Properties

Label 315.2.m.b.197.3
Level $315$
Weight $2$
Character 315.197
Analytic conductor $2.515$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(8,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.m (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 197.3
Root \(-0.203482i\) of defining polynomial
Character \(\chi\) \(=\) 315.197
Dual form 315.2.m.b.8.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.876184 + 0.876184i) q^{2} +0.464602i q^{4} +(-0.0251942 - 2.23593i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-2.15945 - 2.15945i) q^{8} +O(q^{10})\) \(q+(-0.876184 + 0.876184i) q^{2} +0.464602i q^{4} +(-0.0251942 - 2.23593i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-2.15945 - 2.15945i) q^{8} +(1.98116 + 1.93701i) q^{10} -4.66231i q^{11} +(1.54889 - 1.54889i) q^{13} +1.23911 q^{14} +2.85494 q^{16} +(-2.32993 + 2.32993i) q^{17} -3.54791i q^{19} +(1.03882 - 0.0117053i) q^{20} +(4.08504 + 4.08504i) q^{22} +(-1.44259 - 1.44259i) q^{23} +(-4.99873 + 0.112665i) q^{25} +2.71422i q^{26} +(0.328523 - 0.328523i) q^{28} +7.58625 q^{29} +8.12691 q^{31} +(1.81744 - 1.81744i) q^{32} -4.08289i q^{34} +(-1.56322 + 1.59885i) q^{35} +(-6.00046 - 6.00046i) q^{37} +(3.10862 + 3.10862i) q^{38} +(-4.77396 + 4.88277i) q^{40} +6.72475i q^{41} +(5.46460 - 5.46460i) q^{43} +2.16612 q^{44} +2.52796 q^{46} +(-5.16658 + 5.16658i) q^{47} +1.00000i q^{49} +(4.28109 - 4.47852i) q^{50} +(0.719616 + 0.719616i) q^{52} +(-6.86452 - 6.86452i) q^{53} +(-10.4246 + 0.117463i) q^{55} +3.05392i q^{56} +(-6.64695 + 6.64695i) q^{58} +6.40696 q^{59} -13.6036 q^{61} +(-7.12067 + 7.12067i) q^{62} +8.89470i q^{64} +(-3.50222 - 3.42417i) q^{65} +(2.77125 + 2.77125i) q^{67} +(-1.08249 - 1.08249i) q^{68} +(-0.0312185 - 2.77056i) q^{70} +0.576549i q^{71} +(-4.94384 + 4.94384i) q^{73} +10.5150 q^{74} +1.64837 q^{76} +(-3.29675 + 3.29675i) q^{77} -2.50976i q^{79} +(-0.0719280 - 6.38344i) q^{80} +(-5.89212 - 5.89212i) q^{82} +(3.99501 + 3.99501i) q^{83} +(5.26825 + 5.15085i) q^{85} +9.57600i q^{86} +(-10.0680 + 10.0680i) q^{88} -6.86727 q^{89} -2.19046 q^{91} +(0.670232 - 0.670232i) q^{92} -9.05376i q^{94} +(-7.93287 + 0.0893869i) q^{95} +(4.43407 + 4.43407i) q^{97} +(-0.876184 - 0.876184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{5} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{5} - 24 q^{8} + 16 q^{10} - 4 q^{13} + 4 q^{14} - 20 q^{16} - 8 q^{17} + 12 q^{20} - 8 q^{22} - 8 q^{23} - 8 q^{25} + 32 q^{29} - 48 q^{32} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 28 q^{40} + 40 q^{43} + 64 q^{44} + 16 q^{46} - 24 q^{47} + 16 q^{50} + 36 q^{52} + 40 q^{53} - 16 q^{55} - 28 q^{58} + 80 q^{59} - 32 q^{61} - 16 q^{62} - 48 q^{65} - 48 q^{67} - 32 q^{68} + 8 q^{70} - 20 q^{73} + 64 q^{74} + 16 q^{76} - 36 q^{80} + 20 q^{82} - 24 q^{83} + 56 q^{89} - 8 q^{92} - 56 q^{95} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.876184 + 0.876184i −0.619556 + 0.619556i −0.945417 0.325862i \(-0.894346\pi\)
0.325862 + 0.945417i \(0.394346\pi\)
\(3\) 0 0
\(4\) 0.464602i 0.232301i
\(5\) −0.0251942 2.23593i −0.0112672 0.999937i
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −2.15945 2.15945i −0.763479 0.763479i
\(9\) 0 0
\(10\) 1.98116 + 1.93701i 0.626497 + 0.612536i
\(11\) 4.66231i 1.40574i −0.711319 0.702870i \(-0.751902\pi\)
0.711319 0.702870i \(-0.248098\pi\)
\(12\) 0 0
\(13\) 1.54889 1.54889i 0.429584 0.429584i −0.458903 0.888487i \(-0.651757\pi\)
0.888487 + 0.458903i \(0.151757\pi\)
\(14\) 1.23911 0.331167
\(15\) 0 0
\(16\) 2.85494 0.713735
\(17\) −2.32993 + 2.32993i −0.565091 + 0.565091i −0.930749 0.365658i \(-0.880844\pi\)
0.365658 + 0.930749i \(0.380844\pi\)
\(18\) 0 0
\(19\) 3.54791i 0.813946i −0.913440 0.406973i \(-0.866584\pi\)
0.913440 0.406973i \(-0.133416\pi\)
\(20\) 1.03882 0.0117053i 0.232286 0.00261738i
\(21\) 0 0
\(22\) 4.08504 + 4.08504i 0.870934 + 0.870934i
\(23\) −1.44259 1.44259i −0.300802 0.300802i 0.540526 0.841327i \(-0.318225\pi\)
−0.841327 + 0.540526i \(0.818225\pi\)
\(24\) 0 0
\(25\) −4.99873 + 0.112665i −0.999746 + 0.0225330i
\(26\) 2.71422i 0.532303i
\(27\) 0 0
\(28\) 0.328523 0.328523i 0.0620851 0.0620851i
\(29\) 7.58625 1.40873 0.704366 0.709837i \(-0.251232\pi\)
0.704366 + 0.709837i \(0.251232\pi\)
\(30\) 0 0
\(31\) 8.12691 1.45964 0.729818 0.683641i \(-0.239605\pi\)
0.729818 + 0.683641i \(0.239605\pi\)
\(32\) 1.81744 1.81744i 0.321280 0.321280i
\(33\) 0 0
\(34\) 4.08289i 0.700211i
\(35\) −1.56322 + 1.59885i −0.264233 + 0.270256i
\(36\) 0 0
\(37\) −6.00046 6.00046i −0.986470 0.986470i 0.0134395 0.999910i \(-0.495722\pi\)
−0.999910 + 0.0134395i \(0.995722\pi\)
\(38\) 3.10862 + 3.10862i 0.504285 + 0.504285i
\(39\) 0 0
\(40\) −4.77396 + 4.88277i −0.754829 + 0.772033i
\(41\) 6.72475i 1.05023i 0.851032 + 0.525114i \(0.175977\pi\)
−0.851032 + 0.525114i \(0.824023\pi\)
\(42\) 0 0
\(43\) 5.46460 5.46460i 0.833344 0.833344i −0.154629 0.987973i \(-0.549418\pi\)
0.987973 + 0.154629i \(0.0494181\pi\)
\(44\) 2.16612 0.326555
\(45\) 0 0
\(46\) 2.52796 0.372727
\(47\) −5.16658 + 5.16658i −0.753623 + 0.753623i −0.975154 0.221530i \(-0.928895\pi\)
0.221530 + 0.975154i \(0.428895\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 4.28109 4.47852i 0.605438 0.633359i
\(51\) 0 0
\(52\) 0.719616 + 0.719616i 0.0997928 + 0.0997928i
\(53\) −6.86452 6.86452i −0.942915 0.942915i 0.0555419 0.998456i \(-0.482311\pi\)
−0.998456 + 0.0555419i \(0.982311\pi\)
\(54\) 0 0
\(55\) −10.4246 + 0.117463i −1.40565 + 0.0158387i
\(56\) 3.05392i 0.408097i
\(57\) 0 0
\(58\) −6.64695 + 6.64695i −0.872788 + 0.872788i
\(59\) 6.40696 0.834116 0.417058 0.908880i \(-0.363061\pi\)
0.417058 + 0.908880i \(0.363061\pi\)
\(60\) 0 0
\(61\) −13.6036 −1.74176 −0.870879 0.491498i \(-0.836450\pi\)
−0.870879 + 0.491498i \(0.836450\pi\)
\(62\) −7.12067 + 7.12067i −0.904326 + 0.904326i
\(63\) 0 0
\(64\) 8.89470i 1.11184i
\(65\) −3.50222 3.42417i −0.434397 0.424716i
\(66\) 0 0
\(67\) 2.77125 + 2.77125i 0.338562 + 0.338562i 0.855826 0.517264i \(-0.173049\pi\)
−0.517264 + 0.855826i \(0.673049\pi\)
\(68\) −1.08249 1.08249i −0.131271 0.131271i
\(69\) 0 0
\(70\) −0.0312185 2.77056i −0.00373132 0.331146i
\(71\) 0.576549i 0.0684238i 0.999415 + 0.0342119i \(0.0108921\pi\)
−0.999415 + 0.0342119i \(0.989108\pi\)
\(72\) 0 0
\(73\) −4.94384 + 4.94384i −0.578632 + 0.578632i −0.934526 0.355894i \(-0.884176\pi\)
0.355894 + 0.934526i \(0.384176\pi\)
\(74\) 10.5150 1.22235
\(75\) 0 0
\(76\) 1.64837 0.189081
\(77\) −3.29675 + 3.29675i −0.375700 + 0.375700i
\(78\) 0 0
\(79\) 2.50976i 0.282370i −0.989983 0.141185i \(-0.954909\pi\)
0.989983 0.141185i \(-0.0450913\pi\)
\(80\) −0.0719280 6.38344i −0.00804180 0.713690i
\(81\) 0 0
\(82\) −5.89212 5.89212i −0.650675 0.650675i
\(83\) 3.99501 + 3.99501i 0.438509 + 0.438509i 0.891510 0.453001i \(-0.149647\pi\)
−0.453001 + 0.891510i \(0.649647\pi\)
\(84\) 0 0
\(85\) 5.26825 + 5.15085i 0.571422 + 0.558688i
\(86\) 9.57600i 1.03261i
\(87\) 0 0
\(88\) −10.0680 + 10.0680i −1.07325 + 1.07325i
\(89\) −6.86727 −0.727929 −0.363964 0.931413i \(-0.618577\pi\)
−0.363964 + 0.931413i \(0.618577\pi\)
\(90\) 0 0
\(91\) −2.19046 −0.229622
\(92\) 0.670232 0.670232i 0.0698765 0.0698765i
\(93\) 0 0
\(94\) 9.05376i 0.933824i
\(95\) −7.93287 + 0.0893869i −0.813895 + 0.00917090i
\(96\) 0 0
\(97\) 4.43407 + 4.43407i 0.450212 + 0.450212i 0.895425 0.445213i \(-0.146872\pi\)
−0.445213 + 0.895425i \(0.646872\pi\)
\(98\) −0.876184 0.876184i −0.0885080 0.0885080i
\(99\) 0 0
\(100\) −0.0523443 2.32242i −0.00523443 0.232242i
\(101\) 2.63552i 0.262244i −0.991366 0.131122i \(-0.958142\pi\)
0.991366 0.131122i \(-0.0418579\pi\)
\(102\) 0 0
\(103\) 7.45961 7.45961i 0.735017 0.735017i −0.236592 0.971609i \(-0.576030\pi\)
0.971609 + 0.236592i \(0.0760304\pi\)
\(104\) −6.68947 −0.655957
\(105\) 0 0
\(106\) 12.0292 1.16838
\(107\) −4.48615 + 4.48615i −0.433692 + 0.433692i −0.889882 0.456190i \(-0.849214\pi\)
0.456190 + 0.889882i \(0.349214\pi\)
\(108\) 0 0
\(109\) 7.54504i 0.722684i −0.932433 0.361342i \(-0.882319\pi\)
0.932433 0.361342i \(-0.117681\pi\)
\(110\) 9.03093 9.23677i 0.861066 0.880692i
\(111\) 0 0
\(112\) −2.01875 2.01875i −0.190754 0.190754i
\(113\) 1.80305 + 1.80305i 0.169617 + 0.169617i 0.786811 0.617194i \(-0.211731\pi\)
−0.617194 + 0.786811i \(0.711731\pi\)
\(114\) 0 0
\(115\) −3.18919 + 3.26188i −0.297393 + 0.304172i
\(116\) 3.52459i 0.327250i
\(117\) 0 0
\(118\) −5.61368 + 5.61368i −0.516781 + 0.516781i
\(119\) 3.29502 0.302054
\(120\) 0 0
\(121\) −10.7371 −0.976102
\(122\) 11.9192 11.9192i 1.07912 1.07912i
\(123\) 0 0
\(124\) 3.77578i 0.339075i
\(125\) 0.377849 + 11.1740i 0.0337959 + 0.999429i
\(126\) 0 0
\(127\) 14.3511 + 14.3511i 1.27346 + 1.27346i 0.944262 + 0.329195i \(0.106777\pi\)
0.329195 + 0.944262i \(0.393223\pi\)
\(128\) −4.15852 4.15852i −0.367565 0.367565i
\(129\) 0 0
\(130\) 6.06880 0.0683827i 0.532269 0.00599756i
\(131\) 3.22579i 0.281839i 0.990021 + 0.140919i \(0.0450059\pi\)
−0.990021 + 0.140919i \(0.954994\pi\)
\(132\) 0 0
\(133\) −2.50875 + 2.50875i −0.217536 + 0.217536i
\(134\) −4.85626 −0.419517
\(135\) 0 0
\(136\) 10.0627 0.862870
\(137\) 1.36108 1.36108i 0.116285 0.116285i −0.646570 0.762855i \(-0.723797\pi\)
0.762855 + 0.646570i \(0.223797\pi\)
\(138\) 0 0
\(139\) 22.2867i 1.89033i −0.326589 0.945166i \(-0.605899\pi\)
0.326589 0.945166i \(-0.394101\pi\)
\(140\) −0.742831 0.726277i −0.0627806 0.0613816i
\(141\) 0 0
\(142\) −0.505163 0.505163i −0.0423923 0.0423923i
\(143\) −7.22139 7.22139i −0.603883 0.603883i
\(144\) 0 0
\(145\) −0.191130 16.9623i −0.0158725 1.40864i
\(146\) 8.66342i 0.716990i
\(147\) 0 0
\(148\) 2.78783 2.78783i 0.229158 0.229158i
\(149\) 23.4052 1.91743 0.958713 0.284376i \(-0.0917865\pi\)
0.958713 + 0.284376i \(0.0917865\pi\)
\(150\) 0 0
\(151\) 16.9889 1.38254 0.691269 0.722597i \(-0.257052\pi\)
0.691269 + 0.722597i \(0.257052\pi\)
\(152\) −7.66152 + 7.66152i −0.621431 + 0.621431i
\(153\) 0 0
\(154\) 5.77712i 0.465534i
\(155\) −0.204751 18.1712i −0.0164460 1.45954i
\(156\) 0 0
\(157\) 8.07929 + 8.07929i 0.644798 + 0.644798i 0.951731 0.306933i \(-0.0993028\pi\)
−0.306933 + 0.951731i \(0.599303\pi\)
\(158\) 2.19901 + 2.19901i 0.174944 + 0.174944i
\(159\) 0 0
\(160\) −4.10944 4.01787i −0.324880 0.317640i
\(161\) 2.04014i 0.160785i
\(162\) 0 0
\(163\) 9.08622 9.08622i 0.711688 0.711688i −0.255200 0.966888i \(-0.582141\pi\)
0.966888 + 0.255200i \(0.0821414\pi\)
\(164\) −3.12433 −0.243969
\(165\) 0 0
\(166\) −7.00073 −0.543362
\(167\) 13.5425 13.5425i 1.04795 1.04795i 0.0491596 0.998791i \(-0.484346\pi\)
0.998791 0.0491596i \(-0.0156543\pi\)
\(168\) 0 0
\(169\) 8.20190i 0.630915i
\(170\) −9.12905 + 0.102865i −0.700166 + 0.00788941i
\(171\) 0 0
\(172\) 2.53887 + 2.53887i 0.193587 + 0.193587i
\(173\) 16.4883 + 16.4883i 1.25358 + 1.25358i 0.954102 + 0.299483i \(0.0968141\pi\)
0.299483 + 0.954102i \(0.403186\pi\)
\(174\) 0 0
\(175\) 3.61430 + 3.45497i 0.273216 + 0.261171i
\(176\) 13.3106i 1.00333i
\(177\) 0 0
\(178\) 6.01699 6.01699i 0.450993 0.450993i
\(179\) −7.15384 −0.534703 −0.267352 0.963599i \(-0.586148\pi\)
−0.267352 + 0.963599i \(0.586148\pi\)
\(180\) 0 0
\(181\) −4.86285 −0.361453 −0.180726 0.983533i \(-0.557845\pi\)
−0.180726 + 0.983533i \(0.557845\pi\)
\(182\) 1.91924 1.91924i 0.142264 0.142264i
\(183\) 0 0
\(184\) 6.23040i 0.459312i
\(185\) −13.2654 + 13.5678i −0.975293 + 0.997522i
\(186\) 0 0
\(187\) 10.8628 + 10.8628i 0.794370 + 0.794370i
\(188\) −2.40040 2.40040i −0.175067 0.175067i
\(189\) 0 0
\(190\) 6.87233 7.02897i 0.498571 0.509935i
\(191\) 0.990955i 0.0717030i −0.999357 0.0358515i \(-0.988586\pi\)
0.999357 0.0358515i \(-0.0114143\pi\)
\(192\) 0 0
\(193\) 8.22384 8.22384i 0.591965 0.591965i −0.346197 0.938162i \(-0.612527\pi\)
0.938162 + 0.346197i \(0.112527\pi\)
\(194\) −7.77013 −0.557863
\(195\) 0 0
\(196\) −0.464602 −0.0331859
\(197\) 1.80305 1.80305i 0.128462 0.128462i −0.639952 0.768414i \(-0.721046\pi\)
0.768414 + 0.639952i \(0.221046\pi\)
\(198\) 0 0
\(199\) 16.0345i 1.13666i 0.822802 + 0.568328i \(0.192410\pi\)
−0.822802 + 0.568328i \(0.807590\pi\)
\(200\) 11.0378 + 10.5512i 0.780489 + 0.746082i
\(201\) 0 0
\(202\) 2.30920 + 2.30920i 0.162475 + 0.162475i
\(203\) −5.36429 5.36429i −0.376499 0.376499i
\(204\) 0 0
\(205\) 15.0360 0.169425i 1.05016 0.0118331i
\(206\) 13.0720i 0.910769i
\(207\) 0 0
\(208\) 4.42198 4.42198i 0.306609 0.306609i
\(209\) −16.5415 −1.14420
\(210\) 0 0
\(211\) −22.1632 −1.52578 −0.762890 0.646528i \(-0.776220\pi\)
−0.762890 + 0.646528i \(0.776220\pi\)
\(212\) 3.18927 3.18927i 0.219040 0.219040i
\(213\) 0 0
\(214\) 7.86138i 0.537393i
\(215\) −12.3561 12.0808i −0.842681 0.823902i
\(216\) 0 0
\(217\) −5.74659 5.74659i −0.390104 0.390104i
\(218\) 6.61085 + 6.61085i 0.447743 + 0.447743i
\(219\) 0 0
\(220\) −0.0545737 4.84328i −0.00367936 0.326534i
\(221\) 7.21759i 0.485508i
\(222\) 0 0
\(223\) −13.4515 + 13.4515i −0.900781 + 0.900781i −0.995504 0.0947227i \(-0.969804\pi\)
0.0947227 + 0.995504i \(0.469804\pi\)
\(224\) −2.57024 −0.171732
\(225\) 0 0
\(226\) −3.15961 −0.210174
\(227\) 8.57603 8.57603i 0.569211 0.569211i −0.362696 0.931907i \(-0.618144\pi\)
0.931907 + 0.362696i \(0.118144\pi\)
\(228\) 0 0
\(229\) 22.4314i 1.48231i 0.671335 + 0.741154i \(0.265721\pi\)
−0.671335 + 0.741154i \(0.734279\pi\)
\(230\) −0.0636899 5.65232i −0.00419959 0.372703i
\(231\) 0 0
\(232\) −16.3821 16.3821i −1.07554 1.07554i
\(233\) −3.98861 3.98861i −0.261303 0.261303i 0.564281 0.825583i \(-0.309154\pi\)
−0.825583 + 0.564281i \(0.809154\pi\)
\(234\) 0 0
\(235\) 11.6823 + 11.4219i 0.762067 + 0.745084i
\(236\) 2.97669i 0.193766i
\(237\) 0 0
\(238\) −2.88704 + 2.88704i −0.187139 + 0.187139i
\(239\) 9.15757 0.592354 0.296177 0.955133i \(-0.404288\pi\)
0.296177 + 0.955133i \(0.404288\pi\)
\(240\) 0 0
\(241\) −13.5613 −0.873560 −0.436780 0.899568i \(-0.643881\pi\)
−0.436780 + 0.899568i \(0.643881\pi\)
\(242\) 9.40770 9.40770i 0.604750 0.604750i
\(243\) 0 0
\(244\) 6.32024i 0.404612i
\(245\) 2.23593 0.0251942i 0.142848 0.00160960i
\(246\) 0 0
\(247\) −5.49531 5.49531i −0.349658 0.349658i
\(248\) −17.5496 17.5496i −1.11440 1.11440i
\(249\) 0 0
\(250\) −10.1215 9.45938i −0.640140 0.598264i
\(251\) 23.8741i 1.50692i −0.657494 0.753460i \(-0.728383\pi\)
0.657494 0.753460i \(-0.271617\pi\)
\(252\) 0 0
\(253\) −6.72582 + 6.72582i −0.422848 + 0.422848i
\(254\) −25.1485 −1.57796
\(255\) 0 0
\(256\) −10.5021 −0.656383
\(257\) −12.0222 + 12.0222i −0.749921 + 0.749921i −0.974464 0.224543i \(-0.927911\pi\)
0.224543 + 0.974464i \(0.427911\pi\)
\(258\) 0 0
\(259\) 8.48594i 0.527291i
\(260\) 1.59088 1.62714i 0.0986621 0.100911i
\(261\) 0 0
\(262\) −2.82639 2.82639i −0.174615 0.174615i
\(263\) 1.26198 + 1.26198i 0.0778167 + 0.0778167i 0.744944 0.667127i \(-0.232476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(264\) 0 0
\(265\) −15.1756 + 15.5215i −0.932231 + 0.953479i
\(266\) 4.39626i 0.269552i
\(267\) 0 0
\(268\) −1.28753 + 1.28753i −0.0786484 + 0.0786484i
\(269\) 3.41582 0.208266 0.104133 0.994563i \(-0.466793\pi\)
0.104133 + 0.994563i \(0.466793\pi\)
\(270\) 0 0
\(271\) 8.21326 0.498920 0.249460 0.968385i \(-0.419747\pi\)
0.249460 + 0.968385i \(0.419747\pi\)
\(272\) −6.65181 + 6.65181i −0.403325 + 0.403325i
\(273\) 0 0
\(274\) 2.38511i 0.144090i
\(275\) 0.525278 + 23.3056i 0.0316755 + 1.40538i
\(276\) 0 0
\(277\) −4.57498 4.57498i −0.274884 0.274884i 0.556179 0.831063i \(-0.312267\pi\)
−0.831063 + 0.556179i \(0.812267\pi\)
\(278\) 19.5273 + 19.5273i 1.17117 + 1.17117i
\(279\) 0 0
\(280\) 6.82833 0.0769411i 0.408071 0.00459811i
\(281\) 11.0476i 0.659042i −0.944148 0.329521i \(-0.893113\pi\)
0.944148 0.329521i \(-0.106887\pi\)
\(282\) 0 0
\(283\) −4.42604 + 4.42604i −0.263101 + 0.263101i −0.826313 0.563212i \(-0.809566\pi\)
0.563212 + 0.826313i \(0.309566\pi\)
\(284\) −0.267866 −0.0158949
\(285\) 0 0
\(286\) 12.6545 0.748278
\(287\) 4.75511 4.75511i 0.280685 0.280685i
\(288\) 0 0
\(289\) 6.14286i 0.361345i
\(290\) 15.0296 + 14.6946i 0.882566 + 0.862899i
\(291\) 0 0
\(292\) −2.29692 2.29692i −0.134417 0.134417i
\(293\) 22.3120 + 22.3120i 1.30348 + 1.30348i 0.926029 + 0.377452i \(0.123200\pi\)
0.377452 + 0.926029i \(0.376800\pi\)
\(294\) 0 0
\(295\) −0.161419 14.3255i −0.00939815 0.834063i
\(296\) 25.9154i 1.50630i
\(297\) 0 0
\(298\) −20.5072 + 20.5072i −1.18795 + 1.18795i
\(299\) −4.46883 −0.258439
\(300\) 0 0
\(301\) −7.72811 −0.445441
\(302\) −14.8854 + 14.8854i −0.856560 + 0.856560i
\(303\) 0 0
\(304\) 10.1291i 0.580942i
\(305\) 0.342731 + 30.4166i 0.0196247 + 1.74165i
\(306\) 0 0
\(307\) 4.65242 + 4.65242i 0.265527 + 0.265527i 0.827295 0.561768i \(-0.189879\pi\)
−0.561768 + 0.827295i \(0.689879\pi\)
\(308\) −1.53168 1.53168i −0.0872754 0.0872754i
\(309\) 0 0
\(310\) 16.1007 + 15.7419i 0.914458 + 0.894080i
\(311\) 12.7033i 0.720337i −0.932887 0.360169i \(-0.882719\pi\)
0.932887 0.360169i \(-0.117281\pi\)
\(312\) 0 0
\(313\) 9.39195 9.39195i 0.530864 0.530864i −0.389965 0.920830i \(-0.627513\pi\)
0.920830 + 0.389965i \(0.127513\pi\)
\(314\) −14.1579 −0.798977
\(315\) 0 0
\(316\) 1.16604 0.0655949
\(317\) 12.0566 12.0566i 0.677166 0.677166i −0.282192 0.959358i \(-0.591061\pi\)
0.959358 + 0.282192i \(0.0910615\pi\)
\(318\) 0 0
\(319\) 35.3694i 1.98031i
\(320\) 19.8879 0.224095i 1.11177 0.0125273i
\(321\) 0 0
\(322\) −1.78753 1.78753i −0.0996154 0.0996154i
\(323\) 8.26638 + 8.26638i 0.459954 + 0.459954i
\(324\) 0 0
\(325\) −7.56796 + 7.91697i −0.419795 + 0.439155i
\(326\) 15.9224i 0.881861i
\(327\) 0 0
\(328\) 14.5217 14.5217i 0.801828 0.801828i
\(329\) 7.30665 0.402829
\(330\) 0 0
\(331\) −0.841491 −0.0462525 −0.0231263 0.999733i \(-0.507362\pi\)
−0.0231263 + 0.999733i \(0.507362\pi\)
\(332\) −1.85609 + 1.85609i −0.101866 + 0.101866i
\(333\) 0 0
\(334\) 23.7315i 1.29853i
\(335\) 6.12650 6.26614i 0.334726 0.342356i
\(336\) 0 0
\(337\) −16.1936 16.1936i −0.882124 0.882124i 0.111626 0.993750i \(-0.464394\pi\)
−0.993750 + 0.111626i \(0.964394\pi\)
\(338\) −7.18638 7.18638i −0.390887 0.390887i
\(339\) 0 0
\(340\) −2.39309 + 2.44764i −0.129784 + 0.132742i
\(341\) 37.8902i 2.05187i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −23.6010 −1.27248
\(345\) 0 0
\(346\) −28.8936 −1.55333
\(347\) 6.72445 6.72445i 0.360988 0.360988i −0.503189 0.864176i \(-0.667840\pi\)
0.864176 + 0.503189i \(0.167840\pi\)
\(348\) 0 0
\(349\) 25.9697i 1.39013i 0.718949 + 0.695063i \(0.244624\pi\)
−0.718949 + 0.695063i \(0.755376\pi\)
\(350\) −6.19399 + 0.139604i −0.331082 + 0.00746217i
\(351\) 0 0
\(352\) −8.47345 8.47345i −0.451637 0.451637i
\(353\) 20.5943 + 20.5943i 1.09612 + 1.09612i 0.994860 + 0.101264i \(0.0322885\pi\)
0.101264 + 0.994860i \(0.467711\pi\)
\(354\) 0 0
\(355\) 1.28912 0.0145257i 0.0684194 0.000770944i
\(356\) 3.19055i 0.169099i
\(357\) 0 0
\(358\) 6.26808 6.26808i 0.331278 0.331278i
\(359\) 29.4326 1.55339 0.776697 0.629874i \(-0.216893\pi\)
0.776697 + 0.629874i \(0.216893\pi\)
\(360\) 0 0
\(361\) 6.41233 0.337491
\(362\) 4.26075 4.26075i 0.223940 0.223940i
\(363\) 0 0
\(364\) 1.01769i 0.0533415i
\(365\) 11.1786 + 10.9295i 0.585115 + 0.572076i
\(366\) 0 0
\(367\) −13.4205 13.4205i −0.700544 0.700544i 0.263983 0.964527i \(-0.414964\pi\)
−0.964527 + 0.263983i \(0.914964\pi\)
\(368\) −4.11852 4.11852i −0.214693 0.214693i
\(369\) 0 0
\(370\) −0.264918 23.5108i −0.0137724 1.22227i
\(371\) 9.70790i 0.504009i
\(372\) 0 0
\(373\) 1.38704 1.38704i 0.0718184 0.0718184i −0.670285 0.742104i \(-0.733828\pi\)
0.742104 + 0.670285i \(0.233828\pi\)
\(374\) −19.0357 −0.984313
\(375\) 0 0
\(376\) 22.3139 1.15075
\(377\) 11.7502 11.7502i 0.605168 0.605168i
\(378\) 0 0
\(379\) 25.3851i 1.30394i 0.758243 + 0.651972i \(0.226058\pi\)
−0.758243 + 0.651972i \(0.773942\pi\)
\(380\) −0.0415293 3.68563i −0.00213041 0.189069i
\(381\) 0 0
\(382\) 0.868259 + 0.868259i 0.0444240 + 0.0444240i
\(383\) −3.12729 3.12729i −0.159797 0.159797i 0.622680 0.782477i \(-0.286044\pi\)
−0.782477 + 0.622680i \(0.786044\pi\)
\(384\) 0 0
\(385\) 7.45435 + 7.28823i 0.379909 + 0.371443i
\(386\) 14.4112i 0.733511i
\(387\) 0 0
\(388\) −2.06008 + 2.06008i −0.104585 + 0.104585i
\(389\) −10.5100 −0.532876 −0.266438 0.963852i \(-0.585847\pi\)
−0.266438 + 0.963852i \(0.585847\pi\)
\(390\) 0 0
\(391\) 6.72228 0.339960
\(392\) 2.15945 2.15945i 0.109068 0.109068i
\(393\) 0 0
\(394\) 3.15961i 0.159179i
\(395\) −5.61164 + 0.0632315i −0.282352 + 0.00318152i
\(396\) 0 0
\(397\) −3.72909 3.72909i −0.187158 0.187158i 0.607308 0.794466i \(-0.292249\pi\)
−0.794466 + 0.607308i \(0.792249\pi\)
\(398\) −14.0492 14.0492i −0.704222 0.704222i
\(399\) 0 0
\(400\) −14.2711 + 0.321652i −0.713554 + 0.0160826i
\(401\) 17.8421i 0.890994i −0.895283 0.445497i \(-0.853027\pi\)
0.895283 0.445497i \(-0.146973\pi\)
\(402\) 0 0
\(403\) 12.5877 12.5877i 0.627036 0.627036i
\(404\) 1.22447 0.0609195
\(405\) 0 0
\(406\) 9.40021 0.466525
\(407\) −27.9760 + 27.9760i −1.38672 + 1.38672i
\(408\) 0 0
\(409\) 14.9681i 0.740127i −0.929006 0.370064i \(-0.879336\pi\)
0.929006 0.370064i \(-0.120664\pi\)
\(410\) −13.0259 + 13.3228i −0.643303 + 0.657965i
\(411\) 0 0
\(412\) 3.46575 + 3.46575i 0.170745 + 0.170745i
\(413\) −4.53041 4.53041i −0.222927 0.222927i
\(414\) 0 0
\(415\) 8.83189 9.03320i 0.433541 0.443422i
\(416\) 5.63001i 0.276034i
\(417\) 0 0
\(418\) 14.4934 14.4934i 0.708894 0.708894i
\(419\) −6.71408 −0.328004 −0.164002 0.986460i \(-0.552440\pi\)
−0.164002 + 0.986460i \(0.552440\pi\)
\(420\) 0 0
\(421\) −30.1593 −1.46987 −0.734937 0.678136i \(-0.762788\pi\)
−0.734937 + 0.678136i \(0.762788\pi\)
\(422\) 19.4191 19.4191i 0.945307 0.945307i
\(423\) 0 0
\(424\) 29.6471i 1.43979i
\(425\) 11.3842 11.9092i 0.552214 0.577680i
\(426\) 0 0
\(427\) 9.61917 + 9.61917i 0.465504 + 0.465504i
\(428\) −2.08427 2.08427i −0.100747 0.100747i
\(429\) 0 0
\(430\) 21.4112 0.241260i 1.03254 0.0116346i
\(431\) 14.5595i 0.701304i −0.936506 0.350652i \(-0.885960\pi\)
0.936506 0.350652i \(-0.114040\pi\)
\(432\) 0 0
\(433\) 14.3159 14.3159i 0.687976 0.687976i −0.273808 0.961784i \(-0.588283\pi\)
0.961784 + 0.273808i \(0.0882834\pi\)
\(434\) 10.0702 0.483383
\(435\) 0 0
\(436\) 3.50544 0.167880
\(437\) −5.11819 + 5.11819i −0.244836 + 0.244836i
\(438\) 0 0
\(439\) 23.7496i 1.13351i 0.823887 + 0.566754i \(0.191801\pi\)
−0.823887 + 0.566754i \(0.808199\pi\)
\(440\) 22.7650 + 22.2577i 1.08528 + 1.06109i
\(441\) 0 0
\(442\) −6.32394 6.32394i −0.300799 0.300799i
\(443\) −28.0781 28.0781i −1.33403 1.33403i −0.901730 0.432299i \(-0.857702\pi\)
−0.432299 0.901730i \(-0.642298\pi\)
\(444\) 0 0
\(445\) 0.173015 + 15.3547i 0.00820172 + 0.727883i
\(446\) 23.5720i 1.11617i
\(447\) 0 0
\(448\) 6.28950 6.28950i 0.297151 0.297151i
\(449\) −23.1170 −1.09096 −0.545479 0.838125i \(-0.683652\pi\)
−0.545479 + 0.838125i \(0.683652\pi\)
\(450\) 0 0
\(451\) 31.3528 1.47635
\(452\) −0.837701 + 0.837701i −0.0394021 + 0.0394021i
\(453\) 0 0
\(454\) 15.0284i 0.705316i
\(455\) 0.0551869 + 4.89770i 0.00258720 + 0.229608i
\(456\) 0 0
\(457\) −2.41339 2.41339i −0.112893 0.112893i 0.648403 0.761297i \(-0.275437\pi\)
−0.761297 + 0.648403i \(0.775437\pi\)
\(458\) −19.6540 19.6540i −0.918373 0.918373i
\(459\) 0 0
\(460\) −1.51547 1.48170i −0.0706594 0.0690848i
\(461\) 12.9836i 0.604705i −0.953196 0.302353i \(-0.902228\pi\)
0.953196 0.302353i \(-0.0977720\pi\)
\(462\) 0 0
\(463\) 21.5619 21.5619i 1.00207 1.00207i 0.00206902 0.999998i \(-0.499341\pi\)
0.999998 0.00206902i \(-0.000658591\pi\)
\(464\) 21.6583 1.00546
\(465\) 0 0
\(466\) 6.98952 0.323783
\(467\) −4.14681 + 4.14681i −0.191891 + 0.191891i −0.796513 0.604622i \(-0.793324\pi\)
0.604622 + 0.796513i \(0.293324\pi\)
\(468\) 0 0
\(469\) 3.91914i 0.180969i
\(470\) −20.2435 + 0.228102i −0.933764 + 0.0105216i
\(471\) 0 0
\(472\) −13.8355 13.8355i −0.636830 0.636830i
\(473\) −25.4777 25.4777i −1.17146 1.17146i
\(474\) 0 0
\(475\) 0.399725 + 17.7350i 0.0183406 + 0.813740i
\(476\) 1.53087i 0.0701674i
\(477\) 0 0
\(478\) −8.02372 + 8.02372i −0.366996 + 0.366996i
\(479\) 11.3977 0.520774 0.260387 0.965504i \(-0.416150\pi\)
0.260387 + 0.965504i \(0.416150\pi\)
\(480\) 0 0
\(481\) −18.5881 −0.847544
\(482\) 11.8822 11.8822i 0.541219 0.541219i
\(483\) 0 0
\(484\) 4.98849i 0.226750i
\(485\) 9.80255 10.0260i 0.445111 0.455256i
\(486\) 0 0
\(487\) −11.0942 11.0942i −0.502727 0.502727i 0.409558 0.912284i \(-0.365683\pi\)
−0.912284 + 0.409558i \(0.865683\pi\)
\(488\) 29.3762 + 29.3762i 1.32980 + 1.32980i
\(489\) 0 0
\(490\) −1.93701 + 1.98116i −0.0875051 + 0.0894996i
\(491\) 28.4593i 1.28435i 0.766559 + 0.642174i \(0.221967\pi\)
−0.766559 + 0.642174i \(0.778033\pi\)
\(492\) 0 0
\(493\) −17.6754 + 17.6754i −0.796061 + 0.796061i
\(494\) 9.62981 0.433266
\(495\) 0 0
\(496\) 23.2019 1.04179
\(497\) 0.407682 0.407682i 0.0182870 0.0182870i
\(498\) 0 0
\(499\) 13.0081i 0.582323i −0.956674 0.291161i \(-0.905958\pi\)
0.956674 0.291161i \(-0.0940417\pi\)
\(500\) −5.19144 + 0.175550i −0.232168 + 0.00785082i
\(501\) 0 0
\(502\) 20.9181 + 20.9181i 0.933621 + 0.933621i
\(503\) 19.6010 + 19.6010i 0.873966 + 0.873966i 0.992902 0.118936i \(-0.0379482\pi\)
−0.118936 + 0.992902i \(0.537948\pi\)
\(504\) 0 0
\(505\) −5.89282 + 0.0663999i −0.262227 + 0.00295475i
\(506\) 11.7861i 0.523957i
\(507\) 0 0
\(508\) −6.66756 + 6.66756i −0.295825 + 0.295825i
\(509\) −42.4087 −1.87973 −0.939866 0.341545i \(-0.889050\pi\)
−0.939866 + 0.341545i \(0.889050\pi\)
\(510\) 0 0
\(511\) 6.99164 0.309292
\(512\) 17.5189 17.5189i 0.774231 0.774231i
\(513\) 0 0
\(514\) 21.0672i 0.929236i
\(515\) −16.8671 16.4912i −0.743252 0.726689i
\(516\) 0 0
\(517\) 24.0882 + 24.0882i 1.05940 + 1.05940i
\(518\) −7.43525 7.43525i −0.326686 0.326686i
\(519\) 0 0
\(520\) 0.168536 + 14.9572i 0.00739080 + 0.655915i
\(521\) 13.9987i 0.613296i 0.951823 + 0.306648i \(0.0992074\pi\)
−0.951823 + 0.306648i \(0.900793\pi\)
\(522\) 0 0
\(523\) 15.7665 15.7665i 0.689421 0.689421i −0.272683 0.962104i \(-0.587911\pi\)
0.962104 + 0.272683i \(0.0879110\pi\)
\(524\) −1.49871 −0.0654715
\(525\) 0 0
\(526\) −2.21145 −0.0964236
\(527\) −18.9351 + 18.9351i −0.824827 + 0.824827i
\(528\) 0 0
\(529\) 18.8378i 0.819037i
\(530\) −0.303066 26.8963i −0.0131643 1.16830i
\(531\) 0 0
\(532\) −1.16557 1.16557i −0.0505339 0.0505339i
\(533\) 10.4159 + 10.4159i 0.451161 + 0.451161i
\(534\) 0 0
\(535\) 10.1437 + 9.91767i 0.438551 + 0.428778i
\(536\) 11.9687i 0.516971i
\(537\) 0 0
\(538\) −2.99289 + 2.99289i −0.129033 + 0.129033i
\(539\) 4.66231 0.200820
\(540\) 0 0
\(541\) 40.1080 1.72438 0.862189 0.506587i \(-0.169093\pi\)
0.862189 + 0.506587i \(0.169093\pi\)
\(542\) −7.19633 + 7.19633i −0.309109 + 0.309109i
\(543\) 0 0
\(544\) 8.46900i 0.363105i
\(545\) −16.8702 + 0.190092i −0.722638 + 0.00814263i
\(546\) 0 0
\(547\) −8.55083 8.55083i −0.365607 0.365607i 0.500265 0.865872i \(-0.333236\pi\)
−0.865872 + 0.500265i \(0.833236\pi\)
\(548\) 0.632361 + 0.632361i 0.0270131 + 0.0270131i
\(549\) 0 0
\(550\) −20.8803 19.9598i −0.890337 0.851088i
\(551\) 26.9153i 1.14663i
\(552\) 0 0
\(553\) −1.77467 + 1.77467i −0.0754667 + 0.0754667i
\(554\) 8.01704 0.340612
\(555\) 0 0
\(556\) 10.3544 0.439126
\(557\) 15.5128 15.5128i 0.657300 0.657300i −0.297441 0.954740i \(-0.596133\pi\)
0.954740 + 0.297441i \(0.0961330\pi\)
\(558\) 0 0
\(559\) 16.9281i 0.715982i
\(560\) −4.46291 + 4.56463i −0.188592 + 0.192891i
\(561\) 0 0
\(562\) 9.67970 + 9.67970i 0.408313 + 0.408313i
\(563\) 15.5187 + 15.5187i 0.654036 + 0.654036i 0.953962 0.299926i \(-0.0969620\pi\)
−0.299926 + 0.953962i \(0.596962\pi\)
\(564\) 0 0
\(565\) 3.98606 4.07691i 0.167695 0.171517i
\(566\) 7.75605i 0.326011i
\(567\) 0 0
\(568\) 1.24503 1.24503i 0.0522401 0.0522401i
\(569\) −31.6235 −1.32573 −0.662863 0.748741i \(-0.730659\pi\)
−0.662863 + 0.748741i \(0.730659\pi\)
\(570\) 0 0
\(571\) −25.0465 −1.04816 −0.524082 0.851668i \(-0.675592\pi\)
−0.524082 + 0.851668i \(0.675592\pi\)
\(572\) 3.35507 3.35507i 0.140283 0.140283i
\(573\) 0 0
\(574\) 8.33271i 0.347801i
\(575\) 7.37367 + 7.04861i 0.307503 + 0.293947i
\(576\) 0 0
\(577\) −20.1909 20.1909i −0.840557 0.840557i 0.148375 0.988931i \(-0.452596\pi\)
−0.988931 + 0.148375i \(0.952596\pi\)
\(578\) −5.38228 5.38228i −0.223873 0.223873i
\(579\) 0 0
\(580\) 7.88072 0.0887993i 0.327229 0.00368719i
\(581\) 5.64980i 0.234393i
\(582\) 0 0
\(583\) −32.0045 + 32.0045i −1.32549 + 1.32549i
\(584\) 21.3519 0.883548
\(585\) 0 0
\(586\) −39.0989 −1.61516
\(587\) −15.4569 + 15.4569i −0.637976 + 0.637976i −0.950056 0.312080i \(-0.898974\pi\)
0.312080 + 0.950056i \(0.398974\pi\)
\(588\) 0 0
\(589\) 28.8336i 1.18807i
\(590\) 12.6932 + 12.4103i 0.522571 + 0.510926i
\(591\) 0 0
\(592\) −17.1310 17.1310i −0.704079 0.704079i
\(593\) 2.50889 + 2.50889i 0.103028 + 0.103028i 0.756742 0.653714i \(-0.226790\pi\)
−0.653714 + 0.756742i \(0.726790\pi\)
\(594\) 0 0
\(595\) −0.0830154 7.36741i −0.00340330 0.302035i
\(596\) 10.8741i 0.445420i
\(597\) 0 0
\(598\) 3.91552 3.91552i 0.160117 0.160117i
\(599\) 23.0111 0.940207 0.470104 0.882611i \(-0.344217\pi\)
0.470104 + 0.882611i \(0.344217\pi\)
\(600\) 0 0
\(601\) 11.4097 0.465411 0.232706 0.972547i \(-0.425242\pi\)
0.232706 + 0.972547i \(0.425242\pi\)
\(602\) 6.77125 6.77125i 0.275976 0.275976i
\(603\) 0 0
\(604\) 7.89308i 0.321165i
\(605\) 0.270514 + 24.0074i 0.0109979 + 0.976040i
\(606\) 0 0
\(607\) 26.7473 + 26.7473i 1.08564 + 1.08564i 0.995972 + 0.0896663i \(0.0285801\pi\)
0.0896663 + 0.995972i \(0.471420\pi\)
\(608\) −6.44810 6.44810i −0.261505 0.261505i
\(609\) 0 0
\(610\) −26.9508 26.3502i −1.09121 1.06689i
\(611\) 16.0049i 0.647489i
\(612\) 0 0
\(613\) −9.33197 + 9.33197i −0.376915 + 0.376915i −0.869988 0.493073i \(-0.835874\pi\)
0.493073 + 0.869988i \(0.335874\pi\)
\(614\) −8.15275 −0.329018
\(615\) 0 0
\(616\) 14.2383 0.573678
\(617\) −3.34333 + 3.34333i −0.134597 + 0.134597i −0.771196 0.636598i \(-0.780341\pi\)
0.636598 + 0.771196i \(0.280341\pi\)
\(618\) 0 0
\(619\) 15.3147i 0.615549i −0.951459 0.307774i \(-0.900416\pi\)
0.951459 0.307774i \(-0.0995842\pi\)
\(620\) 8.44236 0.0951278i 0.339053 0.00382043i
\(621\) 0 0
\(622\) 11.1304 + 11.1304i 0.446289 + 0.446289i
\(623\) 4.85589 + 4.85589i 0.194547 + 0.194547i
\(624\) 0 0
\(625\) 24.9746 1.12636i 0.998985 0.0450545i
\(626\) 16.4582i 0.657800i
\(627\) 0 0
\(628\) −3.75366 + 3.75366i −0.149787 + 0.149787i
\(629\) 27.9613 1.11489
\(630\) 0 0
\(631\) −25.4390 −1.01271 −0.506355 0.862325i \(-0.669007\pi\)
−0.506355 + 0.862325i \(0.669007\pi\)
\(632\) −5.41970 + 5.41970i −0.215584 + 0.215584i
\(633\) 0 0
\(634\) 21.1276i 0.839085i
\(635\) 31.7265 32.4496i 1.25903 1.28772i
\(636\) 0 0
\(637\) 1.54889 + 1.54889i 0.0613691 + 0.0613691i
\(638\) 30.9902 + 30.9902i 1.22691 + 1.22691i
\(639\) 0 0
\(640\) −9.19338 + 9.40292i −0.363400 + 0.371683i
\(641\) 19.2081i 0.758674i 0.925259 + 0.379337i \(0.123848\pi\)
−0.925259 + 0.379337i \(0.876152\pi\)
\(642\) 0 0
\(643\) −2.50256 + 2.50256i −0.0986915 + 0.0986915i −0.754729 0.656037i \(-0.772231\pi\)
0.656037 + 0.754729i \(0.272231\pi\)
\(644\) −0.947851 −0.0373506
\(645\) 0 0
\(646\) −14.4857 −0.569934
\(647\) −10.7695 + 10.7695i −0.423393 + 0.423393i −0.886370 0.462977i \(-0.846781\pi\)
0.462977 + 0.886370i \(0.346781\pi\)
\(648\) 0 0
\(649\) 29.8712i 1.17255i
\(650\) −0.305797 13.5677i −0.0119944 0.532167i
\(651\) 0 0
\(652\) 4.22148 + 4.22148i 0.165326 + 0.165326i
\(653\) 26.4630 + 26.4630i 1.03558 + 1.03558i 0.999343 + 0.0362330i \(0.0115358\pi\)
0.0362330 + 0.999343i \(0.488464\pi\)
\(654\) 0 0
\(655\) 7.21264 0.0812714i 0.281821 0.00317554i
\(656\) 19.1988i 0.749585i
\(657\) 0 0
\(658\) −6.40197 + 6.40197i −0.249575 + 0.249575i
\(659\) −8.78898 −0.342370 −0.171185 0.985239i \(-0.554760\pi\)
−0.171185 + 0.985239i \(0.554760\pi\)
\(660\) 0 0
\(661\) −7.11790 −0.276854 −0.138427 0.990373i \(-0.544205\pi\)
−0.138427 + 0.990373i \(0.544205\pi\)
\(662\) 0.737301 0.737301i 0.0286560 0.0286560i
\(663\) 0 0
\(664\) 17.2540i 0.669586i
\(665\) 5.67259 + 5.54618i 0.219974 + 0.215072i
\(666\) 0 0
\(667\) −10.9439 10.9439i −0.423749 0.423749i
\(668\) 6.29188 + 6.29188i 0.243440 + 0.243440i
\(669\) 0 0
\(670\) 0.122350 + 10.8582i 0.00472678 + 0.419490i
\(671\) 63.4240i 2.44846i
\(672\) 0 0
\(673\) 0.822154 0.822154i 0.0316917 0.0316917i −0.691083 0.722775i \(-0.742866\pi\)
0.722775 + 0.691083i \(0.242866\pi\)
\(674\) 28.3772 1.09305
\(675\) 0 0
\(676\) −3.81062 −0.146562
\(677\) −19.7788 + 19.7788i −0.760162 + 0.760162i −0.976352 0.216189i \(-0.930637\pi\)
0.216189 + 0.976352i \(0.430637\pi\)
\(678\) 0 0
\(679\) 6.27073i 0.240648i
\(680\) −0.253522 22.4995i −0.00972213 0.862815i
\(681\) 0 0
\(682\) 33.1988 + 33.1988i 1.27125 + 1.27125i
\(683\) −22.2292 22.2292i −0.850576 0.850576i 0.139628 0.990204i \(-0.455409\pi\)
−0.990204 + 0.139628i \(0.955409\pi\)
\(684\) 0 0
\(685\) −3.07757 3.00898i −0.117588 0.114967i
\(686\) 1.23911i 0.0473095i
\(687\) 0 0
\(688\) 15.6011 15.6011i 0.594787 0.594787i
\(689\) −21.2647 −0.810122
\(690\) 0 0
\(691\) 10.5768 0.402361 0.201180 0.979554i \(-0.435522\pi\)
0.201180 + 0.979554i \(0.435522\pi\)
\(692\) −7.66051 + 7.66051i −0.291209 + 0.291209i
\(693\) 0 0
\(694\) 11.7837i 0.447304i
\(695\) −49.8314 + 0.561496i −1.89021 + 0.0212988i
\(696\) 0 0
\(697\) −15.6682 15.6682i −0.593475 0.593475i
\(698\) −22.7542 22.7542i −0.861261 0.861261i
\(699\) 0 0
\(700\) −1.60519 + 1.67921i −0.0606703 + 0.0634683i
\(701\) 20.2841i 0.766121i −0.923723 0.383061i \(-0.874870\pi\)
0.923723 0.383061i \(-0.125130\pi\)
\(702\) 0 0
\(703\) −21.2891 + 21.2891i −0.802934 + 0.802934i
\(704\) 41.4698 1.56295
\(705\) 0 0
\(706\) −36.0888 −1.35822
\(707\) −1.86359 + 1.86359i −0.0700876 + 0.0700876i
\(708\) 0 0
\(709\) 10.7396i 0.403333i 0.979454 + 0.201666i \(0.0646356\pi\)
−0.979454 + 0.201666i \(0.935364\pi\)
\(710\) −1.11678 + 1.14223i −0.0419120 + 0.0428673i
\(711\) 0 0
\(712\) 14.8295 + 14.8295i 0.555759 + 0.555759i
\(713\) −11.7238 11.7238i −0.439061 0.439061i
\(714\) 0 0
\(715\) −15.9646 + 16.3284i −0.597041 + 0.610649i
\(716\) 3.32369i 0.124212i
\(717\) 0 0
\(718\) −25.7884 + 25.7884i −0.962415 + 0.962415i
\(719\) 24.5967 0.917302 0.458651 0.888616i \(-0.348333\pi\)
0.458651 + 0.888616i \(0.348333\pi\)
\(720\) 0 0
\(721\) −10.5495 −0.392883
\(722\) −5.61838 + 5.61838i −0.209095 + 0.209095i
\(723\) 0 0
\(724\) 2.25929i 0.0839658i
\(725\) −37.9216 + 0.854704i −1.40837 + 0.0317429i
\(726\) 0 0
\(727\) −22.1032 22.1032i −0.819763 0.819763i 0.166310 0.986073i \(-0.446815\pi\)
−0.986073 + 0.166310i \(0.946815\pi\)
\(728\) 4.73017 + 4.73017i 0.175312 + 0.175312i
\(729\) 0 0
\(730\) −19.3708 + 0.218268i −0.716945 + 0.00807847i
\(731\) 25.4643i 0.941830i
\(732\) 0 0
\(733\) 3.38234 3.38234i 0.124930 0.124930i −0.641878 0.766807i \(-0.721844\pi\)
0.766807 + 0.641878i \(0.221844\pi\)
\(734\) 23.5177 0.868053
\(735\) 0 0
\(736\) −5.24365 −0.193283
\(737\) 12.9204 12.9204i 0.475930 0.475930i
\(738\) 0 0
\(739\) 18.0189i 0.662838i −0.943484 0.331419i \(-0.892473\pi\)
0.943484 0.331419i \(-0.107527\pi\)
\(740\) −6.30361 6.16314i −0.231725 0.226562i
\(741\) 0 0
\(742\) −8.50591 8.50591i −0.312262 0.312262i
\(743\) −13.7680 13.7680i −0.505099 0.505099i 0.407919 0.913018i \(-0.366255\pi\)
−0.913018 + 0.407919i \(0.866255\pi\)
\(744\) 0 0
\(745\) −0.589675 52.3322i −0.0216040 1.91730i
\(746\) 2.43061i 0.0889910i
\(747\) 0 0
\(748\) −5.04690 + 5.04690i −0.184533 + 0.184533i
\(749\) 6.34437 0.231818
\(750\) 0 0
\(751\) −12.7248 −0.464336 −0.232168 0.972676i \(-0.574582\pi\)
−0.232168 + 0.972676i \(0.574582\pi\)
\(752\) −14.7503 + 14.7503i −0.537888 + 0.537888i
\(753\) 0 0
\(754\) 20.5908i 0.749871i
\(755\) −0.428023 37.9860i −0.0155773 1.38245i
\(756\) 0 0
\(757\) 31.2644 + 31.2644i 1.13633 + 1.13633i 0.989103 + 0.147222i \(0.0470332\pi\)
0.147222 + 0.989103i \(0.452967\pi\)
\(758\) −22.2420 22.2420i −0.807866 0.807866i
\(759\) 0 0
\(760\) 17.3236 + 16.9376i 0.628394 + 0.614390i
\(761\) 35.1072i 1.27264i 0.771427 + 0.636318i \(0.219543\pi\)
−0.771427 + 0.636318i \(0.780457\pi\)
\(762\) 0 0
\(763\) −5.33515 + 5.33515i −0.193145 + 0.193145i
\(764\) 0.460400 0.0166567
\(765\) 0 0
\(766\) 5.48017 0.198006
\(767\) 9.92366 9.92366i 0.358323 0.358323i
\(768\) 0 0
\(769\) 25.2815i 0.911673i 0.890063 + 0.455837i \(0.150660\pi\)
−0.890063 + 0.455837i \(0.849340\pi\)
\(770\) −12.9172 + 0.145550i −0.465504 + 0.00524526i
\(771\) 0 0
\(772\) 3.82081 + 3.82081i 0.137514 + 0.137514i
\(773\) −15.4411 15.4411i −0.555376 0.555376i 0.372611 0.927988i \(-0.378463\pi\)
−0.927988 + 0.372611i \(0.878463\pi\)
\(774\) 0 0
\(775\) −40.6242 + 0.915617i −1.45927 + 0.0328899i
\(776\) 19.1503i 0.687455i
\(777\) 0 0
\(778\) 9.20867 9.20867i 0.330147 0.330147i
\(779\) 23.8588 0.854830
\(780\) 0 0
\(781\) 2.68805 0.0961859
\(782\) −5.88996 + 5.88996i −0.210624 + 0.210624i
\(783\) 0 0
\(784\) 2.85494i 0.101962i
\(785\) 17.8612 18.2683i 0.637492 0.652022i
\(786\) 0 0
\(787\) 17.7487 + 17.7487i 0.632673 + 0.632673i 0.948738 0.316065i \(-0.102362\pi\)
−0.316065 + 0.948738i \(0.602362\pi\)
\(788\) 0.837701 + 0.837701i 0.0298419 + 0.0298419i
\(789\) 0 0
\(790\) 4.86143 4.97224i 0.172962 0.176904i
\(791\) 2.54990i 0.0906639i
\(792\) 0 0
\(793\) −21.0704 + 21.0704i −0.748231 + 0.748231i
\(794\) 6.53474 0.231909
\(795\) 0 0
\(796\) −7.44966 −0.264046
\(797\) 17.3136 17.3136i 0.613280 0.613280i −0.330520 0.943799i \(-0.607224\pi\)
0.943799 + 0.330520i \(0.107224\pi\)
\(798\) 0 0
\(799\) 24.0755i 0.851731i
\(800\) −8.88012 + 9.28964i −0.313960 + 0.328438i
\(801\) 0 0
\(802\) 15.6330 + 15.6330i 0.552021 + 0.552021i
\(803\) 23.0497 + 23.0497i 0.813406 + 0.813406i
\(804\) 0 0
\(805\) 4.56159 0.0513996i 0.160775 0.00181160i
\(806\) 22.0582i 0.776968i
\(807\) 0 0
\(808\) −5.69126 + 5.69126i −0.200218 + 0.200218i
\(809\) −23.6436 −0.831265 −0.415632 0.909533i \(-0.636440\pi\)
−0.415632 + 0.909533i \(0.636440\pi\)
\(810\) 0 0
\(811\) −13.9945 −0.491412 −0.245706 0.969344i \(-0.579020\pi\)
−0.245706 + 0.969344i \(0.579020\pi\)
\(812\) 2.49226 2.49226i 0.0874612 0.0874612i
\(813\) 0 0
\(814\) 49.0243i 1.71830i
\(815\) −20.5450 20.0872i −0.719662 0.703624i
\(816\) 0 0
\(817\) −19.3879 19.3879i −0.678297 0.678297i
\(818\) 13.1149 + 13.1149i 0.458550 + 0.458550i
\(819\) 0 0
\(820\) 0.0787151 + 6.98577i 0.00274885 + 0.243954i
\(821\) 32.7797i 1.14402i −0.820247 0.572010i \(-0.806164\pi\)
0.820247 0.572010i \(-0.193836\pi\)
\(822\) 0 0
\(823\) −15.2743 + 15.2743i −0.532430 + 0.532430i −0.921295 0.388865i \(-0.872867\pi\)
0.388865 + 0.921295i \(0.372867\pi\)
\(824\) −32.2173 −1.12234
\(825\) 0 0
\(826\) 7.93894 0.276231
\(827\) −19.3251 + 19.3251i −0.672000 + 0.672000i −0.958177 0.286177i \(-0.907615\pi\)
0.286177 + 0.958177i \(0.407615\pi\)
\(828\) 0 0
\(829\) 46.8148i 1.62595i 0.582302 + 0.812973i \(0.302152\pi\)
−0.582302 + 0.812973i \(0.697848\pi\)
\(830\) 0.176378 + 15.6531i 0.00612217 + 0.543327i
\(831\) 0 0
\(832\) 13.7769 + 13.7769i 0.477628 + 0.477628i
\(833\) −2.32993 2.32993i −0.0807272 0.0807272i
\(834\) 0 0
\(835\) −30.6212 29.9388i −1.05969 1.03608i
\(836\) 7.68519i 0.265798i
\(837\) 0 0
\(838\) 5.88277 5.88277i 0.203217 0.203217i
\(839\) −31.1400 −1.07507 −0.537535 0.843241i \(-0.680645\pi\)
−0.537535 + 0.843241i \(0.680645\pi\)
\(840\) 0 0
\(841\) 28.5512 0.984524
\(842\) 26.4251 26.4251i 0.910669 0.910669i
\(843\) 0 0
\(844\) 10.2971i 0.354440i
\(845\) 18.3388 0.206641i 0.630875 0.00710865i
\(846\) 0 0
\(847\) 7.59229 + 7.59229i 0.260874 + 0.260874i
\(848\) −19.5978 19.5978i −0.672991 0.672991i
\(849\) 0 0
\(850\) 0.459999 + 20.4093i 0.0157778 + 0.700033i
\(851\) 17.3125i 0.593464i
\(852\) 0 0
\(853\) 34.5421 34.5421i 1.18270 1.18270i 0.203657 0.979042i \(-0.434717\pi\)
0.979042 0.203657i \(-0.0652828\pi\)
\(854\) −16.8563 −0.576812
\(855\) 0 0
\(856\) 19.3752 0.662230
\(857\) 29.4941 29.4941i 1.00750 1.00750i 0.00752899 0.999972i \(-0.497603\pi\)
0.999972 0.00752899i \(-0.00239658\pi\)
\(858\) 0 0
\(859\) 43.7748i 1.49358i −0.665061 0.746789i \(-0.731594\pi\)
0.665061 0.746789i \(-0.268406\pi\)
\(860\) 5.61275 5.74068i 0.191393 0.195756i
\(861\) 0 0
\(862\) 12.7568 + 12.7568i 0.434497 + 0.434497i
\(863\) −9.59074 9.59074i −0.326472 0.326472i 0.524771 0.851243i \(-0.324151\pi\)
−0.851243 + 0.524771i \(0.824151\pi\)
\(864\) 0 0
\(865\) 36.4513 37.2821i 1.23938 1.26763i
\(866\) 25.0867i 0.852479i
\(867\) 0 0
\(868\) 2.66988 2.66988i 0.0906216 0.0906216i
\(869\) −11.7013 −0.396939
\(870\) 0 0
\(871\) 8.58471 0.290882
\(872\) −16.2931 + 16.2931i −0.551754 + 0.551754i
\(873\) 0 0
\(874\) 8.96896i 0.303380i
\(875\) 7.63400 8.16836i 0.258076 0.276141i
\(876\) 0 0
\(877\) 38.7983 + 38.7983i 1.31013 + 1.31013i 0.921319 + 0.388809i \(0.127113\pi\)
0.388809 + 0.921319i \(0.372887\pi\)
\(878\) −20.8091 20.8091i −0.702272 0.702272i
\(879\) 0 0
\(880\) −29.7616 + 0.335351i −1.00326 + 0.0113047i
\(881\) 14.2447i 0.479918i 0.970783 + 0.239959i \(0.0771339\pi\)
−0.970783 + 0.239959i \(0.922866\pi\)
\(882\) 0 0
\(883\) −34.0748 + 34.0748i −1.14671 + 1.14671i −0.159511 + 0.987196i \(0.550992\pi\)
−0.987196 + 0.159511i \(0.949008\pi\)
\(884\) −3.35331 −0.112784
\(885\) 0 0
\(886\) 49.2031 1.65301
\(887\) −0.895283 + 0.895283i −0.0300607 + 0.0300607i −0.721977 0.691917i \(-0.756767\pi\)
0.691917 + 0.721977i \(0.256767\pi\)
\(888\) 0 0
\(889\) 20.2956i 0.680691i
\(890\) −13.6051 13.3020i −0.456045 0.445882i
\(891\) 0 0
\(892\) −6.24961 6.24961i −0.209252 0.209252i
\(893\) 18.3306 + 18.3306i 0.613409 + 0.613409i
\(894\) 0 0
\(895\) 0.180235 + 15.9955i 0.00602461 + 0.534669i
\(896\) 5.88104i 0.196472i
\(897\) 0 0
\(898\) 20.2547 20.2547i 0.675909 0.675909i
\(899\) 61.6528 2.05624
\(900\) 0 0
\(901\) 31.9877 1.06566
\(902\) −27.4709 + 27.4709i −0.914680 + 0.914680i
\(903\) 0 0
\(904\) 7.78718i 0.258998i
\(905\) 0.122516 + 10.8730i 0.00407256 + 0.361430i
\(906\) 0 0
\(907\) 16.4485 + 16.4485i 0.546164 + 0.546164i 0.925329 0.379165i \(-0.123789\pi\)
−0.379165 + 0.925329i \(0.623789\pi\)
\(908\) 3.98444 + 3.98444i 0.132228 + 0.132228i
\(909\) 0 0
\(910\) −4.33964 4.24293i −0.143858 0.140652i
\(911\) 19.8928i 0.659078i −0.944142 0.329539i \(-0.893107\pi\)
0.944142 0.329539i \(-0.106893\pi\)
\(912\) 0 0
\(913\) 18.6260 18.6260i 0.616430 0.616430i
\(914\) 4.22914 0.139888
\(915\) 0 0
\(916\) −10.4217 −0.344342
\(917\) 2.28098 2.28098i 0.0753246 0.0753246i
\(918\) 0 0
\(919\) 39.3303i 1.29739i −0.761050 0.648693i \(-0.775316\pi\)
0.761050 0.648693i \(-0.224684\pi\)
\(920\) 13.9307 0.156970i 0.459282 0.00517516i
\(921\) 0 0
\(922\) 11.3760 + 11.3760i 0.374649 + 0.374649i
\(923\) 0.893009 + 0.893009i 0.0293937 + 0.0293937i
\(924\) 0 0
\(925\) 30.6707 + 29.3187i 1.00845 + 0.963992i
\(926\) 37.7844i 1.24167i
\(927\) 0 0
\(928\) 13.7875 13.7875i 0.452598 0.452598i
\(929\) 26.3786 0.865455 0.432728 0.901525i \(-0.357551\pi\)
0.432728 + 0.901525i \(0.357551\pi\)
\(930\) 0 0
\(931\) 3.54791 0.116278
\(932\) 1.85312 1.85312i 0.0607008 0.0607008i
\(933\) 0 0
\(934\) 7.26673i 0.237775i
\(935\) 24.0148 24.5622i 0.785369 0.803270i
\(936\) 0 0
\(937\) −37.2937 37.2937i −1.21833 1.21833i −0.968215 0.250118i \(-0.919531\pi\)
−0.250118 0.968215i \(-0.580469\pi\)
\(938\) 3.43389 + 3.43389i 0.112121 + 0.112121i
\(939\) 0 0
\(940\) −5.30665 + 5.42760i −0.173084 + 0.177029i
\(941\) 48.3991i 1.57776i −0.614544 0.788882i \(-0.710660\pi\)
0.614544 0.788882i \(-0.289340\pi\)
\(942\) 0 0
\(943\) 9.70107 9.70107i 0.315910 0.315910i
\(944\) 18.2915 0.595338
\(945\) 0 0
\(946\) 44.6463 1.45158
\(947\) −27.4439 + 27.4439i −0.891806 + 0.891806i −0.994693 0.102887i \(-0.967192\pi\)
0.102887 + 0.994693i \(0.467192\pi\)
\(948\) 0 0
\(949\) 15.3149i 0.497142i
\(950\) −15.8894 15.1889i −0.515520 0.492794i
\(951\) 0 0
\(952\) −7.11541 7.11541i −0.230612 0.230612i
\(953\) 7.74667 + 7.74667i 0.250939 + 0.250939i 0.821356 0.570416i \(-0.193218\pi\)
−0.570416 + 0.821356i \(0.693218\pi\)
\(954\) 0 0
\(955\) −2.21570 + 0.0249663i −0.0716984 + 0.000807892i
\(956\) 4.25463i 0.137604i
\(957\) 0 0
\(958\) −9.98648 + 9.98648i −0.322648 + 0.322648i
\(959\) −1.92486 −0.0621569
\(960\) 0 0
\(961\) 35.0467 1.13054
\(962\) 16.2866 16.2866i 0.525101 0.525101i
\(963\) 0 0
\(964\) 6.30061i 0.202929i
\(965\) −18.5951 18.1807i −0.598597 0.585258i
\(966\) 0 0
\(967\) 12.8257 + 12.8257i 0.412448 + 0.412448i 0.882590 0.470143i \(-0.155797\pi\)
−0.470143 + 0.882590i \(0.655797\pi\)
\(968\) 23.1862 + 23.1862i 0.745234 + 0.745234i
\(969\) 0 0
\(970\) 0.195762 + 17.3734i 0.00628555 + 0.557828i
\(971\) 30.4338i 0.976666i −0.872657 0.488333i \(-0.837605\pi\)
0.872657 0.488333i \(-0.162395\pi\)
\(972\) 0 0
\(973\) −15.7591 + 15.7591i −0.505213 + 0.505213i
\(974\) 19.4412 0.622935
\(975\) 0 0
\(976\) −38.8374 −1.24315
\(977\) −4.71670 + 4.71670i −0.150901 + 0.150901i −0.778520 0.627620i \(-0.784029\pi\)
0.627620 + 0.778520i \(0.284029\pi\)
\(978\) 0 0
\(979\) 32.0173i 1.02328i
\(980\) 0.0117053 + 1.03882i 0.000373912 + 0.0331838i
\(981\) 0 0
\(982\) −24.9356 24.9356i −0.795726 0.795726i
\(983\) −28.6631 28.6631i −0.914211 0.914211i 0.0823888 0.996600i \(-0.473745\pi\)
−0.996600 + 0.0823888i \(0.973745\pi\)
\(984\) 0 0
\(985\) −4.07691 3.98606i −0.129901 0.127006i
\(986\) 30.9739i 0.986409i
\(987\) 0 0
\(988\) 2.55313 2.55313i 0.0812260 0.0812260i
\(989\) −15.7664 −0.501342
\(990\) 0 0
\(991\) 40.6787 1.29220 0.646101 0.763252i \(-0.276398\pi\)
0.646101 + 0.763252i \(0.276398\pi\)
\(992\) 14.7701 14.7701i 0.468953 0.468953i
\(993\) 0 0
\(994\) 0.714408i 0.0226597i
\(995\) 35.8520 0.403977i 1.13658 0.0128069i
\(996\) 0 0
\(997\) −24.6947 24.6947i −0.782090 0.782090i 0.198094 0.980183i \(-0.436525\pi\)
−0.980183 + 0.198094i \(0.936525\pi\)
\(998\) 11.3975 + 11.3975i 0.360782 + 0.360782i
\(999\) 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.m.b.197.3 yes 12
3.2 odd 2 315.2.m.a.197.4 yes 12
5.2 odd 4 1575.2.m.c.1268.3 12
5.3 odd 4 315.2.m.a.8.4 12
5.4 even 2 1575.2.m.d.1457.4 12
15.2 even 4 1575.2.m.d.1268.4 12
15.8 even 4 inner 315.2.m.b.8.3 yes 12
15.14 odd 2 1575.2.m.c.1457.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.m.a.8.4 12 5.3 odd 4
315.2.m.a.197.4 yes 12 3.2 odd 2
315.2.m.b.8.3 yes 12 15.8 even 4 inner
315.2.m.b.197.3 yes 12 1.1 even 1 trivial
1575.2.m.c.1268.3 12 5.2 odd 4
1575.2.m.c.1457.3 12 15.14 odd 2
1575.2.m.d.1268.4 12 15.2 even 4
1575.2.m.d.1457.4 12 5.4 even 2