Properties

Label 315.2.bf.c.109.2
Level $315$
Weight $2$
Character 315.109
Analytic conductor $2.515$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(109,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
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: \( x^{16} + 8x^{14} + 26x^{12} - 96x^{10} - 781x^{8} - 2400x^{6} + 16250x^{4} + 125000x^{2} + 390625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.2
Root \(1.46253 + 1.69145i\) of defining polynomial
Character \(\chi\) \(=\) 315.109
Dual form 315.2.bf.c.289.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.05774 + 1.18804i) q^{2} +(1.82288 - 3.15731i) q^{4} +(0.733576 + 2.11231i) q^{5} +(2.03996 + 1.68480i) q^{7} +3.91044i q^{8} +O(q^{10})\) \(q+(-2.05774 + 1.18804i) q^{2} +(1.82288 - 3.15731i) q^{4} +(0.733576 + 2.11231i) q^{5} +(2.03996 + 1.68480i) q^{7} +3.91044i q^{8} +(-4.01902 - 3.47508i) q^{10} +(1.80712 - 3.13003i) q^{11} -3.36961i q^{13} +(-6.19933 - 1.04334i) q^{14} +(-1.00000 - 1.73205i) q^{16} +(4.71533 + 2.72240i) q^{17} +(2.32288 + 4.02334i) q^{19} +(8.00645 + 1.53436i) q^{20} +8.58772i q^{22} +(0.599838 - 0.346317i) q^{23} +(-3.92373 + 3.09908i) q^{25} +(4.00323 + 6.93379i) q^{26} +(9.03805 - 3.36961i) q^{28} -8.00645 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-2.65758 - 1.53436i) q^{32} -12.9373 q^{34} +(-2.06237 + 5.54497i) q^{35} +(4.51902 - 2.60906i) q^{37} +(-9.55977 - 5.51934i) q^{38} +(-8.26006 + 2.86860i) q^{40} +5.17018 q^{41} +8.91514i q^{43} +(-6.58831 - 11.4113i) q^{44} +(-0.822876 + 1.42526i) q^{46} +(-3.38654 + 1.95522i) q^{47} +(1.32288 + 6.87386i) q^{49} +(4.39221 - 11.0387i) q^{50} +(-10.6389 - 6.14237i) q^{52} +(5.57340 + 3.21780i) q^{53} +(7.93725 + 1.52110i) q^{55} +(-6.58831 + 7.97713i) q^{56} +(16.4752 - 9.51198i) q^{58} +(0.388984 - 0.673739i) q^{59} +(-2.82288 - 4.88936i) q^{61} -11.8804i q^{62} +11.2915 q^{64} +(7.11766 - 2.47186i) q^{65} +(-11.9562 - 6.90292i) q^{67} +(17.1909 - 9.92518i) q^{68} +(-2.34381 - 13.8603i) q^{70} +8.00645 q^{71} +(-1.31731 - 0.760548i) q^{73} +(-6.19933 + 10.7376i) q^{74} +16.9373 q^{76} +(8.95993 - 3.34048i) q^{77} +(-4.96863 - 8.60591i) q^{79} +(2.92506 - 3.38290i) q^{80} +(-10.6389 + 6.14237i) q^{82} +3.76135i q^{83} +(-2.29150 + 11.9573i) q^{85} +(-10.5915 - 18.3451i) q^{86} +(12.2398 + 7.06663i) q^{88} +(-1.80712 - 3.13003i) q^{89} +(5.67712 - 6.87386i) q^{91} -2.52517i q^{92} +(4.64575 - 8.04668i) q^{94} +(-6.79455 + 7.85806i) q^{95} -12.2847i q^{97} +(-10.8886 - 12.5730i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 8 q^{10} - 16 q^{16} + 16 q^{19} - 16 q^{25} - 40 q^{31} - 80 q^{34} + 8 q^{40} + 8 q^{46} - 24 q^{61} + 96 q^{64} - 56 q^{70} + 144 q^{76} - 16 q^{79} + 48 q^{85} + 112 q^{91} + 32 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05774 + 1.18804i −1.45505 + 0.840071i −0.998761 0.0497633i \(-0.984153\pi\)
−0.456284 + 0.889834i \(0.650820\pi\)
\(3\) 0 0
\(4\) 1.82288 3.15731i 0.911438 1.57866i
\(5\) 0.733576 + 2.11231i 0.328065 + 0.944655i
\(6\) 0 0
\(7\) 2.03996 + 1.68480i 0.771033 + 0.636796i
\(8\) 3.91044i 1.38255i
\(9\) 0 0
\(10\) −4.01902 3.47508i −1.27093 1.09892i
\(11\) 1.80712 3.13003i 0.544867 0.943738i −0.453748 0.891130i \(-0.649913\pi\)
0.998615 0.0526080i \(-0.0167534\pi\)
\(12\) 0 0
\(13\) 3.36961i 0.934561i −0.884109 0.467280i \(-0.845234\pi\)
0.884109 0.467280i \(-0.154766\pi\)
\(14\) −6.19933 1.04334i −1.65684 0.278845i
\(15\) 0 0
\(16\) −1.00000 1.73205i −0.250000 0.433013i
\(17\) 4.71533 + 2.72240i 1.14363 + 0.660278i 0.947328 0.320265i \(-0.103772\pi\)
0.196307 + 0.980543i \(0.437105\pi\)
\(18\) 0 0
\(19\) 2.32288 + 4.02334i 0.532904 + 0.923017i 0.999262 + 0.0384208i \(0.0122327\pi\)
−0.466357 + 0.884596i \(0.654434\pi\)
\(20\) 8.00645 + 1.53436i 1.79030 + 0.343092i
\(21\) 0 0
\(22\) 8.58772i 1.83091i
\(23\) 0.599838 0.346317i 0.125075 0.0722120i −0.436157 0.899870i \(-0.643661\pi\)
0.561232 + 0.827658i \(0.310328\pi\)
\(24\) 0 0
\(25\) −3.92373 + 3.09908i −0.784747 + 0.619817i
\(26\) 4.00323 + 6.93379i 0.785097 + 1.35983i
\(27\) 0 0
\(28\) 9.03805 3.36961i 1.70803 0.636796i
\(29\) −8.00645 −1.48676 −0.743380 0.668869i \(-0.766779\pi\)
−0.743380 + 0.668869i \(0.766779\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) −2.65758 1.53436i −0.469799 0.271238i
\(33\) 0 0
\(34\) −12.9373 −2.21872
\(35\) −2.06237 + 5.54497i −0.348604 + 0.937270i
\(36\) 0 0
\(37\) 4.51902 2.60906i 0.742923 0.428927i −0.0802083 0.996778i \(-0.525559\pi\)
0.823131 + 0.567851i \(0.192225\pi\)
\(38\) −9.55977 5.51934i −1.55080 0.895355i
\(39\) 0 0
\(40\) −8.26006 + 2.86860i −1.30603 + 0.453565i
\(41\) 5.17018 0.807446 0.403723 0.914881i \(-0.367716\pi\)
0.403723 + 0.914881i \(0.367716\pi\)
\(42\) 0 0
\(43\) 8.91514i 1.35955i 0.733422 + 0.679773i \(0.237922\pi\)
−0.733422 + 0.679773i \(0.762078\pi\)
\(44\) −6.58831 11.4113i −0.993226 1.72032i
\(45\) 0 0
\(46\) −0.822876 + 1.42526i −0.121326 + 0.210143i
\(47\) −3.38654 + 1.95522i −0.493977 + 0.285198i −0.726223 0.687459i \(-0.758726\pi\)
0.232246 + 0.972657i \(0.425393\pi\)
\(48\) 0 0
\(49\) 1.32288 + 6.87386i 0.188982 + 0.981981i
\(50\) 4.39221 11.0387i 0.621152 1.56110i
\(51\) 0 0
\(52\) −10.6389 6.14237i −1.47535 0.851794i
\(53\) 5.57340 + 3.21780i 0.765565 + 0.441999i 0.831290 0.555839i \(-0.187603\pi\)
−0.0657253 + 0.997838i \(0.520936\pi\)
\(54\) 0 0
\(55\) 7.93725 + 1.52110i 1.07026 + 0.205104i
\(56\) −6.58831 + 7.97713i −0.880400 + 1.06599i
\(57\) 0 0
\(58\) 16.4752 9.51198i 2.16330 1.24898i
\(59\) 0.388984 0.673739i 0.0506414 0.0877134i −0.839594 0.543215i \(-0.817207\pi\)
0.890235 + 0.455502i \(0.150540\pi\)
\(60\) 0 0
\(61\) −2.82288 4.88936i −0.361432 0.626019i 0.626765 0.779209i \(-0.284379\pi\)
−0.988197 + 0.153190i \(0.951045\pi\)
\(62\) 11.8804i 1.50881i
\(63\) 0 0
\(64\) 11.2915 1.41144
\(65\) 7.11766 2.47186i 0.882838 0.306597i
\(66\) 0 0
\(67\) −11.9562 6.90292i −1.46068 0.843326i −0.461641 0.887067i \(-0.652739\pi\)
−0.999043 + 0.0437409i \(0.986072\pi\)
\(68\) 17.1909 9.92518i 2.08470 1.20360i
\(69\) 0 0
\(70\) −2.34381 13.8603i −0.280139 1.65662i
\(71\) 8.00645 0.950191 0.475095 0.879934i \(-0.342414\pi\)
0.475095 + 0.879934i \(0.342414\pi\)
\(72\) 0 0
\(73\) −1.31731 0.760548i −0.154179 0.0890154i 0.420926 0.907095i \(-0.361705\pi\)
−0.575105 + 0.818080i \(0.695039\pi\)
\(74\) −6.19933 + 10.7376i −0.720658 + 1.24822i
\(75\) 0 0
\(76\) 16.9373 1.94284
\(77\) 8.95993 3.34048i 1.02108 0.380683i
\(78\) 0 0
\(79\) −4.96863 8.60591i −0.559014 0.968241i −0.997579 0.0695415i \(-0.977846\pi\)
0.438565 0.898700i \(-0.355487\pi\)
\(80\) 2.92506 3.38290i 0.327031 0.378220i
\(81\) 0 0
\(82\) −10.6389 + 6.14237i −1.17487 + 0.678312i
\(83\) 3.76135i 0.412861i 0.978461 + 0.206431i \(0.0661848\pi\)
−0.978461 + 0.206431i \(0.933815\pi\)
\(84\) 0 0
\(85\) −2.29150 + 11.9573i −0.248548 + 1.29695i
\(86\) −10.5915 18.3451i −1.14212 1.97820i
\(87\) 0 0
\(88\) 12.2398 + 7.06663i 1.30476 + 0.753305i
\(89\) −1.80712 3.13003i −0.191554 0.331782i 0.754211 0.656632i \(-0.228020\pi\)
−0.945766 + 0.324850i \(0.894686\pi\)
\(90\) 0 0
\(91\) 5.67712 6.87386i 0.595124 0.720577i
\(92\) 2.52517i 0.263267i
\(93\) 0 0
\(94\) 4.64575 8.04668i 0.479173 0.829951i
\(95\) −6.79455 + 7.85806i −0.697106 + 0.806220i
\(96\) 0 0
\(97\) 12.2847i 1.24733i −0.781693 0.623664i \(-0.785644\pi\)
0.781693 0.623664i \(-0.214356\pi\)
\(98\) −10.8886 12.5730i −1.09991 1.27007i
\(99\) 0 0
\(100\) 2.63230 + 18.0377i 0.263230 + 1.80377i
\(101\) 8.39544 14.5413i 0.835377 1.44692i −0.0583461 0.998296i \(-0.518583\pi\)
0.893723 0.448619i \(-0.148084\pi\)
\(102\) 0 0
\(103\) 10.3554 5.97867i 1.02034 0.589095i 0.106140 0.994351i \(-0.466151\pi\)
0.914203 + 0.405256i \(0.132818\pi\)
\(104\) 13.1766 1.29207
\(105\) 0 0
\(106\) −15.2915 −1.48524
\(107\) −6.90219 + 3.98498i −0.667260 + 0.385243i −0.795038 0.606560i \(-0.792549\pi\)
0.127778 + 0.991803i \(0.459216\pi\)
\(108\) 0 0
\(109\) 6.61438 11.4564i 0.633543 1.09733i −0.353279 0.935518i \(-0.614933\pi\)
0.986822 0.161810i \(-0.0517332\pi\)
\(110\) −18.1400 + 6.29975i −1.72958 + 0.600657i
\(111\) 0 0
\(112\) 0.878205 5.21812i 0.0829825 0.493066i
\(113\) 12.8712i 1.21082i 0.795913 + 0.605411i \(0.206991\pi\)
−0.795913 + 0.605411i \(0.793009\pi\)
\(114\) 0 0
\(115\) 1.17156 + 1.01300i 0.109248 + 0.0944624i
\(116\) −14.5948 + 25.2789i −1.35509 + 2.34708i
\(117\) 0 0
\(118\) 1.84851i 0.170169i
\(119\) 5.03238 + 13.4980i 0.461317 + 1.23736i
\(120\) 0 0
\(121\) −1.03137 1.78639i −0.0937612 0.162399i
\(122\) 11.6175 + 6.70738i 1.05180 + 0.607257i
\(123\) 0 0
\(124\) 9.11438 + 15.7866i 0.818495 + 1.41768i
\(125\) −9.42459 6.01474i −0.842961 0.537975i
\(126\) 0 0
\(127\) 3.36961i 0.299004i −0.988761 0.149502i \(-0.952233\pi\)
0.988761 0.149502i \(-0.0477671\pi\)
\(128\) −17.9199 + 10.3460i −1.58391 + 0.914469i
\(129\) 0 0
\(130\) −11.7097 + 13.5425i −1.02701 + 1.18776i
\(131\) −5.81035 10.0638i −0.507652 0.879280i −0.999961 0.00885883i \(-0.997180\pi\)
0.492308 0.870421i \(-0.336153\pi\)
\(132\) 0 0
\(133\) −2.03996 + 12.1210i −0.176887 + 1.05103i
\(134\) 32.8038 2.83381
\(135\) 0 0
\(136\) −10.6458 + 18.4390i −0.912866 + 1.58113i
\(137\) −2.78670 1.60890i −0.238084 0.137458i 0.376212 0.926534i \(-0.377226\pi\)
−0.614296 + 0.789076i \(0.710560\pi\)
\(138\) 0 0
\(139\) −19.2288 −1.63096 −0.815481 0.578784i \(-0.803527\pi\)
−0.815481 + 0.578784i \(0.803527\pi\)
\(140\) 13.7478 + 16.6193i 1.16190 + 1.40459i
\(141\) 0 0
\(142\) −16.4752 + 9.51198i −1.38257 + 0.798228i
\(143\) −10.5470 6.08929i −0.881981 0.509212i
\(144\) 0 0
\(145\) −5.87334 16.9121i −0.487754 1.40448i
\(146\) 3.61424 0.299117
\(147\) 0 0
\(148\) 19.0240i 1.56376i
\(149\) 2.19610 + 3.80376i 0.179912 + 0.311617i 0.941850 0.336033i \(-0.109085\pi\)
−0.761938 + 0.647650i \(0.775752\pi\)
\(150\) 0 0
\(151\) −3.46863 + 6.00784i −0.282273 + 0.488911i −0.971944 0.235212i \(-0.924422\pi\)
0.689671 + 0.724123i \(0.257755\pi\)
\(152\) −15.7330 + 9.08345i −1.27612 + 0.736765i
\(153\) 0 0
\(154\) −14.4686 + 17.5186i −1.16592 + 1.41169i
\(155\) −10.9805 2.10431i −0.881977 0.169022i
\(156\) 0 0
\(157\) 12.2398 + 7.06663i 0.976839 + 0.563978i 0.901314 0.433165i \(-0.142603\pi\)
0.0755249 + 0.997144i \(0.475937\pi\)
\(158\) 20.4483 + 11.8059i 1.62678 + 0.939223i
\(159\) 0 0
\(160\) 1.29150 6.73921i 0.102102 0.532782i
\(161\) 1.80712 + 0.304137i 0.142421 + 0.0239693i
\(162\) 0 0
\(163\) −9.03805 + 5.21812i −0.707914 + 0.408715i −0.810288 0.586031i \(-0.800690\pi\)
0.102374 + 0.994746i \(0.467356\pi\)
\(164\) 9.42459 16.3239i 0.735937 1.27468i
\(165\) 0 0
\(166\) −4.46863 7.73989i −0.346833 0.600732i
\(167\) 12.4239i 0.961393i 0.876887 + 0.480697i \(0.159616\pi\)
−0.876887 + 0.480697i \(0.840384\pi\)
\(168\) 0 0
\(169\) 1.64575 0.126596
\(170\) −9.49045 27.3275i −0.727885 2.09593i
\(171\) 0 0
\(172\) 28.1479 + 16.2512i 2.14626 + 1.23914i
\(173\) 21.3064 12.3013i 1.61990 0.935247i 0.632950 0.774193i \(-0.281844\pi\)
0.986945 0.161055i \(-0.0514895\pi\)
\(174\) 0 0
\(175\) −13.2256 0.288713i −0.999762 0.0218247i
\(176\) −7.22848 −0.544867
\(177\) 0 0
\(178\) 7.43719 + 4.29386i 0.557441 + 0.321839i
\(179\) −0.777967 + 1.34748i −0.0581480 + 0.100715i −0.893634 0.448796i \(-0.851853\pi\)
0.835486 + 0.549512i \(0.185186\pi\)
\(180\) 0 0
\(181\) 7.35425 0.546637 0.273319 0.961924i \(-0.411879\pi\)
0.273319 + 0.961924i \(0.411879\pi\)
\(182\) −3.51565 + 20.8893i −0.260597 + 1.54842i
\(183\) 0 0
\(184\) 1.35425 + 2.34563i 0.0998365 + 0.172922i
\(185\) 8.82619 + 7.63165i 0.648915 + 0.561090i
\(186\) 0 0
\(187\) 17.0423 9.83940i 1.24626 0.719528i
\(188\) 14.2565i 1.03976i
\(189\) 0 0
\(190\) 4.64575 24.2421i 0.337038 1.75871i
\(191\) 3.61424 + 6.26005i 0.261517 + 0.452961i 0.966645 0.256119i \(-0.0824438\pi\)
−0.705128 + 0.709080i \(0.749110\pi\)
\(192\) 0 0
\(193\) −16.7588 9.67569i −1.20632 0.696471i −0.244370 0.969682i \(-0.578581\pi\)
−0.961954 + 0.273211i \(0.911914\pi\)
\(194\) 14.5948 + 25.2789i 1.04784 + 1.81492i
\(195\) 0 0
\(196\) 24.1144 + 8.35347i 1.72246 + 0.596676i
\(197\) 14.1074i 1.00511i −0.864545 0.502555i \(-0.832394\pi\)
0.864545 0.502555i \(-0.167606\pi\)
\(198\) 0 0
\(199\) 6.17712 10.6991i 0.437885 0.758439i −0.559641 0.828735i \(-0.689061\pi\)
0.997526 + 0.0702963i \(0.0223945\pi\)
\(200\) −12.1188 15.3435i −0.856926 1.08495i
\(201\) 0 0
\(202\) 39.8964i 2.80710i
\(203\) −16.3328 13.4893i −1.14634 0.946763i
\(204\) 0 0
\(205\) 3.79272 + 10.9210i 0.264895 + 0.762758i
\(206\) −14.2058 + 24.6051i −0.989764 + 1.71432i
\(207\) 0 0
\(208\) −5.83633 + 3.36961i −0.404677 + 0.233640i
\(209\) 16.7909 1.16145
\(210\) 0 0
\(211\) 0.937254 0.0645232 0.0322616 0.999479i \(-0.489729\pi\)
0.0322616 + 0.999479i \(0.489729\pi\)
\(212\) 20.3192 11.7313i 1.39553 0.805709i
\(213\) 0 0
\(214\) 9.46863 16.4001i 0.647262 1.12109i
\(215\) −18.8316 + 6.53993i −1.28430 + 0.446020i
\(216\) 0 0
\(217\) −12.3953 + 4.62128i −0.841449 + 0.313713i
\(218\) 31.4326i 2.12888i
\(219\) 0 0
\(220\) 19.2712 22.2876i 1.29926 1.50263i
\(221\) 9.17340 15.8888i 0.617070 1.06880i
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −2.83627 7.60753i −0.189507 0.508299i
\(225\) 0 0
\(226\) −15.2915 26.4857i −1.01718 1.76180i
\(227\) −20.4483 11.8059i −1.35720 0.783582i −0.367957 0.929843i \(-0.619943\pi\)
−0.989246 + 0.146261i \(0.953276\pi\)
\(228\) 0 0
\(229\) 4.14575 + 7.18065i 0.273959 + 0.474511i 0.969872 0.243615i \(-0.0783334\pi\)
−0.695913 + 0.718126i \(0.745000\pi\)
\(230\) −3.61424 0.692633i −0.238316 0.0456709i
\(231\) 0 0
\(232\) 31.3087i 2.05552i
\(233\) −6.04412 + 3.48957i −0.395963 + 0.228610i −0.684741 0.728787i \(-0.740085\pi\)
0.288777 + 0.957396i \(0.406751\pi\)
\(234\) 0 0
\(235\) −6.61431 5.71912i −0.431470 0.373075i
\(236\) −1.41814 2.45629i −0.0923129 0.159891i
\(237\) 0 0
\(238\) −26.3915 21.7967i −1.71071 1.41287i
\(239\) −13.1766 −0.852325 −0.426163 0.904647i \(-0.640135\pi\)
−0.426163 + 0.904647i \(0.640135\pi\)
\(240\) 0 0
\(241\) −0.885622 + 1.53394i −0.0570479 + 0.0988099i −0.893139 0.449781i \(-0.851502\pi\)
0.836091 + 0.548591i \(0.184835\pi\)
\(242\) 4.24460 + 2.45062i 0.272854 + 0.157532i
\(243\) 0 0
\(244\) −20.5830 −1.31769
\(245\) −13.5493 + 7.83683i −0.865634 + 0.500676i
\(246\) 0 0
\(247\) 13.5571 7.82718i 0.862616 0.498031i
\(248\) −16.9327 9.77609i −1.07523 0.620782i
\(249\) 0 0
\(250\) 26.5391 + 1.18002i 1.67848 + 0.0746311i
\(251\) 10.8427 0.684387 0.342193 0.939630i \(-0.388830\pi\)
0.342193 + 0.939630i \(0.388830\pi\)
\(252\) 0 0
\(253\) 2.50334i 0.157384i
\(254\) 4.00323 + 6.93379i 0.251185 + 0.435065i
\(255\) 0 0
\(256\) 13.2915 23.0216i 0.830719 1.43885i
\(257\) 5.44428 3.14326i 0.339605 0.196071i −0.320492 0.947251i \(-0.603848\pi\)
0.660097 + 0.751180i \(0.270515\pi\)
\(258\) 0 0
\(259\) 13.6144 + 2.29129i 0.845956 + 0.142374i
\(260\) 5.17018 26.9786i 0.320641 1.67314i
\(261\) 0 0
\(262\) 23.9124 + 13.8058i 1.47731 + 0.852928i
\(263\) −4.58621 2.64785i −0.282798 0.163273i 0.351891 0.936041i \(-0.385539\pi\)
−0.634689 + 0.772767i \(0.718872\pi\)
\(264\) 0 0
\(265\) −2.70850 + 14.1333i −0.166382 + 0.868199i
\(266\) −10.2026 27.3656i −0.625559 1.67789i
\(267\) 0 0
\(268\) −43.5894 + 25.1663i −2.66264 + 1.53728i
\(269\) −5.03238 + 8.71634i −0.306830 + 0.531444i −0.977667 0.210160i \(-0.932602\pi\)
0.670837 + 0.741604i \(0.265935\pi\)
\(270\) 0 0
\(271\) 2.11438 + 3.66221i 0.128439 + 0.222463i 0.923072 0.384627i \(-0.125670\pi\)
−0.794633 + 0.607090i \(0.792337\pi\)
\(272\) 10.8896i 0.660278i
\(273\) 0 0
\(274\) 7.64575 0.461897
\(275\) 2.60955 + 17.8818i 0.157362 + 1.07831i
\(276\) 0 0
\(277\) −7.15364 4.13015i −0.429820 0.248157i 0.269450 0.963014i \(-0.413158\pi\)
−0.699270 + 0.714858i \(0.746492\pi\)
\(278\) 39.5679 22.8445i 2.37312 1.37012i
\(279\) 0 0
\(280\) −21.6832 8.06475i −1.29582 0.481961i
\(281\) −29.1895 −1.74130 −0.870651 0.491902i \(-0.836302\pi\)
−0.870651 + 0.491902i \(0.836302\pi\)
\(282\) 0 0
\(283\) 22.0280 + 12.7179i 1.30943 + 0.755999i 0.982001 0.188877i \(-0.0604846\pi\)
0.327429 + 0.944876i \(0.393818\pi\)
\(284\) 14.5948 25.2789i 0.866040 1.50003i
\(285\) 0 0
\(286\) 28.9373 1.71110
\(287\) 10.5470 + 8.71073i 0.622567 + 0.514178i
\(288\) 0 0
\(289\) 6.32288 + 10.9515i 0.371934 + 0.644208i
\(290\) 32.1781 + 27.8231i 1.88956 + 1.63383i
\(291\) 0 0
\(292\) −4.80257 + 2.77277i −0.281049 + 0.162264i
\(293\) 27.3730i 1.59915i −0.600566 0.799575i \(-0.705058\pi\)
0.600566 0.799575i \(-0.294942\pi\)
\(294\) 0 0
\(295\) 1.70850 + 0.327416i 0.0994726 + 0.0190629i
\(296\) 10.2026 + 17.6713i 0.593012 + 1.02713i
\(297\) 0 0
\(298\) −9.03805 5.21812i −0.523560 0.302277i
\(299\) −1.16695 2.02122i −0.0674865 0.116890i
\(300\) 0 0
\(301\) −15.0203 + 18.1865i −0.865753 + 1.04825i
\(302\) 16.4835i 0.948517i
\(303\) 0 0
\(304\) 4.64575 8.04668i 0.266452 0.461509i
\(305\) 8.25708 9.54952i 0.472799 0.546804i
\(306\) 0 0
\(307\) 16.8480i 0.961568i −0.876839 0.480784i \(-0.840352\pi\)
0.876839 0.480784i \(-0.159648\pi\)
\(308\) 5.78589 34.3786i 0.329682 1.95890i
\(309\) 0 0
\(310\) 25.0951 8.71517i 1.42531 0.494988i
\(311\) 8.39544 14.5413i 0.476061 0.824563i −0.523562 0.851987i \(-0.675397\pi\)
0.999624 + 0.0274247i \(0.00873065\pi\)
\(312\) 0 0
\(313\) −1.31731 + 0.760548i −0.0744586 + 0.0429887i −0.536767 0.843730i \(-0.680355\pi\)
0.462308 + 0.886719i \(0.347021\pi\)
\(314\) −33.5817 −1.89513
\(315\) 0 0
\(316\) −36.2288 −2.03803
\(317\) 17.3200 9.99972i 0.972790 0.561640i 0.0727041 0.997354i \(-0.476837\pi\)
0.900086 + 0.435713i \(0.143504\pi\)
\(318\) 0 0
\(319\) −14.4686 + 25.0604i −0.810088 + 1.40311i
\(320\) 8.28317 + 23.8512i 0.463043 + 1.33332i
\(321\) 0 0
\(322\) −4.07992 + 1.52110i −0.227365 + 0.0847673i
\(323\) 25.2951i 1.40746i
\(324\) 0 0
\(325\) 10.4427 + 13.2214i 0.579256 + 0.733393i
\(326\) 12.3987 21.4751i 0.686698 1.18940i
\(327\) 0 0
\(328\) 20.2176i 1.11633i
\(329\) −10.2026 1.71708i −0.562485 0.0946657i
\(330\) 0 0
\(331\) 1.79150 + 3.10297i 0.0984699 + 0.170555i 0.911051 0.412293i \(-0.135272\pi\)
−0.812582 + 0.582847i \(0.801939\pi\)
\(332\) 11.8757 + 6.85647i 0.651766 + 0.376297i
\(333\) 0 0
\(334\) −14.7601 25.5653i −0.807638 1.39887i
\(335\) 5.81035 30.3191i 0.317453 1.65651i
\(336\) 0 0
\(337\) 10.1088i 0.550663i −0.961349 0.275331i \(-0.911212\pi\)
0.961349 0.275331i \(-0.0887875\pi\)
\(338\) −3.38654 + 1.95522i −0.184203 + 0.106350i
\(339\) 0 0
\(340\) 33.5759 + 29.0317i 1.82091 + 1.57447i
\(341\) 9.03561 + 15.6501i 0.489305 + 0.847502i
\(342\) 0 0
\(343\) −8.88249 + 16.2512i −0.479610 + 0.877482i
\(344\) −34.8621 −1.87964
\(345\) 0 0
\(346\) −29.2288 + 50.6257i −1.57135 + 2.72165i
\(347\) −23.4933 13.5638i −1.26118 0.728145i −0.287881 0.957666i \(-0.592951\pi\)
−0.973304 + 0.229521i \(0.926284\pi\)
\(348\) 0 0
\(349\) 5.87451 0.314455 0.157228 0.987562i \(-0.449744\pi\)
0.157228 + 0.987562i \(0.449744\pi\)
\(350\) 27.5579 15.1184i 1.47303 0.808115i
\(351\) 0 0
\(352\) −9.60515 + 5.54553i −0.511956 + 0.295578i
\(353\) −5.44428 3.14326i −0.289770 0.167299i 0.348068 0.937469i \(-0.386838\pi\)
−0.637838 + 0.770171i \(0.720171\pi\)
\(354\) 0 0
\(355\) 5.87334 + 16.9121i 0.311724 + 0.897603i
\(356\) −13.1766 −0.698360
\(357\) 0 0
\(358\) 3.69702i 0.195394i
\(359\) −3.22526 5.58631i −0.170223 0.294834i 0.768275 0.640120i \(-0.221115\pi\)
−0.938498 + 0.345286i \(0.887782\pi\)
\(360\) 0 0
\(361\) −1.29150 + 2.23695i −0.0679738 + 0.117734i
\(362\) −15.1332 + 8.73714i −0.795382 + 0.459214i
\(363\) 0 0
\(364\) −11.3542 30.4547i −0.595124 1.59626i
\(365\) 0.640170 3.34048i 0.0335080 0.174849i
\(366\) 0 0
\(367\) −23.6289 13.6421i −1.23342 0.712114i −0.265676 0.964062i \(-0.585595\pi\)
−0.967741 + 0.251949i \(0.918929\pi\)
\(368\) −1.19968 0.692633i −0.0625374 0.0361060i
\(369\) 0 0
\(370\) −27.2288 5.21812i −1.41556 0.271277i
\(371\) 5.94814 + 15.9543i 0.308812 + 0.828304i
\(372\) 0 0
\(373\) 3.48527 2.01222i 0.180460 0.104189i −0.407049 0.913406i \(-0.633442\pi\)
0.587509 + 0.809218i \(0.300109\pi\)
\(374\) −23.3792 + 40.4939i −1.20891 + 2.09389i
\(375\) 0 0
\(376\) −7.64575 13.2428i −0.394300 0.682947i
\(377\) 26.9786i 1.38947i
\(378\) 0 0
\(379\) −8.29150 −0.425906 −0.212953 0.977062i \(-0.568308\pi\)
−0.212953 + 0.977062i \(0.568308\pi\)
\(380\) 12.4248 + 35.7768i 0.637377 + 1.83531i
\(381\) 0 0
\(382\) −14.8744 8.58772i −0.761039 0.439386i
\(383\) −16.2037 + 9.35523i −0.827972 + 0.478030i −0.853158 0.521653i \(-0.825316\pi\)
0.0251859 + 0.999683i \(0.491982\pi\)
\(384\) 0 0
\(385\) 13.6289 + 16.4757i 0.694595 + 0.839679i
\(386\) 45.9804 2.34034
\(387\) 0 0
\(388\) −38.7868 22.3936i −1.96910 1.13686i
\(389\) 5.55916 9.62875i 0.281861 0.488197i −0.689982 0.723826i \(-0.742382\pi\)
0.971843 + 0.235629i \(0.0757151\pi\)
\(390\) 0 0
\(391\) 3.77124 0.190720
\(392\) −26.8798 + 5.17302i −1.35763 + 0.261277i
\(393\) 0 0
\(394\) 16.7601 + 29.0294i 0.844363 + 1.46248i
\(395\) 14.5335 16.8084i 0.731261 0.845722i
\(396\) 0 0
\(397\) 27.8643 16.0875i 1.39847 0.807408i 0.404239 0.914654i \(-0.367537\pi\)
0.994233 + 0.107246i \(0.0342032\pi\)
\(398\) 29.3547i 1.47142i
\(399\) 0 0
\(400\) 9.29150 + 3.69702i 0.464575 + 0.184851i
\(401\) 5.94814 + 10.3025i 0.297036 + 0.514482i 0.975456 0.220192i \(-0.0706685\pi\)
−0.678420 + 0.734674i \(0.737335\pi\)
\(402\) 0 0
\(403\) 14.5908 + 8.42402i 0.726821 + 0.419630i
\(404\) −30.6077 53.0140i −1.52279 2.63755i
\(405\) 0 0
\(406\) 49.6346 + 8.35347i 2.46333 + 0.414576i
\(407\) 18.8595i 0.934833i
\(408\) 0 0
\(409\) 2.20850 3.82523i 0.109203 0.189145i −0.806245 0.591582i \(-0.798503\pi\)
0.915448 + 0.402437i \(0.131837\pi\)
\(410\) −20.7791 17.9668i −1.02620 0.887317i
\(411\) 0 0
\(412\) 43.5935i 2.14770i
\(413\) 1.92863 0.719041i 0.0949016 0.0353817i
\(414\) 0 0
\(415\) −7.94514 + 2.75923i −0.390012 + 0.135445i
\(416\) −5.17018 + 8.95501i −0.253489 + 0.439055i
\(417\) 0 0
\(418\) −34.5513 + 19.9482i −1.68996 + 0.975699i
\(419\) −26.3533 −1.28744 −0.643720 0.765261i \(-0.722610\pi\)
−0.643720 + 0.765261i \(0.722610\pi\)
\(420\) 0 0
\(421\) 17.2288 0.839678 0.419839 0.907599i \(-0.362086\pi\)
0.419839 + 0.907599i \(0.362086\pi\)
\(422\) −1.92863 + 1.11349i −0.0938842 + 0.0542041i
\(423\) 0 0
\(424\) −12.5830 + 21.7944i −0.611085 + 1.05843i
\(425\) −26.9386 + 3.93124i −1.30671 + 0.190693i
\(426\) 0 0
\(427\) 2.47906 14.7301i 0.119970 0.712839i
\(428\) 29.0565i 1.40450i
\(429\) 0 0
\(430\) 30.9809 35.8302i 1.49403 1.72788i
\(431\) −15.3727 + 26.6264i −0.740478 + 1.28255i 0.211799 + 0.977313i \(0.432068\pi\)
−0.952278 + 0.305233i \(0.901266\pi\)
\(432\) 0 0
\(433\) 7.72146i 0.371070i −0.982638 0.185535i \(-0.940598\pi\)
0.982638 0.185535i \(-0.0594018\pi\)
\(434\) 20.0161 24.2355i 0.960805 1.16334i
\(435\) 0 0
\(436\) −24.1144 41.7673i −1.15487 2.00029i
\(437\) 2.78670 + 1.60890i 0.133306 + 0.0769642i
\(438\) 0 0
\(439\) 1.88562 + 3.26599i 0.0899958 + 0.155877i 0.907509 0.420032i \(-0.137981\pi\)
−0.817513 + 0.575910i \(0.804648\pi\)
\(440\) −5.94814 + 31.0381i −0.283567 + 1.47968i
\(441\) 0 0
\(442\) 43.5935i 2.07353i
\(443\) 3.64477 2.10431i 0.173168 0.0999787i −0.410911 0.911676i \(-0.634789\pi\)
0.584079 + 0.811697i \(0.301456\pi\)
\(444\) 0 0
\(445\) 5.28593 6.11332i 0.250577 0.289799i
\(446\) 0 0
\(447\) 0 0
\(448\) 23.0342 + 19.0240i 1.08826 + 0.898798i
\(449\) −10.3404 −0.487991 −0.243996 0.969776i \(-0.578458\pi\)
−0.243996 + 0.969776i \(0.578458\pi\)
\(450\) 0 0
\(451\) 9.34313 16.1828i 0.439951 0.762018i
\(452\) 40.6384 + 23.4626i 1.91147 + 1.10359i
\(453\) 0 0
\(454\) 56.1033 2.63306
\(455\) 18.6844 + 6.94937i 0.875936 + 0.325791i
\(456\) 0 0
\(457\) −2.35106 + 1.35739i −0.109978 + 0.0634959i −0.553980 0.832530i \(-0.686892\pi\)
0.444002 + 0.896026i \(0.353558\pi\)
\(458\) −17.0618 9.85063i −0.797245 0.460290i
\(459\) 0 0
\(460\) 5.33395 1.85240i 0.248697 0.0863687i
\(461\) −10.8427 −0.504996 −0.252498 0.967597i \(-0.581252\pi\)
−0.252498 + 0.967597i \(0.581252\pi\)
\(462\) 0 0
\(463\) 21.1999i 0.985242i 0.870244 + 0.492621i \(0.163961\pi\)
−0.870244 + 0.492621i \(0.836039\pi\)
\(464\) 8.00645 + 13.8676i 0.371690 + 0.643786i
\(465\) 0 0
\(466\) 8.29150 14.3613i 0.384096 0.665275i
\(467\) 10.3721 5.98833i 0.479964 0.277107i −0.240438 0.970665i \(-0.577291\pi\)
0.720401 + 0.693557i \(0.243958\pi\)
\(468\) 0 0
\(469\) −12.7601 34.2255i −0.589208 1.58039i
\(470\) 20.4051 + 3.91044i 0.941218 + 0.180375i
\(471\) 0 0
\(472\) 2.63461 + 1.52110i 0.121268 + 0.0700141i
\(473\) 27.9046 + 16.1107i 1.28306 + 0.740773i
\(474\) 0 0
\(475\) −21.5830 8.58772i −0.990296 0.394032i
\(476\) 51.7907 + 8.71634i 2.37383 + 0.399513i
\(477\) 0 0
\(478\) 27.1141 15.6544i 1.24017 0.716014i
\(479\) 13.8168 23.9314i 0.631306 1.09345i −0.355979 0.934494i \(-0.615853\pi\)
0.987285 0.158960i \(-0.0508140\pi\)
\(480\) 0 0
\(481\) −8.79150 15.2273i −0.400858 0.694306i
\(482\) 4.20861i 0.191697i
\(483\) 0 0
\(484\) −7.52026 −0.341830
\(485\) 25.9492 9.01179i 1.17829 0.409204i
\(486\) 0 0
\(487\) 3.48527 + 2.01222i 0.157933 + 0.0911824i 0.576883 0.816827i \(-0.304269\pi\)
−0.418951 + 0.908009i \(0.637602\pi\)
\(488\) 19.1195 11.0387i 0.865501 0.499697i
\(489\) 0 0
\(490\) 18.5706 32.2233i 0.838934 1.45570i
\(491\) −7.50408 −0.338654 −0.169327 0.985560i \(-0.554159\pi\)
−0.169327 + 0.985560i \(0.554159\pi\)
\(492\) 0 0
\(493\) −37.7530 21.7967i −1.70031 0.981675i
\(494\) −18.5980 + 32.2127i −0.836763 + 1.44932i
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) 16.3328 + 13.4893i 0.732628 + 0.605078i
\(498\) 0 0
\(499\) −2.50000 4.33013i −0.111915 0.193843i 0.804627 0.593780i \(-0.202365\pi\)
−0.916542 + 0.399937i \(0.869032\pi\)
\(500\) −36.1703 + 18.7923i −1.61758 + 0.840415i
\(501\) 0 0
\(502\) −22.3116 + 12.8816i −0.995814 + 0.574933i
\(503\) 12.8712i 0.573899i 0.957946 + 0.286949i \(0.0926412\pi\)
−0.957946 + 0.286949i \(0.907359\pi\)
\(504\) 0 0
\(505\) 36.8745 + 7.06663i 1.64089 + 0.314461i
\(506\) 2.97407 + 5.15124i 0.132214 + 0.229001i
\(507\) 0 0
\(508\) −10.6389 6.14237i −0.472025 0.272524i
\(509\) −7.22848 12.5201i −0.320397 0.554944i 0.660173 0.751114i \(-0.270483\pi\)
−0.980570 + 0.196170i \(0.937150\pi\)
\(510\) 0 0
\(511\) −1.40588 3.77089i −0.0621925 0.166814i
\(512\) 21.7792i 0.962512i
\(513\) 0 0
\(514\) −7.46863 + 12.9360i −0.329427 + 0.570584i
\(515\) 20.2252 + 17.4879i 0.891231 + 0.770611i
\(516\) 0 0
\(517\) 14.1333i 0.621580i
\(518\) −30.7371 + 11.4595i −1.35051 + 0.503503i
\(519\) 0 0
\(520\) 9.66605 + 27.8332i 0.423884 + 1.22056i
\(521\) −0.777967 + 1.34748i −0.0340834 + 0.0590341i −0.882564 0.470192i \(-0.844185\pi\)
0.848481 + 0.529227i \(0.177518\pi\)
\(522\) 0 0
\(523\) −11.9562 + 6.90292i −0.522809 + 0.301844i −0.738083 0.674710i \(-0.764269\pi\)
0.215274 + 0.976554i \(0.430935\pi\)
\(524\) −42.3662 −1.85077
\(525\) 0 0
\(526\) 12.5830 0.548645
\(527\) −23.5766 + 13.6120i −1.02701 + 0.592947i
\(528\) 0 0
\(529\) −11.2601 + 19.5031i −0.489571 + 0.847962i
\(530\) −11.2175 32.3004i −0.487256 1.40304i
\(531\) 0 0
\(532\) 34.5513 + 28.5359i 1.49799 + 1.23719i
\(533\) 17.4215i 0.754607i
\(534\) 0 0
\(535\) −13.4808 11.6563i −0.582826 0.503946i
\(536\) 26.9934 46.7540i 1.16594 2.01946i
\(537\) 0 0
\(538\) 23.9147i 1.03103i
\(539\) 23.9060 + 8.28127i 1.02970 + 0.356700i
\(540\) 0 0
\(541\) −4.20850 7.28933i −0.180937 0.313393i 0.761263 0.648444i \(-0.224580\pi\)
−0.942200 + 0.335051i \(0.891246\pi\)
\(542\) −8.70170 5.02393i −0.373770 0.215796i
\(543\) 0 0
\(544\) −8.35425 14.4700i −0.358185 0.620395i
\(545\) 29.0517 + 5.56747i 1.24444 + 0.238484i
\(546\) 0 0
\(547\) 26.9569i 1.15259i 0.817241 + 0.576296i \(0.195502\pi\)
−0.817241 + 0.576296i \(0.804498\pi\)
\(548\) −10.1596 + 5.86565i −0.433997 + 0.250568i
\(549\) 0 0
\(550\) −26.6141 33.6959i −1.13483 1.43680i
\(551\) −18.5980 32.2127i −0.792301 1.37231i
\(552\) 0 0
\(553\) 4.36347 25.9269i 0.185554 1.10252i
\(554\) 19.6271 0.833877
\(555\) 0 0
\(556\) −35.0516 + 60.7112i −1.48652 + 2.57473i
\(557\) −38.9680 22.4982i −1.65113 0.953280i −0.976609 0.215023i \(-0.931017\pi\)
−0.674520 0.738257i \(-0.735649\pi\)
\(558\) 0 0
\(559\) 30.0405 1.27058
\(560\) 11.6665 1.97284i 0.493001 0.0833678i
\(561\) 0 0
\(562\) 60.0646 34.6783i 2.53367 1.46282i
\(563\) 13.5461 + 7.82087i 0.570902 + 0.329610i 0.757509 0.652824i \(-0.226416\pi\)
−0.186608 + 0.982435i \(0.559749\pi\)
\(564\) 0 0
\(565\) −27.1880 + 9.44200i −1.14381 + 0.397228i
\(566\) −60.4374 −2.54037
\(567\) 0 0
\(568\) 31.3087i 1.31368i
\(569\) 11.3695 + 19.6926i 0.476635 + 0.825555i 0.999642 0.0267732i \(-0.00852318\pi\)
−0.523007 + 0.852328i \(0.675190\pi\)
\(570\) 0 0
\(571\) 16.2601 28.1634i 0.680465 1.17860i −0.294374 0.955690i \(-0.595111\pi\)
0.974839 0.222910i \(-0.0715556\pi\)
\(572\) −38.4516 + 22.2000i −1.60774 + 0.928230i
\(573\) 0 0
\(574\) −32.0516 5.39426i −1.33781 0.225152i
\(575\) −1.28034 + 3.21780i −0.0533939 + 0.134192i
\(576\) 0 0
\(577\) 5.55278 + 3.20590i 0.231165 + 0.133463i 0.611109 0.791546i \(-0.290724\pi\)
−0.379944 + 0.925009i \(0.624057\pi\)
\(578\) −26.0217 15.0237i −1.08236 0.624902i
\(579\) 0 0
\(580\) −64.1033 12.2847i −2.66174 0.510096i
\(581\) −6.33713 + 7.67300i −0.262908 + 0.318329i
\(582\) 0 0
\(583\) 20.1436 11.6299i 0.834263 0.481662i
\(584\) 2.97407 5.15124i 0.123068 0.213160i
\(585\) 0 0
\(586\) 32.5203 + 56.3267i 1.34340 + 2.32684i
\(587\) 13.3185i 0.549712i 0.961485 + 0.274856i \(0.0886302\pi\)
−0.961485 + 0.274856i \(0.911370\pi\)
\(588\) 0 0
\(589\) −23.2288 −0.957124
\(590\) −3.90464 + 1.35602i −0.160751 + 0.0558266i
\(591\) 0 0
\(592\) −9.03805 5.21812i −0.371461 0.214463i
\(593\) −11.2759 + 6.51015i −0.463046 + 0.267340i −0.713324 0.700834i \(-0.752811\pi\)
0.250278 + 0.968174i \(0.419478\pi\)
\(594\) 0 0
\(595\) −24.8203 + 20.5317i −1.01753 + 0.841720i
\(596\) 16.0129 0.655914
\(597\) 0 0
\(598\) 4.80257 + 2.77277i 0.196392 + 0.113387i
\(599\) −5.03238 + 8.71634i −0.205617 + 0.356140i −0.950329 0.311246i \(-0.899254\pi\)
0.744712 + 0.667386i \(0.232587\pi\)
\(600\) 0 0
\(601\) −35.1033 −1.43189 −0.715946 0.698156i \(-0.754004\pi\)
−0.715946 + 0.698156i \(0.754004\pi\)
\(602\) 9.30154 55.2679i 0.379102 2.25255i
\(603\) 0 0
\(604\) 12.6458 + 21.9031i 0.514548 + 0.891224i
\(605\) 3.01683 3.48904i 0.122651 0.141849i
\(606\) 0 0
\(607\) −23.6289 + 13.6421i −0.959066 + 0.553717i −0.895886 0.444285i \(-0.853458\pi\)
−0.0631807 + 0.998002i \(0.520124\pi\)
\(608\) 14.2565i 0.578176i
\(609\) 0 0
\(610\) −5.64575 + 29.4602i −0.228590 + 1.19281i
\(611\) 6.58831 + 11.4113i 0.266535 + 0.461652i
\(612\) 0 0
\(613\) −15.9081 9.18456i −0.642523 0.370961i 0.143063 0.989714i \(-0.454305\pi\)
−0.785586 + 0.618753i \(0.787638\pi\)
\(614\) 20.0161 + 34.6690i 0.807785 + 1.39913i
\(615\) 0 0
\(616\) 13.0627 + 35.0372i 0.526313 + 1.41169i
\(617\) 30.1964i 1.21566i 0.794067 + 0.607831i \(0.207960\pi\)
−0.794067 + 0.607831i \(0.792040\pi\)
\(618\) 0 0
\(619\) 6.50000 11.2583i 0.261257 0.452510i −0.705319 0.708890i \(-0.749196\pi\)
0.966576 + 0.256379i \(0.0825296\pi\)
\(620\) −26.6601 + 30.8331i −1.07069 + 1.23829i
\(621\) 0 0
\(622\) 39.8964i 1.59970i
\(623\) 1.58702 9.42977i 0.0635827 0.377796i
\(624\) 0 0
\(625\) 5.79137 24.3200i 0.231655 0.972798i
\(626\) 1.80712 3.13003i 0.0722271 0.125101i
\(627\) 0 0
\(628\) 44.6231 25.7632i 1.78066 1.02806i
\(629\) 28.4116 1.13284
\(630\) 0 0
\(631\) −39.1660 −1.55917 −0.779587 0.626294i \(-0.784571\pi\)
−0.779587 + 0.626294i \(0.784571\pi\)
\(632\) 33.6529 19.4295i 1.33864 0.772864i
\(633\) 0 0
\(634\) −23.7601 + 41.1538i −0.943635 + 1.63442i
\(635\) 7.11766 2.47186i 0.282456 0.0980928i
\(636\) 0 0
\(637\) 23.1622 4.45757i 0.917720 0.176615i
\(638\) 68.7572i 2.72212i
\(639\) 0 0
\(640\) −34.9996 30.2628i −1.38348 1.19624i
\(641\) −1.02915 + 1.78255i −0.0406491 + 0.0704064i −0.885634 0.464384i \(-0.846276\pi\)
0.844985 + 0.534790i \(0.179609\pi\)
\(642\) 0 0
\(643\) 39.0302i 1.53920i 0.638526 + 0.769600i \(0.279544\pi\)
−0.638526 + 0.769600i \(0.720456\pi\)
\(644\) 4.25441 5.15124i 0.167647 0.202987i
\(645\) 0 0
\(646\) −30.0516 52.0510i −1.18237 2.04792i
\(647\) 35.1942 + 20.3194i 1.38362 + 0.798836i 0.992587 0.121538i \(-0.0387827\pi\)
0.391038 + 0.920374i \(0.372116\pi\)
\(648\) 0 0
\(649\) −1.40588 2.43506i −0.0551857 0.0955844i
\(650\) −37.1960 14.8000i −1.45895 0.580504i
\(651\) 0 0
\(652\) 38.0479i 1.49007i
\(653\) 12.0049 6.93101i 0.469787 0.271231i −0.246364 0.969177i \(-0.579236\pi\)
0.716150 + 0.697946i \(0.245902\pi\)
\(654\) 0 0
\(655\) 16.9956 19.6558i 0.664073 0.768017i
\(656\) −5.17018 8.95501i −0.201861 0.349634i
\(657\) 0 0
\(658\) 23.0342 8.58772i 0.897967 0.334784i
\(659\) 26.3533 1.02658 0.513289 0.858216i \(-0.328427\pi\)
0.513289 + 0.858216i \(0.328427\pi\)
\(660\) 0 0
\(661\) −6.67712 + 11.5651i −0.259710 + 0.449831i −0.966164 0.257928i \(-0.916960\pi\)
0.706454 + 0.707759i \(0.250294\pi\)
\(662\) −7.37291 4.25675i −0.286556 0.165443i
\(663\) 0 0
\(664\) −14.7085 −0.570800
\(665\) −27.0999 + 4.58266i −1.05089 + 0.177708i
\(666\) 0 0
\(667\) −4.80257 + 2.77277i −0.185956 + 0.107362i
\(668\) 39.2263 + 22.6473i 1.51771 + 0.876250i
\(669\) 0 0
\(670\) 24.0640 + 69.2918i 0.929675 + 2.67698i
\(671\) −20.4051 −0.787731
\(672\) 0 0
\(673\) 10.1088i 0.389666i −0.980836 0.194833i \(-0.937583\pi\)
0.980836 0.194833i \(-0.0624165\pi\)
\(674\) 12.0097 + 20.8014i 0.462595 + 0.801239i
\(675\) 0 0
\(676\) 3.00000 5.19615i 0.115385 0.199852i
\(677\) 39.3554 22.7218i 1.51255 0.873271i 0.512658 0.858593i \(-0.328661\pi\)
0.999892 0.0146783i \(-0.00467241\pi\)
\(678\) 0 0
\(679\) 20.6974 25.0604i 0.794293 0.961730i
\(680\) −46.7584 8.96077i −1.79310 0.343630i
\(681\) 0 0
\(682\) −37.1859 21.4693i −1.42392 0.822102i
\(683\) 20.9648 + 12.1040i 0.802196 + 0.463148i 0.844238 0.535968i \(-0.180053\pi\)
−0.0420428 + 0.999116i \(0.513387\pi\)
\(684\) 0 0
\(685\) 1.35425 7.06663i 0.0517432 0.270002i
\(686\) −1.02915 43.9936i −0.0392933 1.67968i
\(687\) 0 0
\(688\) 15.4415 8.91514i 0.588701 0.339887i
\(689\) 10.8427 18.7802i 0.413075 0.715467i
\(690\) 0 0
\(691\) −1.85425 3.21165i −0.0705389 0.122177i 0.828599 0.559843i \(-0.189139\pi\)
−0.899138 + 0.437666i \(0.855805\pi\)
\(692\) 89.6946i 3.40968i
\(693\) 0 0
\(694\) 64.4575 2.44677
\(695\) −14.1057 40.6172i −0.535061 1.54070i
\(696\) 0 0
\(697\) 24.3791 + 14.0753i 0.923423 + 0.533139i
\(698\) −12.0882 + 6.97915i −0.457547 + 0.264165i
\(699\) 0 0
\(700\) −25.0202 + 41.2311i −0.945674 + 1.55839i
\(701\) −42.8685 −1.61912 −0.809561 0.587036i \(-0.800295\pi\)
−0.809561 + 0.587036i \(0.800295\pi\)
\(702\) 0 0
\(703\) 20.9943 + 12.1210i 0.791813 + 0.457154i
\(704\) 20.4051 35.3427i 0.769047 1.33203i
\(705\) 0 0
\(706\) 14.9373 0.562171
\(707\) 41.6256 15.5191i 1.56549 0.583654i
\(708\) 0 0
\(709\) −5.82288 10.0855i −0.218683 0.378770i 0.735723 0.677283i \(-0.236843\pi\)
−0.954405 + 0.298513i \(0.903509\pi\)
\(710\) −32.1781 27.8231i −1.20762 1.04418i
\(711\) 0 0
\(712\) 12.2398 7.06663i 0.458704 0.264833i
\(713\) 3.46317i 0.129697i
\(714\) 0 0
\(715\) 5.12549 26.7454i 0.191683 1.00022i
\(716\) 2.83627 + 4.91257i 0.105997 + 0.183591i
\(717\) 0 0
\(718\) 13.2735 + 7.66347i 0.495363 + 0.285998i
\(719\) −2.97407 5.15124i −0.110914 0.192109i 0.805225 0.592969i \(-0.202045\pi\)
−0.916139 + 0.400861i \(0.868711\pi\)
\(720\) 0 0
\(721\) 31.1974 + 5.25049i 1.16185 + 0.195539i
\(722\) 6.13742i 0.228411i
\(723\) 0 0
\(724\) 13.4059 23.2197i 0.498226 0.862952i
\(725\) 31.4152 24.8127i 1.16673 0.921519i
\(726\) 0 0
\(727\) 20.0062i 0.741989i −0.928635 0.370995i \(-0.879017\pi\)
0.928635 0.370995i \(-0.120983\pi\)
\(728\) 26.8798 + 22.2000i 0.996232 + 0.822788i
\(729\) 0 0
\(730\) 2.65132 + 7.63441i 0.0981298 + 0.282562i
\(731\) −24.2705 + 42.0378i −0.897678 + 1.55482i
\(732\) 0 0
\(733\) −17.7925 + 10.2725i −0.657182 + 0.379424i −0.791203 0.611554i \(-0.790545\pi\)
0.134020 + 0.990979i \(0.457211\pi\)
\(734\) 64.8296 2.39290
\(735\) 0 0
\(736\) −2.12549 −0.0783467
\(737\) −43.2126 + 24.9488i −1.59176 + 0.919002i
\(738\) 0 0
\(739\) −1.96863 + 3.40976i −0.0724171 + 0.125430i −0.899960 0.435972i \(-0.856405\pi\)
0.827543 + 0.561402i \(0.189738\pi\)
\(740\) 40.1846 13.9555i 1.47721 0.513015i
\(741\) 0 0
\(742\) −31.1941 25.7632i −1.14517 0.945796i
\(743\) 4.90125i 0.179809i −0.995950 0.0899047i \(-0.971344\pi\)
0.995950 0.0899047i \(-0.0286562\pi\)
\(744\) 0 0
\(745\) −6.42373 + 7.42921i −0.235347 + 0.272185i
\(746\) −4.78119 + 8.28127i −0.175052 + 0.303199i
\(747\) 0 0
\(748\) 71.7440i 2.62322i
\(749\) −20.7941 3.49963i −0.759800 0.127874i
\(750\) 0 0
\(751\) 12.7288 + 22.0469i 0.464479 + 0.804501i 0.999178 0.0405415i \(-0.0129083\pi\)
−0.534699 + 0.845043i \(0.679575\pi\)
\(752\) 6.77307 + 3.91044i 0.246989 + 0.142599i
\(753\) 0 0
\(754\) −32.0516 55.5151i −1.16725 2.02174i
\(755\) −15.2349 2.91962i −0.554456 0.106256i
\(756\) 0 0
\(757\) 33.6961i 1.22470i −0.790585 0.612352i \(-0.790223\pi\)
0.790585 0.612352i \(-0.209777\pi\)
\(758\) 17.0618 9.85063i 0.619712 0.357791i
\(759\) 0 0
\(760\) −30.7284 26.5696i −1.11464 0.963782i
\(761\) 20.7941 + 36.0164i 0.753785 + 1.30559i 0.945976 + 0.324237i \(0.105108\pi\)
−0.192191 + 0.981358i \(0.561559\pi\)
\(762\) 0 0
\(763\) 32.7949 12.2268i 1.18726 0.442638i
\(764\) 26.3533 0.953427
\(765\) 0 0
\(766\) 22.2288 38.5013i 0.803158 1.39111i
\(767\) −2.27024 1.31072i −0.0819735 0.0473274i
\(768\) 0 0
\(769\) 19.3542 0.697932 0.348966 0.937135i \(-0.386533\pi\)
0.348966 + 0.937135i \(0.386533\pi\)
\(770\) −47.6186 17.7110i −1.71606 0.638262i
\(771\) 0 0
\(772\) −61.0984 + 35.2752i −2.19898 + 1.26958i
\(773\) −20.9191 12.0776i −0.752406 0.434402i 0.0741565 0.997247i \(-0.476374\pi\)
−0.826563 + 0.562845i \(0.809707\pi\)
\(774\) 0 0
\(775\) −3.61009 24.7380i −0.129678 0.888614i
\(776\) 48.0387 1.72449
\(777\) 0 0
\(778\) 26.4180i 0.947131i
\(779\) 12.0097 + 20.8014i 0.430291 + 0.745286i
\(780\) 0 0
\(781\) 14.4686 25.0604i 0.517728 0.896732i
\(782\) −7.76026 + 4.48039i −0.277506 + 0.160218i
\(783\) 0 0
\(784\) 10.5830 9.16515i 0.377964 0.327327i
\(785\) −5.94814 + 31.0381i −0.212298 + 1.10780i
\(786\) 0 0
\(787\) −20.7107 11.9573i −0.738257 0.426233i 0.0831783 0.996535i \(-0.473493\pi\)
−0.821435 + 0.570302i \(0.806826\pi\)
\(788\) −44.5414 25.7160i −1.58672 0.916095i
\(789\) 0 0
\(790\) −9.93725 + 51.8538i −0.353552 + 1.84487i
\(791\) −21.6855 + 26.2568i −0.771046 + 0.933583i
\(792\) 0 0
\(793\) −16.4752 + 9.51198i −0.585053 + 0.337780i
\(794\) −38.2251 + 66.2079i −1.35656 + 2.34963i
\(795\) 0 0
\(796\) −22.5203 39.0062i −0.798209 1.38254i
\(797\) 23.6117i 0.836369i 0.908362 + 0.418185i \(0.137334\pi\)
−0.908362 + 0.418185i \(0.862666\pi\)
\(798\) 0 0
\(799\) −21.2915 −0.753239
\(800\) 15.1827 2.21566i 0.536791 0.0783356i
\(801\) 0 0
\(802\) −24.4795 14.1333i −0.864402 0.499063i
\(803\) −4.76107 + 2.74880i −0.168014 + 0.0970032i
\(804\) 0 0
\(805\) 0.683228 + 4.04031i 0.0240806 + 0.142402i
\(806\) −40.0323 −1.41008
\(807\) 0 0
\(808\) 56.8629 + 32.8298i 2.00043 + 1.15495i
\(809\) 24.6595 42.7115i 0.866983 1.50166i 0.00191780 0.999998i \(-0.499390\pi\)
0.865065 0.501660i \(-0.167277\pi\)
\(810\) 0 0
\(811\) 13.7712 0.483574 0.241787 0.970329i \(-0.422267\pi\)
0.241787 + 0.970329i \(0.422267\pi\)
\(812\) −72.3627 + 26.9786i −2.53943 + 0.946763i
\(813\) 0 0
\(814\) 22.4059 + 38.8081i 0.785326 + 1.36022i
\(815\) −17.6524 15.2633i −0.618336 0.534650i
\(816\) 0 0
\(817\) −35.8686 + 20.7088i −1.25488 + 0.724508i
\(818\) 10.4951i 0.366954i
\(819\) 0 0
\(820\) 41.3948 + 7.93289i 1.44557 + 0.277029i
\(821\) −6.97730 12.0850i −0.243509 0.421771i 0.718202 0.695835i \(-0.244965\pi\)
−0.961711 + 0.274064i \(0.911632\pi\)
\(822\) 0 0
\(823\) 32.4838 + 18.7545i 1.13231 + 0.653742i 0.944516 0.328465i \(-0.106531\pi\)
0.187799 + 0.982208i \(0.439865\pi\)
\(824\) 23.3792 + 40.4939i 0.814452 + 1.41067i
\(825\) 0 0
\(826\) −3.11438 + 3.77089i −0.108363 + 0.131206i
\(827\) 14.5018i 0.504278i 0.967691 + 0.252139i \(0.0811341\pi\)
−0.967691 + 0.252139i \(0.918866\pi\)
\(828\) 0 0
\(829\) −13.5516 + 23.4721i −0.470668 + 0.815220i −0.999437 0.0335452i \(-0.989320\pi\)
0.528770 + 0.848765i \(0.322654\pi\)
\(830\) 13.0710 15.1169i 0.453701 0.524716i
\(831\) 0 0
\(832\) 38.0479i 1.31907i
\(833\) −12.4756 + 36.0139i −0.432253 + 1.24781i
\(834\) 0 0
\(835\) −26.2432 + 9.11390i −0.908185 + 0.315399i
\(836\) 30.6077 53.0140i 1.05859 1.83353i
\(837\) 0 0
\(838\) 54.2283 31.3087i 1.87328 1.08154i
\(839\) 28.6872 0.990391 0.495195 0.868782i \(-0.335096\pi\)
0.495195 + 0.868782i \(0.335096\pi\)
\(840\) 0 0
\(841\) 35.1033 1.21046
\(842\) −35.4524 + 20.4684i −1.22177 + 0.705389i
\(843\) 0 0
\(844\) 1.70850 2.95920i 0.0588089 0.101860i
\(845\) 1.20728 + 3.47634i 0.0415318 + 0.119590i
\(846\) 0 0
\(847\) 0.905757 5.38183i 0.0311222 0.184922i
\(848\) 12.8712i 0.441999i
\(849\) 0 0
\(850\) 50.7623 40.0936i 1.74113 1.37520i
\(851\) 1.80712 3.13003i 0.0619473 0.107296i
\(852\) 0 0
\(853\) 15.6544i 0.535995i −0.963420 0.267997i \(-0.913638\pi\)
0.963420 0.267997i \(-0.0863619\pi\)
\(854\) 12.3987 + 33.2560i 0.424273 + 1.13800i
\(855\) 0 0
\(856\) −15.5830 26.9906i −0.532616 0.922518i
\(857\) −23.8806 13.7875i −0.815746 0.470971i 0.0332013 0.999449i \(-0.489430\pi\)
−0.848947 + 0.528478i \(0.822763\pi\)
\(858\) 0 0
\(859\) 16.4686 + 28.5245i 0.561902 + 0.973243i 0.997330 + 0.0730199i \(0.0232636\pi\)
−0.435428 + 0.900223i \(0.643403\pi\)
\(860\) −13.6790 + 71.3786i −0.466450 + 2.43399i
\(861\) 0 0
\(862\) 73.0537i 2.48822i
\(863\) 32.8782 18.9822i 1.11919 0.646162i 0.177993 0.984032i \(-0.443040\pi\)
0.941193 + 0.337869i \(0.109706\pi\)
\(864\) 0 0
\(865\) 41.6140 + 35.9819i 1.41492 + 1.22342i
\(866\) 9.17340 + 15.8888i 0.311725 + 0.539923i
\(867\) 0 0
\(868\) −8.00429 + 47.5599i −0.271683 + 1.61429i
\(869\) −35.9156 −1.21835
\(870\) 0 0
\(871\) −23.2601 + 40.2877i −0.788139 + 1.36510i
\(872\) 44.7997 + 25.8651i 1.51711 + 0.875903i
\(873\) 0 0
\(874\) −7.64575 −0.258621
\(875\) −9.09213 28.1484i −0.307370 0.951590i
\(876\) 0 0
\(877\) −18.6432 + 10.7637i −0.629536 + 0.363463i −0.780572 0.625065i \(-0.785072\pi\)
0.151036 + 0.988528i \(0.451739\pi\)
\(878\) −7.76026 4.48039i −0.261896 0.151206i
\(879\) 0 0
\(880\) −5.30264 15.2688i −0.178752 0.514712i
\(881\) 24.5217 0.826158 0.413079 0.910695i \(-0.364453\pi\)
0.413079 + 0.910695i \(0.364453\pi\)
\(882\) 0 0
\(883\) 35.8720i 1.20719i −0.797292 0.603594i \(-0.793735\pi\)
0.797292 0.603594i \(-0.206265\pi\)
\(884\) −33.4439 57.9266i −1.12484 1.94828i
\(885\) 0 0
\(886\) −5.00000 + 8.66025i −0.167978 + 0.290947i
\(887\) 32.7948 18.9341i 1.10114 0.635744i 0.164621 0.986357i \(-0.447360\pi\)
0.936521 + 0.350612i \(0.114027\pi\)
\(888\) 0 0
\(889\) 5.67712 6.87386i 0.190405 0.230542i
\(890\) −3.61424 + 18.8595i −0.121150 + 0.632173i
\(891\) 0 0
\(892\) 0 0
\(893\) −15.7330 9.08345i −0.526485 0.303966i
\(894\) 0 0
\(895\) −3.41699 0.654833i −0.114218 0.0218886i
\(896\) −53.9869 9.08594i −1.80357 0.303540i
\(897\) 0 0
\(898\) 21.2778 12.2847i 0.710050 0.409947i
\(899\) 20.0161 34.6690i 0.667575 1.15627i
\(900\) 0 0
\(901\) 17.5203 + 30.3460i 0.583684 + 1.01097i
\(902\) 44.4001i 1.47836i
\(903\) 0 0
\(904\) −50.3320 −1.67402
\(905\) 5.39490 + 15.5345i 0.179332 + 0.516383i
\(906\) 0 0
\(907\) 4.51902 + 2.60906i 0.150052 + 0.0866324i 0.573146 0.819453i \(-0.305723\pi\)
−0.423094 + 0.906086i \(0.639056\pi\)
\(908\) −74.5495 + 43.0412i −2.47401 + 1.42837i
\(909\) 0 0
\(910\) −46.7037 + 7.89773i −1.54821 + 0.261807i
\(911\) 37.1960 1.23236 0.616179 0.787606i \(-0.288680\pi\)
0.616179 + 0.787606i \(0.288680\pi\)
\(912\) 0 0
\(913\) 11.7731 + 6.79721i 0.389633 + 0.224955i
\(914\) 3.22526 5.58631i 0.106682 0.184779i
\(915\) 0 0
\(916\) 30.2288 0.998786
\(917\) 5.10267 30.3191i 0.168505 1.00122i
\(918\) 0 0
\(919\) 11.4373 + 19.8099i 0.377280 + 0.653468i 0.990665 0.136315i \(-0.0435260\pi\)
−0.613385 + 0.789784i \(0.710193\pi\)
\(920\) −3.96126 + 4.58129i −0.130599 + 0.151041i
\(921\) 0 0
\(922\) 22.3116 12.8816i 0.734792 0.424232i
\(923\) 26.9786i 0.888011i
\(924\) 0 0
\(925\) −9.64575 + 24.2421i −0.317150 + 0.797075i
\(926\) −25.1863 43.6240i −0.827673 1.43357i
\(927\) 0 0
\(928\) 21.2778 + 12.2847i 0.698478 + 0.403267i
\(929\) 27.3824 + 47.4277i 0.898388 + 1.55605i 0.829555 + 0.558425i \(0.188594\pi\)
0.0688327 + 0.997628i \(0.478073\pi\)
\(930\) 0 0
\(931\) −24.5830 + 21.2895i −0.805675 + 0.697735i
\(932\) 25.4442i 0.833454i
\(933\) 0 0
\(934\) −14.2288 + 24.6449i −0.465579 + 0.806407i
\(935\) 33.2857 + 28.7808i 1.08856 + 0.941233i
\(936\) 0 0
\(937\) 53.7023i 1.75438i 0.480146 + 0.877188i \(0.340584\pi\)
−0.480146 + 0.877188i \(0.659416\pi\)
\(938\) 66.9184 + 55.2679i 2.18496 + 1.80456i
\(939\) 0 0
\(940\) −30.1141 + 10.4582i −0.982215 + 0.341109i
\(941\) −17.9578 + 31.1039i −0.585408 + 1.01396i 0.409416 + 0.912348i \(0.365732\pi\)
−0.994824 + 0.101609i \(0.967601\pi\)
\(942\) 0 0
\(943\) 3.10127 1.79052i 0.100991 0.0583073i
\(944\) −1.55593 −0.0506414
\(945\) 0 0
\(946\) −76.5608 −2.48921
\(947\) 18.7322 10.8150i 0.608715 0.351442i −0.163748 0.986502i \(-0.552358\pi\)
0.772462 + 0.635061i \(0.219025\pi\)
\(948\) 0 0
\(949\) −2.56275 + 4.43881i −0.0831903 + 0.144090i
\(950\) 54.6149 7.97012i 1.77194 0.258585i
\(951\) 0 0
\(952\) −52.7830 + 19.6788i −1.71071 + 0.637793i
\(953\) 21.1828i 0.686178i 0.939303 + 0.343089i \(0.111473\pi\)
−0.939303 + 0.343089i \(0.888527\pi\)
\(954\) 0 0
\(955\) −10.5719 + 12.2266i −0.342098 + 0.395645i
\(956\) −24.0194 + 41.6027i −0.776841 + 1.34553i
\(957\) 0 0
\(958\) 65.6596i 2.12137i
\(959\) −2.97407 7.97713i −0.0960378 0.257595i
\(960\) 0 0
\(961\) 3.00000 + 5.19615i 0.0967742 + 0.167618i
\(962\) 36.1813 + 20.8893i 1.16653 + 0.673498i
\(963\) 0 0
\(964\) 3.22876 + 5.59237i 0.103991 + 0.180118i
\(965\) 8.14425 42.4976i 0.262173 1.36805i
\(966\) 0 0
\(967\) 33.4846i 1.07679i −0.842692 0.538397i \(-0.819030\pi\)
0.842692 0.538397i \(-0.180970\pi\)
\(968\) 6.98556 4.03312i 0.224525 0.129629i
\(969\) 0 0
\(970\) −42.6905 + 49.3727i −1.37071 + 1.58526i
\(971\) −29.8297 51.6666i −0.957281 1.65806i −0.729061 0.684449i \(-0.760043\pi\)
−0.228220 0.973610i \(-0.573291\pi\)
\(972\) 0 0
\(973\) −39.2259 32.3967i −1.25752 1.03859i
\(974\) −9.56239 −0.306399
\(975\) 0 0
\(976\) −5.64575 + 9.77873i −0.180716 + 0.313009i
\(977\) −26.0675 15.0501i −0.833972 0.481494i 0.0212386 0.999774i \(-0.493239\pi\)
−0.855211 + 0.518280i \(0.826572\pi\)
\(978\) 0 0
\(979\) −13.0627 −0.417487
\(980\) 0.0445851 + 57.0650i 0.00142422 + 1.82288i
\(981\) 0 0
\(982\) 15.4415 8.91514i 0.492757 0.284494i
\(983\) 34.2527 + 19.7758i 1.09249 + 0.630750i 0.934239 0.356648i \(-0.116081\pi\)
0.158253 + 0.987399i \(0.449414\pi\)
\(984\) 0 0
\(985\) 29.7992 10.3488i 0.949482 0.329741i
\(986\) 103.581 3.29871
\(987\) 0 0
\(988\) 57.0719i 1.81570i
\(989\) 3.08746 + 5.34764i 0.0981756 + 0.170045i
\(990\) 0 0
\(991\) −26.1974 + 45.3752i −0.832187 + 1.44139i 0.0641128 + 0.997943i \(0.479578\pi\)
−0.896300 + 0.443448i \(0.853755\pi\)
\(992\) 13.2879 7.67178i 0.421892 0.243579i
\(993\) 0 0
\(994\) −49.6346 8.35347i −1.57432 0.264956i
\(995\) 27.1312 + 5.19943i 0.860118 + 0.164833i
\(996\) 0 0
\(997\) 27.8643 + 16.0875i 0.882473 + 0.509496i 0.871473 0.490444i \(-0.163165\pi\)
0.0109997 + 0.999940i \(0.496499\pi\)
\(998\) 10.2887 + 5.94020i 0.325684 + 0.188034i
\(999\) 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 315.2.bf.c.109.2 yes 16
3.2 odd 2 inner 315.2.bf.c.109.7 yes 16
5.4 even 2 inner 315.2.bf.c.109.8 yes 16
7.2 even 3 inner 315.2.bf.c.289.8 yes 16
7.3 odd 6 2205.2.d.r.1324.2 8
7.4 even 3 2205.2.d.p.1324.1 8
15.14 odd 2 inner 315.2.bf.c.109.1 16
21.2 odd 6 inner 315.2.bf.c.289.1 yes 16
21.11 odd 6 2205.2.d.p.1324.8 8
21.17 even 6 2205.2.d.r.1324.7 8
35.4 even 6 2205.2.d.p.1324.7 8
35.9 even 6 inner 315.2.bf.c.289.2 yes 16
35.24 odd 6 2205.2.d.r.1324.8 8
105.44 odd 6 inner 315.2.bf.c.289.7 yes 16
105.59 even 6 2205.2.d.r.1324.1 8
105.74 odd 6 2205.2.d.p.1324.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bf.c.109.1 16 15.14 odd 2 inner
315.2.bf.c.109.2 yes 16 1.1 even 1 trivial
315.2.bf.c.109.7 yes 16 3.2 odd 2 inner
315.2.bf.c.109.8 yes 16 5.4 even 2 inner
315.2.bf.c.289.1 yes 16 21.2 odd 6 inner
315.2.bf.c.289.2 yes 16 35.9 even 6 inner
315.2.bf.c.289.7 yes 16 105.44 odd 6 inner
315.2.bf.c.289.8 yes 16 7.2 even 3 inner
2205.2.d.p.1324.1 8 7.4 even 3
2205.2.d.p.1324.2 8 105.74 odd 6
2205.2.d.p.1324.7 8 35.4 even 6
2205.2.d.p.1324.8 8 21.11 odd 6
2205.2.d.r.1324.1 8 105.59 even 6
2205.2.d.r.1324.2 8 7.3 odd 6
2205.2.d.r.1324.7 8 21.17 even 6
2205.2.d.r.1324.8 8 35.24 odd 6