Properties

Label 950.2.f.c.607.5
Level $950$
Weight $2$
Character 950.607
Analytic conductor $7.586$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(493,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.493");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 24x^{14} + 212x^{12} + 880x^{10} + 1858x^{8} + 1960x^{6} + 892x^{4} + 96x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 607.5
Root \(-1.66380i\) of defining polynomial
Character \(\chi\) \(=\) 950.607
Dual form 950.2.f.c.493.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-2.20701 - 2.20701i) q^{3} -1.00000i q^{4} -3.12119 q^{6} +(-1.65823 - 1.65823i) q^{7} +(-0.707107 - 0.707107i) q^{8} +6.74181i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-2.20701 - 2.20701i) q^{3} -1.00000i q^{4} -3.12119 q^{6} +(-1.65823 - 1.65823i) q^{7} +(-0.707107 - 0.707107i) q^{8} +6.74181i q^{9} -0.804733 q^{11} +(-2.20701 + 2.20701i) q^{12} +(-3.05219 - 3.05219i) q^{13} -2.34509 q^{14} -1.00000 q^{16} +(4.37090 + 4.37090i) q^{17} +(4.76718 + 4.76718i) q^{18} +(-3.48315 - 2.62062i) q^{19} +7.31946i q^{21} +(-0.569032 + 0.569032i) q^{22} +(-6.20477 + 6.20477i) q^{23} +3.12119i q^{24} -4.31645 q^{26} +(8.25822 - 8.25822i) q^{27} +(-1.65823 + 1.65823i) q^{28} +5.64487 q^{29} -3.13000i q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.77606 + 1.77606i) q^{33} +6.18139 q^{34} +6.74181 q^{36} +(0.524538 - 0.524538i) q^{37} +(-4.31602 + 0.609901i) q^{38} +13.4725i q^{39} +1.45541i q^{41} +(5.17564 + 5.17564i) q^{42} +(-1.90794 + 1.90794i) q^{43} +0.804733i q^{44} +8.77487i q^{46} +(-0.499434 - 0.499434i) q^{47} +(2.20701 + 2.20701i) q^{48} -1.50057i q^{49} -19.2933i q^{51} +(-3.05219 + 3.05219i) q^{52} +(3.40535 + 3.40535i) q^{53} -11.6789i q^{54} +2.34509i q^{56} +(1.90361 + 13.4711i) q^{57} +(3.99153 - 3.99153i) q^{58} -2.77684 q^{59} +6.17945 q^{61} +(-2.21324 - 2.21324i) q^{62} +(11.1794 - 11.1794i) q^{63} +1.00000i q^{64} +2.51172 q^{66} +(0.345265 - 0.345265i) q^{67} +(4.37090 - 4.37090i) q^{68} +27.3880 q^{69} +6.68211i q^{71} +(4.76718 - 4.76718i) q^{72} +(-1.05445 + 1.05445i) q^{73} -0.741809i q^{74} +(-2.62062 + 3.48315i) q^{76} +(1.33443 + 1.33443i) q^{77} +(9.52647 + 9.52647i) q^{78} -7.16924 q^{79} -16.2266 q^{81} +(1.02913 + 1.02913i) q^{82} +(4.12119 - 4.12119i) q^{83} +7.31946 q^{84} +2.69824i q^{86} +(-12.4583 - 12.4583i) q^{87} +(0.569032 + 0.569032i) q^{88} -16.7356 q^{89} +10.1225i q^{91} +(6.20477 + 6.20477i) q^{92} +(-6.90794 + 6.90794i) q^{93} -0.706307 q^{94} +3.12119 q^{96} +(-8.25033 + 8.25033i) q^{97} +(-1.06106 - 1.06106i) q^{98} -5.42535i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −2.20701 2.20701i −1.27422 1.27422i −0.943853 0.330367i \(-0.892828\pi\)
−0.330367 0.943853i \(-0.607172\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) −3.12119 −1.27422
\(7\) −1.65823 1.65823i −0.626751 0.626751i 0.320498 0.947249i \(-0.396150\pi\)
−0.947249 + 0.320498i \(0.896150\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 6.74181i 2.24727i
\(10\) 0 0
\(11\) −0.804733 −0.242636 −0.121318 0.992614i \(-0.538712\pi\)
−0.121318 + 0.992614i \(0.538712\pi\)
\(12\) −2.20701 + 2.20701i −0.637110 + 0.637110i
\(13\) −3.05219 3.05219i −0.846526 0.846526i 0.143172 0.989698i \(-0.454270\pi\)
−0.989698 + 0.143172i \(0.954270\pi\)
\(14\) −2.34509 −0.626751
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 4.37090 + 4.37090i 1.06010 + 1.06010i 0.998075 + 0.0620254i \(0.0197560\pi\)
0.0620254 + 0.998075i \(0.480244\pi\)
\(18\) 4.76718 + 4.76718i 1.12363 + 1.12363i
\(19\) −3.48315 2.62062i −0.799090 0.601212i
\(20\) 0 0
\(21\) 7.31946i 1.59724i
\(22\) −0.569032 + 0.569032i −0.121318 + 0.121318i
\(23\) −6.20477 + 6.20477i −1.29378 + 1.29378i −0.361356 + 0.932428i \(0.617686\pi\)
−0.932428 + 0.361356i \(0.882314\pi\)
\(24\) 3.12119i 0.637110i
\(25\) 0 0
\(26\) −4.31645 −0.846526
\(27\) 8.25822 8.25822i 1.58929 1.58929i
\(28\) −1.65823 + 1.65823i −0.313375 + 0.313375i
\(29\) 5.64487 1.04823 0.524113 0.851649i \(-0.324397\pi\)
0.524113 + 0.851649i \(0.324397\pi\)
\(30\) 0 0
\(31\) 3.13000i 0.562164i −0.959684 0.281082i \(-0.909307\pi\)
0.959684 0.281082i \(-0.0906933\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 1.77606 + 1.77606i 0.309172 + 0.309172i
\(34\) 6.18139 1.06010
\(35\) 0 0
\(36\) 6.74181 1.12363
\(37\) 0.524538 0.524538i 0.0862335 0.0862335i −0.662674 0.748908i \(-0.730579\pi\)
0.748908 + 0.662674i \(0.230579\pi\)
\(38\) −4.31602 + 0.609901i −0.700151 + 0.0989390i
\(39\) 13.4725i 2.15732i
\(40\) 0 0
\(41\) 1.45541i 0.227297i 0.993521 + 0.113649i \(0.0362538\pi\)
−0.993521 + 0.113649i \(0.963746\pi\)
\(42\) 5.17564 + 5.17564i 0.798618 + 0.798618i
\(43\) −1.90794 + 1.90794i −0.290959 + 0.290959i −0.837459 0.546500i \(-0.815960\pi\)
0.546500 + 0.837459i \(0.315960\pi\)
\(44\) 0.804733i 0.121318i
\(45\) 0 0
\(46\) 8.77487i 1.29378i
\(47\) −0.499434 0.499434i −0.0728500 0.0728500i 0.669743 0.742593i \(-0.266404\pi\)
−0.742593 + 0.669743i \(0.766404\pi\)
\(48\) 2.20701 + 2.20701i 0.318555 + 0.318555i
\(49\) 1.50057i 0.214367i
\(50\) 0 0
\(51\) 19.2933i 2.70160i
\(52\) −3.05219 + 3.05219i −0.423263 + 0.423263i
\(53\) 3.40535 + 3.40535i 0.467760 + 0.467760i 0.901188 0.433428i \(-0.142696\pi\)
−0.433428 + 0.901188i \(0.642696\pi\)
\(54\) 11.6789i 1.58929i
\(55\) 0 0
\(56\) 2.34509i 0.313375i
\(57\) 1.90361 + 13.4711i 0.252140 + 1.78429i
\(58\) 3.99153 3.99153i 0.524113 0.524113i
\(59\) −2.77684 −0.361514 −0.180757 0.983528i \(-0.557855\pi\)
−0.180757 + 0.983528i \(0.557855\pi\)
\(60\) 0 0
\(61\) 6.17945 0.791197 0.395599 0.918423i \(-0.370537\pi\)
0.395599 + 0.918423i \(0.370537\pi\)
\(62\) −2.21324 2.21324i −0.281082 0.281082i
\(63\) 11.1794 11.1794i 1.40848 1.40848i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 2.51172 0.309172
\(67\) 0.345265 0.345265i 0.0421808 0.0421808i −0.685702 0.727883i \(-0.740505\pi\)
0.727883 + 0.685702i \(0.240505\pi\)
\(68\) 4.37090 4.37090i 0.530050 0.530050i
\(69\) 27.3880 3.29713
\(70\) 0 0
\(71\) 6.68211i 0.793020i 0.918030 + 0.396510i \(0.129779\pi\)
−0.918030 + 0.396510i \(0.870221\pi\)
\(72\) 4.76718 4.76718i 0.561817 0.561817i
\(73\) −1.05445 + 1.05445i −0.123414 + 0.123414i −0.766116 0.642702i \(-0.777813\pi\)
0.642702 + 0.766116i \(0.277813\pi\)
\(74\) 0.741809i 0.0862335i
\(75\) 0 0
\(76\) −2.62062 + 3.48315i −0.300606 + 0.399545i
\(77\) 1.33443 + 1.33443i 0.152072 + 0.152072i
\(78\) 9.52647 + 9.52647i 1.07866 + 1.07866i
\(79\) −7.16924 −0.806603 −0.403301 0.915067i \(-0.632137\pi\)
−0.403301 + 0.915067i \(0.632137\pi\)
\(80\) 0 0
\(81\) −16.2266 −1.80295
\(82\) 1.02913 + 1.02913i 0.113649 + 0.113649i
\(83\) 4.12119 4.12119i 0.452359 0.452359i −0.443778 0.896137i \(-0.646362\pi\)
0.896137 + 0.443778i \(0.146362\pi\)
\(84\) 7.31946 0.798618
\(85\) 0 0
\(86\) 2.69824i 0.290959i
\(87\) −12.4583 12.4583i −1.33567 1.33567i
\(88\) 0.569032 + 0.569032i 0.0606590 + 0.0606590i
\(89\) −16.7356 −1.77397 −0.886986 0.461797i \(-0.847205\pi\)
−0.886986 + 0.461797i \(0.847205\pi\)
\(90\) 0 0
\(91\) 10.1225i 1.06112i
\(92\) 6.20477 + 6.20477i 0.646892 + 0.646892i
\(93\) −6.90794 + 6.90794i −0.716320 + 0.716320i
\(94\) −0.706307 −0.0728500
\(95\) 0 0
\(96\) 3.12119 0.318555
\(97\) −8.25033 + 8.25033i −0.837694 + 0.837694i −0.988555 0.150861i \(-0.951795\pi\)
0.150861 + 0.988555i \(0.451795\pi\)
\(98\) −1.06106 1.06106i −0.107183 0.107183i
\(99\) 5.42535i 0.545269i
\(100\) 0 0
\(101\) −1.75296 −0.174426 −0.0872132 0.996190i \(-0.527796\pi\)
−0.0872132 + 0.996190i \(0.527796\pi\)
\(102\) −13.6424 13.6424i −1.35080 1.35080i
\(103\) 5.55918 + 5.55918i 0.547762 + 0.547762i 0.925793 0.378031i \(-0.123399\pi\)
−0.378031 + 0.925793i \(0.623399\pi\)
\(104\) 4.31645i 0.423263i
\(105\) 0 0
\(106\) 4.81589 0.467760
\(107\) 2.01985 2.01985i 0.195266 0.195266i −0.602701 0.797967i \(-0.705909\pi\)
0.797967 + 0.602701i \(0.205909\pi\)
\(108\) −8.25822 8.25822i −0.794647 0.794647i
\(109\) −13.3175 −1.27558 −0.637792 0.770209i \(-0.720152\pi\)
−0.637792 + 0.770209i \(0.720152\pi\)
\(110\) 0 0
\(111\) −2.31532 −0.219761
\(112\) 1.65823 + 1.65823i 0.156688 + 0.156688i
\(113\) −10.8883 10.8883i −1.02429 1.02429i −0.999698 0.0245874i \(-0.992173\pi\)
−0.0245874 0.999698i \(-0.507827\pi\)
\(114\) 10.8716 + 8.17945i 1.01822 + 0.766076i
\(115\) 0 0
\(116\) 5.64487i 0.524113i
\(117\) 20.5773 20.5773i 1.90237 1.90237i
\(118\) −1.96353 + 1.96353i −0.180757 + 0.180757i
\(119\) 14.4959i 1.32884i
\(120\) 0 0
\(121\) −10.3524 −0.941128
\(122\) 4.36953 4.36953i 0.395599 0.395599i
\(123\) 3.21211 3.21211i 0.289626 0.289626i
\(124\) −3.13000 −0.281082
\(125\) 0 0
\(126\) 15.8101i 1.40848i
\(127\) −10.4120 + 10.4120i −0.923920 + 0.923920i −0.997304 0.0733839i \(-0.976620\pi\)
0.0733839 + 0.997304i \(0.476620\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 8.42171 0.741491
\(130\) 0 0
\(131\) −15.4836 −1.35281 −0.676405 0.736530i \(-0.736463\pi\)
−0.676405 + 0.736530i \(0.736463\pi\)
\(132\) 1.77606 1.77606i 0.154586 0.154586i
\(133\) 1.43027 + 10.1214i 0.124020 + 0.877640i
\(134\) 0.488279i 0.0421808i
\(135\) 0 0
\(136\) 6.18139i 0.530050i
\(137\) 3.37204 + 3.37204i 0.288092 + 0.288092i 0.836326 0.548233i \(-0.184699\pi\)
−0.548233 + 0.836326i \(0.684699\pi\)
\(138\) 19.3662 19.3662i 1.64856 1.64856i
\(139\) 2.05826i 0.174580i 0.996183 + 0.0872898i \(0.0278206\pi\)
−0.996183 + 0.0872898i \(0.972179\pi\)
\(140\) 0 0
\(141\) 2.20452i 0.185654i
\(142\) 4.72496 + 4.72496i 0.396510 + 0.396510i
\(143\) 2.45620 + 2.45620i 0.205398 + 0.205398i
\(144\) 6.74181i 0.561817i
\(145\) 0 0
\(146\) 1.49122i 0.123414i
\(147\) −3.31177 + 3.31177i −0.273150 + 0.273150i
\(148\) −0.524538 0.524538i −0.0431167 0.0431167i
\(149\) 19.5419i 1.60093i 0.599377 + 0.800467i \(0.295415\pi\)
−0.599377 + 0.800467i \(0.704585\pi\)
\(150\) 0 0
\(151\) 0.641287i 0.0521872i −0.999660 0.0260936i \(-0.991693\pi\)
0.999660 0.0260936i \(-0.00830680\pi\)
\(152\) 0.609901 + 4.31602i 0.0494695 + 0.350075i
\(153\) −29.4678 + 29.4678i −2.38233 + 2.38233i
\(154\) 1.88717 0.152072
\(155\) 0 0
\(156\) 13.4725 1.07866
\(157\) −12.6689 12.6689i −1.01109 1.01109i −0.999938 0.0111472i \(-0.996452\pi\)
−0.0111472 0.999938i \(-0.503548\pi\)
\(158\) −5.06942 + 5.06942i −0.403301 + 0.403301i
\(159\) 15.0313i 1.19206i
\(160\) 0 0
\(161\) 20.5778 1.62176
\(162\) −11.4739 + 11.4739i −0.901475 + 0.901475i
\(163\) 3.47143 3.47143i 0.271904 0.271904i −0.557962 0.829866i \(-0.688417\pi\)
0.829866 + 0.557962i \(0.188417\pi\)
\(164\) 1.45541 0.113649
\(165\) 0 0
\(166\) 5.82824i 0.452359i
\(167\) 13.1032 13.1032i 1.01396 1.01396i 0.0140549 0.999901i \(-0.495526\pi\)
0.999901 0.0140549i \(-0.00447395\pi\)
\(168\) 5.17564 5.17564i 0.399309 0.399309i
\(169\) 5.63178i 0.433214i
\(170\) 0 0
\(171\) 17.6677 23.4827i 1.35108 1.79577i
\(172\) 1.90794 + 1.90794i 0.145479 + 0.145479i
\(173\) −7.50662 7.50662i −0.570718 0.570718i 0.361611 0.932329i \(-0.382227\pi\)
−0.932329 + 0.361611i \(0.882227\pi\)
\(174\) −17.6187 −1.33567
\(175\) 0 0
\(176\) 0.804733 0.0606590
\(177\) 6.12853 + 6.12853i 0.460649 + 0.460649i
\(178\) −11.8339 + 11.8339i −0.886986 + 0.886986i
\(179\) −19.4273 −1.45206 −0.726031 0.687662i \(-0.758637\pi\)
−0.726031 + 0.687662i \(0.758637\pi\)
\(180\) 0 0
\(181\) 4.58541i 0.340831i 0.985372 + 0.170415i \(0.0545110\pi\)
−0.985372 + 0.170415i \(0.945489\pi\)
\(182\) 7.15766 + 7.15766i 0.530561 + 0.530561i
\(183\) −13.6381 13.6381i −1.00816 1.00816i
\(184\) 8.77487 0.646892
\(185\) 0 0
\(186\) 9.76931i 0.716320i
\(187\) −3.51741 3.51741i −0.257218 0.257218i
\(188\) −0.499434 + 0.499434i −0.0364250 + 0.0364250i
\(189\) −27.3880 −1.99218
\(190\) 0 0
\(191\) 4.86413 0.351956 0.175978 0.984394i \(-0.443691\pi\)
0.175978 + 0.984394i \(0.443691\pi\)
\(192\) 2.20701 2.20701i 0.159277 0.159277i
\(193\) −10.3313 10.3313i −0.743660 0.743660i 0.229620 0.973280i \(-0.426252\pi\)
−0.973280 + 0.229620i \(0.926252\pi\)
\(194\) 11.6677i 0.837694i
\(195\) 0 0
\(196\) −1.50057 −0.107183
\(197\) −8.32327 8.32327i −0.593009 0.593009i 0.345434 0.938443i \(-0.387732\pi\)
−0.938443 + 0.345434i \(0.887732\pi\)
\(198\) −3.83630 3.83630i −0.272634 0.272634i
\(199\) 23.1042i 1.63782i −0.573925 0.818908i \(-0.694580\pi\)
0.573925 0.818908i \(-0.305420\pi\)
\(200\) 0 0
\(201\) −1.52401 −0.107495
\(202\) −1.23953 + 1.23953i −0.0872132 + 0.0872132i
\(203\) −9.36048 9.36048i −0.656977 0.656977i
\(204\) −19.2933 −1.35080
\(205\) 0 0
\(206\) 7.86186 0.547762
\(207\) −41.8314 41.8314i −2.90748 2.90748i
\(208\) 3.05219 + 3.05219i 0.211632 + 0.211632i
\(209\) 2.80301 + 2.10890i 0.193888 + 0.145876i
\(210\) 0 0
\(211\) 15.3492i 1.05668i 0.849033 + 0.528340i \(0.177185\pi\)
−0.849033 + 0.528340i \(0.822815\pi\)
\(212\) 3.40535 3.40535i 0.233880 0.233880i
\(213\) 14.7475 14.7475i 1.01048 1.01048i
\(214\) 2.85650i 0.195266i
\(215\) 0 0
\(216\) −11.6789 −0.794647
\(217\) −5.19025 + 5.19025i −0.352337 + 0.352337i
\(218\) −9.41688 + 9.41688i −0.637792 + 0.637792i
\(219\) 4.65437 0.314513
\(220\) 0 0
\(221\) 26.6817i 1.79481i
\(222\) −1.63718 + 1.63718i −0.109880 + 0.109880i
\(223\) 18.5974 + 18.5974i 1.24537 + 1.24537i 0.957742 + 0.287629i \(0.0928672\pi\)
0.287629 + 0.957742i \(0.407133\pi\)
\(224\) 2.34509 0.156688
\(225\) 0 0
\(226\) −15.3984 −1.02429
\(227\) −5.51878 + 5.51878i −0.366294 + 0.366294i −0.866124 0.499830i \(-0.833396\pi\)
0.499830 + 0.866124i \(0.333396\pi\)
\(228\) 13.4711 1.90361i 0.892146 0.126070i
\(229\) 9.94379i 0.657104i −0.944486 0.328552i \(-0.893439\pi\)
0.944486 0.328552i \(-0.106561\pi\)
\(230\) 0 0
\(231\) 5.89021i 0.387547i
\(232\) −3.99153 3.99153i −0.262057 0.262057i
\(233\) 5.11116 5.11116i 0.334843 0.334843i −0.519579 0.854422i \(-0.673911\pi\)
0.854422 + 0.519579i \(0.173911\pi\)
\(234\) 29.1007i 1.90237i
\(235\) 0 0
\(236\) 2.77684i 0.180757i
\(237\) 15.8226 + 15.8226i 1.02779 + 1.02779i
\(238\) −10.2502 10.2502i −0.664419 0.664419i
\(239\) 9.30530i 0.601910i −0.953638 0.300955i \(-0.902695\pi\)
0.953638 0.300955i \(-0.0973053\pi\)
\(240\) 0 0
\(241\) 8.31390i 0.535545i 0.963482 + 0.267773i \(0.0862876\pi\)
−0.963482 + 0.267773i \(0.913712\pi\)
\(242\) −7.32026 + 7.32026i −0.470564 + 0.470564i
\(243\) 11.0376 + 11.0376i 0.708060 + 0.708060i
\(244\) 6.17945i 0.395599i
\(245\) 0 0
\(246\) 4.54261i 0.289626i
\(247\) 2.63261 + 18.6299i 0.167509 + 1.18539i
\(248\) −2.21324 + 2.21324i −0.140541 + 0.140541i
\(249\) −18.1910 −1.15281
\(250\) 0 0
\(251\) 10.7710 0.679862 0.339931 0.940450i \(-0.389596\pi\)
0.339931 + 0.940450i \(0.389596\pi\)
\(252\) −11.1794 11.1794i −0.704239 0.704239i
\(253\) 4.99318 4.99318i 0.313919 0.313919i
\(254\) 14.7249i 0.923920i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −19.8607 + 19.8607i −1.23888 + 1.23888i −0.278417 + 0.960460i \(0.589810\pi\)
−0.960460 + 0.278417i \(0.910190\pi\)
\(258\) 5.95505 5.95505i 0.370745 0.370745i
\(259\) −1.73961 −0.108094
\(260\) 0 0
\(261\) 38.0566i 2.35565i
\(262\) −10.9486 + 10.9486i −0.676405 + 0.676405i
\(263\) −13.1964 + 13.1964i −0.813725 + 0.813725i −0.985190 0.171465i \(-0.945150\pi\)
0.171465 + 0.985190i \(0.445150\pi\)
\(264\) 2.51172i 0.154586i
\(265\) 0 0
\(266\) 8.16829 + 6.14559i 0.500830 + 0.376810i
\(267\) 36.9357 + 36.9357i 2.26043 + 2.26043i
\(268\) −0.345265 0.345265i −0.0210904 0.0210904i
\(269\) 18.1260 1.10516 0.552581 0.833459i \(-0.313643\pi\)
0.552581 + 0.833459i \(0.313643\pi\)
\(270\) 0 0
\(271\) −7.62288 −0.463057 −0.231529 0.972828i \(-0.574373\pi\)
−0.231529 + 0.972828i \(0.574373\pi\)
\(272\) −4.37090 4.37090i −0.265025 0.265025i
\(273\) 22.3404 22.3404i 1.35210 1.35210i
\(274\) 4.76878 0.288092
\(275\) 0 0
\(276\) 27.3880i 1.64856i
\(277\) 1.94710 + 1.94710i 0.116990 + 0.116990i 0.763178 0.646188i \(-0.223638\pi\)
−0.646188 + 0.763178i \(0.723638\pi\)
\(278\) 1.45541 + 1.45541i 0.0872898 + 0.0872898i
\(279\) 21.1018 1.26333
\(280\) 0 0
\(281\) 5.77885i 0.344737i −0.985033 0.172369i \(-0.944858\pi\)
0.985033 0.172369i \(-0.0551420\pi\)
\(282\) 1.55883 + 1.55883i 0.0928269 + 0.0928269i
\(283\) 21.2948 21.2948i 1.26585 1.26585i 0.317634 0.948214i \(-0.397112\pi\)
0.948214 0.317634i \(-0.102888\pi\)
\(284\) 6.68211 0.396510
\(285\) 0 0
\(286\) 3.47359 0.205398
\(287\) 2.41340 2.41340i 0.142459 0.142459i
\(288\) −4.76718 4.76718i −0.280909 0.280909i
\(289\) 21.2096i 1.24762i
\(290\) 0 0
\(291\) 36.4172 2.13481
\(292\) 1.05445 + 1.05445i 0.0617070 + 0.0617070i
\(293\) −5.94185 5.94185i −0.347126 0.347126i 0.511912 0.859038i \(-0.328938\pi\)
−0.859038 + 0.511912i \(0.828938\pi\)
\(294\) 4.68355i 0.273150i
\(295\) 0 0
\(296\) −0.741809 −0.0431167
\(297\) −6.64566 + 6.64566i −0.385620 + 0.385620i
\(298\) 13.8182 + 13.8182i 0.800467 + 0.800467i
\(299\) 37.8763 2.19044
\(300\) 0 0
\(301\) 6.32761 0.364717
\(302\) −0.453459 0.453459i −0.0260936 0.0260936i
\(303\) 3.86881 + 3.86881i 0.222258 + 0.222258i
\(304\) 3.48315 + 2.62062i 0.199772 + 0.150303i
\(305\) 0 0
\(306\) 41.6738i 2.38233i
\(307\) 2.67442 2.67442i 0.152637 0.152637i −0.626658 0.779295i \(-0.715578\pi\)
0.779295 + 0.626658i \(0.215578\pi\)
\(308\) 1.33443 1.33443i 0.0760362 0.0760362i
\(309\) 24.5383i 1.39594i
\(310\) 0 0
\(311\) 18.8112 1.06669 0.533343 0.845899i \(-0.320935\pi\)
0.533343 + 0.845899i \(0.320935\pi\)
\(312\) 9.52647 9.52647i 0.539330 0.539330i
\(313\) −14.6481 + 14.6481i −0.827959 + 0.827959i −0.987234 0.159275i \(-0.949084\pi\)
0.159275 + 0.987234i \(0.449084\pi\)
\(314\) −17.9165 −1.01109
\(315\) 0 0
\(316\) 7.16924i 0.403301i
\(317\) −0.943658 + 0.943658i −0.0530011 + 0.0530011i −0.733111 0.680109i \(-0.761932\pi\)
0.680109 + 0.733111i \(0.261932\pi\)
\(318\) −10.6287 10.6287i −0.596029 0.596029i
\(319\) −4.54261 −0.254337
\(320\) 0 0
\(321\) −8.91567 −0.497624
\(322\) 14.5507 14.5507i 0.810880 0.810880i
\(323\) −3.77004 26.6790i −0.209770 1.48446i
\(324\) 16.2266i 0.901475i
\(325\) 0 0
\(326\) 4.90935i 0.271904i
\(327\) 29.3918 + 29.3918i 1.62537 + 1.62537i
\(328\) 1.02913 1.02913i 0.0568243 0.0568243i
\(329\) 1.65635i 0.0913176i
\(330\) 0 0
\(331\) 14.9698i 0.822817i −0.911451 0.411409i \(-0.865037\pi\)
0.911451 0.411409i \(-0.134963\pi\)
\(332\) −4.12119 4.12119i −0.226180 0.226180i
\(333\) 3.53633 + 3.53633i 0.193790 + 0.193790i
\(334\) 18.5307i 1.01396i
\(335\) 0 0
\(336\) 7.31946i 0.399309i
\(337\) 18.4481 18.4481i 1.00493 1.00493i 0.00494423 0.999988i \(-0.498426\pi\)
0.999988 0.00494423i \(-0.00157380\pi\)
\(338\) 3.98227 + 3.98227i 0.216607 + 0.216607i
\(339\) 48.0612i 2.61033i
\(340\) 0 0
\(341\) 2.51881i 0.136401i
\(342\) −4.11183 29.0978i −0.222342 1.57343i
\(343\) −14.0959 + 14.0959i −0.761105 + 0.761105i
\(344\) 2.69824 0.145479
\(345\) 0 0
\(346\) −10.6160 −0.570718
\(347\) −13.3578 13.3578i −0.717083 0.717083i 0.250924 0.968007i \(-0.419266\pi\)
−0.968007 + 0.250924i \(0.919266\pi\)
\(348\) −12.4583 + 12.4583i −0.667835 + 0.667835i
\(349\) 7.74830i 0.414757i −0.978261 0.207379i \(-0.933507\pi\)
0.978261 0.207379i \(-0.0664932\pi\)
\(350\) 0 0
\(351\) −50.4114 −2.69076
\(352\) 0.569032 0.569032i 0.0303295 0.0303295i
\(353\) 24.2462 24.2462i 1.29049 1.29049i 0.356014 0.934481i \(-0.384136\pi\)
0.934481 0.356014i \(-0.115864\pi\)
\(354\) 8.66705 0.460649
\(355\) 0 0
\(356\) 16.7356i 0.886986i
\(357\) −31.9926 + 31.9926i −1.69323 + 1.69323i
\(358\) −13.7371 + 13.7371i −0.726031 + 0.726031i
\(359\) 0.430016i 0.0226954i 0.999936 + 0.0113477i \(0.00361216\pi\)
−0.999936 + 0.0113477i \(0.996388\pi\)
\(360\) 0 0
\(361\) 5.26469 + 18.2560i 0.277089 + 0.960844i
\(362\) 3.24237 + 3.24237i 0.170415 + 0.170415i
\(363\) 22.8479 + 22.8479i 1.19920 + 1.19920i
\(364\) 10.1225 0.530561
\(365\) 0 0
\(366\) −19.2872 −1.00816
\(367\) 7.94174 + 7.94174i 0.414555 + 0.414555i 0.883322 0.468767i \(-0.155302\pi\)
−0.468767 + 0.883322i \(0.655302\pi\)
\(368\) 6.20477 6.20477i 0.323446 0.323446i
\(369\) −9.81211 −0.510798
\(370\) 0 0
\(371\) 11.2937i 0.586339i
\(372\) 6.90794 + 6.90794i 0.358160 + 0.358160i
\(373\) −5.72661 5.72661i −0.296513 0.296513i 0.543134 0.839646i \(-0.317238\pi\)
−0.839646 + 0.543134i \(0.817238\pi\)
\(374\) −4.97437 −0.257218
\(375\) 0 0
\(376\) 0.706307i 0.0364250i
\(377\) −17.2292 17.2292i −0.887351 0.887351i
\(378\) −19.3662 + 19.3662i −0.996092 + 0.996092i
\(379\) −1.74355 −0.0895599 −0.0447800 0.998997i \(-0.514259\pi\)
−0.0447800 + 0.998997i \(0.514259\pi\)
\(380\) 0 0
\(381\) 45.9590 2.35455
\(382\) 3.43946 3.43946i 0.175978 0.175978i
\(383\) 14.9492 + 14.9492i 0.763867 + 0.763867i 0.977019 0.213152i \(-0.0683730\pi\)
−0.213152 + 0.977019i \(0.568373\pi\)
\(384\) 3.12119i 0.159277i
\(385\) 0 0
\(386\) −14.6106 −0.743660
\(387\) −12.8630 12.8630i −0.653863 0.653863i
\(388\) 8.25033 + 8.25033i 0.418847 + 0.418847i
\(389\) 9.21427i 0.467182i 0.972335 + 0.233591i \(0.0750477\pi\)
−0.972335 + 0.233591i \(0.924952\pi\)
\(390\) 0 0
\(391\) −54.2409 −2.74308
\(392\) −1.06106 + 1.06106i −0.0535916 + 0.0535916i
\(393\) 34.1725 + 34.1725i 1.72378 + 1.72378i
\(394\) −11.7709 −0.593009
\(395\) 0 0
\(396\) −5.42535 −0.272634
\(397\) 9.28722 + 9.28722i 0.466112 + 0.466112i 0.900652 0.434540i \(-0.143089\pi\)
−0.434540 + 0.900652i \(0.643089\pi\)
\(398\) −16.3372 16.3372i −0.818908 0.818908i
\(399\) 19.1815 25.4948i 0.960277 1.27634i
\(400\) 0 0
\(401\) 38.6944i 1.93231i −0.257971 0.966153i \(-0.583054\pi\)
0.257971 0.966153i \(-0.416946\pi\)
\(402\) −1.07764 + 1.07764i −0.0537476 + 0.0537476i
\(403\) −9.55336 + 9.55336i −0.475887 + 0.475887i
\(404\) 1.75296i 0.0872132i
\(405\) 0 0
\(406\) −13.2377 −0.656977
\(407\) −0.422113 + 0.422113i −0.0209234 + 0.0209234i
\(408\) −13.6424 + 13.6424i −0.675400 + 0.675400i
\(409\) 14.6817 0.725964 0.362982 0.931796i \(-0.381759\pi\)
0.362982 + 0.931796i \(0.381759\pi\)
\(410\) 0 0
\(411\) 14.8842i 0.734186i
\(412\) 5.55918 5.55918i 0.273881 0.273881i
\(413\) 4.60464 + 4.60464i 0.226579 + 0.226579i
\(414\) −59.1585 −2.90748
\(415\) 0 0
\(416\) 4.31645 0.211632
\(417\) 4.54261 4.54261i 0.222453 0.222453i
\(418\) 3.47324 0.490807i 0.169882 0.0240062i
\(419\) 1.27584i 0.0623290i −0.999514 0.0311645i \(-0.990078\pi\)
0.999514 0.0311645i \(-0.00992157\pi\)
\(420\) 0 0
\(421\) 6.74319i 0.328643i 0.986407 + 0.164321i \(0.0525434\pi\)
−0.986407 + 0.164321i \(0.947457\pi\)
\(422\) 10.8535 + 10.8535i 0.528340 + 0.528340i
\(423\) 3.36709 3.36709i 0.163714 0.163714i
\(424\) 4.81589i 0.233880i
\(425\) 0 0
\(426\) 20.8561i 1.01048i
\(427\) −10.2469 10.2469i −0.495884 0.495884i
\(428\) −2.01985 2.01985i −0.0976332 0.0976332i
\(429\) 10.8417i 0.523444i
\(430\) 0 0
\(431\) 11.0055i 0.530118i 0.964232 + 0.265059i \(0.0853915\pi\)
−0.964232 + 0.265059i \(0.914608\pi\)
\(432\) −8.25822 + 8.25822i −0.397324 + 0.397324i
\(433\) −3.70282 3.70282i −0.177946 0.177946i 0.612514 0.790460i \(-0.290158\pi\)
−0.790460 + 0.612514i \(0.790158\pi\)
\(434\) 7.34012i 0.352337i
\(435\) 0 0
\(436\) 13.3175i 0.637792i
\(437\) 37.8725 5.35180i 1.81169 0.256011i
\(438\) 3.29114 3.29114i 0.157257 0.157257i
\(439\) −32.4807 −1.55022 −0.775110 0.631826i \(-0.782306\pi\)
−0.775110 + 0.631826i \(0.782306\pi\)
\(440\) 0 0
\(441\) 10.1165 0.481739
\(442\) −18.8668 18.8668i −0.897403 0.897403i
\(443\) −9.15145 + 9.15145i −0.434798 + 0.434798i −0.890257 0.455459i \(-0.849475\pi\)
0.455459 + 0.890257i \(0.349475\pi\)
\(444\) 2.31532i 0.109880i
\(445\) 0 0
\(446\) 26.3006 1.24537
\(447\) 43.1292 43.1292i 2.03994 2.03994i
\(448\) 1.65823 1.65823i 0.0783439 0.0783439i
\(449\) 0.503369 0.0237554 0.0118777 0.999929i \(-0.496219\pi\)
0.0118777 + 0.999929i \(0.496219\pi\)
\(450\) 0 0
\(451\) 1.17122i 0.0551505i
\(452\) −10.8883 + 10.8883i −0.512143 + 0.512143i
\(453\) −1.41533 + 1.41533i −0.0664980 + 0.0664980i
\(454\) 7.80473i 0.366294i
\(455\) 0 0
\(456\) 8.17945 10.8716i 0.383038 0.509108i
\(457\) −8.26087 8.26087i −0.386427 0.386427i 0.486984 0.873411i \(-0.338097\pi\)
−0.873411 + 0.486984i \(0.838097\pi\)
\(458\) −7.03132 7.03132i −0.328552 0.328552i
\(459\) 72.1918 3.36962
\(460\) 0 0
\(461\) 18.1189 0.843882 0.421941 0.906623i \(-0.361349\pi\)
0.421941 + 0.906623i \(0.361349\pi\)
\(462\) −4.16500 4.16500i −0.193774 0.193774i
\(463\) −20.7494 + 20.7494i −0.964308 + 0.964308i −0.999385 0.0350766i \(-0.988832\pi\)
0.0350766 + 0.999385i \(0.488832\pi\)
\(464\) −5.64487 −0.262057
\(465\) 0 0
\(466\) 7.22827i 0.334843i
\(467\) −18.0874 18.0874i −0.836985 0.836985i 0.151476 0.988461i \(-0.451597\pi\)
−0.988461 + 0.151476i \(0.951597\pi\)
\(468\) −20.5773 20.5773i −0.951186 0.951186i
\(469\) −1.14506 −0.0528738
\(470\) 0 0
\(471\) 55.9207i 2.57669i
\(472\) 1.96353 + 1.96353i 0.0903786 + 0.0903786i
\(473\) 1.53539 1.53539i 0.0705971 0.0705971i
\(474\) 22.3765 1.02779
\(475\) 0 0
\(476\) −14.4959 −0.664419
\(477\) −22.9582 + 22.9582i −1.05118 + 1.05118i
\(478\) −6.57984 6.57984i −0.300955 0.300955i
\(479\) 1.97995i 0.0904662i 0.998976 + 0.0452331i \(0.0144031\pi\)
−0.998976 + 0.0452331i \(0.985597\pi\)
\(480\) 0 0
\(481\) −3.20198 −0.145998
\(482\) 5.87881 + 5.87881i 0.267773 + 0.267773i
\(483\) −45.4155 45.4155i −2.06648 2.06648i
\(484\) 10.3524i 0.470564i
\(485\) 0 0
\(486\) 15.6095 0.708060
\(487\) −1.84597 + 1.84597i −0.0836489 + 0.0836489i −0.747693 0.664044i \(-0.768839\pi\)
0.664044 + 0.747693i \(0.268839\pi\)
\(488\) −4.36953 4.36953i −0.197799 0.197799i
\(489\) −15.3230 −0.692930
\(490\) 0 0
\(491\) −5.60811 −0.253091 −0.126545 0.991961i \(-0.540389\pi\)
−0.126545 + 0.991961i \(0.540389\pi\)
\(492\) −3.21211 3.21211i −0.144813 0.144813i
\(493\) 24.6732 + 24.6732i 1.11122 + 1.11122i
\(494\) 15.0349 + 11.3118i 0.676450 + 0.508942i
\(495\) 0 0
\(496\) 3.13000i 0.140541i
\(497\) 11.0805 11.0805i 0.497026 0.497026i
\(498\) −12.8630 + 12.8630i −0.576405 + 0.576405i
\(499\) 18.8853i 0.845422i 0.906264 + 0.422711i \(0.138922\pi\)
−0.906264 + 0.422711i \(0.861078\pi\)
\(500\) 0 0
\(501\) −57.8379 −2.58400
\(502\) 7.61628 7.61628i 0.339931 0.339931i
\(503\) 26.9767 26.9767i 1.20283 1.20283i 0.229532 0.973301i \(-0.426280\pi\)
0.973301 0.229532i \(-0.0737196\pi\)
\(504\) −15.8101 −0.704239
\(505\) 0 0
\(506\) 7.06142i 0.313919i
\(507\) 12.4294 12.4294i 0.552009 0.552009i
\(508\) 10.4120 + 10.4120i 0.461960 + 0.461960i
\(509\) −30.3840 −1.34675 −0.673374 0.739302i \(-0.735156\pi\)
−0.673374 + 0.739302i \(0.735156\pi\)
\(510\) 0 0
\(511\) 3.49704 0.154700
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −50.4063 + 7.12296i −2.22549 + 0.314486i
\(514\) 28.0873i 1.23888i
\(515\) 0 0
\(516\) 8.42171i 0.370745i
\(517\) 0.401911 + 0.401911i 0.0176760 + 0.0176760i
\(518\) −1.23009 + 1.23009i −0.0540469 + 0.0540469i
\(519\) 33.1344i 1.45444i
\(520\) 0 0
\(521\) 41.3468i 1.81143i −0.423882 0.905717i \(-0.639333\pi\)
0.423882 0.905717i \(-0.360667\pi\)
\(522\) 26.9101 + 26.9101i 1.17782 + 1.17782i
\(523\) −10.9169 10.9169i −0.477361 0.477361i 0.426926 0.904287i \(-0.359597\pi\)
−0.904287 + 0.426926i \(0.859597\pi\)
\(524\) 15.4836i 0.676405i
\(525\) 0 0
\(526\) 18.6625i 0.813725i
\(527\) 13.6809 13.6809i 0.595950 0.595950i
\(528\) −1.77606 1.77606i −0.0772929 0.0772929i
\(529\) 53.9983i 2.34775i
\(530\) 0 0
\(531\) 18.7210i 0.812420i
\(532\) 10.1214 1.43027i 0.438820 0.0620101i
\(533\) 4.44220 4.44220i 0.192413 0.192413i
\(534\) 52.2350 2.26043
\(535\) 0 0
\(536\) −0.488279 −0.0210904
\(537\) 42.8762 + 42.8762i 1.85024 + 1.85024i
\(538\) 12.8170 12.8170i 0.552581 0.552581i
\(539\) 1.20755i 0.0520130i
\(540\) 0 0
\(541\) 41.7436 1.79470 0.897350 0.441320i \(-0.145490\pi\)
0.897350 + 0.441320i \(0.145490\pi\)
\(542\) −5.39019 + 5.39019i −0.231529 + 0.231529i
\(543\) 10.1201 10.1201i 0.434293 0.434293i
\(544\) −6.18139 −0.265025
\(545\) 0 0
\(546\) 31.5941i 1.35210i
\(547\) 16.6189 16.6189i 0.710571 0.710571i −0.256083 0.966655i \(-0.582432\pi\)
0.966655 + 0.256083i \(0.0824322\pi\)
\(548\) 3.37204 3.37204i 0.144046 0.144046i
\(549\) 41.6607i 1.77803i
\(550\) 0 0
\(551\) −19.6619 14.7931i −0.837627 0.630206i
\(552\) −19.3662 19.3662i −0.824282 0.824282i
\(553\) 11.8882 + 11.8882i 0.505539 + 0.505539i
\(554\) 2.75362 0.116990
\(555\) 0 0
\(556\) 2.05826 0.0872898
\(557\) −14.9213 14.9213i −0.632234 0.632234i 0.316394 0.948628i \(-0.397528\pi\)
−0.948628 + 0.316394i \(0.897528\pi\)
\(558\) 14.9213 14.9213i 0.631667 0.631667i
\(559\) 11.6468 0.492609
\(560\) 0 0
\(561\) 15.5259i 0.655506i
\(562\) −4.08626 4.08626i −0.172369 0.172369i
\(563\) 24.7032 + 24.7032i 1.04112 + 1.04112i 0.999118 + 0.0419980i \(0.0133723\pi\)
0.0419980 + 0.999118i \(0.486628\pi\)
\(564\) 2.20452 0.0928269
\(565\) 0 0
\(566\) 30.1155i 1.26585i
\(567\) 26.9073 + 26.9073i 1.13000 + 1.13000i
\(568\) 4.72496 4.72496i 0.198255 0.198255i
\(569\) 19.1003 0.800725 0.400362 0.916357i \(-0.368884\pi\)
0.400362 + 0.916357i \(0.368884\pi\)
\(570\) 0 0
\(571\) −33.3161 −1.39424 −0.697118 0.716957i \(-0.745535\pi\)
−0.697118 + 0.716957i \(0.745535\pi\)
\(572\) 2.45620 2.45620i 0.102699 0.102699i
\(573\) −10.7352 10.7352i −0.448469 0.448469i
\(574\) 3.41307i 0.142459i
\(575\) 0 0
\(576\) −6.74181 −0.280909
\(577\) −15.5550 15.5550i −0.647564 0.647564i 0.304840 0.952404i \(-0.401397\pi\)
−0.952404 + 0.304840i \(0.901397\pi\)
\(578\) 14.9975 + 14.9975i 0.623812 + 0.623812i
\(579\) 45.6024i 1.89517i
\(580\) 0 0
\(581\) −13.6677 −0.567033
\(582\) 25.7508 25.7508i 1.06741 1.06741i
\(583\) −2.74039 2.74039i −0.113496 0.113496i
\(584\) 1.49122 0.0617070
\(585\) 0 0
\(586\) −8.40304 −0.347126
\(587\) 12.0651 + 12.0651i 0.497979 + 0.497979i 0.910808 0.412829i \(-0.135459\pi\)
−0.412829 + 0.910808i \(0.635459\pi\)
\(588\) 3.31177 + 3.31177i 0.136575 + 0.136575i
\(589\) −8.20254 + 10.9023i −0.337980 + 0.449220i
\(590\) 0 0
\(591\) 36.7391i 1.51125i
\(592\) −0.524538 + 0.524538i −0.0215584 + 0.0215584i
\(593\) −11.1513 + 11.1513i −0.457931 + 0.457931i −0.897976 0.440045i \(-0.854963\pi\)
0.440045 + 0.897976i \(0.354963\pi\)
\(594\) 9.39838i 0.385620i
\(595\) 0 0
\(596\) 19.5419 0.800467
\(597\) −50.9913 + 50.9913i −2.08694 + 2.08694i
\(598\) 26.7826 26.7826i 1.09522 1.09522i
\(599\) 9.96626 0.407210 0.203605 0.979053i \(-0.434734\pi\)
0.203605 + 0.979053i \(0.434734\pi\)
\(600\) 0 0
\(601\) 13.6021i 0.554840i 0.960749 + 0.277420i \(0.0894794\pi\)
−0.960749 + 0.277420i \(0.910521\pi\)
\(602\) 4.47430 4.47430i 0.182359 0.182359i
\(603\) 2.32771 + 2.32771i 0.0947917 + 0.0947917i
\(604\) −0.641287 −0.0260936
\(605\) 0 0
\(606\) 5.47133 0.222258
\(607\) −11.0390 + 11.0390i −0.448060 + 0.448060i −0.894709 0.446649i \(-0.852617\pi\)
0.446649 + 0.894709i \(0.352617\pi\)
\(608\) 4.31602 0.609901i 0.175038 0.0247347i
\(609\) 41.3174i 1.67426i
\(610\) 0 0
\(611\) 3.04874i 0.123339i
\(612\) 29.4678 + 29.4678i 1.19117 + 1.19117i
\(613\) −11.0338 + 11.0338i −0.445651 + 0.445651i −0.893906 0.448255i \(-0.852046\pi\)
0.448255 + 0.893906i \(0.352046\pi\)
\(614\) 3.78220i 0.152637i
\(615\) 0 0
\(616\) 1.88717i 0.0760362i
\(617\) −4.29188 4.29188i −0.172785 0.172785i 0.615417 0.788202i \(-0.288988\pi\)
−0.788202 + 0.615417i \(0.788988\pi\)
\(618\) −17.3512 17.3512i −0.697969 0.697969i
\(619\) 34.2230i 1.37554i −0.725929 0.687770i \(-0.758590\pi\)
0.725929 0.687770i \(-0.241410\pi\)
\(620\) 0 0
\(621\) 102.481i 4.11241i
\(622\) 13.3015 13.3015i 0.533343 0.533343i
\(623\) 27.7514 + 27.7514i 1.11184 + 1.11184i
\(624\) 13.4725i 0.539330i
\(625\) 0 0
\(626\) 20.7155i 0.827959i
\(627\) −1.53190 10.8406i −0.0611782 0.432933i
\(628\) −12.6689 + 12.6689i −0.505543 + 0.505543i
\(629\) 4.58541 0.182832
\(630\) 0 0
\(631\) −14.1221 −0.562192 −0.281096 0.959680i \(-0.590698\pi\)
−0.281096 + 0.959680i \(0.590698\pi\)
\(632\) 5.06942 + 5.06942i 0.201651 + 0.201651i
\(633\) 33.8758 33.8758i 1.34644 1.34644i
\(634\) 1.33453i 0.0530011i
\(635\) 0 0
\(636\) −15.0313 −0.596029
\(637\) −4.58002 + 4.58002i −0.181467 + 0.181467i
\(638\) −3.21211 + 3.21211i −0.127169 + 0.127169i
\(639\) −45.0495 −1.78213
\(640\) 0 0
\(641\) 18.1482i 0.716812i 0.933566 + 0.358406i \(0.116680\pi\)
−0.933566 + 0.358406i \(0.883320\pi\)
\(642\) −6.30433 + 6.30433i −0.248812 + 0.248812i
\(643\) 7.69230 7.69230i 0.303355 0.303355i −0.538970 0.842325i \(-0.681186\pi\)
0.842325 + 0.538970i \(0.181186\pi\)
\(644\) 20.5778i 0.810880i
\(645\) 0 0
\(646\) −21.5307 16.1991i −0.847115 0.637345i
\(647\) −18.0736 18.0736i −0.710545 0.710545i 0.256104 0.966649i \(-0.417561\pi\)
−0.966649 + 0.256104i \(0.917561\pi\)
\(648\) 11.4739 + 11.4739i 0.450738 + 0.450738i
\(649\) 2.23462 0.0877164
\(650\) 0 0
\(651\) 22.9099 0.897909
\(652\) −3.47143 3.47143i −0.135952 0.135952i
\(653\) −14.3290 + 14.3290i −0.560736 + 0.560736i −0.929516 0.368781i \(-0.879775\pi\)
0.368781 + 0.929516i \(0.379775\pi\)
\(654\) 41.5663 1.62537
\(655\) 0 0
\(656\) 1.45541i 0.0568243i
\(657\) −7.10890 7.10890i −0.277345 0.277345i
\(658\) 1.17122 + 1.17122i 0.0456588 + 0.0456588i
\(659\) 15.0999 0.588208 0.294104 0.955773i \(-0.404979\pi\)
0.294104 + 0.955773i \(0.404979\pi\)
\(660\) 0 0
\(661\) 37.7035i 1.46650i 0.679962 + 0.733248i \(0.261996\pi\)
−0.679962 + 0.733248i \(0.738004\pi\)
\(662\) −10.5853 10.5853i −0.411409 0.411409i
\(663\) −58.8868 + 58.8868i −2.28698 + 2.28698i
\(664\) −5.82824 −0.226180
\(665\) 0 0
\(666\) 5.00113 0.193790
\(667\) −35.0251 + 35.0251i −1.35618 + 1.35618i
\(668\) −13.1032 13.1032i −0.506978 0.506978i
\(669\) 82.0892i 3.17375i
\(670\) 0 0
\(671\) −4.97281 −0.191973
\(672\) −5.17564 5.17564i −0.199655 0.199655i
\(673\) −20.8241 20.8241i −0.802710 0.802710i 0.180808 0.983518i \(-0.442129\pi\)
−0.983518 + 0.180808i \(0.942129\pi\)
\(674\) 26.0896i 1.00493i
\(675\) 0 0
\(676\) 5.63178 0.216607
\(677\) 22.3987 22.3987i 0.860850 0.860850i −0.130587 0.991437i \(-0.541686\pi\)
0.991437 + 0.130587i \(0.0416861\pi\)
\(678\) 33.9844 + 33.9844i 1.30516 + 1.30516i
\(679\) 27.3618 1.05005
\(680\) 0 0
\(681\) 24.3600 0.933478
\(682\) 1.78107 + 1.78107i 0.0682007 + 0.0682007i
\(683\) 3.33340 + 3.33340i 0.127549 + 0.127549i 0.767999 0.640451i \(-0.221252\pi\)
−0.640451 + 0.767999i \(0.721252\pi\)
\(684\) −23.4827 17.6677i −0.897885 0.675542i
\(685\) 0 0
\(686\) 19.9346i 0.761105i
\(687\) −21.9461 + 21.9461i −0.837295 + 0.837295i
\(688\) 1.90794 1.90794i 0.0727397 0.0727397i
\(689\) 20.7876i 0.791943i
\(690\) 0 0
\(691\) −0.218008 −0.00829342 −0.00414671 0.999991i \(-0.501320\pi\)
−0.00414671 + 0.999991i \(0.501320\pi\)
\(692\) −7.50662 + 7.50662i −0.285359 + 0.285359i
\(693\) −8.99647 + 8.99647i −0.341748 + 0.341748i
\(694\) −18.8907 −0.717083
\(695\) 0 0
\(696\) 17.6187i 0.667835i
\(697\) −6.36146 + 6.36146i −0.240958 + 0.240958i
\(698\) −5.47888 5.47888i −0.207379 0.207379i
\(699\) −22.5608 −0.853328
\(700\) 0 0
\(701\) −4.66660 −0.176255 −0.0881275 0.996109i \(-0.528088\pi\)
−0.0881275 + 0.996109i \(0.528088\pi\)
\(702\) −35.6462 + 35.6462i −1.34538 + 1.34538i
\(703\) −3.20166 + 0.452430i −0.120753 + 0.0170637i
\(704\) 0.804733i 0.0303295i
\(705\) 0 0
\(706\) 34.2893i 1.29049i
\(707\) 2.90681 + 2.90681i 0.109322 + 0.109322i
\(708\) 6.12853 6.12853i 0.230324 0.230324i
\(709\) 0.424223i 0.0159320i 0.999968 + 0.00796602i \(0.00253569\pi\)
−0.999968 + 0.00796602i \(0.997464\pi\)
\(710\) 0 0
\(711\) 48.3336i 1.81265i
\(712\) 11.8339 + 11.8339i 0.443493 + 0.443493i
\(713\) 19.4209 + 19.4209i 0.727319 + 0.727319i
\(714\) 45.2444i 1.69323i
\(715\) 0 0
\(716\) 19.4273i 0.726031i
\(717\) −20.5369 + 20.5369i −0.766965 + 0.766965i
\(718\) 0.304067 + 0.304067i 0.0113477 + 0.0113477i
\(719\) 9.56441i 0.356692i −0.983968 0.178346i \(-0.942925\pi\)
0.983968 0.178346i \(-0.0570747\pi\)
\(720\) 0 0
\(721\) 18.4368i 0.686621i
\(722\) 16.6317 + 9.18628i 0.618967 + 0.341878i
\(723\) 18.3489 18.3489i 0.682402 0.682402i
\(724\) 4.58541 0.170415
\(725\) 0 0
\(726\) 32.3118 1.19920
\(727\) −2.48083 2.48083i −0.0920089 0.0920089i 0.659604 0.751613i \(-0.270724\pi\)
−0.751613 + 0.659604i \(0.770724\pi\)
\(728\) 7.15766 7.15766i 0.265281 0.265281i
\(729\) 0.0403915i 0.00149598i
\(730\) 0 0
\(731\) −16.6789 −0.616891
\(732\) −13.6381 + 13.6381i −0.504080 + 0.504080i
\(733\) 16.0819 16.0819i 0.594000 0.594000i −0.344710 0.938709i \(-0.612023\pi\)
0.938709 + 0.344710i \(0.112023\pi\)
\(734\) 11.2313 0.414555
\(735\) 0 0
\(736\) 8.77487i 0.323446i
\(737\) −0.277846 + 0.277846i −0.0102346 + 0.0102346i
\(738\) −6.93821 + 6.93821i −0.255399 + 0.255399i
\(739\) 35.9583i 1.32275i −0.750056 0.661374i \(-0.769973\pi\)
0.750056 0.661374i \(-0.230027\pi\)
\(740\) 0 0
\(741\) 35.3062 46.9266i 1.29701 1.72389i
\(742\) −7.98584 7.98584i −0.293169 0.293169i
\(743\) 24.1408 + 24.1408i 0.885639 + 0.885639i 0.994101 0.108462i \(-0.0345926\pi\)
−0.108462 + 0.994101i \(0.534593\pi\)
\(744\) 9.76931 0.358160
\(745\) 0 0
\(746\) −8.09865 −0.296513
\(747\) 27.7843 + 27.7843i 1.01657 + 1.01657i
\(748\) −3.51741 + 3.51741i −0.128609 + 0.128609i
\(749\) −6.69874 −0.244767
\(750\) 0 0
\(751\) 1.42885i 0.0521395i −0.999660 0.0260697i \(-0.991701\pi\)
0.999660 0.0260697i \(-0.00829920\pi\)
\(752\) 0.499434 + 0.499434i 0.0182125 + 0.0182125i
\(753\) −23.7718 23.7718i −0.866294 0.866294i
\(754\) −24.3658 −0.887351
\(755\) 0 0
\(756\) 27.3880i 0.996092i
\(757\) 17.6271 + 17.6271i 0.640668 + 0.640668i 0.950720 0.310051i \(-0.100346\pi\)
−0.310051 + 0.950720i \(0.600346\pi\)
\(758\) −1.23287 + 1.23287i −0.0447800 + 0.0447800i
\(759\) −22.0400 −0.800002
\(760\) 0 0
\(761\) −33.0942 −1.19966 −0.599832 0.800126i \(-0.704766\pi\)
−0.599832 + 0.800126i \(0.704766\pi\)
\(762\) 32.4980 32.4980i 1.17728 1.17728i
\(763\) 22.0834 + 22.0834i 0.799473 + 0.799473i
\(764\) 4.86413i 0.175978i
\(765\) 0 0
\(766\) 21.1413 0.763867
\(767\) 8.47547 + 8.47547i 0.306031 + 0.306031i
\(768\) −2.20701 2.20701i −0.0796387 0.0796387i
\(769\) 2.61399i 0.0942629i −0.998889 0.0471314i \(-0.984992\pi\)
0.998889 0.0471314i \(-0.0150080\pi\)
\(770\) 0 0
\(771\) 87.6657 3.15720
\(772\) −10.3313 + 10.3313i −0.371830 + 0.371830i
\(773\) −14.4070 14.4070i −0.518182 0.518182i 0.398839 0.917021i \(-0.369413\pi\)
−0.917021 + 0.398839i \(0.869413\pi\)
\(774\) −18.1910 −0.653863
\(775\) 0 0
\(776\) 11.6677 0.418847
\(777\) 3.83933 + 3.83933i 0.137735 + 0.137735i
\(778\) 6.51547 + 6.51547i 0.233591 + 0.233591i
\(779\) 3.81408 5.06942i 0.136654 0.181631i
\(780\) 0 0
\(781\) 5.37731i 0.192415i
\(782\) −38.3541 + 38.3541i −1.37154 + 1.37154i
\(783\) 46.6166 46.6166i 1.66594 1.66594i
\(784\) 1.50057i 0.0535916i
\(785\) 0 0
\(786\) 48.3273 1.72378
\(787\) 28.5405 28.5405i 1.01736 1.01736i 0.0175140 0.999847i \(-0.494425\pi\)
0.999847 0.0175140i \(-0.00557518\pi\)
\(788\) −8.32327 + 8.32327i −0.296504 + 0.296504i
\(789\) 58.2492 2.07373
\(790\) 0 0
\(791\) 36.1105i 1.28394i
\(792\) −3.83630 + 3.83630i −0.136317 + 0.136317i
\(793\) −18.8609 18.8609i −0.669769 0.669769i
\(794\) 13.1341 0.466112
\(795\) 0 0
\(796\) −23.1042 −0.818908
\(797\) −19.4519 + 19.4519i −0.689021 + 0.689021i −0.962016 0.272995i \(-0.911986\pi\)
0.272995 + 0.962016i \(0.411986\pi\)
\(798\) −4.46414 31.5909i −0.158029 1.11831i
\(799\) 4.36596i 0.154457i
\(800\) 0 0
\(801\) 112.828i 3.98659i
\(802\) −27.3611 27.3611i −0.966153 0.966153i
\(803\) 0.848550 0.848550i 0.0299447 0.0299447i
\(804\) 1.52401i 0.0537476i
\(805\) 0 0
\(806\) 13.5105i 0.475887i
\(807\) −40.0043 40.0043i −1.40822 1.40822i
\(808\) 1.23953 + 1.23953i 0.0436066 + 0.0436066i
\(809\) 1.15579i 0.0406353i 0.999794 + 0.0203176i \(0.00646775\pi\)
−0.999794 + 0.0203176i \(0.993532\pi\)
\(810\) 0 0
\(811\) 39.4268i 1.38446i −0.721675 0.692232i \(-0.756628\pi\)
0.721675 0.692232i \(-0.243372\pi\)
\(812\) −9.36048 + 9.36048i −0.328488 + 0.328488i
\(813\) 16.8238 + 16.8238i 0.590036 + 0.590036i
\(814\) 0.596958i 0.0209234i
\(815\) 0 0
\(816\) 19.2933i 0.675400i
\(817\) 11.6457 1.64566i 0.407430 0.0575743i
\(818\) 10.3815 10.3815i 0.362982 0.362982i
\(819\) −68.2437 −2.38463
\(820\) 0 0
\(821\) 12.3926 0.432504 0.216252 0.976338i \(-0.430617\pi\)
0.216252 + 0.976338i \(0.430617\pi\)
\(822\) −10.5248 10.5248i −0.367093 0.367093i
\(823\) −15.3766 + 15.3766i −0.535994 + 0.535994i −0.922350 0.386356i \(-0.873734\pi\)
0.386356 + 0.922350i \(0.373734\pi\)
\(824\) 7.86186i 0.273881i
\(825\) 0 0
\(826\) 6.51194 0.226579
\(827\) 26.9516 26.9516i 0.937197 0.937197i −0.0609437 0.998141i \(-0.519411\pi\)
0.998141 + 0.0609437i \(0.0194110\pi\)
\(828\) −41.8314 + 41.8314i −1.45374 + 1.45374i
\(829\) −12.4871 −0.433696 −0.216848 0.976205i \(-0.569578\pi\)
−0.216848 + 0.976205i \(0.569578\pi\)
\(830\) 0 0
\(831\) 8.59455i 0.298142i
\(832\) 3.05219 3.05219i 0.105816 0.105816i
\(833\) 6.55883 6.55883i 0.227250 0.227250i
\(834\) 6.42422i 0.222453i
\(835\) 0 0
\(836\) 2.10890 2.80301i 0.0729378 0.0969440i
\(837\) −25.8482 25.8482i −0.893445 0.893445i
\(838\) −0.902156 0.902156i −0.0311645 0.0311645i
\(839\) −6.90128 −0.238259 −0.119129 0.992879i \(-0.538010\pi\)
−0.119129 + 0.992879i \(0.538010\pi\)
\(840\) 0 0
\(841\) 2.86456 0.0987778
\(842\) 4.76815 + 4.76815i 0.164321 + 0.164321i
\(843\) −12.7540 + 12.7540i −0.439271 + 0.439271i
\(844\) 15.3492 0.528340
\(845\) 0 0
\(846\) 4.76179i 0.163714i
\(847\) 17.1666 + 17.1666i 0.589853 + 0.589853i
\(848\) −3.40535 3.40535i −0.116940 0.116940i
\(849\) −93.9960 −3.22593
\(850\) 0 0
\(851\) 6.50927i 0.223135i
\(852\) −14.7475 14.7475i −0.505241 0.505241i
\(853\) 19.4959 19.4959i 0.667527 0.667527i −0.289616 0.957143i \(-0.593528\pi\)
0.957143 + 0.289616i \(0.0935276\pi\)
\(854\) −14.4913 −0.495884
\(855\) 0 0
\(856\) −2.85650 −0.0976332
\(857\) 31.0425 31.0425i 1.06039 1.06039i 0.0623378 0.998055i \(-0.480144\pi\)
0.998055 0.0623378i \(-0.0198556\pi\)
\(858\) −7.66626 7.66626i −0.261722 0.261722i
\(859\) 33.3721i 1.13864i 0.822115 + 0.569321i \(0.192794\pi\)
−0.822115 + 0.569321i \(0.807206\pi\)
\(860\) 0 0
\(861\) −10.6528 −0.363047
\(862\) 7.78210 + 7.78210i 0.265059 + 0.265059i
\(863\) 10.3810 + 10.3810i 0.353373 + 0.353373i 0.861363 0.507990i \(-0.169611\pi\)
−0.507990 + 0.861363i \(0.669611\pi\)
\(864\) 11.6789i 0.397324i
\(865\) 0 0
\(866\) −5.23658 −0.177946
\(867\) 46.8099 46.8099i 1.58975 1.58975i
\(868\) 5.19025 + 5.19025i 0.176168 + 0.176168i
\(869\) 5.76932 0.195711
\(870\) 0 0
\(871\) −2.10763 −0.0714144
\(872\) 9.41688 + 9.41688i 0.318896 + 0.318896i
\(873\) −55.6221 55.6221i −1.88252 1.88252i
\(874\) 22.9956 30.5642i 0.777838 1.03385i
\(875\) 0 0
\(876\) 4.65437i 0.157257i
\(877\) −1.64017 + 1.64017i −0.0553847 + 0.0553847i −0.734257 0.678872i \(-0.762469\pi\)
0.678872 + 0.734257i \(0.262469\pi\)
\(878\) −22.9673 + 22.9673i −0.775110 + 0.775110i
\(879\) 26.2275i 0.884631i
\(880\) 0 0
\(881\) −44.0880 −1.48536 −0.742681 0.669645i \(-0.766446\pi\)
−0.742681 + 0.669645i \(0.766446\pi\)
\(882\) 7.15346 7.15346i 0.240870 0.240870i
\(883\) −15.3555 + 15.3555i −0.516754 + 0.516754i −0.916588 0.399834i \(-0.869068\pi\)
0.399834 + 0.916588i \(0.369068\pi\)
\(884\) −26.6817 −0.897403
\(885\) 0 0
\(886\) 12.9421i 0.434798i
\(887\) −20.5729 + 20.5729i −0.690769 + 0.690769i −0.962401 0.271632i \(-0.912437\pi\)
0.271632 + 0.962401i \(0.412437\pi\)
\(888\) 1.63718 + 1.63718i 0.0549402 + 0.0549402i
\(889\) 34.5311 1.15814
\(890\) 0 0
\(891\) 13.0580 0.437461
\(892\) 18.5974 18.5974i 0.622686 0.622686i
\(893\) 0.430777 + 3.04843i 0.0144154 + 0.102012i
\(894\) 60.9939i 2.03994i
\(895\) 0 0
\(896\) 2.34509i 0.0783439i
\(897\) −83.5935 83.5935i −2.79111 2.79111i
\(898\) 0.355936 0.355936i 0.0118777 0.0118777i
\(899\) 17.6684i 0.589275i
\(900\) 0 0
\(901\) 29.7689i 0.991746i
\(902\) −0.828176 0.828176i −0.0275752 0.0275752i
\(903\) −13.9651 13.9651i −0.464730 0.464730i
\(904\) 15.3984i 0.512143i
\(905\) 0 0
\(906\) 2.00158i 0.0664980i
\(907\) −34.7376 + 34.7376i −1.15344 + 1.15344i −0.167584 + 0.985858i \(0.553597\pi\)
−0.985858 + 0.167584i \(0.946403\pi\)
\(908\) 5.51878 + 5.51878i 0.183147 + 0.183147i
\(909\) 11.8182i 0.391983i
\(910\) 0 0
\(911\) 30.8489i 1.02207i 0.859560 + 0.511035i \(0.170738\pi\)
−0.859560 + 0.511035i \(0.829262\pi\)
\(912\) −1.90361 13.4711i −0.0630350 0.446073i
\(913\) −3.31645 + 3.31645i −0.109759 + 0.109759i
\(914\) −11.6826 −0.386427
\(915\) 0 0
\(916\) −9.94379 −0.328552
\(917\) 25.6754 + 25.6754i 0.847875 + 0.847875i
\(918\) 51.0473 51.0473i 1.68481 1.68481i
\(919\) 31.7256i 1.04653i 0.852170 + 0.523265i \(0.175286\pi\)
−0.852170 + 0.523265i \(0.824714\pi\)
\(920\) 0 0
\(921\) −11.8050 −0.388986
\(922\) 12.8120 12.8120i 0.421941 0.421941i
\(923\) 20.3951 20.3951i 0.671313 0.671313i
\(924\) −5.89021 −0.193774
\(925\) 0 0
\(926\) 29.3441i 0.964308i
\(927\) −37.4789 + 37.4789i −1.23097 + 1.23097i
\(928\) −3.99153 + 3.99153i −0.131028 + 0.131028i
\(929\) 5.78107i 0.189671i 0.995493 + 0.0948354i \(0.0302325\pi\)
−0.995493 + 0.0948354i \(0.969768\pi\)
\(930\) 0 0
\(931\) −3.93241 + 5.22670i −0.128880 + 0.171298i
\(932\) −5.11116 5.11116i −0.167422 0.167422i
\(933\) −41.5166 41.5166i −1.35919 1.35919i
\(934\) −25.5794 −0.836985
\(935\) 0 0
\(936\) −29.1007 −0.951186
\(937\) −12.5571 12.5571i −0.410222 0.410222i 0.471594 0.881816i \(-0.343679\pi\)
−0.881816 + 0.471594i \(0.843679\pi\)
\(938\) −0.809677 + 0.809677i −0.0264369 + 0.0264369i
\(939\) 64.6571 2.11000
\(940\) 0 0
\(941\) 26.4197i 0.861258i −0.902529 0.430629i \(-0.858292\pi\)
0.902529 0.430629i \(-0.141708\pi\)
\(942\) 39.5419 + 39.5419i 1.28834 + 1.28834i
\(943\) −9.03049 9.03049i −0.294073 0.294073i
\(944\) 2.77684 0.0903786
\(945\) 0 0
\(946\) 2.17136i 0.0705971i
\(947\) −0.351274 0.351274i −0.0114149 0.0114149i 0.701376 0.712791i \(-0.252569\pi\)
−0.712791 + 0.701376i \(0.752569\pi\)
\(948\) 15.8226 15.8226i 0.513894 0.513894i
\(949\) 6.43677 0.208946
\(950\) 0 0
\(951\) 4.16533 0.135070
\(952\) −10.2502 + 10.2502i −0.332209 + 0.332209i
\(953\) −37.8897 37.8897i −1.22737 1.22737i −0.964956 0.262411i \(-0.915482\pi\)
−0.262411 0.964956i \(-0.584518\pi\)
\(954\) 32.4678i 1.05118i
\(955\) 0 0
\(956\) −9.30530 −0.300955
\(957\) 10.0256 + 10.0256i 0.324082 + 0.324082i
\(958\) 1.40004 + 1.40004i 0.0452331 + 0.0452331i
\(959\) 11.1832i 0.361124i
\(960\) 0 0
\(961\) 21.2031 0.683971
\(962\) −2.26414 + 2.26414i −0.0729989 + 0.0729989i
\(963\) 13.6175 + 13.6175i 0.438816 + 0.438816i
\(964\) 8.31390 0.267773
\(965\) 0 0
\(966\) −64.2273 −2.06648
\(967\) −29.9302 29.9302i −0.962489 0.962489i 0.0368326 0.999321i \(-0.488273\pi\)
−0.999321 + 0.0368326i \(0.988273\pi\)
\(968\) 7.32026 + 7.32026i 0.235282 + 0.235282i
\(969\) −50.5604 + 67.2014i −1.62423 + 2.15882i
\(970\) 0 0
\(971\) 20.7610i 0.666252i 0.942882 + 0.333126i \(0.108103\pi\)
−0.942882 + 0.333126i \(0.891897\pi\)
\(972\) 11.0376 11.0376i 0.354030 0.354030i
\(973\) 3.41307 3.41307i 0.109418 0.109418i
\(974\) 2.61060i 0.0836489i
\(975\) 0 0
\(976\) −6.17945 −0.197799
\(977\) 3.40331 3.40331i 0.108882 0.108882i −0.650567 0.759449i \(-0.725469\pi\)
0.759449 + 0.650567i \(0.225469\pi\)
\(978\) −10.8350 + 10.8350i −0.346465 + 0.346465i
\(979\) 13.4677 0.430429
\(980\) 0 0
\(981\) 89.7839i 2.86658i
\(982\) −3.96554 + 3.96554i −0.126545 + 0.126545i
\(983\) −29.7757 29.7757i −0.949699 0.949699i 0.0490954 0.998794i \(-0.484366\pi\)
−0.998794 + 0.0490954i \(0.984366\pi\)
\(984\) −4.54261 −0.144813
\(985\) 0 0
\(986\) 34.8932 1.11122
\(987\) 3.65559 3.65559i 0.116359 0.116359i
\(988\) 18.6299 2.63261i 0.592696 0.0837544i
\(989\) 23.6767i 0.752875i
\(990\) 0 0
\(991\) 45.0530i 1.43116i −0.698532 0.715578i \(-0.746163\pi\)
0.698532 0.715578i \(-0.253837\pi\)
\(992\) 2.21324 + 2.21324i 0.0702705 + 0.0702705i
\(993\) −33.0386 + 33.0386i −1.04845 + 1.04845i
\(994\) 15.6701i 0.497026i
\(995\) 0 0
\(996\) 18.1910i 0.576405i
\(997\) 0.131537 + 0.131537i 0.00416581 + 0.00416581i 0.709187 0.705021i \(-0.249062\pi\)
−0.705021 + 0.709187i \(0.749062\pi\)
\(998\) 13.3539 + 13.3539i 0.422711 + 0.422711i
\(999\) 8.66350i 0.274101i
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 950.2.f.c.607.5 16
5.2 odd 4 190.2.f.b.113.5 yes 16
5.3 odd 4 inner 950.2.f.c.493.4 16
5.4 even 2 190.2.f.b.37.4 16
15.2 even 4 1710.2.p.b.1063.4 16
15.14 odd 2 1710.2.p.b.37.8 16
19.18 odd 2 inner 950.2.f.c.607.4 16
95.18 even 4 inner 950.2.f.c.493.5 16
95.37 even 4 190.2.f.b.113.4 yes 16
95.94 odd 2 190.2.f.b.37.5 yes 16
285.227 odd 4 1710.2.p.b.1063.8 16
285.284 even 2 1710.2.p.b.37.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.f.b.37.4 16 5.4 even 2
190.2.f.b.37.5 yes 16 95.94 odd 2
190.2.f.b.113.4 yes 16 95.37 even 4
190.2.f.b.113.5 yes 16 5.2 odd 4
950.2.f.c.493.4 16 5.3 odd 4 inner
950.2.f.c.493.5 16 95.18 even 4 inner
950.2.f.c.607.4 16 19.18 odd 2 inner
950.2.f.c.607.5 16 1.1 even 1 trivial
1710.2.p.b.37.4 16 285.284 even 2
1710.2.p.b.37.8 16 15.14 odd 2
1710.2.p.b.1063.4 16 15.2 even 4
1710.2.p.b.1063.8 16 285.227 odd 4