Properties

Label 378.2.l.a.143.3
Level $378$
Weight $2$
Character 378.143
Analytic conductor $3.018$
Analytic rank $0$
Dimension $16$
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] = [378,2,Mod(143,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 143.3
Root \(0.320287 + 1.70218i\) of defining polynomial
Character \(\chi\) \(=\) 378.143
Dual form 378.2.l.a.341.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(0.0338034 - 0.0585493i) q^{5} +(1.19767 + 2.35915i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(0.0338034 - 0.0585493i) q^{5} +(1.19767 + 2.35915i) q^{7} +1.00000i q^{8} +(-0.0585493 - 0.0338034i) q^{10} +(3.40282 - 1.96462i) q^{11} +(3.32589 - 1.92020i) q^{13} +(2.35915 - 1.19767i) q^{14} +1.00000 q^{16} +(-0.775337 + 1.34292i) q^{17} +(5.06375 - 2.92356i) q^{19} +(-0.0338034 + 0.0585493i) q^{20} +(-1.96462 - 3.40282i) q^{22} +(-4.78687 - 2.76370i) q^{23} +(2.49771 + 4.32617i) q^{25} +(-1.92020 - 3.32589i) q^{26} +(-1.19767 - 2.35915i) q^{28} +(-1.20840 - 0.697671i) q^{29} +1.26595i q^{31} -1.00000i q^{32} +(1.34292 + 0.775337i) q^{34} +(0.178612 + 0.00962461i) q^{35} +(-4.35534 - 7.54368i) q^{37} +(-2.92356 - 5.06375i) q^{38} +(0.0585493 + 0.0338034i) q^{40} +(5.17415 + 8.96188i) q^{41} +(0.735847 - 1.27452i) q^{43} +(-3.40282 + 1.96462i) q^{44} +(-2.76370 + 4.78687i) q^{46} +3.54265 q^{47} +(-4.13117 + 5.65097i) q^{49} +(4.32617 - 2.49771i) q^{50} +(-3.32589 + 1.92020i) q^{52} +(6.28910 + 3.63101i) q^{53} -0.265644i q^{55} +(-2.35915 + 1.19767i) q^{56} +(-0.697671 + 1.20840i) q^{58} -9.40086 q^{59} -0.0815124i q^{61} +1.26595 q^{62} -1.00000 q^{64} -0.259638i q^{65} -15.3451 q^{67} +(0.775337 - 1.34292i) q^{68} +(0.00962461 - 0.178612i) q^{70} -4.30975i q^{71} +(6.12768 + 3.53782i) q^{73} +(-7.54368 + 4.35534i) q^{74} +(-5.06375 + 2.92356i) q^{76} +(8.71030 + 5.67480i) q^{77} -6.84639 q^{79} +(0.0338034 - 0.0585493i) q^{80} +(8.96188 - 5.17415i) q^{82} +(-3.93194 + 6.81032i) q^{83} +(0.0524181 + 0.0907908i) q^{85} +(-1.27452 - 0.735847i) q^{86} +(1.96462 + 3.40282i) q^{88} +(-5.84745 - 10.1281i) q^{89} +(8.51336 + 5.54650i) q^{91} +(4.78687 + 2.76370i) q^{92} -3.54265i q^{94} -0.395305i q^{95} +(-0.363295 - 0.209749i) q^{97} +(5.65097 + 4.13117i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 2 q^{7} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 16 q^{16} + 18 q^{17} + 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{29} - 30 q^{35} - 2 q^{37} + 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} + 36 q^{47} - 8 q^{49} + 12 q^{50} - 6 q^{52} + 36 q^{53} - 6 q^{56} + 6 q^{58} - 60 q^{59} - 36 q^{62} - 16 q^{64} - 28 q^{67} - 18 q^{68} - 18 q^{70} - 18 q^{74} + 42 q^{77} + 32 q^{79} - 12 q^{85} - 24 q^{86} + 24 q^{89} - 12 q^{91} - 6 q^{92} + 6 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 0.0338034 0.0585493i 0.0151174 0.0261840i −0.858368 0.513035i \(-0.828521\pi\)
0.873485 + 0.486851i \(0.161854\pi\)
\(6\) 0 0
\(7\) 1.19767 + 2.35915i 0.452677 + 0.891675i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.0585493 0.0338034i −0.0185149 0.0106896i
\(11\) 3.40282 1.96462i 1.02599 0.592356i 0.110157 0.993914i \(-0.464865\pi\)
0.915833 + 0.401559i \(0.131531\pi\)
\(12\) 0 0
\(13\) 3.32589 1.92020i 0.922435 0.532568i 0.0380241 0.999277i \(-0.487894\pi\)
0.884411 + 0.466709i \(0.154560\pi\)
\(14\) 2.35915 1.19767i 0.630509 0.320091i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.775337 + 1.34292i −0.188047 + 0.325707i −0.944599 0.328227i \(-0.893549\pi\)
0.756552 + 0.653933i \(0.226882\pi\)
\(18\) 0 0
\(19\) 5.06375 2.92356i 1.16170 0.670710i 0.209991 0.977703i \(-0.432656\pi\)
0.951712 + 0.306994i \(0.0993230\pi\)
\(20\) −0.0338034 + 0.0585493i −0.00755868 + 0.0130920i
\(21\) 0 0
\(22\) −1.96462 3.40282i −0.418859 0.725484i
\(23\) −4.78687 2.76370i −0.998132 0.576272i −0.0904369 0.995902i \(-0.528826\pi\)
−0.907695 + 0.419630i \(0.862160\pi\)
\(24\) 0 0
\(25\) 2.49771 + 4.32617i 0.499543 + 0.865234i
\(26\) −1.92020 3.32589i −0.376583 0.652260i
\(27\) 0 0
\(28\) −1.19767 2.35915i −0.226338 0.445837i
\(29\) −1.20840 0.697671i −0.224394 0.129554i 0.383589 0.923504i \(-0.374688\pi\)
−0.607983 + 0.793950i \(0.708021\pi\)
\(30\) 0 0
\(31\) 1.26595i 0.227372i 0.993517 + 0.113686i \(0.0362657\pi\)
−0.993517 + 0.113686i \(0.963734\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 1.34292 + 0.775337i 0.230309 + 0.132969i
\(35\) 0.178612 + 0.00962461i 0.0301909 + 0.00162686i
\(36\) 0 0
\(37\) −4.35534 7.54368i −0.716014 1.24017i −0.962567 0.271044i \(-0.912631\pi\)
0.246553 0.969129i \(-0.420702\pi\)
\(38\) −2.92356 5.06375i −0.474263 0.821448i
\(39\) 0 0
\(40\) 0.0585493 + 0.0338034i 0.00925745 + 0.00534479i
\(41\) 5.17415 + 8.96188i 0.808066 + 1.39961i 0.914202 + 0.405260i \(0.132819\pi\)
−0.106136 + 0.994352i \(0.533848\pi\)
\(42\) 0 0
\(43\) 0.735847 1.27452i 0.112216 0.194363i −0.804448 0.594023i \(-0.797539\pi\)
0.916663 + 0.399660i \(0.130872\pi\)
\(44\) −3.40282 + 1.96462i −0.512995 + 0.296178i
\(45\) 0 0
\(46\) −2.76370 + 4.78687i −0.407486 + 0.705786i
\(47\) 3.54265 0.516748 0.258374 0.966045i \(-0.416813\pi\)
0.258374 + 0.966045i \(0.416813\pi\)
\(48\) 0 0
\(49\) −4.13117 + 5.65097i −0.590167 + 0.807281i
\(50\) 4.32617 2.49771i 0.611813 0.353230i
\(51\) 0 0
\(52\) −3.32589 + 1.92020i −0.461218 + 0.266284i
\(53\) 6.28910 + 3.63101i 0.863874 + 0.498758i 0.865308 0.501241i \(-0.167123\pi\)
−0.00143340 + 0.999999i \(0.500456\pi\)
\(54\) 0 0
\(55\) 0.265644i 0.0358194i
\(56\) −2.35915 + 1.19767i −0.315255 + 0.160045i
\(57\) 0 0
\(58\) −0.697671 + 1.20840i −0.0916087 + 0.158671i
\(59\) −9.40086 −1.22389 −0.611944 0.790901i \(-0.709612\pi\)
−0.611944 + 0.790901i \(0.709612\pi\)
\(60\) 0 0
\(61\) 0.0815124i 0.0104366i −0.999986 0.00521830i \(-0.998339\pi\)
0.999986 0.00521830i \(-0.00166104\pi\)
\(62\) 1.26595 0.160776
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.259638i 0.0322041i
\(66\) 0 0
\(67\) −15.3451 −1.87471 −0.937354 0.348379i \(-0.886732\pi\)
−0.937354 + 0.348379i \(0.886732\pi\)
\(68\) 0.775337 1.34292i 0.0940234 0.162853i
\(69\) 0 0
\(70\) 0.00962461 0.178612i 0.00115036 0.0213482i
\(71\) 4.30975i 0.511474i −0.966746 0.255737i \(-0.917682\pi\)
0.966746 0.255737i \(-0.0823181\pi\)
\(72\) 0 0
\(73\) 6.12768 + 3.53782i 0.717191 + 0.414070i 0.813718 0.581260i \(-0.197440\pi\)
−0.0965271 + 0.995330i \(0.530773\pi\)
\(74\) −7.54368 + 4.35534i −0.876935 + 0.506299i
\(75\) 0 0
\(76\) −5.06375 + 2.92356i −0.580852 + 0.335355i
\(77\) 8.71030 + 5.67480i 0.992630 + 0.646703i
\(78\) 0 0
\(79\) −6.84639 −0.770279 −0.385140 0.922858i \(-0.625847\pi\)
−0.385140 + 0.922858i \(0.625847\pi\)
\(80\) 0.0338034 0.0585493i 0.00377934 0.00654601i
\(81\) 0 0
\(82\) 8.96188 5.17415i 0.989675 0.571389i
\(83\) −3.93194 + 6.81032i −0.431587 + 0.747530i −0.997010 0.0772707i \(-0.975379\pi\)
0.565423 + 0.824801i \(0.308713\pi\)
\(84\) 0 0
\(85\) 0.0524181 + 0.0907908i 0.00568554 + 0.00984765i
\(86\) −1.27452 0.735847i −0.137435 0.0793484i
\(87\) 0 0
\(88\) 1.96462 + 3.40282i 0.209429 + 0.362742i
\(89\) −5.84745 10.1281i −0.619828 1.07357i −0.989517 0.144418i \(-0.953869\pi\)
0.369688 0.929156i \(-0.379464\pi\)
\(90\) 0 0
\(91\) 8.51336 + 5.54650i 0.892443 + 0.581431i
\(92\) 4.78687 + 2.76370i 0.499066 + 0.288136i
\(93\) 0 0
\(94\) 3.54265i 0.365396i
\(95\) 0.395305i 0.0405574i
\(96\) 0 0
\(97\) −0.363295 0.209749i −0.0368870 0.0212967i 0.481443 0.876477i \(-0.340113\pi\)
−0.518330 + 0.855181i \(0.673446\pi\)
\(98\) 5.65097 + 4.13117i 0.570834 + 0.417311i
\(99\) 0 0
\(100\) −2.49771 4.32617i −0.249771 0.432617i
\(101\) 8.69621 + 15.0623i 0.865305 + 1.49875i 0.866744 + 0.498753i \(0.166209\pi\)
−0.00143888 + 0.999999i \(0.500458\pi\)
\(102\) 0 0
\(103\) 0.867010 + 0.500568i 0.0854290 + 0.0493225i 0.542106 0.840310i \(-0.317627\pi\)
−0.456677 + 0.889633i \(0.650960\pi\)
\(104\) 1.92020 + 3.32589i 0.188291 + 0.326130i
\(105\) 0 0
\(106\) 3.63101 6.28910i 0.352675 0.610851i
\(107\) −8.02352 + 4.63238i −0.775663 + 0.447829i −0.834891 0.550415i \(-0.814469\pi\)
0.0592279 + 0.998244i \(0.481136\pi\)
\(108\) 0 0
\(109\) 0.821501 1.42288i 0.0786855 0.136287i −0.823998 0.566593i \(-0.808261\pi\)
0.902683 + 0.430306i \(0.141594\pi\)
\(110\) −0.265644 −0.0253281
\(111\) 0 0
\(112\) 1.19767 + 2.35915i 0.113169 + 0.222919i
\(113\) −13.6537 + 7.88296i −1.28443 + 0.741567i −0.977655 0.210215i \(-0.932584\pi\)
−0.306776 + 0.951782i \(0.599250\pi\)
\(114\) 0 0
\(115\) −0.323625 + 0.186845i −0.0301782 + 0.0174234i
\(116\) 1.20840 + 0.697671i 0.112197 + 0.0647771i
\(117\) 0 0
\(118\) 9.40086i 0.865419i
\(119\) −4.09675 0.220756i −0.375549 0.0202367i
\(120\) 0 0
\(121\) 2.21947 3.84424i 0.201770 0.349476i
\(122\) −0.0815124 −0.00737979
\(123\) 0 0
\(124\) 1.26595i 0.113686i
\(125\) 0.675760 0.0604418
\(126\) 0 0
\(127\) −19.0776 −1.69286 −0.846430 0.532501i \(-0.821252\pi\)
−0.846430 + 0.532501i \(0.821252\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −0.259638 −0.0227717
\(131\) 9.33404 16.1670i 0.815519 1.41252i −0.0934359 0.995625i \(-0.529785\pi\)
0.908955 0.416895i \(-0.136882\pi\)
\(132\) 0 0
\(133\) 12.9618 + 8.44468i 1.12393 + 0.732246i
\(134\) 15.3451i 1.32562i
\(135\) 0 0
\(136\) −1.34292 0.775337i −0.115155 0.0664846i
\(137\) −5.44329 + 3.14269i −0.465052 + 0.268498i −0.714166 0.699976i \(-0.753194\pi\)
0.249114 + 0.968474i \(0.419861\pi\)
\(138\) 0 0
\(139\) 5.49596 3.17309i 0.466161 0.269138i −0.248470 0.968640i \(-0.579928\pi\)
0.714631 + 0.699501i \(0.246594\pi\)
\(140\) −0.178612 0.00962461i −0.0150955 0.000813428i
\(141\) 0 0
\(142\) −4.30975 −0.361667
\(143\) 7.54494 13.0682i 0.630939 1.09282i
\(144\) 0 0
\(145\) −0.0816962 + 0.0471673i −0.00678450 + 0.00391703i
\(146\) 3.53782 6.12768i 0.292792 0.507130i
\(147\) 0 0
\(148\) 4.35534 + 7.54368i 0.358007 + 0.620087i
\(149\) −7.21992 4.16842i −0.591479 0.341491i 0.174203 0.984710i \(-0.444265\pi\)
−0.765682 + 0.643219i \(0.777598\pi\)
\(150\) 0 0
\(151\) −7.07721 12.2581i −0.575935 0.997548i −0.995939 0.0900264i \(-0.971305\pi\)
0.420005 0.907522i \(-0.362028\pi\)
\(152\) 2.92356 + 5.06375i 0.237132 + 0.410724i
\(153\) 0 0
\(154\) 5.67480 8.71030i 0.457288 0.701896i
\(155\) 0.0741205 + 0.0427935i 0.00595350 + 0.00343726i
\(156\) 0 0
\(157\) 16.4593i 1.31360i −0.754065 0.656799i \(-0.771910\pi\)
0.754065 0.656799i \(-0.228090\pi\)
\(158\) 6.84639i 0.544670i
\(159\) 0 0
\(160\) −0.0585493 0.0338034i −0.00462873 0.00267240i
\(161\) 0.786889 14.6030i 0.0620155 1.15087i
\(162\) 0 0
\(163\) −4.53345 7.85216i −0.355087 0.615029i 0.632046 0.774931i \(-0.282215\pi\)
−0.987133 + 0.159902i \(0.948882\pi\)
\(164\) −5.17415 8.96188i −0.404033 0.699806i
\(165\) 0 0
\(166\) 6.81032 + 3.93194i 0.528584 + 0.305178i
\(167\) −7.64922 13.2488i −0.591914 1.02523i −0.993974 0.109612i \(-0.965039\pi\)
0.402060 0.915613i \(-0.368294\pi\)
\(168\) 0 0
\(169\) 0.874352 1.51442i 0.0672579 0.116494i
\(170\) 0.0907908 0.0524181i 0.00696334 0.00402029i
\(171\) 0 0
\(172\) −0.735847 + 1.27452i −0.0561078 + 0.0971815i
\(173\) 2.30125 0.174961 0.0874804 0.996166i \(-0.472118\pi\)
0.0874804 + 0.996166i \(0.472118\pi\)
\(174\) 0 0
\(175\) −7.21464 + 11.0738i −0.545375 + 0.837101i
\(176\) 3.40282 1.96462i 0.256497 0.148089i
\(177\) 0 0
\(178\) −10.1281 + 5.84745i −0.759132 + 0.438285i
\(179\) 13.8077 + 7.97186i 1.03203 + 0.595845i 0.917567 0.397582i \(-0.130151\pi\)
0.114467 + 0.993427i \(0.463484\pi\)
\(180\) 0 0
\(181\) 18.4526i 1.37157i 0.727804 + 0.685785i \(0.240541\pi\)
−0.727804 + 0.685785i \(0.759459\pi\)
\(182\) 5.54650 8.51336i 0.411134 0.631052i
\(183\) 0 0
\(184\) 2.76370 4.78687i 0.203743 0.352893i
\(185\) −0.588903 −0.0432970
\(186\) 0 0
\(187\) 6.09297i 0.445562i
\(188\) −3.54265 −0.258374
\(189\) 0 0
\(190\) −0.395305 −0.0286784
\(191\) 23.3437i 1.68909i −0.535484 0.844546i \(-0.679871\pi\)
0.535484 0.844546i \(-0.320129\pi\)
\(192\) 0 0
\(193\) 21.2878 1.53233 0.766164 0.642646i \(-0.222163\pi\)
0.766164 + 0.642646i \(0.222163\pi\)
\(194\) −0.209749 + 0.363295i −0.0150591 + 0.0260831i
\(195\) 0 0
\(196\) 4.13117 5.65097i 0.295084 0.403641i
\(197\) 12.8467i 0.915288i −0.889136 0.457644i \(-0.848693\pi\)
0.889136 0.457644i \(-0.151307\pi\)
\(198\) 0 0
\(199\) −3.24154 1.87150i −0.229787 0.132667i 0.380687 0.924704i \(-0.375688\pi\)
−0.610474 + 0.792037i \(0.709021\pi\)
\(200\) −4.32617 + 2.49771i −0.305906 + 0.176615i
\(201\) 0 0
\(202\) 15.0623 8.69621i 1.05978 0.611863i
\(203\) 0.198643 3.68638i 0.0139420 0.258733i
\(204\) 0 0
\(205\) 0.699616 0.0488633
\(206\) 0.500568 0.867010i 0.0348762 0.0604074i
\(207\) 0 0
\(208\) 3.32589 1.92020i 0.230609 0.133142i
\(209\) 11.4874 19.8967i 0.794597 1.37628i
\(210\) 0 0
\(211\) 4.69581 + 8.13339i 0.323273 + 0.559925i 0.981161 0.193190i \(-0.0618834\pi\)
−0.657888 + 0.753116i \(0.728550\pi\)
\(212\) −6.28910 3.63101i −0.431937 0.249379i
\(213\) 0 0
\(214\) 4.63238 + 8.02352i 0.316663 + 0.548477i
\(215\) −0.0497483 0.0861666i −0.00339281 0.00587651i
\(216\) 0 0
\(217\) −2.98657 + 1.51619i −0.202741 + 0.102926i
\(218\) −1.42288 0.821501i −0.0963697 0.0556391i
\(219\) 0 0
\(220\) 0.265644i 0.0179097i
\(221\) 5.95522i 0.400591i
\(222\) 0 0
\(223\) −17.7695 10.2592i −1.18993 0.687008i −0.231642 0.972801i \(-0.574410\pi\)
−0.958291 + 0.285793i \(0.907743\pi\)
\(224\) 2.35915 1.19767i 0.157627 0.0800227i
\(225\) 0 0
\(226\) 7.88296 + 13.6537i 0.524367 + 0.908230i
\(227\) 9.38828 + 16.2610i 0.623122 + 1.07928i 0.988901 + 0.148577i \(0.0474694\pi\)
−0.365779 + 0.930702i \(0.619197\pi\)
\(228\) 0 0
\(229\) −4.31740 2.49265i −0.285302 0.164719i 0.350519 0.936556i \(-0.386005\pi\)
−0.635821 + 0.771836i \(0.719338\pi\)
\(230\) 0.186845 + 0.323625i 0.0123202 + 0.0213392i
\(231\) 0 0
\(232\) 0.697671 1.20840i 0.0458043 0.0793354i
\(233\) −12.7747 + 7.37548i −0.836899 + 0.483184i −0.856209 0.516630i \(-0.827186\pi\)
0.0193101 + 0.999814i \(0.493853\pi\)
\(234\) 0 0
\(235\) 0.119754 0.207419i 0.00781186 0.0135305i
\(236\) 9.40086 0.611944
\(237\) 0 0
\(238\) −0.220756 + 4.09675i −0.0143095 + 0.265553i
\(239\) 0.155388 0.0897132i 0.0100512 0.00580307i −0.494966 0.868912i \(-0.664819\pi\)
0.505017 + 0.863109i \(0.331486\pi\)
\(240\) 0 0
\(241\) 5.31183 3.06679i 0.342165 0.197549i −0.319064 0.947733i \(-0.603368\pi\)
0.661229 + 0.750184i \(0.270035\pi\)
\(242\) −3.84424 2.21947i −0.247117 0.142673i
\(243\) 0 0
\(244\) 0.0815124i 0.00521830i
\(245\) 0.191212 + 0.432899i 0.0122161 + 0.0276569i
\(246\) 0 0
\(247\) 11.2276 19.4468i 0.714397 1.23737i
\(248\) −1.26595 −0.0803880
\(249\) 0 0
\(250\) 0.675760i 0.0427388i
\(251\) 1.11296 0.0702495 0.0351247 0.999383i \(-0.488817\pi\)
0.0351247 + 0.999383i \(0.488817\pi\)
\(252\) 0 0
\(253\) −21.7185 −1.36543
\(254\) 19.0776i 1.19703i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −2.37366 + 4.11130i −0.148065 + 0.256456i −0.930512 0.366261i \(-0.880638\pi\)
0.782447 + 0.622717i \(0.213971\pi\)
\(258\) 0 0
\(259\) 12.5804 19.3098i 0.781708 1.19985i
\(260\) 0.259638i 0.0161020i
\(261\) 0 0
\(262\) −16.1670 9.33404i −0.998803 0.576659i
\(263\) −3.65146 + 2.10817i −0.225159 + 0.129995i −0.608337 0.793679i \(-0.708163\pi\)
0.383178 + 0.923675i \(0.374830\pi\)
\(264\) 0 0
\(265\) 0.425186 0.245482i 0.0261190 0.0150798i
\(266\) 8.44468 12.9618i 0.517776 0.794739i
\(267\) 0 0
\(268\) 15.3451 0.937354
\(269\) −7.97265 + 13.8090i −0.486101 + 0.841952i −0.999872 0.0159753i \(-0.994915\pi\)
0.513771 + 0.857927i \(0.328248\pi\)
\(270\) 0 0
\(271\) 14.1913 8.19335i 0.862060 0.497710i −0.00264173 0.999997i \(-0.500841\pi\)
0.864702 + 0.502286i \(0.167508\pi\)
\(272\) −0.775337 + 1.34292i −0.0470117 + 0.0814267i
\(273\) 0 0
\(274\) 3.14269 + 5.44329i 0.189857 + 0.328841i
\(275\) 16.9986 + 9.81413i 1.02505 + 0.591814i
\(276\) 0 0
\(277\) 0.928004 + 1.60735i 0.0557583 + 0.0965763i 0.892557 0.450934i \(-0.148909\pi\)
−0.836799 + 0.547510i \(0.815576\pi\)
\(278\) −3.17309 5.49596i −0.190309 0.329626i
\(279\) 0 0
\(280\) −0.00962461 + 0.178612i −0.000575180 + 0.0106741i
\(281\) 0.628441 + 0.362830i 0.0374896 + 0.0216446i 0.518628 0.855000i \(-0.326443\pi\)
−0.481138 + 0.876645i \(0.659776\pi\)
\(282\) 0 0
\(283\) 11.6276i 0.691192i 0.938383 + 0.345596i \(0.112323\pi\)
−0.938383 + 0.345596i \(0.887677\pi\)
\(284\) 4.30975i 0.255737i
\(285\) 0 0
\(286\) −13.0682 7.54494i −0.772740 0.446142i
\(287\) −14.9455 + 22.9400i −0.882205 + 1.35410i
\(288\) 0 0
\(289\) 7.29770 + 12.6400i 0.429277 + 0.743529i
\(290\) 0.0471673 + 0.0816962i 0.00276976 + 0.00479737i
\(291\) 0 0
\(292\) −6.12768 3.53782i −0.358595 0.207035i
\(293\) 6.45034 + 11.1723i 0.376833 + 0.652694i 0.990600 0.136794i \(-0.0436797\pi\)
−0.613766 + 0.789488i \(0.710346\pi\)
\(294\) 0 0
\(295\) −0.317781 + 0.550413i −0.0185019 + 0.0320463i
\(296\) 7.54368 4.35534i 0.438467 0.253149i
\(297\) 0 0
\(298\) −4.16842 + 7.21992i −0.241470 + 0.418239i
\(299\) −21.2275 −1.22762
\(300\) 0 0
\(301\) 3.88809 + 0.209512i 0.224106 + 0.0120761i
\(302\) −12.2581 + 7.07721i −0.705373 + 0.407247i
\(303\) 0 0
\(304\) 5.06375 2.92356i 0.290426 0.167677i
\(305\) −0.00477249 0.00275540i −0.000273272 0.000157774i
\(306\) 0 0
\(307\) 20.5111i 1.17063i 0.810806 + 0.585315i \(0.199029\pi\)
−0.810806 + 0.585315i \(0.800971\pi\)
\(308\) −8.71030 5.67480i −0.496315 0.323352i
\(309\) 0 0
\(310\) 0.0427935 0.0741205i 0.00243051 0.00420976i
\(311\) 15.0288 0.852206 0.426103 0.904675i \(-0.359886\pi\)
0.426103 + 0.904675i \(0.359886\pi\)
\(312\) 0 0
\(313\) 1.11536i 0.0630438i 0.999503 + 0.0315219i \(0.0100354\pi\)
−0.999503 + 0.0315219i \(0.989965\pi\)
\(314\) −16.4593 −0.928855
\(315\) 0 0
\(316\) 6.84639 0.385140
\(317\) 1.23344i 0.0692768i 0.999400 + 0.0346384i \(0.0110280\pi\)
−0.999400 + 0.0346384i \(0.988972\pi\)
\(318\) 0 0
\(319\) −5.48263 −0.306969
\(320\) −0.0338034 + 0.0585493i −0.00188967 + 0.00327300i
\(321\) 0 0
\(322\) −14.6030 0.786889i −0.813791 0.0438516i
\(323\) 9.06696i 0.504499i
\(324\) 0 0
\(325\) 16.6142 + 9.59223i 0.921592 + 0.532081i
\(326\) −7.85216 + 4.53345i −0.434891 + 0.251085i
\(327\) 0 0
\(328\) −8.96188 + 5.17415i −0.494837 + 0.285694i
\(329\) 4.24292 + 8.35763i 0.233920 + 0.460771i
\(330\) 0 0
\(331\) −5.02462 −0.276178 −0.138089 0.990420i \(-0.544096\pi\)
−0.138089 + 0.990420i \(0.544096\pi\)
\(332\) 3.93194 6.81032i 0.215793 0.373765i
\(333\) 0 0
\(334\) −13.2488 + 7.64922i −0.724944 + 0.418546i
\(335\) −0.518719 + 0.898447i −0.0283406 + 0.0490874i
\(336\) 0 0
\(337\) 10.6356 + 18.4213i 0.579356 + 1.00347i 0.995553 + 0.0941995i \(0.0300292\pi\)
−0.416198 + 0.909274i \(0.636638\pi\)
\(338\) −1.51442 0.874352i −0.0823737 0.0475585i
\(339\) 0 0
\(340\) −0.0524181 0.0907908i −0.00284277 0.00492382i
\(341\) 2.48712 + 4.30781i 0.134685 + 0.233281i
\(342\) 0 0
\(343\) −18.2793 2.97805i −0.986987 0.160799i
\(344\) 1.27452 + 0.735847i 0.0687177 + 0.0396742i
\(345\) 0 0
\(346\) 2.30125i 0.123716i
\(347\) 21.5735i 1.15813i −0.815282 0.579063i \(-0.803418\pi\)
0.815282 0.579063i \(-0.196582\pi\)
\(348\) 0 0
\(349\) −24.1105 13.9202i −1.29061 0.745132i −0.311845 0.950133i \(-0.600947\pi\)
−0.978762 + 0.205001i \(0.934280\pi\)
\(350\) 11.0738 + 7.21464i 0.591920 + 0.385639i
\(351\) 0 0
\(352\) −1.96462 3.40282i −0.104715 0.181371i
\(353\) −2.85124 4.93850i −0.151756 0.262850i 0.780117 0.625634i \(-0.215160\pi\)
−0.931873 + 0.362784i \(0.881826\pi\)
\(354\) 0 0
\(355\) −0.252333 0.145685i −0.0133924 0.00773213i
\(356\) 5.84745 + 10.1281i 0.309914 + 0.536787i
\(357\) 0 0
\(358\) 7.97186 13.8077i 0.421326 0.729758i
\(359\) 18.5815 10.7280i 0.980693 0.566203i 0.0782137 0.996937i \(-0.475078\pi\)
0.902479 + 0.430733i \(0.141745\pi\)
\(360\) 0 0
\(361\) 7.59435 13.1538i 0.399703 0.692305i
\(362\) 18.4526 0.969846
\(363\) 0 0
\(364\) −8.51336 5.54650i −0.446221 0.290715i
\(365\) 0.414273 0.239181i 0.0216841 0.0125193i
\(366\) 0 0
\(367\) −7.97484 + 4.60428i −0.416283 + 0.240341i −0.693486 0.720470i \(-0.743926\pi\)
0.277203 + 0.960811i \(0.410593\pi\)
\(368\) −4.78687 2.76370i −0.249533 0.144068i
\(369\) 0 0
\(370\) 0.588903i 0.0306156i
\(371\) −1.03383 + 19.1857i −0.0536739 + 0.996071i
\(372\) 0 0
\(373\) −14.1000 + 24.4219i −0.730071 + 1.26452i 0.226782 + 0.973946i \(0.427180\pi\)
−0.956852 + 0.290574i \(0.906154\pi\)
\(374\) 6.09297 0.315060
\(375\) 0 0
\(376\) 3.54265i 0.182698i
\(377\) −5.35867 −0.275986
\(378\) 0 0
\(379\) −4.72569 −0.242742 −0.121371 0.992607i \(-0.538729\pi\)
−0.121371 + 0.992607i \(0.538729\pi\)
\(380\) 0.395305i 0.0202787i
\(381\) 0 0
\(382\) −23.3437 −1.19437
\(383\) −17.1174 + 29.6483i −0.874660 + 1.51496i −0.0175357 + 0.999846i \(0.505582\pi\)
−0.857124 + 0.515110i \(0.827751\pi\)
\(384\) 0 0
\(385\) 0.626693 0.318154i 0.0319392 0.0162146i
\(386\) 21.2878i 1.08352i
\(387\) 0 0
\(388\) 0.363295 + 0.209749i 0.0184435 + 0.0106484i
\(389\) 16.0167 9.24726i 0.812080 0.468855i −0.0355974 0.999366i \(-0.511333\pi\)
0.847678 + 0.530511i \(0.178000\pi\)
\(390\) 0 0
\(391\) 7.42288 4.28560i 0.375391 0.216732i
\(392\) −5.65097 4.13117i −0.285417 0.208656i
\(393\) 0 0
\(394\) −12.8467 −0.647206
\(395\) −0.231432 + 0.400851i −0.0116446 + 0.0201690i
\(396\) 0 0
\(397\) −1.76126 + 1.01687i −0.0883952 + 0.0510350i −0.543546 0.839379i \(-0.682919\pi\)
0.455151 + 0.890414i \(0.349585\pi\)
\(398\) −1.87150 + 3.24154i −0.0938100 + 0.162484i
\(399\) 0 0
\(400\) 2.49771 + 4.32617i 0.124886 + 0.216308i
\(401\) 27.2137 + 15.7118i 1.35899 + 0.784611i 0.989487 0.144620i \(-0.0461961\pi\)
0.369499 + 0.929231i \(0.379529\pi\)
\(402\) 0 0
\(403\) 2.43088 + 4.21041i 0.121091 + 0.209736i
\(404\) −8.69621 15.0623i −0.432653 0.749376i
\(405\) 0 0
\(406\) −3.68638 0.198643i −0.182952 0.00985847i
\(407\) −29.6409 17.1132i −1.46925 0.848270i
\(408\) 0 0
\(409\) 0.550583i 0.0272246i −0.999907 0.0136123i \(-0.995667\pi\)
0.999907 0.0136123i \(-0.00433306\pi\)
\(410\) 0.699616i 0.0345516i
\(411\) 0 0
\(412\) −0.867010 0.500568i −0.0427145 0.0246612i
\(413\) −11.2591 22.1780i −0.554026 1.09131i
\(414\) 0 0
\(415\) 0.265826 + 0.460425i 0.0130489 + 0.0226014i
\(416\) −1.92020 3.32589i −0.0941457 0.163065i
\(417\) 0 0
\(418\) −19.8967 11.4874i −0.973179 0.561865i
\(419\) −11.5649 20.0310i −0.564984 0.978580i −0.997051 0.0767392i \(-0.975549\pi\)
0.432068 0.901841i \(-0.357784\pi\)
\(420\) 0 0
\(421\) 5.49773 9.52235i 0.267943 0.464091i −0.700387 0.713763i \(-0.746989\pi\)
0.968330 + 0.249672i \(0.0803228\pi\)
\(422\) 8.13339 4.69581i 0.395927 0.228589i
\(423\) 0 0
\(424\) −3.63101 + 6.28910i −0.176338 + 0.305426i
\(425\) −7.74628 −0.375750
\(426\) 0 0
\(427\) 0.192300 0.0976251i 0.00930605 0.00472441i
\(428\) 8.02352 4.63238i 0.387832 0.223915i
\(429\) 0 0
\(430\) −0.0861666 + 0.0497483i −0.00415532 + 0.00239908i
\(431\) 7.19720 + 4.15530i 0.346677 + 0.200154i 0.663221 0.748424i \(-0.269189\pi\)
−0.316544 + 0.948578i \(0.602522\pi\)
\(432\) 0 0
\(433\) 26.1051i 1.25453i −0.778806 0.627265i \(-0.784174\pi\)
0.778806 0.627265i \(-0.215826\pi\)
\(434\) 1.51619 + 2.98657i 0.0727796 + 0.143360i
\(435\) 0 0
\(436\) −0.821501 + 1.42288i −0.0393428 + 0.0681437i
\(437\) −32.3193 −1.54604
\(438\) 0 0
\(439\) 40.8308i 1.94875i 0.224940 + 0.974373i \(0.427782\pi\)
−0.224940 + 0.974373i \(0.572218\pi\)
\(440\) 0.265644 0.0126641
\(441\) 0 0
\(442\) 5.95522 0.283261
\(443\) 18.2565i 0.867391i 0.901059 + 0.433696i \(0.142791\pi\)
−0.901059 + 0.433696i \(0.857209\pi\)
\(444\) 0 0
\(445\) −0.790656 −0.0374807
\(446\) −10.2592 + 17.7695i −0.485788 + 0.841410i
\(447\) 0 0
\(448\) −1.19767 2.35915i −0.0565846 0.111459i
\(449\) 26.0881i 1.23117i 0.788070 + 0.615586i \(0.211081\pi\)
−0.788070 + 0.615586i \(0.788919\pi\)
\(450\) 0 0
\(451\) 35.2134 + 20.3305i 1.65813 + 0.957325i
\(452\) 13.6537 7.88296i 0.642216 0.370783i
\(453\) 0 0
\(454\) 16.2610 9.38828i 0.763166 0.440614i
\(455\) 0.612524 0.310960i 0.0287156 0.0145781i
\(456\) 0 0
\(457\) −6.39973 −0.299367 −0.149683 0.988734i \(-0.547825\pi\)
−0.149683 + 0.988734i \(0.547825\pi\)
\(458\) −2.49265 + 4.31740i −0.116474 + 0.201739i
\(459\) 0 0
\(460\) 0.323625 0.186845i 0.0150891 0.00871170i
\(461\) −1.04099 + 1.80304i −0.0484836 + 0.0839761i −0.889249 0.457424i \(-0.848772\pi\)
0.840765 + 0.541400i \(0.182106\pi\)
\(462\) 0 0
\(463\) −0.959084 1.66118i −0.0445724 0.0772017i 0.842879 0.538104i \(-0.180859\pi\)
−0.887451 + 0.460902i \(0.847526\pi\)
\(464\) −1.20840 0.697671i −0.0560986 0.0323885i
\(465\) 0 0
\(466\) 7.37548 + 12.7747i 0.341663 + 0.591777i
\(467\) 17.1178 + 29.6488i 0.792116 + 1.37199i 0.924654 + 0.380807i \(0.124354\pi\)
−0.132539 + 0.991178i \(0.542313\pi\)
\(468\) 0 0
\(469\) −18.3784 36.2015i −0.848637 1.67163i
\(470\) −0.207419 0.119754i −0.00956754 0.00552382i
\(471\) 0 0
\(472\) 9.40086i 0.432710i
\(473\) 5.78264i 0.265886i
\(474\) 0 0
\(475\) 25.2956 + 14.6044i 1.16064 + 0.670096i
\(476\) 4.09675 + 0.220756i 0.187774 + 0.0101183i
\(477\) 0 0
\(478\) −0.0897132 0.155388i −0.00410339 0.00710728i
\(479\) −5.29123 9.16468i −0.241763 0.418745i 0.719454 0.694540i \(-0.244392\pi\)
−0.961216 + 0.275795i \(0.911059\pi\)
\(480\) 0 0
\(481\) −28.9708 16.7263i −1.32095 0.762653i
\(482\) −3.06679 5.31183i −0.139688 0.241947i
\(483\) 0 0
\(484\) −2.21947 + 3.84424i −0.100885 + 0.174738i
\(485\) −0.0245613 + 0.0141804i −0.00111527 + 0.000643901i
\(486\) 0 0
\(487\) 5.95804 10.3196i 0.269985 0.467627i −0.698873 0.715246i \(-0.746315\pi\)
0.968858 + 0.247619i \(0.0796481\pi\)
\(488\) 0.0815124 0.00368990
\(489\) 0 0
\(490\) 0.432899 0.191212i 0.0195564 0.00863809i
\(491\) 14.9826 8.65023i 0.676157 0.390379i −0.122248 0.992500i \(-0.539010\pi\)
0.798406 + 0.602120i \(0.205677\pi\)
\(492\) 0 0
\(493\) 1.87384 1.08186i 0.0843933 0.0487245i
\(494\) −19.4468 11.2276i −0.874954 0.505155i
\(495\) 0 0
\(496\) 1.26595i 0.0568429i
\(497\) 10.1674 5.16167i 0.456068 0.231532i
\(498\) 0 0
\(499\) 6.41484 11.1108i 0.287168 0.497389i −0.685965 0.727635i \(-0.740620\pi\)
0.973133 + 0.230246i \(0.0739530\pi\)
\(500\) −0.675760 −0.0302209
\(501\) 0 0
\(502\) 1.11296i 0.0496739i
\(503\) 10.9868 0.489878 0.244939 0.969539i \(-0.421232\pi\)
0.244939 + 0.969539i \(0.421232\pi\)
\(504\) 0 0
\(505\) 1.17585 0.0523245
\(506\) 21.7185i 0.965505i
\(507\) 0 0
\(508\) 19.0776 0.846430
\(509\) 14.4838 25.0868i 0.641985 1.11195i −0.343004 0.939334i \(-0.611444\pi\)
0.984989 0.172617i \(-0.0552223\pi\)
\(510\) 0 0
\(511\) −1.00730 + 18.6933i −0.0445602 + 0.826941i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 4.11130 + 2.37366i 0.181342 + 0.104698i
\(515\) 0.0586158 0.0338419i 0.00258292 0.00149125i
\(516\) 0 0
\(517\) 12.0550 6.95996i 0.530178 0.306099i
\(518\) −19.3098 12.5804i −0.848422 0.552751i
\(519\) 0 0
\(520\) 0.259638 0.0113859
\(521\) 5.72133 9.90963i 0.250656 0.434149i −0.713051 0.701113i \(-0.752687\pi\)
0.963707 + 0.266964i \(0.0860204\pi\)
\(522\) 0 0
\(523\) 14.1536 8.17161i 0.618896 0.357320i −0.157543 0.987512i \(-0.550357\pi\)
0.776439 + 0.630192i \(0.217024\pi\)
\(524\) −9.33404 + 16.1670i −0.407759 + 0.706260i
\(525\) 0 0
\(526\) 2.10817 + 3.65146i 0.0919206 + 0.159211i
\(527\) −1.70008 0.981539i −0.0740565 0.0427565i
\(528\) 0 0
\(529\) 3.77610 + 6.54039i 0.164178 + 0.284365i
\(530\) −0.245482 0.425186i −0.0106630 0.0184689i
\(531\) 0 0
\(532\) −12.9618 8.44468i −0.561965 0.366123i
\(533\) 34.4173 + 19.8708i 1.49078 + 0.860700i
\(534\) 0 0
\(535\) 0.626362i 0.0270800i
\(536\) 15.3451i 0.662809i
\(537\) 0 0
\(538\) 13.8090 + 7.97265i 0.595350 + 0.343725i
\(539\) −2.95563 + 27.3454i −0.127308 + 1.17785i
\(540\) 0 0
\(541\) 15.9752 + 27.6699i 0.686830 + 1.18962i 0.972858 + 0.231403i \(0.0743314\pi\)
−0.286029 + 0.958221i \(0.592335\pi\)
\(542\) −8.19335 14.1913i −0.351934 0.609568i
\(543\) 0 0
\(544\) 1.34292 + 0.775337i 0.0575774 + 0.0332423i
\(545\) −0.0555391 0.0961966i −0.00237903 0.00412061i
\(546\) 0 0
\(547\) 15.4351 26.7344i 0.659958 1.14308i −0.320668 0.947192i \(-0.603908\pi\)
0.980626 0.195889i \(-0.0627591\pi\)
\(548\) 5.44329 3.14269i 0.232526 0.134249i
\(549\) 0 0
\(550\) 9.81413 16.9986i 0.418476 0.724821i
\(551\) −8.15871 −0.347573
\(552\) 0 0
\(553\) −8.19972 16.1517i −0.348688 0.686839i
\(554\) 1.60735 0.928004i 0.0682897 0.0394271i
\(555\) 0 0
\(556\) −5.49596 + 3.17309i −0.233081 + 0.134569i
\(557\) −12.2398 7.06667i −0.518618 0.299424i 0.217751 0.976004i \(-0.430128\pi\)
−0.736369 + 0.676580i \(0.763461\pi\)
\(558\) 0 0
\(559\) 5.65190i 0.239050i
\(560\) 0.178612 + 0.00962461i 0.00754773 + 0.000406714i
\(561\) 0 0
\(562\) 0.362830 0.628441i 0.0153051 0.0265092i
\(563\) 5.11436 0.215544 0.107772 0.994176i \(-0.465628\pi\)
0.107772 + 0.994176i \(0.465628\pi\)
\(564\) 0 0
\(565\) 1.06588i 0.0448421i
\(566\) 11.6276 0.488746
\(567\) 0 0
\(568\) 4.30975 0.180833
\(569\) 37.2203i 1.56035i −0.625559 0.780177i \(-0.715129\pi\)
0.625559 0.780177i \(-0.284871\pi\)
\(570\) 0 0
\(571\) 5.27738 0.220851 0.110426 0.993884i \(-0.464779\pi\)
0.110426 + 0.993884i \(0.464779\pi\)
\(572\) −7.54494 + 13.0682i −0.315470 + 0.546410i
\(573\) 0 0
\(574\) 22.9400 + 14.9455i 0.957496 + 0.623813i
\(575\) 27.6118i 1.15149i
\(576\) 0 0
\(577\) −9.72172 5.61284i −0.404721 0.233666i 0.283798 0.958884i \(-0.408405\pi\)
−0.688519 + 0.725218i \(0.741739\pi\)
\(578\) 12.6400 7.29770i 0.525754 0.303544i
\(579\) 0 0
\(580\) 0.0816962 0.0471673i 0.00339225 0.00195852i
\(581\) −20.7757 1.11951i −0.861923 0.0464452i
\(582\) 0 0
\(583\) 28.5343 1.18177
\(584\) −3.53782 + 6.12768i −0.146396 + 0.253565i
\(585\) 0 0
\(586\) 11.1723 6.45034i 0.461524 0.266461i
\(587\) −12.4037 + 21.4838i −0.511955 + 0.886732i 0.487949 + 0.872872i \(0.337745\pi\)
−0.999904 + 0.0138602i \(0.995588\pi\)
\(588\) 0 0
\(589\) 3.70108 + 6.41046i 0.152500 + 0.264138i
\(590\) 0.550413 + 0.317781i 0.0226602 + 0.0130828i
\(591\) 0 0
\(592\) −4.35534 7.54368i −0.179004 0.310043i
\(593\) 6.47382 + 11.2130i 0.265848 + 0.460462i 0.967785 0.251777i \(-0.0810148\pi\)
−0.701938 + 0.712238i \(0.747681\pi\)
\(594\) 0 0
\(595\) −0.151410 + 0.232400i −0.00620718 + 0.00952746i
\(596\) 7.21992 + 4.16842i 0.295739 + 0.170745i
\(597\) 0 0
\(598\) 21.2275i 0.868056i
\(599\) 24.1574i 0.987043i −0.869734 0.493522i \(-0.835709\pi\)
0.869734 0.493522i \(-0.164291\pi\)
\(600\) 0 0
\(601\) −15.3377 8.85525i −0.625640 0.361213i 0.153422 0.988161i \(-0.450971\pi\)
−0.779061 + 0.626948i \(0.784304\pi\)
\(602\) 0.209512 3.88809i 0.00853908 0.158467i
\(603\) 0 0
\(604\) 7.07721 + 12.2581i 0.287967 + 0.498774i
\(605\) −0.150052 0.259897i −0.00610046 0.0105663i
\(606\) 0 0
\(607\) −5.27200 3.04379i −0.213984 0.123544i 0.389178 0.921163i \(-0.372759\pi\)
−0.603162 + 0.797619i \(0.706093\pi\)
\(608\) −2.92356 5.06375i −0.118566 0.205362i
\(609\) 0 0
\(610\) −0.00275540 + 0.00477249i −0.000111563 + 0.000193233i
\(611\) 11.7824 6.80260i 0.476667 0.275204i
\(612\) 0 0
\(613\) 16.5026 28.5834i 0.666535 1.15447i −0.312332 0.949973i \(-0.601110\pi\)
0.978867 0.204499i \(-0.0655566\pi\)
\(614\) 20.5111 0.827760
\(615\) 0 0
\(616\) −5.67480 + 8.71030i −0.228644 + 0.350948i
\(617\) 8.36942 4.83209i 0.336940 0.194533i −0.321978 0.946747i \(-0.604348\pi\)
0.658918 + 0.752215i \(0.271014\pi\)
\(618\) 0 0
\(619\) 15.6756 9.05034i 0.630057 0.363764i −0.150717 0.988577i \(-0.548158\pi\)
0.780774 + 0.624813i \(0.214825\pi\)
\(620\) −0.0741205 0.0427935i −0.00297675 0.00171863i
\(621\) 0 0
\(622\) 15.0288i 0.602601i
\(623\) 16.8903 25.9251i 0.676697 1.03867i
\(624\) 0 0
\(625\) −12.4657 + 21.5913i −0.498629 + 0.863651i
\(626\) 1.11536 0.0445787
\(627\) 0 0
\(628\) 16.4593i 0.656799i
\(629\) 13.5074 0.538577
\(630\) 0 0
\(631\) −5.07079 −0.201865 −0.100932 0.994893i \(-0.532183\pi\)
−0.100932 + 0.994893i \(0.532183\pi\)
\(632\) 6.84639i 0.272335i
\(633\) 0 0
\(634\) 1.23344 0.0489861
\(635\) −0.644887 + 1.11698i −0.0255916 + 0.0443259i
\(636\) 0 0
\(637\) −2.88881 + 26.7272i −0.114459 + 1.05897i
\(638\) 5.48263i 0.217060i
\(639\) 0 0
\(640\) 0.0585493 + 0.0338034i 0.00231436 + 0.00133620i
\(641\) 7.62707 4.40349i 0.301251 0.173927i −0.341754 0.939790i \(-0.611021\pi\)
0.643005 + 0.765862i \(0.277688\pi\)
\(642\) 0 0
\(643\) −2.52364 + 1.45702i −0.0995227 + 0.0574594i −0.548935 0.835865i \(-0.684967\pi\)
0.449413 + 0.893324i \(0.351633\pi\)
\(644\) −0.786889 + 14.6030i −0.0310078 + 0.575437i
\(645\) 0 0
\(646\) 9.06696 0.356735
\(647\) 5.15173 8.92306i 0.202535 0.350802i −0.746809 0.665038i \(-0.768415\pi\)
0.949345 + 0.314237i \(0.101749\pi\)
\(648\) 0 0
\(649\) −31.9895 + 18.4691i −1.25570 + 0.724976i
\(650\) 9.59223 16.6142i 0.376238 0.651664i
\(651\) 0 0
\(652\) 4.53345 + 7.85216i 0.177544 + 0.307515i
\(653\) −15.3666 8.87194i −0.601343 0.347186i 0.168227 0.985748i \(-0.446196\pi\)
−0.769570 + 0.638563i \(0.779529\pi\)
\(654\) 0 0
\(655\) −0.631045 1.09300i −0.0246570 0.0427071i
\(656\) 5.17415 + 8.96188i 0.202016 + 0.349903i
\(657\) 0 0
\(658\) 8.35763 4.24292i 0.325814 0.165406i
\(659\) 4.08467 + 2.35828i 0.159116 + 0.0918657i 0.577444 0.816430i \(-0.304050\pi\)
−0.418328 + 0.908296i \(0.637384\pi\)
\(660\) 0 0
\(661\) 9.42879i 0.366737i 0.983044 + 0.183369i \(0.0587002\pi\)
−0.983044 + 0.183369i \(0.941300\pi\)
\(662\) 5.02462i 0.195288i
\(663\) 0 0
\(664\) −6.81032 3.93194i −0.264292 0.152589i
\(665\) 0.932583 0.473445i 0.0361640 0.0183594i
\(666\) 0 0
\(667\) 3.85631 + 6.67932i 0.149317 + 0.258624i
\(668\) 7.64922 + 13.2488i 0.295957 + 0.512613i
\(669\) 0 0
\(670\) 0.898447 + 0.518719i 0.0347100 + 0.0200398i
\(671\) −0.160141 0.277372i −0.00618218 0.0107078i
\(672\) 0 0
\(673\) −6.42728 + 11.1324i −0.247753 + 0.429122i −0.962902 0.269851i \(-0.913026\pi\)
0.715149 + 0.698972i \(0.246359\pi\)
\(674\) 18.4213 10.6356i 0.709563 0.409666i
\(675\) 0 0
\(676\) −0.874352 + 1.51442i −0.0336289 + 0.0582470i
\(677\) −49.1893 −1.89050 −0.945248 0.326352i \(-0.894181\pi\)
−0.945248 + 0.326352i \(0.894181\pi\)
\(678\) 0 0
\(679\) 0.0597202 1.10828i 0.00229185 0.0425318i
\(680\) −0.0907908 + 0.0524181i −0.00348167 + 0.00201014i
\(681\) 0 0
\(682\) 4.30781 2.48712i 0.164955 0.0952366i
\(683\) −36.2732 20.9424i −1.38796 0.801337i −0.394872 0.918736i \(-0.629211\pi\)
−0.993085 + 0.117399i \(0.962544\pi\)
\(684\) 0 0
\(685\) 0.424934i 0.0162359i
\(686\) −2.97805 + 18.2793i −0.113702 + 0.697905i
\(687\) 0 0
\(688\) 0.735847 1.27452i 0.0280539 0.0485908i
\(689\) 27.8891 1.06249
\(690\) 0 0
\(691\) 6.42914i 0.244576i 0.992495 + 0.122288i \(0.0390231\pi\)
−0.992495 + 0.122288i \(0.960977\pi\)
\(692\) −2.30125 −0.0874804
\(693\) 0 0
\(694\) −21.5735 −0.818919
\(695\) 0.429046i 0.0162746i
\(696\) 0 0
\(697\) −16.0468 −0.607817
\(698\) −13.9202 + 24.1105i −0.526888 + 0.912597i
\(699\) 0 0
\(700\) 7.21464 11.0738i 0.272688 0.418551i
\(701\) 33.7907i 1.27626i −0.769930 0.638129i \(-0.779709\pi\)
0.769930 0.638129i \(-0.220291\pi\)
\(702\) 0 0
\(703\) −44.1087 25.4662i −1.66359 0.960475i
\(704\) −3.40282 + 1.96462i −0.128249 + 0.0740444i
\(705\) 0 0
\(706\) −4.93850 + 2.85124i −0.185863 + 0.107308i
\(707\) −25.1190 + 38.5553i −0.944696 + 1.45002i
\(708\) 0 0
\(709\) −29.6833 −1.11478 −0.557390 0.830251i \(-0.688197\pi\)
−0.557390 + 0.830251i \(0.688197\pi\)
\(710\) −0.145685 + 0.252333i −0.00546744 + 0.00946989i
\(711\) 0 0
\(712\) 10.1281 5.84745i 0.379566 0.219142i
\(713\) 3.49871 6.05995i 0.131028 0.226947i
\(714\) 0 0
\(715\) −0.510090 0.883501i −0.0190763 0.0330411i
\(716\) −13.8077 7.97186i −0.516017 0.297923i
\(717\) 0 0
\(718\) −10.7280 18.5815i −0.400366 0.693455i
\(719\) 18.1588 + 31.4519i 0.677207 + 1.17296i 0.975818 + 0.218583i \(0.0701434\pi\)
−0.298611 + 0.954375i \(0.596523\pi\)
\(720\) 0 0
\(721\) −0.142523 + 2.64492i −0.00530784 + 0.0985020i
\(722\) −13.1538 7.59435i −0.489534 0.282632i
\(723\) 0 0
\(724\) 18.4526i 0.685785i
\(725\) 6.97033i 0.258872i
\(726\) 0 0
\(727\) 14.9225 + 8.61552i 0.553446 + 0.319532i 0.750511 0.660858i \(-0.229808\pi\)
−0.197065 + 0.980390i \(0.563141\pi\)
\(728\) −5.54650 + 8.51336i −0.205567 + 0.315526i
\(729\) 0 0
\(730\) −0.239181 0.414273i −0.00885248 0.0153329i
\(731\) 1.14106 + 1.97637i 0.0422036 + 0.0730987i
\(732\) 0 0
\(733\) −37.2907 21.5298i −1.37736 0.795222i −0.385523 0.922698i \(-0.625979\pi\)
−0.991842 + 0.127477i \(0.959312\pi\)
\(734\) 4.60428 + 7.97484i 0.169947 + 0.294357i
\(735\) 0 0
\(736\) −2.76370 + 4.78687i −0.101871 + 0.176446i
\(737\) −52.2168 + 30.1474i −1.92343 + 1.11049i
\(738\) 0 0
\(739\) −1.87511 + 3.24778i −0.0689770 + 0.119472i −0.898451 0.439073i \(-0.855307\pi\)
0.829474 + 0.558545i \(0.188640\pi\)
\(740\) 0.588903 0.0216485
\(741\) 0 0
\(742\) 19.1857 + 1.03383i 0.704329 + 0.0379532i
\(743\) 23.9862 13.8484i 0.879967 0.508049i 0.00931965 0.999957i \(-0.497033\pi\)
0.870648 + 0.491907i \(0.163700\pi\)
\(744\) 0 0
\(745\) −0.488116 + 0.281814i −0.0178832 + 0.0103249i
\(746\) 24.4219 + 14.1000i 0.894151 + 0.516238i
\(747\) 0 0
\(748\) 6.09297i 0.222781i
\(749\) −20.5380 13.3806i −0.750443 0.488917i
\(750\) 0 0
\(751\) 2.08856 3.61750i 0.0762127 0.132004i −0.825400 0.564548i \(-0.809051\pi\)
0.901613 + 0.432544i \(0.142384\pi\)
\(752\) 3.54265 0.129187
\(753\) 0 0
\(754\) 5.35867i 0.195151i
\(755\) −0.956936 −0.0348264
\(756\) 0 0
\(757\) 35.9359 1.30611 0.653057 0.757309i \(-0.273486\pi\)
0.653057 + 0.757309i \(0.273486\pi\)
\(758\) 4.72569i 0.171645i
\(759\) 0 0
\(760\) 0.395305 0.0143392
\(761\) 14.5715 25.2385i 0.528216 0.914896i −0.471243 0.882003i \(-0.656195\pi\)
0.999459 0.0328930i \(-0.0104720\pi\)
\(762\) 0 0
\(763\) 4.34068 + 0.233900i 0.157143 + 0.00846775i
\(764\) 23.3437i 0.844546i
\(765\) 0 0
\(766\) 29.6483 + 17.1174i 1.07124 + 0.618478i
\(767\) −31.2662 + 18.0515i −1.12896 + 0.651804i
\(768\) 0 0
\(769\) 0.795911 0.459519i 0.0287013 0.0165707i −0.485581 0.874192i \(-0.661392\pi\)
0.514282 + 0.857621i \(0.328058\pi\)
\(770\) −0.318154 0.626693i −0.0114655 0.0225845i
\(771\) 0 0
\(772\) −21.2878 −0.766164
\(773\) 4.69708 8.13558i 0.168942 0.292616i −0.769106 0.639121i \(-0.779298\pi\)
0.938048 + 0.346505i \(0.112632\pi\)
\(774\) 0 0
\(775\) −5.47672 + 3.16199i −0.196730 + 0.113582i
\(776\) 0.209749 0.363295i 0.00752954 0.0130415i
\(777\) 0 0
\(778\) −9.24726 16.0167i −0.331530 0.574228i
\(779\) 52.4011 + 30.2538i 1.87747 + 1.08396i
\(780\) 0 0
\(781\) −8.46703 14.6653i −0.302974 0.524767i
\(782\) −4.28560 7.42288i −0.153253 0.265442i
\(783\) 0 0
\(784\) −4.13117 + 5.65097i −0.147542 + 0.201820i
\(785\) −0.963683 0.556383i −0.0343953 0.0198581i
\(786\) 0 0
\(787\) 30.5960i 1.09063i −0.838231 0.545315i \(-0.816410\pi\)
0.838231 0.545315i \(-0.183590\pi\)
\(788\) 12.8467i 0.457644i
\(789\) 0 0
\(790\) 0.400851 + 0.231432i 0.0142617 + 0.00823397i
\(791\) −34.9497 22.7699i −1.24267 0.809604i
\(792\) 0 0
\(793\) −0.156520 0.271101i −0.00555820 0.00962709i
\(794\) 1.01687 + 1.76126i 0.0360872 + 0.0625049i
\(795\) 0 0
\(796\) 3.24154 + 1.87150i 0.114893 + 0.0663337i
\(797\) 1.64717 + 2.85299i 0.0583459 + 0.101058i 0.893723 0.448619i \(-0.148084\pi\)
−0.835377 + 0.549677i \(0.814751\pi\)
\(798\) 0 0
\(799\) −2.74674 + 4.75750i −0.0971728 + 0.168308i
\(800\) 4.32617 2.49771i 0.152953 0.0883075i
\(801\) 0 0
\(802\) 15.7118 27.2137i 0.554804 0.960948i
\(803\) 27.8019 0.981107
\(804\) 0 0
\(805\) −0.828393 0.539702i −0.0291970 0.0190220i
\(806\) 4.21041 2.43088i 0.148305 0.0856242i
\(807\) 0 0
\(808\) −15.0623 + 8.69621i −0.529889 + 0.305932i
\(809\) −19.7833 11.4219i −0.695542 0.401572i 0.110143 0.993916i \(-0.464869\pi\)
−0.805685 + 0.592344i \(0.798203\pi\)
\(810\) 0 0
\(811\) 23.9412i 0.840691i 0.907364 + 0.420345i \(0.138091\pi\)
−0.907364 + 0.420345i \(0.861909\pi\)
\(812\) −0.198643 + 3.68638i −0.00697099 + 0.129367i
\(813\) 0 0
\(814\) −17.1132 + 29.6409i −0.599818 + 1.03891i
\(815\) −0.612985 −0.0214719
\(816\) 0 0
\(817\) 8.60515i 0.301056i
\(818\) −0.550583 −0.0192507
\(819\) 0 0
\(820\) −0.699616 −0.0244316
\(821\) 2.28557i 0.0797669i −0.999204 0.0398834i \(-0.987301\pi\)
0.999204 0.0398834i \(-0.0126987\pi\)
\(822\) 0 0
\(823\) −22.9703 −0.800694 −0.400347 0.916364i \(-0.631110\pi\)
−0.400347 + 0.916364i \(0.631110\pi\)
\(824\) −0.500568 + 0.867010i −0.0174381 + 0.0302037i
\(825\) 0 0
\(826\) −22.1780 + 11.2591i −0.771672 + 0.391755i
\(827\) 15.1679i 0.527438i 0.964600 + 0.263719i \(0.0849492\pi\)
−0.964600 + 0.263719i \(0.915051\pi\)
\(828\) 0 0
\(829\) −5.73806 3.31287i −0.199291 0.115061i 0.397034 0.917804i \(-0.370040\pi\)
−0.596325 + 0.802743i \(0.703373\pi\)
\(830\) 0.460425 0.265826i 0.0159816 0.00922697i
\(831\) 0 0
\(832\) −3.32589 + 1.92020i −0.115304 + 0.0665710i
\(833\) −4.38577 9.92925i −0.151958 0.344028i
\(834\) 0 0
\(835\) −1.03428 −0.0357927
\(836\) −11.4874 + 19.8967i −0.397299 + 0.688141i
\(837\) 0 0
\(838\) −20.0310 + 11.5649i −0.691961 + 0.399504i
\(839\) −23.8462 + 41.3029i −0.823264 + 1.42593i 0.0799756 + 0.996797i \(0.474516\pi\)
−0.903239 + 0.429138i \(0.858818\pi\)
\(840\) 0 0
\(841\) −13.5265 23.4286i −0.466431 0.807883i
\(842\) −9.52235 5.49773i −0.328162 0.189464i
\(843\) 0 0
\(844\) −4.69581 8.13339i −0.161637 0.279963i
\(845\) −0.0591122 0.102385i −0.00203352 0.00352216i
\(846\) 0 0
\(847\) 11.7273 + 0.631934i 0.402956 + 0.0217135i
\(848\) 6.28910 + 3.63101i 0.215969 + 0.124690i
\(849\) 0 0
\(850\) 7.74628i 0.265695i
\(851\) 48.1475i 1.65048i
\(852\) 0 0
\(853\) 22.0983 + 12.7585i 0.756632 + 0.436842i 0.828085 0.560602i \(-0.189430\pi\)
−0.0714529 + 0.997444i \(0.522764\pi\)
\(854\) −0.0976251 0.192300i −0.00334066 0.00658037i
\(855\) 0 0
\(856\) −4.63238 8.02352i −0.158332 0.274238i
\(857\) 3.19043 + 5.52598i 0.108983 + 0.188764i 0.915358 0.402640i \(-0.131907\pi\)
−0.806376 + 0.591404i \(0.798574\pi\)
\(858\) 0 0
\(859\) 29.7468 + 17.1743i 1.01495 + 0.585980i 0.912636 0.408773i \(-0.134043\pi\)
0.102310 + 0.994753i \(0.467376\pi\)
\(860\) 0.0497483 + 0.0861666i 0.00169640 + 0.00293826i
\(861\) 0 0
\(862\) 4.15530 7.19720i 0.141530 0.245137i
\(863\) 31.3380 18.0930i 1.06676 0.615893i 0.139464 0.990227i \(-0.455462\pi\)
0.927294 + 0.374334i \(0.122129\pi\)
\(864\) 0 0
\(865\) 0.0777901 0.134736i 0.00264494 0.00458118i
\(866\) −26.1051 −0.887087
\(867\) 0 0
\(868\) 2.98657 1.51619i 0.101371 0.0514629i
\(869\) −23.2971 + 13.4506i −0.790299 + 0.456279i
\(870\) 0 0
\(871\) −51.0362 + 29.4658i −1.72930 + 0.998410i
\(872\) 1.42288 + 0.821501i 0.0481849 + 0.0278195i
\(873\) 0 0
\(874\) 32.3193i 1.09322i
\(875\) 0.809338 + 1.59422i 0.0273606 + 0.0538944i
\(876\) 0 0
\(877\) −17.0155 + 29.4716i −0.574571 + 0.995186i 0.421517 + 0.906820i \(0.361498\pi\)
−0.996088 + 0.0883657i \(0.971836\pi\)
\(878\) 40.8308 1.37797
\(879\) 0 0
\(880\) 0.265644i 0.00895485i
\(881\) −26.6961 −0.899416 −0.449708 0.893176i \(-0.648472\pi\)
−0.449708 + 0.893176i \(0.648472\pi\)
\(882\) 0 0
\(883\) 11.2126 0.377333 0.188667 0.982041i \(-0.439583\pi\)
0.188667 + 0.982041i \(0.439583\pi\)
\(884\) 5.95522i 0.200296i
\(885\) 0 0
\(886\) 18.2565 0.613338
\(887\) −5.09353 + 8.82225i −0.171024 + 0.296222i −0.938778 0.344522i \(-0.888041\pi\)
0.767754 + 0.640745i \(0.221374\pi\)
\(888\) 0 0
\(889\) −22.8486 45.0068i −0.766318 1.50948i
\(890\) 0.790656i 0.0265028i
\(891\) 0 0
\(892\) 17.7695 + 10.2592i 0.594966 + 0.343504i
\(893\) 17.9391 10.3571i 0.600308 0.346588i
\(894\) 0 0
\(895\) 0.933494 0.538953i 0.0312033 0.0180152i
\(896\) −2.35915 + 1.19767i −0.0788136 + 0.0400114i
\(897\) 0 0
\(898\) 26.0881 0.870570
\(899\) 0.883217 1.52978i 0.0294569 0.0510209i
\(900\) 0 0
\(901\) −9.75235 + 5.63052i −0.324898 + 0.187580i
\(902\) 20.3305 35.2134i 0.676931 1.17248i
\(903\) 0 0
\(904\) −7.88296 13.6537i −0.262183 0.454115i
\(905\) 1.08039 + 0.623761i 0.0359132 + 0.0207345i
\(906\) 0 0
\(907\) 7.57428 + 13.1190i 0.251500 + 0.435611i 0.963939 0.266123i \(-0.0857428\pi\)
−0.712439 + 0.701734i \(0.752409\pi\)
\(908\) −9.38828 16.2610i −0.311561 0.539640i
\(909\) 0 0
\(910\) −0.310960 0.612524i −0.0103082 0.0203050i
\(911\) 8.43020 + 4.86718i 0.279305 + 0.161257i 0.633109 0.774063i \(-0.281779\pi\)
−0.353804 + 0.935320i \(0.615112\pi\)
\(912\) 0 0
\(913\) 30.8991i 1.02261i
\(914\) 6.39973i 0.211684i
\(915\) 0 0
\(916\) 4.31740 + 2.49265i 0.142651 + 0.0823596i
\(917\) 49.3195 + 2.65761i 1.62867 + 0.0877621i
\(918\) 0 0
\(919\) −4.01638 6.95658i −0.132488 0.229476i 0.792147 0.610330i \(-0.208963\pi\)
−0.924635 + 0.380854i \(0.875630\pi\)
\(920\) −0.186845 0.323625i −0.00616011 0.0106696i
\(921\) 0 0
\(922\) 1.80304 + 1.04099i 0.0593800 + 0.0342831i
\(923\) −8.27560 14.3338i −0.272395 0.471801i
\(924\) 0 0
\(925\) 21.7568 37.6839i 0.715360 1.23904i
\(926\) −1.66118 + 0.959084i −0.0545898 + 0.0315175i
\(927\) 0 0
\(928\) −0.697671 + 1.20840i −0.0229022 + 0.0396677i
\(929\) 26.2128 0.860014 0.430007 0.902826i \(-0.358511\pi\)
0.430007 + 0.902826i \(0.358511\pi\)
\(930\) 0 0
\(931\) −4.39828 + 40.6928i −0.144148 + 1.33365i
\(932\) 12.7747 7.37548i 0.418449 0.241592i
\(933\) 0 0
\(934\) 29.6488 17.1178i 0.970140 0.560111i
\(935\) 0.356739 + 0.205963i 0.0116666 + 0.00673573i
\(936\) 0 0
\(937\) 37.5797i 1.22768i 0.789432 + 0.613838i \(0.210375\pi\)
−0.789432 + 0.613838i \(0.789625\pi\)
\(938\) −36.2015 + 18.3784i −1.18202 + 0.600077i
\(939\) 0 0
\(940\) −0.119754 + 0.207419i −0.00390593 + 0.00676527i
\(941\) −9.27309 −0.302294 −0.151147 0.988511i \(-0.548297\pi\)
−0.151147 + 0.988511i \(0.548297\pi\)
\(942\) 0 0
\(943\) 57.1992i 1.86266i
\(944\) −9.40086 −0.305972
\(945\) 0 0
\(946\) −5.78264 −0.188010
\(947\) 13.8586i 0.450343i 0.974319 + 0.225171i \(0.0722942\pi\)
−0.974319 + 0.225171i \(0.927706\pi\)
\(948\) 0 0
\(949\) 27.1733 0.882083
\(950\) 14.6044 25.2956i 0.473830 0.820697i
\(951\) 0 0
\(952\) 0.220756 4.09675i 0.00715475 0.132777i
\(953\) 2.65523i 0.0860115i −0.999075 0.0430057i \(-0.986307\pi\)
0.999075 0.0430057i \(-0.0136934\pi\)
\(954\) 0 0
\(955\) −1.36676 0.789097i −0.0442272 0.0255346i
\(956\) −0.155388 + 0.0897132i −0.00502560 + 0.00290153i
\(957\) 0 0
\(958\) −9.16468 + 5.29123i −0.296098 + 0.170952i
\(959\) −13.9333 9.07763i −0.449931 0.293132i
\(960\) 0 0
\(961\) 29.3974 0.948302
\(962\) −16.7263 + 28.9708i −0.539277 + 0.934055i
\(963\) 0 0
\(964\) −5.31183 + 3.06679i −0.171083 + 0.0987746i
\(965\) 0.719600 1.24638i 0.0231647 0.0401225i
\(966\) 0 0
\(967\) 7.14946 + 12.3832i 0.229911 + 0.398218i 0.957782 0.287497i \(-0.0928231\pi\)
−0.727870 + 0.685715i \(0.759490\pi\)
\(968\) 3.84424 + 2.21947i 0.123558 + 0.0713365i
\(969\) 0 0
\(970\) 0.0141804 + 0.0245613i 0.000455307 + 0.000788614i
\(971\) −0.130666 0.226320i −0.00419326 0.00726295i 0.863921 0.503627i \(-0.168001\pi\)
−0.868114 + 0.496364i \(0.834668\pi\)
\(972\) 0 0
\(973\) 14.0681 + 9.16546i 0.451004 + 0.293831i
\(974\) −10.3196 5.95804i −0.330662 0.190908i
\(975\) 0 0
\(976\) 0.0815124i 0.00260915i
\(977\) 39.1574i 1.25276i 0.779519 + 0.626378i \(0.215464\pi\)
−0.779519 + 0.626378i \(0.784536\pi\)
\(978\) 0 0
\(979\) −39.7957 22.9760i −1.27188 0.734318i
\(980\) −0.191212 0.432899i −0.00610805 0.0138285i
\(981\) 0 0
\(982\) −8.65023 14.9826i −0.276040 0.478115i
\(983\) −13.1844 22.8361i −0.420517 0.728357i 0.575473 0.817821i \(-0.304818\pi\)
−0.995990 + 0.0894636i \(0.971485\pi\)
\(984\) 0 0
\(985\) −0.752163 0.434262i −0.0239659 0.0138367i
\(986\) −1.08186 1.87384i −0.0344534 0.0596751i
\(987\) 0 0
\(988\) −11.2276 + 19.4468i −0.357199 + 0.618686i
\(989\) −7.04481 + 4.06732i −0.224012 + 0.129333i
\(990\) 0 0
\(991\) −22.9516 + 39.7534i −0.729082 + 1.26281i 0.228189 + 0.973617i \(0.426720\pi\)
−0.957271 + 0.289191i \(0.906614\pi\)
\(992\) 1.26595 0.0401940
\(993\) 0 0
\(994\) −5.16167 10.1674i −0.163718 0.322489i
\(995\) −0.219150 + 0.126526i −0.00694753 + 0.00401116i
\(996\) 0 0
\(997\) −18.5929 + 10.7346i −0.588844 + 0.339969i −0.764640 0.644457i \(-0.777083\pi\)
0.175796 + 0.984427i \(0.443750\pi\)
\(998\) −11.1108 6.41484i −0.351707 0.203058i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 378.2.l.a.143.3 16
3.2 odd 2 126.2.l.a.101.6 yes 16
4.3 odd 2 3024.2.ca.c.2033.5 16
7.2 even 3 2646.2.t.b.1979.2 16
7.3 odd 6 2646.2.m.a.1763.6 16
7.4 even 3 2646.2.m.b.1763.7 16
7.5 odd 6 378.2.t.a.89.3 16
7.6 odd 2 2646.2.l.a.521.2 16
9.2 odd 6 1134.2.k.a.647.6 16
9.4 even 3 126.2.t.a.59.7 yes 16
9.5 odd 6 378.2.t.a.17.3 16
9.7 even 3 1134.2.k.b.647.3 16
12.11 even 2 1008.2.ca.c.353.4 16
21.2 odd 6 882.2.t.a.803.6 16
21.5 even 6 126.2.t.a.47.7 yes 16
21.11 odd 6 882.2.m.b.587.4 16
21.17 even 6 882.2.m.a.587.1 16
21.20 even 2 882.2.l.b.227.7 16
28.19 even 6 3024.2.df.c.1601.5 16
36.23 even 6 3024.2.df.c.17.5 16
36.31 odd 6 1008.2.df.c.689.2 16
63.4 even 3 882.2.m.a.293.1 16
63.5 even 6 inner 378.2.l.a.341.7 16
63.13 odd 6 882.2.t.a.815.6 16
63.23 odd 6 2646.2.l.a.1097.6 16
63.31 odd 6 882.2.m.b.293.4 16
63.32 odd 6 2646.2.m.a.881.6 16
63.40 odd 6 126.2.l.a.5.2 16
63.41 even 6 2646.2.t.b.2285.2 16
63.47 even 6 1134.2.k.b.971.3 16
63.58 even 3 882.2.l.b.509.3 16
63.59 even 6 2646.2.m.b.881.7 16
63.61 odd 6 1134.2.k.a.971.6 16
84.47 odd 6 1008.2.df.c.929.2 16
252.103 even 6 1008.2.ca.c.257.4 16
252.131 odd 6 3024.2.ca.c.2609.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.l.a.5.2 16 63.40 odd 6
126.2.l.a.101.6 yes 16 3.2 odd 2
126.2.t.a.47.7 yes 16 21.5 even 6
126.2.t.a.59.7 yes 16 9.4 even 3
378.2.l.a.143.3 16 1.1 even 1 trivial
378.2.l.a.341.7 16 63.5 even 6 inner
378.2.t.a.17.3 16 9.5 odd 6
378.2.t.a.89.3 16 7.5 odd 6
882.2.l.b.227.7 16 21.20 even 2
882.2.l.b.509.3 16 63.58 even 3
882.2.m.a.293.1 16 63.4 even 3
882.2.m.a.587.1 16 21.17 even 6
882.2.m.b.293.4 16 63.31 odd 6
882.2.m.b.587.4 16 21.11 odd 6
882.2.t.a.803.6 16 21.2 odd 6
882.2.t.a.815.6 16 63.13 odd 6
1008.2.ca.c.257.4 16 252.103 even 6
1008.2.ca.c.353.4 16 12.11 even 2
1008.2.df.c.689.2 16 36.31 odd 6
1008.2.df.c.929.2 16 84.47 odd 6
1134.2.k.a.647.6 16 9.2 odd 6
1134.2.k.a.971.6 16 63.61 odd 6
1134.2.k.b.647.3 16 9.7 even 3
1134.2.k.b.971.3 16 63.47 even 6
2646.2.l.a.521.2 16 7.6 odd 2
2646.2.l.a.1097.6 16 63.23 odd 6
2646.2.m.a.881.6 16 63.32 odd 6
2646.2.m.a.1763.6 16 7.3 odd 6
2646.2.m.b.881.7 16 63.59 even 6
2646.2.m.b.1763.7 16 7.4 even 3
2646.2.t.b.1979.2 16 7.2 even 3
2646.2.t.b.2285.2 16 63.41 even 6
3024.2.ca.c.2033.5 16 4.3 odd 2
3024.2.ca.c.2609.5 16 252.131 odd 6
3024.2.df.c.17.5 16 36.23 even 6
3024.2.df.c.1601.5 16 28.19 even 6