Properties

Label 1470.2.b.b.881.2
Level $1470$
Weight $2$
Character 1470.881
Analytic conductor $11.738$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(881,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.b (of order \(2\), degree \(1\), 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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} - 864 x^{3} + 891 x^{2} - 972 x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 881.2
Root \(0.312065 - 1.70371i\) of defining polynomial
Character \(\chi\) \(=\) 1470.881
Dual form 1470.2.b.b.881.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-0.581597 - 1.63149i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.63149 + 0.581597i) q^{6} +1.00000i q^{8} +(-2.32349 + 1.89773i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-0.581597 - 1.63149i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.63149 + 0.581597i) q^{6} +1.00000i q^{8} +(-2.32349 + 1.89773i) q^{9} +1.00000i q^{10} +0.963479i q^{11} +(0.581597 + 1.63149i) q^{12} +1.98782i q^{13} +(0.581597 + 1.63149i) q^{15} +1.00000 q^{16} -2.63227 q^{17} +(1.89773 + 2.32349i) q^{18} -5.16784i q^{19} +1.00000 q^{20} +0.963479 q^{22} +2.69411i q^{23} +(1.63149 - 0.581597i) q^{24} +1.00000 q^{25} +1.98782 q^{26} +(4.44746 + 2.68703i) q^{27} +9.90498i q^{29} +(1.63149 - 0.581597i) q^{30} +3.42151i q^{31} -1.00000i q^{32} +(1.57190 - 0.560356i) q^{33} +2.63227i q^{34} +(2.32349 - 1.89773i) q^{36} +9.14603 q^{37} -5.16784 q^{38} +(3.24309 - 1.15611i) q^{39} -1.00000i q^{40} -1.12202 q^{41} +1.54917 q^{43} -0.963479i q^{44} +(2.32349 - 1.89773i) q^{45} +2.69411 q^{46} +10.3888 q^{47} +(-0.581597 - 1.63149i) q^{48} -1.00000i q^{50} +(1.53092 + 4.29451i) q^{51} -1.98782i q^{52} +13.1742i q^{53} +(2.68703 - 4.44746i) q^{54} -0.963479i q^{55} +(-8.43126 + 3.00560i) q^{57} +9.90498 q^{58} +2.10246 q^{59} +(-0.581597 - 1.63149i) q^{60} -8.96260i q^{61} +3.42151 q^{62} -1.00000 q^{64} -1.98782i q^{65} +(-0.560356 - 1.57190i) q^{66} -1.79547 q^{67} +2.63227 q^{68} +(4.39541 - 1.56689i) q^{69} -11.1501i q^{71} +(-1.89773 - 2.32349i) q^{72} -11.7735i q^{73} -9.14603i q^{74} +(-0.581597 - 1.63149i) q^{75} +5.16784i q^{76} +(-1.15611 - 3.24309i) q^{78} -0.408348 q^{79} -1.00000 q^{80} +(1.79722 - 8.81873i) q^{81} +1.12202i q^{82} -4.53092 q^{83} +2.63227 q^{85} -1.54917i q^{86} +(16.1598 - 5.76070i) q^{87} -0.963479 q^{88} -11.5214 q^{89} +(-1.89773 - 2.32349i) q^{90} -2.69411i q^{92} +(5.58215 - 1.98994i) q^{93} -10.3888i q^{94} +5.16784i q^{95} +(-1.63149 + 0.581597i) q^{96} +14.6992i q^{97} +(-1.82842 - 2.23863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9} - 4 q^{12} - 4 q^{15} + 12 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 2 q^{24} + 12 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{30} + 20 q^{33} + 6 q^{36} + 16 q^{37} - 16 q^{38} + 12 q^{39} - 4 q^{41} + 6 q^{45} - 4 q^{46} - 32 q^{47} + 4 q^{48} + 4 q^{51} - 28 q^{54} - 36 q^{57} - 16 q^{58} - 24 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{64} + 20 q^{66} + 8 q^{67} + 24 q^{68} + 50 q^{69} - 8 q^{72} + 4 q^{75} + 32 q^{78} + 8 q^{79} - 12 q^{80} - 10 q^{81} - 40 q^{83} + 24 q^{85} + 56 q^{87} - 52 q^{89} - 8 q^{90} + 28 q^{93} - 2 q^{96} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.581597 1.63149i −0.335785 0.941939i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.63149 + 0.581597i −0.666051 + 0.237436i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −2.32349 + 1.89773i −0.774497 + 0.632578i
\(10\) 1.00000i 0.316228i
\(11\) 0.963479i 0.290500i 0.989395 + 0.145250i \(0.0463986\pi\)
−0.989395 + 0.145250i \(0.953601\pi\)
\(12\) 0.581597 + 1.63149i 0.167892 + 0.470969i
\(13\) 1.98782i 0.551321i 0.961255 + 0.275660i \(0.0888966\pi\)
−0.961255 + 0.275660i \(0.911103\pi\)
\(14\) 0 0
\(15\) 0.581597 + 1.63149i 0.150168 + 0.421248i
\(16\) 1.00000 0.250000
\(17\) −2.63227 −0.638420 −0.319210 0.947684i \(-0.603418\pi\)
−0.319210 + 0.947684i \(0.603418\pi\)
\(18\) 1.89773 + 2.32349i 0.447300 + 0.547652i
\(19\) 5.16784i 1.18558i −0.805355 0.592792i \(-0.798026\pi\)
0.805355 0.592792i \(-0.201974\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 0.963479 0.205414
\(23\) 2.69411i 0.561762i 0.959743 + 0.280881i \(0.0906265\pi\)
−0.959743 + 0.280881i \(0.909373\pi\)
\(24\) 1.63149 0.581597i 0.333026 0.118718i
\(25\) 1.00000 0.200000
\(26\) 1.98782 0.389843
\(27\) 4.44746 + 2.68703i 0.855914 + 0.517119i
\(28\) 0 0
\(29\) 9.90498i 1.83931i 0.392730 + 0.919654i \(0.371531\pi\)
−0.392730 + 0.919654i \(0.628469\pi\)
\(30\) 1.63149 0.581597i 0.297867 0.106185i
\(31\) 3.42151i 0.614522i 0.951625 + 0.307261i \(0.0994125\pi\)
−0.951625 + 0.307261i \(0.900588\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.57190 0.560356i 0.273633 0.0975454i
\(34\) 2.63227i 0.451431i
\(35\) 0 0
\(36\) 2.32349 1.89773i 0.387248 0.316289i
\(37\) 9.14603 1.50360 0.751799 0.659392i \(-0.229186\pi\)
0.751799 + 0.659392i \(0.229186\pi\)
\(38\) −5.16784 −0.838335
\(39\) 3.24309 1.15611i 0.519311 0.185125i
\(40\) 1.00000i 0.158114i
\(41\) −1.12202 −0.175230 −0.0876152 0.996154i \(-0.527925\pi\)
−0.0876152 + 0.996154i \(0.527925\pi\)
\(42\) 0 0
\(43\) 1.54917 0.236246 0.118123 0.992999i \(-0.462312\pi\)
0.118123 + 0.992999i \(0.462312\pi\)
\(44\) 0.963479i 0.145250i
\(45\) 2.32349 1.89773i 0.346366 0.282897i
\(46\) 2.69411 0.397225
\(47\) 10.3888 1.51536 0.757679 0.652628i \(-0.226334\pi\)
0.757679 + 0.652628i \(0.226334\pi\)
\(48\) −0.581597 1.63149i −0.0839462 0.235485i
\(49\) 0 0
\(50\) 1.00000i 0.141421i
\(51\) 1.53092 + 4.29451i 0.214372 + 0.601352i
\(52\) 1.98782i 0.275660i
\(53\) 13.1742i 1.80961i 0.425825 + 0.904806i \(0.359984\pi\)
−0.425825 + 0.904806i \(0.640016\pi\)
\(54\) 2.68703 4.44746i 0.365658 0.605222i
\(55\) 0.963479i 0.129915i
\(56\) 0 0
\(57\) −8.43126 + 3.00560i −1.11675 + 0.398101i
\(58\) 9.90498 1.30059
\(59\) 2.10246 0.273717 0.136859 0.990591i \(-0.456299\pi\)
0.136859 + 0.990591i \(0.456299\pi\)
\(60\) −0.581597 1.63149i −0.0750838 0.210624i
\(61\) 8.96260i 1.14754i −0.819015 0.573772i \(-0.805480\pi\)
0.819015 0.573772i \(-0.194520\pi\)
\(62\) 3.42151 0.434533
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.98782i 0.246558i
\(66\) −0.560356 1.57190i −0.0689750 0.193488i
\(67\) −1.79547 −0.219351 −0.109676 0.993967i \(-0.534981\pi\)
−0.109676 + 0.993967i \(0.534981\pi\)
\(68\) 2.63227 0.319210
\(69\) 4.39541 1.56689i 0.529145 0.188631i
\(70\) 0 0
\(71\) 11.1501i 1.32328i −0.749823 0.661639i \(-0.769861\pi\)
0.749823 0.661639i \(-0.230139\pi\)
\(72\) −1.89773 2.32349i −0.223650 0.273826i
\(73\) 11.7735i 1.37798i −0.724770 0.688991i \(-0.758054\pi\)
0.724770 0.688991i \(-0.241946\pi\)
\(74\) 9.14603i 1.06320i
\(75\) −0.581597 1.63149i −0.0671570 0.188388i
\(76\) 5.16784i 0.592792i
\(77\) 0 0
\(78\) −1.15611 3.24309i −0.130903 0.367208i
\(79\) −0.408348 −0.0459428 −0.0229714 0.999736i \(-0.507313\pi\)
−0.0229714 + 0.999736i \(0.507313\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.79722 8.81873i 0.199691 0.979859i
\(82\) 1.12202i 0.123907i
\(83\) −4.53092 −0.497333 −0.248667 0.968589i \(-0.579992\pi\)
−0.248667 + 0.968589i \(0.579992\pi\)
\(84\) 0 0
\(85\) 2.63227 0.285510
\(86\) 1.54917i 0.167051i
\(87\) 16.1598 5.76070i 1.73252 0.617612i
\(88\) −0.963479 −0.102707
\(89\) −11.5214 −1.22127 −0.610633 0.791914i \(-0.709085\pi\)
−0.610633 + 0.791914i \(0.709085\pi\)
\(90\) −1.89773 2.32349i −0.200039 0.244917i
\(91\) 0 0
\(92\) 2.69411i 0.280881i
\(93\) 5.58215 1.98994i 0.578842 0.206347i
\(94\) 10.3888i 1.07152i
\(95\) 5.16784i 0.530210i
\(96\) −1.63149 + 0.581597i −0.166513 + 0.0593589i
\(97\) 14.6992i 1.49248i 0.665679 + 0.746239i \(0.268142\pi\)
−0.665679 + 0.746239i \(0.731858\pi\)
\(98\) 0 0
\(99\) −1.82842 2.23863i −0.183764 0.224991i
\(100\) −1.00000 −0.100000
\(101\) 15.1630 1.50877 0.754386 0.656431i \(-0.227935\pi\)
0.754386 + 0.656431i \(0.227935\pi\)
\(102\) 4.29451 1.53092i 0.425220 0.151584i
\(103\) 9.07046i 0.893739i 0.894599 + 0.446870i \(0.147461\pi\)
−0.894599 + 0.446870i \(0.852539\pi\)
\(104\) −1.98782 −0.194921
\(105\) 0 0
\(106\) 13.1742 1.27959
\(107\) 13.8590i 1.33980i 0.742452 + 0.669899i \(0.233663\pi\)
−0.742452 + 0.669899i \(0.766337\pi\)
\(108\) −4.44746 2.68703i −0.427957 0.258559i
\(109\) −16.7334 −1.60277 −0.801385 0.598150i \(-0.795903\pi\)
−0.801385 + 0.598150i \(0.795903\pi\)
\(110\) −0.963479 −0.0918641
\(111\) −5.31930 14.9216i −0.504886 1.41630i
\(112\) 0 0
\(113\) 13.9355i 1.31095i 0.755219 + 0.655473i \(0.227530\pi\)
−0.755219 + 0.655473i \(0.772470\pi\)
\(114\) 3.00560 + 8.43126i 0.281500 + 0.789660i
\(115\) 2.69411i 0.251227i
\(116\) 9.90498i 0.919654i
\(117\) −3.77234 4.61867i −0.348753 0.426996i
\(118\) 2.10246i 0.193547i
\(119\) 0 0
\(120\) −1.63149 + 0.581597i −0.148934 + 0.0530923i
\(121\) 10.0717 0.915610
\(122\) −8.96260 −0.811436
\(123\) 0.652564 + 1.83056i 0.0588397 + 0.165056i
\(124\) 3.42151i 0.307261i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.1937 1.43696 0.718479 0.695548i \(-0.244839\pi\)
0.718479 + 0.695548i \(0.244839\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −0.900992 2.52745i −0.0793279 0.222530i
\(130\) −1.98782 −0.174343
\(131\) −5.92214 −0.517420 −0.258710 0.965955i \(-0.583297\pi\)
−0.258710 + 0.965955i \(0.583297\pi\)
\(132\) −1.57190 + 0.560356i −0.136816 + 0.0487727i
\(133\) 0 0
\(134\) 1.79547i 0.155105i
\(135\) −4.44746 2.68703i −0.382776 0.231263i
\(136\) 2.63227i 0.225716i
\(137\) 7.62107i 0.651112i 0.945523 + 0.325556i \(0.105551\pi\)
−0.945523 + 0.325556i \(0.894449\pi\)
\(138\) −1.56689 4.39541i −0.133382 0.374162i
\(139\) 7.13772i 0.605413i 0.953084 + 0.302707i \(0.0978902\pi\)
−0.953084 + 0.302707i \(0.902110\pi\)
\(140\) 0 0
\(141\) −6.04207 16.9491i −0.508834 1.42737i
\(142\) −11.1501 −0.935698
\(143\) −1.91522 −0.160159
\(144\) −2.32349 + 1.89773i −0.193624 + 0.158144i
\(145\) 9.90498i 0.822563i
\(146\) −11.7735 −0.974380
\(147\) 0 0
\(148\) −9.14603 −0.751799
\(149\) 11.9687i 0.980516i −0.871577 0.490258i \(-0.836903\pi\)
0.871577 0.490258i \(-0.163097\pi\)
\(150\) −1.63149 + 0.581597i −0.133210 + 0.0474872i
\(151\) 8.99700 0.732165 0.366083 0.930582i \(-0.380699\pi\)
0.366083 + 0.930582i \(0.380699\pi\)
\(152\) 5.16784 0.419167
\(153\) 6.11606 4.99535i 0.494454 0.403850i
\(154\) 0 0
\(155\) 3.42151i 0.274823i
\(156\) −3.24309 + 1.15611i −0.259655 + 0.0925626i
\(157\) 6.58680i 0.525684i 0.964839 + 0.262842i \(0.0846598\pi\)
−0.964839 + 0.262842i \(0.915340\pi\)
\(158\) 0.408348i 0.0324864i
\(159\) 21.4935 7.66205i 1.70454 0.607640i
\(160\) 1.00000i 0.0790569i
\(161\) 0 0
\(162\) −8.81873 1.79722i −0.692865 0.141203i
\(163\) 2.65049 0.207603 0.103801 0.994598i \(-0.466899\pi\)
0.103801 + 0.994598i \(0.466899\pi\)
\(164\) 1.12202 0.0876152
\(165\) −1.57190 + 0.560356i −0.122372 + 0.0436236i
\(166\) 4.53092i 0.351668i
\(167\) 7.68946 0.595029 0.297514 0.954717i \(-0.403842\pi\)
0.297514 + 0.954717i \(0.403842\pi\)
\(168\) 0 0
\(169\) 9.04859 0.696045
\(170\) 2.63227i 0.201886i
\(171\) 9.80719 + 12.0074i 0.749974 + 0.918232i
\(172\) −1.54917 −0.118123
\(173\) −21.2908 −1.61871 −0.809355 0.587320i \(-0.800183\pi\)
−0.809355 + 0.587320i \(0.800183\pi\)
\(174\) −5.76070 16.1598i −0.436717 1.22507i
\(175\) 0 0
\(176\) 0.963479i 0.0726249i
\(177\) −1.22278 3.43014i −0.0919101 0.257825i
\(178\) 11.5214i 0.863565i
\(179\) 1.32636i 0.0991371i 0.998771 + 0.0495686i \(0.0157846\pi\)
−0.998771 + 0.0495686i \(0.984215\pi\)
\(180\) −2.32349 + 1.89773i −0.173183 + 0.141449i
\(181\) 2.17439i 0.161621i 0.996729 + 0.0808107i \(0.0257509\pi\)
−0.996729 + 0.0808107i \(0.974249\pi\)
\(182\) 0 0
\(183\) −14.6224 + 5.21262i −1.08092 + 0.385328i
\(184\) −2.69411 −0.198613
\(185\) −9.14603 −0.672430
\(186\) −1.98994 5.58215i −0.145910 0.409303i
\(187\) 2.53614i 0.185461i
\(188\) −10.3888 −0.757679
\(189\) 0 0
\(190\) 5.16784 0.374915
\(191\) 17.0570i 1.23420i 0.786885 + 0.617099i \(0.211692\pi\)
−0.786885 + 0.617099i \(0.788308\pi\)
\(192\) 0.581597 + 1.63149i 0.0419731 + 0.117742i
\(193\) 2.05067 0.147611 0.0738053 0.997273i \(-0.476486\pi\)
0.0738053 + 0.997273i \(0.476486\pi\)
\(194\) 14.6992 1.05534
\(195\) −3.24309 + 1.15611i −0.232243 + 0.0827905i
\(196\) 0 0
\(197\) 12.9420i 0.922083i −0.887379 0.461041i \(-0.847476\pi\)
0.887379 0.461041i \(-0.152524\pi\)
\(198\) −2.23863 + 1.82842i −0.159093 + 0.129941i
\(199\) 17.1869i 1.21835i 0.793037 + 0.609174i \(0.208499\pi\)
−0.793037 + 0.609174i \(0.791501\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 1.04424 + 2.92928i 0.0736548 + 0.206615i
\(202\) 15.1630i 1.06686i
\(203\) 0 0
\(204\) −1.53092 4.29451i −0.107186 0.300676i
\(205\) 1.12202 0.0783654
\(206\) 9.07046 0.631969
\(207\) −5.11271 6.25975i −0.355358 0.435083i
\(208\) 1.98782i 0.137830i
\(209\) 4.97911 0.344412
\(210\) 0 0
\(211\) 2.19691 0.151242 0.0756208 0.997137i \(-0.475906\pi\)
0.0756208 + 0.997137i \(0.475906\pi\)
\(212\) 13.1742i 0.904806i
\(213\) −18.1913 + 6.48488i −1.24645 + 0.444336i
\(214\) 13.8590 0.947381
\(215\) −1.54917 −0.105653
\(216\) −2.68703 + 4.44746i −0.182829 + 0.302611i
\(217\) 0 0
\(218\) 16.7334i 1.13333i
\(219\) −19.2083 + 6.84742i −1.29797 + 0.462706i
\(220\) 0.963479i 0.0649577i
\(221\) 5.23247i 0.351974i
\(222\) −14.9216 + 5.31930i −1.00147 + 0.357008i
\(223\) 23.8443i 1.59673i 0.602173 + 0.798365i \(0.294302\pi\)
−0.602173 + 0.798365i \(0.705698\pi\)
\(224\) 0 0
\(225\) −2.32349 + 1.89773i −0.154899 + 0.126516i
\(226\) 13.9355 0.926978
\(227\) 4.67171 0.310072 0.155036 0.987909i \(-0.450451\pi\)
0.155036 + 0.987909i \(0.450451\pi\)
\(228\) 8.43126 3.00560i 0.558374 0.199051i
\(229\) 23.1514i 1.52989i 0.644097 + 0.764944i \(0.277233\pi\)
−0.644097 + 0.764944i \(0.722767\pi\)
\(230\) −2.69411 −0.177645
\(231\) 0 0
\(232\) −9.90498 −0.650293
\(233\) 13.2418i 0.867499i −0.901033 0.433750i \(-0.857190\pi\)
0.901033 0.433750i \(-0.142810\pi\)
\(234\) −4.61867 + 3.77234i −0.301932 + 0.246606i
\(235\) −10.3888 −0.677688
\(236\) −2.10246 −0.136859
\(237\) 0.237494 + 0.666214i 0.0154269 + 0.0432753i
\(238\) 0 0
\(239\) 14.7280i 0.952675i −0.879263 0.476337i \(-0.841964\pi\)
0.879263 0.476337i \(-0.158036\pi\)
\(240\) 0.581597 + 1.63149i 0.0375419 + 0.105312i
\(241\) 5.92695i 0.381788i 0.981611 + 0.190894i \(0.0611387\pi\)
−0.981611 + 0.190894i \(0.938861\pi\)
\(242\) 10.0717i 0.647434i
\(243\) −15.4329 + 2.19680i −0.990020 + 0.140925i
\(244\) 8.96260i 0.573772i
\(245\) 0 0
\(246\) 1.83056 0.652564i 0.116712 0.0416059i
\(247\) 10.2727 0.653638
\(248\) −3.42151 −0.217266
\(249\) 2.63517 + 7.39213i 0.166997 + 0.468457i
\(250\) 1.00000i 0.0632456i
\(251\) 19.4694 1.22890 0.614450 0.788956i \(-0.289378\pi\)
0.614450 + 0.788956i \(0.289378\pi\)
\(252\) 0 0
\(253\) −2.59572 −0.163192
\(254\) 16.1937i 1.01608i
\(255\) −1.53092 4.29451i −0.0958700 0.268933i
\(256\) 1.00000 0.0625000
\(257\) −2.83792 −0.177024 −0.0885122 0.996075i \(-0.528211\pi\)
−0.0885122 + 0.996075i \(0.528211\pi\)
\(258\) −2.52745 + 0.900992i −0.157352 + 0.0560933i
\(259\) 0 0
\(260\) 1.98782i 0.123279i
\(261\) −18.7970 23.0141i −1.16350 1.42454i
\(262\) 5.92214i 0.365871i
\(263\) 18.0716i 1.11435i 0.830397 + 0.557173i \(0.188114\pi\)
−0.830397 + 0.557173i \(0.811886\pi\)
\(264\) 0.560356 + 1.57190i 0.0344875 + 0.0967439i
\(265\) 13.1742i 0.809283i
\(266\) 0 0
\(267\) 6.70081 + 18.7970i 0.410083 + 1.15036i
\(268\) 1.79547 0.109676
\(269\) −17.1417 −1.04515 −0.522575 0.852593i \(-0.675029\pi\)
−0.522575 + 0.852593i \(0.675029\pi\)
\(270\) −2.68703 + 4.44746i −0.163527 + 0.270664i
\(271\) 20.3877i 1.23847i 0.785207 + 0.619233i \(0.212556\pi\)
−0.785207 + 0.619233i \(0.787444\pi\)
\(272\) −2.63227 −0.159605
\(273\) 0 0
\(274\) 7.62107 0.460406
\(275\) 0.963479i 0.0580999i
\(276\) −4.39541 + 1.56689i −0.264572 + 0.0943155i
\(277\) 7.62035 0.457862 0.228931 0.973443i \(-0.426477\pi\)
0.228931 + 0.973443i \(0.426477\pi\)
\(278\) 7.13772 0.428092
\(279\) −6.49312 7.94986i −0.388733 0.475946i
\(280\) 0 0
\(281\) 4.58608i 0.273583i −0.990600 0.136791i \(-0.956321\pi\)
0.990600 0.136791i \(-0.0436790\pi\)
\(282\) −16.9491 + 6.04207i −1.00931 + 0.359800i
\(283\) 15.9756i 0.949653i 0.880079 + 0.474826i \(0.157489\pi\)
−0.880079 + 0.474826i \(0.842511\pi\)
\(284\) 11.1501i 0.661639i
\(285\) 8.43126 3.00560i 0.499425 0.178036i
\(286\) 1.91522i 0.113249i
\(287\) 0 0
\(288\) 1.89773 + 2.32349i 0.111825 + 0.136913i
\(289\) −10.0711 −0.592420
\(290\) −9.90498 −0.581640
\(291\) 23.9815 8.54900i 1.40582 0.501151i
\(292\) 11.7735i 0.688991i
\(293\) 1.03780 0.0606290 0.0303145 0.999540i \(-0.490349\pi\)
0.0303145 + 0.999540i \(0.490349\pi\)
\(294\) 0 0
\(295\) −2.10246 −0.122410
\(296\) 9.14603i 0.531602i
\(297\) −2.58889 + 4.28503i −0.150223 + 0.248643i
\(298\) −11.9687 −0.693329
\(299\) −5.35540 −0.309711
\(300\) 0.581597 + 1.63149i 0.0335785 + 0.0941939i
\(301\) 0 0
\(302\) 8.99700i 0.517719i
\(303\) −8.81873 24.7382i −0.506623 1.42117i
\(304\) 5.16784i 0.296396i
\(305\) 8.96260i 0.513197i
\(306\) −4.99535 6.11606i −0.285565 0.349632i
\(307\) 3.19308i 0.182238i −0.995840 0.0911192i \(-0.970956\pi\)
0.995840 0.0911192i \(-0.0290444\pi\)
\(308\) 0 0
\(309\) 14.7983 5.27535i 0.841848 0.300104i
\(310\) −3.42151 −0.194329
\(311\) 30.9813 1.75679 0.878395 0.477935i \(-0.158615\pi\)
0.878395 + 0.477935i \(0.158615\pi\)
\(312\) 1.15611 + 3.24309i 0.0654517 + 0.183604i
\(313\) 9.85129i 0.556828i 0.960461 + 0.278414i \(0.0898087\pi\)
−0.960461 + 0.278414i \(0.910191\pi\)
\(314\) 6.58680 0.371715
\(315\) 0 0
\(316\) 0.408348 0.0229714
\(317\) 18.6337i 1.04657i 0.852156 + 0.523287i \(0.175295\pi\)
−0.852156 + 0.523287i \(0.824705\pi\)
\(318\) −7.66205 21.4935i −0.429667 1.20529i
\(319\) −9.54323 −0.534318
\(320\) 1.00000 0.0559017
\(321\) 22.6107 8.06034i 1.26201 0.449884i
\(322\) 0 0
\(323\) 13.6032i 0.756901i
\(324\) −1.79722 + 8.81873i −0.0998456 + 0.489929i
\(325\) 1.98782i 0.110264i
\(326\) 2.65049i 0.146797i
\(327\) 9.73209 + 27.3003i 0.538186 + 1.50971i
\(328\) 1.12202i 0.0619533i
\(329\) 0 0
\(330\) 0.560356 + 1.57190i 0.0308466 + 0.0865303i
\(331\) −34.6782 −1.90609 −0.953044 0.302832i \(-0.902068\pi\)
−0.953044 + 0.302832i \(0.902068\pi\)
\(332\) 4.53092 0.248667
\(333\) −21.2507 + 17.3567i −1.16453 + 0.951143i
\(334\) 7.68946i 0.420749i
\(335\) 1.79547 0.0980968
\(336\) 0 0
\(337\) 15.1938 0.827657 0.413828 0.910355i \(-0.364191\pi\)
0.413828 + 0.910355i \(0.364191\pi\)
\(338\) 9.04859i 0.492178i
\(339\) 22.7356 8.10486i 1.23483 0.440196i
\(340\) −2.63227 −0.142755
\(341\) −3.29656 −0.178519
\(342\) 12.0074 9.80719i 0.649288 0.530312i
\(343\) 0 0
\(344\) 1.54917i 0.0835257i
\(345\) −4.39541 + 1.56689i −0.236641 + 0.0843584i
\(346\) 21.2908i 1.14460i
\(347\) 15.4938i 0.831752i −0.909421 0.415876i \(-0.863475\pi\)
0.909421 0.415876i \(-0.136525\pi\)
\(348\) −16.1598 + 5.76070i −0.866258 + 0.308806i
\(349\) 1.85927i 0.0995246i 0.998761 + 0.0497623i \(0.0158464\pi\)
−0.998761 + 0.0497623i \(0.984154\pi\)
\(350\) 0 0
\(351\) −5.34132 + 8.84073i −0.285098 + 0.471883i
\(352\) 0.963479 0.0513536
\(353\) −34.9105 −1.85810 −0.929050 0.369955i \(-0.879373\pi\)
−0.929050 + 0.369955i \(0.879373\pi\)
\(354\) −3.43014 + 1.22278i −0.182310 + 0.0649903i
\(355\) 11.1501i 0.591787i
\(356\) 11.5214 0.610633
\(357\) 0 0
\(358\) 1.32636 0.0701005
\(359\) 8.21688i 0.433670i −0.976208 0.216835i \(-0.930427\pi\)
0.976208 0.216835i \(-0.0695734\pi\)
\(360\) 1.89773 + 2.32349i 0.100019 + 0.122459i
\(361\) −7.70660 −0.405611
\(362\) 2.17439 0.114284
\(363\) −5.85767 16.4318i −0.307448 0.862448i
\(364\) 0 0
\(365\) 11.7735i 0.616252i
\(366\) 5.21262 + 14.6224i 0.272468 + 0.764323i
\(367\) 13.3705i 0.697934i 0.937135 + 0.348967i \(0.113467\pi\)
−0.937135 + 0.348967i \(0.886533\pi\)
\(368\) 2.69411i 0.140440i
\(369\) 2.60701 2.12930i 0.135715 0.110847i
\(370\) 9.14603i 0.475480i
\(371\) 0 0
\(372\) −5.58215 + 1.98994i −0.289421 + 0.103174i
\(373\) 10.0857 0.522218 0.261109 0.965309i \(-0.415912\pi\)
0.261109 + 0.965309i \(0.415912\pi\)
\(374\) −2.53614 −0.131141
\(375\) 0.581597 + 1.63149i 0.0300335 + 0.0842496i
\(376\) 10.3888i 0.535760i
\(377\) −19.6893 −1.01405
\(378\) 0 0
\(379\) −22.9625 −1.17951 −0.589753 0.807583i \(-0.700775\pi\)
−0.589753 + 0.807583i \(0.700775\pi\)
\(380\) 5.16784i 0.265105i
\(381\) −9.41820 26.4198i −0.482509 1.35353i
\(382\) 17.0570 0.872710
\(383\) 16.8876 0.862918 0.431459 0.902132i \(-0.357999\pi\)
0.431459 + 0.902132i \(0.357999\pi\)
\(384\) 1.63149 0.581597i 0.0832564 0.0296795i
\(385\) 0 0
\(386\) 2.05067i 0.104376i
\(387\) −3.59948 + 2.93991i −0.182972 + 0.149444i
\(388\) 14.6992i 0.746239i
\(389\) 20.1754i 1.02293i −0.859303 0.511467i \(-0.829102\pi\)
0.859303 0.511467i \(-0.170898\pi\)
\(390\) 1.15611 + 3.24309i 0.0585417 + 0.164220i
\(391\) 7.09164i 0.358640i
\(392\) 0 0
\(393\) 3.44429 + 9.66188i 0.173742 + 0.487377i
\(394\) −12.9420 −0.652011
\(395\) 0.408348 0.0205462
\(396\) 1.82842 + 2.23863i 0.0918818 + 0.112496i
\(397\) 19.0214i 0.954655i −0.878725 0.477327i \(-0.841606\pi\)
0.878725 0.477327i \(-0.158394\pi\)
\(398\) 17.1869 0.861502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 4.78840i 0.239121i 0.992827 + 0.119561i \(0.0381486\pi\)
−0.992827 + 0.119561i \(0.961851\pi\)
\(402\) 2.92928 1.04424i 0.146099 0.0520818i
\(403\) −6.80134 −0.338799
\(404\) −15.1630 −0.754386
\(405\) −1.79722 + 8.81873i −0.0893046 + 0.438206i
\(406\) 0 0
\(407\) 8.81201i 0.436795i
\(408\) −4.29451 + 1.53092i −0.212610 + 0.0757919i
\(409\) 0.339562i 0.0167903i −0.999965 0.00839514i \(-0.997328\pi\)
0.999965 0.00839514i \(-0.00267229\pi\)
\(410\) 1.12202i 0.0554127i
\(411\) 12.4337 4.43239i 0.613308 0.218634i
\(412\) 9.07046i 0.446870i
\(413\) 0 0
\(414\) −6.25975 + 5.11271i −0.307650 + 0.251276i
\(415\) 4.53092 0.222414
\(416\) 1.98782 0.0974607
\(417\) 11.6451 4.15127i 0.570262 0.203289i
\(418\) 4.97911i 0.243536i
\(419\) 15.1963 0.742389 0.371194 0.928555i \(-0.378948\pi\)
0.371194 + 0.928555i \(0.378948\pi\)
\(420\) 0 0
\(421\) −19.5755 −0.954052 −0.477026 0.878889i \(-0.658285\pi\)
−0.477026 + 0.878889i \(0.658285\pi\)
\(422\) 2.19691i 0.106944i
\(423\) −24.1382 + 19.7151i −1.17364 + 0.958581i
\(424\) −13.1742 −0.639794
\(425\) −2.63227 −0.127684
\(426\) 6.48488 + 18.1913i 0.314193 + 0.881370i
\(427\) 0 0
\(428\) 13.8590i 0.669899i
\(429\) 1.11388 + 3.12465i 0.0537788 + 0.150860i
\(430\) 1.54917i 0.0747076i
\(431\) 1.19150i 0.0573926i −0.999588 0.0286963i \(-0.990864\pi\)
0.999588 0.0286963i \(-0.00913558\pi\)
\(432\) 4.44746 + 2.68703i 0.213978 + 0.129280i
\(433\) 18.9398i 0.910188i −0.890443 0.455094i \(-0.849606\pi\)
0.890443 0.455094i \(-0.150394\pi\)
\(434\) 0 0
\(435\) −16.1598 + 5.76070i −0.774804 + 0.276204i
\(436\) 16.7334 0.801385
\(437\) 13.9228 0.666016
\(438\) 6.84742 + 19.2083i 0.327182 + 0.917807i
\(439\) 2.85620i 0.136319i −0.997674 0.0681594i \(-0.978287\pi\)
0.997674 0.0681594i \(-0.0217127\pi\)
\(440\) 0.963479 0.0459320
\(441\) 0 0
\(442\) −5.23247 −0.248883
\(443\) 34.9144i 1.65883i 0.558630 + 0.829417i \(0.311327\pi\)
−0.558630 + 0.829417i \(0.688673\pi\)
\(444\) 5.31930 + 14.9216i 0.252443 + 0.708149i
\(445\) 11.5214 0.546167
\(446\) 23.8443 1.12906
\(447\) −19.5268 + 6.96096i −0.923586 + 0.329242i
\(448\) 0 0
\(449\) 20.6789i 0.975895i −0.872873 0.487948i \(-0.837746\pi\)
0.872873 0.487948i \(-0.162254\pi\)
\(450\) 1.89773 + 2.32349i 0.0894600 + 0.109530i
\(451\) 1.08104i 0.0509044i
\(452\) 13.9355i 0.655473i
\(453\) −5.23262 14.6785i −0.245850 0.689655i
\(454\) 4.67171i 0.219254i
\(455\) 0 0
\(456\) −3.00560 8.43126i −0.140750 0.394830i
\(457\) 4.34281 0.203148 0.101574 0.994828i \(-0.467612\pi\)
0.101574 + 0.994828i \(0.467612\pi\)
\(458\) 23.1514 1.08179
\(459\) −11.7069 7.07299i −0.546432 0.330139i
\(460\) 2.69411i 0.125614i
\(461\) −10.7827 −0.502203 −0.251101 0.967961i \(-0.580793\pi\)
−0.251101 + 0.967961i \(0.580793\pi\)
\(462\) 0 0
\(463\) −18.5503 −0.862105 −0.431053 0.902327i \(-0.641858\pi\)
−0.431053 + 0.902327i \(0.641858\pi\)
\(464\) 9.90498i 0.459827i
\(465\) −5.58215 + 1.98994i −0.258866 + 0.0922813i
\(466\) −13.2418 −0.613415
\(467\) −5.55332 −0.256977 −0.128489 0.991711i \(-0.541013\pi\)
−0.128489 + 0.991711i \(0.541013\pi\)
\(468\) 3.77234 + 4.61867i 0.174377 + 0.213498i
\(469\) 0 0
\(470\) 10.3888i 0.479198i
\(471\) 10.7463 3.83086i 0.495162 0.176517i
\(472\) 2.10246i 0.0967736i
\(473\) 1.49259i 0.0686295i
\(474\) 0.666214 0.237494i 0.0306002 0.0109085i
\(475\) 5.16784i 0.237117i
\(476\) 0 0
\(477\) −25.0011 30.6101i −1.14472 1.40154i
\(478\) −14.7280 −0.673643
\(479\) −1.51336 −0.0691470 −0.0345735 0.999402i \(-0.511007\pi\)
−0.0345735 + 0.999402i \(0.511007\pi\)
\(480\) 1.63149 0.581597i 0.0744668 0.0265461i
\(481\) 18.1806i 0.828965i
\(482\) 5.92695 0.269965
\(483\) 0 0
\(484\) −10.0717 −0.457805
\(485\) 14.6992i 0.667456i
\(486\) 2.19680 + 15.4329i 0.0996490 + 0.700050i
\(487\) −10.6043 −0.480527 −0.240264 0.970708i \(-0.577234\pi\)
−0.240264 + 0.970708i \(0.577234\pi\)
\(488\) 8.96260 0.405718
\(489\) −1.54152 4.32424i −0.0697098 0.195549i
\(490\) 0 0
\(491\) 12.2648i 0.553504i −0.960941 0.276752i \(-0.910742\pi\)
0.960941 0.276752i \(-0.0892580\pi\)
\(492\) −0.652564 1.83056i −0.0294198 0.0825281i
\(493\) 26.0726i 1.17425i
\(494\) 10.2727i 0.462192i
\(495\) 1.82842 + 2.23863i 0.0821816 + 0.100619i
\(496\) 3.42151i 0.153631i
\(497\) 0 0
\(498\) 7.39213 2.63517i 0.331249 0.118085i
\(499\) 27.8286 1.24578 0.622889 0.782311i \(-0.285959\pi\)
0.622889 + 0.782311i \(0.285959\pi\)
\(500\) 1.00000 0.0447214
\(501\) −4.47217 12.5452i −0.199802 0.560480i
\(502\) 19.4694i 0.868964i
\(503\) −31.7645 −1.41631 −0.708154 0.706058i \(-0.750472\pi\)
−0.708154 + 0.706058i \(0.750472\pi\)
\(504\) 0 0
\(505\) −15.1630 −0.674743
\(506\) 2.59572i 0.115394i
\(507\) −5.26263 14.7626i −0.233721 0.655632i
\(508\) −16.1937 −0.718479
\(509\) −39.3135 −1.74254 −0.871270 0.490803i \(-0.836703\pi\)
−0.871270 + 0.490803i \(0.836703\pi\)
\(510\) −4.29451 + 1.53092i −0.190164 + 0.0677903i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 13.8861 22.9838i 0.613088 1.01476i
\(514\) 2.83792i 0.125175i
\(515\) 9.07046i 0.399692i
\(516\) 0.900992 + 2.52745i 0.0396640 + 0.111265i
\(517\) 10.0094i 0.440211i
\(518\) 0 0
\(519\) 12.3827 + 34.7356i 0.543538 + 1.52473i
\(520\) 1.98782 0.0871715
\(521\) −8.79770 −0.385434 −0.192717 0.981254i \(-0.561730\pi\)
−0.192717 + 0.981254i \(0.561730\pi\)
\(522\) −23.0141 + 18.7970i −1.00730 + 0.822722i
\(523\) 7.76366i 0.339481i −0.985489 0.169741i \(-0.945707\pi\)
0.985489 0.169741i \(-0.0542930\pi\)
\(524\) 5.92214 0.258710
\(525\) 0 0
\(526\) 18.0716 0.787961
\(527\) 9.00636i 0.392323i
\(528\) 1.57190 0.560356i 0.0684082 0.0243864i
\(529\) 15.7418 0.684424
\(530\) −13.1742 −0.572249
\(531\) −4.88505 + 3.98991i −0.211993 + 0.173147i
\(532\) 0 0
\(533\) 2.23037i 0.0966081i
\(534\) 18.7970 6.70081i 0.813426 0.289972i
\(535\) 13.8590i 0.599176i
\(536\) 1.79547i 0.0775523i
\(537\) 2.16394 0.771409i 0.0933811 0.0332888i
\(538\) 17.1417i 0.739033i
\(539\) 0 0
\(540\) 4.44746 + 2.68703i 0.191388 + 0.115631i
\(541\) −37.1600 −1.59763 −0.798816 0.601576i \(-0.794540\pi\)
−0.798816 + 0.601576i \(0.794540\pi\)
\(542\) 20.3877 0.875727
\(543\) 3.54749 1.26462i 0.152238 0.0542701i
\(544\) 2.63227i 0.112858i
\(545\) 16.7334 0.716780
\(546\) 0 0
\(547\) 35.9929 1.53895 0.769473 0.638679i \(-0.220519\pi\)
0.769473 + 0.638679i \(0.220519\pi\)
\(548\) 7.62107i 0.325556i
\(549\) 17.0086 + 20.8245i 0.725910 + 0.888769i
\(550\) 0.963479 0.0410829
\(551\) 51.1874 2.18065
\(552\) 1.56689 + 4.39541i 0.0666911 + 0.187081i
\(553\) 0 0
\(554\) 7.62035i 0.323758i
\(555\) 5.31930 + 14.9216i 0.225792 + 0.633387i
\(556\) 7.13772i 0.302707i
\(557\) 32.2770i 1.36762i −0.729660 0.683810i \(-0.760322\pi\)
0.729660 0.683810i \(-0.239678\pi\)
\(558\) −7.94986 + 6.49312i −0.336544 + 0.274876i
\(559\) 3.07947i 0.130248i
\(560\) 0 0
\(561\) −4.13767 + 1.47501i −0.174693 + 0.0622749i
\(562\) −4.58608 −0.193452
\(563\) −0.464662 −0.0195832 −0.00979159 0.999952i \(-0.503117\pi\)
−0.00979159 + 0.999952i \(0.503117\pi\)
\(564\) 6.04207 + 16.9491i 0.254417 + 0.713687i
\(565\) 13.9355i 0.586272i
\(566\) 15.9756 0.671506
\(567\) 0 0
\(568\) 11.1501 0.467849
\(569\) 11.0130i 0.461690i −0.972991 0.230845i \(-0.925851\pi\)
0.972991 0.230845i \(-0.0741490\pi\)
\(570\) −3.00560 8.43126i −0.125891 0.353147i
\(571\) 11.0838 0.463842 0.231921 0.972735i \(-0.425499\pi\)
0.231921 + 0.972735i \(0.425499\pi\)
\(572\) 1.91522 0.0800793
\(573\) 27.8282 9.92027i 1.16254 0.414425i
\(574\) 0 0
\(575\) 2.69411i 0.112352i
\(576\) 2.32349 1.89773i 0.0968121 0.0790722i
\(577\) 10.1245i 0.421489i −0.977541 0.210745i \(-0.932411\pi\)
0.977541 0.210745i \(-0.0675888\pi\)
\(578\) 10.0711i 0.418904i
\(579\) −1.19266 3.34564i −0.0495654 0.139040i
\(580\) 9.90498i 0.411282i
\(581\) 0 0
\(582\) −8.54900 23.9815i −0.354367 0.994066i
\(583\) −12.6930 −0.525692
\(584\) 11.7735 0.487190
\(585\) 3.77234 + 4.61867i 0.155967 + 0.190959i
\(586\) 1.03780i 0.0428712i
\(587\) −36.0697 −1.48876 −0.744378 0.667759i \(-0.767254\pi\)
−0.744378 + 0.667759i \(0.767254\pi\)
\(588\) 0 0
\(589\) 17.6818 0.728568
\(590\) 2.10246i 0.0865570i
\(591\) −21.1148 + 7.52705i −0.868545 + 0.309621i
\(592\) 9.14603 0.375900
\(593\) 31.8476 1.30783 0.653913 0.756570i \(-0.273126\pi\)
0.653913 + 0.756570i \(0.273126\pi\)
\(594\) 4.28503 + 2.58889i 0.175817 + 0.106224i
\(595\) 0 0
\(596\) 11.9687i 0.490258i
\(597\) 28.0402 9.99585i 1.14761 0.409103i
\(598\) 5.35540i 0.218999i
\(599\) 13.5175i 0.552312i −0.961113 0.276156i \(-0.910939\pi\)
0.961113 0.276156i \(-0.0890607\pi\)
\(600\) 1.63149 0.581597i 0.0666051 0.0237436i
\(601\) 15.7057i 0.640650i 0.947308 + 0.320325i \(0.103792\pi\)
−0.947308 + 0.320325i \(0.896208\pi\)
\(602\) 0 0
\(603\) 4.17175 3.40731i 0.169887 0.138757i
\(604\) −8.99700 −0.366083
\(605\) −10.0717 −0.409473
\(606\) −24.7382 + 8.81873i −1.00492 + 0.358236i
\(607\) 1.05341i 0.0427565i −0.999771 0.0213782i \(-0.993195\pi\)
0.999771 0.0213782i \(-0.00680542\pi\)
\(608\) −5.16784 −0.209584
\(609\) 0 0
\(610\) 8.96260 0.362885
\(611\) 20.6510i 0.835448i
\(612\) −6.11606 + 4.99535i −0.247227 + 0.201925i
\(613\) −5.40639 −0.218362 −0.109181 0.994022i \(-0.534823\pi\)
−0.109181 + 0.994022i \(0.534823\pi\)
\(614\) −3.19308 −0.128862
\(615\) −0.652564 1.83056i −0.0263139 0.0738154i
\(616\) 0 0
\(617\) 3.10356i 0.124945i 0.998047 + 0.0624723i \(0.0198985\pi\)
−0.998047 + 0.0624723i \(0.980101\pi\)
\(618\) −5.27535 14.7983i −0.212206 0.595276i
\(619\) 18.3738i 0.738504i −0.929329 0.369252i \(-0.879614\pi\)
0.929329 0.369252i \(-0.120386\pi\)
\(620\) 3.42151i 0.137411i
\(621\) −7.23916 + 11.9820i −0.290497 + 0.480819i
\(622\) 30.9813i 1.24224i
\(623\) 0 0
\(624\) 3.24309 1.15611i 0.129828 0.0462813i
\(625\) 1.00000 0.0400000
\(626\) 9.85129 0.393737
\(627\) −2.89583 8.12334i −0.115648 0.324415i
\(628\) 6.58680i 0.262842i
\(629\) −24.0748 −0.959927
\(630\) 0 0
\(631\) 3.40873 0.135699 0.0678496 0.997696i \(-0.478386\pi\)
0.0678496 + 0.997696i \(0.478386\pi\)
\(632\) 0.408348i 0.0162432i
\(633\) −1.27772 3.58423i −0.0507847 0.142460i
\(634\) 18.6337 0.740040
\(635\) −16.1937 −0.642627
\(636\) −21.4935 + 7.66205i −0.852272 + 0.303820i
\(637\) 0 0
\(638\) 9.54323i 0.377820i
\(639\) 21.1600 + 25.9072i 0.837075 + 1.02487i
\(640\) 1.00000i 0.0395285i
\(641\) 17.6475i 0.697036i −0.937302 0.348518i \(-0.886685\pi\)
0.937302 0.348518i \(-0.113315\pi\)
\(642\) −8.06034 22.6107i −0.318116 0.892374i
\(643\) 7.27025i 0.286711i −0.989671 0.143355i \(-0.954211\pi\)
0.989671 0.143355i \(-0.0457892\pi\)
\(644\) 0 0
\(645\) 0.900992 + 2.52745i 0.0354765 + 0.0995182i
\(646\) 13.6032 0.535210
\(647\) 11.5139 0.452658 0.226329 0.974051i \(-0.427328\pi\)
0.226329 + 0.974051i \(0.427328\pi\)
\(648\) 8.81873 + 1.79722i 0.346432 + 0.0706015i
\(649\) 2.02568i 0.0795148i
\(650\) 1.98782 0.0779686
\(651\) 0 0
\(652\) −2.65049 −0.103801
\(653\) 19.0233i 0.744441i 0.928144 + 0.372221i \(0.121404\pi\)
−0.928144 + 0.372221i \(0.878596\pi\)
\(654\) 27.3003 9.73209i 1.06753 0.380555i
\(655\) 5.92214 0.231397
\(656\) −1.12202 −0.0438076
\(657\) 22.3429 + 27.3556i 0.871681 + 1.06724i
\(658\) 0 0
\(659\) 14.0201i 0.546146i −0.961993 0.273073i \(-0.911960\pi\)
0.961993 0.273073i \(-0.0880401\pi\)
\(660\) 1.57190 0.560356i 0.0611862 0.0218118i
\(661\) 10.9172i 0.424632i −0.977201 0.212316i \(-0.931899\pi\)
0.977201 0.212316i \(-0.0681006\pi\)
\(662\) 34.6782i 1.34781i
\(663\) −8.53671 + 3.04319i −0.331538 + 0.118188i
\(664\) 4.53092i 0.175834i
\(665\) 0 0
\(666\) 17.3567 + 21.2507i 0.672559 + 0.823449i
\(667\) −26.6851 −1.03325
\(668\) −7.68946 −0.297514
\(669\) 38.9016 13.8677i 1.50402 0.536158i
\(670\) 1.79547i 0.0693649i
\(671\) 8.63527 0.333361
\(672\) 0 0
\(673\) 13.4579 0.518765 0.259382 0.965775i \(-0.416481\pi\)
0.259382 + 0.965775i \(0.416481\pi\)
\(674\) 15.1938i 0.585242i
\(675\) 4.44746 + 2.68703i 0.171183 + 0.103424i
\(676\) −9.04859 −0.348023
\(677\) −32.2781 −1.24055 −0.620274 0.784385i \(-0.712979\pi\)
−0.620274 + 0.784385i \(0.712979\pi\)
\(678\) −8.10486 22.7356i −0.311265 0.873157i
\(679\) 0 0
\(680\) 2.63227i 0.100943i
\(681\) −2.71705 7.62183i −0.104118 0.292069i
\(682\) 3.29656i 0.126232i
\(683\) 46.4991i 1.77924i 0.456704 + 0.889619i \(0.349030\pi\)
−0.456704 + 0.889619i \(0.650970\pi\)
\(684\) −9.80719 12.0074i −0.374987 0.459116i
\(685\) 7.62107i 0.291186i
\(686\) 0 0
\(687\) 37.7712 13.4648i 1.44106 0.513713i
\(688\) 1.54917 0.0590616
\(689\) −26.1878 −0.997677
\(690\) 1.56689 + 4.39541i 0.0596504 + 0.167330i
\(691\) 48.4752i 1.84408i −0.387092 0.922041i \(-0.626520\pi\)
0.387092 0.922041i \(-0.373480\pi\)
\(692\) 21.2908 0.809355
\(693\) 0 0
\(694\) −15.4938 −0.588137
\(695\) 7.13772i 0.270749i
\(696\) 5.76070 + 16.1598i 0.218359 + 0.612537i
\(697\) 2.95347 0.111871
\(698\) 1.85927 0.0703745
\(699\) −21.6038 + 7.70139i −0.817131 + 0.291293i
\(700\) 0 0
\(701\) 20.0722i 0.758118i −0.925372 0.379059i \(-0.876248\pi\)
0.925372 0.379059i \(-0.123752\pi\)
\(702\) 8.84073 + 5.34132i 0.333672 + 0.201595i
\(703\) 47.2653i 1.78264i
\(704\) 0.963479i 0.0363125i
\(705\) 6.04207 + 16.9491i 0.227557 + 0.638341i
\(706\) 34.9105i 1.31387i
\(707\) 0 0
\(708\) 1.22278 + 3.43014i 0.0459551 + 0.128912i
\(709\) 22.6496 0.850623 0.425311 0.905047i \(-0.360165\pi\)
0.425311 + 0.905047i \(0.360165\pi\)
\(710\) 11.1501 0.418457
\(711\) 0.948793 0.774936i 0.0355825 0.0290624i
\(712\) 11.5214i 0.431783i
\(713\) −9.21795 −0.345215
\(714\) 0 0
\(715\) 1.91522 0.0716251
\(716\) 1.32636i 0.0495686i
\(717\) −24.0285 + 8.56575i −0.897361 + 0.319894i
\(718\) −8.21688 −0.306651
\(719\) 1.22573 0.0457121 0.0228561 0.999739i \(-0.492724\pi\)
0.0228561 + 0.999739i \(0.492724\pi\)
\(720\) 2.32349 1.89773i 0.0865914 0.0707243i
\(721\) 0 0
\(722\) 7.70660i 0.286810i
\(723\) 9.66973 3.44709i 0.359621 0.128199i
\(724\) 2.17439i 0.0808107i
\(725\) 9.90498i 0.367862i
\(726\) −16.4318 + 5.85767i −0.609843 + 0.217399i
\(727\) 33.9559i 1.25936i −0.776856 0.629678i \(-0.783187\pi\)
0.776856 0.629678i \(-0.216813\pi\)
\(728\) 0 0
\(729\) 12.5598 + 23.9009i 0.465177 + 0.885218i
\(730\) 11.7735 0.435756
\(731\) −4.07784 −0.150824
\(732\) 14.6224 5.21262i 0.540458 0.192664i
\(733\) 20.8063i 0.768500i −0.923229 0.384250i \(-0.874460\pi\)
0.923229 0.384250i \(-0.125540\pi\)
\(734\) 13.3705 0.493514
\(735\) 0 0
\(736\) 2.69411 0.0993063
\(737\) 1.72989i 0.0637214i
\(738\) −2.12930 2.60701i −0.0783805 0.0959652i
\(739\) 9.86421 0.362861 0.181430 0.983404i \(-0.441927\pi\)
0.181430 + 0.983404i \(0.441927\pi\)
\(740\) 9.14603 0.336215
\(741\) −5.97458 16.7598i −0.219482 0.615687i
\(742\) 0 0
\(743\) 18.9248i 0.694283i −0.937813 0.347141i \(-0.887152\pi\)
0.937813 0.347141i \(-0.112848\pi\)
\(744\) 1.98994 + 5.58215i 0.0729548 + 0.204652i
\(745\) 11.9687i 0.438500i
\(746\) 10.0857i 0.369264i
\(747\) 10.5276 8.59848i 0.385183 0.314602i
\(748\) 2.53614i 0.0927304i
\(749\) 0 0
\(750\) 1.63149 0.581597i 0.0595734 0.0212369i
\(751\) 9.78087 0.356909 0.178455 0.983948i \(-0.442890\pi\)
0.178455 + 0.983948i \(0.442890\pi\)
\(752\) 10.3888 0.378839
\(753\) −11.3234 31.7641i −0.412646 1.15755i
\(754\) 19.6893i 0.717041i
\(755\) −8.99700 −0.327434
\(756\) 0 0
\(757\) 25.5979 0.930373 0.465187 0.885213i \(-0.345987\pi\)
0.465187 + 0.885213i \(0.345987\pi\)
\(758\) 22.9625i 0.834037i
\(759\) 1.50966 + 4.23488i 0.0547973 + 0.153716i
\(760\) −5.16784 −0.187457
\(761\) 1.50256 0.0544677 0.0272338 0.999629i \(-0.491330\pi\)
0.0272338 + 0.999629i \(0.491330\pi\)
\(762\) −26.4198 + 9.41820i −0.957088 + 0.341185i
\(763\) 0 0
\(764\) 17.0570i 0.617099i
\(765\) −6.11606 + 4.99535i −0.221127 + 0.180607i
\(766\) 16.8876i 0.610175i
\(767\) 4.17931i 0.150906i
\(768\) −0.581597 1.63149i −0.0209866 0.0588712i
\(769\) 34.5776i 1.24690i 0.781863 + 0.623451i \(0.214270\pi\)
−0.781863 + 0.623451i \(0.785730\pi\)
\(770\) 0 0
\(771\) 1.65052 + 4.63002i 0.0594421 + 0.166746i
\(772\) −2.05067 −0.0738053
\(773\) 31.8854 1.14684 0.573418 0.819263i \(-0.305617\pi\)
0.573418 + 0.819263i \(0.305617\pi\)
\(774\) 2.93991 + 3.59948i 0.105673 + 0.129381i
\(775\) 3.42151i 0.122904i
\(776\) −14.6992 −0.527670
\(777\) 0 0
\(778\) −20.1754 −0.723324
\(779\) 5.79843i 0.207750i
\(780\) 3.24309 1.15611i 0.116121 0.0413953i
\(781\) 10.7429 0.384412
\(782\) −7.09164 −0.253597
\(783\) −26.6149 + 44.0520i −0.951140 + 1.57429i
\(784\) 0 0
\(785\) 6.58680i 0.235093i
\(786\) 9.66188 3.44429i 0.344628 0.122854i
\(787\) 36.8450i 1.31338i 0.754159 + 0.656692i \(0.228045\pi\)
−0.754159 + 0.656692i \(0.771955\pi\)
\(788\) 12.9420i 0.461041i
\(789\) 29.4836 10.5104i 1.04965 0.374180i
\(790\) 0.408348i 0.0145284i
\(791\) 0 0
\(792\) 2.23863 1.82842i 0.0795464 0.0649703i
\(793\) 17.8160 0.632665
\(794\) −19.0214 −0.675043
\(795\) −21.4935 + 7.66205i −0.762295 + 0.271745i
\(796\) 17.1869i 0.609174i
\(797\) −23.2407 −0.823228 −0.411614 0.911358i \(-0.635035\pi\)
−0.411614 + 0.911358i \(0.635035\pi\)
\(798\) 0 0
\(799\) −27.3461 −0.967434
\(800\) 1.00000i 0.0353553i
\(801\) 26.7699 21.8645i 0.945867 0.772545i
\(802\) 4.78840 0.169084
\(803\) 11.3435 0.400303
\(804\) −1.04424 2.92928i −0.0368274 0.103308i
\(805\) 0 0
\(806\) 6.80134i 0.239567i
\(807\) 9.96958 + 27.9665i 0.350946 + 0.984468i
\(808\) 15.1630i 0.533431i
\(809\) 29.5774i 1.03989i 0.854200 + 0.519944i \(0.174047\pi\)
−0.854200 + 0.519944i \(0.825953\pi\)
\(810\) 8.81873 + 1.79722i 0.309859 + 0.0631479i
\(811\) 23.3350i 0.819404i −0.912219 0.409702i \(-0.865633\pi\)
0.912219 0.409702i \(-0.134367\pi\)
\(812\) 0 0
\(813\) 33.2623 11.8574i 1.16656 0.415858i
\(814\) 8.81201 0.308861
\(815\) −2.65049 −0.0928427
\(816\) 1.53092 + 4.29451i 0.0535929 + 0.150338i
\(817\) 8.00587i 0.280090i
\(818\) −0.339562 −0.0118725
\(819\) 0 0
\(820\) −1.12202 −0.0391827
\(821\) 14.6669i 0.511879i −0.966693 0.255939i \(-0.917615\pi\)
0.966693 0.255939i \(-0.0823847\pi\)
\(822\) −4.43239 12.4337i −0.154597 0.433674i
\(823\) 51.9093 1.80944 0.904722 0.426002i \(-0.140078\pi\)
0.904722 + 0.426002i \(0.140078\pi\)
\(824\) −9.07046 −0.315985
\(825\) 1.57190 0.560356i 0.0547266 0.0195091i
\(826\) 0 0
\(827\) 3.36232i 0.116919i −0.998290 0.0584596i \(-0.981381\pi\)
0.998290 0.0584596i \(-0.0186189\pi\)
\(828\) 5.11271 + 6.25975i 0.177679 + 0.217541i
\(829\) 6.86065i 0.238280i 0.992877 + 0.119140i \(0.0380138\pi\)
−0.992877 + 0.119140i \(0.961986\pi\)
\(830\) 4.53092i 0.157271i
\(831\) −4.43197 12.4325i −0.153743 0.431278i
\(832\) 1.98782i 0.0689151i
\(833\) 0 0
\(834\) −4.15127 11.6451i −0.143747 0.403236i
\(835\) −7.68946 −0.266105
\(836\) −4.97911 −0.172206
\(837\) −9.19370 + 15.2170i −0.317781 + 0.525978i
\(838\) 15.1963i 0.524948i
\(839\) −8.29693 −0.286442 −0.143221 0.989691i \(-0.545746\pi\)
−0.143221 + 0.989691i \(0.545746\pi\)
\(840\) 0 0
\(841\) −69.1085 −2.38305
\(842\) 19.5755i 0.674616i
\(843\) −7.48213 + 2.66725i −0.257698 + 0.0918649i
\(844\) −2.19691 −0.0756208
\(845\) −9.04859 −0.311281
\(846\) 19.7151 + 24.1382i 0.677819 + 0.829888i
\(847\) 0 0
\(848\) 13.1742i 0.452403i
\(849\) 26.0640 9.29137i 0.894515 0.318879i
\(850\) 2.63227i 0.0902862i
\(851\) 24.6404i 0.844664i
\(852\) 18.1913 6.48488i 0.623223 0.222168i
\(853\) 50.8963i 1.74266i −0.490700 0.871328i \(-0.663259\pi\)
0.490700 0.871328i \(-0.336741\pi\)
\(854\) 0 0
\(855\) −9.80719 12.0074i −0.335399 0.410646i
\(856\) −13.8590 −0.473690
\(857\) 2.07412 0.0708505 0.0354252 0.999372i \(-0.488721\pi\)
0.0354252 + 0.999372i \(0.488721\pi\)
\(858\) 3.12465 1.11388i 0.106674 0.0380274i
\(859\) 18.3210i 0.625103i 0.949901 + 0.312552i \(0.101184\pi\)
−0.949901 + 0.312552i \(0.898816\pi\)
\(860\) 1.54917 0.0528263
\(861\) 0 0
\(862\) −1.19150 −0.0405827
\(863\) 24.4440i 0.832084i −0.909345 0.416042i \(-0.863417\pi\)
0.909345 0.416042i \(-0.136583\pi\)
\(864\) 2.68703 4.44746i 0.0914145 0.151306i
\(865\) 21.2908 0.723909
\(866\) −18.9398 −0.643600
\(867\) 5.85734 + 16.4309i 0.198926 + 0.558023i
\(868\) 0 0
\(869\) 0.393435i 0.0133464i
\(870\) 5.76070 + 16.1598i 0.195306 + 0.547869i
\(871\) 3.56906i 0.120933i
\(872\) 16.7334i 0.566664i
\(873\) −27.8951 34.1534i −0.944108 1.15592i
\(874\) 13.9228i 0.470944i
\(875\) 0 0
\(876\) 19.2083 6.84742i 0.648987 0.231353i
\(877\) 30.5364 1.03114 0.515571 0.856847i \(-0.327580\pi\)
0.515571 + 0.856847i \(0.327580\pi\)
\(878\) −2.85620 −0.0963920
\(879\) −0.603581 1.69316i −0.0203583 0.0571088i
\(880\) 0.963479i 0.0324789i
\(881\) 12.8329 0.432352 0.216176 0.976354i \(-0.430642\pi\)
0.216176 + 0.976354i \(0.430642\pi\)
\(882\) 0 0
\(883\) 12.8658 0.432970 0.216485 0.976286i \(-0.430541\pi\)
0.216485 + 0.976286i \(0.430541\pi\)
\(884\) 5.23247i 0.175987i
\(885\) 1.22278 + 3.43014i 0.0411034 + 0.115303i
\(886\) 34.9144 1.17297
\(887\) 10.9822 0.368745 0.184373 0.982856i \(-0.440975\pi\)
0.184373 + 0.982856i \(0.440975\pi\)
\(888\) 14.9216 5.31930i 0.500737 0.178504i
\(889\) 0 0
\(890\) 11.5214i 0.386198i
\(891\) 8.49666 + 1.73158i 0.284649 + 0.0580102i
\(892\) 23.8443i 0.798365i
\(893\) 53.6875i 1.79658i
\(894\) 6.96096 + 19.5268i 0.232809 + 0.653074i
\(895\) 1.32636i 0.0443355i
\(896\) 0 0
\(897\) 3.11468 + 8.73726i 0.103996 + 0.291729i
\(898\) −20.6789 −0.690062
\(899\) −33.8900 −1.13030
\(900\) 2.32349 1.89773i 0.0774497 0.0632578i
\(901\) 34.6780i 1.15529i
\(902\) −1.08104 −0.0359948
\(903\) 0 0
\(904\) −13.9355 −0.463489
\(905\) 2.17439i 0.0722793i
\(906\) −14.6785 + 5.23262i −0.487660 + 0.173842i
\(907\) −28.7217 −0.953688 −0.476844 0.878988i \(-0.658219\pi\)
−0.476844 + 0.878988i \(0.658219\pi\)
\(908\) −4.67171 −0.155036
\(909\) −35.2310 + 28.7753i −1.16854 + 0.954415i
\(910\) 0 0
\(911\) 41.5041i 1.37509i 0.726141 + 0.687546i \(0.241312\pi\)
−0.726141 + 0.687546i \(0.758688\pi\)
\(912\) −8.43126 + 3.00560i −0.279187 + 0.0995253i
\(913\) 4.36545i 0.144475i
\(914\) 4.34281i 0.143647i
\(915\) 14.6224 5.21262i 0.483400 0.172324i
\(916\) 23.1514i 0.764944i
\(917\) 0 0
\(918\) −7.07299 + 11.7069i −0.233443 + 0.386386i
\(919\) 21.8342 0.720244 0.360122 0.932905i \(-0.382735\pi\)
0.360122 + 0.932905i \(0.382735\pi\)
\(920\) 2.69411 0.0888223
\(921\) −5.20946 + 1.85708i −0.171657 + 0.0611929i
\(922\) 10.7827i 0.355111i
\(923\) 22.1644 0.729550
\(924\) 0 0
\(925\) 9.14603 0.300720
\(926\) 18.5503i 0.609600i
\(927\) −17.2133 21.0751i −0.565359 0.692198i
\(928\) 9.90498 0.325147
\(929\) 3.41675 0.112100 0.0560500 0.998428i \(-0.482149\pi\)
0.0560500 + 0.998428i \(0.482149\pi\)
\(930\) 1.98994 + 5.58215i 0.0652527 + 0.183046i
\(931\) 0 0
\(932\) 13.2418i 0.433750i
\(933\) −18.0186 50.5456i −0.589904 1.65479i
\(934\) 5.55332i 0.181710i
\(935\) 2.53614i 0.0829406i
\(936\) 4.61867 3.77234i 0.150966 0.123303i
\(937\) 3.57133i 0.116670i 0.998297 + 0.0583351i \(0.0185792\pi\)
−0.998297 + 0.0583351i \(0.981421\pi\)
\(938\) 0 0
\(939\) 16.0722 5.72948i 0.524498 0.186974i
\(940\) 10.3888 0.338844
\(941\) 18.4180 0.600411 0.300205 0.953875i \(-0.402945\pi\)
0.300205 + 0.953875i \(0.402945\pi\)
\(942\) −3.83086 10.7463i −0.124816 0.350132i
\(943\) 3.02285i 0.0984376i
\(944\) 2.10246 0.0684293
\(945\) 0 0
\(946\) 1.49259 0.0485284
\(947\) 20.8836i 0.678625i −0.940674 0.339312i \(-0.889806\pi\)
0.940674 0.339312i \(-0.110194\pi\)
\(948\) −0.237494 0.666214i −0.00771344 0.0216376i
\(949\) 23.4035 0.759710
\(950\) −5.16784 −0.167667
\(951\) 30.4007 10.8373i 0.985809 0.351424i
\(952\) 0 0
\(953\) 52.2153i 1.69142i 0.533644 + 0.845709i \(0.320822\pi\)
−0.533644 + 0.845709i \(0.679178\pi\)
\(954\) −30.6101 + 25.0011i −0.991037 + 0.809439i
\(955\) 17.0570i 0.551951i
\(956\) 14.7280i 0.476337i
\(957\) 5.55031 + 15.5696i 0.179416 + 0.503295i
\(958\) 1.51336i 0.0488943i
\(959\) 0 0
\(960\) −0.581597 1.63149i −0.0187709 0.0526560i
\(961\) 19.2932 0.622363
\(962\) 18.1806 0.586167
\(963\) −26.3006 32.2012i −0.847527 1.03767i
\(964\) 5.92695i 0.190894i
\(965\) −2.05067 −0.0660135
\(966\) 0 0
\(967\) −46.2991 −1.48888 −0.744440 0.667689i \(-0.767283\pi\)
−0.744440 + 0.667689i \(0.767283\pi\)
\(968\) 10.0717i 0.323717i
\(969\) 22.1934 7.91156i 0.712954 0.254156i
\(970\) −14.6992 −0.471963
\(971\) 9.45635 0.303469 0.151734 0.988421i \(-0.451514\pi\)
0.151734 + 0.988421i \(0.451514\pi\)
\(972\) 15.4329 2.19680i 0.495010 0.0704625i
\(973\) 0 0
\(974\) 10.6043i 0.339784i
\(975\) 3.24309 1.15611i 0.103862 0.0370251i
\(976\) 8.96260i 0.286886i
\(977\) 4.82225i 0.154278i 0.997020 + 0.0771388i \(0.0245785\pi\)
−0.997020 + 0.0771388i \(0.975422\pi\)
\(978\) −4.32424 + 1.54152i −0.138274 + 0.0492923i
\(979\) 11.1006i 0.354777i
\(980\) 0 0
\(981\) 38.8799 31.7555i 1.24134 1.01388i
\(982\) −12.2648 −0.391386
\(983\) 44.6626 1.42452 0.712258 0.701918i \(-0.247673\pi\)
0.712258 + 0.701918i \(0.247673\pi\)
\(984\) −1.83056 + 0.652564i −0.0583562 + 0.0208030i
\(985\) 12.9420i 0.412368i
\(986\) −26.0726 −0.830321
\(987\) 0 0
\(988\) −10.2727 −0.326819
\(989\) 4.17364i 0.132714i
\(990\) 2.23863 1.82842i 0.0711485 0.0581112i
\(991\) −33.3133 −1.05823 −0.529116 0.848550i \(-0.677476\pi\)
−0.529116 + 0.848550i \(0.677476\pi\)
\(992\) 3.42151 0.108633
\(993\) 20.1687 + 56.5770i 0.640036 + 1.79542i
\(994\) 0 0
\(995\) 17.1869i 0.544862i
\(996\) −2.63517 7.39213i −0.0834985 0.234229i
\(997\) 17.0203i 0.539037i −0.962995 0.269519i \(-0.913135\pi\)
0.962995 0.269519i \(-0.0868646\pi\)
\(998\) 27.8286i 0.880897i
\(999\) 40.6766 + 24.5756i 1.28695 + 0.777539i
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 1470.2.b.b.881.2 12
3.2 odd 2 1470.2.b.a.881.11 12
7.2 even 3 210.2.r.a.101.3 12
7.3 odd 6 210.2.r.b.131.5 yes 12
7.6 odd 2 1470.2.b.a.881.5 12
21.2 odd 6 210.2.r.b.101.5 yes 12
21.17 even 6 210.2.r.a.131.3 yes 12
21.20 even 2 inner 1470.2.b.b.881.8 12
35.2 odd 12 1050.2.u.f.899.4 12
35.3 even 12 1050.2.u.h.299.5 12
35.9 even 6 1050.2.s.g.101.4 12
35.17 even 12 1050.2.u.e.299.2 12
35.23 odd 12 1050.2.u.g.899.3 12
35.24 odd 6 1050.2.s.f.551.2 12
105.2 even 12 1050.2.u.h.899.5 12
105.17 odd 12 1050.2.u.g.299.3 12
105.23 even 12 1050.2.u.e.899.2 12
105.38 odd 12 1050.2.u.f.299.4 12
105.44 odd 6 1050.2.s.f.101.2 12
105.59 even 6 1050.2.s.g.551.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.r.a.101.3 12 7.2 even 3
210.2.r.a.131.3 yes 12 21.17 even 6
210.2.r.b.101.5 yes 12 21.2 odd 6
210.2.r.b.131.5 yes 12 7.3 odd 6
1050.2.s.f.101.2 12 105.44 odd 6
1050.2.s.f.551.2 12 35.24 odd 6
1050.2.s.g.101.4 12 35.9 even 6
1050.2.s.g.551.4 12 105.59 even 6
1050.2.u.e.299.2 12 35.17 even 12
1050.2.u.e.899.2 12 105.23 even 12
1050.2.u.f.299.4 12 105.38 odd 12
1050.2.u.f.899.4 12 35.2 odd 12
1050.2.u.g.299.3 12 105.17 odd 12
1050.2.u.g.899.3 12 35.23 odd 12
1050.2.u.h.299.5 12 35.3 even 12
1050.2.u.h.899.5 12 105.2 even 12
1470.2.b.a.881.5 12 7.6 odd 2
1470.2.b.a.881.11 12 3.2 odd 2
1470.2.b.b.881.2 12 1.1 even 1 trivial
1470.2.b.b.881.8 12 21.20 even 2 inner