Properties

Label 351.2.t.c.181.10
Level $351$
Weight $2$
Character 351.181
Analytic conductor $2.803$
Analytic rank $0$
Dimension $20$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [351,2,Mod(64,351)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(351, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("351.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 351 = 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 351.t (of order \(6\), degree \(2\), not 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: \(2.80274911095\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{9} \)
Twist minimal: no (minimal twist has level 117)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 181.10
Root \(-1.66095 - 0.491165i\) of defining polynomial
Character \(\chi\) \(=\) 351.181
Dual form 351.2.t.c.64.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.14539 + 1.23864i) q^{2} +(2.06847 + 3.58269i) q^{4} +(0.771397 - 0.445366i) q^{5} +(0.850723 + 0.491165i) q^{7} +5.29379i q^{8} +2.20660 q^{10} +(-2.49915 - 1.44288i) q^{11} +(0.714352 - 3.53408i) q^{13} +(1.21676 + 2.10748i) q^{14} +(-2.42018 + 4.19187i) q^{16} -5.34353 q^{17} +7.19723i q^{19} +(3.19122 + 1.84245i) q^{20} +(-3.57443 - 6.19110i) q^{22} +(-2.31688 - 4.01296i) q^{23} +(-2.10330 + 3.64302i) q^{25} +(5.91002 - 6.69715i) q^{26} +4.06384i q^{28} +(0.971133 - 1.68205i) q^{29} +(8.73604 - 5.04375i) q^{31} +(-1.21534 + 0.701678i) q^{32} +(-11.4640 - 6.61872i) q^{34} +0.874993 q^{35} -4.82809i q^{37} +(-8.91479 + 15.4409i) q^{38} +(2.35768 + 4.08361i) q^{40} +(-2.39352 + 1.38190i) q^{41} +(-2.45501 + 4.25220i) q^{43} -11.9382i q^{44} -11.4791i q^{46} +(3.82403 + 2.20780i) q^{47} +(-3.01751 - 5.22649i) q^{49} +(-9.02479 + 5.21047i) q^{50} +(14.1391 - 4.75082i) q^{52} -6.30850 q^{53} -2.57044 q^{55} +(-2.60013 + 4.50355i) q^{56} +(4.16692 - 2.40577i) q^{58} +(2.74727 - 1.58614i) q^{59} +(2.76034 - 4.78105i) q^{61} +24.9896 q^{62} +6.20421 q^{64} +(-1.02291 - 3.04432i) q^{65} +(-3.15059 + 1.81899i) q^{67} +(-11.0529 - 19.1442i) q^{68} +(1.87720 + 1.08380i) q^{70} -6.69715i q^{71} +9.33980i q^{73} +(5.98027 - 10.3581i) q^{74} +(-25.7854 + 14.8872i) q^{76} +(-1.41739 - 2.45499i) q^{77} +(-2.37380 + 4.11154i) q^{79} +4.31146i q^{80} -6.84670 q^{82} +(4.78313 + 2.76154i) q^{83} +(-4.12198 + 2.37983i) q^{85} +(-10.5339 + 6.08176i) q^{86} +(7.63833 - 13.2300i) q^{88} +17.5838i q^{89} +(2.34353 - 2.65566i) q^{91} +(9.58479 - 16.6013i) q^{92} +(5.46935 + 9.47320i) q^{94} +(3.20540 + 5.55192i) q^{95} +(0.213335 + 0.123169i) q^{97} -14.9505i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(326\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.14539 + 1.23864i 1.51702 + 0.875852i 0.999800 + 0.0199997i \(0.00636654\pi\)
0.517220 + 0.855852i \(0.326967\pi\)
\(3\) 0 0
\(4\) 2.06847 + 3.58269i 1.03423 + 1.79135i
\(5\) 0.771397 0.445366i 0.344979 0.199174i −0.317493 0.948261i \(-0.602841\pi\)
0.662472 + 0.749087i \(0.269508\pi\)
\(6\) 0 0
\(7\) 0.850723 + 0.491165i 0.321543 + 0.185643i 0.652080 0.758150i \(-0.273897\pi\)
−0.330537 + 0.943793i \(0.607230\pi\)
\(8\) 5.29379i 1.87164i
\(9\) 0 0
\(10\) 2.20660 0.697787
\(11\) −2.49915 1.44288i −0.753521 0.435046i 0.0734436 0.997299i \(-0.476601\pi\)
−0.826965 + 0.562254i \(0.809934\pi\)
\(12\) 0 0
\(13\) 0.714352 3.53408i 0.198126 0.980177i
\(14\) 1.21676 + 2.10748i 0.325191 + 0.563248i
\(15\) 0 0
\(16\) −2.42018 + 4.19187i −0.605045 + 1.04797i
\(17\) −5.34353 −1.29600 −0.647998 0.761642i \(-0.724394\pi\)
−0.647998 + 0.761642i \(0.724394\pi\)
\(18\) 0 0
\(19\) 7.19723i 1.65116i 0.564287 + 0.825579i \(0.309151\pi\)
−0.564287 + 0.825579i \(0.690849\pi\)
\(20\) 3.19122 + 1.84245i 0.713578 + 0.411984i
\(21\) 0 0
\(22\) −3.57443 6.19110i −0.762071 1.31995i
\(23\) −2.31688 4.01296i −0.483103 0.836759i 0.516709 0.856161i \(-0.327157\pi\)
−0.999812 + 0.0194021i \(0.993824\pi\)
\(24\) 0 0
\(25\) −2.10330 + 3.64302i −0.420660 + 0.728604i
\(26\) 5.91002 6.69715i 1.15905 1.31342i
\(27\) 0 0
\(28\) 4.06384i 0.767993i
\(29\) 0.971133 1.68205i 0.180335 0.312349i −0.761660 0.647977i \(-0.775615\pi\)
0.941995 + 0.335628i \(0.108949\pi\)
\(30\) 0 0
\(31\) 8.73604 5.04375i 1.56904 0.905885i 0.572757 0.819725i \(-0.305874\pi\)
0.996281 0.0861597i \(-0.0274595\pi\)
\(32\) −1.21534 + 0.701678i −0.214844 + 0.124040i
\(33\) 0 0
\(34\) −11.4640 6.61872i −1.96605 1.13510i
\(35\) 0.874993 0.147901
\(36\) 0 0
\(37\) 4.82809i 0.793732i −0.917876 0.396866i \(-0.870098\pi\)
0.917876 0.396866i \(-0.129902\pi\)
\(38\) −8.91479 + 15.4409i −1.44617 + 2.50484i
\(39\) 0 0
\(40\) 2.35768 + 4.08361i 0.372781 + 0.645676i
\(41\) −2.39352 + 1.38190i −0.373804 + 0.215816i −0.675119 0.737709i \(-0.735908\pi\)
0.301315 + 0.953525i \(0.402574\pi\)
\(42\) 0 0
\(43\) −2.45501 + 4.25220i −0.374386 + 0.648455i −0.990235 0.139409i \(-0.955480\pi\)
0.615849 + 0.787864i \(0.288813\pi\)
\(44\) 11.9382i 1.79976i
\(45\) 0 0
\(46\) 11.4791i 1.69251i
\(47\) 3.82403 + 2.20780i 0.557791 + 0.322041i 0.752259 0.658868i \(-0.228964\pi\)
−0.194467 + 0.980909i \(0.562298\pi\)
\(48\) 0 0
\(49\) −3.01751 5.22649i −0.431073 0.746641i
\(50\) −9.02479 + 5.21047i −1.27630 + 0.736871i
\(51\) 0 0
\(52\) 14.1391 4.75082i 1.96074 0.658820i
\(53\) −6.30850 −0.866540 −0.433270 0.901264i \(-0.642640\pi\)
−0.433270 + 0.901264i \(0.642640\pi\)
\(54\) 0 0
\(55\) −2.57044 −0.346599
\(56\) −2.60013 + 4.50355i −0.347456 + 0.601812i
\(57\) 0 0
\(58\) 4.16692 2.40577i 0.547143 0.315893i
\(59\) 2.74727 1.58614i 0.357664 0.206498i −0.310391 0.950609i \(-0.600460\pi\)
0.668056 + 0.744111i \(0.267127\pi\)
\(60\) 0 0
\(61\) 2.76034 4.78105i 0.353426 0.612151i −0.633422 0.773807i \(-0.718350\pi\)
0.986847 + 0.161656i \(0.0516834\pi\)
\(62\) 24.9896 3.17368
\(63\) 0 0
\(64\) 6.20421 0.775526
\(65\) −1.02291 3.04432i −0.126876 0.377602i
\(66\) 0 0
\(67\) −3.15059 + 1.81899i −0.384906 + 0.222225i −0.679950 0.733258i \(-0.737999\pi\)
0.295045 + 0.955483i \(0.404665\pi\)
\(68\) −11.0529 19.1442i −1.34036 2.32158i
\(69\) 0 0
\(70\) 1.87720 + 1.08380i 0.224369 + 0.129539i
\(71\) 6.69715i 0.794805i −0.917644 0.397403i \(-0.869912\pi\)
0.917644 0.397403i \(-0.130088\pi\)
\(72\) 0 0
\(73\) 9.33980i 1.09314i 0.837413 + 0.546570i \(0.184067\pi\)
−0.837413 + 0.546570i \(0.815933\pi\)
\(74\) 5.98027 10.3581i 0.695192 1.20411i
\(75\) 0 0
\(76\) −25.7854 + 14.8872i −2.95779 + 1.70768i
\(77\) −1.41739 2.45499i −0.161526 0.279772i
\(78\) 0 0
\(79\) −2.37380 + 4.11154i −0.267073 + 0.462584i −0.968105 0.250546i \(-0.919390\pi\)
0.701031 + 0.713130i \(0.252723\pi\)
\(80\) 4.31146i 0.482036i
\(81\) 0 0
\(82\) −6.84670 −0.756092
\(83\) 4.78313 + 2.76154i 0.525016 + 0.303118i 0.738985 0.673722i \(-0.235306\pi\)
−0.213968 + 0.976841i \(0.568639\pi\)
\(84\) 0 0
\(85\) −4.12198 + 2.37983i −0.447092 + 0.258129i
\(86\) −10.5339 + 6.08176i −1.13590 + 0.655813i
\(87\) 0 0
\(88\) 7.63833 13.2300i 0.814248 1.41032i
\(89\) 17.5838i 1.86388i 0.362615 + 0.931939i \(0.381884\pi\)
−0.362615 + 0.931939i \(0.618116\pi\)
\(90\) 0 0
\(91\) 2.34353 2.65566i 0.245669 0.278388i
\(92\) 9.58479 16.6013i 0.999283 1.73081i
\(93\) 0 0
\(94\) 5.46935 + 9.47320i 0.564121 + 0.977086i
\(95\) 3.20540 + 5.55192i 0.328867 + 0.569615i
\(96\) 0 0
\(97\) 0.213335 + 0.123169i 0.0216609 + 0.0125059i 0.510791 0.859705i \(-0.329352\pi\)
−0.489130 + 0.872211i \(0.662686\pi\)
\(98\) 14.9505i 1.51023i
\(99\) 0 0
\(100\) −17.4024 −1.74024
\(101\) −2.38713 + 4.13463i −0.237528 + 0.411411i −0.960004 0.279985i \(-0.909671\pi\)
0.722476 + 0.691396i \(0.243004\pi\)
\(102\) 0 0
\(103\) 1.71676 + 2.97351i 0.169157 + 0.292988i 0.938124 0.346300i \(-0.112562\pi\)
−0.768967 + 0.639289i \(0.779229\pi\)
\(104\) 18.7087 + 3.78163i 1.83454 + 0.370820i
\(105\) 0 0
\(106\) −13.5342 7.81398i −1.31456 0.758960i
\(107\) 2.34075 0.226289 0.113144 0.993579i \(-0.463908\pi\)
0.113144 + 0.993579i \(0.463908\pi\)
\(108\) 0 0
\(109\) 10.2127i 0.978195i 0.872229 + 0.489097i \(0.162674\pi\)
−0.872229 + 0.489097i \(0.837326\pi\)
\(110\) −5.51461 3.18386i −0.525797 0.303569i
\(111\) 0 0
\(112\) −4.11780 + 2.37742i −0.389096 + 0.224645i
\(113\) −0.605276 1.04837i −0.0569396 0.0986222i 0.836151 0.548500i \(-0.184801\pi\)
−0.893090 + 0.449878i \(0.851468\pi\)
\(114\) 0 0
\(115\) −3.57447 2.06372i −0.333321 0.192443i
\(116\) 8.03503 0.746034
\(117\) 0 0
\(118\) 7.85863 0.723446
\(119\) −4.54586 2.62456i −0.416719 0.240593i
\(120\) 0 0
\(121\) −1.33618 2.31432i −0.121471 0.210393i
\(122\) 11.8440 6.83815i 1.07231 0.619097i
\(123\) 0 0
\(124\) 36.1404 + 20.8657i 3.24550 + 1.87379i
\(125\) 8.20061i 0.733485i
\(126\) 0 0
\(127\) 7.58237 0.672827 0.336413 0.941714i \(-0.390786\pi\)
0.336413 + 0.941714i \(0.390786\pi\)
\(128\) 15.7411 + 9.08815i 1.39133 + 0.803286i
\(129\) 0 0
\(130\) 1.57629 7.79828i 0.138250 0.683955i
\(131\) 9.40603 + 16.2917i 0.821809 + 1.42342i 0.904334 + 0.426826i \(0.140368\pi\)
−0.0825247 + 0.996589i \(0.526298\pi\)
\(132\) 0 0
\(133\) −3.53503 + 6.12285i −0.306526 + 0.530918i
\(134\) −9.01232 −0.778546
\(135\) 0 0
\(136\) 28.2875i 2.42564i
\(137\) −15.6417 9.03076i −1.33636 0.771550i −0.350098 0.936713i \(-0.613852\pi\)
−0.986266 + 0.165163i \(0.947185\pi\)
\(138\) 0 0
\(139\) 2.42577 + 4.20155i 0.205751 + 0.356371i 0.950372 0.311117i \(-0.100703\pi\)
−0.744621 + 0.667488i \(0.767370\pi\)
\(140\) 1.80989 + 3.13483i 0.152964 + 0.264941i
\(141\) 0 0
\(142\) 8.29537 14.3680i 0.696132 1.20574i
\(143\) −6.88453 + 7.80145i −0.575713 + 0.652390i
\(144\) 0 0
\(145\) 1.73004i 0.143672i
\(146\) −11.5687 + 20.0375i −0.957429 + 1.65832i
\(147\) 0 0
\(148\) 17.2975 9.98674i 1.42185 0.820905i
\(149\) 10.6241 6.13383i 0.870360 0.502503i 0.00289232 0.999996i \(-0.499079\pi\)
0.867468 + 0.497493i \(0.165746\pi\)
\(150\) 0 0
\(151\) −4.82142 2.78365i −0.392362 0.226530i 0.290821 0.956777i \(-0.406072\pi\)
−0.683183 + 0.730247i \(0.739405\pi\)
\(152\) −38.1006 −3.09037
\(153\) 0 0
\(154\) 7.02254i 0.565893i
\(155\) 4.49263 7.78147i 0.360857 0.625023i
\(156\) 0 0
\(157\) 2.02526 + 3.50785i 0.161633 + 0.279957i 0.935455 0.353447i \(-0.114991\pi\)
−0.773821 + 0.633404i \(0.781657\pi\)
\(158\) −10.1855 + 5.88057i −0.810311 + 0.467833i
\(159\) 0 0
\(160\) −0.625007 + 1.08254i −0.0494111 + 0.0855826i
\(161\) 4.55188i 0.358739i
\(162\) 0 0
\(163\) 10.3387i 0.809787i −0.914364 0.404894i \(-0.867309\pi\)
0.914364 0.404894i \(-0.132691\pi\)
\(164\) −9.90182 5.71682i −0.773202 0.446409i
\(165\) 0 0
\(166\) 6.84112 + 11.8492i 0.530974 + 0.919673i
\(167\) −11.4388 + 6.60418i −0.885159 + 0.511047i −0.872356 0.488871i \(-0.837409\pi\)
−0.0128030 + 0.999918i \(0.504075\pi\)
\(168\) 0 0
\(169\) −11.9794 5.04915i −0.921492 0.388396i
\(170\) −11.7910 −0.904330
\(171\) 0 0
\(172\) −20.3124 −1.54881
\(173\) 5.71416 9.89721i 0.434439 0.752471i −0.562810 0.826586i \(-0.690280\pi\)
0.997250 + 0.0741150i \(0.0236132\pi\)
\(174\) 0 0
\(175\) −3.57865 + 2.06613i −0.270520 + 0.156185i
\(176\) 12.0968 6.98407i 0.911828 0.526444i
\(177\) 0 0
\(178\) −21.7800 + 37.7241i −1.63248 + 2.82754i
\(179\) −0.150491 −0.0112482 −0.00562411 0.999984i \(-0.501790\pi\)
−0.00562411 + 0.999984i \(0.501790\pi\)
\(180\) 0 0
\(181\) −22.0219 −1.63687 −0.818436 0.574598i \(-0.805159\pi\)
−0.818436 + 0.574598i \(0.805159\pi\)
\(182\) 8.31719 2.79462i 0.616511 0.207151i
\(183\) 0 0
\(184\) 21.2438 12.2651i 1.56611 0.904195i
\(185\) −2.15027 3.72437i −0.158091 0.273821i
\(186\) 0 0
\(187\) 13.3543 + 7.71009i 0.976561 + 0.563818i
\(188\) 18.2671i 1.33226i
\(189\) 0 0
\(190\) 15.8814i 1.15216i
\(191\) −9.97868 + 17.2836i −0.722032 + 1.25060i 0.238152 + 0.971228i \(0.423458\pi\)
−0.960184 + 0.279369i \(0.909875\pi\)
\(192\) 0 0
\(193\) −8.70542 + 5.02608i −0.626630 + 0.361785i −0.779446 0.626470i \(-0.784499\pi\)
0.152816 + 0.988255i \(0.451166\pi\)
\(194\) 0.305125 + 0.528492i 0.0219067 + 0.0379435i
\(195\) 0 0
\(196\) 12.4833 21.6216i 0.891661 1.54440i
\(197\) 3.94715i 0.281223i −0.990065 0.140611i \(-0.955093\pi\)
0.990065 0.140611i \(-0.0449068\pi\)
\(198\) 0 0
\(199\) 11.4749 0.813433 0.406716 0.913554i \(-0.366674\pi\)
0.406716 + 0.913554i \(0.366674\pi\)
\(200\) −19.2854 11.1344i −1.36368 0.787323i
\(201\) 0 0
\(202\) −10.2427 + 5.91360i −0.720670 + 0.416079i
\(203\) 1.65233 0.953973i 0.115971 0.0669558i
\(204\) 0 0
\(205\) −1.23090 + 2.13198i −0.0859698 + 0.148904i
\(206\) 8.50578i 0.592626i
\(207\) 0 0
\(208\) 13.0855 + 11.5476i 0.907319 + 0.800680i
\(209\) 10.3848 17.9869i 0.718329 1.24418i
\(210\) 0 0
\(211\) −5.48306 9.49694i −0.377469 0.653796i 0.613224 0.789909i \(-0.289872\pi\)
−0.990693 + 0.136113i \(0.956539\pi\)
\(212\) −13.0489 22.6014i −0.896204 1.55227i
\(213\) 0 0
\(214\) 5.02182 + 2.89935i 0.343285 + 0.198195i
\(215\) 4.37351i 0.298271i
\(216\) 0 0
\(217\) 9.90926 0.672684
\(218\) −12.6498 + 21.9101i −0.856754 + 1.48394i
\(219\) 0 0
\(220\) −5.31688 9.20911i −0.358464 0.620878i
\(221\) −3.81716 + 18.8845i −0.256770 + 1.27031i
\(222\) 0 0
\(223\) −11.1218 6.42116i −0.744770 0.429993i 0.0790313 0.996872i \(-0.474817\pi\)
−0.823801 + 0.566879i \(0.808151\pi\)
\(224\) −1.37856 −0.0921088
\(225\) 0 0
\(226\) 2.99888i 0.199482i
\(227\) 20.4534 + 11.8088i 1.35754 + 0.783777i 0.989292 0.145950i \(-0.0466240\pi\)
0.368249 + 0.929727i \(0.379957\pi\)
\(228\) 0 0
\(229\) 10.7715 6.21892i 0.711800 0.410958i −0.0999271 0.994995i \(-0.531861\pi\)
0.811727 + 0.584037i \(0.198528\pi\)
\(230\) −5.11242 8.85497i −0.337103 0.583880i
\(231\) 0 0
\(232\) 8.90443 + 5.14098i 0.584605 + 0.337522i
\(233\) 18.7821 1.23046 0.615230 0.788348i \(-0.289063\pi\)
0.615230 + 0.788348i \(0.289063\pi\)
\(234\) 0 0
\(235\) 3.93312 0.256568
\(236\) 11.3653 + 6.56175i 0.739817 + 0.427134i
\(237\) 0 0
\(238\) −6.50177 11.2614i −0.421447 0.729968i
\(239\) 17.1326 9.89154i 1.10822 0.639830i 0.169851 0.985470i \(-0.445671\pi\)
0.938367 + 0.345639i \(0.112338\pi\)
\(240\) 0 0
\(241\) −9.86550 5.69585i −0.635493 0.366902i 0.147384 0.989079i \(-0.452915\pi\)
−0.782876 + 0.622178i \(0.786248\pi\)
\(242\) 6.62017i 0.425561i
\(243\) 0 0
\(244\) 22.8387 1.46210
\(245\) −4.65540 2.68780i −0.297423 0.171717i
\(246\) 0 0
\(247\) 25.4356 + 5.14136i 1.61843 + 0.327137i
\(248\) 26.7006 + 46.2468i 1.69549 + 2.93667i
\(249\) 0 0
\(250\) −10.1576 + 17.5935i −0.642424 + 1.11271i
\(251\) 18.6950 1.18002 0.590010 0.807396i \(-0.299124\pi\)
0.590010 + 0.807396i \(0.299124\pi\)
\(252\) 0 0
\(253\) 13.3720i 0.840688i
\(254\) 16.2672 + 9.39184i 1.02069 + 0.589297i
\(255\) 0 0
\(256\) 16.3097 + 28.2492i 1.01936 + 1.76558i
\(257\) −4.37976 7.58598i −0.273202 0.473200i 0.696478 0.717578i \(-0.254749\pi\)
−0.969680 + 0.244378i \(0.921416\pi\)
\(258\) 0 0
\(259\) 2.37139 4.10736i 0.147351 0.255219i
\(260\) 8.79102 9.96185i 0.545196 0.617808i
\(261\) 0 0
\(262\) 46.6028i 2.87913i
\(263\) 3.86402 6.69268i 0.238266 0.412688i −0.721951 0.691944i \(-0.756754\pi\)
0.960217 + 0.279256i \(0.0900878\pi\)
\(264\) 0 0
\(265\) −4.86636 + 2.80959i −0.298938 + 0.172592i
\(266\) −15.1680 + 8.75727i −0.930012 + 0.536942i
\(267\) 0 0
\(268\) −13.0338 7.52505i −0.796165 0.459666i
\(269\) −14.8448 −0.905102 −0.452551 0.891739i \(-0.649486\pi\)
−0.452551 + 0.891739i \(0.649486\pi\)
\(270\) 0 0
\(271\) 19.3486i 1.17534i −0.809100 0.587671i \(-0.800045\pi\)
0.809100 0.587671i \(-0.199955\pi\)
\(272\) 12.9323 22.3994i 0.784136 1.35816i
\(273\) 0 0
\(274\) −22.3718 38.7490i −1.35153 2.34091i
\(275\) 10.5129 6.06963i 0.633952 0.366012i
\(276\) 0 0
\(277\) −0.587762 + 1.01803i −0.0353152 + 0.0611677i −0.883143 0.469104i \(-0.844577\pi\)
0.847828 + 0.530272i \(0.177910\pi\)
\(278\) 12.0186i 0.720829i
\(279\) 0 0
\(280\) 4.63203i 0.276817i
\(281\) −3.96724 2.29048i −0.236665 0.136639i 0.376978 0.926222i \(-0.376963\pi\)
−0.613643 + 0.789583i \(0.710297\pi\)
\(282\) 0 0
\(283\) −0.0159162 0.0275676i −0.000946118 0.00163872i 0.865552 0.500819i \(-0.166968\pi\)
−0.866498 + 0.499180i \(0.833634\pi\)
\(284\) 23.9938 13.8528i 1.42377 0.822014i
\(285\) 0 0
\(286\) −24.4332 + 8.20969i −1.44477 + 0.485449i
\(287\) −2.71496 −0.160259
\(288\) 0 0
\(289\) 11.5533 0.679607
\(290\) 2.14290 3.71161i 0.125835 0.217953i
\(291\) 0 0
\(292\) −33.4616 + 19.3191i −1.95819 + 1.13056i
\(293\) −9.44674 + 5.45408i −0.551884 + 0.318631i −0.749882 0.661572i \(-0.769890\pi\)
0.197997 + 0.980203i \(0.436556\pi\)
\(294\) 0 0
\(295\) 1.41282 2.44708i 0.0822578 0.142475i
\(296\) 25.5589 1.48558
\(297\) 0 0
\(298\) 30.3905 1.76047
\(299\) −15.8372 + 5.32137i −0.915887 + 0.307743i
\(300\) 0 0
\(301\) −4.17707 + 2.41163i −0.240762 + 0.139004i
\(302\) −6.89589 11.9440i −0.396814 0.687302i
\(303\) 0 0
\(304\) −30.1699 17.4186i −1.73036 0.999025i
\(305\) 4.91745i 0.281572i
\(306\) 0 0
\(307\) 6.90363i 0.394011i 0.980402 + 0.197005i \(0.0631217\pi\)
−0.980402 + 0.197005i \(0.936878\pi\)
\(308\) 5.86364 10.1561i 0.334112 0.578699i
\(309\) 0 0
\(310\) 19.2769 11.1295i 1.09485 0.632115i
\(311\) −7.69804 13.3334i −0.436516 0.756067i 0.560902 0.827882i \(-0.310454\pi\)
−0.997418 + 0.0718148i \(0.977121\pi\)
\(312\) 0 0
\(313\) 8.67077 15.0182i 0.490101 0.848879i −0.509834 0.860273i \(-0.670293\pi\)
0.999935 + 0.0113932i \(0.00362663\pi\)
\(314\) 10.0343i 0.566267i
\(315\) 0 0
\(316\) −19.6405 −1.10486
\(317\) 9.21059 + 5.31774i 0.517318 + 0.298674i 0.735837 0.677159i \(-0.236789\pi\)
−0.218518 + 0.975833i \(0.570122\pi\)
\(318\) 0 0
\(319\) −4.85401 + 2.80246i −0.271772 + 0.156908i
\(320\) 4.78591 2.76314i 0.267540 0.154464i
\(321\) 0 0
\(322\) 5.63815 9.76557i 0.314202 0.544214i
\(323\) 38.4586i 2.13989i
\(324\) 0 0
\(325\) 11.3722 + 10.0356i 0.630817 + 0.556676i
\(326\) 12.8059 22.1805i 0.709254 1.22846i
\(327\) 0 0
\(328\) −7.31548 12.6708i −0.403930 0.699627i
\(329\) 2.16879 + 3.75646i 0.119569 + 0.207100i
\(330\) 0 0
\(331\) 27.4350 + 15.8396i 1.50796 + 0.870623i 0.999957 + 0.00926968i \(0.00295067\pi\)
0.508006 + 0.861353i \(0.330383\pi\)
\(332\) 22.8486i 1.25398i
\(333\) 0 0
\(334\) −32.7208 −1.79041
\(335\) −1.62024 + 2.80633i −0.0885229 + 0.153326i
\(336\) 0 0
\(337\) −12.1482 21.0414i −0.661757 1.14620i −0.980154 0.198239i \(-0.936478\pi\)
0.318397 0.947958i \(-0.396856\pi\)
\(338\) −19.4464 25.6706i −1.05774 1.39630i
\(339\) 0 0
\(340\) −17.0524 9.84519i −0.924795 0.533930i
\(341\) −29.1102 −1.57641
\(342\) 0 0
\(343\) 12.8047i 0.691389i
\(344\) −22.5103 12.9963i −1.21367 0.700714i
\(345\) 0 0
\(346\) 24.5182 14.1556i 1.31811 0.761009i
\(347\) 1.91224 + 3.31209i 0.102654 + 0.177802i 0.912777 0.408457i \(-0.133933\pi\)
−0.810123 + 0.586260i \(0.800600\pi\)
\(348\) 0 0
\(349\) 20.3799 + 11.7664i 1.09091 + 0.629839i 0.933819 0.357745i \(-0.116454\pi\)
0.157093 + 0.987584i \(0.449788\pi\)
\(350\) −10.2368 −0.547180
\(351\) 0 0
\(352\) 4.04976 0.215853
\(353\) −20.4327 11.7968i −1.08752 0.627881i −0.154606 0.987976i \(-0.549411\pi\)
−0.932916 + 0.360095i \(0.882744\pi\)
\(354\) 0 0
\(355\) −2.98268 5.16616i −0.158304 0.274191i
\(356\) −62.9973 + 36.3715i −3.33885 + 1.92769i
\(357\) 0 0
\(358\) −0.322862 0.186404i −0.0170638 0.00985177i
\(359\) 0.220474i 0.0116362i −0.999983 0.00581809i \(-0.998148\pi\)
0.999983 0.00581809i \(-0.00185196\pi\)
\(360\) 0 0
\(361\) −32.8001 −1.72632
\(362\) −47.2455 27.2772i −2.48317 1.43366i
\(363\) 0 0
\(364\) 14.3619 + 2.90301i 0.752768 + 0.152159i
\(365\) 4.15963 + 7.20469i 0.217725 + 0.377111i
\(366\) 0 0
\(367\) 10.2569 17.7655i 0.535407 0.927353i −0.463736 0.885973i \(-0.653491\pi\)
0.999144 0.0413794i \(-0.0131752\pi\)
\(368\) 22.4291 1.16920
\(369\) 0 0
\(370\) 10.6536i 0.553856i
\(371\) −5.36679 3.09852i −0.278630 0.160867i
\(372\) 0 0
\(373\) −5.42755 9.40079i −0.281028 0.486754i 0.690610 0.723227i \(-0.257342\pi\)
−0.971638 + 0.236473i \(0.924009\pi\)
\(374\) 19.1001 + 33.0823i 0.987642 + 1.71065i
\(375\) 0 0
\(376\) −11.6876 + 20.2436i −0.602744 + 1.04398i
\(377\) −5.25077 4.63364i −0.270428 0.238644i
\(378\) 0 0
\(379\) 19.6987i 1.01185i −0.862577 0.505927i \(-0.831151\pi\)
0.862577 0.505927i \(-0.168849\pi\)
\(380\) −13.2605 + 22.9679i −0.680251 + 1.17823i
\(381\) 0 0
\(382\) −42.8164 + 24.7200i −2.19068 + 1.26479i
\(383\) 17.6164 10.1708i 0.900156 0.519705i 0.0229052 0.999738i \(-0.492708\pi\)
0.877251 + 0.480032i \(0.159375\pi\)
\(384\) 0 0
\(385\) −2.18674 1.26251i −0.111446 0.0643436i
\(386\) −24.9020 −1.26748
\(387\) 0 0
\(388\) 1.01909i 0.0517362i
\(389\) 10.6980 18.5295i 0.542412 0.939485i −0.456353 0.889799i \(-0.650845\pi\)
0.998765 0.0496861i \(-0.0158221\pi\)
\(390\) 0 0
\(391\) 12.3803 + 21.4434i 0.626100 + 1.08444i
\(392\) 27.6679 15.9741i 1.39744 0.806814i
\(393\) 0 0
\(394\) 4.88911 8.46818i 0.246310 0.426621i
\(395\) 4.22884i 0.212776i
\(396\) 0 0
\(397\) 27.7995i 1.39522i −0.716479 0.697608i \(-0.754248\pi\)
0.716479 0.697608i \(-0.245752\pi\)
\(398\) 24.6181 + 14.2133i 1.23399 + 0.712447i
\(399\) 0 0
\(400\) −10.1807 17.6335i −0.509036 0.881676i
\(401\) 13.1515 7.59301i 0.656754 0.379177i −0.134285 0.990943i \(-0.542874\pi\)
0.791039 + 0.611766i \(0.209541\pi\)
\(402\) 0 0
\(403\) −11.5844 34.4768i −0.577060 1.71741i
\(404\) −19.7508 −0.982639
\(405\) 0 0
\(406\) 4.72652 0.234573
\(407\) −6.96636 + 12.0661i −0.345310 + 0.598094i
\(408\) 0 0
\(409\) −2.06606 + 1.19284i −0.102160 + 0.0589823i −0.550210 0.835027i \(-0.685452\pi\)
0.448049 + 0.894009i \(0.352119\pi\)
\(410\) −5.28152 + 3.04929i −0.260836 + 0.150594i
\(411\) 0 0
\(412\) −7.10210 + 12.3012i −0.349896 + 0.606037i
\(413\) 3.11622 0.153339
\(414\) 0 0
\(415\) 4.91958 0.241493
\(416\) 1.61160 + 4.79636i 0.0790153 + 0.235161i
\(417\) 0 0
\(418\) 44.5587 25.7260i 2.17944 1.25830i
\(419\) 16.6455 + 28.8308i 0.813183 + 1.40848i 0.910625 + 0.413234i \(0.135601\pi\)
−0.0974415 + 0.995241i \(0.531066\pi\)
\(420\) 0 0
\(421\) 21.0487 + 12.1525i 1.02585 + 0.592275i 0.915793 0.401650i \(-0.131563\pi\)
0.110057 + 0.993925i \(0.464897\pi\)
\(422\) 27.1662i 1.32243i
\(423\) 0 0
\(424\) 33.3959i 1.62185i
\(425\) 11.2390 19.4666i 0.545173 0.944268i
\(426\) 0 0
\(427\) 4.69657 2.71157i 0.227283 0.131222i
\(428\) 4.84176 + 8.38618i 0.234035 + 0.405361i
\(429\) 0 0
\(430\) −5.41722 + 9.38289i −0.261241 + 0.452483i
\(431\) 12.1410i 0.584812i 0.956294 + 0.292406i \(0.0944559\pi\)
−0.956294 + 0.292406i \(0.905544\pi\)
\(432\) 0 0
\(433\) −13.2730 −0.637859 −0.318930 0.947778i \(-0.603323\pi\)
−0.318930 + 0.947778i \(0.603323\pi\)
\(434\) 21.2592 + 12.2740i 1.02048 + 0.589172i
\(435\) 0 0
\(436\) −36.5888 + 21.1245i −1.75228 + 1.01168i
\(437\) 28.8822 16.6751i 1.38162 0.797680i
\(438\) 0 0
\(439\) 6.55074 11.3462i 0.312650 0.541526i −0.666285 0.745697i \(-0.732117\pi\)
0.978935 + 0.204171i \(0.0654500\pi\)
\(440\) 13.6074i 0.648708i
\(441\) 0 0
\(442\) −31.5804 + 35.7864i −1.50213 + 1.70219i
\(443\) −17.2195 + 29.8250i −0.818123 + 1.41703i 0.0889410 + 0.996037i \(0.471652\pi\)
−0.907064 + 0.420993i \(0.861682\pi\)
\(444\) 0 0
\(445\) 7.83122 + 13.5641i 0.371236 + 0.642999i
\(446\) −15.9070 27.5518i −0.753220 1.30462i
\(447\) 0 0
\(448\) 5.27806 + 3.04729i 0.249365 + 0.143971i
\(449\) 5.32385i 0.251248i 0.992078 + 0.125624i \(0.0400933\pi\)
−0.992078 + 0.125624i \(0.959907\pi\)
\(450\) 0 0
\(451\) 7.97567 0.375559
\(452\) 2.50399 4.33703i 0.117778 0.203997i
\(453\) 0 0
\(454\) 29.2537 + 50.6689i 1.37294 + 2.37801i
\(455\) 0.625053 3.09229i 0.0293029 0.144969i
\(456\) 0 0
\(457\) 10.7297 + 6.19481i 0.501916 + 0.289781i 0.729504 0.683976i \(-0.239751\pi\)
−0.227589 + 0.973757i \(0.573084\pi\)
\(458\) 30.8121 1.43975
\(459\) 0 0
\(460\) 17.0750i 0.796124i
\(461\) −11.2633 6.50288i −0.524585 0.302869i 0.214223 0.976785i \(-0.431278\pi\)
−0.738809 + 0.673915i \(0.764611\pi\)
\(462\) 0 0
\(463\) 5.56377 3.21224i 0.258570 0.149286i −0.365112 0.930964i \(-0.618969\pi\)
0.623682 + 0.781678i \(0.285636\pi\)
\(464\) 4.70063 + 8.14173i 0.218221 + 0.377971i
\(465\) 0 0
\(466\) 40.2950 + 23.2644i 1.86663 + 1.07770i
\(467\) −13.9598 −0.645982 −0.322991 0.946402i \(-0.604688\pi\)
−0.322991 + 0.946402i \(0.604688\pi\)
\(468\) 0 0
\(469\) −3.57370 −0.165018
\(470\) 8.43808 + 4.87173i 0.389220 + 0.224716i
\(471\) 0 0
\(472\) 8.39669 + 14.5435i 0.386489 + 0.669419i
\(473\) 12.2709 7.08459i 0.564215 0.325750i
\(474\) 0 0
\(475\) −26.2196 15.1379i −1.20304 0.694575i
\(476\) 21.7152i 0.995316i
\(477\) 0 0
\(478\) 49.0083 2.24159
\(479\) 29.9863 + 17.3126i 1.37011 + 0.791033i 0.990941 0.134295i \(-0.0428769\pi\)
0.379168 + 0.925328i \(0.376210\pi\)
\(480\) 0 0
\(481\) −17.0628 3.44895i −0.777998 0.157259i
\(482\) −14.1102 24.4396i −0.642703 1.11319i
\(483\) 0 0
\(484\) 5.52767 9.57421i 0.251258 0.435191i
\(485\) 0.219421 0.00996341
\(486\) 0 0
\(487\) 5.78811i 0.262284i −0.991364 0.131142i \(-0.958136\pi\)
0.991364 0.131142i \(-0.0418644\pi\)
\(488\) 25.3099 + 14.6127i 1.14573 + 0.661485i
\(489\) 0 0
\(490\) −6.65843 11.5327i −0.300797 0.520996i
\(491\) −12.4622 21.5851i −0.562410 0.974123i −0.997285 0.0736326i \(-0.976541\pi\)
0.434875 0.900491i \(-0.356793\pi\)
\(492\) 0 0
\(493\) −5.18928 + 8.98810i −0.233713 + 0.404803i
\(494\) 48.2009 + 42.5358i 2.16866 + 1.91378i
\(495\) 0 0
\(496\) 48.8272i 2.19240i
\(497\) 3.28941 5.69742i 0.147550 0.255564i
\(498\) 0 0
\(499\) −34.4839 + 19.9093i −1.54371 + 0.891262i −0.545112 + 0.838363i \(0.683513\pi\)
−0.998600 + 0.0528989i \(0.983154\pi\)
\(500\) −29.3803 + 16.9627i −1.31392 + 0.758595i
\(501\) 0 0
\(502\) 40.1082 + 23.1565i 1.79011 + 1.03352i
\(503\) 12.9120 0.575720 0.287860 0.957673i \(-0.407056\pi\)
0.287860 + 0.957673i \(0.407056\pi\)
\(504\) 0 0
\(505\) 4.25259i 0.189238i
\(506\) −16.5631 + 28.6881i −0.736318 + 1.27534i
\(507\) 0 0
\(508\) 15.6839 + 27.1653i 0.695860 + 1.20527i
\(509\) −32.1750 + 18.5763i −1.42613 + 0.823378i −0.996813 0.0797749i \(-0.974580\pi\)
−0.429319 + 0.903153i \(0.641247\pi\)
\(510\) 0 0
\(511\) −4.58738 + 7.94558i −0.202934 + 0.351492i
\(512\) 44.4550i 1.96465i
\(513\) 0 0
\(514\) 21.6998i 0.957139i
\(515\) 2.64860 + 1.52917i 0.116711 + 0.0673832i
\(516\) 0 0
\(517\) −6.37120 11.0352i −0.280205 0.485329i
\(518\) 10.1751 5.87460i 0.447068 0.258115i
\(519\) 0 0
\(520\) 16.1160 5.41507i 0.706734 0.237466i
\(521\) 24.6907 1.08172 0.540859 0.841114i \(-0.318099\pi\)
0.540859 + 0.841114i \(0.318099\pi\)
\(522\) 0 0
\(523\) −33.4434 −1.46238 −0.731189 0.682175i \(-0.761034\pi\)
−0.731189 + 0.682175i \(0.761034\pi\)
\(524\) −38.9121 + 67.3978i −1.69989 + 2.94429i
\(525\) 0 0
\(526\) 16.5797 9.57227i 0.722908 0.417371i
\(527\) −46.6813 + 26.9515i −2.03347 + 1.17402i
\(528\) 0 0
\(529\) 0.764121 1.32350i 0.0332227 0.0575433i
\(530\) −13.9203 −0.604660
\(531\) 0 0
\(532\) −29.2484 −1.26808
\(533\) 3.17392 + 9.44603i 0.137478 + 0.409153i
\(534\) 0 0
\(535\) 1.80565 1.04249i 0.0780649 0.0450708i
\(536\) −9.62937 16.6786i −0.415925 0.720404i
\(537\) 0 0
\(538\) −31.8478 18.3874i −1.37306 0.792735i
\(539\) 17.4157i 0.750146i
\(540\) 0 0
\(541\) 10.9418i 0.470423i 0.971944 + 0.235211i \(0.0755782\pi\)
−0.971944 + 0.235211i \(0.924422\pi\)
\(542\) 23.9659 41.5102i 1.02943 1.78302i
\(543\) 0 0
\(544\) 6.49422 3.74944i 0.278437 0.160756i
\(545\) 4.54837 + 7.87800i 0.194831 + 0.337457i
\(546\) 0 0
\(547\) −5.47407 + 9.48136i −0.234054 + 0.405394i −0.958997 0.283415i \(-0.908533\pi\)
0.724943 + 0.688809i \(0.241866\pi\)
\(548\) 74.7194i 3.19185i
\(549\) 0 0
\(550\) 30.0724 1.28229
\(551\) 12.1061 + 6.98947i 0.515738 + 0.297761i
\(552\) 0 0
\(553\) −4.03889 + 2.33185i −0.171751 + 0.0991605i
\(554\) −2.52196 + 1.45605i −0.107148 + 0.0618618i
\(555\) 0 0
\(556\) −10.0352 + 17.3815i −0.425589 + 0.737141i
\(557\) 12.5825i 0.533136i 0.963816 + 0.266568i \(0.0858898\pi\)
−0.963816 + 0.266568i \(0.914110\pi\)
\(558\) 0 0
\(559\) 13.2739 + 11.7138i 0.561425 + 0.495440i
\(560\) −2.11764 + 3.66786i −0.0894866 + 0.154995i
\(561\) 0 0
\(562\) −5.67418 9.82797i −0.239351 0.414568i
\(563\) −6.07784 10.5271i −0.256151 0.443666i 0.709057 0.705151i \(-0.249121\pi\)
−0.965207 + 0.261486i \(0.915788\pi\)
\(564\) 0 0
\(565\) −0.933815 0.539139i −0.0392859 0.0226817i
\(566\) 0.0788577i 0.00331464i
\(567\) 0 0
\(568\) 35.4533 1.48759
\(569\) 17.6882 30.6369i 0.741529 1.28437i −0.210270 0.977643i \(-0.567434\pi\)
0.951799 0.306722i \(-0.0992323\pi\)
\(570\) 0 0
\(571\) 6.24561 + 10.8177i 0.261371 + 0.452707i 0.966606 0.256266i \(-0.0824922\pi\)
−0.705236 + 0.708973i \(0.749159\pi\)
\(572\) −42.1906 8.52810i −1.76408 0.356578i
\(573\) 0 0
\(574\) −5.82465 3.36286i −0.243116 0.140363i
\(575\) 19.4924 0.812888
\(576\) 0 0
\(577\) 25.1610i 1.04747i 0.851882 + 0.523734i \(0.175461\pi\)
−0.851882 + 0.523734i \(0.824539\pi\)
\(578\) 24.7864 + 14.3104i 1.03098 + 0.595235i
\(579\) 0 0
\(580\) 6.19819 3.57853i 0.257366 0.148590i
\(581\) 2.71274 + 4.69861i 0.112544 + 0.194931i
\(582\) 0 0
\(583\) 15.7659 + 9.10243i 0.652956 + 0.376984i
\(584\) −49.4430 −2.04596
\(585\) 0 0
\(586\) −27.0226 −1.11629
\(587\) 3.21529 + 1.85635i 0.132709 + 0.0766197i 0.564885 0.825170i \(-0.308921\pi\)
−0.432176 + 0.901789i \(0.642254\pi\)
\(588\) 0 0
\(589\) 36.3011 + 62.8753i 1.49576 + 2.59073i
\(590\) 6.06212 3.49997i 0.249574 0.144091i
\(591\) 0 0
\(592\) 20.2387 + 11.6848i 0.831806 + 0.480244i
\(593\) 31.6710i 1.30057i −0.759689 0.650287i \(-0.774649\pi\)
0.759689 0.650287i \(-0.225351\pi\)
\(594\) 0 0
\(595\) −4.67555 −0.191679
\(596\) 43.9512 + 25.3752i 1.80031 + 1.03941i
\(597\) 0 0
\(598\) −40.5682 8.20015i −1.65896 0.335329i
\(599\) −14.2298 24.6468i −0.581415 1.00704i −0.995312 0.0967168i \(-0.969166\pi\)
0.413897 0.910324i \(-0.364167\pi\)
\(600\) 0 0
\(601\) −0.635544 + 1.10079i −0.0259244 + 0.0449023i −0.878697 0.477381i \(-0.841586\pi\)
0.852772 + 0.522283i \(0.174920\pi\)
\(602\) −11.9486 −0.486988
\(603\) 0 0
\(604\) 23.0315i 0.937140i
\(605\) −2.06144 1.19017i −0.0838096 0.0483875i
\(606\) 0 0
\(607\) 0.373604 + 0.647101i 0.0151641 + 0.0262650i 0.873508 0.486810i \(-0.161840\pi\)
−0.858344 + 0.513075i \(0.828506\pi\)
\(608\) −5.05014 8.74709i −0.204810 0.354741i
\(609\) 0 0
\(610\) 6.09096 10.5499i 0.246616 0.427151i
\(611\) 10.5342 11.9373i 0.426170 0.482930i
\(612\) 0 0
\(613\) 41.1308i 1.66126i −0.556826 0.830629i \(-0.687981\pi\)
0.556826 0.830629i \(-0.312019\pi\)
\(614\) −8.55112 + 14.8110i −0.345095 + 0.597723i
\(615\) 0 0
\(616\) 12.9962 7.50336i 0.523632 0.302319i
\(617\) −10.9623 + 6.32908i −0.441325 + 0.254799i −0.704159 0.710042i \(-0.748676\pi\)
0.262835 + 0.964841i \(0.415343\pi\)
\(618\) 0 0
\(619\) 7.38692 + 4.26484i 0.296905 + 0.171418i 0.641052 0.767498i \(-0.278498\pi\)
−0.344147 + 0.938916i \(0.611832\pi\)
\(620\) 37.1715 1.49284
\(621\) 0 0
\(622\) 38.1404i 1.52929i
\(623\) −8.63654 + 14.9589i −0.346016 + 0.599317i
\(624\) 0 0
\(625\) −6.86422 11.8892i −0.274569 0.475567i
\(626\) 37.2044 21.4800i 1.48699 0.858512i
\(627\) 0 0
\(628\) −8.37836 + 14.5117i −0.334333 + 0.579082i
\(629\) 25.7990i 1.02867i
\(630\) 0 0
\(631\) 2.50848i 0.0998612i 0.998753 + 0.0499306i \(0.0159000\pi\)
−0.998753 + 0.0499306i \(0.984100\pi\)
\(632\) −21.7656 12.5664i −0.865791 0.499865i
\(633\) 0 0
\(634\) 13.1735 + 22.8173i 0.523188 + 0.906189i
\(635\) 5.84902 3.37693i 0.232111 0.134009i
\(636\) 0 0
\(637\) −20.6264 + 6.93057i −0.817247 + 0.274599i
\(638\) −13.8850 −0.549712
\(639\) 0 0
\(640\) 16.1902 0.639974
\(641\) −20.6692 + 35.8000i −0.816383 + 1.41402i 0.0919475 + 0.995764i \(0.470691\pi\)
−0.908331 + 0.418253i \(0.862643\pi\)
\(642\) 0 0
\(643\) 17.6848 10.2103i 0.697419 0.402655i −0.108966 0.994045i \(-0.534754\pi\)
0.806385 + 0.591390i \(0.201421\pi\)
\(644\) 16.3080 9.41542i 0.642625 0.371020i
\(645\) 0 0
\(646\) 47.6365 82.5088i 1.87423 3.24626i
\(647\) −15.7134 −0.617756 −0.308878 0.951102i \(-0.599953\pi\)
−0.308878 + 0.951102i \(0.599953\pi\)
\(648\) 0 0
\(649\) −9.15445 −0.359344
\(650\) 11.9673 + 35.6164i 0.469396 + 1.39699i
\(651\) 0 0
\(652\) 37.0403 21.3852i 1.45061 0.837509i
\(653\) −16.1168 27.9151i −0.630700 1.09240i −0.987409 0.158188i \(-0.949435\pi\)
0.356709 0.934215i \(-0.383899\pi\)
\(654\) 0 0
\(655\) 14.5116 + 8.37826i 0.567014 + 0.327366i
\(656\) 13.3778i 0.522314i
\(657\) 0 0
\(658\) 10.7454i 0.418900i
\(659\) −2.33379 + 4.04224i −0.0909115 + 0.157463i −0.907895 0.419198i \(-0.862311\pi\)
0.816983 + 0.576661i \(0.195645\pi\)
\(660\) 0 0
\(661\) −19.5539 + 11.2894i −0.760557 + 0.439108i −0.829496 0.558513i \(-0.811372\pi\)
0.0689389 + 0.997621i \(0.478039\pi\)
\(662\) 39.2392 + 67.9642i 1.52507 + 2.64151i
\(663\) 0 0
\(664\) −14.6190 + 25.3209i −0.567328 + 0.982641i
\(665\) 6.29753i 0.244208i
\(666\) 0 0
\(667\) −9.00000 −0.348481
\(668\) −47.3215 27.3211i −1.83092 1.05708i
\(669\) 0 0
\(670\) −6.95207 + 4.01378i −0.268582 + 0.155066i
\(671\) −13.7970 + 7.96570i −0.532627 + 0.307512i
\(672\) 0 0
\(673\) 1.89964 3.29028i 0.0732259 0.126831i −0.827088 0.562073i \(-0.810004\pi\)
0.900313 + 0.435242i \(0.143337\pi\)
\(674\) 60.1893i 2.31841i
\(675\) 0 0
\(676\) −6.68945 53.3625i −0.257287 2.05240i
\(677\) −14.9160 + 25.8352i −0.573267 + 0.992927i 0.422961 + 0.906148i \(0.360991\pi\)
−0.996228 + 0.0867791i \(0.972343\pi\)
\(678\) 0 0
\(679\) 0.120993 + 0.209566i 0.00464327 + 0.00804239i
\(680\) −12.5983 21.8209i −0.483123 0.836794i
\(681\) 0 0
\(682\) −62.4527 36.0571i −2.39144 1.38070i
\(683\) 0.0316640i 0.00121159i −1.00000 0.000605795i \(-0.999807\pi\)
1.00000 0.000605795i \(-0.000192831\pi\)
\(684\) 0 0
\(685\) −16.0880 −0.614690
\(686\) 15.8604 27.4711i 0.605554 1.04885i
\(687\) 0 0
\(688\) −11.8831 20.5822i −0.453040 0.784689i
\(689\) −4.50649 + 22.2947i −0.171684 + 0.849362i
\(690\) 0 0
\(691\) 6.85148 + 3.95570i 0.260642 + 0.150482i 0.624628 0.780923i \(-0.285251\pi\)
−0.363985 + 0.931405i \(0.618584\pi\)
\(692\) 47.2782 1.79725
\(693\) 0 0
\(694\) 9.47431i 0.359640i
\(695\) 3.74246 + 2.16071i 0.141959 + 0.0819603i
\(696\) 0 0
\(697\) 12.7898 7.38421i 0.484449 0.279697i
\(698\) 29.1486 + 50.4869i 1.10329 + 1.91096i
\(699\) 0 0
\(700\) −14.8046 8.54746i −0.559562 0.323064i
\(701\) −35.2396 −1.33098 −0.665491 0.746406i \(-0.731778\pi\)
−0.665491 + 0.746406i \(0.731778\pi\)
\(702\) 0 0
\(703\) 34.7488 1.31058
\(704\) −15.5052 8.95195i −0.584375 0.337389i
\(705\) 0 0
\(706\) −29.2241 50.6175i −1.09986 1.90502i
\(707\) −4.06157 + 2.34495i −0.152751 + 0.0881909i
\(708\) 0 0
\(709\) 19.4230 + 11.2139i 0.729447 + 0.421147i 0.818220 0.574905i \(-0.194961\pi\)
−0.0887726 + 0.996052i \(0.528294\pi\)
\(710\) 14.7779i 0.554605i
\(711\) 0 0
\(712\) −93.0849 −3.48851
\(713\) −40.4807 23.3716i −1.51601 0.875272i
\(714\) 0 0
\(715\) −1.83620 + 9.08415i −0.0686701 + 0.339728i
\(716\) −0.311285 0.539162i −0.0116333 0.0201494i
\(717\) 0 0
\(718\) 0.273088 0.473003i 0.0101916 0.0176523i
\(719\) 37.6708 1.40488 0.702442 0.711741i \(-0.252093\pi\)
0.702442 + 0.711741i \(0.252093\pi\)
\(720\) 0 0
\(721\) 3.37284i 0.125611i
\(722\) −70.3691 40.6276i −2.61887 1.51200i
\(723\) 0 0
\(724\) −45.5515 78.8975i −1.69291 2.93220i
\(725\) 4.08516 + 7.07571i 0.151719 + 0.262785i
\(726\) 0 0
\(727\) −22.0067 + 38.1168i −0.816185 + 1.41367i 0.0922894 + 0.995732i \(0.470582\pi\)
−0.908474 + 0.417941i \(0.862752\pi\)
\(728\) 14.0585 + 12.4062i 0.521042 + 0.459803i
\(729\) 0 0
\(730\) 20.6092i 0.762779i
\(731\) 13.1184 22.7218i 0.485202 0.840395i
\(732\) 0 0
\(733\) 15.2722 8.81743i 0.564093 0.325679i −0.190694 0.981650i \(-0.561074\pi\)
0.754787 + 0.655970i \(0.227740\pi\)
\(734\) 44.0102 25.4093i 1.62445 0.937875i
\(735\) 0 0
\(736\) 5.63161 + 3.25141i 0.207584 + 0.119849i
\(737\) 10.4984 0.386713
\(738\) 0 0
\(739\) 13.4319i 0.494100i 0.969003 + 0.247050i \(0.0794612\pi\)
−0.969003 + 0.247050i \(0.920539\pi\)
\(740\) 8.89551 15.4075i 0.327005 0.566390i
\(741\) 0 0
\(742\) −7.67590 13.2951i −0.281791 0.488077i
\(743\) −28.3946 + 16.3936i −1.04170 + 0.601423i −0.920313 0.391182i \(-0.872066\pi\)
−0.121383 + 0.992606i \(0.538733\pi\)
\(744\) 0 0
\(745\) 5.46360 9.46323i 0.200171 0.346706i
\(746\) 26.8911i 0.984555i
\(747\) 0 0
\(748\) 63.7923i 2.33248i
\(749\) 1.99133 + 1.14969i 0.0727616 + 0.0420089i
\(750\) 0 0
\(751\) −12.4916 21.6360i −0.455824 0.789511i 0.542911 0.839790i \(-0.317322\pi\)
−0.998735 + 0.0502796i \(0.983989\pi\)
\(752\) −18.5097 + 10.6866i −0.674978 + 0.389699i
\(753\) 0 0
\(754\) −5.52554 16.4448i −0.201228 0.598884i
\(755\) −4.95897 −0.180475
\(756\) 0 0
\(757\) 21.6436 0.786652 0.393326 0.919399i \(-0.371324\pi\)
0.393326 + 0.919399i \(0.371324\pi\)
\(758\) 24.3996 42.2614i 0.886234 1.53500i
\(759\) 0 0
\(760\) −29.3907 + 16.9687i −1.06611 + 0.615521i
\(761\) 17.2650 9.96794i 0.625855 0.361338i −0.153290 0.988181i \(-0.548987\pi\)
0.779145 + 0.626844i \(0.215654\pi\)
\(762\) 0 0
\(763\) −5.01610 + 8.68813i −0.181595 + 0.314532i
\(764\) −82.5623 −2.98700
\(765\) 0 0
\(766\) 50.3921 1.82074
\(767\) −3.64302 10.8421i −0.131542 0.391487i
\(768\) 0 0
\(769\) −32.9151 + 19.0035i −1.18695 + 0.685285i −0.957612 0.288062i \(-0.906989\pi\)
−0.229337 + 0.973347i \(0.573656\pi\)
\(770\) −3.12760 5.41717i −0.112711 0.195221i
\(771\) 0 0
\(772\) −36.0138 20.7926i −1.29616 0.748341i
\(773\) 36.5619i 1.31504i 0.753437 + 0.657520i \(0.228395\pi\)
−0.753437 + 0.657520i \(0.771605\pi\)
\(774\) 0 0
\(775\) 42.4341i 1.52428i
\(776\) −0.652032 + 1.12935i −0.0234066 + 0.0405414i
\(777\) 0 0
\(778\) 45.9029 26.5021i 1.64570 0.950145i
\(779\) −9.94583 17.2267i −0.356346 0.617210i
\(780\) 0 0
\(781\) −9.66320 + 16.7372i −0.345777 + 0.598903i
\(782\) 61.3392i 2.19348i
\(783\) 0 0
\(784\) 29.2117 1.04328
\(785\) 3.12456 + 1.80396i 0.111520 + 0.0643862i
\(786\) 0 0
\(787\) −1.39487 + 0.805329i −0.0497218 + 0.0287069i −0.524655 0.851315i \(-0.675806\pi\)
0.474933 + 0.880022i \(0.342472\pi\)
\(788\) 14.1414 8.16455i 0.503767 0.290850i
\(789\) 0 0
\(790\) −5.23802 + 9.07251i −0.186360 + 0.322785i
\(791\) 1.18916i 0.0422817i
\(792\) 0 0
\(793\) −14.9247 13.1706i −0.529993 0.467702i
\(794\) 34.4336 59.6408i 1.22200 2.11657i
\(795\) 0 0
\(796\) 23.7354 + 41.1109i 0.841280 + 1.45714i
\(797\) 0.0491630 + 0.0851528i 0.00174144 + 0.00301627i 0.866895 0.498491i \(-0.166112\pi\)
−0.865153 + 0.501507i \(0.832779\pi\)
\(798\) 0 0
\(799\) −20.4338 11.7975i −0.722896 0.417364i
\(800\) 5.90335i 0.208715i
\(801\) 0 0
\(802\) 37.6201 1.32841
\(803\) 13.4762 23.3415i 0.475566 0.823705i
\(804\) 0 0
\(805\) −2.02725 3.51131i −0.0714513 0.123757i
\(806\) 17.8514 88.3152i 0.628788 3.11077i
\(807\) 0 0
\(808\) −21.8879 12.6370i −0.770013 0.444567i
\(809\) −33.5971 −1.18121 −0.590605 0.806961i \(-0.701111\pi\)
−0.590605 + 0.806961i \(0.701111\pi\)
\(810\) 0 0
\(811\) 13.9011i 0.488134i 0.969758 + 0.244067i \(0.0784817\pi\)
−0.969758 + 0.244067i \(0.921518\pi\)
\(812\) 6.83558 + 3.94652i 0.239882 + 0.138496i
\(813\) 0 0
\(814\) −29.8911 + 17.2577i −1.04768 + 0.604881i
\(815\) −4.60449 7.97521i −0.161288 0.279360i
\(816\) 0 0
\(817\) −30.6041 17.6693i −1.07070 0.618170i
\(818\) −5.91002 −0.206639
\(819\) 0 0
\(820\) −10.1843 −0.355651
\(821\) 36.3185 + 20.9685i 1.26753 + 0.731806i 0.974519 0.224304i \(-0.0720109\pi\)
0.293007 + 0.956110i \(0.405344\pi\)
\(822\) 0 0
\(823\) −22.4560 38.8949i −0.782766 1.35579i −0.930324 0.366737i \(-0.880475\pi\)
0.147558 0.989053i \(-0.452859\pi\)
\(824\) −15.7411 + 9.08815i −0.548368 + 0.316601i
\(825\) 0 0
\(826\) 6.68552 + 3.85988i 0.232619 + 0.134303i
\(827\) 17.5703i 0.610980i 0.952195 + 0.305490i \(0.0988202\pi\)
−0.952195 + 0.305490i \(0.901180\pi\)
\(828\) 0 0
\(829\) 0.797445 0.0276964 0.0138482 0.999904i \(-0.495592\pi\)
0.0138482 + 0.999904i \(0.495592\pi\)
\(830\) 10.5544 + 6.09360i 0.366350 + 0.211512i
\(831\) 0 0
\(832\) 4.43199 21.9261i 0.153652 0.760152i
\(833\) 16.1242 + 27.9279i 0.558670 + 0.967644i
\(834\) 0 0
\(835\) −5.88255 + 10.1889i −0.203574 + 0.352601i
\(836\) 85.9222 2.97168
\(837\) 0 0
\(838\) 82.4710i 2.84891i
\(839\) 14.4922 + 8.36709i 0.500327 + 0.288864i 0.728849 0.684675i \(-0.240056\pi\)
−0.228522 + 0.973539i \(0.573389\pi\)
\(840\) 0 0
\(841\) 12.6138 + 21.8477i 0.434959 + 0.753371i
\(842\) 30.1051 + 52.1436i 1.03749 + 1.79699i
\(843\) 0 0
\(844\) 22.6831 39.2882i 0.780783 1.35236i
\(845\) −11.4896 + 1.44032i −0.395254 + 0.0495485i
\(846\) 0 0
\(847\) 2.62513i 0.0902006i
\(848\) 15.2677 26.4444i 0.524295 0.908106i
\(849\) 0 0
\(850\) 48.2243 27.8423i 1.65408 0.954983i
\(851\) −19.3749 + 11.1861i −0.664163 + 0.383455i
\(852\) 0 0
\(853\) −19.7398 11.3968i −0.675876 0.390217i 0.122423 0.992478i \(-0.460933\pi\)
−0.798300 + 0.602261i \(0.794267\pi\)
\(854\) 13.4346 0.459724
\(855\) 0 0
\(856\) 12.3914i 0.423531i
\(857\) 21.7623 37.6934i 0.743386 1.28758i −0.207559 0.978223i \(-0.566552\pi\)
0.950945 0.309360i \(-0.100115\pi\)
\(858\) 0 0
\(859\) 8.51911 + 14.7555i 0.290668 + 0.503452i 0.973968 0.226686i \(-0.0727890\pi\)
−0.683300 + 0.730138i \(0.739456\pi\)
\(860\) −15.6689 + 9.04647i −0.534307 + 0.308482i
\(861\) 0 0
\(862\) −15.0384 + 26.0472i −0.512209 + 0.887172i
\(863\) 47.3664i 1.61237i −0.591663 0.806186i \(-0.701528\pi\)
0.591663 0.806186i \(-0.298472\pi\)
\(864\) 0 0
\(865\) 10.1796i 0.346116i
\(866\) −28.4758 16.4405i −0.967646 0.558671i
\(867\) 0 0
\(868\) 20.4970 + 35.5018i 0.695713 + 1.20501i
\(869\) 11.8649 6.85023i 0.402491 0.232378i
\(870\) 0 0
\(871\) 4.17783 + 12.4338i 0.141560 + 0.421304i
\(872\) −54.0637 −1.83083
\(873\) 0 0
\(874\) 82.6180 2.79460
\(875\) −4.02785 + 6.97645i −0.136166 + 0.235847i
\(876\) 0 0
\(877\) 40.4664 23.3633i 1.36645 0.788922i 0.375980 0.926628i \(-0.377306\pi\)
0.990473 + 0.137706i \(0.0439728\pi\)
\(878\) 28.1078 16.2281i 0.948593 0.547670i
\(879\) 0 0
\(880\) 6.22094 10.7750i 0.209708 0.363225i
\(881\) 15.7253 0.529797 0.264899 0.964276i \(-0.414662\pi\)
0.264899 + 0.964276i \(0.414662\pi\)
\(882\) 0 0
\(883\) −24.3745 −0.820269 −0.410134 0.912025i \(-0.634518\pi\)
−0.410134 + 0.912025i \(0.634518\pi\)
\(884\) −75.5528 + 25.3862i −2.54112 + 0.853829i
\(885\) 0 0
\(886\) −73.8851 + 42.6576i −2.48222 + 1.43311i
\(887\) −1.96001 3.39484i −0.0658107 0.113987i 0.831243 0.555910i \(-0.187630\pi\)
−0.897053 + 0.441922i \(0.854297\pi\)
\(888\) 0 0
\(889\) 6.45050 + 3.72420i 0.216343 + 0.124906i
\(890\) 38.8003i 1.30059i
\(891\) 0 0
\(892\) 53.1279i 1.77885i
\(893\) −15.8901 + 27.5224i −0.531741 + 0.921002i
\(894\) 0 0
\(895\) −0.116088 + 0.0670235i −0.00388040 + 0.00224035i
\(896\) 8.92756 + 15.4630i 0.298249 + 0.516582i
\(897\) 0 0
\(898\) −6.59435 + 11.4217i −0.220056 + 0.381149i
\(899\) 19.5926i 0.653450i
\(900\) 0 0
\(901\) 33.7097 1.12303
\(902\) 17.1109 + 9.87899i 0.569731 + 0.328934i
\(903\) 0 0
\(904\) 5.54985 3.20420i 0.184585 0.106570i
\(905\) −16.9876 + 9.80779i −0.564687 + 0.326022i
\(906\) 0 0
\(907\) −21.7796 + 37.7234i −0.723181 + 1.25259i 0.236537 + 0.971622i \(0.423987\pi\)
−0.959718 + 0.280964i \(0.909346\pi\)
\(908\) 97.7044i 3.24243i
\(909\) 0 0
\(910\) 5.17123 5.85996i 0.171424 0.194256i
\(911\) −14.0645 + 24.3604i −0.465976 + 0.807095i −0.999245 0.0388513i \(-0.987630\pi\)
0.533269 + 0.845946i \(0.320963\pi\)
\(912\) 0 0
\(913\) −7.96916 13.8030i −0.263741 0.456812i
\(914\) 15.3463 + 26.5806i 0.507611 + 0.879208i
\(915\) 0 0
\(916\) 44.5609 + 25.7273i 1.47234 + 0.850053i
\(917\) 18.4797i 0.610252i
\(918\) 0 0
\(919\) −17.9402 −0.591793 −0.295897 0.955220i \(-0.595618\pi\)
−0.295897 + 0.955220i \(0.595618\pi\)
\(920\) 10.9249 18.9225i 0.360184 0.623856i
\(921\) 0 0
\(922\) −16.1095 27.9024i −0.530538 0.918918i
\(923\) −23.6682 4.78412i −0.779050 0.157471i
\(924\) 0 0
\(925\) 17.5888 + 10.1549i 0.578316 + 0.333891i
\(926\) 15.9153 0.523008
\(927\) 0 0
\(928\) 2.72569i 0.0894752i
\(929\) 37.2632 + 21.5139i 1.22257 + 0.705849i 0.965464 0.260536i \(-0.0838992\pi\)
0.257101 + 0.966384i \(0.417233\pi\)
\(930\) 0 0
\(931\) 37.6162 21.7177i 1.23282 0.711770i
\(932\) 38.8503 + 67.2906i 1.27258 + 2.20418i
\(933\) 0 0
\(934\) −29.9492 17.2912i −0.979967 0.565784i
\(935\) 13.7353 0.449191
\(936\) 0 0
\(937\) 20.5616 0.671719 0.335860 0.941912i \(-0.390973\pi\)
0.335860 + 0.941912i \(0.390973\pi\)
\(938\) −7.66699 4.42654i −0.250336 0.144532i
\(939\) 0 0
\(940\) 8.13553 + 14.0912i 0.265352 + 0.459603i
\(941\) 31.2579 18.0468i 1.01898 0.588308i 0.105171 0.994454i \(-0.466461\pi\)
0.913808 + 0.406147i \(0.133128\pi\)
\(942\) 0 0
\(943\) 11.0910 + 6.40338i 0.361172 + 0.208523i
\(944\) 15.3550i 0.499761i
\(945\) 0 0
\(946\) 35.1011 1.14123
\(947\) −5.32031 3.07168i −0.172887 0.0998163i 0.411059 0.911609i \(-0.365159\pi\)
−0.583946 + 0.811792i \(0.698492\pi\)
\(948\) 0 0
\(949\) 33.0076 + 6.67191i 1.07147 + 0.216579i
\(950\) −37.5009 64.9535i −1.21669 2.10737i
\(951\) 0 0
\(952\) 13.8939 24.0649i 0.450302 0.779947i
\(953\) −19.7667 −0.640305 −0.320152 0.947366i \(-0.603734\pi\)
−0.320152 + 0.947366i \(0.603734\pi\)
\(954\) 0 0
\(955\) 17.7767i 0.575240i
\(956\) 70.8766 + 40.9206i 2.29231 + 1.32347i
\(957\) 0 0
\(958\) 42.8882 + 74.2846i 1.38566 + 2.40003i
\(959\) −8.87119 15.3654i −0.286466 0.496173i
\(960\) 0 0
\(961\) 35.3789 61.2780i 1.14125 1.97671i
\(962\) −32.3344 28.5341i −1.04250 0.919976i
\(963\) 0 0
\(964\) 47.1267i 1.51785i
\(965\) −4.47689 + 7.75420i −0.144116 + 0.249617i
\(966\) 0 0
\(967\) −26.4324 + 15.2608i −0.850009 + 0.490753i −0.860654 0.509190i \(-0.829945\pi\)
0.0106449 + 0.999943i \(0.496612\pi\)
\(968\) 12.2516 7.07344i 0.393780 0.227349i
\(969\) 0 0
\(970\) 0.470745 + 0.271784i 0.0151147 + 0.00872647i
\(971\) 4.05102 0.130004 0.0650018 0.997885i \(-0.479295\pi\)
0.0650018 + 0.997885i \(0.479295\pi\)
\(972\) 0 0
\(973\) 4.76581i 0.152785i
\(974\) 7.16940 12.4178i 0.229722 0.397891i
\(975\) 0 0
\(976\) 13.3610 + 23.1420i 0.427677 + 0.740758i
\(977\) 25.1440 14.5169i 0.804426 0.464436i −0.0405902 0.999176i \(-0.512924\pi\)
0.845017 + 0.534740i \(0.179590\pi\)
\(978\) 0 0
\(979\) 25.3714 43.9445i 0.810872 1.40447i
\(980\) 22.2385i 0.710382i
\(981\) 0 0
\(982\) 61.7447i 1.97035i
\(983\) 5.23002 + 3.01955i 0.166812 + 0.0963088i 0.581082 0.813845i \(-0.302630\pi\)
−0.414270 + 0.910154i \(0.635963\pi\)
\(984\) 0 0
\(985\) −1.75793 3.04482i −0.0560122 0.0970160i
\(986\) −22.2661 + 12.8553i −0.709096 + 0.409397i
\(987\) 0 0
\(988\) 34.1927 + 101.762i 1.08782 + 3.23750i
\(989\) 22.7519 0.723467
\(990\) 0 0
\(991\) −49.4199 −1.56987 −0.784937 0.619575i \(-0.787305\pi\)
−0.784937 + 0.619575i \(0.787305\pi\)
\(992\) −7.07818 + 12.2598i −0.224732 + 0.389248i
\(993\) 0 0
\(994\) 14.1141 8.14879i 0.447673 0.258464i
\(995\) 8.85169 5.11052i 0.280617 0.162014i
\(996\) 0 0
\(997\) 10.6174 18.3899i 0.336257 0.582414i −0.647469 0.762092i \(-0.724172\pi\)
0.983725 + 0.179678i \(0.0575056\pi\)
\(998\) −98.6419 −3.12246
\(999\) 0 0
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 351.2.t.c.181.10 20
3.2 odd 2 117.2.t.c.25.1 20
9.2 odd 6 1053.2.b.j.649.10 10
9.4 even 3 inner 351.2.t.c.64.1 20
9.5 odd 6 117.2.t.c.103.10 yes 20
9.7 even 3 1053.2.b.i.649.1 10
13.12 even 2 inner 351.2.t.c.181.1 20
39.38 odd 2 117.2.t.c.25.10 yes 20
117.25 even 6 1053.2.b.i.649.10 10
117.38 odd 6 1053.2.b.j.649.1 10
117.77 odd 6 117.2.t.c.103.1 yes 20
117.103 even 6 inner 351.2.t.c.64.10 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.t.c.25.1 20 3.2 odd 2
117.2.t.c.25.10 yes 20 39.38 odd 2
117.2.t.c.103.1 yes 20 117.77 odd 6
117.2.t.c.103.10 yes 20 9.5 odd 6
351.2.t.c.64.1 20 9.4 even 3 inner
351.2.t.c.64.10 20 117.103 even 6 inner
351.2.t.c.181.1 20 13.12 even 2 inner
351.2.t.c.181.10 20 1.1 even 1 trivial
1053.2.b.i.649.1 10 9.7 even 3
1053.2.b.i.649.10 10 117.25 even 6
1053.2.b.j.649.1 10 117.38 odd 6
1053.2.b.j.649.10 10 9.2 odd 6