402i −0.711669 1.23265i −0.964230 0.265066i \(-0.914606\pi\)
0.252562 0.967581i \(-0.418727\pi\)
\(98\) 0.394935 + 12.3802i 0.0398945 + 1.25059i
\(99\) −12.0922 1.11613i −1.21532 0.112175i
\(100\) −1.60544 + 2.78071i −0.160544 + 0.278071i
\(101\) 1.24444 + 2.15544i 0.123827 + 0.214474i 0.921274 0.388915i \(-0.127150\pi\)
−0.797447 + 0.603389i \(0.793817\pi\)
\(102\) 8.77239 + 16.9503i 0.868596 + 1.67833i
\(103\) 5.00180 2.88779i 0.492842 0.284543i −0.232911 0.972498i \(-0.574825\pi\)
0.725753 + 0.687956i \(0.241492\pi\)
\(104\) 4.69507 + 2.94708i 0.460389 + 0.288985i
\(105\) −6.55705 + 1.54722i −0.639902 + 0.150993i
\(106\) −1.92177 1.10954i −0.186659 0.107768i
\(107\) 14.2977i 1.38221i 0.722754 + 0.691106i \(0.242876\pi\)
−0.722754 + 0.691106i \(0.757124\pi\)
\(108\) −5.82164 0.808884i −0.560187 0.0778349i
\(109\) 3.15718 + 1.82280i 0.302403 + 0.174592i 0.643522 0.765428i \(-0.277473\pi\)
−0.341119 + 0.940020i \(0.610806\pi\)
\(110\) 9.11955 + 5.26518i 0.869515 + 0.502015i
\(111\) −15.3957 + 7.96786i −1.46130 + 0.756276i
\(112\) −9.17215 + 9.46942i −0.866687 + 0.894776i
\(113\) 9.39981 5.42699i 0.884260 0.510528i 0.0121995 0.999926i \(-0.496117\pi\)
0.872061 + 0.489398i \(0.162783\pi\)
\(114\) 12.4054 + 0.571301i 1.16187 + 0.0535072i
\(115\) 0.481021 + 0.833153i 0.0448554 + 0.0776919i
\(116\) −0.918677 0.530398i −0.0852970 0.0492462i
\(117\) −9.98531 + 4.15855i −0.923142 + 0.384459i
\(118\) 19.9801i 1.83931i
\(119\) −11.4629 + 11.8344i −1.05080 + 1.08486i
\(120\) −3.29681 2.11138i −0.300956 0.192742i
\(121\) −2.69266 + 4.66383i −0.244788 + 0.423985i
\(122\) −6.37299 3.67945i −0.576984 0.333122i
\(123\) −0.273718 + 5.94358i −0.0246803 + 0.535915i
\(124\) 1.87441 3.24658i 0.168327 0.291551i
\(125\) 11.5240i 1.03074i
\(126\) −2.59324 13.8035i −0.231025 1.22971i
\(127\) −6.74644 + 11.6852i −0.598650 + 1.03689i 0.394371 + 0.918952i \(0.370963\pi\)
−0.993021 + 0.117941i \(0.962371\pi\)
\(128\) −11.1390 −0.984556
\(129\) −6.48587 + 10.1274i −0.571049 + 0.891663i
\(130\) 9.37326 + 0.346380i 0.822089 + 0.0303795i
\(131\) −6.98355 12.0959i −0.610155 1.05682i −0.991214 0.132269i \(-0.957774\pi\)
0.381059 0.924551i \(-0.375560\pi\)
\(132\) −4.27704 + 6.67837i −0.372268 + 0.581278i
\(133\) 2.93937 + 10.3095i 0.254876 + 0.893945i
\(134\) 0.771449 0.445396i 0.0666430 0.0384764i
\(135\) 7.07843 2.87277i 0.609214 0.247249i
\(136\) −9.57414 −0.820976
\(137\) 17.4533 1.49114 0.745568 0.666430i \(-0.232178\pi\)
0.745568 + 0.666430i \(0.232178\pi\)
\(138\) −1.78118 + 0.921828i −0.151624 + 0.0784712i
\(139\) 5.45898 3.15175i 0.463025 0.267328i −0.250290 0.968171i \(-0.580526\pi\)
0.713315 + 0.700843i \(0.247193\pi\)
\(140\) −1.07084 + 4.26746i −0.0905022 + 0.360666i
\(141\) 12.2064 + 7.81738i 1.02797 + 0.658342i
\(142\) −4.60195 7.97081i −0.386187 0.668895i
\(143\) −0.538971 + 14.5849i −0.0450710 + 1.21965i
\(144\) 8.63241 12.2039i 0.719368 1.01700i
\(145\) 1.37874 0.114498
\(146\) −10.8282 + 18.7550i −0.896149 + 1.55218i
\(147\) 10.5846 5.91321i 0.873004 0.487713i
\(148\) 11.3211i 0.930587i
\(149\) 10.3426 17.9139i 0.847296 1.46756i −0.0363157 0.999340i \(-0.511562\pi\)
0.883612 0.468220i \(-0.155104\pi\)
\(150\) 8.69082 + 0.400236i 0.709602 + 0.0326791i
\(151\) −8.90661 5.14223i −0.724810 0.418469i 0.0917108 0.995786i \(-0.470766\pi\)
−0.816520 + 0.577317i \(0.804100\pi\)
\(152\) −3.11480 + 5.39500i −0.252644 + 0.437592i
\(153\) 10.7884 15.2519i 0.872189 1.23304i
\(154\) −18.3809 4.61235i −1.48118 0.371673i
\(155\) 4.87242i 0.391362i
\(156\) −0.585335 + 7.03966i −0.0468643 + 0.563624i
\(157\) −3.26325 1.88404i −0.260436 0.150363i 0.364098 0.931361i \(-0.381377\pi\)
−0.624533 + 0.780998i \(0.714711\pi\)
\(158\) 10.6340 + 18.4185i 0.845992 + 1.46530i
\(159\) −0.0999253 + 2.16981i −0.00792460 + 0.172077i
\(160\) −7.31090 + 4.22095i −0.577978 + 0.333696i
\(161\) −1.24360 1.20456i −0.0980091 0.0949324i
\(162\) 5.30372 + 15.0164i 0.416700 + 1.17980i
\(163\) 8.40059 + 4.85008i 0.657985 + 0.379888i 0.791509 0.611158i \(-0.209296\pi\)
−0.133524 + 0.991046i \(0.542629\pi\)
\(164\) 3.36507 + 1.94282i 0.262768 + 0.151709i
\(165\) 0.474185 10.2966i 0.0369152 0.801587i
\(166\) 26.0340i 2.02063i
\(167\) 0.655208 + 0.378285i 0.0507015 + 0.0292725i 0.525137 0.851018i \(-0.324014\pi\)
−0.474435 + 0.880291i \(0.657348\pi\)
\(168\) 6.74752 + 2.02733i 0.520582 + 0.156412i
\(169\) 5.65132 + 11.7074i 0.434717 + 0.900567i
\(170\) −14.0295 + 8.09996i −1.07602 + 0.621239i
\(171\) −5.08457 11.0412i −0.388826 0.844341i
\(172\) 3.92693 + 6.80165i 0.299426 + 0.518621i
\(173\) 0.356798 0.617993i 0.0271269 0.0469851i −0.852143 0.523309i \(-0.824698\pi\)
0.879270 + 0.476323i \(0.158031\pi\)
\(174\) −0.132228 + 2.87123i −0.0100242 + 0.217668i
\(175\) 2.05923 + 7.22249i 0.155663 + 0.545969i
\(176\) −10.0849 17.4675i −0.760177 1.31667i
\(177\) 17.3690 8.98908i 1.30553 0.675660i
\(178\) 4.53017i 0.339551i
\(179\) 0.854044 0.493082i 0.0638342 0.0368547i −0.467743 0.883864i \(-0.654933\pi\)
0.531577 + 0.847010i \(0.321599\pi\)
\(180\) 0.458528 4.96774i 0.0341766 0.370273i
\(181\) 10.9251i 0.812056i −0.913861 0.406028i \(-0.866914\pi\)
0.913861 0.406028i \(-0.133086\pi\)
\(182\) −16.3929 + 4.02564i −1.21512 + 0.298401i
\(183\) −0.331373 + 7.19552i −0.0244958 + 0.531908i
\(184\) 1.00608i 0.0741691i
\(185\) −7.35711 12.7429i −0.540905 0.936875i
\(186\) −10.1469 0.467290i −0.744004 0.0342634i
\(187\) −12.6036 21.8301i −0.921668 1.59638i
\(188\) 8.19799 4.73311i 0.597900 0.345197i
\(189\) −10.8329 + 8.46457i −0.787975 + 0.615707i
\(190\) 10.5408i 0.764710i
\(191\) 3.82542 + 2.20861i 0.276797 + 0.159809i 0.631973 0.774991i \(-0.282245\pi\)
−0.355175 + 0.934800i \(0.615579\pi\)
\(192\) −0.155381 0.300233i −0.0112137 0.0216674i
\(193\) 8.07496 4.66208i 0.581249 0.335584i −0.180381 0.983597i \(-0.557733\pi\)
0.761629 + 0.648013i \(0.224400\pi\)
\(194\) 12.4027 + 21.4820i 0.890459 + 1.54232i
\(195\) −3.91594 8.30414i −0.280426 0.594672i
\(196\) −0.252459 7.91394i −0.0180328 0.565281i
\(197\) 2.75695 4.77517i 0.196424 0.340217i −0.750942 0.660368i \(-0.770400\pi\)
0.947367 + 0.320151i \(0.103734\pi\)
\(198\) 21.3972 + 1.97499i 1.52064 + 0.140356i
\(199\) 19.5662i 1.38701i 0.720451 + 0.693506i \(0.243935\pi\)
−0.720451 + 0.693506i \(0.756065\pi\)
\(200\) −2.18213 + 3.77957i −0.154300 + 0.267256i
\(201\) −0.734266 0.470246i −0.0517911 0.0331686i
\(202\) −2.20205 3.81406i −0.154935 0.268356i
\(203\) −2.38613 + 0.680319i −0.167474 + 0.0477490i
\(204\) −5.60766 10.8353i −0.392615 0.758622i
\(205\) −5.05024 −0.352724
\(206\) −8.85070 + 5.10995i −0.616657 + 0.356027i
\(207\) 1.60272 + 1.13367i 0.111396 + 0.0787958i
\(208\) −15.2165 9.55132i −1.05507 0.662265i
\(209\) −16.4016 −1.13452
\(210\) 11.6027 2.73781i 0.800663 0.188927i
\(211\) 9.34045 16.1781i 0.643023 1.11375i −0.341731 0.939798i \(-0.611013\pi\)
0.984754 0.173951i \(-0.0556534\pi\)
\(212\) 1.22847 + 0.709260i 0.0843720 + 0.0487122i
\(213\) −4.85871 + 7.58662i −0.332913 + 0.519827i
\(214\) 25.2998i 1.72946i
\(215\) −8.84022 5.10390i −0.602898 0.348083i
\(216\) −7.91283 1.09944i −0.538400 0.0748077i
\(217\) −2.40423 8.43253i −0.163210 0.572437i
\(218\) −5.58663 3.22545i −0.378375 0.218455i
\(219\) 21.1756 + 0.975195i 1.43092 + 0.0658975i
\(220\) −5.82959 3.36571i −0.393031 0.226916i
\(221\) −19.0168 11.9368i −1.27921 0.802955i
\(222\) 27.2428 14.0991i 1.82842 0.946273i
\(223\) −4.29313 + 7.43591i −0.287489 + 0.497945i −0.973210 0.229919i \(-0.926154\pi\)
0.685721 + 0.727865i \(0.259487\pi\)
\(224\) 10.5700 10.9125i 0.706236 0.729124i
\(225\) −3.56209 7.73512i −0.237473 0.515674i
\(226\) −16.6330 + 9.60306i −1.10641 + 0.638786i
\(227\) 4.17198i 0.276904i −0.990369 0.138452i \(-0.955787\pi\)
0.990369 0.138452i \(-0.0442127\pi\)
\(228\) −7.93002 0.365199i −0.525178 0.0241859i
\(229\) 2.16262 + 3.74576i 0.142910 + 0.247527i 0.928591 0.371104i \(-0.121021\pi\)
−0.785681 + 0.618631i \(0.787687\pi\)
\(230\) −0.851168 1.47427i −0.0561243 0.0972102i
\(231\) 4.26005 + 18.0539i 0.280291 + 1.18786i
\(232\) −1.24868 0.720923i −0.0819796 0.0473309i
\(233\) 4.32000 2.49415i 0.283013 0.163397i −0.351774 0.936085i \(-0.614421\pi\)
0.634786 + 0.772688i \(0.281088\pi\)
\(234\) 17.6690 7.35857i 1.15506 0.481045i
\(235\) −6.15171 + 10.6551i −0.401293 + 0.695060i
\(236\) 12.7721i 0.831391i
\(237\) 11.2273 17.5308i 0.729289 1.13875i
\(238\) 20.2837 20.9410i 1.31479 1.35741i
\(239\) 15.4855 1.00168 0.500838 0.865541i \(-0.333025\pi\)
0.500838 + 0.865541i \(0.333025\pi\)
\(240\) 10.6848 + 6.84287i 0.689700 + 0.441705i
\(241\) −14.2965 −0.920916 −0.460458 0.887682i \(-0.652315\pi\)
−0.460458 + 0.887682i \(0.652315\pi\)
\(242\) 4.76467 8.25266i 0.306285 0.530501i
\(243\) 10.6678 11.3665i 0.684341 0.729162i
\(244\) 4.07388 + 2.35205i 0.260803 + 0.150575i
\(245\) 5.42711 + 8.74377i 0.346725 + 0.558619i
\(246\) 0.484344 10.5172i 0.0308807 0.670551i
\(247\) −12.9132 + 6.83245i −0.821645 + 0.434739i
\(248\) 2.54772 4.41279i 0.161781 0.280212i
\(249\) −22.6317 + 11.7128i −1.43423 + 0.742265i
\(250\) 20.3918i 1.28969i
\(251\) −2.21716 3.84023i −0.139946 0.242393i 0.787530 0.616276i \(-0.211359\pi\)
−0.927476 + 0.373883i \(0.878026\pi\)
\(252\) 1.65771 + 8.82376i 0.104426 + 0.555845i
\(253\) 2.29397 1.32442i 0.144221 0.0832659i
\(254\) 11.9378 20.6770i 0.749047 1.29739i
\(255\) 13.3533 + 8.55189i 0.836218 + 0.535540i
\(256\) 20.1008 1.25630
\(257\) −2.81687 −0.175712 −0.0878559 0.996133i \(-0.528001\pi\)
−0.0878559 + 0.996133i \(0.528001\pi\)
\(258\) 11.4768 17.9204i 0.714512 1.11567i
\(259\) 19.0205 + 18.4234i 1.18188 + 1.14478i
\(260\) −5.99177 0.221420i −0.371594 0.0137319i
\(261\) 2.55549 1.17683i 0.158181 0.0728437i
\(262\) 12.3574 + 21.4036i 0.763443 + 1.32232i
\(263\) −24.0024 + 13.8578i −1.48005 + 0.854508i −0.999745 0.0225935i \(-0.992808\pi\)
−0.480306 + 0.877101i \(0.659474\pi\)
\(264\) −5.81340 + 9.07732i −0.357790 + 0.558670i
\(265\) −1.84368 −0.113256
\(266\) −5.20122 18.2426i −0.318907 1.11853i
\(267\) 3.93814 2.03813i 0.241010 0.124732i
\(268\) −0.493141 + 0.284715i −0.0301234 + 0.0173918i
\(269\) −5.78651 −0.352810 −0.176405 0.984318i \(-0.556447\pi\)
−0.176405 + 0.984318i \(0.556447\pi\)
\(270\) −12.5253 + 5.08337i −0.762265 + 0.309364i
\(271\) −13.0082 −0.790189 −0.395095 0.918640i \(-0.629288\pi\)
−0.395095 + 0.918640i \(0.629288\pi\)
\(272\) 31.0293 1.88143
\(273\) 10.8748 + 12.4394i 0.658170 + 0.752869i
\(274\) −30.8836 −1.86575
\(275\) −11.4904 −0.692900
\(276\) 1.13860 0.589270i 0.0685359 0.0354699i
\(277\) 12.7590 0.766614 0.383307 0.923621i \(-0.374785\pi\)
0.383307 + 0.923621i \(0.374785\pi\)
\(278\) −9.65968 + 5.57702i −0.579349 + 0.334487i
\(279\) 4.15887 + 9.03104i 0.248985 + 0.540674i
\(280\) −1.45549 + 5.80037i −0.0869823 + 0.346639i
\(281\) 3.87071 0.230907 0.115454 0.993313i \(-0.463168\pi\)
0.115454 + 0.993313i \(0.463168\pi\)
\(282\) −21.5993 13.8329i −1.28622 0.823736i
\(283\) −15.0181 + 8.67072i −0.892735 + 0.515421i −0.874836 0.484419i \(-0.839031\pi\)
−0.0178990 + 0.999840i \(0.505698\pi\)
\(284\) 2.94175 + 5.09526i 0.174561 + 0.302348i
\(285\) 9.16327 4.74233i 0.542785 0.280911i
\(286\) 0.953709 25.8080i 0.0563940 1.52606i
\(287\) 8.74029 2.49197i 0.515923 0.147097i
\(288\) −9.94797 + 14.0638i −0.586190 + 0.828718i
\(289\) 21.7789 1.28111
\(290\) −2.43968 −0.143263
\(291\) 13.0946 20.4466i 0.767622 1.19860i
\(292\) 6.92183 11.9890i 0.405070 0.701601i
\(293\) 2.06067 1.18973i 0.120386 0.0695048i −0.438598 0.898683i \(-0.644525\pi\)
0.558984 + 0.829179i \(0.311191\pi\)
\(294\) −18.7295 + 10.4634i −1.09233 + 0.610240i
\(295\) 8.30004 + 14.3761i 0.483247 + 0.837009i
\(296\) 15.3877i 0.894394i
\(297\) −7.90978 19.4895i −0.458972 1.13089i
\(298\) −18.3012 + 31.6986i −1.06016 + 1.83625i
\(299\) 1.25435 1.99834i 0.0725410 0.115567i
\(300\) −5.55552 0.255847i −0.320748 0.0147713i
\(301\) 17.8179 + 4.47107i 1.02701 + 0.257708i
\(302\) 15.7603 + 9.09919i 0.906901 + 0.523600i
\(303\) −2.32491 + 3.63022i −0.133562 + 0.208551i
\(304\) 10.0949 17.4849i 0.578982 1.00283i
\(305\) −6.11401 −0.350087
\(306\) −19.0901 + 26.9883i −1.09131 + 1.54282i
\(307\) 5.15215 0.294049 0.147024 0.989133i \(-0.453030\pi\)
0.147024 + 0.989133i \(0.453030\pi\)
\(308\) 11.7498 + 2.94840i 0.669510 + 0.168001i
\(309\) 8.42410 + 5.39505i 0.479230 + 0.306914i
\(310\) 8.62175i 0.489682i
\(311\) 0.0551115 0.0954559i 0.00312509 0.00541281i −0.864459 0.502704i \(-0.832339\pi\)
0.867584 + 0.497291i \(0.165672\pi\)
\(312\) −0.795594 + 9.56838i −0.0450416 + 0.541703i
\(313\) −5.85152 + 3.37837i −0.330747 + 0.190957i −0.656173 0.754611i \(-0.727826\pi\)
0.325426 + 0.945568i \(0.394492\pi\)
\(314\) 5.77433 + 3.33381i 0.325864 + 0.188138i
\(315\) −7.60009 8.85465i −0.428217 0.498903i
\(316\) −6.79765 11.7739i −0.382398 0.662332i
\(317\) 3.19208 + 5.52884i 0.179285 + 0.310531i 0.941636 0.336633i \(-0.109288\pi\)
−0.762351 + 0.647164i \(0.775955\pi\)
\(318\) 0.176818 3.83947i 0.00991547 0.215307i
\(319\) 3.79616i 0.212544i
\(320\) 0.248499 0.143471i 0.0138915 0.00802028i
\(321\) −21.9935 + 11.3824i −1.22756 + 0.635306i
\(322\) 2.20055 + 2.13147i 0.122632 + 0.118782i
\(323\) 12.6161 21.8518i 0.701980 1.21587i
\(324\) −3.39035 9.59910i −0.188353 0.533283i
\(325\) −9.04656 + 4.78660i −0.501813 + 0.265513i
\(326\) −14.8649 8.58223i −0.823289 0.475326i
\(327\) −0.290485 + 6.30767i −0.0160639 + 0.348815i
\(328\) 4.57384 + 2.64071i 0.252548 + 0.145809i
\(329\) 5.38895 21.4759i 0.297103 1.18400i
\(330\) −0.839071 + 18.2198i −0.0461893 + 1.00297i
\(331\) 10.8871 + 6.28568i 0.598411 + 0.345492i 0.768416 0.639951i \(-0.221045\pi\)
−0.170006 + 0.985443i \(0.554379\pi\)
\(332\) 16.6420i 0.913348i
\(333\) −24.5132 17.3393i −1.34331 0.950187i
\(334\) −1.15939 0.669376i −0.0634391 0.0366266i
\(335\) 0.370049 0.640945i 0.0202180 0.0350185i
\(336\) −21.8683 6.57046i −1.19302 0.358448i
\(337\) −8.16338 −0.444688 −0.222344 0.974968i \(-0.571371\pi\)
−0.222344 + 0.974968i \(0.571371\pi\)
\(338\) −10.0000 20.7162i −0.543930 1.12681i
\(339\) 15.8313 + 10.1389i 0.859838 + 0.550667i
\(340\) 8.96826 5.17782i 0.486372 0.280807i
\(341\) 13.4155 0.726491
\(342\) 8.99715 + 19.5374i 0.486510 + 1.05646i
\(343\) −13.7070 12.4546i −0.740109 0.672487i
\(344\) 5.33753 + 9.24487i 0.287780 + 0.498450i
\(345\) −0.898657 + 1.40321i −0.0483821 + 0.0755461i
\(346\) −0.631356 + 1.09354i −0.0339419 + 0.0587891i
\(347\) 7.87474i 0.422738i 0.977406 + 0.211369i \(0.0677922\pi\)
−0.977406 + 0.211369i \(0.932208\pi\)
\(348\) 0.0845255 1.83541i 0.00453104 0.0983882i
\(349\) 12.4452 21.5557i 0.666175 1.15385i −0.312791 0.949822i \(-0.601264\pi\)
0.978965 0.204027i \(-0.0654029\pi\)
\(350\) −3.64381 12.7802i −0.194770 0.683131i
\(351\) −14.3462 12.0493i −0.765746 0.643144i
\(352\) 11.6218 + 20.1296i 0.619444 + 1.07291i
\(353\) −12.5215 + 7.22929i −0.666452 + 0.384776i −0.794731 0.606962i \(-0.792388\pi\)
0.128279 + 0.991738i \(0.459055\pi\)
\(354\) −30.7344 + 15.9062i −1.63351 + 0.845404i
\(355\) −6.62240 3.82345i −0.351481 0.202927i
\(356\) 2.89587i 0.153481i
\(357\) −27.3300 8.21145i −1.44646 0.434596i
\(358\) −1.51123 + 0.872510i −0.0798711 + 0.0461136i
\(359\) 6.65008 + 11.5183i 0.350978 + 0.607912i 0.986421 0.164236i \(-0.0525159\pi\)
−0.635443 + 0.772148i \(0.719183\pi\)
\(360\) 0.623236 6.75221i 0.0328474 0.355872i
\(361\) 1.29106 + 2.23619i 0.0679508 + 0.117694i
\(362\) 19.3320i 1.01607i
\(363\) −9.31779 0.429109i −0.489057 0.0225224i
\(364\) 10.4790 2.57335i 0.549250 0.134880i
\(365\) 17.9929i 0.941789i
\(366\) 0.586365 12.7325i 0.0306498 0.665538i
\(367\) 29.4619 17.0098i 1.53790 0.887905i 0.538936 0.842347i \(-0.318827\pi\)
0.998962 0.0455584i \(-0.0145067\pi\)
\(368\) 3.26064i 0.169973i
\(369\) −9.36064 + 4.31065i −0.487295 + 0.224404i
\(370\) 13.0184 + 22.5486i 0.676795 + 1.17224i
\(371\) 3.19079 0.909737i 0.165658 0.0472312i
\(372\) 6.48628 + 0.298711i 0.336298 + 0.0154874i
\(373\) −7.10859 + 12.3124i −0.368069 + 0.637514i −0.989264 0.146142i \(-0.953314\pi\)
0.621195 + 0.783656i \(0.286648\pi\)
\(374\) 22.3021 + 38.6284i 1.15322 + 1.99743i
\(375\) 17.7269 9.17432i 0.915412 0.473760i
\(376\) 11.1428 6.43329i 0.574646 0.331772i
\(377\) −1.58138 2.98876i −0.0814450 0.153929i
\(378\) 19.1688 14.9781i 0.985936 0.770389i
\(379\) −26.6898 15.4094i −1.37096 0.791527i −0.379915 0.925021i \(-0.624047\pi\)
−0.991050 + 0.133494i \(0.957380\pi\)
\(380\) 6.73811i 0.345658i
\(381\) −23.3456 1.07513i −1.19603 0.0550805i
\(382\) −6.76908 3.90813i −0.346336 0.199957i
\(383\) 26.4916 + 15.2949i 1.35366 + 0.781535i 0.988760 0.149513i \(-0.0477705\pi\)
0.364898 + 0.931047i \(0.381104\pi\)
\(384\) −8.86777 17.1346i −0.452531 0.874394i
\(385\) −15.1415 + 4.31706i −0.771684 + 0.220018i
\(386\) −14.2887 + 8.24956i −0.727274 + 0.419892i
\(387\) −20.7418 1.91449i −1.05437 0.0973192i
\(388\) −7.92828 13.7322i −0.402498 0.697146i
\(389\) −14.0905 8.13513i −0.714415 0.412467i 0.0982789 0.995159i \(-0.468666\pi\)
−0.812693 + 0.582691i \(0.802000\pi\)
\(390\) 6.92926 + 14.6942i 0.350877 + 0.744070i
\(391\) 4.07500i 0.206082i
\(392\) −0.343145 10.7567i −0.0173314 0.543296i
\(393\) 13.0469 20.3720i 0.658127 1.02763i
\(394\) −4.87842 + 8.44968i −0.245771 + 0.425689i
\(395\) 15.3027 + 8.83503i 0.769963 + 0.444539i
\(396\) −13.6780 1.26249i −0.687344 0.0634427i
\(397\) −3.41285 + 5.91122i −0.171286 + 0.296676i −0.938870 0.344273i \(-0.888126\pi\)
0.767584 + 0.640949i \(0.221459\pi\)
\(398\) 34.6224i 1.73547i
\(399\) −13.5185 + 12.7289i −0.676773 + 0.637242i
\(400\) 7.07217 12.2494i 0.353609 0.612468i
\(401\) 11.8446 0.591493 0.295747 0.955266i \(-0.404432\pi\)
0.295747 + 0.955266i \(0.404432\pi\)
\(402\) 1.29928 + 0.832102i 0.0648024 + 0.0415015i
\(403\) 10.5622 5.58854i 0.526141 0.278385i
\(404\) 1.40764 + 2.43810i 0.0700326 + 0.121300i
\(405\) 10.0542 + 8.60139i 0.499597 + 0.427406i
\(406\) 4.22227 1.20383i 0.209548 0.0597449i
\(407\) −35.0858 + 20.2568i −1.73914 + 1.00409i
\(408\) −7.62200 14.7274i −0.377345 0.729117i
\(409\) 25.5419 1.26297 0.631483 0.775390i \(-0.282446\pi\)
0.631483 + 0.775390i \(0.282446\pi\)
\(410\) 8.93641 0.441338
\(411\) 13.8946 + 26.8476i 0.685371 + 1.32429i
\(412\) 5.65772 3.26649i 0.278736 0.160928i
\(413\) −21.4583 20.7847i −1.05589 1.02275i
\(414\) −2.83601 2.00604i −0.139382 0.0985914i
\(415\) −10.8149 18.7320i −0.530885 0.919519i
\(416\) 17.5354 + 11.0069i 0.859744 + 0.539659i
\(417\) 9.19409 + 5.88818i 0.450237 + 0.288346i
\(418\) 29.0226 1.41954
\(419\) 3.45929 5.99167i 0.168997 0.292712i −0.769070 0.639164i \(-0.779280\pi\)
0.938068 + 0.346452i \(0.112614\pi\)
\(420\) −7.41692 + 1.75012i −0.361909 + 0.0853969i
\(421\) 20.2500i 0.986922i −0.869768 0.493461i \(-0.835731\pi\)
0.869768 0.493461i \(-0.164269\pi\)
\(422\) −16.5279 + 28.6272i −0.804568 + 1.39355i
\(423\) −2.30753 + 25.0000i −0.112196 + 1.21554i
\(424\) 1.66976 + 0.964034i 0.0810905 + 0.0468176i
\(425\) 8.83846 15.3087i 0.428728 0.742579i
\(426\) 8.59749 13.4245i 0.416550 0.650421i
\(427\) 10.5813 3.01688i 0.512066 0.145997i
\(428\) 16.1727i 0.781736i
\(429\) −22.8643 + 10.7820i −1.10390 + 0.520559i
\(430\) 15.6428 + 9.03137i 0.754362 + 0.435531i
\(431\) −6.59042 11.4149i −0.317449 0.549839i 0.662506 0.749057i \(-0.269493\pi\)
−0.979955 + 0.199218i \(0.936160\pi\)
\(432\) 25.6450 + 3.56324i 1.23385 + 0.171436i
\(433\) 0.0845003 0.0487863i 0.00406083 0.00234452i −0.497968 0.867195i \(-0.665920\pi\)
0.502029 + 0.864851i \(0.332587\pi\)
\(434\) 4.25429 + 14.9214i 0.204212 + 0.716249i
\(435\) 1.09762 + 2.12084i 0.0526266 + 0.101687i
\(436\) 3.57120 + 2.06184i 0.171030 + 0.0987440i
\(437\) 2.29625 + 1.32574i 0.109844 + 0.0634187i
\(438\) −37.4703 1.72561i −1.79040 0.0824528i
\(439\) 33.9619i 1.62092i −0.585797 0.810458i \(-0.699219\pi\)
0.585797 0.810458i \(-0.300781\pi\)
\(440\) −7.92364 4.57472i −0.377745 0.218091i
\(441\) 17.5224 + 11.5743i 0.834402 + 0.551156i
\(442\) 33.6503 + 21.1222i 1.60058 + 1.00468i
\(443\) 18.4704 10.6639i 0.877553 0.506655i 0.00770209 0.999970i \(-0.497548\pi\)
0.869851 + 0.493315i \(0.164215\pi\)
\(444\) −17.4147 + 9.01274i −0.826464 + 0.427726i
\(445\) 1.88191 + 3.25956i 0.0892109 + 0.154518i
\(446\) 7.59669 13.1579i 0.359714 0.623043i
\(447\) 35.7898 + 1.64822i 1.69280 + 0.0779579i
\(448\) −0.359276 + 0.370920i −0.0169742 + 0.0175243i
\(449\) 8.07975 + 13.9945i 0.381307 + 0.660443i 0.991249 0.132003i \(-0.0421408\pi\)
−0.609943 + 0.792446i \(0.708807\pi\)
\(450\) 6.30312 + 13.6873i 0.297132 + 0.645226i
\(451\) 13.9051i 0.654767i
\(452\) 10.6325 6.13867i 0.500110 0.288739i
\(453\) 0.819478 17.7944i 0.0385024 0.836052i
\(454\) 7.38233i 0.346470i
\(455\) −10.1227 + 9.70642i −0.474561 + 0.455044i
\(456\) −10.7786 0.496382i −0.504753 0.0232452i
\(457\) 31.5656i 1.47657i −0.674487 0.738287i \(-0.735635\pi\)
0.674487 0.738287i \(-0.264365\pi\)
\(458\) −3.82675 6.62813i −0.178812 0.309712i
\(459\) 32.0499 + 4.45316i 1.49596 + 0.207856i
\(460\) 0.544101 + 0.942410i 0.0253688 + 0.0439401i
\(461\) −17.0721 + 9.85656i −0.795126 + 0.459066i −0.841764 0.539846i \(-0.818483\pi\)
0.0466383 + 0.998912i \(0.485149\pi\)
\(462\) −7.53817 31.9464i −0.350707 1.48628i
\(463\) 21.7217i 1.00949i 0.863267 + 0.504747i \(0.168414\pi\)
−0.863267 + 0.504747i \(0.831586\pi\)
\(464\) 4.04689 + 2.33647i 0.187872 + 0.108468i
\(465\) −7.49500 + 3.87894i −0.347573 + 0.179882i
\(466\) −7.64425 + 4.41341i −0.354113 + 0.204447i
\(467\) −13.4911 23.3673i −0.624294 1.08131i −0.988677 0.150059i \(-0.952053\pi\)
0.364383 0.931249i \(-0.381280\pi\)
\(468\) −11.2948 + 4.70390i −0.522100 + 0.217438i
\(469\) −0.324167 + 1.29186i −0.0149686 + 0.0596525i
\(470\) 10.8855 18.8542i 0.502109 0.869678i
\(471\) 0.300244 6.51959i 0.0138345 0.300407i
\(472\) 17.3599i 0.799056i
\(473\) −14.0529 + 24.3403i −0.646153 + 1.11917i
\(474\) −19.8667 + 31.0208i −0.912506 + 1.42483i
\(475\) −5.75092 9.96089i −0.263870 0.457037i
\(476\) −12.9661 + 13.3864i −0.594302 + 0.613563i
\(477\) −3.41726 + 1.57368i −0.156466 + 0.0720537i
\(478\) −27.4017 −1.25332
\(479\) −34.3514 + 19.8328i −1.56956 + 0.906185i −0.573338 + 0.819319i \(0.694352\pi\)
−0.996220 + 0.0868655i \(0.972315\pi\)
\(480\) −12.3131 7.88571i −0.562015 0.359932i
\(481\) −19.1850 + 30.5642i −0.874762 + 1.39361i
\(482\) 25.2976 1.15227
\(483\) 0.862883 2.87192i 0.0392625 0.130677i
\(484\) −3.04577 + 5.27543i −0.138444 + 0.239792i
\(485\) 17.8480 + 10.3045i 0.810434 + 0.467905i
\(486\) −18.8767 + 20.1131i −0.856266 + 0.912347i
\(487\) 15.3235i 0.694376i 0.937796 + 0.347188i \(0.112863\pi\)
−0.937796 + 0.347188i \(0.887137\pi\)
\(488\) 5.53726 + 3.19694i 0.250660 + 0.144719i
\(489\) −0.772920 + 16.7834i −0.0349527 + 0.758971i
\(490\) −9.60327 15.4721i −0.433832 0.698959i
\(491\) −34.7344 20.0539i −1.56754 0.905021i −0.996455 0.0841315i \(-0.973188\pi\)
−0.571087 0.820889i \(-0.693478\pi\)
\(492\) −0.309613 + 6.72301i −0.0139584 + 0.303097i
\(493\) 5.05761 + 2.92001i 0.227783 + 0.131511i
\(494\) 22.8499 12.0900i 1.02806 0.543957i
\(495\) 16.2162 7.46771i 0.728865 0.335649i
\(496\) −8.25703 + 14.3016i −0.370751 + 0.642160i
\(497\) 13.3478 + 3.34938i 0.598731 + 0.150240i
\(498\) 40.0469 20.7257i 1.79454 0.928742i
\(499\) −37.5327 + 21.6695i −1.68019 + 0.970061i −0.718667 + 0.695355i \(0.755247\pi\)
−0.961528 + 0.274706i \(0.911419\pi\)
\(500\) 13.0353i 0.582955i
\(501\) −0.0602843 + 1.30903i −0.00269330 + 0.0584831i
\(502\) 3.92327 + 6.79530i 0.175104 + 0.303289i
\(503\) 4.38781 + 7.59991i 0.195643 + 0.338863i 0.947111 0.320906i \(-0.103987\pi\)
−0.751468 + 0.659769i \(0.770654\pi\)
\(504\) 2.25317 + 11.9933i 0.100364 + 0.534226i
\(505\) −3.16884 1.82953i −0.141012 0.0814130i
\(506\) −4.05919 + 2.34357i −0.180453 + 0.104185i
\(507\) −13.5099 + 18.0134i −0.599994 + 0.800005i
\(508\) −7.63115 + 13.2175i −0.338578 + 0.586434i
\(509\) 0.918134i 0.0406956i 0.999793 + 0.0203478i \(0.00647735\pi\)
−0.999793 + 0.0203478i \(0.993523\pi\)
\(510\) −23.6287 15.1326i −1.04630 0.670082i
\(511\) −8.87834 31.1397i −0.392755 1.37754i
\(512\) −13.2904 −0.587360
\(513\) 12.9363 16.6113i 0.571152 0.733406i
\(514\) 4.98446 0.219855
\(515\) −4.24551 + 7.35344i −0.187080 + 0.324031i
\(516\) −7.33641 + 11.4554i −0.322967 + 0.504297i
\(517\) 29.3373 + 16.9379i 1.29025 + 0.744927i
\(518\) −33.6568 32.6003i −1.47880 1.43237i
\(519\) 1.23468 + 0.0568602i 0.0541963 + 0.00249589i
\(520\) −8.14408 0.300957i −0.357141 0.0131978i
\(521\) −2.42918 + 4.20746i −0.106424 + 0.184332i −0.914319 0.404994i \(-0.867274\pi\)
0.807895 + 0.589327i \(0.200607\pi\)
\(522\) −4.52195 + 2.08240i −0.197920 + 0.0911440i
\(523\) 29.0461i 1.27010i 0.772472 + 0.635048i \(0.219020\pi\)
−0.772472 + 0.635048i \(0.780980\pi\)
\(524\) −7.89935 13.6821i −0.345085 0.597704i
\(525\) −9.47066 + 8.91746i −0.413333 + 0.389190i
\(526\) 42.4723 24.5214i 1.85188 1.06918i
\(527\) −10.3192 + 17.8734i −0.449513 + 0.778579i
\(528\) 18.8409 29.4191i 0.819944 1.28030i
\(529\) 22.5718 0.981382
\(530\) 3.26239 0.141709
\(531\) 27.6549 + 19.5616i 1.20012 + 0.848901i
\(532\) 3.32483 + 11.6614i 0.144150 + 0.505587i
\(533\) 5.79250 + 10.9477i 0.250901 + 0.474197i
\(534\) −6.96855 + 3.60648i −0.301559 + 0.156068i
\(535\) −10.5100 18.2038i −0.454385 0.787018i
\(536\) −0.670283 + 0.386988i −0.0289518 + 0.0167153i
\(537\) 1.43839 + 0.921191i 0.0620712 + 0.0397523i
\(538\) 10.2392 0.441445
\(539\) 24.0748 14.9428i 1.03697 0.643631i
\(540\) 8.00667 3.24950i 0.344552 0.139836i
\(541\) 30.9836 17.8884i 1.33209 0.769081i 0.346469 0.938062i \(-0.387381\pi\)
0.985619 + 0.168980i \(0.0540473\pi\)
\(542\) 23.0180 0.988706
\(543\) 16.8056 8.69750i 0.721195 0.373245i
\(544\) −35.7580 −1.53311
\(545\) −5.35961 −0.229580
\(546\) −19.2429 22.0116i −0.823520 0.942010i
\(547\) −15.8453 −0.677495 −0.338747 0.940877i \(-0.610003\pi\)
−0.338747 + 0.940877i \(0.610003\pi\)
\(548\) 19.7421 0.843340
\(549\) −11.3323 + 5.21864i −0.483652 + 0.222726i
\(550\) 20.3324 0.866975
\(551\) 3.29083 1.89996i 0.140194 0.0809411i
\(552\) 1.54760 0.800942i 0.0658704 0.0340904i
\(553\) −30.8434 7.73957i −1.31160 0.329120i
\(554\) −22.5771 −0.959209
\(555\) 13.7448 21.4617i 0.583432 0.911000i
\(556\) 6.17486 3.56506i 0.261872 0.151192i
\(557\) 11.1091 + 19.2414i 0.470706 + 0.815286i 0.999439 0.0335020i \(-0.0106660\pi\)
−0.528733 + 0.848788i \(0.677333\pi\)
\(558\) −7.35913 15.9804i −0.311537 0.676506i
\(559\) −0.924497 + 25.0175i −0.0391021 + 1.05813i
\(560\) 4.71717 18.7987i 0.199337 0.794389i
\(561\) 23.5464 36.7666i 0.994132 1.55229i
\(562\) −6.84923 −0.288917
\(563\) 19.3664 0.816195 0.408098 0.912938i \(-0.366192\pi\)
0.408098 + 0.912938i \(0.366192\pi\)
\(564\) 13.8072 + 8.84253i 0.581386 + 0.372338i
\(565\) −7.97853 + 13.8192i −0.335659 + 0.581379i
\(566\) 26.5746 15.3429i 1.11701 0.644908i
\(567\) −21.6447 9.92503i −0.908993 0.416812i
\(568\) 3.99846 + 6.92554i 0.167772 + 0.290589i
\(569\) 45.1423i 1.89246i −0.323492 0.946231i \(-0.604857\pi\)
0.323492 0.946231i \(-0.395143\pi\)
\(570\) −16.2144 + 8.39156i −0.679147 + 0.351484i
\(571\) −21.2583 + 36.8205i −0.889634 + 1.54089i −0.0493249 + 0.998783i \(0.515707\pi\)
−0.840309 + 0.542108i \(0.817626\pi\)
\(572\) −0.609650 + 16.4975i −0.0254907 + 0.689795i
\(573\) −0.351968 + 7.64273i −0.0147037 + 0.319280i
\(574\) −15.4660 + 4.40955i −0.645537 + 0.184051i
\(575\) 1.60868 + 0.928771i 0.0670866 + 0.0387324i
\(576\) 0.338134 0.478032i 0.0140889 0.0199180i
\(577\) 8.00365 13.8627i 0.333196 0.577113i −0.649940 0.759985i \(-0.725206\pi\)
0.983137 + 0.182872i \(0.0585395\pi\)
\(578\) −38.5378 −1.60296
\(579\) 13.6000 + 8.70984i 0.565195 + 0.361968i
\(580\) 1.55954 0.0647564
\(581\) 27.9601 + 27.0824i 1.15998 + 1.12357i
\(582\) −23.1710 + 36.1803i −0.960469 + 1.49972i
\(583\) 5.07631i 0.210239i
\(584\) 9.40823 16.2955i 0.389315 0.674314i
\(585\) 9.65638 12.6346i 0.399242 0.522378i
\(586\) −3.64637 + 2.10523i −0.150630 + 0.0869662i
\(587\) 0.541925 + 0.312880i 0.0223676 + 0.0129140i 0.511142 0.859496i \(-0.329223\pi\)
−0.488774 + 0.872410i \(0.662556\pi\)
\(588\) 11.9726 6.68865i 0.493744 0.275835i
\(589\) 6.71442 + 11.6297i 0.276663 + 0.479194i
\(590\) −14.6869 25.4385i −0.604652 1.04729i
\(591\) 9.54024 + 0.439353i 0.392433 + 0.0180726i
\(592\) 49.8708i 2.04968i
\(593\) −38.7786 + 22.3888i −1.59244 + 0.919398i −0.599558 + 0.800331i \(0.704657\pi\)
−0.992886 + 0.119067i \(0.962010\pi\)
\(594\) 13.9964 + 34.4866i 0.574278 + 1.41500i
\(595\) 5.89529 23.4937i 0.241683 0.963147i
\(596\) 11.6989 20.2630i 0.479204 0.830006i
\(597\) −30.0978 + 15.5767i −1.23182 + 0.637512i
\(598\) −2.21958 + 3.53607i −0.0907653 + 0.144601i
\(599\) −24.3795 14.0755i −0.996119 0.575110i −0.0890214 0.996030i \(-0.528374\pi\)
−0.907098 + 0.420920i \(0.861707\pi\)
\(600\) −7.55113 0.347750i −0.308274 0.0141968i
\(601\) −16.2551 9.38487i −0.663058 0.382817i 0.130383 0.991464i \(-0.458379\pi\)
−0.793441 + 0.608647i \(0.791713\pi\)
\(602\) −31.5289 7.91157i −1.28502 0.322451i
\(603\) 0.138807 1.50385i 0.00565266 0.0612415i
\(604\) −10.0746 5.81657i −0.409930 0.236673i
\(605\) 7.91729i 0.321884i
\(606\) 4.11393 6.42368i 0.167117 0.260944i
\(607\) 13.0101 + 7.51137i 0.528063 + 0.304877i 0.740227 0.672357i \(-0.234718\pi\)
−0.212164 + 0.977234i \(0.568051\pi\)
\(608\) −11.6333 + 20.1495i −0.471794 + 0.817172i
\(609\) −2.94611 3.12887i −0.119382 0.126788i
\(610\) 10.8188 0.438039
\(611\) 30.1534 + 1.11429i 1.21988 + 0.0450794i
\(612\) 12.2031 17.2520i 0.493283 0.697371i
\(613\) 21.5988 12.4701i 0.872367 0.503661i 0.00423279 0.999991i \(-0.498653\pi\)
0.868134 + 0.496330i \(0.165319\pi\)
\(614\) −9.11674 −0.367922
\(615\) −4.02051 7.76854i −0.162123 0.313258i
\(616\) 15.9705 + 4.00750i 0.643471 + 0.161467i
\(617\) 1.66926 + 2.89124i 0.0672018 + 0.116397i 0.897669 0.440671i \(-0.145260\pi\)
−0.830467 + 0.557068i \(0.811926\pi\)
\(618\) −14.9065 9.54656i −0.599626 0.384019i
\(619\) −2.61184 + 4.52383i −0.104979 + 0.181828i −0.913729 0.406323i \(-0.866811\pi\)
0.808751 + 0.588151i \(0.200144\pi\)
\(620\) 5.51137i 0.221342i
\(621\) −0.467951 + 3.36790i −0.0187782 + 0.135149i
\(622\) −0.0975199 + 0.168909i −0.00391019 + 0.00677265i
\(623\) −4.86534 4.71261i −0.194926 0.188807i
\(624\) 2.57848 31.0106i 0.103222 1.24142i
\(625\) 1.37450 + 2.38071i 0.0549801 + 0.0952284i
\(626\) 10.3543 5.97804i 0.413840 0.238931i
\(627\) −13.0574 25.2298i −0.521460 1.00758i
\(628\) −3.69118 2.13111i −0.147294 0.0850404i
\(629\) 62.3262i 2.48511i
\(630\) 13.4484 + 15.6683i 0.535796 + 0.624241i
\(631\) 22.4114 12.9392i 0.892183 0.515102i 0.0175274 0.999846i \(-0.494421\pi\)
0.874656 + 0.484744i \(0.161087\pi\)
\(632\) −9.23944 16.0032i −0.367525 0.636573i
\(633\) 32.3220 + 1.48851i 1.28468 + 0.0591632i
\(634\) −5.64839 9.78330i −0.224326 0.388544i
\(635\) 19.8367i 0.787195i
\(636\) −0.113029 + 2.45435i −0.00448190 + 0.0973212i
\(637\) 12.7296 21.7935i 0.504365 0.863491i
\(638\) 6.71731i 0.265941i
\(639\) −15.5382 1.43419i −0.614680 0.0567357i
\(640\) 14.1821 8.18803i 0.560596 0.323660i
\(641\) 43.9834i 1.73724i 0.495478 + 0.868620i \(0.334993\pi\)
−0.495478 + 0.868620i \(0.665007\pi\)
\(642\) 38.9175 20.1413i 1.53595 0.794912i
\(643\) −21.4046 37.0739i −0.844116 1.46205i −0.886386 0.462946i \(-0.846792\pi\)
0.0422698 0.999106i \(-0.486541\pi\)
\(644\) −1.40668 1.36252i −0.0554309 0.0536908i
\(645\) 0.813370 17.6617i 0.0320264 0.695430i
\(646\) −22.3243 + 38.6668i −0.878336 + 1.52132i
\(647\) −11.4329 19.8024i −0.449475 0.778514i 0.548877 0.835903i \(-0.315056\pi\)
−0.998352 + 0.0573895i \(0.981722\pi\)
\(648\) −4.60820 13.0472i −0.181027 0.512542i
\(649\) 39.5826 22.8530i 1.55375 0.897060i
\(650\) 16.0079 8.46990i 0.627882 0.332217i
\(651\) 11.0573 10.4115i 0.433372 0.408058i
\(652\) 9.50222 + 5.48611i 0.372136 + 0.214853i
\(653\) 26.5794i 1.04013i 0.854126 + 0.520066i \(0.174093\pi\)
−0.854126 + 0.520066i \(0.825907\pi\)
\(654\) 0.514014 11.1614i 0.0200995 0.436447i
\(655\) 17.7828 + 10.2669i 0.694833 + 0.401162i
\(656\) −14.8235 8.55838i −0.578762 0.334149i
\(657\) 15.3579 + 33.3498i 0.599168 + 1.30110i
\(658\) −9.53577 + 38.0016i −0.371743 + 1.48146i
\(659\) −13.8783 + 8.01265i −0.540622 + 0.312129i −0.745331 0.666694i \(-0.767709\pi\)
0.204709 + 0.978823i \(0.434375\pi\)
\(660\) 0.536368 11.6468i 0.0208781 0.453352i
\(661\) 17.8281 + 30.8792i 0.693433 + 1.20106i 0.970706 + 0.240270i \(0.0772359\pi\)
−0.277273 + 0.960791i \(0.589431\pi\)
\(662\) −19.2648 11.1225i −0.748747 0.432289i
\(663\) 3.22246 38.7555i 0.125150 1.50514i
\(664\) 22.6200i 0.877825i
\(665\) −11.3207 10.9653i −0.438997 0.425216i
\(666\) 43.3761 + 30.6819i 1.68079 + 1.18890i
\(667\) −0.306843 + 0.531468i −0.0118810 + 0.0205785i
\(668\) 0.741131 + 0.427892i 0.0286752 + 0.0165556i
\(669\) −14.8561 0.684162i −0.574369 0.0264512i
\(670\) −0.654803 + 1.13415i −0.0252973 + 0.0438161i
\(671\) 16.8341i 0.649872i
\(672\) 25.2010 + 7.57179i 0.972150 + 0.292088i
\(673\) −13.1015 + 22.6924i −0.505025 + 0.874729i 0.494958 + 0.868917i \(0.335183\pi\)
−0.999983 + 0.00581216i \(0.998150\pi\)
\(674\) 14.4451 0.556405
\(675\) 9.06277 11.6373i 0.348826 0.447921i
\(676\) 6.39242 + 13.2426i 0.245862 + 0.509332i
\(677\) 16.3605 + 28.3372i 0.628785 + 1.08909i 0.987796 + 0.155754i \(0.0497809\pi\)
−0.359011 + 0.933333i \(0.616886\pi\)
\(678\) −28.0135 17.9407i −1.07585 0.689009i
\(679\) −35.9735 9.02687i −1.38054 0.346419i
\(680\) 12.1898 7.03776i 0.467456 0.269886i
\(681\) 6.41756 3.32133i 0.245922 0.127274i
\(682\) −23.7388 −0.909005
\(683\) 1.68089 0.0643174 0.0321587 0.999483i \(-0.489762\pi\)
0.0321587 + 0.999483i \(0.489762\pi\)
\(684\) −5.75134 12.4891i −0.219908 0.477533i
\(685\) −22.2215 + 12.8296i −0.849038 + 0.490192i
\(686\) 24.2546 + 22.0385i 0.926045 + 0.841433i
\(687\) −4.04026 + 6.30866i −0.154146 + 0.240690i
\(688\) −17.2986 29.9621i −0.659504 1.14230i
\(689\) 2.11465 + 3.99664i 0.0805617 + 0.152260i
\(690\) 1.59018 2.48298i 0.0605370 0.0945253i
\(691\) 23.4005 0.890198 0.445099 0.895481i \(-0.353169\pi\)
0.445099 + 0.895481i \(0.353169\pi\)
\(692\) 0.403588 0.699035i 0.0153421 0.0265733i
\(693\) −24.3800 + 20.9258i −0.926121 + 0.794906i
\(694\) 13.9344i 0.528941i
\(695\) −4.63357 + 8.02557i −0.175761 + 0.304427i
\(696\) 0.114888 2.49471i 0.00435482 0.0945616i
\(697\) −18.5258 10.6959i −0.701713 0.405134i
\(698\) −22.0218 + 38.1428i −0.833536 + 1.44373i
\(699\) 7.27580 + 4.65965i 0.275196 + 0.176244i
\(700\) 2.32927 + 8.16963i 0.0880382 + 0.308783i
\(701\) 48.2236i 1.82138i 0.413090 + 0.910690i \(0.364450\pi\)
−0.413090 + 0.910690i \(0.635550\pi\)
\(702\) 25.3857 + 21.3212i 0.958121 + 0.804719i
\(703\) −35.1206 20.2769i −1.32460 0.764757i
\(704\) −0.395028 0.684208i −0.0148882 0.0257871i
\(705\) −21.2876 0.980350i −0.801736 0.0369221i
\(706\) 22.1568 12.7922i 0.833883 0.481443i
\(707\) 6.38697 + 1.60269i 0.240207 + 0.0602752i
\(708\) 19.6467 10.1679i 0.738367 0.382132i
\(709\) 10.0463 + 5.80021i 0.377295 + 0.217831i 0.676641 0.736313i \(-0.263435\pi\)
−0.299346 + 0.954145i \(0.596768\pi\)
\(710\) 11.7184 + 6.76560i 0.439782 + 0.253908i
\(711\) 35.9048 + 3.31405i 1.34654 + 0.124287i
\(712\) 3.93610i 0.147512i
\(713\) −1.87819 1.08438i −0.0703389 0.0406102i
\(714\) 48.3605 + 14.5302i 1.80985 + 0.543778i
\(715\) −10.0348 18.9656i −0.375282 0.709273i
\(716\) 0.966041 0.557744i 0.0361026 0.0208439i
\(717\) 12.3281 + 23.8207i 0.460400 + 0.889599i
\(718\) −11.7673 20.3816i −0.439153 0.760635i
\(719\) 2.66743 4.62012i 0.0994782 0.172301i −0.811991 0.583671i \(-0.801616\pi\)
0.911469 + 0.411369i \(0.134949\pi\)
\(720\) −2.01987 + 21.8835i −0.0752762 + 0.815551i
\(721\) 3.71911 14.8213i 0.138507 0.551972i
\(722\) −2.28454 3.95694i −0.0850218 0.147262i
\(723\) −11.3814 21.9916i −0.423280 0.817875i
\(724\) 12.3578i 0.459273i
\(725\) 2.30545 1.33105i 0.0856224 0.0494341i
\(726\) 16.4878 + 0.759309i 0.611921 + 0.0281806i
\(727\) 20.1065i 0.745707i 0.927890 + 0.372854i \(0.121621\pi\)
−0.927890 + 0.372854i \(0.878379\pi\)
\(728\) 14.2432 3.49773i 0.527888 0.129635i
\(729\) 25.9772 + 7.36089i 0.962120 + 0.272626i
\(730\) 31.8384i 1.17839i
\(731\) −21.6190 37.4452i −0.799608 1.38496i
\(732\) −0.374829 + 8.13912i −0.0138541 + 0.300831i
\(733\) −14.4074 24.9544i −0.532151 0.921712i −0.999295 0.0375313i \(-0.988051\pi\)
0.467145 0.884181i \(-0.345283\pi\)
\(734\) −52.1328 + 30.0989i −1.92426 + 1.11097i
\(735\) −9.12960 + 15.3092i −0.336750 + 0.564688i
\(736\) 3.75756i 0.138505i
\(737\) −1.76475 1.01888i −0.0650055 0.0375309i
\(738\) 16.5637 7.62771i 0.609717 0.280780i
\(739\) −27.8758 + 16.0941i −1.02543 + 0.592031i −0.915672 0.401927i \(-0.868341\pi\)
−0.109757 + 0.993958i \(0.535007\pi\)
\(740\) −8.32190 14.4139i −0.305919 0.529867i
\(741\) −20.7902 14.4244i −0.763749 0.529893i
\(742\) −5.64611 + 1.60978i −0.207275 + 0.0590970i
\(743\) −16.4270 + 28.4524i −0.602649 + 1.04382i 0.389770 + 0.920912i \(0.372555\pi\)
−0.992418 + 0.122906i \(0.960779\pi\)
\(744\) 8.81623 + 0.406011i 0.323219 + 0.0148851i
\(745\) 30.4104i 1.11415i
\(746\) 12.5787 21.7869i 0.460538 0.797675i
\(747\) −36.0343 25.4887i −1.31843 0.932584i
\(748\) −14.2564 24.6928i −0.521266 0.902860i
\(749\) 27.1716 + 26.3187i 0.992830 + 0.961664i
\(750\) −31.3677 + 16.2340i −1.14539 + 0.592781i
\(751\) 19.9608 0.728379 0.364190 0.931325i \(-0.381346\pi\)
0.364190 + 0.931325i \(0.381346\pi\)
\(752\) −36.1132 + 20.8499i −1.31691 + 0.760319i
\(753\) 4.14216 6.46777i 0.150949 0.235699i
\(754\) 2.79825 + 5.28862i 0.101906 + 0.192600i
\(755\) 15.1198 0.550266
\(756\) −12.2535 + 9.57459i −0.445654 + 0.348224i
\(757\) −17.0915 + 29.6033i −0.621200 + 1.07595i 0.368063 + 0.929801i \(0.380021\pi\)
−0.989263 + 0.146148i \(0.953312\pi\)
\(758\) 47.2277 + 27.2669i 1.71539 + 0.990380i
\(759\) 3.86354 + 2.47433i 0.140237 + 0.0898124i
\(760\) 9.15851i 0.332214i
\(761\) −13.5561 7.82661i −0.491408 0.283714i 0.233751 0.972297i \(-0.424900\pi\)
−0.725158 + 0.688582i \(0.758233\pi\)
\(762\) 41.3101 + 1.90244i 1.49651 + 0.0689182i
\(763\) 9.27570 2.64463i 0.335803 0.0957419i
\(764\) 4.32707 + 2.49824i 0.156548 + 0.0903830i
\(765\) −2.52434 + 27.3490i −0.0912677 + 0.988804i
\(766\) −46.8770 27.0644i −1.69373 0.977877i
\(767\) 21.6439 34.4815i 0.781516 1.24505i
\(768\) 16.0023 + 30.9201i 0.577433 + 1.11573i
\(769\) −5.51070 + 9.54482i −0.198721 + 0.344195i −0.948114 0.317931i \(-0.897012\pi\)
0.749393 + 0.662126i \(0.230345\pi\)
\(770\) 26.7930 7.63904i 0.965552 0.275292i
\(771\) −2.24252 4.33306i −0.0807624 0.156051i
\(772\) 9.13389 5.27346i 0.328736 0.189796i
\(773\) 17.6727i 0.635642i −0.948151 0.317821i \(-0.897049\pi\)
0.948151 0.317821i \(-0.102951\pi\)
\(774\) 36.7027 + 3.38770i 1.31925 + 0.121768i
\(775\) 4.70391 + 8.14741i 0.168969 + 0.292664i
\(776\) −10.7762 18.6649i −0.386843 0.670032i
\(777\) −13.1976 + 43.9253i −0.473461 + 1.57581i
\(778\) 24.9331 + 14.3951i 0.893895 + 0.516090i
\(779\) −12.0542 + 6.95947i −0.431885 + 0.249349i
\(780\) −4.42946 9.39313i −0.158600 0.336328i
\(781\) −10.5273 + 18.2339i −0.376698 + 0.652459i
\(782\) 7.21072i 0.257855i
\(783\) 3.84469 + 2.99412i 0.137398 + 0.107001i
\(784\) 1.11211 + 34.8619i 0.0397183 + 1.24507i
\(785\) 5.53967 0.197719
\(786\) −23.0864 + 36.0483i −0.823466 + 1.28580i
\(787\) −8.87825 −0.316475 −0.158238 0.987401i \(-0.550581\pi\)
−0.158238 + 0.987401i \(0.550581\pi\)
\(788\) 3.11849 5.40138i 0.111091 0.192416i
\(789\) −40.4251 25.8895i −1.43917 0.921691i
\(790\) −27.0782 15.6336i −0.963399 0.556219i
\(791\) 6.98927 27.8534i 0.248510 0.990352i
\(792\) −18.5913 1.71599i −0.660612 0.0609752i
\(793\) 7.01262 + 13.2537i 0.249025 + 0.470652i
\(794\) 6.03904 10.4599i 0.214317 0.371209i
\(795\) −1.46775 2.83604i −0.0520559 0.100584i
\(796\) 22.1321i 0.784450i
\(797\) −3.59132 6.22034i −0.127211 0.220336i 0.795384 0.606106i \(-0.207269\pi\)
−0.922595 + 0.385770i \(0.873936\pi\)
\(798\) 23.9211 22.5238i 0.846796 0.797334i
\(799\) −45.1325 + 26.0573i −1.59667 + 0.921840i
\(800\) −8.14996 + 14.1161i −0.288144 + 0.499081i
\(801\) 6.27033 + 4.43529i 0.221551 + 0.156713i
\(802\) −20.9591 −0.740092
\(803\) 49.5408 1.74826
\(804\) −0.830555 0.531913i −0.0292914 0.0187591i
\(805\) 2.46879 + 0.619494i 0.0870133 + 0.0218343i
\(806\) −18.6898 + 9.88893i −0.658321 + 0.348323i
\(807\) −4.60666 8.90111i −0.162162 0.313334i
\(808\) 1.91328 + 3.31389i 0.0673088 + 0.116582i
\(809\) 19.5390 11.2808i 0.686955 0.396614i −0.115515 0.993306i \(-0.536852\pi\)
0.802470 + 0.596692i \(0.203519\pi\)
\(810\) −17.7909 15.2202i −0.625110 0.534782i
\(811\) −21.8927 −0.768757 −0.384379 0.923176i \(-0.625584\pi\)
−0.384379 + 0.923176i \(0.625584\pi\)
\(812\) −2.69904 + 0.769534i −0.0947179 + 0.0270054i
\(813\) −10.3558 20.0098i −0.363195 0.701775i
\(814\) 62.0843 35.8444i 2.17605 1.25635i
\(815\) −14.2608 −0.499534
\(816\) 24.7025 + 47.7308i 0.864759 + 1.67091i
\(817\) −28.1337 −0.984273
\(818\) −45.1965 −1.58026
\(819\) −10.4776 + 26.6312i −0.366116 + 0.930569i
\(820\) −5.71252 −0.199490
\(821\) −28.5392 −0.996026 −0.498013 0.867170i \(-0.665937\pi\)
−0.498013 + 0.867170i \(0.665937\pi\)
\(822\) −24.5865 47.5068i −0.857554 1.65699i
\(823\) −32.4802 −1.13219 −0.566095 0.824340i \(-0.691546\pi\)
−0.566095 + 0.824340i \(0.691546\pi\)
\(824\) 7.69004 4.43985i 0.267895 0.154669i
\(825\) −9.14757 17.6752i −0.318478 0.615371i
\(826\) 37.9705 + 36.7786i 1.32116 + 1.27969i
\(827\) 7.10236 0.246973 0.123487 0.992346i \(-0.460592\pi\)
0.123487 + 0.992346i \(0.460592\pi\)
\(828\) 1.81289 + 1.28234i 0.0630023 + 0.0445644i
\(829\) 22.5580 13.0239i 0.783472 0.452338i −0.0541873 0.998531i \(-0.517257\pi\)
0.837659 + 0.546193i \(0.183923\pi\)
\(830\) 19.1371 + 33.1464i 0.664257 + 1.15053i
\(831\) 10.1575 + 19.6266i 0.352359 + 0.680838i
\(832\) −0.596033 0.374128i −0.0206637 0.0129705i
\(833\) 1.38986 + 43.5687i 0.0481560 + 1.50957i
\(834\) −16.2690 10.4192i −0.563348 0.360786i
\(835\) −1.11228 −0.0384919
\(836\) −18.5525 −0.641650
\(837\) −10.5811 + 13.5870i −0.365737 + 0.469636i
\(838\) −6.12122 + 10.6023i −0.211454 + 0.366249i
\(839\) 22.4098 12.9383i 0.773672 0.446680i −0.0605109 0.998168i \(-0.519273\pi\)
0.834183 + 0.551488i \(0.185940\pi\)
\(840\) −10.0812 + 2.37878i −0.347833 + 0.0820756i
\(841\) −14.0603 24.3531i −0.484836 0.839761i
\(842\) 35.8323i 1.23486i
\(843\) 3.08148 + 5.95413i 0.106132 + 0.205071i
\(844\) 10.5653 18.2997i 0.363674 0.629901i
\(845\) −15.8011 10.7516i −0.543574 0.369866i
\(846\) 4.08318 44.2376i 0.140383 1.52092i
\(847\) 3.90668 + 13.7022i 0.134235 + 0.470813i
\(848\) −5.41159 3.12438i −0.185835 0.107292i
\(849\) −25.2937 16.1989i −0.868079 0.555944i
\(850\) −15.6397 + 27.0887i −0.536437 + 0.929135i
\(851\) 6.54941 0.224511
\(852\) −5.49587 + 8.58151i −0.188285 + 0.293998i
\(853\) −16.5705 −0.567365 −0.283682 0.958918i \(-0.591556\pi\)
−0.283682 + 0.958918i \(0.591556\pi\)
\(854\) −18.7237 + 5.33837i −0.640711 + 0.182675i
\(855\) 14.5898 + 10.3200i 0.498961 + 0.352938i
\(856\) 21.9821i 0.751332i
\(857\) 8.47666 14.6820i 0.289557 0.501528i −0.684147 0.729344i \(-0.739825\pi\)
0.973704 + 0.227816i \(0.0731586\pi\)
\(858\) 40.4584 19.0788i 1.38123 0.651338i
\(859\) 24.1112 13.9206i 0.822663 0.474965i −0.0286709 0.999589i \(-0.509127\pi\)
0.851334 + 0.524624i \(0.175794\pi\)
\(860\) −9.99950 5.77322i −0.340980 0.196865i
\(861\) 10.7915 + 11.4609i 0.367772 + 0.390586i
\(862\) 11.6618 + 20.1988i 0.397201 + 0.687973i
\(863\) 7.09342 + 12.2862i 0.241463 + 0.418226i 0.961131 0.276092i \(-0.0890395\pi\)
−0.719668 + 0.694318i \(0.755706\pi\)
\(864\) −29.5533 4.10626i −1.00542 0.139698i
\(865\) 1.04910i 0.0356705i
\(866\) −0.149524 + 0.0863274i −0.00508102 + 0.00293353i
\(867\) 17.3382 + 33.5014i 0.588837 + 1.13777i
\(868\) −2.71951 9.53835i −0.0923063 0.323753i
\(869\) 24.3260 42.1339i 0.825204 1.42930i
\(870\) −1.94223 3.75284i −0.0658478 0.127233i
\(871\) −1.81385 0.0670290i −0.0614599 0.00227119i
\(872\) 4.85402 + 2.80247i 0.164378 + 0.0949036i
\(873\) 41.8767 + 3.86527i 1.41731 + 0.130820i
\(874\) −4.06322 2.34590i −0.137440 0.0793512i
\(875\) −21.9005 21.2130i −0.740372 0.717131i
\(876\) 23.9525 + 1.10308i 0.809282 + 0.0372696i
\(877\) 31.4019 + 18.1299i 1.06037 + 0.612204i 0.925534 0.378665i \(-0.123617\pi\)
0.134834 + 0.990868i \(0.456950\pi\)
\(878\) 60.0957i 2.02813i
\(879\) 3.47061 + 2.22269i 0.117061 + 0.0749694i
\(880\) 25.6801 + 14.8264i 0.865675 + 0.499798i
\(881\) −11.8685 + 20.5569i −0.399860 + 0.692578i −0.993708 0.111999i \(-0.964275\pi\)
0.593848 + 0.804577i \(0.297608\pi\)
\(882\) −31.0060 20.4807i −1.04403 0.689622i
\(883\) −42.8249 −1.44117 −0.720586 0.693366i \(-0.756127\pi\)
−0.720586 + 0.693366i \(0.756127\pi\)
\(884\) −21.5106 13.5021i −0.723480 0.454126i
\(885\) −15.5064 + 24.2124i −0.521241 + 0.813891i
\(886\) −32.6833 + 18.8697i −1.09802 + 0.633941i
\(887\) 52.2151 1.75321 0.876605 0.481210i \(-0.159802\pi\)
0.876605 + 0.481210i \(0.159802\pi\)
\(888\) −23.6702 + 12.2502i −0.794321 + 0.411090i
\(889\) 9.78816 + 34.3307i 0.328284 + 1.15142i
\(890\) −3.33004 5.76780i −0.111623 0.193337i
\(891\) 23.6827 27.6828i 0.793401 0.927410i
\(892\) −4.85611 + 8.41104i −0.162595 + 0.281622i
\(893\) 33.9094i 1.13473i
\(894\) −63.3301 2.91652i −2.11807 0.0975430i
\(895\) −0.724909 + 1.25558i −0.0242311 + 0.0419694i
\(896\) −20.5042 + 21.1687i −0.684997 + 0.707198i
\(897\) 4.07255 + 0.338625i 0.135978 + 0.0113064i
\(898\) −14.2971 24.7634i −0.477101 0.826364i
\(899\) −2.69170 + 1.55406i −0.0897734 + 0.0518307i
\(900\) −4.02921 8.74948i −0.134307 0.291649i
\(901\) −6.76314 3.90470i −0.225313 0.130084i
\(902\) 24.6052i 0.819263i
\(903\) 7.30727 + 30.9679i 0.243171 + 1.03055i
\(904\) 14.4518 8.34374i 0.480659 0.277509i
\(905\) 8.03081 + 13.9098i 0.266953 + 0.462377i
\(906\) −1.45007 + 31.4872i −0.0481753 + 1.04609i
\(907\) −3.79115 6.56647i −0.125883 0.218036i 0.796195 0.605041i \(-0.206843\pi\)
−0.922078 + 0.387005i \(0.873510\pi\)
\(908\) 4.71909i 0.156608i
\(909\) −7.43506 0.686264i −0.246605 0.0227619i
\(910\) 17.9122 17.1755i 0.593784 0.569363i
\(911\) 8.93235i 0.295942i −0.988992 0.147971i \(-0.952726\pi\)
0.988992 0.147971i \(-0.0472742\pi\)
\(912\) 34.9327 + 1.60875i 1.15674 + 0.0532709i
\(913\) −51.5760 + 29.7774i −1.70692 + 0.985490i
\(914\) 55.8553i 1.84753i
\(915\) −4.86738 9.40489i −0.160911 0.310916i
\(916\) 2.44622 + 4.23697i 0.0808253 + 0.139993i
\(917\) −35.8423 8.99393i −1.18362 0.297006i
\(918\) −56.7124 7.87988i −1.87179 0.260075i
\(919\) 13.2244 22.9054i 0.436234 0.755580i −0.561161 0.827707i \(-0.689645\pi\)
0.997395 + 0.0721266i \(0.0229786\pi\)
\(920\) 0.739548 + 1.28093i 0.0243822 + 0.0422312i
\(921\) 4.10164 + 7.92531i 0.135154 + 0.261148i
\(922\) 30.2091 17.4412i 0.994882 0.574396i
\(923\) −0.692561 + 18.7411i −0.0227959 + 0.616872i
\(924\) 4.81870 + 20.4215i 0.158524 + 0.671817i
\(925\) −24.6044 14.2053i −0.808987 0.467069i
\(926\) 38.4366i 1.26311i
\(927\) −1.59251 + 17.2534i −0.0523049 + 0.566676i
\(928\) −4.66362 2.69254i −0.153091 0.0883871i
\(929\) −21.7041 12.5309i −0.712089 0.411125i 0.0997447 0.995013i \(-0.468197\pi\)
−0.811834 + 0.583888i \(0.801531\pi\)
\(930\) 13.2624 6.86380i 0.434892 0.225073i
\(931\) 25.0030 + 13.3912i 0.819440 + 0.438880i
\(932\) 4.88651 2.82123i 0.160063 0.0924124i
\(933\) 0.190710 + 0.00878269i 0.00624355 + 0.000287532i
\(934\) 23.8725 + 41.3484i 0.781133 + 1.35296i
\(935\) 32.0937 + 18.5293i 1.04958 + 0.605974i
\(936\) −15.3520 + 6.39359i −0.501794 + 0.208981i
\(937\) 3.20511i 0.104706i −0.998629 0.0523532i \(-0.983328\pi\)
0.998629 0.0523532i \(-0.0166722\pi\)
\(938\) 0.573614 2.28595i 0.0187292 0.0746388i
\(939\) −9.85520 6.31158i −0.321612 0.205971i
\(940\) −6.95842 + 12.0523i −0.226959 + 0.393104i
\(941\) 26.0269 + 15.0266i 0.848452 + 0.489854i 0.860128 0.510078i \(-0.170384\pi\)
−0.0116765 + 0.999932i \(0.503717\pi\)
\(942\) −0.531283 + 11.5364i −0.0173101 + 0.375877i
\(943\) 1.12395 1.94674i 0.0366009 0.0633946i
\(944\) 56.2626i 1.83119i
\(945\) 7.57023 18.7401i 0.246260 0.609614i
\(946\) 24.8666 43.0703i 0.808484 1.40033i
\(947\) 28.4906 0.925821 0.462910 0.886405i \(-0.346805\pi\)
0.462910 + 0.886405i \(0.346805\pi\)
\(948\) 12.6996 19.8297i 0.412463 0.644039i
\(949\) 39.0041 20.6374i 1.26613 0.669917i
\(950\) 10.1763 + 17.6258i 0.330162 + 0.571857i
\(951\) −5.96353 + 9.31175i −0.193381 + 0.301954i
\(952\) −17.6237 + 18.1949i −0.571188 + 0.589700i
\(953\) 49.5123 28.5859i 1.60386 0.925989i 0.613154 0.789964i \(-0.289901\pi\)
0.990705 0.136025i \(-0.0434327\pi\)
\(954\) 6.04685 2.78462i 0.195774 0.0901556i
\(955\) −6.49400 −0.210141
\(956\) 17.5163 0.566517
\(957\) 5.83945 3.02213i 0.188763 0.0976916i
\(958\) 60.7850 35.0942i 1.96387 1.13384i
\(959\) 32.1274 33.1686i 1.03745 1.07107i
\(960\) 0.418526 + 0.268037i 0.0135079 + 0.00865085i
\(961\) 10.0080 + 17.3344i 0.322839 + 0.559173i
\(962\) 33.9479 54.0833i 1.09453 1.74372i
\(963\) −35.0181 24.7699i −1.12844 0.798200i
\(964\) −16.1713 −0.520841
\(965\) −6.85400 + 11.8715i −0.220638 + 0.382157i
\(966\) −1.52687 + 5.08186i −0.0491263 + 0.163506i
\(967\) 4.15192i 0.133517i 0.997769 + 0.0667583i \(0.0212656\pi\)
−0.997769 + 0.0667583i \(0.978734\pi\)
\(968\) −4.13985 + 7.17043i −0.133060 + 0.230466i
\(969\) 43.6573 + 2.01053i 1.40247 + 0.0645877i
\(970\) −31.5820 18.2339i −1.01404 0.585455i
\(971\) −3.03356 + 5.25429i −0.0973517 + 0.168618i −0.910588 0.413316i \(-0.864370\pi\)
0.813236 + 0.581934i \(0.197704\pi\)
\(972\) 12.0668 12.8571i 0.387042 0.412391i
\(973\) 4.05905 16.1760i 0.130127 0.518578i
\(974\) 27.1150i 0.868822i
\(975\) −14.5650 10.1053i −0.466453 0.323628i
\(976\) −17.9459 10.3611i −0.574435 0.331650i
\(977\) −14.4677 25.0588i −0.462863 0.801702i 0.536239 0.844066i \(-0.319844\pi\)
−0.999102 + 0.0423639i \(0.986511\pi\)
\(978\) 1.36768 29.6983i 0.0437337 0.949645i
\(979\) 8.97474 5.18157i 0.286834 0.165604i
\(980\) 6.13880 + 9.89041i 0.196097 + 0.315937i
\(981\) −9.93405 + 4.57472i −0.317170 + 0.146059i
\(982\) 61.4626 + 35.4855i 1.96135 + 1.13239i
\(983\) 5.87166 + 3.39000i 0.187277 + 0.108124i 0.590707 0.806886i \(-0.298849\pi\)
−0.403430 + 0.915010i \(0.632182\pi\)
\(984\) −0.420829 + 9.13799i −0.0134155 + 0.291308i
\(985\) 8.10630i 0.258288i
\(986\) −8.94944 5.16696i −0.285008 0.164550i
\(987\) 37.3255 8.80741i 1.18808 0.280343i
\(988\) −14.6066 + 7.72844i −0.464697 + 0.245875i
\(989\) 3.93485 2.27179i 0.125121 0.0722387i
\(990\) −28.6946 + 13.2141i −0.911975 + 0.419973i
\(991\) −11.9865 20.7613i −0.380765 0.659504i 0.610407 0.792088i \(-0.291006\pi\)
−0.991172 + 0.132584i \(0.957673\pi\)
\(992\) 9.51538 16.4811i 0.302114 0.523276i
\(993\) −1.00170 + 21.7512i −0.0317880 + 0.690253i
\(994\) −23.6190 5.92673i −0.749148 0.187984i
\(995\) −14.3827 24.9116i −0.455963 0.789751i
\(996\) −25.5996 + 13.2487i −0.811154 + 0.419802i
\(997\) 45.6137i 1.44460i −0.691579 0.722301i \(-0.743085\pi\)
0.691579 0.722301i \(-0.256915\pi\)
\(998\) 66.4142 38.3443i 2.10230 1.21377i
\(999\) 7.15720 51.5113i 0.226444 1.62974i
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.br.b.17.7 yes 64
3.2 odd 2 inner 273.2.br.b.17.26 yes 64
7.5 odd 6 273.2.y.b.173.26 yes 64
13.10 even 6 273.2.y.b.101.7 64
21.5 even 6 273.2.y.b.173.7 yes 64
39.23 odd 6 273.2.y.b.101.26 yes 64
91.75 odd 6 inner 273.2.br.b.257.26 yes 64
273.257 even 6 inner 273.2.br.b.257.7 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.y.b.101.7 64 13.10 even 6
273.2.y.b.101.26 yes 64 39.23 odd 6
273.2.y.b.173.7 yes 64 21.5 even 6
273.2.y.b.173.26 yes 64 7.5 odd 6
273.2.br.b.17.7 yes 64 1.1 even 1 trivial
273.2.br.b.17.26 yes 64 3.2 odd 2 inner
273.2.br.b.257.7 yes 64 273.257 even 6 inner
273.2.br.b.257.26 yes 64 91.75 odd 6 inner