Properties

Label 507.2.f.g.239.19
Level $507$
Weight $2$
Character 507.239
Analytic conductor $4.048$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(239,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(4))
 
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("507.239");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.f (of order \(4\), 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 239.19
Character \(\chi\) \(=\) 507.239
Dual form 507.2.f.g.437.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.38407 + 1.38407i) q^{2} +(0.526444 - 1.65011i) q^{3} +1.83129i q^{4} +(-1.04664 - 1.04664i) q^{5} +(3.01250 - 1.55523i) q^{6} +(-3.17096 - 3.17096i) q^{7} +(0.233508 - 0.233508i) q^{8} +(-2.44571 - 1.73738i) q^{9} +O(q^{10})\) \(q+(1.38407 + 1.38407i) q^{2} +(0.526444 - 1.65011i) q^{3} +1.83129i q^{4} +(-1.04664 - 1.04664i) q^{5} +(3.01250 - 1.55523i) q^{6} +(-3.17096 - 3.17096i) q^{7} +(0.233508 - 0.233508i) q^{8} +(-2.44571 - 1.73738i) q^{9} -2.89724i q^{10} +(-0.108328 + 0.108328i) q^{11} +(3.02182 + 0.964071i) q^{12} -8.77764i q^{14} +(-2.27806 + 1.17607i) q^{15} +4.30896 q^{16} +3.16727 q^{17} +(-0.980382 - 5.78968i) q^{18} +(-0.846216 + 0.846216i) q^{19} +(1.91670 - 1.91670i) q^{20} +(-6.90175 + 3.56309i) q^{21} -0.299868 q^{22} +6.70271 q^{23} +(-0.262385 - 0.508243i) q^{24} -2.80909i q^{25} +(-4.15440 + 3.12106i) q^{27} +(5.80694 - 5.80694i) q^{28} +1.98510i q^{29} +(-4.78076 - 1.52523i) q^{30} +(-3.64859 + 3.64859i) q^{31} +(5.49688 + 5.49688i) q^{32} +(0.121725 + 0.235783i) q^{33} +(4.38372 + 4.38372i) q^{34} +6.63770i q^{35} +(3.18164 - 4.47881i) q^{36} +(-2.31488 - 2.31488i) q^{37} -2.34244 q^{38} -0.488797 q^{40} +(5.91863 + 5.91863i) q^{41} +(-14.4841 - 4.62094i) q^{42} -2.78318i q^{43} +(-0.198381 - 0.198381i) q^{44} +(0.741369 + 4.37819i) q^{45} +(9.27700 + 9.27700i) q^{46} +(4.06533 - 4.06533i) q^{47} +(2.26843 - 7.11025i) q^{48} +13.1099i q^{49} +(3.88798 - 3.88798i) q^{50} +(1.66739 - 5.22634i) q^{51} +0.628103i q^{53} +(-10.0697 - 1.43021i) q^{54} +0.226762 q^{55} -1.48089 q^{56} +(0.950863 + 1.84183i) q^{57} +(-2.74752 + 2.74752i) q^{58} +(6.20927 - 6.20927i) q^{59} +(-2.15372 - 4.17179i) q^{60} +5.83263 q^{61} -10.0998 q^{62} +(2.24610 + 13.2644i) q^{63} +6.59818i q^{64} +(-0.157864 + 0.494815i) q^{66} +(-0.475547 + 0.475547i) q^{67} +5.80019i q^{68} +(3.52860 - 11.0602i) q^{69} +(-9.18702 + 9.18702i) q^{70} +(-8.09127 - 8.09127i) q^{71} +(-0.976786 + 0.165402i) q^{72} +(3.92370 + 3.92370i) q^{73} -6.40789i q^{74} +(-4.63531 - 1.47883i) q^{75} +(-1.54967 - 1.54967i) q^{76} +0.687010 q^{77} -5.46386 q^{79} +(-4.50993 - 4.50993i) q^{80} +(2.96302 + 8.49826i) q^{81} +16.3836i q^{82} +(6.40765 + 6.40765i) q^{83} +(-6.52505 - 12.6391i) q^{84} +(-3.31499 - 3.31499i) q^{85} +(3.85212 - 3.85212i) q^{86} +(3.27563 + 1.04505i) q^{87} +0.0505912i q^{88} +(-3.75466 + 3.75466i) q^{89} +(-5.03360 + 7.08582i) q^{90} +12.2746i q^{92} +(4.09979 + 7.94134i) q^{93} +11.2534 q^{94} +1.77137 q^{95} +(11.9642 - 6.17664i) q^{96} +(-3.16443 + 3.16443i) q^{97} +(-18.1451 + 18.1451i) q^{98} +(0.453148 - 0.0767327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38407 + 1.38407i 0.978684 + 0.978684i 0.999778 0.0210936i \(-0.00671481\pi\)
−0.0210936 + 0.999778i \(0.506715\pi\)
\(3\) 0.526444 1.65011i 0.303943 0.952690i
\(4\) 1.83129i 0.915644i
\(5\) −1.04664 1.04664i −0.468071 0.468071i 0.433218 0.901289i \(-0.357378\pi\)
−0.901289 + 0.433218i \(0.857378\pi\)
\(6\) 3.01250 1.55523i 1.22985 0.634919i
\(7\) −3.17096 3.17096i −1.19851 1.19851i −0.974613 0.223896i \(-0.928122\pi\)
−0.223896 0.974613i \(-0.571878\pi\)
\(8\) 0.233508 0.233508i 0.0825576 0.0825576i
\(9\) −2.44571 1.73738i −0.815238 0.579127i
\(10\) 2.89724i 0.916188i
\(11\) −0.108328 + 0.108328i −0.0326623 + 0.0326623i −0.723249 0.690587i \(-0.757352\pi\)
0.690587 + 0.723249i \(0.257352\pi\)
\(12\) 3.02182 + 0.964071i 0.872325 + 0.278303i
\(13\) 0 0
\(14\) 8.77764i 2.34592i
\(15\) −2.27806 + 1.17607i −0.588194 + 0.303660i
\(16\) 4.30896 1.07724
\(17\) 3.16727 0.768177 0.384088 0.923296i \(-0.374516\pi\)
0.384088 + 0.923296i \(0.374516\pi\)
\(18\) −0.980382 5.78968i −0.231078 1.36464i
\(19\) −0.846216 + 0.846216i −0.194135 + 0.194135i −0.797480 0.603345i \(-0.793834\pi\)
0.603345 + 0.797480i \(0.293834\pi\)
\(20\) 1.91670 1.91670i 0.428587 0.428587i
\(21\) −6.90175 + 3.56309i −1.50609 + 0.777530i
\(22\) −0.299868 −0.0639321
\(23\) 6.70271 1.39761 0.698805 0.715312i \(-0.253715\pi\)
0.698805 + 0.715312i \(0.253715\pi\)
\(24\) −0.262385 0.508243i −0.0535590 0.103745i
\(25\) 2.80909i 0.561819i
\(26\) 0 0
\(27\) −4.15440 + 3.12106i −0.799514 + 0.600648i
\(28\) 5.80694 5.80694i 1.09741 1.09741i
\(29\) 1.98510i 0.368624i 0.982868 + 0.184312i \(0.0590058\pi\)
−0.982868 + 0.184312i \(0.940994\pi\)
\(30\) −4.78076 1.52523i −0.872843 0.278469i
\(31\) −3.64859 + 3.64859i −0.655306 + 0.655306i −0.954266 0.298960i \(-0.903360\pi\)
0.298960 + 0.954266i \(0.403360\pi\)
\(32\) 5.49688 + 5.49688i 0.971720 + 0.971720i
\(33\) 0.121725 + 0.235783i 0.0211896 + 0.0410445i
\(34\) 4.38372 + 4.38372i 0.751802 + 0.751802i
\(35\) 6.63770i 1.12198i
\(36\) 3.18164 4.47881i 0.530274 0.746468i
\(37\) −2.31488 2.31488i −0.380563 0.380563i 0.490742 0.871305i \(-0.336726\pi\)
−0.871305 + 0.490742i \(0.836726\pi\)
\(38\) −2.34244 −0.379994
\(39\) 0 0
\(40\) −0.488797 −0.0772856
\(41\) 5.91863 + 5.91863i 0.924334 + 0.924334i 0.997332 0.0729976i \(-0.0232566\pi\)
−0.0729976 + 0.997332i \(0.523257\pi\)
\(42\) −14.4841 4.62094i −2.23494 0.713026i
\(43\) 2.78318i 0.424432i −0.977223 0.212216i \(-0.931932\pi\)
0.977223 0.212216i \(-0.0680680\pi\)
\(44\) −0.198381 0.198381i −0.0299070 0.0299070i
\(45\) 0.741369 + 4.37819i 0.110517 + 0.652662i
\(46\) 9.27700 + 9.27700i 1.36782 + 1.36782i
\(47\) 4.06533 4.06533i 0.592990 0.592990i −0.345448 0.938438i \(-0.612273\pi\)
0.938438 + 0.345448i \(0.112273\pi\)
\(48\) 2.26843 7.11025i 0.327419 1.02628i
\(49\) 13.1099i 1.87285i
\(50\) 3.88798 3.88798i 0.549843 0.549843i
\(51\) 1.66739 5.22634i 0.233482 0.731835i
\(52\) 0 0
\(53\) 0.628103i 0.0862766i 0.999069 + 0.0431383i \(0.0137356\pi\)
−0.999069 + 0.0431383i \(0.986264\pi\)
\(54\) −10.0697 1.43021i −1.37032 0.194627i
\(55\) 0.226762 0.0305765
\(56\) −1.48089 −0.197892
\(57\) 0.950863 + 1.84183i 0.125945 + 0.243957i
\(58\) −2.74752 + 2.74752i −0.360767 + 0.360767i
\(59\) 6.20927 6.20927i 0.808378 0.808378i −0.176011 0.984388i \(-0.556319\pi\)
0.984388 + 0.176011i \(0.0563193\pi\)
\(60\) −2.15372 4.17179i −0.278045 0.538576i
\(61\) 5.83263 0.746792 0.373396 0.927672i \(-0.378193\pi\)
0.373396 + 0.927672i \(0.378193\pi\)
\(62\) −10.0998 −1.28267
\(63\) 2.24610 + 13.2644i 0.282981 + 1.67116i
\(64\) 6.59818i 0.824773i
\(65\) 0 0
\(66\) −0.157864 + 0.494815i −0.0194317 + 0.0609075i
\(67\) −0.475547 + 0.475547i −0.0580973 + 0.0580973i −0.735558 0.677461i \(-0.763080\pi\)
0.677461 + 0.735558i \(0.263080\pi\)
\(68\) 5.80019i 0.703377i
\(69\) 3.52860 11.0602i 0.424794 1.33149i
\(70\) −9.18702 + 9.18702i −1.09806 + 1.09806i
\(71\) −8.09127 8.09127i −0.960257 0.960257i 0.0389831 0.999240i \(-0.487588\pi\)
−0.999240 + 0.0389831i \(0.987588\pi\)
\(72\) −0.976786 + 0.165402i −0.115115 + 0.0194928i
\(73\) 3.92370 + 3.92370i 0.459235 + 0.459235i 0.898404 0.439169i \(-0.144727\pi\)
−0.439169 + 0.898404i \(0.644727\pi\)
\(74\) 6.40789i 0.744902i
\(75\) −4.63531 1.47883i −0.535239 0.170761i
\(76\) −1.54967 1.54967i −0.177759 0.177759i
\(77\) 0.687010 0.0782921
\(78\) 0 0
\(79\) −5.46386 −0.614733 −0.307366 0.951591i \(-0.599448\pi\)
−0.307366 + 0.951591i \(0.599448\pi\)
\(80\) −4.50993 4.50993i −0.504225 0.504225i
\(81\) 2.96302 + 8.49826i 0.329225 + 0.944252i
\(82\) 16.3836i 1.80926i
\(83\) 6.40765 + 6.40765i 0.703331 + 0.703331i 0.965124 0.261793i \(-0.0843139\pi\)
−0.261793 + 0.965124i \(0.584314\pi\)
\(84\) −6.52505 12.6391i −0.711941 1.37904i
\(85\) −3.31499 3.31499i −0.359561 0.359561i
\(86\) 3.85212 3.85212i 0.415384 0.415384i
\(87\) 3.27563 + 1.04505i 0.351185 + 0.112041i
\(88\) 0.0505912i 0.00539304i
\(89\) −3.75466 + 3.75466i −0.397993 + 0.397993i −0.877525 0.479532i \(-0.840807\pi\)
0.479532 + 0.877525i \(0.340807\pi\)
\(90\) −5.03360 + 7.08582i −0.530588 + 0.746911i
\(91\) 0 0
\(92\) 12.2746i 1.27971i
\(93\) 4.09979 + 7.94134i 0.425128 + 0.823479i
\(94\) 11.2534 1.16070
\(95\) 1.77137 0.181738
\(96\) 11.9642 6.17664i 1.22110 0.630401i
\(97\) −3.16443 + 3.16443i −0.321299 + 0.321299i −0.849265 0.527966i \(-0.822955\pi\)
0.527966 + 0.849265i \(0.322955\pi\)
\(98\) −18.1451 + 18.1451i −1.83293 + 1.83293i
\(99\) 0.453148 0.0767327i 0.0455431 0.00771193i
\(100\) 5.14426 0.514426
\(101\) 1.68098 0.167263 0.0836317 0.996497i \(-0.473348\pi\)
0.0836317 + 0.996497i \(0.473348\pi\)
\(102\) 9.54140 4.92583i 0.944740 0.487730i
\(103\) 4.41524i 0.435046i 0.976055 + 0.217523i \(0.0697977\pi\)
−0.976055 + 0.217523i \(0.930202\pi\)
\(104\) 0 0
\(105\) 10.9529 + 3.49438i 1.06890 + 0.341016i
\(106\) −0.869337 + 0.869337i −0.0844375 + 0.0844375i
\(107\) 15.4776i 1.49628i −0.663541 0.748140i \(-0.730947\pi\)
0.663541 0.748140i \(-0.269053\pi\)
\(108\) −5.71556 7.60790i −0.549980 0.732070i
\(109\) 8.78130 8.78130i 0.841096 0.841096i −0.147905 0.989002i \(-0.547253\pi\)
0.989002 + 0.147905i \(0.0472531\pi\)
\(110\) 0.313854 + 0.313854i 0.0299248 + 0.0299248i
\(111\) −5.03845 + 2.60114i −0.478228 + 0.246889i
\(112\) −13.6635 13.6635i −1.29108 1.29108i
\(113\) 4.79085i 0.450685i 0.974280 + 0.225343i \(0.0723502\pi\)
−0.974280 + 0.225343i \(0.927650\pi\)
\(114\) −1.23316 + 3.86528i −0.115496 + 0.362017i
\(115\) −7.01531 7.01531i −0.654181 0.654181i
\(116\) −3.63530 −0.337529
\(117\) 0 0
\(118\) 17.1881 1.58229
\(119\) −10.0433 10.0433i −0.920667 0.920667i
\(120\) −0.257325 + 0.806568i −0.0234904 + 0.0736293i
\(121\) 10.9765i 0.997866i
\(122\) 8.07276 + 8.07276i 0.730873 + 0.730873i
\(123\) 12.8822 6.65055i 1.16155 0.599660i
\(124\) −6.68162 6.68162i −0.600027 0.600027i
\(125\) −8.17330 + 8.17330i −0.731042 + 0.731042i
\(126\) −15.2501 + 21.4676i −1.35859 + 1.91249i
\(127\) 15.9755i 1.41759i −0.705413 0.708796i \(-0.749239\pi\)
0.705413 0.708796i \(-0.250761\pi\)
\(128\) 1.86142 1.86142i 0.164528 0.164528i
\(129\) −4.59255 1.46519i −0.404352 0.129003i
\(130\) 0 0
\(131\) 18.7681i 1.63978i 0.572524 + 0.819888i \(0.305965\pi\)
−0.572524 + 0.819888i \(0.694035\pi\)
\(132\) −0.431786 + 0.222913i −0.0375821 + 0.0194021i
\(133\) 5.36663 0.465346
\(134\) −1.31638 −0.113718
\(135\) 7.61477 + 1.08153i 0.655375 + 0.0930835i
\(136\) 0.739584 0.739584i 0.0634188 0.0634188i
\(137\) 4.18839 4.18839i 0.357838 0.357838i −0.505177 0.863016i \(-0.668573\pi\)
0.863016 + 0.505177i \(0.168573\pi\)
\(138\) 20.1919 10.4242i 1.71885 0.887369i
\(139\) −14.9698 −1.26972 −0.634859 0.772628i \(-0.718942\pi\)
−0.634859 + 0.772628i \(0.718942\pi\)
\(140\) −12.1555 −1.02733
\(141\) −4.56807 8.84841i −0.384701 0.745170i
\(142\) 22.3977i 1.87958i
\(143\) 0 0
\(144\) −10.5385 7.48630i −0.878206 0.623858i
\(145\) 2.07769 2.07769i 0.172542 0.172542i
\(146\) 10.8613i 0.898891i
\(147\) 21.6328 + 6.90165i 1.78424 + 0.569239i
\(148\) 4.23920 4.23920i 0.348460 0.348460i
\(149\) −12.4536 12.4536i −1.02024 1.02024i −0.999791 0.0204461i \(-0.993491\pi\)
−0.0204461 0.999791i \(-0.506509\pi\)
\(150\) −4.36878 8.46238i −0.356709 0.690951i
\(151\) 7.85127 + 7.85127i 0.638928 + 0.638928i 0.950291 0.311363i \(-0.100786\pi\)
−0.311363 + 0.950291i \(0.600786\pi\)
\(152\) 0.395197i 0.0320547i
\(153\) −7.74624 5.50276i −0.626247 0.444872i
\(154\) 0.950869 + 0.950869i 0.0766232 + 0.0766232i
\(155\) 7.63751 0.613459
\(156\) 0 0
\(157\) 10.4654 0.835227 0.417614 0.908625i \(-0.362867\pi\)
0.417614 + 0.908625i \(0.362867\pi\)
\(158\) −7.56236 7.56236i −0.601629 0.601629i
\(159\) 1.03644 + 0.330661i 0.0821948 + 0.0262231i
\(160\) 11.5065i 0.909668i
\(161\) −21.2540 21.2540i −1.67505 1.67505i
\(162\) −7.66115 + 15.8632i −0.601917 + 1.24633i
\(163\) 1.37114 + 1.37114i 0.107396 + 0.107396i 0.758763 0.651367i \(-0.225804\pi\)
−0.651367 + 0.758763i \(0.725804\pi\)
\(164\) −10.8387 + 10.8387i −0.846362 + 0.846362i
\(165\) 0.119377 0.374181i 0.00929351 0.0291300i
\(166\) 17.7372i 1.37668i
\(167\) −9.88695 + 9.88695i −0.765075 + 0.765075i −0.977235 0.212160i \(-0.931950\pi\)
0.212160 + 0.977235i \(0.431950\pi\)
\(168\) −0.779605 + 2.44363i −0.0601478 + 0.188530i
\(169\) 0 0
\(170\) 9.17635i 0.703794i
\(171\) 3.53980 0.599403i 0.270695 0.0458375i
\(172\) 5.09681 0.388628
\(173\) −17.9530 −1.36494 −0.682471 0.730912i \(-0.739095\pi\)
−0.682471 + 0.730912i \(0.739095\pi\)
\(174\) 3.08729 + 5.98012i 0.234047 + 0.453351i
\(175\) −8.90752 + 8.90752i −0.673345 + 0.673345i
\(176\) −0.466783 + 0.466783i −0.0351851 + 0.0351851i
\(177\) −6.97713 13.5148i −0.524433 1.01583i
\(178\) −10.3934 −0.779018
\(179\) −1.76719 −0.132086 −0.0660431 0.997817i \(-0.521037\pi\)
−0.0660431 + 0.997817i \(0.521037\pi\)
\(180\) −8.01773 + 1.35766i −0.597606 + 0.101194i
\(181\) 16.9949i 1.26322i 0.775286 + 0.631611i \(0.217606\pi\)
−0.775286 + 0.631611i \(0.782394\pi\)
\(182\) 0 0
\(183\) 3.07055 9.62447i 0.226982 0.711461i
\(184\) 1.56514 1.56514i 0.115383 0.115383i
\(185\) 4.84568i 0.356261i
\(186\) −5.31697 + 16.6657i −0.389859 + 1.22199i
\(187\) −0.343106 + 0.343106i −0.0250904 + 0.0250904i
\(188\) 7.44479 + 7.44479i 0.542967 + 0.542967i
\(189\) 23.0702 + 3.27667i 1.67811 + 0.238343i
\(190\) 2.45169 + 2.45169i 0.177864 + 0.177864i
\(191\) 22.3761i 1.61908i −0.587066 0.809539i \(-0.699717\pi\)
0.587066 0.809539i \(-0.300283\pi\)
\(192\) 10.8877 + 3.47358i 0.785753 + 0.250684i
\(193\) 13.9367 + 13.9367i 1.00318 + 1.00318i 0.999995 + 0.00318807i \(0.00101480\pi\)
0.00318807 + 0.999995i \(0.498985\pi\)
\(194\) −8.75956 −0.628900
\(195\) 0 0
\(196\) −24.0081 −1.71486
\(197\) 1.05277 + 1.05277i 0.0750064 + 0.0750064i 0.743615 0.668608i \(-0.233110\pi\)
−0.668608 + 0.743615i \(0.733110\pi\)
\(198\) 0.733391 + 0.520985i 0.0521198 + 0.0370248i
\(199\) 19.6776i 1.39491i −0.716629 0.697454i \(-0.754316\pi\)
0.716629 0.697454i \(-0.245684\pi\)
\(200\) −0.655946 0.655946i −0.0463824 0.0463824i
\(201\) 0.534355 + 1.03505i 0.0376905 + 0.0730070i
\(202\) 2.32659 + 2.32659i 0.163698 + 0.163698i
\(203\) 6.29468 6.29468i 0.441800 0.441800i
\(204\) 9.57095 + 3.05348i 0.670100 + 0.213786i
\(205\) 12.3893i 0.865309i
\(206\) −6.11099 + 6.11099i −0.425773 + 0.425773i
\(207\) −16.3929 11.6451i −1.13938 0.809393i
\(208\) 0 0
\(209\) 0.183339i 0.0126818i
\(210\) 10.3231 + 19.9960i 0.712363 + 1.37986i
\(211\) −23.5891 −1.62394 −0.811969 0.583700i \(-0.801604\pi\)
−0.811969 + 0.583700i \(0.801604\pi\)
\(212\) −1.15024 −0.0789986
\(213\) −17.6111 + 9.09186i −1.20669 + 0.622964i
\(214\) 21.4221 21.4221i 1.46438 1.46438i
\(215\) −2.91299 + 2.91299i −0.198664 + 0.198664i
\(216\) −0.241293 + 1.69888i −0.0164179 + 0.115594i
\(217\) 23.1390 1.57078
\(218\) 24.3078 1.64633
\(219\) 8.54015 4.40892i 0.577090 0.297927i
\(220\) 0.415266i 0.0279972i
\(221\) 0 0
\(222\) −10.5737 3.37340i −0.709661 0.226408i
\(223\) 8.91990 8.91990i 0.597321 0.597321i −0.342278 0.939599i \(-0.611198\pi\)
0.939599 + 0.342278i \(0.111198\pi\)
\(224\) 34.8607i 2.32923i
\(225\) −4.88046 + 6.87024i −0.325364 + 0.458016i
\(226\) −6.63086 + 6.63086i −0.441079 + 0.441079i
\(227\) 15.7094 + 15.7094i 1.04267 + 1.04267i 0.999048 + 0.0436223i \(0.0138898\pi\)
0.0436223 + 0.999048i \(0.486110\pi\)
\(228\) −3.37293 + 1.74130i −0.223378 + 0.115321i
\(229\) 7.05247 + 7.05247i 0.466040 + 0.466040i 0.900629 0.434589i \(-0.143106\pi\)
−0.434589 + 0.900629i \(0.643106\pi\)
\(230\) 19.4193i 1.28047i
\(231\) 0.361672 1.13364i 0.0237963 0.0745881i
\(232\) 0.463538 + 0.463538i 0.0304327 + 0.0304327i
\(233\) 22.9574 1.50399 0.751996 0.659168i \(-0.229091\pi\)
0.751996 + 0.659168i \(0.229091\pi\)
\(234\) 0 0
\(235\) −8.50987 −0.555123
\(236\) 11.3710 + 11.3710i 0.740186 + 0.740186i
\(237\) −2.87642 + 9.01596i −0.186844 + 0.585650i
\(238\) 27.8012i 1.80208i
\(239\) 12.6819 + 12.6819i 0.820323 + 0.820323i 0.986154 0.165831i \(-0.0530305\pi\)
−0.165831 + 0.986154i \(0.553031\pi\)
\(240\) −9.81609 + 5.06764i −0.633626 + 0.327115i
\(241\) 1.99604 + 1.99604i 0.128576 + 0.128576i 0.768466 0.639890i \(-0.221020\pi\)
−0.639890 + 0.768466i \(0.721020\pi\)
\(242\) −15.1923 + 15.1923i −0.976596 + 0.976596i
\(243\) 15.5829 0.415449i 0.999645 0.0266510i
\(244\) 10.6812i 0.683796i
\(245\) 13.7214 13.7214i 0.876627 0.876627i
\(246\) 27.0347 + 8.62503i 1.72367 + 0.549912i
\(247\) 0 0
\(248\) 1.70395i 0.108201i
\(249\) 13.9466 7.20004i 0.883828 0.456284i
\(250\) −22.6248 −1.43092
\(251\) 17.1932 1.08522 0.542612 0.839984i \(-0.317435\pi\)
0.542612 + 0.839984i \(0.317435\pi\)
\(252\) −24.2910 + 4.11325i −1.53019 + 0.259110i
\(253\) −0.726094 + 0.726094i −0.0456491 + 0.0456491i
\(254\) 22.1111 22.1111i 1.38738 1.38738i
\(255\) −7.21526 + 3.72494i −0.451837 + 0.233265i
\(256\) 18.3490 1.14681
\(257\) 9.50799 0.593092 0.296546 0.955019i \(-0.404165\pi\)
0.296546 + 0.955019i \(0.404165\pi\)
\(258\) −4.32848 8.38433i −0.269480 0.521986i
\(259\) 14.6807i 0.912217i
\(260\) 0 0
\(261\) 3.44888 4.85499i 0.213480 0.300517i
\(262\) −25.9763 + 25.9763i −1.60482 + 1.60482i
\(263\) 7.24943i 0.447019i 0.974702 + 0.223510i \(0.0717514\pi\)
−0.974702 + 0.223510i \(0.928249\pi\)
\(264\) 0.0834809 + 0.0266334i 0.00513789 + 0.00163917i
\(265\) 0.657397 0.657397i 0.0403836 0.0403836i
\(266\) 7.42778 + 7.42778i 0.455427 + 0.455427i
\(267\) 4.21897 + 8.17221i 0.258197 + 0.500131i
\(268\) −0.870863 0.870863i −0.0531964 0.0531964i
\(269\) 26.7779i 1.63268i 0.577573 + 0.816339i \(0.304000\pi\)
−0.577573 + 0.816339i \(0.696000\pi\)
\(270\) 9.04245 + 12.0363i 0.550306 + 0.732505i
\(271\) 1.19552 + 1.19552i 0.0726228 + 0.0726228i 0.742485 0.669862i \(-0.233647\pi\)
−0.669862 + 0.742485i \(0.733647\pi\)
\(272\) 13.6477 0.827511
\(273\) 0 0
\(274\) 11.5940 0.700421
\(275\) 0.304305 + 0.304305i 0.0183503 + 0.0183503i
\(276\) 20.2544 + 6.46189i 1.21917 + 0.388960i
\(277\) 24.9616i 1.49980i 0.661552 + 0.749899i \(0.269898\pi\)
−0.661552 + 0.749899i \(0.730102\pi\)
\(278\) −20.7192 20.7192i −1.24265 1.24265i
\(279\) 15.2624 2.58442i 0.913735 0.154725i
\(280\) 1.54996 + 1.54996i 0.0926276 + 0.0926276i
\(281\) 2.53054 2.53054i 0.150959 0.150959i −0.627587 0.778546i \(-0.715957\pi\)
0.778546 + 0.627587i \(0.215957\pi\)
\(282\) 5.92428 18.5693i 0.352786 1.10579i
\(283\) 5.11893i 0.304289i 0.988358 + 0.152144i \(0.0486179\pi\)
−0.988358 + 0.152144i \(0.951382\pi\)
\(284\) 14.8174 14.8174i 0.879254 0.879254i
\(285\) 0.932525 2.92295i 0.0552380 0.173140i
\(286\) 0 0
\(287\) 37.5354i 2.21565i
\(288\) −3.89362 22.9939i −0.229434 1.35493i
\(289\) −6.96837 −0.409904
\(290\) 5.75132 0.337729
\(291\) 3.55575 + 6.88754i 0.208442 + 0.403755i
\(292\) −7.18543 + 7.18543i −0.420496 + 0.420496i
\(293\) 0.198293 0.198293i 0.0115844 0.0115844i −0.701291 0.712875i \(-0.747393\pi\)
0.712875 + 0.701291i \(0.247393\pi\)
\(294\) 20.3889 + 39.4937i 1.18911 + 2.30332i
\(295\) −12.9977 −0.756757
\(296\) −1.08108 −0.0628367
\(297\) 0.111940 0.788139i 0.00649542 0.0457325i
\(298\) 34.4732i 1.99698i
\(299\) 0 0
\(300\) 2.70817 8.48859i 0.156356 0.490089i
\(301\) −8.82536 + 8.82536i −0.508685 + 0.508685i
\(302\) 21.7334i 1.25062i
\(303\) 0.884941 2.77379i 0.0508385 0.159350i
\(304\) −3.64631 + 3.64631i −0.209130 + 0.209130i
\(305\) −6.10466 6.10466i −0.349552 0.349552i
\(306\) −3.10514 18.3375i −0.177509 1.04829i
\(307\) −12.9424 12.9424i −0.738660 0.738660i 0.233659 0.972319i \(-0.424930\pi\)
−0.972319 + 0.233659i \(0.924930\pi\)
\(308\) 1.25811i 0.0716877i
\(309\) 7.28562 + 2.32438i 0.414464 + 0.132229i
\(310\) 10.5708 + 10.5708i 0.600383 + 0.600383i
\(311\) −6.76425 −0.383565 −0.191783 0.981437i \(-0.561427\pi\)
−0.191783 + 0.981437i \(0.561427\pi\)
\(312\) 0 0
\(313\) −25.3673 −1.43385 −0.716923 0.697153i \(-0.754450\pi\)
−0.716923 + 0.697153i \(0.754450\pi\)
\(314\) 14.4848 + 14.4848i 0.817424 + 0.817424i
\(315\) 11.5322 16.2339i 0.649766 0.914677i
\(316\) 10.0059i 0.562876i
\(317\) 5.65535 + 5.65535i 0.317636 + 0.317636i 0.847859 0.530222i \(-0.177892\pi\)
−0.530222 + 0.847859i \(0.677892\pi\)
\(318\) 0.976843 + 1.89216i 0.0547786 + 0.106107i
\(319\) −0.215043 0.215043i −0.0120401 0.0120401i
\(320\) 6.90592 6.90592i 0.386052 0.386052i
\(321\) −25.5398 8.14811i −1.42549 0.454783i
\(322\) 58.8339i 3.27869i
\(323\) −2.68020 + 2.68020i −0.149130 + 0.149130i
\(324\) −15.5628 + 5.42615i −0.864599 + 0.301453i
\(325\) 0 0
\(326\) 3.79550i 0.210214i
\(327\) −9.86723 19.1130i −0.545659 1.05695i
\(328\) 2.76410 0.152622
\(329\) −25.7820 −1.42141
\(330\) 0.683119 0.352666i 0.0376044 0.0194136i
\(331\) 16.6395 16.6395i 0.914589 0.914589i −0.0820401 0.996629i \(-0.526144\pi\)
0.996629 + 0.0820401i \(0.0261436\pi\)
\(332\) −11.7343 + 11.7343i −0.644001 + 0.644001i
\(333\) 1.63970 + 9.68334i 0.0898552 + 0.530644i
\(334\) −27.3684 −1.49753
\(335\) 0.995452 0.0543873
\(336\) −29.7394 + 15.3532i −1.62242 + 0.837586i
\(337\) 8.25174i 0.449501i 0.974416 + 0.224750i \(0.0721567\pi\)
−0.974416 + 0.224750i \(0.927843\pi\)
\(338\) 0 0
\(339\) 7.90542 + 2.52212i 0.429364 + 0.136983i
\(340\) 6.07071 6.07071i 0.329230 0.329230i
\(341\) 0.790492i 0.0428075i
\(342\) 5.72894 + 4.06971i 0.309786 + 0.220065i
\(343\) 19.3744 19.3744i 1.04612 1.04612i
\(344\) −0.649896 0.649896i −0.0350400 0.0350400i
\(345\) −15.2692 + 7.88285i −0.822066 + 0.424399i
\(346\) −24.8482 24.8482i −1.33585 1.33585i
\(347\) 3.83606i 0.205930i 0.994685 + 0.102965i \(0.0328330\pi\)
−0.994685 + 0.102965i \(0.967167\pi\)
\(348\) −1.91378 + 5.99863i −0.102589 + 0.321560i
\(349\) −8.17613 8.17613i −0.437658 0.437658i 0.453565 0.891223i \(-0.350152\pi\)
−0.891223 + 0.453565i \(0.850152\pi\)
\(350\) −24.6572 −1.31798
\(351\) 0 0
\(352\) −1.19094 −0.0634771
\(353\) 7.24062 + 7.24062i 0.385379 + 0.385379i 0.873036 0.487656i \(-0.162148\pi\)
−0.487656 + 0.873036i \(0.662148\pi\)
\(354\) 9.04857 28.3622i 0.480926 1.50743i
\(355\) 16.9373i 0.898937i
\(356\) −6.87586 6.87586i −0.364420 0.364420i
\(357\) −21.8598 + 11.2853i −1.15694 + 0.597281i
\(358\) −2.44592 2.44592i −0.129271 0.129271i
\(359\) 7.50270 7.50270i 0.395977 0.395977i −0.480834 0.876812i \(-0.659666\pi\)
0.876812 + 0.480834i \(0.159666\pi\)
\(360\) 1.19546 + 0.849227i 0.0630062 + 0.0447582i
\(361\) 17.5678i 0.924623i
\(362\) −23.5221 + 23.5221i −1.23629 + 1.23629i
\(363\) 18.1125 + 5.77853i 0.950658 + 0.303294i
\(364\) 0 0
\(365\) 8.21340i 0.429909i
\(366\) 17.5708 9.07107i 0.918439 0.474152i
\(367\) −14.0058 −0.731096 −0.365548 0.930792i \(-0.619118\pi\)
−0.365548 + 0.930792i \(0.619118\pi\)
\(368\) 28.8817 1.50556
\(369\) −4.19236 24.7582i −0.218246 1.28886i
\(370\) −6.70675 + 6.70675i −0.348667 + 0.348667i
\(371\) 1.99169 1.99169i 0.103403 0.103403i
\(372\) −14.5429 + 7.50789i −0.754014 + 0.389266i
\(373\) −19.9776 −1.03440 −0.517200 0.855865i \(-0.673026\pi\)
−0.517200 + 0.855865i \(0.673026\pi\)
\(374\) −0.949764 −0.0491111
\(375\) 9.18404 + 17.7896i 0.474262 + 0.918652i
\(376\) 1.89858i 0.0979116i
\(377\) 0 0
\(378\) 27.3955 + 36.4658i 1.40907 + 1.87560i
\(379\) −6.29483 + 6.29483i −0.323344 + 0.323344i −0.850048 0.526705i \(-0.823427\pi\)
0.526705 + 0.850048i \(0.323427\pi\)
\(380\) 3.24388i 0.166408i
\(381\) −26.3612 8.41019i −1.35053 0.430867i
\(382\) 30.9701 30.9701i 1.58457 1.58457i
\(383\) 16.5930 + 16.5930i 0.847862 + 0.847862i 0.989866 0.142004i \(-0.0453545\pi\)
−0.142004 + 0.989866i \(0.545355\pi\)
\(384\) −2.09161 4.05147i −0.106737 0.206751i
\(385\) −0.719052 0.719052i −0.0366463 0.0366463i
\(386\) 38.5786i 1.96360i
\(387\) −4.83545 + 6.80687i −0.245800 + 0.346013i
\(388\) −5.79498 5.79498i −0.294195 0.294195i
\(389\) −33.0750 −1.67697 −0.838484 0.544926i \(-0.816558\pi\)
−0.838484 + 0.544926i \(0.816558\pi\)
\(390\) 0 0
\(391\) 21.2293 1.07361
\(392\) 3.06128 + 3.06128i 0.154618 + 0.154618i
\(393\) 30.9694 + 9.88036i 1.56220 + 0.498398i
\(394\) 2.91420i 0.146815i
\(395\) 5.71869 + 5.71869i 0.287739 + 0.287739i
\(396\) 0.140520 + 0.829845i 0.00706138 + 0.0417013i
\(397\) −23.6911 23.6911i −1.18902 1.18902i −0.977338 0.211684i \(-0.932105\pi\)
−0.211684 0.977338i \(-0.567895\pi\)
\(398\) 27.2351 27.2351i 1.36517 1.36517i
\(399\) 2.82523 8.85552i 0.141438 0.443331i
\(400\) 12.1043i 0.605213i
\(401\) 12.1119 12.1119i 0.604838 0.604838i −0.336755 0.941592i \(-0.609329\pi\)
0.941592 + 0.336755i \(0.109329\pi\)
\(402\) −0.693000 + 2.17217i −0.0345637 + 0.108338i
\(403\) 0 0
\(404\) 3.07835i 0.153154i
\(405\) 5.79340 11.9958i 0.287876 0.596078i
\(406\) 17.4245 0.864765
\(407\) 0.501534 0.0248601
\(408\) −0.831044 1.60974i −0.0411428 0.0796942i
\(409\) 8.69291 8.69291i 0.429837 0.429837i −0.458736 0.888573i \(-0.651698\pi\)
0.888573 + 0.458736i \(0.151698\pi\)
\(410\) 17.1477 17.1477i 0.846864 0.846864i
\(411\) −4.70634 9.11625i −0.232147 0.449672i
\(412\) −8.08557 −0.398348
\(413\) −39.3786 −1.93770
\(414\) −6.57121 38.8066i −0.322957 1.90724i
\(415\) 13.4130i 0.658418i
\(416\) 0 0
\(417\) −7.88074 + 24.7017i −0.385922 + 1.20965i
\(418\) 0.253753 0.253753i 0.0124115 0.0124115i
\(419\) 18.0119i 0.879940i −0.898012 0.439970i \(-0.854989\pi\)
0.898012 0.439970i \(-0.145011\pi\)
\(420\) −6.39921 + 20.0579i −0.312250 + 0.978728i
\(421\) −15.2469 + 15.2469i −0.743088 + 0.743088i −0.973171 0.230083i \(-0.926100\pi\)
0.230083 + 0.973171i \(0.426100\pi\)
\(422\) −32.6489 32.6489i −1.58932 1.58932i
\(423\) −17.0057 + 2.87961i −0.826843 + 0.140011i
\(424\) 0.146667 + 0.146667i 0.00712278 + 0.00712278i
\(425\) 8.89717i 0.431576i
\(426\) −36.9587 11.7912i −1.79065 0.571283i
\(427\) −18.4950 18.4950i −0.895037 0.895037i
\(428\) 28.3440 1.37006
\(429\) 0 0
\(430\) −8.06355 −0.388859
\(431\) −21.3784 21.3784i −1.02976 1.02976i −0.999543 0.0302162i \(-0.990380\pi\)
−0.0302162 0.999543i \(-0.509620\pi\)
\(432\) −17.9011 + 13.4485i −0.861268 + 0.647042i
\(433\) 19.2897i 0.927005i −0.886096 0.463503i \(-0.846592\pi\)
0.886096 0.463503i \(-0.153408\pi\)
\(434\) 32.0260 + 32.0260i 1.53730 + 1.53730i
\(435\) −2.33462 4.52219i −0.111937 0.216823i
\(436\) 16.0811 + 16.0811i 0.770145 + 0.770145i
\(437\) −5.67194 + 5.67194i −0.271326 + 0.271326i
\(438\) 17.9224 + 5.71789i 0.856365 + 0.273211i
\(439\) 17.3861i 0.829793i 0.909869 + 0.414896i \(0.136182\pi\)
−0.909869 + 0.414896i \(0.863818\pi\)
\(440\) 0.0529507 0.0529507i 0.00252432 0.00252432i
\(441\) 22.7769 32.0632i 1.08462 1.52682i
\(442\) 0 0
\(443\) 1.43321i 0.0680940i 0.999420 + 0.0340470i \(0.0108396\pi\)
−0.999420 + 0.0340470i \(0.989160\pi\)
\(444\) −4.76344 9.22685i −0.226063 0.437887i
\(445\) 7.85954 0.372578
\(446\) 24.6915 1.16918
\(447\) −27.1059 + 13.9936i −1.28206 + 0.661876i
\(448\) 20.9226 20.9226i 0.988498 0.988498i
\(449\) −27.3135 + 27.3135i −1.28900 + 1.28900i −0.353610 + 0.935393i \(0.615046\pi\)
−0.935393 + 0.353610i \(0.884954\pi\)
\(450\) −16.2638 + 2.75398i −0.766681 + 0.129824i
\(451\) −1.28231 −0.0603817
\(452\) −8.77343 −0.412667
\(453\) 17.0887 8.82219i 0.802898 0.414503i
\(454\) 43.4858i 2.04089i
\(455\) 0 0
\(456\) 0.652117 + 0.208049i 0.0305382 + 0.00974279i
\(457\) −3.28879 + 3.28879i −0.153843 + 0.153843i −0.779832 0.625989i \(-0.784696\pi\)
0.625989 + 0.779832i \(0.284696\pi\)
\(458\) 19.5222i 0.912212i
\(459\) −13.1581 + 9.88524i −0.614168 + 0.461404i
\(460\) 12.8471 12.8471i 0.598997 0.598997i
\(461\) −5.76221 5.76221i −0.268373 0.268373i 0.560072 0.828444i \(-0.310774\pi\)
−0.828444 + 0.560072i \(0.810774\pi\)
\(462\) 2.06962 1.06846i 0.0962872 0.0497091i
\(463\) 4.68191 + 4.68191i 0.217587 + 0.217587i 0.807481 0.589894i \(-0.200830\pi\)
−0.589894 + 0.807481i \(0.700830\pi\)
\(464\) 8.55373i 0.397097i
\(465\) 4.02072 12.6027i 0.186456 0.584437i
\(466\) 31.7747 + 31.7747i 1.47193 + 1.47193i
\(467\) −15.0964 −0.698578 −0.349289 0.937015i \(-0.613577\pi\)
−0.349289 + 0.937015i \(0.613577\pi\)
\(468\) 0 0
\(469\) 3.01588 0.139260
\(470\) −11.7782 11.7782i −0.543290 0.543290i
\(471\) 5.50943 17.2690i 0.253861 0.795713i
\(472\) 2.89983i 0.133475i
\(473\) 0.301498 + 0.301498i 0.0138629 + 0.0138629i
\(474\) −16.4599 + 8.49755i −0.756027 + 0.390305i
\(475\) 2.37710 + 2.37710i 0.109069 + 0.109069i
\(476\) 18.3922 18.3922i 0.843004 0.843004i
\(477\) 1.09125 1.53616i 0.0499650 0.0703359i
\(478\) 35.1052i 1.60567i
\(479\) 13.0148 13.0148i 0.594660 0.594660i −0.344227 0.938886i \(-0.611859\pi\)
0.938886 + 0.344227i \(0.111859\pi\)
\(480\) −18.9870 6.05753i −0.866632 0.276487i
\(481\) 0 0
\(482\) 5.52530i 0.251671i
\(483\) −46.2604 + 23.8823i −2.10492 + 1.08668i
\(484\) −20.1012 −0.913691
\(485\) 6.62402 0.300781
\(486\) 22.1428 + 20.9928i 1.00442 + 0.952253i
\(487\) −20.1793 + 20.1793i −0.914411 + 0.914411i −0.996615 0.0822048i \(-0.973804\pi\)
0.0822048 + 0.996615i \(0.473804\pi\)
\(488\) 1.36197 1.36197i 0.0616533 0.0616533i
\(489\) 2.98436 1.54070i 0.134957 0.0696729i
\(490\) 37.9826 1.71588
\(491\) 37.9959 1.71473 0.857366 0.514708i \(-0.172100\pi\)
0.857366 + 0.514708i \(0.172100\pi\)
\(492\) 12.1791 + 23.5910i 0.549075 + 1.06357i
\(493\) 6.28737i 0.283169i
\(494\) 0 0
\(495\) −0.554594 0.393971i −0.0249271 0.0177077i
\(496\) −15.7216 + 15.7216i −0.705921 + 0.705921i
\(497\) 51.3141i 2.30175i
\(498\) 29.2684 + 9.33767i 1.31155 + 0.418431i
\(499\) 11.2432 11.2432i 0.503315 0.503315i −0.409152 0.912466i \(-0.634175\pi\)
0.912466 + 0.409152i \(0.134175\pi\)
\(500\) −14.9677 14.9677i −0.669375 0.669375i
\(501\) 11.1096 + 21.5195i 0.496341 + 0.961419i
\(502\) 23.7965 + 23.7965i 1.06209 + 1.06209i
\(503\) 4.11260i 0.183372i −0.995788 0.0916859i \(-0.970774\pi\)
0.995788 0.0916859i \(-0.0292256\pi\)
\(504\) 3.62183 + 2.57287i 0.161329 + 0.114605i
\(505\) −1.75938 1.75938i −0.0782912 0.0782912i
\(506\) −2.00993 −0.0893521
\(507\) 0 0
\(508\) 29.2557 1.29801
\(509\) 17.2162 + 17.2162i 0.763093 + 0.763093i 0.976880 0.213787i \(-0.0685799\pi\)
−0.213787 + 0.976880i \(0.568580\pi\)
\(510\) −15.1420 4.83084i −0.670498 0.213913i
\(511\) 24.8838i 1.10079i
\(512\) 21.6735 + 21.6735i 0.957841 + 0.957841i
\(513\) 0.874427 6.15661i 0.0386069 0.271821i
\(514\) 13.1597 + 13.1597i 0.580450 + 0.580450i
\(515\) 4.62116 4.62116i 0.203633 0.203633i
\(516\) 2.68319 8.41029i 0.118121 0.370242i
\(517\) 0.880782i 0.0387368i
\(518\) −20.3191 + 20.3191i −0.892772 + 0.892772i
\(519\) −9.45126 + 29.6244i −0.414864 + 1.30037i
\(520\) 0 0
\(521\) 14.5577i 0.637784i 0.947791 + 0.318892i \(0.103311\pi\)
−0.947791 + 0.318892i \(0.896689\pi\)
\(522\) 11.4931 1.94616i 0.503040 0.0851811i
\(523\) −3.71977 −0.162654 −0.0813270 0.996687i \(-0.525916\pi\)
−0.0813270 + 0.996687i \(0.525916\pi\)
\(524\) −34.3698 −1.50145
\(525\) 10.0091 + 19.3877i 0.436831 + 0.846147i
\(526\) −10.0337 + 10.0337i −0.437491 + 0.437491i
\(527\) −11.5561 + 11.5561i −0.503391 + 0.503391i
\(528\) 0.524507 + 1.01598i 0.0228262 + 0.0442148i
\(529\) 21.9263 0.953316
\(530\) 1.81976 0.0790455
\(531\) −25.9739 + 4.39823i −1.12717 + 0.190867i
\(532\) 9.82785i 0.426091i
\(533\) 0 0
\(534\) −5.47155 + 17.1502i −0.236777 + 0.742163i
\(535\) −16.1995 + 16.1995i −0.700365 + 0.700365i
\(536\) 0.222088i 0.00959274i
\(537\) −0.930329 + 2.91606i −0.0401467 + 0.125837i
\(538\) −37.0624 + 37.0624i −1.59788 + 1.59788i
\(539\) −1.42018 1.42018i −0.0611715 0.0611715i
\(540\) −1.98060 + 13.9448i −0.0852313 + 0.600091i
\(541\) 2.30265 + 2.30265i 0.0989985 + 0.0989985i 0.754871 0.655873i \(-0.227699\pi\)
−0.655873 + 0.754871i \(0.727699\pi\)
\(542\) 3.30937i 0.142150i
\(543\) 28.0434 + 8.94687i 1.20346 + 0.383947i
\(544\) 17.4101 + 17.4101i 0.746453 + 0.746453i
\(545\) −18.3817 −0.787386
\(546\) 0 0
\(547\) −25.9324 −1.10879 −0.554395 0.832253i \(-0.687050\pi\)
−0.554395 + 0.832253i \(0.687050\pi\)
\(548\) 7.67015 + 7.67015i 0.327653 + 0.327653i
\(549\) −14.2649 10.1335i −0.608813 0.432487i
\(550\) 0.842357i 0.0359182i
\(551\) −1.67983 1.67983i −0.0715630 0.0715630i
\(552\) −1.75869 3.40660i −0.0748547 0.144995i
\(553\) 17.3257 + 17.3257i 0.736763 + 0.736763i
\(554\) −34.5486 + 34.5486i −1.46783 + 1.46783i
\(555\) 7.99589 + 2.55098i 0.339407 + 0.108283i
\(556\) 27.4140i 1.16261i
\(557\) 6.37725 6.37725i 0.270213 0.270213i −0.558973 0.829186i \(-0.688805\pi\)
0.829186 + 0.558973i \(0.188805\pi\)
\(558\) 24.7012 + 17.5472i 1.04568 + 0.742831i
\(559\) 0 0
\(560\) 28.6016i 1.20864i
\(561\) 0.385536 + 0.746788i 0.0162773 + 0.0315294i
\(562\) 7.00488 0.295483
\(563\) −8.75049 −0.368789 −0.184395 0.982852i \(-0.559032\pi\)
−0.184395 + 0.982852i \(0.559032\pi\)
\(564\) 16.2040 8.36545i 0.682311 0.352249i
\(565\) 5.01429 5.01429i 0.210953 0.210953i
\(566\) −7.08494 + 7.08494i −0.297802 + 0.297802i
\(567\) 17.5520 36.3433i 0.737115 1.52627i
\(568\) −3.77875 −0.158553
\(569\) −31.5099 −1.32096 −0.660481 0.750843i \(-0.729648\pi\)
−0.660481 + 0.750843i \(0.729648\pi\)
\(570\) 5.33623 2.75488i 0.223510 0.115389i
\(571\) 34.4177i 1.44034i −0.693799 0.720169i \(-0.744064\pi\)
0.693799 0.720169i \(-0.255936\pi\)
\(572\) 0 0
\(573\) −36.9230 11.7798i −1.54248 0.492107i
\(574\) 51.9516 51.9516i 2.16842 2.16842i
\(575\) 18.8285i 0.785204i
\(576\) 11.4635 16.1373i 0.477648 0.672386i
\(577\) −27.5186 + 27.5186i −1.14562 + 1.14562i −0.158211 + 0.987405i \(0.550573\pi\)
−0.987405 + 0.158211i \(0.949427\pi\)
\(578\) −9.64470 9.64470i −0.401167 0.401167i
\(579\) 30.3339 15.6601i 1.26063 0.650813i
\(580\) 3.80484 + 3.80484i 0.157988 + 0.157988i
\(581\) 40.6368i 1.68590i
\(582\) −4.61142 + 14.4542i −0.191150 + 0.599147i
\(583\) −0.0680414 0.0680414i −0.00281799 0.00281799i
\(584\) 1.83243 0.0758266
\(585\) 0 0
\(586\) 0.548902 0.0226749
\(587\) 2.80955 + 2.80955i 0.115963 + 0.115963i 0.762707 0.646744i \(-0.223870\pi\)
−0.646744 + 0.762707i \(0.723870\pi\)
\(588\) −12.6389 + 39.6159i −0.521220 + 1.63373i
\(589\) 6.17499i 0.254436i
\(590\) −17.9897 17.9897i −0.740625 0.740625i
\(591\) 2.29140 1.18295i 0.0942555 0.0486602i
\(592\) −9.97470 9.97470i −0.409958 0.409958i
\(593\) 11.5666 11.5666i 0.474985 0.474985i −0.428539 0.903523i \(-0.640971\pi\)
0.903523 + 0.428539i \(0.140971\pi\)
\(594\) 1.24577 0.935905i 0.0511146 0.0384007i
\(595\) 21.0234i 0.861876i
\(596\) 22.8061 22.8061i 0.934174 0.934174i
\(597\) −32.4702 10.3592i −1.32892 0.423972i
\(598\) 0 0
\(599\) 2.33031i 0.0952139i 0.998866 + 0.0476069i \(0.0151595\pi\)
−0.998866 + 0.0476069i \(0.984841\pi\)
\(600\) −1.42770 + 0.737063i −0.0582856 + 0.0300905i
\(601\) −3.90549 −0.159308 −0.0796542 0.996823i \(-0.525382\pi\)
−0.0796542 + 0.996823i \(0.525382\pi\)
\(602\) −24.4298 −0.995684
\(603\) 1.98926 0.336846i 0.0810088 0.0137174i
\(604\) −14.3779 + 14.3779i −0.585030 + 0.585030i
\(605\) 11.4885 11.4885i 0.467073 0.467073i
\(606\) 5.06394 2.61430i 0.205708 0.106199i
\(607\) 27.1575 1.10229 0.551144 0.834410i \(-0.314192\pi\)
0.551144 + 0.834410i \(0.314192\pi\)
\(608\) −9.30309 −0.377290
\(609\) −7.07310 13.7007i −0.286617 0.555180i
\(610\) 16.8985i 0.684201i
\(611\) 0 0
\(612\) 10.0771 14.1856i 0.407344 0.573419i
\(613\) 4.38429 4.38429i 0.177080 0.177080i −0.613002 0.790082i \(-0.710038\pi\)
0.790082 + 0.613002i \(0.210038\pi\)
\(614\) 35.8262i 1.44583i
\(615\) −20.4437 6.52229i −0.824371 0.263004i
\(616\) 0.160422 0.160422i 0.00646360 0.00646360i
\(617\) 29.0963 + 29.0963i 1.17137 + 1.17137i 0.981882 + 0.189492i \(0.0606842\pi\)
0.189492 + 0.981882i \(0.439316\pi\)
\(618\) 6.86670 + 13.3009i 0.276219 + 0.535040i
\(619\) −7.15152 7.15152i −0.287444 0.287444i 0.548625 0.836069i \(-0.315152\pi\)
−0.836069 + 0.548625i \(0.815152\pi\)
\(620\) 13.9865i 0.561711i
\(621\) −27.8457 + 20.9195i −1.11741 + 0.839472i
\(622\) −9.36218 9.36218i −0.375389 0.375389i
\(623\) 23.8117 0.953996
\(624\) 0 0
\(625\) 3.06353 0.122541
\(626\) −35.1101 35.1101i −1.40328 1.40328i
\(627\) −0.302529 0.0965176i −0.0120818 0.00385454i
\(628\) 19.1651i 0.764771i
\(629\) −7.33185 7.33185i −0.292340 0.292340i
\(630\) 38.4302 6.50748i 1.53109 0.259264i
\(631\) −8.97854 8.97854i −0.357430 0.357430i 0.505435 0.862865i \(-0.331332\pi\)
−0.862865 + 0.505435i \(0.831332\pi\)
\(632\) −1.27586 + 1.27586i −0.0507508 + 0.0507508i
\(633\) −12.4183 + 38.9245i −0.493584 + 1.54711i
\(634\) 15.6548i 0.621731i
\(635\) −16.7205 + 16.7205i −0.663534 + 0.663534i
\(636\) −0.605536 + 1.89802i −0.0240111 + 0.0752612i
\(637\) 0 0
\(638\) 0.595269i 0.0235669i
\(639\) 5.73132 + 33.8465i 0.226727 + 1.33895i
\(640\) −3.89647 −0.154021
\(641\) 30.3342 1.19813 0.599065 0.800700i \(-0.295539\pi\)
0.599065 + 0.800700i \(0.295539\pi\)
\(642\) −24.0712 46.6263i −0.950016 1.84019i
\(643\) −33.4616 + 33.4616i −1.31960 + 1.31960i −0.405502 + 0.914094i \(0.632903\pi\)
−0.914094 + 0.405502i \(0.867097\pi\)
\(644\) 38.9222 38.9222i 1.53375 1.53375i
\(645\) 3.27322 + 6.34027i 0.128883 + 0.249648i
\(646\) −7.41916 −0.291903
\(647\) −19.2475 −0.756696 −0.378348 0.925663i \(-0.623508\pi\)
−0.378348 + 0.925663i \(0.623508\pi\)
\(648\) 2.67630 + 1.29252i 0.105135 + 0.0507751i
\(649\) 1.34528i 0.0528069i
\(650\) 0 0
\(651\) 12.1814 38.1819i 0.477427 1.49647i
\(652\) −2.51095 + 2.51095i −0.0983366 + 0.0983366i
\(653\) 9.85148i 0.385518i −0.981246 0.192759i \(-0.938256\pi\)
0.981246 0.192759i \(-0.0617436\pi\)
\(654\) 12.7967 40.1106i 0.500391 1.56845i
\(655\) 19.6434 19.6434i 0.767532 0.767532i
\(656\) 25.5031 + 25.5031i 0.995730 + 0.995730i
\(657\) −2.77929 16.4132i −0.108430 0.640341i
\(658\) −35.6840 35.6840i −1.39111 1.39111i
\(659\) 4.63004i 0.180361i −0.995925 0.0901805i \(-0.971256\pi\)
0.995925 0.0901805i \(-0.0287444\pi\)
\(660\) 0.685234 + 0.218614i 0.0266727 + 0.00850955i
\(661\) −21.7120 21.7120i −0.844498 0.844498i 0.144942 0.989440i \(-0.453700\pi\)
−0.989440 + 0.144942i \(0.953700\pi\)
\(662\) 46.0604 1.79019
\(663\) 0 0
\(664\) 2.99247 0.116131
\(665\) −5.61693 5.61693i −0.217815 0.217815i
\(666\) −11.1329 + 15.6719i −0.431393 + 0.607272i
\(667\) 13.3056i 0.515193i
\(668\) −18.1059 18.1059i −0.700537 0.700537i
\(669\) −10.0230 19.4146i −0.387510 0.750613i
\(670\) 1.37777 + 1.37777i 0.0532280 + 0.0532280i
\(671\) −0.631840 + 0.631840i −0.0243919 + 0.0243919i
\(672\) −57.5240 18.3522i −2.21903 0.707952i
\(673\) 36.0212i 1.38851i −0.719727 0.694257i \(-0.755733\pi\)
0.719727 0.694257i \(-0.244267\pi\)
\(674\) −11.4210 + 11.4210i −0.439919 + 0.439919i
\(675\) 8.76734 + 11.6701i 0.337455 + 0.449182i
\(676\) 0 0
\(677\) 5.60187i 0.215297i 0.994189 + 0.107649i \(0.0343322\pi\)
−0.994189 + 0.107649i \(0.965668\pi\)
\(678\) 7.45086 + 14.4324i 0.286149 + 0.554274i
\(679\) 20.0685 0.770159
\(680\) −1.54816 −0.0593690
\(681\) 34.1924 17.6521i 1.31025 0.676430i
\(682\) 1.09409 1.09409i 0.0418950 0.0418950i
\(683\) 1.82603 1.82603i 0.0698711 0.0698711i −0.671308 0.741179i \(-0.734267\pi\)
0.741179 + 0.671308i \(0.234267\pi\)
\(684\) 1.09768 + 6.48240i 0.0419709 + 0.247861i
\(685\) −8.76747 −0.334988
\(686\) 53.6309 2.04764
\(687\) 15.3501 7.92460i 0.585642 0.302343i
\(688\) 11.9926i 0.457215i
\(689\) 0 0
\(690\) −32.0440 10.2232i −1.21989 0.389191i
\(691\) 17.7451 17.7451i 0.675054 0.675054i −0.283823 0.958877i \(-0.591603\pi\)
0.958877 + 0.283823i \(0.0916027\pi\)
\(692\) 32.8772i 1.24980i
\(693\) −1.68023 1.19360i −0.0638266 0.0453410i
\(694\) −5.30936 + 5.30936i −0.201541 + 0.201541i
\(695\) 15.6679 + 15.6679i 0.594319 + 0.594319i
\(696\) 1.00891 0.520860i 0.0382428 0.0197432i
\(697\) 18.7459 + 18.7459i 0.710052 + 0.710052i
\(698\) 22.6327i 0.856659i
\(699\) 12.0858 37.8823i 0.457127 1.43284i
\(700\) −16.3122 16.3122i −0.616544 0.616544i
\(701\) −0.474084 −0.0179059 −0.00895296 0.999960i \(-0.502850\pi\)
−0.00895296 + 0.999960i \(0.502850\pi\)
\(702\) 0 0
\(703\) 3.91777 0.147761
\(704\) −0.714771 0.714771i −0.0269390 0.0269390i
\(705\) −4.47997 + 14.0422i −0.168725 + 0.528860i
\(706\) 20.0430i 0.754329i
\(707\) −5.33031 5.33031i −0.200467 0.200467i
\(708\) 24.7495 12.7771i 0.930143 0.480194i
\(709\) −35.1122 35.1122i −1.31867 1.31867i −0.914832 0.403834i \(-0.867677\pi\)
−0.403834 0.914832i \(-0.632323\pi\)
\(710\) −23.4423 + 23.4423i −0.879775 + 0.879775i
\(711\) 13.3630 + 9.49280i 0.501153 + 0.356008i
\(712\) 1.75349i 0.0657147i
\(713\) −24.4554 + 24.4554i −0.915862 + 0.915862i
\(714\) −45.8750 14.6358i −1.71683 0.547730i
\(715\) 0 0
\(716\) 3.23624i 0.120944i
\(717\) 27.6028 14.2502i 1.03085 0.532183i
\(718\) 20.7685 0.775074
\(719\) 1.69544 0.0632292 0.0316146 0.999500i \(-0.489935\pi\)
0.0316146 + 0.999500i \(0.489935\pi\)
\(720\) 3.19453 + 18.8654i 0.119053 + 0.703073i
\(721\) 14.0005 14.0005i 0.521407 0.521407i
\(722\) −24.3151 + 24.3151i −0.904914 + 0.904914i
\(723\) 4.34448 2.24287i 0.161573 0.0834134i
\(724\) −31.1226 −1.15666
\(725\) 5.57634 0.207100
\(726\) 17.0710 + 33.0668i 0.633564 + 1.22722i
\(727\) 20.3423i 0.754455i −0.926121 0.377227i \(-0.876878\pi\)
0.926121 0.377227i \(-0.123122\pi\)
\(728\) 0 0
\(729\) 7.51800 25.9322i 0.278445 0.960452i
\(730\) 11.3679 11.3679i 0.420745 0.420745i
\(731\) 8.81511i 0.326038i
\(732\) 17.6252 + 5.62307i 0.651446 + 0.207835i
\(733\) 3.64797 3.64797i 0.134741 0.134741i −0.636520 0.771261i \(-0.719627\pi\)
0.771261 + 0.636520i \(0.219627\pi\)
\(734\) −19.3850 19.3850i −0.715512 0.715512i
\(735\) −15.4182 29.8653i −0.568709 1.10160i
\(736\) 36.8439 + 36.8439i 1.35809 + 1.35809i
\(737\) 0.103031i 0.00379518i
\(738\) 28.4645 40.0695i 1.04779 1.47498i
\(739\) 26.5480 + 26.5480i 0.976584 + 0.976584i 0.999732 0.0231482i \(-0.00736897\pi\)
−0.0231482 + 0.999732i \(0.507369\pi\)
\(740\) −8.87383 −0.326209
\(741\) 0 0
\(742\) 5.51326 0.202398
\(743\) 6.45650 + 6.45650i 0.236866 + 0.236866i 0.815551 0.578685i \(-0.196434\pi\)
−0.578685 + 0.815551i \(0.696434\pi\)
\(744\) 2.81170 + 0.897034i 0.103082 + 0.0328869i
\(745\) 26.0688i 0.955087i
\(746\) −27.6503 27.6503i −1.01235 1.01235i
\(747\) −4.53875 26.8038i −0.166064 0.980699i
\(748\) −0.628326 0.628326i −0.0229739 0.0229739i
\(749\) −49.0789 + 49.0789i −1.79330 + 1.79330i
\(750\) −11.9107 + 37.3334i −0.434917 + 1.36322i
\(751\) 23.1057i 0.843137i −0.906796 0.421569i \(-0.861480\pi\)
0.906796 0.421569i \(-0.138520\pi\)
\(752\) 17.5173 17.5173i 0.638792 0.638792i
\(753\) 9.05125 28.3706i 0.329846 1.03388i
\(754\) 0 0
\(755\) 16.4349i 0.598127i
\(756\) −6.00053 + 42.2481i −0.218237 + 1.53655i
\(757\) 37.9154 1.37806 0.689029 0.724734i \(-0.258037\pi\)
0.689029 + 0.724734i \(0.258037\pi\)
\(758\) −17.4249 −0.632902
\(759\) 0.815886 + 1.58038i 0.0296148 + 0.0573642i
\(760\) 0.413628 0.413628i 0.0150039 0.0150039i
\(761\) −33.0810 + 33.0810i −1.19919 + 1.19919i −0.224774 + 0.974411i \(0.572165\pi\)
−0.974411 + 0.224774i \(0.927835\pi\)
\(762\) −24.8455 48.1260i −0.900056 1.74342i
\(763\) −55.6903 −2.01612
\(764\) 40.9771 1.48250
\(765\) 2.34812 + 13.8669i 0.0848965 + 0.501360i
\(766\) 45.9317i 1.65958i
\(767\) 0 0
\(768\) 9.65974 30.2779i 0.348566 1.09256i
\(769\) −21.6783 + 21.6783i −0.781738 + 0.781738i −0.980124 0.198386i \(-0.936430\pi\)
0.198386 + 0.980124i \(0.436430\pi\)
\(770\) 1.99043i 0.0717302i
\(771\) 5.00543 15.6892i 0.180266 0.565033i
\(772\) −25.5221 + 25.5221i −0.918559 + 0.918559i
\(773\) 1.91473 + 1.91473i 0.0688681 + 0.0688681i 0.740702 0.671834i \(-0.234493\pi\)
−0.671834 + 0.740702i \(0.734493\pi\)
\(774\) −16.1138 + 2.72858i −0.579197 + 0.0980769i
\(775\) 10.2492 + 10.2492i 0.368163 + 0.368163i
\(776\) 1.47784i 0.0530513i
\(777\) 24.2248 + 7.72859i 0.869060 + 0.277262i
\(778\) −45.7780 45.7780i −1.64122 1.64122i
\(779\) −10.0169 −0.358892
\(780\) 0 0
\(781\) 1.75303 0.0627283
\(782\) 29.3828 + 29.3828i 1.05073 + 1.05073i
\(783\) −6.19562 8.24690i −0.221413 0.294720i
\(784\) 56.4902i 2.01751i
\(785\) −10.9535 10.9535i −0.390946 0.390946i
\(786\) 29.1887 + 56.5388i 1.04113 + 2.01667i
\(787\) 37.8082 + 37.8082i 1.34772 + 1.34772i 0.888137 + 0.459578i \(0.151999\pi\)
0.459578 + 0.888137i \(0.348001\pi\)
\(788\) −1.92792 + 1.92792i −0.0686792 + 0.0686792i
\(789\) 11.9623 + 3.81642i 0.425871 + 0.135868i
\(790\) 15.8301i 0.563210i
\(791\) 15.1916 15.1916i 0.540151 0.540151i
\(792\) 0.0878960 0.123731i 0.00312325 0.00439661i
\(793\) 0 0
\(794\) 65.5802i 2.32735i
\(795\) −0.738693 1.43086i −0.0261987 0.0507473i
\(796\) 36.0354 1.27724
\(797\) −36.4286 −1.29037 −0.645183 0.764028i \(-0.723219\pi\)
−0.645183 + 0.764028i \(0.723219\pi\)
\(798\) 16.1670 8.34633i 0.572304 0.295457i
\(799\) 12.8760 12.8760i 0.455521 0.455521i
\(800\) 15.4412 15.4412i 0.545930 0.545930i
\(801\) 15.7061 2.65955i 0.554947 0.0939706i
\(802\) 33.5273 1.18389
\(803\) −0.850098 −0.0299993
\(804\) −1.89548 + 0.978558i −0.0668484 + 0.0345111i
\(805\) 44.4905i 1.56808i
\(806\) 0 0
\(807\) 44.1864 + 14.0971i 1.55544 + 0.496241i
\(808\) 0.392522 0.392522i 0.0138089 0.0138089i
\(809\) 27.9069i 0.981154i 0.871398 + 0.490577i \(0.163214\pi\)
−0.871398 + 0.490577i \(0.836786\pi\)
\(810\) 24.6215 8.58459i 0.865111 0.301632i
\(811\) 9.41030 9.41030i 0.330440 0.330440i −0.522313 0.852754i \(-0.674931\pi\)
0.852754 + 0.522313i \(0.174931\pi\)
\(812\) 11.5274 + 11.5274i 0.404531 + 0.404531i
\(813\) 2.60212 1.34337i 0.0912602 0.0471139i
\(814\) 0.694157 + 0.694157i 0.0243302 + 0.0243302i
\(815\) 2.87018i 0.100538i
\(816\) 7.18473 22.5201i 0.251516 0.788361i
\(817\) 2.35518 + 2.35518i 0.0823971 + 0.0823971i
\(818\) 24.0632 0.841349
\(819\) 0 0
\(820\) 22.6884 0.792315
\(821\) −9.06140 9.06140i −0.316245 0.316245i 0.531078 0.847323i \(-0.321787\pi\)
−0.847323 + 0.531078i \(0.821787\pi\)
\(822\) 6.10361 19.1314i 0.212888 0.667285i
\(823\) 20.7304i 0.722615i 0.932447 + 0.361308i \(0.117670\pi\)
−0.932447 + 0.361308i \(0.882330\pi\)
\(824\) 1.03099 + 1.03099i 0.0359164 + 0.0359164i
\(825\) 0.662335 0.341936i 0.0230596 0.0119047i
\(826\) −54.5027 54.5027i −1.89639 1.89639i
\(827\) −30.0036 + 30.0036i −1.04333 + 1.04333i −0.0443105 + 0.999018i \(0.514109\pi\)
−0.999018 + 0.0443105i \(0.985891\pi\)
\(828\) 21.3256 30.0201i 0.741116 1.04327i
\(829\) 1.86550i 0.0647914i 0.999475 + 0.0323957i \(0.0103137\pi\)
−0.999475 + 0.0323957i \(0.989686\pi\)
\(830\) 18.5645 18.5645i 0.644383 0.644383i
\(831\) 41.1894 + 13.1409i 1.42884 + 0.455853i
\(832\) 0 0
\(833\) 41.5228i 1.43868i
\(834\) −45.0964 + 23.2814i −1.56156 + 0.806168i
\(835\) 20.6961 0.716219
\(836\) 0.335746 0.0116120
\(837\) 3.77022 26.5451i 0.130318 0.917534i
\(838\) 24.9297 24.9297i 0.861183 0.861183i
\(839\) 18.7951 18.7951i 0.648880 0.648880i −0.303843 0.952722i \(-0.598270\pi\)
0.952722 + 0.303843i \(0.0982697\pi\)
\(840\) 3.37356 1.74163i 0.116399 0.0600919i
\(841\) 25.0594 0.864116
\(842\) −42.2055 −1.45450
\(843\) −2.84348 5.50785i −0.0979346 0.189701i
\(844\) 43.1984i 1.48695i
\(845\) 0 0
\(846\) −27.5226 19.5514i −0.946245 0.672191i
\(847\) 34.8061 34.8061i 1.19595 1.19595i
\(848\) 2.70647i 0.0929405i
\(849\) 8.44678 + 2.69483i 0.289893 + 0.0924863i
\(850\) 12.3143 12.3143i 0.422377 0.422377i
\(851\) −15.5159 15.5159i −0.531879 0.531879i
\(852\) −16.6498 32.2509i −0.570414 1.10490i
\(853\) −15.8825 15.8825i −0.543806 0.543806i 0.380837 0.924642i \(-0.375636\pi\)
−0.924642 + 0.380837i \(0.875636\pi\)
\(854\) 51.1967i 1.75192i
\(855\) −4.33225 3.07753i −0.148160 0.105249i
\(856\) −3.61415 3.61415i −0.123529 0.123529i
\(857\) 48.2304 1.64752 0.823759 0.566941i \(-0.191873\pi\)
0.823759 + 0.566941i \(0.191873\pi\)
\(858\) 0 0
\(859\) −20.5416 −0.700870 −0.350435 0.936587i \(-0.613966\pi\)
−0.350435 + 0.936587i \(0.613966\pi\)
\(860\) −5.33452 5.33452i −0.181906 0.181906i
\(861\) −61.9375 19.7603i −2.11083 0.673430i
\(862\) 59.1782i 2.01562i
\(863\) −3.75723 3.75723i −0.127898 0.127898i 0.640260 0.768158i \(-0.278826\pi\)
−0.768158 + 0.640260i \(0.778826\pi\)
\(864\) −39.9923 5.68013i −1.36056 0.193242i
\(865\) 18.7903 + 18.7903i 0.638890 + 0.638890i
\(866\) 26.6983 26.6983i 0.907245 0.907245i
\(867\) −3.66846 + 11.4986i −0.124587 + 0.390512i
\(868\) 42.3742i 1.43828i
\(869\) 0.591892 0.591892i 0.0200786 0.0200786i
\(870\) 3.02775 9.49030i 0.102650 0.321751i
\(871\) 0 0
\(872\) 4.10101i 0.138878i
\(873\) 13.2371 2.24147i 0.448008 0.0758622i
\(874\) −15.7007 −0.531084
\(875\) 51.8344 1.75232
\(876\) 8.07401 + 15.6395i 0.272796 + 0.528409i
\(877\) 33.7528 33.7528i 1.13975 1.13975i 0.151257 0.988494i \(-0.451668\pi\)
0.988494 0.151257i \(-0.0483322\pi\)
\(878\) −24.0635 + 24.0635i −0.812105 + 0.812105i
\(879\) −0.222815 0.431595i −0.00751535 0.0145573i
\(880\) 0.977107 0.0329383
\(881\) 22.4226 0.755437 0.377718 0.925920i \(-0.376709\pi\)
0.377718 + 0.925920i \(0.376709\pi\)
\(882\) 75.9024 12.8527i 2.55577 0.432774i
\(883\) 21.7280i 0.731205i 0.930771 + 0.365602i \(0.119137\pi\)
−0.930771 + 0.365602i \(0.880863\pi\)
\(884\) 0 0
\(885\) −6.84257 + 21.4476i −0.230011 + 0.720955i
\(886\) −1.98366 + 1.98366i −0.0666425 + 0.0666425i
\(887\) 24.1403i 0.810553i −0.914194 0.405276i \(-0.867175\pi\)
0.914194 0.405276i \(-0.132825\pi\)
\(888\) −0.569131 + 1.78391i −0.0190988 + 0.0598640i
\(889\) −50.6575 + 50.6575i −1.69900 + 1.69900i
\(890\) 10.8781 + 10.8781i 0.364636 + 0.364636i
\(891\) −1.24158 0.599624i −0.0415946 0.0200882i
\(892\) 16.3349 + 16.3349i 0.546933 + 0.546933i
\(893\) 6.88030i 0.230240i
\(894\) −56.8845 18.1482i −1.90250 0.606967i
\(895\) 1.84961 + 1.84961i 0.0618258 + 0.0618258i
\(896\) −11.8050 −0.394376
\(897\) 0 0
\(898\) −75.6075 −2.52305
\(899\) −7.24282 7.24282i −0.241562 0.241562i
\(900\) −12.5814 8.93753i −0.419379 0.297918i
\(901\) 1.98937i 0.0662757i
\(902\) −1.77481 1.77481i −0.0590946 0.0590946i
\(903\) 9.91673 + 19.2088i 0.330008 + 0.639230i
\(904\) 1.11870 + 1.11870i 0.0372075 + 0.0372075i
\(905\) 17.7875 17.7875i 0.591277 0.591277i
\(906\) 35.8624 + 11.4414i 1.19145 + 0.380116i
\(907\) 23.1138i 0.767481i 0.923441 + 0.383741i \(0.125364\pi\)
−0.923441 + 0.383741i \(0.874636\pi\)
\(908\) −28.7685 + 28.7685i −0.954715 + 0.954715i
\(909\) −4.11119 2.92050i −0.136359 0.0968667i
\(910\) 0 0
\(911\) 8.77371i 0.290686i 0.989381 + 0.145343i \(0.0464286\pi\)
−0.989381 + 0.145343i \(0.953571\pi\)
\(912\) 4.09723 + 7.93639i 0.135673 + 0.262800i
\(913\) −1.38826 −0.0459447
\(914\) −9.10382 −0.301128
\(915\) −13.2871 + 6.85958i −0.439258 + 0.226771i
\(916\) −12.9151 + 12.9151i −0.426727 + 0.426727i
\(917\) 59.5128 59.5128i 1.96529 1.96529i
\(918\) −31.8936 4.52987i −1.05264 0.149508i
\(919\) −0.279814 −0.00923020 −0.00461510 0.999989i \(-0.501469\pi\)
−0.00461510 + 0.999989i \(0.501469\pi\)
\(920\) −3.27626 −0.108015
\(921\) −28.1697 + 14.5429i −0.928224 + 0.479204i
\(922\) 15.9506i 0.525304i
\(923\) 0 0
\(924\) 2.07602 + 0.662327i 0.0682962 + 0.0217889i
\(925\) −6.50270 + 6.50270i −0.213807 + 0.213807i
\(926\) 12.9602i 0.425898i
\(927\) 7.67094 10.7984i 0.251947 0.354666i
\(928\) −10.9119 + 10.9119i −0.358200 + 0.358200i
\(929\) −13.0263 13.0263i −0.427378 0.427378i 0.460357 0.887734i \(-0.347722\pi\)
−0.887734 + 0.460357i \(0.847722\pi\)
\(930\) 23.0080 11.8781i 0.754461 0.389497i
\(931\) −11.0938 11.0938i −0.363586 0.363586i
\(932\) 42.0417i 1.37712i
\(933\) −3.56100 + 11.1617i −0.116582 + 0.365419i
\(934\) −20.8945 20.8945i −0.683687 0.683687i
\(935\) 0.718216 0.0234882
\(936\) 0 0
\(937\) 58.7234 1.91841 0.959205 0.282712i \(-0.0912341\pi\)
0.959205 + 0.282712i \(0.0912341\pi\)
\(938\) 4.17418 + 4.17418i 0.136292 + 0.136292i
\(939\) −13.3545 + 41.8588i −0.435807 + 1.36601i
\(940\) 15.5840i 0.508295i
\(941\) 21.2364 + 21.2364i 0.692286 + 0.692286i 0.962734 0.270448i \(-0.0871720\pi\)
−0.270448 + 0.962734i \(0.587172\pi\)
\(942\) 31.5269 16.2760i 1.02720 0.530302i
\(943\) 39.6708 + 39.6708i 1.29186 + 1.29186i
\(944\) 26.7555 26.7555i 0.870817 0.870817i
\(945\) −20.7166 27.5756i −0.673912 0.897035i
\(946\) 0.834588i 0.0271348i
\(947\) −25.2698 + 25.2698i −0.821159 + 0.821159i −0.986274 0.165115i \(-0.947200\pi\)
0.165115 + 0.986274i \(0.447200\pi\)
\(948\) −16.5108 5.26755i −0.536247 0.171082i
\(949\) 0 0
\(950\) 6.58014i 0.213488i
\(951\) 12.3092 6.35472i 0.399152 0.206066i
\(952\) −4.69038 −0.152016
\(953\) 20.1011 0.651140 0.325570 0.945518i \(-0.394444\pi\)
0.325570 + 0.945518i \(0.394444\pi\)
\(954\) 3.63652 0.615780i 0.117737 0.0199366i
\(955\) −23.4197 + 23.4197i −0.757844 + 0.757844i
\(956\) −23.2242 + 23.2242i −0.751124 + 0.751124i
\(957\) −0.468053 + 0.241636i −0.0151300 + 0.00781099i
\(958\) 36.0266 1.16397
\(959\) −26.5624 −0.857745
\(960\) −7.75993 15.0311i −0.250451 0.485126i
\(961\) 4.37562i 0.141149i
\(962\) 0 0
\(963\) −26.8905 + 37.8538i −0.866535 + 1.21982i
\(964\) −3.65532 + 3.65532i −0.117730 + 0.117730i
\(965\) 29.1733i 0.939122i
\(966\) −97.0824 30.9728i −3.12357 0.996533i
\(967\) 4.09441 4.09441i 0.131667 0.131667i −0.638202 0.769869i \(-0.720321\pi\)
0.769869 + 0.638202i \(0.220321\pi\)
\(968\) 2.56311 + 2.56311i 0.0823814 + 0.0823814i
\(969\) 3.01164 + 5.83359i 0.0967479 + 0.187402i
\(970\) 9.16810 + 9.16810i 0.294370 + 0.294370i
\(971\) 36.5458i 1.17281i −0.810018 0.586405i \(-0.800543\pi\)
0.810018 0.586405i \(-0.199457\pi\)
\(972\) 0.760806 + 28.5368i 0.0244029 + 0.915319i
\(973\) 47.4685 + 47.4685i 1.52177 + 1.52177i
\(974\) −55.8590 −1.78984
\(975\) 0 0
\(976\) 25.1326 0.804474
\(977\) −1.85263 1.85263i −0.0592709 0.0592709i 0.676850 0.736121i \(-0.263345\pi\)
−0.736121 + 0.676850i \(0.763345\pi\)
\(978\) 6.26299 + 1.99812i 0.200268 + 0.0638929i
\(979\) 0.813473i 0.0259987i
\(980\) 25.1278 + 25.1278i 0.802678 + 0.802678i
\(981\) −36.7330 + 6.22009i −1.17279 + 0.198592i
\(982\) 52.5889 + 52.5889i 1.67818 + 1.67818i
\(983\) −6.87065 + 6.87065i −0.219140 + 0.219140i −0.808136 0.588996i \(-0.799523\pi\)
0.588996 + 0.808136i \(0.299523\pi\)
\(984\) 1.45514 4.56106i 0.0463882 0.145401i
\(985\) 2.20373i 0.0702167i
\(986\) −8.70214 + 8.70214i −0.277133 + 0.277133i
\(987\) −13.5728 + 42.5431i −0.432026 + 1.35416i
\(988\) 0 0
\(989\) 18.6549i 0.593190i
\(990\) −0.222313 1.31288i −0.00706557 0.0417260i
\(991\) −29.0606 −0.923141 −0.461570 0.887104i \(-0.652714\pi\)
−0.461570 + 0.887104i \(0.652714\pi\)
\(992\) −40.1117 −1.27355
\(993\) −18.6972 36.2167i −0.593337 1.14930i
\(994\) −71.0222 + 71.0222i −2.25269 + 2.25269i
\(995\) −20.5954 + 20.5954i −0.652916 + 0.652916i
\(996\) 13.1854 + 25.5402i 0.417794 + 0.809273i
\(997\) 23.4421 0.742418 0.371209 0.928549i \(-0.378943\pi\)
0.371209 + 0.928549i \(0.378943\pi\)
\(998\) 31.1227 0.985172
\(999\) 16.8418 + 2.39205i 0.532850 + 0.0756811i
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 507.2.f.g.239.19 yes 48
3.2 odd 2 inner 507.2.f.g.239.6 yes 48
13.2 odd 12 507.2.k.k.488.20 96
13.3 even 3 507.2.k.k.188.6 96
13.4 even 6 507.2.k.k.80.5 96
13.5 odd 4 inner 507.2.f.g.437.19 yes 48
13.6 odd 12 507.2.k.k.89.5 96
13.7 odd 12 507.2.k.k.89.19 96
13.8 odd 4 inner 507.2.f.g.437.5 yes 48
13.9 even 3 507.2.k.k.80.19 96
13.10 even 6 507.2.k.k.188.20 96
13.11 odd 12 507.2.k.k.488.6 96
13.12 even 2 inner 507.2.f.g.239.5 48
39.2 even 12 507.2.k.k.488.5 96
39.5 even 4 inner 507.2.f.g.437.6 yes 48
39.8 even 4 inner 507.2.f.g.437.20 yes 48
39.11 even 12 507.2.k.k.488.19 96
39.17 odd 6 507.2.k.k.80.20 96
39.20 even 12 507.2.k.k.89.6 96
39.23 odd 6 507.2.k.k.188.5 96
39.29 odd 6 507.2.k.k.188.19 96
39.32 even 12 507.2.k.k.89.20 96
39.35 odd 6 507.2.k.k.80.6 96
39.38 odd 2 inner 507.2.f.g.239.20 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.f.g.239.5 48 13.12 even 2 inner
507.2.f.g.239.6 yes 48 3.2 odd 2 inner
507.2.f.g.239.19 yes 48 1.1 even 1 trivial
507.2.f.g.239.20 yes 48 39.38 odd 2 inner
507.2.f.g.437.5 yes 48 13.8 odd 4 inner
507.2.f.g.437.6 yes 48 39.5 even 4 inner
507.2.f.g.437.19 yes 48 13.5 odd 4 inner
507.2.f.g.437.20 yes 48 39.8 even 4 inner
507.2.k.k.80.5 96 13.4 even 6
507.2.k.k.80.6 96 39.35 odd 6
507.2.k.k.80.19 96 13.9 even 3
507.2.k.k.80.20 96 39.17 odd 6
507.2.k.k.89.5 96 13.6 odd 12
507.2.k.k.89.6 96 39.20 even 12
507.2.k.k.89.19 96 13.7 odd 12
507.2.k.k.89.20 96 39.32 even 12
507.2.k.k.188.5 96 39.23 odd 6
507.2.k.k.188.6 96 13.3 even 3
507.2.k.k.188.19 96 39.29 odd 6
507.2.k.k.188.20 96 13.10 even 6
507.2.k.k.488.5 96 39.2 even 12
507.2.k.k.488.6 96 13.11 odd 12
507.2.k.k.488.19 96 39.11 even 12
507.2.k.k.488.20 96 13.2 odd 12