Properties

Label 92.2.e.a.85.1
Level $92$
Weight $2$
Character 92.85
Analytic conductor $0.735$
Analytic rank $0$
Dimension $20$
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] = [92,2,Mod(9,92)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(92, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("92.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 92.e (of order \(11\), degree \(10\), 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: \(0.734623698596\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + 14788 x^{12} - 23925 x^{11} + 35080 x^{10} - 43945 x^{9} + 57269 x^{8} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 85.1
Root \(-0.420431 + 0.123450i\) of defining polynomial
Character \(\chi\) \(=\) 92.85
Dual form 92.2.e.a.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.368621 + 0.236898i) q^{3} +(0.781296 + 1.71080i) q^{5} +(4.72847 - 1.38840i) q^{7} +(-1.16648 + 2.55425i) q^{9} +O(q^{10})\) \(q+(-0.368621 + 0.236898i) q^{3} +(0.781296 + 1.71080i) q^{5} +(4.72847 - 1.38840i) q^{7} +(-1.16648 + 2.55425i) q^{9} +(-2.86466 - 3.30599i) q^{11} +(-3.72299 - 1.09317i) q^{13} +(-0.693287 - 0.445548i) q^{15} +(-0.170460 + 1.18558i) q^{17} +(-0.220090 - 1.53076i) q^{19} +(-1.41410 + 1.63196i) q^{21} +(-4.25781 + 2.20705i) q^{23} +(0.957892 - 1.10547i) q^{25} +(-0.362184 - 2.51905i) q^{27} +(0.772612 - 5.37364i) q^{29} +(-2.63810 - 1.69540i) q^{31} +(1.83915 + 0.540024i) q^{33} +(6.06962 + 7.00471i) q^{35} +(-1.08028 + 2.36547i) q^{37} +(1.63134 - 0.479005i) q^{39} +(4.38557 + 9.60306i) q^{41} +(4.09254 - 2.63012i) q^{43} -5.28117 q^{45} -2.40483 q^{47} +(14.5420 - 9.34557i) q^{49} +(-0.218025 - 0.477409i) q^{51} +(-10.1568 + 2.98231i) q^{53} +(3.41774 - 7.48381i) q^{55} +(0.443765 + 0.512132i) q^{57} +(5.25467 + 1.54291i) q^{59} +(8.58911 + 5.51989i) q^{61} +(-1.96936 + 13.6972i) q^{63} +(-1.03857 - 7.22338i) q^{65} +(-6.95204 + 8.02308i) q^{67} +(1.04667 - 1.82223i) q^{69} +(0.461121 - 0.532163i) q^{71} +(-0.964609 - 6.70901i) q^{73} +(-0.0912159 + 0.634420i) q^{75} +(-18.1355 - 11.6550i) q^{77} +(-1.13462 - 0.333154i) q^{79} +(-4.78628 - 5.52366i) q^{81} +(-2.80407 + 6.14005i) q^{83} +(-2.16146 + 0.634662i) q^{85} +(0.988203 + 2.16386i) q^{87} +(9.29920 - 5.97623i) q^{89} -19.1218 q^{91} +1.37410 q^{93} +(2.44687 - 1.57251i) q^{95} +(3.84506 + 8.41951i) q^{97} +(11.7859 - 3.46065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/92\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(47\)
\(\chi(n)\) \(e\left(\frac{4}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.368621 + 0.236898i −0.212823 + 0.136773i −0.642710 0.766110i \(-0.722190\pi\)
0.429887 + 0.902883i \(0.358554\pi\)
\(4\) 0 0
\(5\) 0.781296 + 1.71080i 0.349406 + 0.765093i 0.999984 + 0.00565324i \(0.00179949\pi\)
−0.650578 + 0.759440i \(0.725473\pi\)
\(6\) 0 0
\(7\) 4.72847 1.38840i 1.78719 0.524767i 0.790991 0.611828i \(-0.209566\pi\)
0.996203 + 0.0870608i \(0.0277474\pi\)
\(8\) 0 0
\(9\) −1.16648 + 2.55425i −0.388828 + 0.851415i
\(10\) 0 0
\(11\) −2.86466 3.30599i −0.863727 0.996794i −0.999981 0.00611985i \(-0.998052\pi\)
0.136255 0.990674i \(-0.456493\pi\)
\(12\) 0 0
\(13\) −3.72299 1.09317i −1.03257 0.303190i −0.278816 0.960345i \(-0.589942\pi\)
−0.753756 + 0.657154i \(0.771760\pi\)
\(14\) 0 0
\(15\) −0.693287 0.445548i −0.179006 0.115040i
\(16\) 0 0
\(17\) −0.170460 + 1.18558i −0.0413426 + 0.287544i 0.958653 + 0.284578i \(0.0918534\pi\)
−0.999996 + 0.00296653i \(0.999056\pi\)
\(18\) 0 0
\(19\) −0.220090 1.53076i −0.0504922 0.351181i −0.999369 0.0355329i \(-0.988687\pi\)
0.948876 0.315648i \(-0.102222\pi\)
\(20\) 0 0
\(21\) −1.41410 + 1.63196i −0.308582 + 0.356123i
\(22\) 0 0
\(23\) −4.25781 + 2.20705i −0.887815 + 0.460201i
\(24\) 0 0
\(25\) 0.957892 1.10547i 0.191578 0.221093i
\(26\) 0 0
\(27\) −0.362184 2.51905i −0.0697024 0.484790i
\(28\) 0 0
\(29\) 0.772612 5.37364i 0.143471 0.997859i −0.783142 0.621843i \(-0.786384\pi\)
0.926613 0.376017i \(-0.122707\pi\)
\(30\) 0 0
\(31\) −2.63810 1.69540i −0.473817 0.304504i 0.281851 0.959458i \(-0.409051\pi\)
−0.755668 + 0.654954i \(0.772688\pi\)
\(32\) 0 0
\(33\) 1.83915 + 0.540024i 0.320156 + 0.0940062i
\(34\) 0 0
\(35\) 6.06962 + 7.00471i 1.02595 + 1.18401i
\(36\) 0 0
\(37\) −1.08028 + 2.36547i −0.177596 + 0.388882i −0.977406 0.211373i \(-0.932207\pi\)
0.799809 + 0.600254i \(0.204934\pi\)
\(38\) 0 0
\(39\) 1.63134 0.479005i 0.261224 0.0767022i
\(40\) 0 0
\(41\) 4.38557 + 9.60306i 0.684911 + 1.49975i 0.857354 + 0.514727i \(0.172107\pi\)
−0.172443 + 0.985019i \(0.555166\pi\)
\(42\) 0 0
\(43\) 4.09254 2.63012i 0.624107 0.401089i −0.190017 0.981781i \(-0.560854\pi\)
0.814123 + 0.580692i \(0.197218\pi\)
\(44\) 0 0
\(45\) −5.28117 −0.787270
\(46\) 0 0
\(47\) −2.40483 −0.350781 −0.175391 0.984499i \(-0.556119\pi\)
−0.175391 + 0.984499i \(0.556119\pi\)
\(48\) 0 0
\(49\) 14.5420 9.34557i 2.07743 1.33508i
\(50\) 0 0
\(51\) −0.218025 0.477409i −0.0305297 0.0668506i
\(52\) 0 0
\(53\) −10.1568 + 2.98231i −1.39514 + 0.409651i −0.891014 0.453977i \(-0.850005\pi\)
−0.504130 + 0.863628i \(0.668187\pi\)
\(54\) 0 0
\(55\) 3.41774 7.48381i 0.460848 1.00912i
\(56\) 0 0
\(57\) 0.443765 + 0.512132i 0.0587781 + 0.0678335i
\(58\) 0 0
\(59\) 5.25467 + 1.54291i 0.684100 + 0.200870i 0.605272 0.796018i \(-0.293064\pi\)
0.0788275 + 0.996888i \(0.474882\pi\)
\(60\) 0 0
\(61\) 8.58911 + 5.51989i 1.09972 + 0.706749i 0.959030 0.283304i \(-0.0914305\pi\)
0.140693 + 0.990053i \(0.455067\pi\)
\(62\) 0 0
\(63\) −1.96936 + 13.6972i −0.248116 + 1.72569i
\(64\) 0 0
\(65\) −1.03857 7.22338i −0.128818 0.895950i
\(66\) 0 0
\(67\) −6.95204 + 8.02308i −0.849327 + 0.980175i −0.999965 0.00841372i \(-0.997322\pi\)
0.150638 + 0.988589i \(0.451867\pi\)
\(68\) 0 0
\(69\) 1.04667 1.82223i 0.126004 0.219371i
\(70\) 0 0
\(71\) 0.461121 0.532163i 0.0547250 0.0631561i −0.727727 0.685867i \(-0.759423\pi\)
0.782452 + 0.622711i \(0.213969\pi\)
\(72\) 0 0
\(73\) −0.964609 6.70901i −0.112899 0.785230i −0.965075 0.261974i \(-0.915626\pi\)
0.852176 0.523255i \(-0.175283\pi\)
\(74\) 0 0
\(75\) −0.0912159 + 0.634420i −0.0105327 + 0.0732565i
\(76\) 0 0
\(77\) −18.1355 11.6550i −2.06673 1.32821i
\(78\) 0 0
\(79\) −1.13462 0.333154i −0.127655 0.0374828i 0.217281 0.976109i \(-0.430281\pi\)
−0.344936 + 0.938626i \(0.612099\pi\)
\(80\) 0 0
\(81\) −4.78628 5.52366i −0.531809 0.613740i
\(82\) 0 0
\(83\) −2.80407 + 6.14005i −0.307786 + 0.673958i −0.998805 0.0488792i \(-0.984435\pi\)
0.691018 + 0.722837i \(0.257162\pi\)
\(84\) 0 0
\(85\) −2.16146 + 0.634662i −0.234443 + 0.0688388i
\(86\) 0 0
\(87\) 0.988203 + 2.16386i 0.105947 + 0.231991i
\(88\) 0 0
\(89\) 9.29920 5.97623i 0.985713 0.633479i 0.0547144 0.998502i \(-0.482575\pi\)
0.930999 + 0.365023i \(0.118939\pi\)
\(90\) 0 0
\(91\) −19.1218 −2.00451
\(92\) 0 0
\(93\) 1.37410 0.142487
\(94\) 0 0
\(95\) 2.44687 1.57251i 0.251044 0.161336i
\(96\) 0 0
\(97\) 3.84506 + 8.41951i 0.390407 + 0.854872i 0.998154 + 0.0607409i \(0.0193464\pi\)
−0.607747 + 0.794131i \(0.707926\pi\)
\(98\) 0 0
\(99\) 11.7859 3.46065i 1.18453 0.347808i
\(100\) 0 0
\(101\) 1.68544 3.69059i 0.167707 0.367228i −0.807054 0.590478i \(-0.798939\pi\)
0.974761 + 0.223250i \(0.0716666\pi\)
\(102\) 0 0
\(103\) −4.25438 4.90982i −0.419197 0.483779i 0.506395 0.862302i \(-0.330978\pi\)
−0.925592 + 0.378522i \(0.876432\pi\)
\(104\) 0 0
\(105\) −3.89679 1.14420i −0.380288 0.111662i
\(106\) 0 0
\(107\) −1.61218 1.03608i −0.155855 0.100162i 0.460389 0.887717i \(-0.347710\pi\)
−0.616244 + 0.787555i \(0.711346\pi\)
\(108\) 0 0
\(109\) −1.90076 + 13.2201i −0.182060 + 1.26625i 0.669822 + 0.742522i \(0.266370\pi\)
−0.851882 + 0.523733i \(0.824539\pi\)
\(110\) 0 0
\(111\) −0.162164 1.12788i −0.0153920 0.107053i
\(112\) 0 0
\(113\) −3.82059 + 4.40920i −0.359411 + 0.414782i −0.906442 0.422330i \(-0.861212\pi\)
0.547031 + 0.837112i \(0.315758\pi\)
\(114\) 0 0
\(115\) −7.10242 5.55990i −0.662304 0.518464i
\(116\) 0 0
\(117\) 7.13503 8.23427i 0.659634 0.761258i
\(118\) 0 0
\(119\) 0.840043 + 5.84262i 0.0770066 + 0.535592i
\(120\) 0 0
\(121\) −1.15785 + 8.05302i −0.105259 + 0.732093i
\(122\) 0 0
\(123\) −3.89156 2.50095i −0.350890 0.225503i
\(124\) 0 0
\(125\) 11.6625 + 3.42442i 1.04313 + 0.306290i
\(126\) 0 0
\(127\) 8.93614 + 10.3129i 0.792955 + 0.915118i 0.997973 0.0636398i \(-0.0202709\pi\)
−0.205018 + 0.978758i \(0.565725\pi\)
\(128\) 0 0
\(129\) −0.885525 + 1.93903i −0.0779662 + 0.170722i
\(130\) 0 0
\(131\) 16.0487 4.71232i 1.40218 0.411718i 0.508749 0.860915i \(-0.330108\pi\)
0.893433 + 0.449197i \(0.148290\pi\)
\(132\) 0 0
\(133\) −3.16601 6.93259i −0.274528 0.601132i
\(134\) 0 0
\(135\) 4.02661 2.58774i 0.346555 0.222718i
\(136\) 0 0
\(137\) 15.3511 1.31154 0.655768 0.754963i \(-0.272345\pi\)
0.655768 + 0.754963i \(0.272345\pi\)
\(138\) 0 0
\(139\) 9.33601 0.791870 0.395935 0.918278i \(-0.370420\pi\)
0.395935 + 0.918278i \(0.370420\pi\)
\(140\) 0 0
\(141\) 0.886472 0.569701i 0.0746544 0.0479774i
\(142\) 0 0
\(143\) 7.05109 + 15.4397i 0.589642 + 1.29113i
\(144\) 0 0
\(145\) 9.79685 2.87662i 0.813585 0.238890i
\(146\) 0 0
\(147\) −3.14653 + 6.88994i −0.259521 + 0.568272i
\(148\) 0 0
\(149\) −13.3736 15.4339i −1.09561 1.26440i −0.961908 0.273375i \(-0.911860\pi\)
−0.133699 0.991022i \(-0.542685\pi\)
\(150\) 0 0
\(151\) −17.1954 5.04901i −1.39934 0.410883i −0.506882 0.862016i \(-0.669202\pi\)
−0.892457 + 0.451133i \(0.851020\pi\)
\(152\) 0 0
\(153\) −2.82941 1.81835i −0.228744 0.147005i
\(154\) 0 0
\(155\) 0.839360 5.83788i 0.0674190 0.468909i
\(156\) 0 0
\(157\) 1.85221 + 12.8824i 0.147823 + 1.02813i 0.919774 + 0.392448i \(0.128372\pi\)
−0.771952 + 0.635681i \(0.780719\pi\)
\(158\) 0 0
\(159\) 3.03750 3.50546i 0.240890 0.278001i
\(160\) 0 0
\(161\) −17.0687 + 16.3475i −1.34520 + 1.28836i
\(162\) 0 0
\(163\) −4.19935 + 4.84631i −0.328919 + 0.379593i −0.895988 0.444077i \(-0.853532\pi\)
0.567070 + 0.823670i \(0.308077\pi\)
\(164\) 0 0
\(165\) 0.513050 + 3.56834i 0.0399409 + 0.277795i
\(166\) 0 0
\(167\) 3.51397 24.4402i 0.271919 1.89124i −0.156527 0.987674i \(-0.550030\pi\)
0.428446 0.903567i \(-0.359061\pi\)
\(168\) 0 0
\(169\) 1.72935 + 1.11138i 0.133027 + 0.0854911i
\(170\) 0 0
\(171\) 4.16668 + 1.22345i 0.318634 + 0.0935593i
\(172\) 0 0
\(173\) 5.17919 + 5.97710i 0.393766 + 0.454430i 0.917668 0.397348i \(-0.130070\pi\)
−0.523902 + 0.851779i \(0.675524\pi\)
\(174\) 0 0
\(175\) 2.99453 6.55710i 0.226365 0.495671i
\(176\) 0 0
\(177\) −2.30249 + 0.676073i −0.173066 + 0.0508167i
\(178\) 0 0
\(179\) 1.49842 + 3.28107i 0.111997 + 0.245239i 0.957328 0.289004i \(-0.0933240\pi\)
−0.845331 + 0.534243i \(0.820597\pi\)
\(180\) 0 0
\(181\) −0.707821 + 0.454889i −0.0526119 + 0.0338116i −0.566682 0.823936i \(-0.691773\pi\)
0.514070 + 0.857748i \(0.328137\pi\)
\(182\) 0 0
\(183\) −4.47378 −0.330711
\(184\) 0 0
\(185\) −4.89087 −0.359584
\(186\) 0 0
\(187\) 4.40781 2.83273i 0.322331 0.207150i
\(188\) 0 0
\(189\) −5.21003 11.4084i −0.378974 0.829837i
\(190\) 0 0
\(191\) −10.2099 + 2.99788i −0.738759 + 0.216919i −0.629398 0.777083i \(-0.716699\pi\)
−0.109361 + 0.994002i \(0.534880\pi\)
\(192\) 0 0
\(193\) −5.62373 + 12.3142i −0.404805 + 0.886399i 0.591956 + 0.805970i \(0.298356\pi\)
−0.996760 + 0.0804281i \(0.974371\pi\)
\(194\) 0 0
\(195\) 2.09404 + 2.41665i 0.149957 + 0.173060i
\(196\) 0 0
\(197\) 6.29705 + 1.84898i 0.448646 + 0.131734i 0.498248 0.867035i \(-0.333977\pi\)
−0.0496017 + 0.998769i \(0.515795\pi\)
\(198\) 0 0
\(199\) −14.7385 9.47187i −1.04479 0.671443i −0.0986200 0.995125i \(-0.531443\pi\)
−0.946166 + 0.323682i \(0.895079\pi\)
\(200\) 0 0
\(201\) 0.662012 4.60440i 0.0466947 0.324769i
\(202\) 0 0
\(203\) −3.80751 26.4818i −0.267234 1.85866i
\(204\) 0 0
\(205\) −13.0025 + 15.0057i −0.908133 + 1.04804i
\(206\) 0 0
\(207\) −0.670664 13.4500i −0.0466144 0.934838i
\(208\) 0 0
\(209\) −4.43020 + 5.11273i −0.306444 + 0.353655i
\(210\) 0 0
\(211\) 0.413560 + 2.87637i 0.0284706 + 0.198017i 0.999093 0.0425924i \(-0.0135617\pi\)
−0.970622 + 0.240610i \(0.922653\pi\)
\(212\) 0 0
\(213\) −0.0439106 + 0.305405i −0.00300870 + 0.0209260i
\(214\) 0 0
\(215\) 7.69709 + 4.94662i 0.524937 + 0.337357i
\(216\) 0 0
\(217\) −14.8281 4.35392i −1.00660 0.295563i
\(218\) 0 0
\(219\) 1.94493 + 2.24456i 0.131426 + 0.151674i
\(220\) 0 0
\(221\) 1.93065 4.22754i 0.129870 0.284375i
\(222\) 0 0
\(223\) −8.98602 + 2.63853i −0.601748 + 0.176689i −0.568397 0.822755i \(-0.692436\pi\)
−0.0333512 + 0.999444i \(0.510618\pi\)
\(224\) 0 0
\(225\) 1.70627 + 3.73620i 0.113751 + 0.249080i
\(226\) 0 0
\(227\) −15.5483 + 9.99227i −1.03197 + 0.663210i −0.942989 0.332823i \(-0.891999\pi\)
−0.0889855 + 0.996033i \(0.528362\pi\)
\(228\) 0 0
\(229\) 7.98568 0.527709 0.263854 0.964563i \(-0.415006\pi\)
0.263854 + 0.964563i \(0.415006\pi\)
\(230\) 0 0
\(231\) 9.44616 0.621512
\(232\) 0 0
\(233\) −4.03131 + 2.59077i −0.264100 + 0.169727i −0.665989 0.745962i \(-0.731990\pi\)
0.401889 + 0.915688i \(0.368354\pi\)
\(234\) 0 0
\(235\) −1.87889 4.11419i −0.122565 0.268380i
\(236\) 0 0
\(237\) 0.497167 0.145982i 0.0322945 0.00948252i
\(238\) 0 0
\(239\) 4.35978 9.54659i 0.282011 0.617517i −0.714622 0.699511i \(-0.753401\pi\)
0.996633 + 0.0819934i \(0.0261286\pi\)
\(240\) 0 0
\(241\) −0.200330 0.231193i −0.0129044 0.0148924i 0.749261 0.662275i \(-0.230409\pi\)
−0.762165 + 0.647383i \(0.775864\pi\)
\(242\) 0 0
\(243\) 10.3984 + 3.05326i 0.667061 + 0.195867i
\(244\) 0 0
\(245\) 27.3500 + 17.5768i 1.74733 + 1.12294i
\(246\) 0 0
\(247\) −0.853987 + 5.93961i −0.0543379 + 0.377929i
\(248\) 0 0
\(249\) −0.420929 2.92763i −0.0266753 0.185531i
\(250\) 0 0
\(251\) 9.59046 11.0680i 0.605345 0.698605i −0.367511 0.930019i \(-0.619790\pi\)
0.972855 + 0.231414i \(0.0743353\pi\)
\(252\) 0 0
\(253\) 19.4936 + 7.75385i 1.22555 + 0.487481i
\(254\) 0 0
\(255\) 0.646409 0.745995i 0.0404797 0.0467161i
\(256\) 0 0
\(257\) −3.87846 26.9753i −0.241932 1.68267i −0.642405 0.766365i \(-0.722063\pi\)
0.400473 0.916309i \(-0.368846\pi\)
\(258\) 0 0
\(259\) −1.82382 + 12.6849i −0.113327 + 0.788203i
\(260\) 0 0
\(261\) 12.8243 + 8.24171i 0.793807 + 0.510149i
\(262\) 0 0
\(263\) −7.56887 2.22242i −0.466717 0.137040i 0.0399148 0.999203i \(-0.487291\pi\)
−0.506631 + 0.862163i \(0.669110\pi\)
\(264\) 0 0
\(265\) −13.0376 15.0462i −0.800893 0.924280i
\(266\) 0 0
\(267\) −2.01212 + 4.40592i −0.123140 + 0.269638i
\(268\) 0 0
\(269\) −3.92411 + 1.15222i −0.239257 + 0.0702523i −0.399163 0.916880i \(-0.630699\pi\)
0.159906 + 0.987132i \(0.448881\pi\)
\(270\) 0 0
\(271\) 9.94666 + 21.7801i 0.604216 + 1.32305i 0.926460 + 0.376393i \(0.122836\pi\)
−0.322244 + 0.946657i \(0.604437\pi\)
\(272\) 0 0
\(273\) 7.04869 4.52992i 0.426606 0.274163i
\(274\) 0 0
\(275\) −6.39869 −0.385856
\(276\) 0 0
\(277\) −6.86931 −0.412737 −0.206368 0.978474i \(-0.566165\pi\)
−0.206368 + 0.978474i \(0.566165\pi\)
\(278\) 0 0
\(279\) 7.40778 4.76069i 0.443492 0.285015i
\(280\) 0 0
\(281\) −5.09904 11.1653i −0.304183 0.666069i 0.694382 0.719606i \(-0.255678\pi\)
−0.998566 + 0.0535373i \(0.982950\pi\)
\(282\) 0 0
\(283\) −2.44911 + 0.719124i −0.145585 + 0.0427475i −0.353713 0.935354i \(-0.615081\pi\)
0.208128 + 0.978102i \(0.433263\pi\)
\(284\) 0 0
\(285\) −0.529443 + 1.15932i −0.0313615 + 0.0686721i
\(286\) 0 0
\(287\) 34.0700 + 39.3188i 2.01109 + 2.32092i
\(288\) 0 0
\(289\) 14.9348 + 4.38527i 0.878521 + 0.257957i
\(290\) 0 0
\(291\) −3.41194 2.19272i −0.200011 0.128539i
\(292\) 0 0
\(293\) 0.943729 6.56378i 0.0551333 0.383460i −0.943508 0.331350i \(-0.892496\pi\)
0.998641 0.0521107i \(-0.0165949\pi\)
\(294\) 0 0
\(295\) 1.46584 + 10.1952i 0.0853447 + 0.593585i
\(296\) 0 0
\(297\) −7.29041 + 8.41358i −0.423032 + 0.488205i
\(298\) 0 0
\(299\) 18.2645 3.56230i 1.05626 0.206013i
\(300\) 0 0
\(301\) 15.6998 18.1185i 0.904921 1.04433i
\(302\) 0 0
\(303\) 0.253008 + 1.75971i 0.0145349 + 0.101092i
\(304\) 0 0
\(305\) −2.73278 + 19.0069i −0.156479 + 1.08833i
\(306\) 0 0
\(307\) −3.69823 2.37671i −0.211069 0.135646i 0.430835 0.902431i \(-0.358219\pi\)
−0.641904 + 0.766785i \(0.721855\pi\)
\(308\) 0 0
\(309\) 2.73138 + 0.802006i 0.155383 + 0.0456245i
\(310\) 0 0
\(311\) −11.0320 12.7317i −0.625570 0.721946i 0.351185 0.936306i \(-0.385779\pi\)
−0.976755 + 0.214360i \(0.931233\pi\)
\(312\) 0 0
\(313\) 2.67930 5.86686i 0.151443 0.331614i −0.818671 0.574263i \(-0.805289\pi\)
0.970114 + 0.242648i \(0.0780161\pi\)
\(314\) 0 0
\(315\) −24.9719 + 7.33240i −1.40700 + 0.413134i
\(316\) 0 0
\(317\) −12.7314 27.8778i −0.715064 1.56577i −0.820694 0.571367i \(-0.806413\pi\)
0.105630 0.994406i \(-0.466314\pi\)
\(318\) 0 0
\(319\) −19.9785 + 12.8394i −1.11858 + 0.718867i
\(320\) 0 0
\(321\) 0.839728 0.0468690
\(322\) 0 0
\(323\) 1.85235 0.103068
\(324\) 0 0
\(325\) −4.77468 + 3.06850i −0.264852 + 0.170210i
\(326\) 0 0
\(327\) −2.43115 5.32348i −0.134443 0.294389i
\(328\) 0 0
\(329\) −11.3712 + 3.33888i −0.626914 + 0.184079i
\(330\) 0 0
\(331\) 12.6296 27.6549i 0.694184 1.52005i −0.152700 0.988273i \(-0.548797\pi\)
0.846884 0.531778i \(-0.178476\pi\)
\(332\) 0 0
\(333\) −4.78187 5.51858i −0.262045 0.302416i
\(334\) 0 0
\(335\) −19.1575 5.62514i −1.04669 0.307334i
\(336\) 0 0
\(337\) −18.2067 11.7007i −0.991781 0.637379i −0.0591647 0.998248i \(-0.518844\pi\)
−0.932616 + 0.360869i \(0.882480\pi\)
\(338\) 0 0
\(339\) 0.363818 2.53041i 0.0197599 0.137433i
\(340\) 0 0
\(341\) 1.95226 + 13.5783i 0.105721 + 0.735306i
\(342\) 0 0
\(343\) 33.1954 38.3096i 1.79238 2.06852i
\(344\) 0 0
\(345\) 3.93523 + 0.366945i 0.211866 + 0.0197557i
\(346\) 0 0
\(347\) −12.7458 + 14.7094i −0.684229 + 0.789642i −0.986532 0.163569i \(-0.947699\pi\)
0.302303 + 0.953212i \(0.402245\pi\)
\(348\) 0 0
\(349\) 3.04180 + 21.1562i 0.162824 + 1.13247i 0.893278 + 0.449504i \(0.148399\pi\)
−0.730454 + 0.682962i \(0.760692\pi\)
\(350\) 0 0
\(351\) −1.40533 + 9.77431i −0.0750112 + 0.521714i
\(352\) 0 0
\(353\) 4.94762 + 3.17964i 0.263335 + 0.169235i 0.665645 0.746268i \(-0.268156\pi\)
−0.402310 + 0.915503i \(0.631793\pi\)
\(354\) 0 0
\(355\) 1.27070 + 0.373110i 0.0674415 + 0.0198026i
\(356\) 0 0
\(357\) −1.69376 1.95471i −0.0896435 0.103454i
\(358\) 0 0
\(359\) −11.7559 + 25.7417i −0.620450 + 1.35860i 0.294741 + 0.955577i \(0.404767\pi\)
−0.915191 + 0.403020i \(0.867961\pi\)
\(360\) 0 0
\(361\) 15.9356 4.67911i 0.838714 0.246269i
\(362\) 0 0
\(363\) −1.48094 3.24280i −0.0777291 0.170203i
\(364\) 0 0
\(365\) 10.7241 6.89197i 0.561326 0.360742i
\(366\) 0 0
\(367\) 7.82639 0.408534 0.204267 0.978915i \(-0.434519\pi\)
0.204267 + 0.978915i \(0.434519\pi\)
\(368\) 0 0
\(369\) −29.6443 −1.54322
\(370\) 0 0
\(371\) −43.8855 + 28.2035i −2.27842 + 1.46425i
\(372\) 0 0
\(373\) −5.01953 10.9912i −0.259901 0.569105i 0.734029 0.679118i \(-0.237638\pi\)
−0.993930 + 0.110014i \(0.964910\pi\)
\(374\) 0 0
\(375\) −5.11028 + 1.50051i −0.263894 + 0.0774862i
\(376\) 0 0
\(377\) −8.75072 + 19.1614i −0.450685 + 0.986863i
\(378\) 0 0
\(379\) −5.29294 6.10838i −0.271880 0.313766i 0.603347 0.797479i \(-0.293833\pi\)
−0.875227 + 0.483713i \(0.839288\pi\)
\(380\) 0 0
\(381\) −5.73714 1.68458i −0.293923 0.0863035i
\(382\) 0 0
\(383\) 1.34988 + 0.867513i 0.0689755 + 0.0443279i 0.574674 0.818382i \(-0.305129\pi\)
−0.505699 + 0.862710i \(0.668765\pi\)
\(384\) 0 0
\(385\) 5.77014 40.1322i 0.294073 2.04533i
\(386\) 0 0
\(387\) 1.94408 + 13.5213i 0.0988229 + 0.687329i
\(388\) 0 0
\(389\) 11.4321 13.1934i 0.579632 0.668930i −0.387894 0.921704i \(-0.626797\pi\)
0.967525 + 0.252774i \(0.0813428\pi\)
\(390\) 0 0
\(391\) −1.89083 5.42417i −0.0956235 0.274312i
\(392\) 0 0
\(393\) −4.79954 + 5.53897i −0.242105 + 0.279404i
\(394\) 0 0
\(395\) −0.316513 2.20140i −0.0159255 0.110764i
\(396\) 0 0
\(397\) 2.43126 16.9098i 0.122021 0.848677i −0.833239 0.552912i \(-0.813516\pi\)
0.955261 0.295765i \(-0.0955744\pi\)
\(398\) 0 0
\(399\) 2.80937 + 1.80547i 0.140645 + 0.0903868i
\(400\) 0 0
\(401\) 1.01219 + 0.297205i 0.0505463 + 0.0148417i 0.306908 0.951739i \(-0.400706\pi\)
−0.256362 + 0.966581i \(0.582524\pi\)
\(402\) 0 0
\(403\) 7.96826 + 9.19587i 0.396927 + 0.458079i
\(404\) 0 0
\(405\) 5.71037 12.5040i 0.283751 0.621328i
\(406\) 0 0
\(407\) 10.9149 3.20489i 0.541029 0.158861i
\(408\) 0 0
\(409\) −8.51568 18.6467i −0.421073 0.922022i −0.994692 0.102899i \(-0.967188\pi\)
0.573619 0.819123i \(-0.305539\pi\)
\(410\) 0 0
\(411\) −5.65874 + 3.63665i −0.279125 + 0.179383i
\(412\) 0 0
\(413\) 26.9887 1.32803
\(414\) 0 0
\(415\) −12.6952 −0.623183
\(416\) 0 0
\(417\) −3.44145 + 2.21168i −0.168528 + 0.108307i
\(418\) 0 0
\(419\) 7.76828 + 17.0102i 0.379505 + 0.831000i 0.998944 + 0.0459551i \(0.0146331\pi\)
−0.619438 + 0.785045i \(0.712640\pi\)
\(420\) 0 0
\(421\) −1.92934 + 0.566505i −0.0940303 + 0.0276098i −0.328409 0.944536i \(-0.606513\pi\)
0.234379 + 0.972145i \(0.424694\pi\)
\(422\) 0 0
\(423\) 2.80520 6.14254i 0.136394 0.298660i
\(424\) 0 0
\(425\) 1.14733 + 1.32409i 0.0556537 + 0.0642278i
\(426\) 0 0
\(427\) 48.2772 + 14.1755i 2.33630 + 0.685999i
\(428\) 0 0
\(429\) −6.25682 4.02101i −0.302082 0.194136i
\(430\) 0 0
\(431\) 2.08461 14.4988i 0.100412 0.698383i −0.875975 0.482356i \(-0.839781\pi\)
0.976387 0.216027i \(-0.0693099\pi\)
\(432\) 0 0
\(433\) 5.18739 + 36.0791i 0.249290 + 1.73385i 0.602333 + 0.798245i \(0.294238\pi\)
−0.353043 + 0.935607i \(0.614853\pi\)
\(434\) 0 0
\(435\) −2.92986 + 3.38124i −0.140476 + 0.162118i
\(436\) 0 0
\(437\) 4.31557 + 6.03195i 0.206442 + 0.288547i
\(438\) 0 0
\(439\) −12.9843 + 14.9846i −0.619705 + 0.715178i −0.975651 0.219328i \(-0.929613\pi\)
0.355946 + 0.934507i \(0.384159\pi\)
\(440\) 0 0
\(441\) 6.90787 + 48.0453i 0.328946 + 2.28787i
\(442\) 0 0
\(443\) −0.130477 + 0.907490i −0.00619917 + 0.0431161i −0.992686 0.120723i \(-0.961479\pi\)
0.986487 + 0.163839i \(0.0523878\pi\)
\(444\) 0 0
\(445\) 17.4896 + 11.2399i 0.829085 + 0.532820i
\(446\) 0 0
\(447\) 8.58604 + 2.52109i 0.406106 + 0.119243i
\(448\) 0 0
\(449\) −18.1257 20.9182i −0.855404 0.987189i 0.144593 0.989491i \(-0.453813\pi\)
−0.999997 + 0.00230182i \(0.999267\pi\)
\(450\) 0 0
\(451\) 19.1845 42.0081i 0.903362 1.97809i
\(452\) 0 0
\(453\) 7.53466 2.21238i 0.354009 0.103947i
\(454\) 0 0
\(455\) −14.9398 32.7136i −0.700388 1.53364i
\(456\) 0 0
\(457\) 0.915093 0.588094i 0.0428062 0.0275099i −0.519063 0.854736i \(-0.673719\pi\)
0.561869 + 0.827226i \(0.310083\pi\)
\(458\) 0 0
\(459\) 3.04826 0.142280
\(460\) 0 0
\(461\) 26.7366 1.24525 0.622624 0.782521i \(-0.286066\pi\)
0.622624 + 0.782521i \(0.286066\pi\)
\(462\) 0 0
\(463\) −17.7874 + 11.4312i −0.826649 + 0.531255i −0.884211 0.467087i \(-0.845303\pi\)
0.0575626 + 0.998342i \(0.481667\pi\)
\(464\) 0 0
\(465\) 1.07358 + 2.35080i 0.0497859 + 0.109016i
\(466\) 0 0
\(467\) 24.0957 7.07515i 1.11502 0.327399i 0.328215 0.944603i \(-0.393553\pi\)
0.786803 + 0.617204i \(0.211735\pi\)
\(468\) 0 0
\(469\) −21.7332 + 47.5891i −1.00355 + 2.19746i
\(470\) 0 0
\(471\) −3.73458 4.30994i −0.172081 0.198592i
\(472\) 0 0
\(473\) −20.4189 5.99552i −0.938861 0.275674i
\(474\) 0 0
\(475\) −1.90303 1.22300i −0.0873170 0.0561152i
\(476\) 0 0
\(477\) 4.23021 29.4218i 0.193688 1.34713i
\(478\) 0 0
\(479\) 0.465539 + 3.23790i 0.0212710 + 0.147943i 0.997689 0.0679453i \(-0.0216443\pi\)
−0.976418 + 0.215888i \(0.930735\pi\)
\(480\) 0 0
\(481\) 6.60772 7.62571i 0.301286 0.347703i
\(482\) 0 0
\(483\) 2.41917 10.0696i 0.110076 0.458181i
\(484\) 0 0
\(485\) −11.4000 + 13.1563i −0.517646 + 0.597395i
\(486\) 0 0
\(487\) 1.07399 + 7.46975i 0.0486670 + 0.338487i 0.999579 + 0.0290243i \(0.00924001\pi\)
−0.950912 + 0.309462i \(0.899851\pi\)
\(488\) 0 0
\(489\) 0.399886 2.78127i 0.0180835 0.125773i
\(490\) 0 0
\(491\) 25.8706 + 16.6260i 1.16753 + 0.750323i 0.973052 0.230585i \(-0.0740640\pi\)
0.194473 + 0.980908i \(0.437700\pi\)
\(492\) 0 0
\(493\) 6.23915 + 1.83198i 0.280997 + 0.0825082i
\(494\) 0 0
\(495\) 15.1287 + 17.4595i 0.679987 + 0.784746i
\(496\) 0 0
\(497\) 1.44154 3.15654i 0.0646620 0.141590i
\(498\) 0 0
\(499\) 10.8788 3.19429i 0.487000 0.142996i −0.0290090 0.999579i \(-0.509235\pi\)
0.516009 + 0.856583i \(0.327417\pi\)
\(500\) 0 0
\(501\) 4.49452 + 9.84162i 0.200800 + 0.439691i
\(502\) 0 0
\(503\) 0.248763 0.159871i 0.0110918 0.00712828i −0.535083 0.844799i \(-0.679720\pi\)
0.546175 + 0.837671i \(0.316083\pi\)
\(504\) 0 0
\(505\) 7.63069 0.339561
\(506\) 0 0
\(507\) −0.900758 −0.0400041
\(508\) 0 0
\(509\) −27.5602 + 17.7118i −1.22158 + 0.785064i −0.982559 0.185950i \(-0.940464\pi\)
−0.239024 + 0.971014i \(0.576827\pi\)
\(510\) 0 0
\(511\) −13.8759 30.3841i −0.613835 1.34411i
\(512\) 0 0
\(513\) −3.77635 + 1.10884i −0.166730 + 0.0489563i
\(514\) 0 0
\(515\) 5.07579 11.1144i 0.223666 0.489760i
\(516\) 0 0
\(517\) 6.88903 + 7.95036i 0.302979 + 0.349656i
\(518\) 0 0
\(519\) −3.32512 0.976343i −0.145956 0.0428567i
\(520\) 0 0
\(521\) 27.1264 + 17.4331i 1.18843 + 0.763758i 0.976917 0.213617i \(-0.0685246\pi\)
0.211513 + 0.977375i \(0.432161\pi\)
\(522\) 0 0
\(523\) −0.486415 + 3.38309i −0.0212695 + 0.147932i −0.997689 0.0679508i \(-0.978354\pi\)
0.976419 + 0.215883i \(0.0692630\pi\)
\(524\) 0 0
\(525\) 0.449520 + 3.12648i 0.0196187 + 0.136451i
\(526\) 0 0
\(527\) 2.45972 2.83867i 0.107147 0.123654i
\(528\) 0 0
\(529\) 13.2579 18.7944i 0.576431 0.817146i
\(530\) 0 0
\(531\) −10.0705 + 11.6219i −0.437021 + 0.504349i
\(532\) 0 0
\(533\) −5.82967 40.5463i −0.252511 1.75625i
\(534\) 0 0
\(535\) 0.512944 3.56760i 0.0221765 0.154241i
\(536\) 0 0
\(537\) −1.32963 0.854500i −0.0573777 0.0368744i
\(538\) 0 0
\(539\) −72.5542 21.3038i −3.12513 0.917621i
\(540\) 0 0
\(541\) −20.3348 23.4676i −0.874261 1.00895i −0.999858 0.0168698i \(-0.994630\pi\)
0.125597 0.992081i \(-0.459916\pi\)
\(542\) 0 0
\(543\) 0.153155 0.335363i 0.00657251 0.0143918i
\(544\) 0 0
\(545\) −24.1020 + 7.07698i −1.03242 + 0.303145i
\(546\) 0 0
\(547\) −1.67952 3.67764i −0.0718111 0.157244i 0.870322 0.492483i \(-0.163910\pi\)
−0.942133 + 0.335238i \(0.891183\pi\)
\(548\) 0 0
\(549\) −24.1182 + 15.4998i −1.02934 + 0.661517i
\(550\) 0 0
\(551\) −8.39581 −0.357674
\(552\) 0 0
\(553\) −5.82756 −0.247813
\(554\) 0 0
\(555\) 1.80287 1.15864i 0.0765277 0.0491814i
\(556\) 0 0
\(557\) 6.65168 + 14.5652i 0.281841 + 0.617145i 0.996615 0.0822100i \(-0.0261978\pi\)
−0.714774 + 0.699355i \(0.753471\pi\)
\(558\) 0 0
\(559\) −18.1117 + 5.31806i −0.766041 + 0.224930i
\(560\) 0 0
\(561\) −0.953742 + 2.08840i −0.0402670 + 0.0881724i
\(562\) 0 0
\(563\) 15.7618 + 18.1901i 0.664282 + 0.766622i 0.983470 0.181069i \(-0.0579559\pi\)
−0.319189 + 0.947691i \(0.603410\pi\)
\(564\) 0 0
\(565\) −10.5283 3.09138i −0.442927 0.130055i
\(566\) 0 0
\(567\) −30.3008 19.4732i −1.27252 0.817796i
\(568\) 0 0
\(569\) −3.07405 + 21.3805i −0.128871 + 0.896315i 0.818118 + 0.575050i \(0.195017\pi\)
−0.946989 + 0.321266i \(0.895892\pi\)
\(570\) 0 0
\(571\) −4.76443 33.1373i −0.199385 1.38675i −0.806074 0.591815i \(-0.798412\pi\)
0.606689 0.794939i \(-0.292497\pi\)
\(572\) 0 0
\(573\) 3.05337 3.52378i 0.127556 0.147208i
\(574\) 0 0
\(575\) −1.63871 + 6.82098i −0.0683389 + 0.284454i
\(576\) 0 0
\(577\) 14.4595 16.6872i 0.601958 0.694697i −0.370219 0.928945i \(-0.620717\pi\)
0.972177 + 0.234248i \(0.0752628\pi\)
\(578\) 0 0
\(579\) −0.844199 5.87153i −0.0350837 0.244013i
\(580\) 0 0
\(581\) −4.73408 + 32.9262i −0.196403 + 1.36601i
\(582\) 0 0
\(583\) 38.9552 + 25.0350i 1.61336 + 1.03684i
\(584\) 0 0
\(585\) 19.6618 + 5.77321i 0.812913 + 0.238693i
\(586\) 0 0
\(587\) −21.0521 24.2955i −0.868915 1.00278i −0.999935 0.0114017i \(-0.996371\pi\)
0.131020 0.991380i \(-0.458175\pi\)
\(588\) 0 0
\(589\) −2.01464 + 4.41145i −0.0830119 + 0.181771i
\(590\) 0 0
\(591\) −2.75924 + 0.810186i −0.113500 + 0.0333266i
\(592\) 0 0
\(593\) 1.32781 + 2.90751i 0.0545268 + 0.119397i 0.934934 0.354821i \(-0.115458\pi\)
−0.880408 + 0.474218i \(0.842731\pi\)
\(594\) 0 0
\(595\) −9.33924 + 6.00196i −0.382871 + 0.246056i
\(596\) 0 0
\(597\) 7.67679 0.314190
\(598\) 0 0
\(599\) 25.8422 1.05588 0.527942 0.849280i \(-0.322964\pi\)
0.527942 + 0.849280i \(0.322964\pi\)
\(600\) 0 0
\(601\) 20.8313 13.3874i 0.849725 0.546085i −0.0417643 0.999127i \(-0.513298\pi\)
0.891489 + 0.453043i \(0.149661\pi\)
\(602\) 0 0
\(603\) −12.3835 27.1160i −0.504294 1.10425i
\(604\) 0 0
\(605\) −14.6817 + 4.31095i −0.596897 + 0.175265i
\(606\) 0 0
\(607\) 6.09301 13.3418i 0.247308 0.541528i −0.744745 0.667349i \(-0.767429\pi\)
0.992053 + 0.125820i \(0.0401563\pi\)
\(608\) 0 0
\(609\) 7.67701 + 8.85974i 0.311088 + 0.359015i
\(610\) 0 0
\(611\) 8.95318 + 2.62889i 0.362207 + 0.106354i
\(612\) 0 0
\(613\) −20.3237 13.0613i −0.820867 0.527539i 0.0614967 0.998107i \(-0.480413\pi\)
−0.882364 + 0.470568i \(0.844049\pi\)
\(614\) 0 0
\(615\) 1.23817 8.61166i 0.0499278 0.347256i
\(616\) 0 0
\(617\) 0.991474 + 6.89585i 0.0399152 + 0.277617i 0.999998 0.00210023i \(-0.000668525\pi\)
−0.960083 + 0.279717i \(0.909759\pi\)
\(618\) 0 0
\(619\) −10.1549 + 11.7194i −0.408160 + 0.471042i −0.922194 0.386728i \(-0.873605\pi\)
0.514034 + 0.857770i \(0.328151\pi\)
\(620\) 0 0
\(621\) 7.10176 + 9.92626i 0.284984 + 0.398327i
\(622\) 0 0
\(623\) 35.6736 41.1695i 1.42923 1.64942i
\(624\) 0 0
\(625\) 2.21252 + 15.3884i 0.0885009 + 0.615538i
\(626\) 0 0
\(627\) 0.421869 2.93416i 0.0168478 0.117179i
\(628\) 0 0
\(629\) −2.62030 1.68397i −0.104478 0.0671442i
\(630\) 0 0
\(631\) 27.0925 + 7.95506i 1.07853 + 0.316686i 0.772292 0.635268i \(-0.219110\pi\)
0.306242 + 0.951954i \(0.400928\pi\)
\(632\) 0 0
\(633\) −0.833853 0.962318i −0.0331427 0.0382487i
\(634\) 0 0
\(635\) −10.6615 + 23.3453i −0.423087 + 0.926432i
\(636\) 0 0
\(637\) −64.3560 + 18.8966i −2.54988 + 0.748711i
\(638\) 0 0
\(639\) 0.821382 + 1.79858i 0.0324934 + 0.0711506i
\(640\) 0 0
\(641\) −8.94192 + 5.74662i −0.353185 + 0.226978i −0.705187 0.709021i \(-0.749137\pi\)
0.352003 + 0.935999i \(0.385501\pi\)
\(642\) 0 0
\(643\) 3.25974 0.128551 0.0642757 0.997932i \(-0.479526\pi\)
0.0642757 + 0.997932i \(0.479526\pi\)
\(644\) 0 0
\(645\) −4.00915 −0.157860
\(646\) 0 0
\(647\) −13.6085 + 8.74564i −0.535005 + 0.343827i −0.780082 0.625677i \(-0.784823\pi\)
0.245078 + 0.969503i \(0.421187\pi\)
\(648\) 0 0
\(649\) −9.95198 21.7918i −0.390650 0.855403i
\(650\) 0 0
\(651\) 6.49737 1.90780i 0.254652 0.0747726i
\(652\) 0 0
\(653\) 7.69174 16.8426i 0.301001 0.659100i −0.697336 0.716744i \(-0.745632\pi\)
0.998337 + 0.0576440i \(0.0183588\pi\)
\(654\) 0 0
\(655\) 20.6006 + 23.7744i 0.804933 + 0.928942i
\(656\) 0 0
\(657\) 18.2616 + 5.36210i 0.712455 + 0.209196i
\(658\) 0 0
\(659\) 25.1248 + 16.1467i 0.978724 + 0.628988i 0.929119 0.369781i \(-0.120567\pi\)
0.0496051 + 0.998769i \(0.484204\pi\)
\(660\) 0 0
\(661\) −1.53664 + 10.6876i −0.0597685 + 0.415699i 0.937868 + 0.346991i \(0.112797\pi\)
−0.997637 + 0.0687078i \(0.978112\pi\)
\(662\) 0 0
\(663\) 0.289818 + 2.01573i 0.0112556 + 0.0782844i
\(664\) 0 0
\(665\) 9.38669 10.8328i 0.364000 0.420078i
\(666\) 0 0
\(667\) 8.57022 + 24.5851i 0.331840 + 0.951940i
\(668\) 0 0
\(669\) 2.68737 3.10139i 0.103900 0.119907i
\(670\) 0 0
\(671\) −6.35617 44.2081i −0.245377 1.70664i
\(672\) 0 0
\(673\) −1.42944 + 9.94197i −0.0551008 + 0.383235i 0.943547 + 0.331240i \(0.107467\pi\)
−0.998647 + 0.0519947i \(0.983442\pi\)
\(674\) 0 0
\(675\) −3.13165 2.01259i −0.120537 0.0774647i
\(676\) 0 0
\(677\) −6.79281 1.99455i −0.261069 0.0766567i 0.148579 0.988901i \(-0.452530\pi\)
−0.409648 + 0.912244i \(0.634348\pi\)
\(678\) 0 0
\(679\) 29.8709 + 34.4729i 1.14634 + 1.32295i
\(680\) 0 0
\(681\) 3.36426 7.36671i 0.128919 0.282293i
\(682\) 0 0
\(683\) 29.3356 8.61372i 1.12250 0.329595i 0.332742 0.943018i \(-0.392026\pi\)
0.789754 + 0.613423i \(0.210208\pi\)
\(684\) 0 0
\(685\) 11.9938 + 26.2627i 0.458259 + 1.00345i
\(686\) 0 0
\(687\) −2.94369 + 1.89179i −0.112309 + 0.0721764i
\(688\) 0 0
\(689\) 41.0738 1.56479
\(690\) 0 0
\(691\) −38.7392 −1.47371 −0.736854 0.676052i \(-0.763690\pi\)
−0.736854 + 0.676052i \(0.763690\pi\)
\(692\) 0 0
\(693\) 50.9244 32.7272i 1.93446 1.24320i
\(694\) 0 0
\(695\) 7.29419 + 15.9720i 0.276684 + 0.605854i
\(696\) 0 0
\(697\) −12.1327 + 3.56249i −0.459559 + 0.134939i
\(698\) 0 0
\(699\) 0.872276 1.91002i 0.0329925 0.0722436i
\(700\) 0 0
\(701\) 6.49305 + 7.49338i 0.245239 + 0.283021i 0.865002 0.501768i \(-0.167317\pi\)
−0.619763 + 0.784789i \(0.712771\pi\)
\(702\) 0 0
\(703\) 3.85874 + 1.13303i 0.145535 + 0.0427330i
\(704\) 0 0
\(705\) 1.66724 + 1.07147i 0.0627919 + 0.0403539i
\(706\) 0 0
\(707\) 2.84551 19.7909i 0.107016 0.744315i
\(708\) 0 0
\(709\) −6.17957 42.9799i −0.232079 1.61414i −0.689085 0.724680i \(-0.741988\pi\)
0.457007 0.889463i \(-0.348922\pi\)
\(710\) 0 0
\(711\) 2.17447 2.50948i 0.0815491 0.0941127i
\(712\) 0 0
\(713\) 14.9744 + 1.39630i 0.560795 + 0.0522920i
\(714\) 0 0
\(715\) −20.9053 + 24.1260i −0.781814 + 0.902261i
\(716\) 0 0
\(717\) 0.654463 + 4.55189i 0.0244414 + 0.169993i
\(718\) 0 0
\(719\) −2.66577 + 18.5408i −0.0994163 + 0.691455i 0.877772 + 0.479079i \(0.159029\pi\)
−0.977188 + 0.212376i \(0.931880\pi\)
\(720\) 0 0
\(721\) −26.9335 17.3091i −1.00306 0.644626i
\(722\) 0 0
\(723\) 0.128615 + 0.0377647i 0.00478324 + 0.00140449i
\(724\) 0 0
\(725\) −5.20029 6.00146i −0.193134 0.222889i
\(726\) 0 0
\(727\) −12.2504 + 26.8247i −0.454343 + 0.994872i 0.534398 + 0.845233i \(0.320538\pi\)
−0.988741 + 0.149639i \(0.952189\pi\)
\(728\) 0 0
\(729\) 16.4820 4.83954i 0.610443 0.179242i
\(730\) 0 0
\(731\) 2.42059 + 5.30035i 0.0895286 + 0.196040i
\(732\) 0 0
\(733\) −18.0771 + 11.6174i −0.667693 + 0.429100i −0.830093 0.557625i \(-0.811713\pi\)
0.162400 + 0.986725i \(0.448076\pi\)
\(734\) 0 0
\(735\) −14.2457 −0.525460
\(736\) 0 0
\(737\) 46.4394 1.71062
\(738\) 0 0
\(739\) −7.12581 + 4.57948i −0.262127 + 0.168459i −0.665103 0.746752i \(-0.731612\pi\)
0.402976 + 0.915211i \(0.367976\pi\)
\(740\) 0 0
\(741\) −1.09229 2.39177i −0.0401261 0.0878639i
\(742\) 0 0
\(743\) −14.0803 + 4.13436i −0.516557 + 0.151675i −0.529612 0.848240i \(-0.677663\pi\)
0.0130549 + 0.999915i \(0.495844\pi\)
\(744\) 0 0
\(745\) 15.9556 34.9380i 0.584569 1.28003i
\(746\) 0 0
\(747\) −12.4123 14.3245i −0.454142 0.524108i
\(748\) 0 0
\(749\) −9.06164 2.66074i −0.331105 0.0972212i
\(750\) 0 0
\(751\) −20.5806 13.2264i −0.750998 0.482637i 0.108296 0.994119i \(-0.465460\pi\)
−0.859294 + 0.511482i \(0.829097\pi\)
\(752\) 0 0
\(753\) −0.913258 + 6.35185i −0.0332810 + 0.231474i
\(754\) 0 0
\(755\) −4.79682 33.3626i −0.174574 1.21419i
\(756\) 0 0
\(757\) −9.25536 + 10.6813i −0.336392 + 0.388217i −0.898593 0.438784i \(-0.855409\pi\)
0.562201 + 0.827001i \(0.309955\pi\)
\(758\) 0 0
\(759\) −9.02263 + 1.75978i −0.327501 + 0.0638758i
\(760\) 0 0
\(761\) −1.37866 + 1.59106i −0.0499765 + 0.0576759i −0.780187 0.625546i \(-0.784876\pi\)
0.730211 + 0.683222i \(0.239422\pi\)
\(762\) 0 0
\(763\) 9.36713 + 65.1498i 0.339113 + 2.35858i
\(764\) 0 0
\(765\) 0.900228 6.26123i 0.0325478 0.226375i
\(766\) 0 0
\(767\) −17.8764 11.4885i −0.645481 0.414825i
\(768\) 0 0
\(769\) 25.1904 + 7.39656i 0.908388 + 0.266727i 0.702362 0.711820i \(-0.252129\pi\)
0.206026 + 0.978547i \(0.433947\pi\)
\(770\) 0 0
\(771\) 7.82008 + 9.02486i 0.281633 + 0.325022i
\(772\) 0 0
\(773\) 7.38626 16.1737i 0.265665 0.581726i −0.729043 0.684468i \(-0.760034\pi\)
0.994708 + 0.102742i \(0.0327617\pi\)
\(774\) 0 0
\(775\) −4.40123 + 1.29232i −0.158097 + 0.0464214i
\(776\) 0 0
\(777\) −2.33274 5.10799i −0.0836865 0.183248i
\(778\) 0 0
\(779\) 13.7348 8.82681i 0.492100 0.316253i
\(780\) 0 0
\(781\) −3.08028 −0.110221
\(782\) 0 0
\(783\) −13.8163 −0.493753
\(784\) 0 0
\(785\) −20.5921 + 13.2337i −0.734964 + 0.472333i
\(786\) 0 0
\(787\) 13.1874 + 28.8765i 0.470082 + 1.02934i 0.985073 + 0.172140i \(0.0550681\pi\)
−0.514991 + 0.857196i \(0.672205\pi\)
\(788\) 0 0
\(789\) 3.31653 0.973821i 0.118072 0.0346689i
\(790\) 0 0
\(791\) −11.9438 + 26.1533i −0.424673 + 0.929903i
\(792\) 0 0
\(793\) −25.9430 29.9398i −0.921264 1.06320i
\(794\) 0 0
\(795\) 8.37034 + 2.45775i 0.296865 + 0.0871675i
\(796\) 0 0
\(797\) −7.25548 4.66282i −0.257002 0.165165i 0.405795 0.913964i \(-0.366995\pi\)
−0.662798 + 0.748799i \(0.730631\pi\)
\(798\) 0 0
\(799\) 0.409928 2.85111i 0.0145022 0.100865i
\(800\) 0 0
\(801\) 4.41739 + 30.7236i 0.156081 + 1.08557i
\(802\) 0 0
\(803\) −19.4166 + 22.4080i −0.685198 + 0.790761i
\(804\) 0 0
\(805\) −41.3030 16.4288i −1.45574 0.579040i
\(806\) 0 0
\(807\) 1.17355 1.35435i 0.0413109 0.0476753i
\(808\) 0 0
\(809\) −3.59346 24.9931i −0.126339 0.878710i −0.950138 0.311828i \(-0.899059\pi\)
0.823799 0.566882i \(-0.191850\pi\)
\(810\) 0 0
\(811\) 3.24877 22.5957i 0.114080 0.793442i −0.849800 0.527105i \(-0.823278\pi\)
0.963880 0.266337i \(-0.0858134\pi\)
\(812\) 0 0
\(813\) −8.82622 5.67227i −0.309549 0.198935i
\(814\) 0 0
\(815\) −11.5720 3.39785i −0.405350 0.119021i
\(816\) 0 0
\(817\) −4.92681 5.68585i −0.172367 0.198923i
\(818\) 0 0
\(819\) 22.3053 48.8418i 0.779410 1.70667i
\(820\) 0 0
\(821\) 16.3969 4.81455i 0.572254 0.168029i 0.0172130 0.999852i \(-0.494521\pi\)
0.555041 + 0.831823i \(0.312702\pi\)
\(822\) 0 0
\(823\) −6.15836 13.4849i −0.214667 0.470055i 0.771411 0.636337i \(-0.219551\pi\)
−0.986078 + 0.166282i \(0.946824\pi\)
\(824\) 0 0
\(825\) 2.35869 1.51584i 0.0821190 0.0527747i
\(826\) 0 0
\(827\) −35.6981 −1.24135 −0.620673 0.784070i \(-0.713141\pi\)
−0.620673 + 0.784070i \(0.713141\pi\)
\(828\) 0 0
\(829\) −48.6807 −1.69075 −0.845376 0.534172i \(-0.820623\pi\)
−0.845376 + 0.534172i \(0.820623\pi\)
\(830\) 0 0
\(831\) 2.53217 1.62733i 0.0878399 0.0564513i
\(832\) 0 0
\(833\) 8.60105 + 18.8337i 0.298009 + 0.652548i
\(834\) 0 0
\(835\) 44.5578 13.0833i 1.54199 0.452768i
\(836\) 0 0
\(837\) −3.31532 + 7.25955i −0.114594 + 0.250927i
\(838\) 0 0
\(839\) −26.1538 30.1831i −0.902930 1.04204i −0.998911 0.0466532i \(-0.985144\pi\)
0.0959815 0.995383i \(-0.469401\pi\)
\(840\) 0 0
\(841\) −0.453748 0.133232i −0.0156465 0.00459422i
\(842\) 0 0
\(843\) 4.52466 + 2.90782i 0.155838 + 0.100151i
\(844\) 0 0
\(845\) −0.550223 + 3.82689i −0.0189283 + 0.131649i
\(846\) 0 0
\(847\) 5.70599 + 39.6861i 0.196060 + 1.36363i
\(848\) 0 0
\(849\) 0.732434 0.845274i 0.0251371 0.0290097i
\(850\) 0 0
\(851\) −0.621098 12.4560i −0.0212910 0.426985i
\(852\) 0 0
\(853\) −12.9783 + 14.9777i −0.444368 + 0.512828i −0.933105 0.359603i \(-0.882912\pi\)
0.488738 + 0.872431i \(0.337458\pi\)
\(854\) 0 0
\(855\) 1.16234 + 8.08422i 0.0397510 + 0.276475i
\(856\) 0 0
\(857\) 7.96630 55.4068i 0.272124 1.89266i −0.154119 0.988052i \(-0.549254\pi\)
0.426243 0.904609i \(-0.359837\pi\)
\(858\) 0 0
\(859\) −22.2351 14.2896i −0.758650 0.487555i 0.103236 0.994657i \(-0.467080\pi\)
−0.861886 + 0.507102i \(0.830717\pi\)
\(860\) 0 0
\(861\) −21.8734 6.42262i −0.745445 0.218882i
\(862\) 0 0
\(863\) 3.75417 + 4.33254i 0.127793 + 0.147481i 0.816040 0.577995i \(-0.196165\pi\)
−0.688247 + 0.725477i \(0.741619\pi\)
\(864\) 0 0
\(865\) −6.17914 + 13.5304i −0.210097 + 0.460049i
\(866\) 0 0
\(867\) −6.54415 + 1.92154i −0.222251 + 0.0652588i
\(868\) 0 0
\(869\) 2.14889 + 4.70541i 0.0728961 + 0.159620i
\(870\) 0 0
\(871\) 34.6530 22.2701i 1.17417 0.754594i
\(872\) 0 0
\(873\) −25.9907 −0.879652
\(874\) 0 0
\(875\) 59.9003 2.02500
\(876\) 0 0
\(877\) 13.4023 8.61310i 0.452562 0.290844i −0.294435 0.955672i \(-0.595131\pi\)
0.746997 + 0.664828i \(0.231495\pi\)
\(878\) 0 0
\(879\) 1.20707 + 2.64311i 0.0407134 + 0.0891500i
\(880\) 0 0
\(881\) −12.1413 + 3.56502i −0.409052 + 0.120108i −0.479783 0.877387i \(-0.659285\pi\)
0.0707316 + 0.997495i \(0.477467\pi\)
\(882\) 0 0
\(883\) −21.1509 + 46.3141i −0.711786 + 1.55859i 0.113284 + 0.993563i \(0.463863\pi\)
−0.825070 + 0.565031i \(0.808864\pi\)
\(884\) 0 0
\(885\) −2.95555 3.41089i −0.0993498 0.114656i
\(886\) 0 0
\(887\) −36.6085 10.7492i −1.22919 0.360923i −0.398247 0.917278i \(-0.630381\pi\)
−0.830945 + 0.556355i \(0.812200\pi\)
\(888\) 0 0
\(889\) 56.5727 + 36.3571i 1.89739 + 1.21938i
\(890\) 0 0
\(891\) −4.55012 + 31.6468i −0.152435 + 1.06021i
\(892\) 0 0
\(893\) 0.529281 + 3.68123i 0.0177117 + 0.123188i
\(894\) 0 0
\(895\) −4.44255 + 5.12698i −0.148498 + 0.171376i
\(896\) 0 0
\(897\) −5.88875 + 5.63995i −0.196620 + 0.188313i
\(898\) 0 0
\(899\) −11.1487 + 12.8663i −0.371831 + 0.429115i
\(900\) 0 0
\(901\) −1.80442 12.5500i −0.0601139 0.418102i
\(902\) 0 0
\(903\) −1.49502 + 10.3981i −0.0497512 + 0.346028i
\(904\) 0 0
\(905\) −1.33124 0.855536i −0.0442519 0.0284390i
\(906\) 0 0
\(907\) 50.1722 + 14.7319i 1.66594 + 0.489164i 0.972802 0.231639i \(-0.0744089\pi\)
0.693139 + 0.720804i \(0.256227\pi\)
\(908\) 0 0
\(909\) 7.46064 + 8.61004i 0.247454 + 0.285577i
\(910\) 0 0
\(911\) −18.2870 + 40.0430i −0.605876 + 1.32668i 0.319484 + 0.947592i \(0.396491\pi\)
−0.925359 + 0.379091i \(0.876237\pi\)
\(912\) 0 0
\(913\) 28.3316 8.31892i 0.937640 0.275316i
\(914\) 0 0
\(915\) −3.49534 7.65373i −0.115552 0.253025i
\(916\) 0 0
\(917\) 69.3432 44.5642i 2.28991 1.47164i
\(918\) 0 0
\(919\) 3.28315 0.108301 0.0541506 0.998533i \(-0.482755\pi\)
0.0541506 + 0.998533i \(0.482755\pi\)
\(920\) 0 0
\(921\) 1.92628 0.0634730
\(922\) 0 0
\(923\) −2.29849 + 1.47715i −0.0756559 + 0.0486211i
\(924\) 0 0
\(925\) 1.58016 + 3.46008i 0.0519555 + 0.113767i
\(926\) 0 0
\(927\) 17.5036 5.13951i 0.574892 0.168804i
\(928\) 0 0
\(929\) 2.83159 6.20032i 0.0929015 0.203426i −0.857477 0.514523i \(-0.827969\pi\)
0.950378 + 0.311097i \(0.100696\pi\)
\(930\) 0 0
\(931\) −17.5064 20.2035i −0.573749 0.662142i
\(932\) 0 0
\(933\) 7.08274 + 2.07968i 0.231878 + 0.0680857i
\(934\) 0 0
\(935\) 8.29003 + 5.32768i 0.271113 + 0.174234i
\(936\) 0 0
\(937\) −5.62857 + 39.1475i −0.183877 + 1.27889i 0.663610 + 0.748079i \(0.269023\pi\)
−0.847487 + 0.530816i \(0.821886\pi\)
\(938\) 0 0
\(939\) 0.402201 + 2.79737i 0.0131253 + 0.0912886i
\(940\) 0 0
\(941\) −1.78856 + 2.06411i −0.0583055 + 0.0672882i −0.784153 0.620567i \(-0.786902\pi\)
0.725848 + 0.687856i \(0.241448\pi\)
\(942\) 0 0
\(943\) −39.8673 31.2089i −1.29826 1.01630i
\(944\) 0 0
\(945\) 15.4469 17.8266i 0.502487 0.579900i
\(946\) 0 0
\(947\) −0.370338 2.57576i −0.0120344 0.0837010i 0.982919 0.184038i \(-0.0589170\pi\)
−0.994954 + 0.100337i \(0.968008\pi\)
\(948\) 0 0
\(949\) −3.74284 + 26.0320i −0.121498 + 0.845036i
\(950\) 0 0
\(951\) 11.2972 + 7.26029i 0.366338 + 0.235431i
\(952\) 0 0
\(953\) −21.8091 6.40372i −0.706465 0.207437i −0.0912867 0.995825i \(-0.529098\pi\)
−0.615179 + 0.788388i \(0.710916\pi\)
\(954\) 0 0
\(955\) −13.1057 15.1248i −0.424090 0.489426i
\(956\) 0 0
\(957\) 4.32285 9.46572i 0.139738 0.305983i
\(958\) 0 0
\(959\) 72.5873 21.3136i 2.34397 0.688251i
\(960\) 0 0
\(961\) −8.79268 19.2533i −0.283635 0.621074i
\(962\) 0 0
\(963\) 4.52699 2.90932i 0.145880 0.0937516i
\(964\) 0 0
\(965\) −25.4610 −0.819618
\(966\) 0 0
\(967\) 23.9400 0.769858 0.384929 0.922946i \(-0.374226\pi\)
0.384929 + 0.922946i \(0.374226\pi\)
\(968\) 0 0
\(969\) −0.682815 + 0.438818i −0.0219352 + 0.0140969i
\(970\) 0 0
\(971\) 21.2660 + 46.5659i 0.682457 + 1.49437i 0.860019 + 0.510262i \(0.170452\pi\)
−0.177562 + 0.984110i \(0.556821\pi\)
\(972\) 0 0
\(973\) 44.1451 12.9622i 1.41523 0.415548i
\(974\) 0 0
\(975\) 1.03312 2.26223i 0.0330865 0.0724492i
\(976\) 0 0
\(977\) 3.82983 + 4.41985i 0.122527 + 0.141404i 0.813699 0.581287i \(-0.197451\pi\)
−0.691172 + 0.722691i \(0.742905\pi\)
\(978\) 0 0
\(979\) −46.3964 13.6232i −1.48283 0.435400i
\(980\) 0 0
\(981\) −31.5501 20.2760i −1.00732 0.647364i
\(982\) 0 0
\(983\) −5.25276 + 36.5338i −0.167537 + 1.16525i 0.716417 + 0.697673i \(0.245781\pi\)
−0.883954 + 0.467574i \(0.845128\pi\)
\(984\) 0 0
\(985\) 1.75662 + 12.2176i 0.0559707 + 0.389285i
\(986\) 0 0
\(987\) 3.40068 3.92459i 0.108245 0.124921i
\(988\) 0 0
\(989\) −11.6205 + 20.2310i −0.369510 + 0.643307i
\(990\) 0 0
\(991\) 25.7157 29.6775i 0.816885 0.942736i −0.182294 0.983244i \(-0.558352\pi\)
0.999179 + 0.0405085i \(0.0128978\pi\)
\(992\) 0 0
\(993\) 1.89587 + 13.1861i 0.0601637 + 0.418448i
\(994\) 0 0
\(995\) 4.68933 32.6150i 0.148662 1.03396i
\(996\) 0 0
\(997\) 25.8118 + 16.5882i 0.817468 + 0.525354i 0.881273 0.472608i \(-0.156687\pi\)
−0.0638053 + 0.997962i \(0.520324\pi\)
\(998\) 0 0
\(999\) 6.34999 + 1.86453i 0.200905 + 0.0589910i
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 92.2.e.a.85.1 yes 20
3.2 odd 2 828.2.q.a.361.1 20
4.3 odd 2 368.2.m.d.177.2 20
23.6 even 11 2116.2.a.j.1.5 10
23.13 even 11 inner 92.2.e.a.13.1 20
23.17 odd 22 2116.2.a.i.1.5 10
69.59 odd 22 828.2.q.a.289.1 20
92.59 odd 22 368.2.m.d.289.2 20
92.63 even 22 8464.2.a.cd.1.6 10
92.75 odd 22 8464.2.a.ce.1.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
92.2.e.a.13.1 20 23.13 even 11 inner
92.2.e.a.85.1 yes 20 1.1 even 1 trivial
368.2.m.d.177.2 20 4.3 odd 2
368.2.m.d.289.2 20 92.59 odd 22
828.2.q.a.289.1 20 69.59 odd 22
828.2.q.a.361.1 20 3.2 odd 2
2116.2.a.i.1.5 10 23.17 odd 22
2116.2.a.j.1.5 10 23.6 even 11
8464.2.a.cd.1.6 10 92.63 even 22
8464.2.a.ce.1.6 10 92.75 odd 22