Properties

Label 1155.2.k.a.769.2
Level $1155$
Weight $2$
Character 1155.769
Analytic conductor $9.223$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(769,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.769");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.k (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 769.2
Character \(\chi\) \(=\) 1155.769
Dual form 1155.2.k.a.769.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.66471 q^{2} -1.00000 q^{3} +5.10065 q^{4} +(1.18527 + 1.89608i) q^{5} +2.66471 q^{6} +(2.09935 - 1.61019i) q^{7} -8.26233 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.66471 q^{2} -1.00000 q^{3} +5.10065 q^{4} +(1.18527 + 1.89608i) q^{5} +2.66471 q^{6} +(2.09935 - 1.61019i) q^{7} -8.26233 q^{8} +1.00000 q^{9} +(-3.15840 - 5.05250i) q^{10} +(1.90151 + 2.71740i) q^{11} -5.10065 q^{12} +0.864827i q^{13} +(-5.59415 + 4.29069i) q^{14} +(-1.18527 - 1.89608i) q^{15} +11.8154 q^{16} +1.53725i q^{17} -2.66471 q^{18} -2.68287 q^{19} +(6.04566 + 9.67127i) q^{20} +(-2.09935 + 1.61019i) q^{21} +(-5.06697 - 7.24106i) q^{22} +7.32990i q^{23} +8.26233 q^{24} +(-2.19026 + 4.49475i) q^{25} -2.30451i q^{26} -1.00000 q^{27} +(10.7081 - 8.21304i) q^{28} +1.42095i q^{29} +(3.15840 + 5.05250i) q^{30} +0.551846i q^{31} -14.9598 q^{32} +(-1.90151 - 2.71740i) q^{33} -4.09632i q^{34} +(5.54136 + 2.07203i) q^{35} +5.10065 q^{36} +5.97120i q^{37} +7.14906 q^{38} -0.864827i q^{39} +(-9.79311 - 15.6661i) q^{40} +0.607303 q^{41} +(5.59415 - 4.29069i) q^{42} -0.823316 q^{43} +(9.69896 + 13.8605i) q^{44} +(1.18527 + 1.89608i) q^{45} -19.5320i q^{46} -8.37543 q^{47} -11.8154 q^{48} +(1.81456 - 6.76072i) q^{49} +(5.83640 - 11.9772i) q^{50} -1.53725i q^{51} +4.41118i q^{52} -8.21534i q^{53} +2.66471 q^{54} +(-2.89860 + 6.82628i) q^{55} +(-17.3455 + 13.3039i) q^{56} +2.68287 q^{57} -3.78641i q^{58} -14.3900i q^{59} +(-6.04566 - 9.67127i) q^{60} +6.95852 q^{61} -1.47051i q^{62} +(2.09935 - 1.61019i) q^{63} +16.2328 q^{64} +(-1.63978 + 1.02505i) q^{65} +(5.06697 + 7.24106i) q^{66} -7.78444i q^{67} +7.84099i q^{68} -7.32990i q^{69} +(-14.7661 - 5.52135i) q^{70} -4.38660 q^{71} -8.26233 q^{72} +3.89027i q^{73} -15.9115i q^{74} +(2.19026 - 4.49475i) q^{75} -13.6844 q^{76} +(8.36748 + 2.64297i) q^{77} +2.30451i q^{78} +8.94533i q^{79} +(14.0044 + 22.4029i) q^{80} +1.00000 q^{81} -1.61828 q^{82} +13.1440i q^{83} +(-10.7081 + 8.21304i) q^{84} +(-2.91476 + 1.82206i) q^{85} +2.19389 q^{86} -1.42095i q^{87} +(-15.7109 - 22.4520i) q^{88} +7.51433i q^{89} +(-3.15840 - 5.05250i) q^{90} +(1.39254 + 1.81558i) q^{91} +37.3873i q^{92} -0.551846i q^{93} +22.3180 q^{94} +(-3.17993 - 5.08694i) q^{95} +14.9598 q^{96} +18.3921 q^{97} +(-4.83526 + 18.0153i) q^{98} +(1.90151 + 2.71740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66471 −1.88423 −0.942116 0.335288i \(-0.891166\pi\)
−0.942116 + 0.335288i \(0.891166\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.10065 2.55033
\(5\) 1.18527 + 1.89608i 0.530070 + 0.847954i
\(6\) 2.66471 1.08786
\(7\) 2.09935 1.61019i 0.793480 0.608596i
\(8\) −8.26233 −2.92118
\(9\) 1.00000 0.333333
\(10\) −3.15840 5.05250i −0.998774 1.59774i
\(11\) 1.90151 + 2.71740i 0.573328 + 0.819326i
\(12\) −5.10065 −1.47243
\(13\) 0.864827i 0.239860i 0.992782 + 0.119930i \(0.0382670\pi\)
−0.992782 + 0.119930i \(0.961733\pi\)
\(14\) −5.59415 + 4.29069i −1.49510 + 1.14673i
\(15\) −1.18527 1.89608i −0.306036 0.489567i
\(16\) 11.8154 2.95384
\(17\) 1.53725i 0.372838i 0.982470 + 0.186419i \(0.0596882\pi\)
−0.982470 + 0.186419i \(0.940312\pi\)
\(18\) −2.66471 −0.628077
\(19\) −2.68287 −0.615493 −0.307746 0.951468i \(-0.599575\pi\)
−0.307746 + 0.951468i \(0.599575\pi\)
\(20\) 6.04566 + 9.67127i 1.35185 + 2.16256i
\(21\) −2.09935 + 1.61019i −0.458116 + 0.351373i
\(22\) −5.06697 7.24106i −1.08028 1.54380i
\(23\) 7.32990i 1.52839i 0.644985 + 0.764195i \(0.276864\pi\)
−0.644985 + 0.764195i \(0.723136\pi\)
\(24\) 8.26233 1.68654
\(25\) −2.19026 + 4.49475i −0.438052 + 0.898949i
\(26\) 2.30451i 0.451951i
\(27\) −1.00000 −0.192450
\(28\) 10.7081 8.21304i 2.02364 1.55212i
\(29\) 1.42095i 0.263864i 0.991259 + 0.131932i \(0.0421180\pi\)
−0.991259 + 0.131932i \(0.957882\pi\)
\(30\) 3.15840 + 5.05250i 0.576642 + 0.922457i
\(31\) 0.551846i 0.0991145i 0.998771 + 0.0495573i \(0.0157810\pi\)
−0.998771 + 0.0495573i \(0.984219\pi\)
\(32\) −14.9598 −2.64455
\(33\) −1.90151 2.71740i −0.331011 0.473038i
\(34\) 4.09632i 0.702513i
\(35\) 5.54136 + 2.07203i 0.936661 + 0.350237i
\(36\) 5.10065 0.850109
\(37\) 5.97120i 0.981660i 0.871255 + 0.490830i \(0.163306\pi\)
−0.871255 + 0.490830i \(0.836694\pi\)
\(38\) 7.14906 1.15973
\(39\) 0.864827i 0.138483i
\(40\) −9.79311 15.6661i −1.54843 2.47702i
\(41\) 0.607303 0.0948447 0.0474224 0.998875i \(-0.484899\pi\)
0.0474224 + 0.998875i \(0.484899\pi\)
\(42\) 5.59415 4.29069i 0.863197 0.662068i
\(43\) −0.823316 −0.125554 −0.0627772 0.998028i \(-0.519996\pi\)
−0.0627772 + 0.998028i \(0.519996\pi\)
\(44\) 9.69896 + 13.8605i 1.46217 + 2.08955i
\(45\) 1.18527 + 1.89608i 0.176690 + 0.282651i
\(46\) 19.5320i 2.87984i
\(47\) −8.37543 −1.22168 −0.610841 0.791753i \(-0.709168\pi\)
−0.610841 + 0.791753i \(0.709168\pi\)
\(48\) −11.8154 −1.70540
\(49\) 1.81456 6.76072i 0.259223 0.965818i
\(50\) 5.83640 11.9772i 0.825392 1.69383i
\(51\) 1.53725i 0.215258i
\(52\) 4.41118i 0.611721i
\(53\) 8.21534i 1.12846i −0.825616 0.564232i \(-0.809172\pi\)
0.825616 0.564232i \(-0.190828\pi\)
\(54\) 2.66471 0.362620
\(55\) −2.89860 + 6.82628i −0.390847 + 0.920455i
\(56\) −17.3455 + 13.3039i −2.31790 + 1.77781i
\(57\) 2.68287 0.355355
\(58\) 3.78641i 0.497180i
\(59\) 14.3900i 1.87341i −0.350114 0.936707i \(-0.613857\pi\)
0.350114 0.936707i \(-0.386143\pi\)
\(60\) −6.04566 9.67127i −0.780492 1.24855i
\(61\) 6.95852 0.890947 0.445473 0.895295i \(-0.353035\pi\)
0.445473 + 0.895295i \(0.353035\pi\)
\(62\) 1.47051i 0.186755i
\(63\) 2.09935 1.61019i 0.264493 0.202865i
\(64\) 16.2328 2.02910
\(65\) −1.63978 + 1.02505i −0.203390 + 0.127142i
\(66\) 5.06697 + 7.24106i 0.623701 + 0.891313i
\(67\) 7.78444i 0.951021i −0.879710 0.475510i \(-0.842263\pi\)
0.879710 0.475510i \(-0.157737\pi\)
\(68\) 7.84099i 0.950859i
\(69\) 7.32990i 0.882416i
\(70\) −14.7661 5.52135i −1.76489 0.659928i
\(71\) −4.38660 −0.520594 −0.260297 0.965529i \(-0.583820\pi\)
−0.260297 + 0.965529i \(0.583820\pi\)
\(72\) −8.26233 −0.973725
\(73\) 3.89027i 0.455322i 0.973740 + 0.227661i \(0.0731078\pi\)
−0.973740 + 0.227661i \(0.926892\pi\)
\(74\) 15.9115i 1.84967i
\(75\) 2.19026 4.49475i 0.252910 0.519009i
\(76\) −13.6844 −1.56971
\(77\) 8.36748 + 2.64297i 0.953563 + 0.301195i
\(78\) 2.30451i 0.260934i
\(79\) 8.94533i 1.00643i 0.864162 + 0.503214i \(0.167849\pi\)
−0.864162 + 0.503214i \(0.832151\pi\)
\(80\) 14.0044 + 22.4029i 1.56574 + 2.50472i
\(81\) 1.00000 0.111111
\(82\) −1.61828 −0.178709
\(83\) 13.1440i 1.44274i 0.692549 + 0.721371i \(0.256488\pi\)
−0.692549 + 0.721371i \(0.743512\pi\)
\(84\) −10.7081 + 8.21304i −1.16835 + 0.896116i
\(85\) −2.91476 + 1.82206i −0.316150 + 0.197630i
\(86\) 2.19389 0.236574
\(87\) 1.42095i 0.152342i
\(88\) −15.7109 22.4520i −1.67479 2.39340i
\(89\) 7.51433i 0.796517i 0.917273 + 0.398259i \(0.130385\pi\)
−0.917273 + 0.398259i \(0.869615\pi\)
\(90\) −3.15840 5.05250i −0.332925 0.532581i
\(91\) 1.39254 + 1.81558i 0.145978 + 0.190324i
\(92\) 37.3873i 3.89790i
\(93\) 0.551846i 0.0572238i
\(94\) 22.3180 2.30193
\(95\) −3.17993 5.08694i −0.326254 0.521909i
\(96\) 14.9598 1.52683
\(97\) 18.3921 1.86744 0.933719 0.358007i \(-0.116544\pi\)
0.933719 + 0.358007i \(0.116544\pi\)
\(98\) −4.83526 + 18.0153i −0.488435 + 1.81982i
\(99\) 1.90151 + 2.71740i 0.191109 + 0.273109i
\(100\) −11.1718 + 22.9262i −1.11718 + 2.29262i
\(101\) −17.7370 −1.76490 −0.882451 0.470405i \(-0.844108\pi\)
−0.882451 + 0.470405i \(0.844108\pi\)
\(102\) 4.09632i 0.405596i
\(103\) −15.5720 −1.53436 −0.767180 0.641432i \(-0.778341\pi\)
−0.767180 + 0.641432i \(0.778341\pi\)
\(104\) 7.14549i 0.700673i
\(105\) −5.54136 2.07203i −0.540782 0.202209i
\(106\) 21.8915i 2.12629i
\(107\) 16.4098 1.58639 0.793197 0.608965i \(-0.208415\pi\)
0.793197 + 0.608965i \(0.208415\pi\)
\(108\) −5.10065 −0.490811
\(109\) 11.4582i 1.09749i 0.835988 + 0.548747i \(0.184895\pi\)
−0.835988 + 0.548747i \(0.815105\pi\)
\(110\) 7.72392 18.1900i 0.736447 1.73435i
\(111\) 5.97120i 0.566762i
\(112\) 24.8046 19.0250i 2.34382 1.79770i
\(113\) 3.87929i 0.364933i 0.983212 + 0.182466i \(0.0584081\pi\)
−0.983212 + 0.182466i \(0.941592\pi\)
\(114\) −7.14906 −0.669571
\(115\) −13.8981 + 8.68792i −1.29600 + 0.810153i
\(116\) 7.24777i 0.672939i
\(117\) 0.864827i 0.0799533i
\(118\) 38.3450i 3.52995i
\(119\) 2.47527 + 3.22723i 0.226908 + 0.295840i
\(120\) 9.79311 + 15.6661i 0.893984 + 1.43011i
\(121\) −3.76850 + 10.3343i −0.342591 + 0.939485i
\(122\) −18.5424 −1.67875
\(123\) −0.607303 −0.0547586
\(124\) 2.81478i 0.252774i
\(125\) −11.1185 + 1.17458i −0.994466 + 0.105057i
\(126\) −5.59415 + 4.29069i −0.498367 + 0.382245i
\(127\) 16.1339 1.43165 0.715825 0.698279i \(-0.246051\pi\)
0.715825 + 0.698279i \(0.246051\pi\)
\(128\) −13.3359 −1.17874
\(129\) 0.823316 0.0724889
\(130\) 4.36954 2.73147i 0.383234 0.239566i
\(131\) −7.98104 −0.697307 −0.348653 0.937252i \(-0.613361\pi\)
−0.348653 + 0.937252i \(0.613361\pi\)
\(132\) −9.69896 13.8605i −0.844186 1.20640i
\(133\) −5.63229 + 4.31994i −0.488381 + 0.374586i
\(134\) 20.7432i 1.79194i
\(135\) −1.18527 1.89608i −0.102012 0.163189i
\(136\) 12.7013i 1.08913i
\(137\) 13.3208i 1.13807i 0.822312 + 0.569037i \(0.192684\pi\)
−0.822312 + 0.569037i \(0.807316\pi\)
\(138\) 19.5320i 1.66268i
\(139\) −5.61484 −0.476245 −0.238122 0.971235i \(-0.576532\pi\)
−0.238122 + 0.971235i \(0.576532\pi\)
\(140\) 28.2646 + 10.5687i 2.38879 + 0.893219i
\(141\) 8.37543 0.705338
\(142\) 11.6890 0.980919
\(143\) −2.35008 + 1.64448i −0.196523 + 0.137518i
\(144\) 11.8154 0.984614
\(145\) −2.69424 + 1.68421i −0.223744 + 0.139866i
\(146\) 10.3664i 0.857932i
\(147\) −1.81456 + 6.76072i −0.149662 + 0.557615i
\(148\) 30.4571i 2.50355i
\(149\) 6.63536i 0.543590i 0.962355 + 0.271795i \(0.0876172\pi\)
−0.962355 + 0.271795i \(0.912383\pi\)
\(150\) −5.83640 + 11.9772i −0.476540 + 0.977932i
\(151\) 16.7964i 1.36687i −0.730010 0.683436i \(-0.760485\pi\)
0.730010 0.683436i \(-0.239515\pi\)
\(152\) 22.1668 1.79796
\(153\) 1.53725i 0.124279i
\(154\) −22.2969 7.04274i −1.79673 0.567520i
\(155\) −1.04635 + 0.654088i −0.0840446 + 0.0525376i
\(156\) 4.41118i 0.353177i
\(157\) −6.52197 −0.520510 −0.260255 0.965540i \(-0.583807\pi\)
−0.260255 + 0.965540i \(0.583807\pi\)
\(158\) 23.8367i 1.89634i
\(159\) 8.21534i 0.651519i
\(160\) −17.7314 28.3651i −1.40179 2.24245i
\(161\) 11.8026 + 15.3880i 0.930172 + 1.21275i
\(162\) −2.66471 −0.209359
\(163\) 3.51503i 0.275318i −0.990480 0.137659i \(-0.956042\pi\)
0.990480 0.137659i \(-0.0439578\pi\)
\(164\) 3.09764 0.241885
\(165\) 2.89860 6.82628i 0.225656 0.531425i
\(166\) 35.0249i 2.71846i
\(167\) 16.2402i 1.25671i −0.777928 0.628354i \(-0.783729\pi\)
0.777928 0.628354i \(-0.216271\pi\)
\(168\) 17.3455 13.3039i 1.33824 1.02642i
\(169\) 12.2521 0.942467
\(170\) 7.76697 4.85525i 0.595699 0.372381i
\(171\) −2.68287 −0.205164
\(172\) −4.19945 −0.320205
\(173\) 9.54156i 0.725432i −0.931900 0.362716i \(-0.881850\pi\)
0.931900 0.362716i \(-0.118150\pi\)
\(174\) 3.78641i 0.287047i
\(175\) 2.63928 + 12.9628i 0.199511 + 0.979896i
\(176\) 22.4671 + 32.1071i 1.69352 + 2.42016i
\(177\) 14.3900i 1.08162i
\(178\) 20.0235i 1.50082i
\(179\) −14.7615 −1.10333 −0.551664 0.834066i \(-0.686007\pi\)
−0.551664 + 0.834066i \(0.686007\pi\)
\(180\) 6.04566 + 9.67127i 0.450617 + 0.720854i
\(181\) 23.2469i 1.72793i 0.503555 + 0.863963i \(0.332025\pi\)
−0.503555 + 0.863963i \(0.667975\pi\)
\(182\) −3.71070 4.83798i −0.275056 0.358615i
\(183\) −6.95852 −0.514388
\(184\) 60.5621i 4.46470i
\(185\) −11.3219 + 7.07750i −0.832403 + 0.520348i
\(186\) 1.47051i 0.107823i
\(187\) −4.17732 + 2.92310i −0.305476 + 0.213758i
\(188\) −42.7202 −3.11569
\(189\) −2.09935 + 1.61019i −0.152705 + 0.117124i
\(190\) 8.47358 + 13.5552i 0.614738 + 0.983398i
\(191\) 15.8968 1.15025 0.575125 0.818066i \(-0.304953\pi\)
0.575125 + 0.818066i \(0.304953\pi\)
\(192\) −16.2328 −1.17150
\(193\) −8.32276 −0.599085 −0.299543 0.954083i \(-0.596834\pi\)
−0.299543 + 0.954083i \(0.596834\pi\)
\(194\) −49.0096 −3.51868
\(195\) 1.63978 1.02505i 0.117427 0.0734057i
\(196\) 9.25543 34.4841i 0.661102 2.46315i
\(197\) −13.2323 −0.942762 −0.471381 0.881930i \(-0.656244\pi\)
−0.471381 + 0.881930i \(0.656244\pi\)
\(198\) −5.06697 7.24106i −0.360094 0.514600i
\(199\) 3.83430i 0.271806i −0.990722 0.135903i \(-0.956606\pi\)
0.990722 0.135903i \(-0.0433936\pi\)
\(200\) 18.0967 37.1371i 1.27963 2.62599i
\(201\) 7.78444i 0.549072i
\(202\) 47.2640 3.32548
\(203\) 2.28800 + 2.98307i 0.160586 + 0.209371i
\(204\) 7.84099i 0.548979i
\(205\) 0.719819 + 1.15150i 0.0502743 + 0.0804240i
\(206\) 41.4949 2.89109
\(207\) 7.32990i 0.509463i
\(208\) 10.2182i 0.708508i
\(209\) −5.10151 7.29042i −0.352879 0.504289i
\(210\) 14.7661 + 5.52135i 1.01896 + 0.381009i
\(211\) 17.3558i 1.19482i 0.801934 + 0.597412i \(0.203804\pi\)
−0.801934 + 0.597412i \(0.796196\pi\)
\(212\) 41.9036i 2.87795i
\(213\) 4.38660 0.300565
\(214\) −43.7273 −2.98913
\(215\) −0.975853 1.56107i −0.0665526 0.106464i
\(216\) 8.26233 0.562180
\(217\) 0.888579 + 1.15852i 0.0603207 + 0.0786454i
\(218\) 30.5327i 2.06793i
\(219\) 3.89027i 0.262880i
\(220\) −14.7848 + 34.8185i −0.996789 + 2.34746i
\(221\) −1.32946 −0.0894289
\(222\) 15.9115i 1.06791i
\(223\) −8.79032 −0.588644 −0.294322 0.955706i \(-0.595094\pi\)
−0.294322 + 0.955706i \(0.595094\pi\)
\(224\) −31.4059 + 24.0882i −2.09840 + 1.60946i
\(225\) −2.19026 + 4.49475i −0.146017 + 0.299650i
\(226\) 10.3372i 0.687618i
\(227\) 16.2488i 1.07847i −0.842155 0.539236i \(-0.818713\pi\)
0.842155 0.539236i \(-0.181287\pi\)
\(228\) 13.6844 0.906271
\(229\) 24.5602i 1.62299i 0.584362 + 0.811493i \(0.301345\pi\)
−0.584362 + 0.811493i \(0.698655\pi\)
\(230\) 37.0343 23.1508i 2.44197 1.52652i
\(231\) −8.36748 2.64297i −0.550540 0.173895i
\(232\) 11.7404i 0.770792i
\(233\) −17.2426 −1.12960 −0.564802 0.825227i \(-0.691047\pi\)
−0.564802 + 0.825227i \(0.691047\pi\)
\(234\) 2.30451i 0.150650i
\(235\) −9.92716 15.8805i −0.647576 1.03593i
\(236\) 73.3983i 4.77782i
\(237\) 8.94533i 0.581061i
\(238\) −6.59587 8.59962i −0.427547 0.557431i
\(239\) 2.60857i 0.168734i 0.996435 + 0.0843671i \(0.0268868\pi\)
−0.996435 + 0.0843671i \(0.973113\pi\)
\(240\) −14.0044 22.4029i −0.903982 1.44610i
\(241\) 1.02093 0.0657638 0.0328819 0.999459i \(-0.489531\pi\)
0.0328819 + 0.999459i \(0.489531\pi\)
\(242\) 10.0419 27.5380i 0.645520 1.77021i
\(243\) −1.00000 −0.0641500
\(244\) 35.4930 2.27221
\(245\) 14.9696 4.57274i 0.956375 0.292142i
\(246\) 1.61828 0.103178
\(247\) 2.32022i 0.147632i
\(248\) 4.55954i 0.289531i
\(249\) 13.1440i 0.832967i
\(250\) 29.6274 3.12990i 1.87380 0.197952i
\(251\) 15.9683i 1.00791i 0.863730 + 0.503955i \(0.168122\pi\)
−0.863730 + 0.503955i \(0.831878\pi\)
\(252\) 10.7081 8.21304i 0.674545 0.517373i
\(253\) −19.9183 + 13.9379i −1.25225 + 0.876268i
\(254\) −42.9920 −2.69756
\(255\) 2.91476 1.82206i 0.182529 0.114102i
\(256\) 3.07071 0.191919
\(257\) 24.0879 1.50256 0.751282 0.659981i \(-0.229436\pi\)
0.751282 + 0.659981i \(0.229436\pi\)
\(258\) −2.19389 −0.136586
\(259\) 9.61479 + 12.5357i 0.597434 + 0.778928i
\(260\) −8.36397 + 5.22845i −0.518711 + 0.324255i
\(261\) 1.42095i 0.0879546i
\(262\) 21.2671 1.31389
\(263\) 18.4313 1.13652 0.568260 0.822849i \(-0.307617\pi\)
0.568260 + 0.822849i \(0.307617\pi\)
\(264\) 15.7109 + 22.4520i 0.966941 + 1.38183i
\(265\) 15.5770 9.73741i 0.956885 0.598164i
\(266\) 15.0084 11.5114i 0.920223 0.705807i
\(267\) 7.51433i 0.459870i
\(268\) 39.7057i 2.42541i
\(269\) 10.2977i 0.627861i −0.949446 0.313931i \(-0.898354\pi\)
0.949446 0.313931i \(-0.101646\pi\)
\(270\) 3.15840 + 5.05250i 0.192214 + 0.307486i
\(271\) 23.6065 1.43399 0.716995 0.697078i \(-0.245517\pi\)
0.716995 + 0.697078i \(0.245517\pi\)
\(272\) 18.1632i 1.10131i
\(273\) −1.39254 1.81558i −0.0842802 0.109884i
\(274\) 35.4960i 2.14439i
\(275\) −16.3788 + 2.59501i −0.987680 + 0.156485i
\(276\) 37.3873i 2.25045i
\(277\) 26.2554 1.57754 0.788768 0.614691i \(-0.210719\pi\)
0.788768 + 0.614691i \(0.210719\pi\)
\(278\) 14.9619 0.897356
\(279\) 0.551846i 0.0330382i
\(280\) −45.7846 17.1198i −2.73615 1.02310i
\(281\) 31.7030i 1.89124i −0.325272 0.945620i \(-0.605456\pi\)
0.325272 0.945620i \(-0.394544\pi\)
\(282\) −22.3180 −1.32902
\(283\) 7.26679i 0.431966i 0.976397 + 0.215983i \(0.0692955\pi\)
−0.976397 + 0.215983i \(0.930704\pi\)
\(284\) −22.3745 −1.32768
\(285\) 3.17993 + 5.08694i 0.188363 + 0.301325i
\(286\) 6.26227 4.38205i 0.370296 0.259116i
\(287\) 1.27494 0.977874i 0.0752575 0.0577221i
\(288\) −14.9598 −0.881516
\(289\) 14.6369 0.860992
\(290\) 7.17935 4.48793i 0.421586 0.263540i
\(291\) −18.3921 −1.07817
\(292\) 19.8429i 1.16122i
\(293\) 31.4376i 1.83661i 0.395877 + 0.918303i \(0.370441\pi\)
−0.395877 + 0.918303i \(0.629559\pi\)
\(294\) 4.83526 18.0153i 0.281998 1.05068i
\(295\) 27.2846 17.0560i 1.58857 0.993040i
\(296\) 49.3361i 2.86760i
\(297\) −1.90151 2.71740i −0.110337 0.157679i
\(298\) 17.6813i 1.02425i
\(299\) −6.33910 −0.366599
\(300\) 11.1718 22.9262i 0.645003 1.32364i
\(301\) −1.72843 + 1.32570i −0.0996250 + 0.0764119i
\(302\) 44.7575i 2.57550i
\(303\) 17.7370 1.01897
\(304\) −31.6991 −1.81807
\(305\) 8.24773 + 13.1939i 0.472264 + 0.755482i
\(306\) 4.09632i 0.234171i
\(307\) 13.8197i 0.788733i 0.918953 + 0.394366i \(0.129036\pi\)
−0.918953 + 0.394366i \(0.870964\pi\)
\(308\) 42.6796 + 13.4809i 2.43190 + 0.768145i
\(309\) 15.5720 0.885863
\(310\) 2.78820 1.74295i 0.158359 0.0989930i
\(311\) 4.57177i 0.259241i 0.991564 + 0.129621i \(0.0413759\pi\)
−0.991564 + 0.129621i \(0.958624\pi\)
\(312\) 7.14549i 0.404533i
\(313\) −26.4180 −1.49323 −0.746616 0.665256i \(-0.768323\pi\)
−0.746616 + 0.665256i \(0.768323\pi\)
\(314\) 17.3791 0.980762
\(315\) 5.54136 + 2.07203i 0.312220 + 0.116746i
\(316\) 45.6270i 2.56672i
\(317\) 7.88446i 0.442835i 0.975179 + 0.221418i \(0.0710684\pi\)
−0.975179 + 0.221418i \(0.928932\pi\)
\(318\) 21.8915i 1.22761i
\(319\) −3.86129 + 2.70195i −0.216190 + 0.151280i
\(320\) 19.2402 + 30.7787i 1.07556 + 1.72058i
\(321\) −16.4098 −0.915905
\(322\) −31.4503 41.0046i −1.75266 2.28510i
\(323\) 4.12424i 0.229479i
\(324\) 5.10065 0.283370
\(325\) −3.88718 1.89420i −0.215622 0.105071i
\(326\) 9.36651i 0.518763i
\(327\) 11.4582i 0.633639i
\(328\) −5.01774 −0.277058
\(329\) −17.5830 + 13.4861i −0.969381 + 0.743510i
\(330\) −7.72392 + 18.1900i −0.425188 + 1.00133i
\(331\) −5.20944 −0.286337 −0.143168 0.989698i \(-0.545729\pi\)
−0.143168 + 0.989698i \(0.545729\pi\)
\(332\) 67.0430i 3.67946i
\(333\) 5.97120i 0.327220i
\(334\) 43.2755i 2.36793i
\(335\) 14.7599 9.22668i 0.806422 0.504107i
\(336\) −24.8046 + 19.0250i −1.35320 + 1.03790i
\(337\) 0.820269 0.0446829 0.0223414 0.999750i \(-0.492888\pi\)
0.0223414 + 0.999750i \(0.492888\pi\)
\(338\) −32.6482 −1.77583
\(339\) 3.87929i 0.210694i
\(340\) −14.8672 + 9.29370i −0.806285 + 0.504022i
\(341\) −1.49959 + 1.04934i −0.0812071 + 0.0568251i
\(342\) 7.14906 0.386577
\(343\) −7.07667 17.1149i −0.382104 0.924119i
\(344\) 6.80251 0.366767
\(345\) 13.8981 8.68792i 0.748249 0.467742i
\(346\) 25.4255i 1.36688i
\(347\) −9.64321 −0.517675 −0.258837 0.965921i \(-0.583339\pi\)
−0.258837 + 0.965921i \(0.583339\pi\)
\(348\) 7.24777i 0.388521i
\(349\) −7.03905 −0.376792 −0.188396 0.982093i \(-0.560329\pi\)
−0.188396 + 0.982093i \(0.560329\pi\)
\(350\) −7.03290 34.5420i −0.375924 1.84635i
\(351\) 0.864827i 0.0461610i
\(352\) −28.4463 40.6518i −1.51619 2.16675i
\(353\) 10.8364 0.576766 0.288383 0.957515i \(-0.406882\pi\)
0.288383 + 0.957515i \(0.406882\pi\)
\(354\) 38.3450i 2.03802i
\(355\) −5.19931 8.31736i −0.275951 0.441440i
\(356\) 38.3280i 2.03138i
\(357\) −2.47527 3.22723i −0.131005 0.170803i
\(358\) 39.3351 2.07893
\(359\) 4.49768i 0.237378i −0.992931 0.118689i \(-0.962131\pi\)
0.992931 0.118689i \(-0.0378692\pi\)
\(360\) −9.79311 15.6661i −0.516142 0.825674i
\(361\) −11.8022 −0.621169
\(362\) 61.9460i 3.25581i
\(363\) 3.76850 10.3343i 0.197795 0.542412i
\(364\) 7.10286 + 9.26063i 0.372291 + 0.485389i
\(365\) −7.37628 + 4.61103i −0.386092 + 0.241352i
\(366\) 18.5424 0.969227
\(367\) 1.71236 0.0893847 0.0446924 0.999001i \(-0.485769\pi\)
0.0446924 + 0.999001i \(0.485769\pi\)
\(368\) 86.6055i 4.51462i
\(369\) 0.607303 0.0316149
\(370\) 30.1695 18.8594i 1.56844 0.980456i
\(371\) −13.2283 17.2469i −0.686778 0.895414i
\(372\) 2.81478i 0.145939i
\(373\) −27.0598 −1.40110 −0.700552 0.713601i \(-0.747063\pi\)
−0.700552 + 0.713601i \(0.747063\pi\)
\(374\) 11.1313 7.78921i 0.575588 0.402770i
\(375\) 11.1185 1.17458i 0.574155 0.0606549i
\(376\) 69.2006 3.56875
\(377\) −1.22888 −0.0632903
\(378\) 5.59415 4.29069i 0.287732 0.220689i
\(379\) −21.3719 −1.09780 −0.548899 0.835889i \(-0.684953\pi\)
−0.548899 + 0.835889i \(0.684953\pi\)
\(380\) −16.2197 25.9467i −0.832054 1.33104i
\(381\) −16.1339 −0.826564
\(382\) −42.3602 −2.16734
\(383\) 28.3248 1.44733 0.723665 0.690152i \(-0.242456\pi\)
0.723665 + 0.690152i \(0.242456\pi\)
\(384\) 13.3359 0.680545
\(385\) 4.90644 + 18.9981i 0.250055 + 0.968232i
\(386\) 22.1777 1.12881
\(387\) −0.823316 −0.0418515
\(388\) 93.8119 4.76258
\(389\) 15.0506 0.763095 0.381547 0.924349i \(-0.375391\pi\)
0.381547 + 0.924349i \(0.375391\pi\)
\(390\) −4.36954 + 2.73147i −0.221260 + 0.138313i
\(391\) −11.2679 −0.569842
\(392\) −14.9925 + 55.8593i −0.757235 + 2.82132i
\(393\) 7.98104 0.402590
\(394\) 35.2602 1.77638
\(395\) −16.9611 + 10.6026i −0.853405 + 0.533477i
\(396\) 9.69896 + 13.8605i 0.487391 + 0.696517i
\(397\) −1.61424 −0.0810162 −0.0405081 0.999179i \(-0.512898\pi\)
−0.0405081 + 0.999179i \(0.512898\pi\)
\(398\) 10.2173i 0.512146i
\(399\) 5.63229 4.31994i 0.281967 0.216267i
\(400\) −25.8788 + 53.1071i −1.29394 + 2.65535i
\(401\) 11.4134 0.569956 0.284978 0.958534i \(-0.408014\pi\)
0.284978 + 0.958534i \(0.408014\pi\)
\(402\) 20.7432i 1.03458i
\(403\) −0.477251 −0.0237736
\(404\) −90.4705 −4.50108
\(405\) 1.18527 + 1.89608i 0.0588966 + 0.0942171i
\(406\) −6.09685 7.94901i −0.302582 0.394503i
\(407\) −16.2261 + 11.3543i −0.804300 + 0.562813i
\(408\) 12.7013i 0.628807i
\(409\) 39.2972 1.94312 0.971560 0.236794i \(-0.0760968\pi\)
0.971560 + 0.236794i \(0.0760968\pi\)
\(410\) −1.91810 3.06840i −0.0947284 0.151537i
\(411\) 13.3208i 0.657067i
\(412\) −79.4276 −3.91312
\(413\) −23.1706 30.2096i −1.14015 1.48652i
\(414\) 19.5320i 0.959947i
\(415\) −24.9221 + 15.5792i −1.22338 + 0.764754i
\(416\) 12.9376i 0.634320i
\(417\) 5.61484 0.274960
\(418\) 13.5940 + 19.4268i 0.664905 + 0.950197i
\(419\) 4.32026i 0.211059i −0.994416 0.105529i \(-0.966346\pi\)
0.994416 0.105529i \(-0.0336537\pi\)
\(420\) −28.2646 10.5687i −1.37917 0.515700i
\(421\) −5.64413 −0.275078 −0.137539 0.990496i \(-0.543919\pi\)
−0.137539 + 0.990496i \(0.543919\pi\)
\(422\) 46.2482i 2.25133i
\(423\) −8.37543 −0.407227
\(424\) 67.8779i 3.29644i
\(425\) −6.90956 3.36698i −0.335163 0.163323i
\(426\) −11.6890 −0.566334
\(427\) 14.6084 11.2046i 0.706949 0.542226i
\(428\) 83.7007 4.04582
\(429\) 2.35008 1.64448i 0.113463 0.0793962i
\(430\) 2.60036 + 4.15980i 0.125400 + 0.200604i
\(431\) 40.0098i 1.92720i −0.267344 0.963601i \(-0.586146\pi\)
0.267344 0.963601i \(-0.413854\pi\)
\(432\) −11.8154 −0.568467
\(433\) −8.18707 −0.393445 −0.196723 0.980459i \(-0.563030\pi\)
−0.196723 + 0.980459i \(0.563030\pi\)
\(434\) −2.36780 3.08711i −0.113658 0.148186i
\(435\) 2.69424 1.68421i 0.129179 0.0807518i
\(436\) 58.4442i 2.79897i
\(437\) 19.6652i 0.940713i
\(438\) 10.3664i 0.495327i
\(439\) 16.4327 0.784289 0.392144 0.919904i \(-0.371733\pi\)
0.392144 + 0.919904i \(0.371733\pi\)
\(440\) 23.9492 56.4010i 1.14173 2.68881i
\(441\) 1.81456 6.76072i 0.0864075 0.321939i
\(442\) 3.54261 0.168505
\(443\) 14.4277i 0.685482i 0.939430 + 0.342741i \(0.111355\pi\)
−0.939430 + 0.342741i \(0.888645\pi\)
\(444\) 30.4571i 1.44543i
\(445\) −14.2478 + 8.90652i −0.675410 + 0.422210i
\(446\) 23.4236 1.10914
\(447\) 6.63536i 0.313842i
\(448\) 34.0783 26.1379i 1.61005 1.23490i
\(449\) 1.50128 0.0708500 0.0354250 0.999372i \(-0.488722\pi\)
0.0354250 + 0.999372i \(0.488722\pi\)
\(450\) 5.83640 11.9772i 0.275131 0.564610i
\(451\) 1.15479 + 1.65028i 0.0543771 + 0.0777088i
\(452\) 19.7869i 0.930698i
\(453\) 16.7964i 0.789164i
\(454\) 43.2983i 2.03209i
\(455\) −1.79195 + 4.79232i −0.0840078 + 0.224667i
\(456\) −22.1668 −1.03805
\(457\) −19.1770 −0.897061 −0.448531 0.893767i \(-0.648053\pi\)
−0.448531 + 0.893767i \(0.648053\pi\)
\(458\) 65.4458i 3.05808i
\(459\) 1.53725i 0.0717527i
\(460\) −70.8894 + 44.3141i −3.30524 + 2.06616i
\(461\) 17.1758 0.799956 0.399978 0.916525i \(-0.369018\pi\)
0.399978 + 0.916525i \(0.369018\pi\)
\(462\) 22.2969 + 7.04274i 1.03734 + 0.327658i
\(463\) 23.7081i 1.10181i −0.834568 0.550905i \(-0.814283\pi\)
0.834568 0.550905i \(-0.185717\pi\)
\(464\) 16.7890i 0.779412i
\(465\) 1.04635 0.654088i 0.0485231 0.0303326i
\(466\) 45.9466 2.12843
\(467\) 21.4893 0.994408 0.497204 0.867634i \(-0.334360\pi\)
0.497204 + 0.867634i \(0.334360\pi\)
\(468\) 4.41118i 0.203907i
\(469\) −12.5344 16.3423i −0.578787 0.754616i
\(470\) 26.4529 + 42.3169i 1.22018 + 1.95193i
\(471\) 6.52197 0.300517
\(472\) 118.895i 5.47257i
\(473\) −1.56555 2.23728i −0.0719838 0.102870i
\(474\) 23.8367i 1.09485i
\(475\) 5.87619 12.0588i 0.269618 0.553297i
\(476\) 12.6255 + 16.4610i 0.578689 + 0.754488i
\(477\) 8.21534i 0.376155i
\(478\) 6.95106i 0.317934i
\(479\) −8.33633 −0.380897 −0.190448 0.981697i \(-0.560994\pi\)
−0.190448 + 0.981697i \(0.560994\pi\)
\(480\) 17.7314 + 28.3651i 0.809326 + 1.29468i
\(481\) −5.16406 −0.235461
\(482\) −2.72047 −0.123914
\(483\) −11.8026 15.3880i −0.537035 0.700180i
\(484\) −19.2218 + 52.7119i −0.873719 + 2.39599i
\(485\) 21.7997 + 34.8730i 0.989872 + 1.58350i
\(486\) 2.66471 0.120873
\(487\) 6.05352i 0.274311i 0.990550 + 0.137156i \(0.0437961\pi\)
−0.990550 + 0.137156i \(0.956204\pi\)
\(488\) −57.4936 −2.60261
\(489\) 3.51503i 0.158955i
\(490\) −39.8897 + 12.1850i −1.80203 + 0.550462i
\(491\) 25.3715i 1.14500i −0.819905 0.572500i \(-0.805974\pi\)
0.819905 0.572500i \(-0.194026\pi\)
\(492\) −3.09764 −0.139652
\(493\) −2.18436 −0.0983785
\(494\) 6.18270i 0.278173i
\(495\) −2.89860 + 6.82628i −0.130282 + 0.306818i
\(496\) 6.52027i 0.292769i
\(497\) −9.20902 + 7.06327i −0.413081 + 0.316831i
\(498\) 35.0249i 1.56950i
\(499\) 31.5146 1.41079 0.705394 0.708815i \(-0.250770\pi\)
0.705394 + 0.708815i \(0.250770\pi\)
\(500\) −56.7115 + 5.99111i −2.53621 + 0.267931i
\(501\) 16.2402i 0.725560i
\(502\) 42.5508i 1.89913i
\(503\) 19.5773i 0.872907i −0.899727 0.436454i \(-0.856234\pi\)
0.899727 0.436454i \(-0.143766\pi\)
\(504\) −17.3455 + 13.3039i −0.772632 + 0.592605i
\(505\) −21.0232 33.6309i −0.935520 1.49656i
\(506\) 53.0763 37.1404i 2.35953 1.65109i
\(507\) −12.2521 −0.544134
\(508\) 82.2934 3.65118
\(509\) 24.6470i 1.09246i 0.837635 + 0.546230i \(0.183937\pi\)
−0.837635 + 0.546230i \(0.816063\pi\)
\(510\) −7.76697 + 4.85525i −0.343927 + 0.214994i
\(511\) 6.26409 + 8.16705i 0.277107 + 0.361289i
\(512\) 18.4893 0.817117
\(513\) 2.68287 0.118452
\(514\) −64.1873 −2.83118
\(515\) −18.4571 29.5259i −0.813317 1.30107i
\(516\) 4.19945 0.184870
\(517\) −15.9260 22.7594i −0.700424 1.00096i
\(518\) −25.6206 33.4038i −1.12570 1.46768i
\(519\) 9.54156i 0.418828i
\(520\) 13.5484 8.46934i 0.594138 0.371405i
\(521\) 7.65022i 0.335162i 0.985858 + 0.167581i \(0.0535956\pi\)
−0.985858 + 0.167581i \(0.946404\pi\)
\(522\) 3.78641i 0.165727i
\(523\) 22.3884i 0.978978i 0.872010 + 0.489489i \(0.162817\pi\)
−0.872010 + 0.489489i \(0.837183\pi\)
\(524\) −40.7085 −1.77836
\(525\) −2.63928 12.9628i −0.115188 0.565743i
\(526\) −49.1139 −2.14147
\(527\) −0.848326 −0.0369537
\(528\) −22.4671 32.1071i −0.977754 1.39728i
\(529\) −30.7275 −1.33598
\(530\) −41.5080 + 25.9473i −1.80299 + 1.12708i
\(531\) 14.3900i 0.624471i
\(532\) −28.7284 + 22.0345i −1.24553 + 0.955317i
\(533\) 0.525212i 0.0227494i
\(534\) 20.0235i 0.866501i
\(535\) 19.4501 + 31.1143i 0.840899 + 1.34519i
\(536\) 64.3176i 2.77810i
\(537\) 14.7615 0.637007
\(538\) 27.4403i 1.18304i
\(539\) 21.8220 7.92473i 0.939939 0.341342i
\(540\) −6.04566 9.67127i −0.260164 0.416185i
\(541\) 18.5873i 0.799129i 0.916705 + 0.399565i \(0.130839\pi\)
−0.916705 + 0.399565i \(0.869161\pi\)
\(542\) −62.9042 −2.70197
\(543\) 23.2469i 0.997618i
\(544\) 22.9970i 0.985988i
\(545\) −21.7257 + 13.5811i −0.930625 + 0.581748i
\(546\) 3.71070 + 4.83798i 0.158803 + 0.207046i
\(547\) 3.02733 0.129439 0.0647197 0.997903i \(-0.479385\pi\)
0.0647197 + 0.997903i \(0.479385\pi\)
\(548\) 67.9448i 2.90246i
\(549\) 6.95852 0.296982
\(550\) 43.6447 6.91493i 1.86102 0.294853i
\(551\) 3.81222i 0.162406i
\(552\) 60.5621i 2.57769i
\(553\) 14.4037 + 18.7794i 0.612508 + 0.798581i
\(554\) −69.9630 −2.97244
\(555\) 11.3219 7.07750i 0.480588 0.300423i
\(556\) −28.6394 −1.21458
\(557\) 37.3665 1.58327 0.791634 0.610996i \(-0.209231\pi\)
0.791634 + 0.610996i \(0.209231\pi\)
\(558\) 1.47051i 0.0622516i
\(559\) 0.712025i 0.0301155i
\(560\) 65.4732 + 24.4818i 2.76675 + 1.03454i
\(561\) 4.17732 2.92310i 0.176367 0.123414i
\(562\) 84.4791i 3.56354i
\(563\) 3.28145i 0.138297i 0.997606 + 0.0691483i \(0.0220282\pi\)
−0.997606 + 0.0691483i \(0.977972\pi\)
\(564\) 42.7202 1.79884
\(565\) −7.35545 + 4.59801i −0.309446 + 0.193440i
\(566\) 19.3639i 0.813923i
\(567\) 2.09935 1.61019i 0.0881645 0.0676217i
\(568\) 36.2436 1.52075
\(569\) 23.1895i 0.972154i 0.873916 + 0.486077i \(0.161573\pi\)
−0.873916 + 0.486077i \(0.838427\pi\)
\(570\) −8.47358 13.5552i −0.354919 0.567765i
\(571\) 18.0124i 0.753794i 0.926255 + 0.376897i \(0.123009\pi\)
−0.926255 + 0.376897i \(0.876991\pi\)
\(572\) −11.9869 + 8.38792i −0.501199 + 0.350717i
\(573\) −15.8968 −0.664097
\(574\) −3.39735 + 2.60575i −0.141802 + 0.108762i
\(575\) −32.9461 16.0544i −1.37395 0.669515i
\(576\) 16.2328 0.676365
\(577\) 26.7730 1.11458 0.557288 0.830319i \(-0.311842\pi\)
0.557288 + 0.830319i \(0.311842\pi\)
\(578\) −39.0029 −1.62231
\(579\) 8.32276 0.345882
\(580\) −13.7424 + 8.59058i −0.570621 + 0.356704i
\(581\) 21.1644 + 27.5939i 0.878047 + 1.14479i
\(582\) 49.0096 2.03151
\(583\) 22.3243 15.6216i 0.924580 0.646979i
\(584\) 32.1427i 1.33008i
\(585\) −1.63978 + 1.02505i −0.0677967 + 0.0423808i
\(586\) 83.7721i 3.46059i
\(587\) 40.2952 1.66316 0.831581 0.555403i \(-0.187436\pi\)
0.831581 + 0.555403i \(0.187436\pi\)
\(588\) −9.25543 + 34.4841i −0.381688 + 1.42210i
\(589\) 1.48053i 0.0610042i
\(590\) −72.7054 + 45.4493i −2.99323 + 1.87112i
\(591\) 13.2323 0.544304
\(592\) 70.5520i 2.89967i
\(593\) 29.8747i 1.22681i 0.789769 + 0.613404i \(0.210200\pi\)
−0.789769 + 0.613404i \(0.789800\pi\)
\(594\) 5.06697 + 7.24106i 0.207900 + 0.297104i
\(595\) −3.18523 + 8.51847i −0.130582 + 0.349223i
\(596\) 33.8447i 1.38633i
\(597\) 3.83430i 0.156928i
\(598\) 16.8918 0.690758
\(599\) 5.01487 0.204902 0.102451 0.994738i \(-0.467332\pi\)
0.102451 + 0.994738i \(0.467332\pi\)
\(600\) −18.0967 + 37.1371i −0.738794 + 1.51612i
\(601\) 8.64771 0.352748 0.176374 0.984323i \(-0.443563\pi\)
0.176374 + 0.984323i \(0.443563\pi\)
\(602\) 4.60575 3.53259i 0.187717 0.143978i
\(603\) 7.78444i 0.317007i
\(604\) 85.6727i 3.48597i
\(605\) −24.0614 + 5.10360i −0.978237 + 0.207491i
\(606\) −47.2640 −1.91997
\(607\) 48.8060i 1.98098i −0.137601 0.990488i \(-0.543939\pi\)
0.137601 0.990488i \(-0.456061\pi\)
\(608\) 40.1352 1.62770
\(609\) −2.28800 2.98307i −0.0927146 0.120880i
\(610\) −21.9778 35.1579i −0.889854 1.42350i
\(611\) 7.24329i 0.293032i
\(612\) 7.84099i 0.316953i
\(613\) 18.4910 0.746846 0.373423 0.927661i \(-0.378184\pi\)
0.373423 + 0.927661i \(0.378184\pi\)
\(614\) 36.8255i 1.48616i
\(615\) −0.719819 1.15150i −0.0290259 0.0464328i
\(616\) −69.1349 21.8371i −2.78552 0.879842i
\(617\) 4.90065i 0.197293i −0.995123 0.0986465i \(-0.968549\pi\)
0.995123 0.0986465i \(-0.0314513\pi\)
\(618\) −41.4949 −1.66917
\(619\) 22.3396i 0.897902i −0.893556 0.448951i \(-0.851798\pi\)
0.893556 0.448951i \(-0.148202\pi\)
\(620\) −5.33705 + 3.33628i −0.214341 + 0.133988i
\(621\) 7.32990i 0.294139i
\(622\) 12.1824i 0.488470i
\(623\) 12.0995 + 15.7752i 0.484757 + 0.632021i
\(624\) 10.2182i 0.409057i
\(625\) −15.4055 19.6894i −0.616220 0.787574i
\(626\) 70.3961 2.81359
\(627\) 5.10151 + 7.29042i 0.203735 + 0.291151i
\(628\) −33.2663 −1.32747
\(629\) −9.17924 −0.366000
\(630\) −14.7661 5.52135i −0.588295 0.219976i
\(631\) −14.9662 −0.595796 −0.297898 0.954598i \(-0.596286\pi\)
−0.297898 + 0.954598i \(0.596286\pi\)
\(632\) 73.9093i 2.93995i
\(633\) 17.3558i 0.689832i
\(634\) 21.0098i 0.834404i
\(635\) 19.1230 + 30.5912i 0.758874 + 1.21397i
\(636\) 41.9036i 1.66159i
\(637\) 5.84685 + 1.56928i 0.231661 + 0.0621771i
\(638\) 10.2892 7.19991i 0.407353 0.285047i
\(639\) −4.38660 −0.173531
\(640\) −15.8067 25.2860i −0.624813 0.999516i
\(641\) −13.6017 −0.537233 −0.268617 0.963247i \(-0.586566\pi\)
−0.268617 + 0.963247i \(0.586566\pi\)
\(642\) 43.7273 1.72578
\(643\) 19.3513 0.763140 0.381570 0.924340i \(-0.375384\pi\)
0.381570 + 0.924340i \(0.375384\pi\)
\(644\) 60.2008 + 78.4891i 2.37224 + 3.09290i
\(645\) 0.975853 + 1.56107i 0.0384242 + 0.0614673i
\(646\) 10.9899i 0.432392i
\(647\) 36.1077 1.41954 0.709770 0.704434i \(-0.248799\pi\)
0.709770 + 0.704434i \(0.248799\pi\)
\(648\) −8.26233 −0.324575
\(649\) 39.1033 27.3627i 1.53494 1.07408i
\(650\) 10.3582 + 5.04748i 0.406281 + 0.197978i
\(651\) −0.888579 1.15852i −0.0348262 0.0454060i
\(652\) 17.9289i 0.702151i
\(653\) 33.8487i 1.32460i −0.749238 0.662301i \(-0.769580\pi\)
0.749238 0.662301i \(-0.230420\pi\)
\(654\) 30.5327i 1.19392i
\(655\) −9.45970 15.1327i −0.369621 0.591284i
\(656\) 7.17551 0.280156
\(657\) 3.89027i 0.151774i
\(658\) 46.8534 35.9364i 1.82654 1.40095i
\(659\) 29.3891i 1.14484i −0.819962 0.572418i \(-0.806005\pi\)
0.819962 0.572418i \(-0.193995\pi\)
\(660\) 14.7848 34.8185i 0.575496 1.35531i
\(661\) 16.7396i 0.651096i 0.945526 + 0.325548i \(0.105549\pi\)
−0.945526 + 0.325548i \(0.894451\pi\)
\(662\) 13.8816 0.539525
\(663\) 1.32946 0.0516318
\(664\) 108.600i 4.21450i
\(665\) −14.8668 5.55899i −0.576508 0.215568i
\(666\) 15.9115i 0.616558i
\(667\) −10.4154 −0.403287
\(668\) 82.8359i 3.20502i
\(669\) 8.79032 0.339854
\(670\) −39.3309 + 24.5864i −1.51949 + 0.949854i
\(671\) 13.2317 + 18.9091i 0.510805 + 0.729976i
\(672\) 31.4059 24.0882i 1.21151 0.929222i
\(673\) −15.6776 −0.604327 −0.302163 0.953256i \(-0.597709\pi\)
−0.302163 + 0.953256i \(0.597709\pi\)
\(674\) −2.18578 −0.0841929
\(675\) 2.19026 4.49475i 0.0843032 0.173003i
\(676\) 62.4936 2.40360
\(677\) 16.2016i 0.622679i −0.950299 0.311340i \(-0.899222\pi\)
0.950299 0.311340i \(-0.100778\pi\)
\(678\) 10.3372i 0.396996i
\(679\) 38.6116 29.6149i 1.48178 1.13651i
\(680\) 24.0827 15.0545i 0.923529 0.577312i
\(681\) 16.2488i 0.622656i
\(682\) 3.99595 2.79619i 0.153013 0.107072i
\(683\) 40.3376i 1.54347i 0.635942 + 0.771737i \(0.280612\pi\)
−0.635942 + 0.771737i \(0.719388\pi\)
\(684\) −13.6844 −0.523236
\(685\) −25.2574 + 15.7888i −0.965034 + 0.603258i
\(686\) 18.8572 + 45.6062i 0.719973 + 1.74125i
\(687\) 24.5602i 0.937032i
\(688\) −9.72778 −0.370868
\(689\) 7.10485 0.270673
\(690\) −37.0343 + 23.1508i −1.40987 + 0.881334i
\(691\) 19.3016i 0.734268i −0.930168 0.367134i \(-0.880339\pi\)
0.930168 0.367134i \(-0.119661\pi\)
\(692\) 48.6682i 1.85009i
\(693\) 8.36748 + 2.64297i 0.317854 + 0.100398i
\(694\) 25.6963 0.975419
\(695\) −6.65512 10.6462i −0.252443 0.403834i
\(696\) 11.7404i 0.445017i
\(697\) 0.933577i 0.0353617i
\(698\) 18.7570 0.709963
\(699\) 17.2426 0.652177
\(700\) 13.4620 + 66.1188i 0.508817 + 2.49905i
\(701\) 15.8130i 0.597250i −0.954370 0.298625i \(-0.903472\pi\)
0.954370 0.298625i \(-0.0965280\pi\)
\(702\) 2.30451i 0.0869781i
\(703\) 16.0200i 0.604204i
\(704\) 30.8668 + 44.1109i 1.16334 + 1.66249i
\(705\) 9.92716 + 15.8805i 0.373878 + 0.598094i
\(706\) −28.8759 −1.08676
\(707\) −37.2363 + 28.5600i −1.40041 + 1.07411i
\(708\) 73.3983i 2.75848i
\(709\) 17.8940 0.672025 0.336012 0.941858i \(-0.390922\pi\)
0.336012 + 0.941858i \(0.390922\pi\)
\(710\) 13.8546 + 22.1633i 0.519955 + 0.831774i
\(711\) 8.94533i 0.335476i
\(712\) 62.0859i 2.32677i
\(713\) −4.04498 −0.151486
\(714\) 6.59587 + 8.59962i 0.246844 + 0.321833i
\(715\) −5.90355 2.50679i −0.220780 0.0937486i
\(716\) −75.2935 −2.81385
\(717\) 2.60857i 0.0974187i
\(718\) 11.9850i 0.447276i
\(719\) 4.73442i 0.176564i 0.996096 + 0.0882821i \(0.0281377\pi\)
−0.996096 + 0.0882821i \(0.971862\pi\)
\(720\) 14.0044 + 22.4029i 0.521914 + 0.834908i
\(721\) −32.6912 + 25.0740i −1.21748 + 0.933805i
\(722\) 31.4494 1.17043
\(723\) −1.02093 −0.0379687
\(724\) 118.574i 4.40678i
\(725\) −6.38681 3.11225i −0.237200 0.115586i
\(726\) −10.0419 + 27.5380i −0.372691 + 1.02203i
\(727\) 3.40475 0.126275 0.0631377 0.998005i \(-0.479889\pi\)
0.0631377 + 0.998005i \(0.479889\pi\)
\(728\) −11.5056 15.0009i −0.426426 0.555970i
\(729\) 1.00000 0.0370370
\(730\) 19.6556 12.2870i 0.727487 0.454764i
\(731\) 1.26564i 0.0468115i
\(732\) −35.4930 −1.31186
\(733\) 51.5861i 1.90537i −0.303953 0.952687i \(-0.598306\pi\)
0.303953 0.952687i \(-0.401694\pi\)
\(734\) −4.56295 −0.168421
\(735\) −14.9696 + 4.57274i −0.552163 + 0.168668i
\(736\) 109.654i 4.04190i
\(737\) 21.1534 14.8022i 0.779196 0.545246i
\(738\) −1.61828 −0.0595698
\(739\) 2.40223i 0.0883674i 0.999023 + 0.0441837i \(0.0140687\pi\)
−0.999023 + 0.0441837i \(0.985931\pi\)
\(740\) −57.7491 + 36.0999i −2.12290 + 1.32706i
\(741\) 2.32022i 0.0852353i
\(742\) 35.2495 + 45.9579i 1.29405 + 1.68717i
\(743\) −20.2751 −0.743823 −0.371911 0.928268i \(-0.621297\pi\)
−0.371911 + 0.928268i \(0.621297\pi\)
\(744\) 4.55954i 0.167161i
\(745\) −12.5812 + 7.86470i −0.460939 + 0.288140i
\(746\) 72.1064 2.64000
\(747\) 13.1440i 0.480914i
\(748\) −21.3071 + 14.9097i −0.779064 + 0.545154i
\(749\) 34.4499 26.4229i 1.25877 0.965473i
\(750\) −29.6274 + 3.12990i −1.08184 + 0.114288i
\(751\) −25.0938 −0.915685 −0.457843 0.889033i \(-0.651378\pi\)
−0.457843 + 0.889033i \(0.651378\pi\)
\(752\) −98.9588 −3.60865
\(753\) 15.9683i 0.581917i
\(754\) 3.27459 0.119254
\(755\) 31.8474 19.9083i 1.15904 0.724537i
\(756\) −10.7081 + 8.21304i −0.389449 + 0.298705i
\(757\) 38.8462i 1.41189i −0.708268 0.705944i \(-0.750523\pi\)
0.708268 0.705944i \(-0.249477\pi\)
\(758\) 56.9497 2.06851
\(759\) 19.9183 13.9379i 0.722987 0.505914i
\(760\) 26.2736 + 42.0300i 0.953045 + 1.52459i
\(761\) 46.7951 1.69632 0.848161 0.529738i \(-0.177710\pi\)
0.848161 + 0.529738i \(0.177710\pi\)
\(762\) 42.9920 1.55744
\(763\) 18.4499 + 24.0548i 0.667930 + 0.870841i
\(764\) 81.0839 2.93351
\(765\) −2.91476 + 1.82206i −0.105383 + 0.0658767i
\(766\) −75.4772 −2.72710
\(767\) 12.4448 0.449357
\(768\) −3.07071 −0.110805
\(769\) −1.96503 −0.0708606 −0.0354303 0.999372i \(-0.511280\pi\)
−0.0354303 + 0.999372i \(0.511280\pi\)
\(770\) −13.0742 50.6243i −0.471162 1.82437i
\(771\) −24.0879 −0.867506
\(772\) −42.4515 −1.52786
\(773\) −12.5159 −0.450166 −0.225083 0.974340i \(-0.572265\pi\)
−0.225083 + 0.974340i \(0.572265\pi\)
\(774\) 2.19389 0.0788579
\(775\) −2.48041 1.20869i −0.0890989 0.0434174i
\(776\) −151.962 −5.45511
\(777\) −9.61479 12.5357i −0.344929 0.449714i
\(778\) −40.1054 −1.43785
\(779\) −1.62931 −0.0583762
\(780\) 8.36397 5.22845i 0.299478 0.187209i
\(781\) −8.34118 11.9201i −0.298471 0.426536i
\(782\) 30.0256 1.07371
\(783\) 1.42095i 0.0507806i
\(784\) 21.4397 79.8804i 0.765703 2.85287i
\(785\) −7.73031 12.3662i −0.275907 0.441369i
\(786\) −21.2671 −0.758573
\(787\) 22.0607i 0.786379i −0.919457 0.393190i \(-0.871372\pi\)
0.919457 0.393190i \(-0.128628\pi\)
\(788\) −67.4934 −2.40435
\(789\) −18.4313 −0.656170
\(790\) 45.1963 28.2529i 1.60801 1.00519i
\(791\) 6.24640 + 8.14399i 0.222096 + 0.289567i
\(792\) −15.7109 22.4520i −0.558264 0.797798i
\(793\) 6.01791i 0.213702i
\(794\) 4.30146 0.152653
\(795\) −15.5770 + 9.73741i −0.552458 + 0.345350i
\(796\) 19.5575i 0.693195i
\(797\) −30.0551 −1.06461 −0.532303 0.846554i \(-0.678673\pi\)
−0.532303 + 0.846554i \(0.678673\pi\)
\(798\) −15.0084 + 11.5114i −0.531291 + 0.407498i
\(799\) 12.8751i 0.455490i
\(800\) 32.7659 67.2406i 1.15845 2.37731i
\(801\) 7.51433i 0.265506i
\(802\) −30.4132 −1.07393
\(803\) −10.5714 + 7.39740i −0.373057 + 0.261049i
\(804\) 39.7057i 1.40031i
\(805\) −15.1878 + 40.6176i −0.535299 + 1.43158i
\(806\) 1.27173 0.0447949
\(807\) 10.2977i 0.362496i
\(808\) 146.549 5.15559
\(809\) 33.2719i 1.16978i 0.811114 + 0.584888i \(0.198862\pi\)
−0.811114 + 0.584888i \(0.801138\pi\)
\(810\) −3.15840 5.05250i −0.110975 0.177527i
\(811\) −7.58505 −0.266347 −0.133174 0.991093i \(-0.542517\pi\)
−0.133174 + 0.991093i \(0.542517\pi\)
\(812\) 11.6703 + 15.2156i 0.409548 + 0.533964i
\(813\) −23.6065 −0.827915
\(814\) 43.2379 30.2559i 1.51549 1.06047i
\(815\) 6.66478 4.16626i 0.233457 0.145938i
\(816\) 18.1632i 0.635839i
\(817\) 2.20885 0.0772778
\(818\) −104.715 −3.66129
\(819\) 1.39254 + 1.81558i 0.0486592 + 0.0634414i
\(820\) 3.67155 + 5.87339i 0.128216 + 0.205108i
\(821\) 9.21308i 0.321539i −0.986992 0.160769i \(-0.948602\pi\)
0.986992 0.160769i \(-0.0513976\pi\)
\(822\) 35.4960i 1.23807i
\(823\) 31.0541i 1.08248i −0.840869 0.541239i \(-0.817955\pi\)
0.840869 0.541239i \(-0.182045\pi\)
\(824\) 128.661 4.48213
\(825\) 16.3788 2.59501i 0.570238 0.0903465i
\(826\) 61.7429 + 80.4997i 2.14831 + 2.80094i
\(827\) −25.0716 −0.871823 −0.435912 0.899989i \(-0.643574\pi\)
−0.435912 + 0.899989i \(0.643574\pi\)
\(828\) 37.3873i 1.29930i
\(829\) 20.3332i 0.706201i 0.935585 + 0.353101i \(0.114873\pi\)
−0.935585 + 0.353101i \(0.885127\pi\)
\(830\) 66.4101 41.5140i 2.30513 1.44097i
\(831\) −26.2554 −0.910791
\(832\) 14.0385i 0.486698i
\(833\) 10.3929 + 2.78943i 0.360094 + 0.0966481i
\(834\) −14.9619 −0.518088
\(835\) 30.7928 19.2491i 1.06563 0.666142i
\(836\) −26.0210 37.1859i −0.899957 1.28610i
\(837\) 0.551846i 0.0190746i
\(838\) 11.5122i 0.397683i
\(839\) 3.91149i 0.135040i −0.997718 0.0675198i \(-0.978491\pi\)
0.997718 0.0675198i \(-0.0215086\pi\)
\(840\) 45.7846 + 17.1198i 1.57972 + 0.590689i
\(841\) 26.9809 0.930376
\(842\) 15.0400 0.518311
\(843\) 31.7030i 1.09191i
\(844\) 88.5261i 3.04719i
\(845\) 14.5220 + 23.2310i 0.499573 + 0.799169i
\(846\) 22.3180 0.767310
\(847\) 8.72886 + 27.7634i 0.299927 + 0.953962i
\(848\) 97.0673i 3.33330i
\(849\) 7.26679i 0.249396i
\(850\) 18.4119 + 8.97202i 0.631524 + 0.307738i
\(851\) −43.7683 −1.50036
\(852\) 22.3745 0.766539
\(853\) 1.00626i 0.0344538i 0.999852 + 0.0172269i \(0.00548377\pi\)
−0.999852 + 0.0172269i \(0.994516\pi\)
\(854\) −38.9270 + 29.8568i −1.33206 + 1.02168i
\(855\) −3.17993 5.08694i −0.108751 0.173970i
\(856\) −135.583 −4.63414
\(857\) 33.8944i 1.15781i −0.815395 0.578905i \(-0.803480\pi\)
0.815395 0.578905i \(-0.196520\pi\)
\(858\) −6.26227 + 4.38205i −0.213790 + 0.149601i
\(859\) 34.4495i 1.17540i −0.809078 0.587701i \(-0.800033\pi\)
0.809078 0.587701i \(-0.199967\pi\)
\(860\) −4.97749 7.96250i −0.169731 0.271519i
\(861\) −1.27494 + 0.977874i −0.0434499 + 0.0333259i
\(862\) 106.614i 3.63129i
\(863\) 3.22432i 0.109757i −0.998493 0.0548785i \(-0.982523\pi\)
0.998493 0.0548785i \(-0.0174772\pi\)
\(864\) 14.9598 0.508943
\(865\) 18.0916 11.3093i 0.615133 0.384529i
\(866\) 21.8161 0.741342
\(867\) −14.6369 −0.497094
\(868\) 4.53233 + 5.90921i 0.153837 + 0.200572i
\(869\) −24.3080 + 17.0097i −0.824593 + 0.577013i
\(870\) −7.17935 + 4.48793i −0.243403 + 0.152155i
\(871\) 6.73219 0.228112
\(872\) 94.6713i 3.20597i
\(873\) 18.3921 0.622479
\(874\) 52.4019i 1.77252i
\(875\) −21.4503 + 20.3687i −0.725152 + 0.688589i
\(876\) 19.8429i 0.670431i
\(877\) −7.74745 −0.261613 −0.130806 0.991408i \(-0.541757\pi\)
−0.130806 + 0.991408i \(0.541757\pi\)
\(878\) −43.7882 −1.47778
\(879\) 31.4376i 1.06037i
\(880\) −34.2481 + 80.6550i −1.15450 + 2.71888i
\(881\) 22.6712i 0.763813i −0.924201 0.381907i \(-0.875268\pi\)
0.924201 0.381907i \(-0.124732\pi\)
\(882\) −4.83526 + 18.0153i −0.162812 + 0.606608i
\(883\) 8.85959i 0.298149i 0.988826 + 0.149074i \(0.0476294\pi\)
−0.988826 + 0.149074i \(0.952371\pi\)
\(884\) −6.78110 −0.228073
\(885\) −27.2846 + 17.0560i −0.917161 + 0.573332i
\(886\) 38.4456i 1.29161i
\(887\) 50.8004i 1.70571i 0.522147 + 0.852856i \(0.325131\pi\)
−0.522147 + 0.852856i \(0.674869\pi\)
\(888\) 49.3361i 1.65561i
\(889\) 33.8707 25.9787i 1.13599 0.871296i
\(890\) 37.9662 23.7333i 1.27263 0.795541i
\(891\) 1.90151 + 2.71740i 0.0637031 + 0.0910362i
\(892\) −44.8364 −1.50123
\(893\) 22.4702 0.751936
\(894\) 17.6813i 0.591350i
\(895\) −17.4964 27.9891i −0.584841 0.935572i
\(896\) −27.9967 + 21.4734i −0.935305 + 0.717375i
\(897\) 6.33910 0.211656
\(898\) −4.00048 −0.133498
\(899\) −0.784146 −0.0261527
\(900\) −11.1718 + 22.9262i −0.372392 + 0.764205i
\(901\) 12.6290 0.420734
\(902\) −3.07719 4.39752i −0.102459 0.146421i
\(903\) 1.72843 1.32570i 0.0575185 0.0441164i
\(904\) 32.0520i 1.06603i
\(905\) −44.0780 + 27.5538i −1.46520 + 0.915921i
\(906\) 44.7575i 1.48697i
\(907\) 34.0993i 1.13225i −0.824320 0.566125i \(-0.808442\pi\)
0.824320 0.566125i \(-0.191558\pi\)
\(908\) 82.8796i 2.75046i
\(909\) −17.7370 −0.588300
\(910\) 4.77501 12.7701i 0.158290 0.423325i
\(911\) 13.9029 0.460622 0.230311 0.973117i \(-0.426026\pi\)
0.230311 + 0.973117i \(0.426026\pi\)
\(912\) 31.6991 1.04966
\(913\) −35.7175 + 24.9935i −1.18208 + 0.827164i
\(914\) 51.1010 1.69027
\(915\) −8.24773 13.1939i −0.272662 0.436178i
\(916\) 125.273i 4.13915i
\(917\) −16.7550 + 12.8510i −0.553299 + 0.424378i
\(918\) 4.09632i 0.135199i
\(919\) 31.1901i 1.02887i 0.857531 + 0.514433i \(0.171997\pi\)
−0.857531 + 0.514433i \(0.828003\pi\)
\(920\) 114.831 71.7825i 3.78586 2.36660i
\(921\) 13.8197i 0.455375i
\(922\) −45.7684 −1.50730
\(923\) 3.79365i 0.124870i
\(924\) −42.6796 13.4809i −1.40406 0.443489i
\(925\) −26.8391 13.0785i −0.882463 0.430019i
\(926\) 63.1752i 2.07607i
\(927\) −15.5720 −0.511453
\(928\) 21.2571i 0.697800i
\(929\) 30.5461i 1.00218i −0.865394 0.501092i \(-0.832932\pi\)
0.865394 0.501092i \(-0.167068\pi\)
\(930\) −2.78820 + 1.74295i −0.0914288 + 0.0571536i
\(931\) −4.86822 + 18.1381i −0.159550 + 0.594454i
\(932\) −87.9488 −2.88086
\(933\) 4.57177i 0.149673i
\(934\) −57.2628 −1.87370
\(935\) −10.4937 4.45588i −0.343181 0.145723i
\(936\) 7.14549i 0.233558i
\(937\) 2.87984i 0.0940802i −0.998893 0.0470401i \(-0.985021\pi\)
0.998893 0.0470401i \(-0.0149789\pi\)
\(938\) 33.4006 + 43.5474i 1.09057 + 1.42187i
\(939\) 26.4180 0.862117
\(940\) −50.6350 81.0010i −1.65153 2.64196i
\(941\) −26.5254 −0.864702 −0.432351 0.901705i \(-0.642316\pi\)
−0.432351 + 0.901705i \(0.642316\pi\)
\(942\) −17.3791 −0.566243
\(943\) 4.45147i 0.144960i
\(944\) 170.023i 5.53377i
\(945\) −5.54136 2.07203i −0.180261 0.0674031i
\(946\) 4.17172 + 5.96168i 0.135634 + 0.193831i
\(947\) 6.15057i 0.199867i −0.994994 0.0999333i \(-0.968137\pi\)
0.994994 0.0999333i \(-0.0318630\pi\)
\(948\) 45.6270i 1.48190i
\(949\) −3.36441 −0.109213
\(950\) −15.6583 + 32.1332i −0.508023 + 1.04254i
\(951\) 7.88446i 0.255671i
\(952\) −20.4515 26.6645i −0.662837 0.864200i
\(953\) −11.6177 −0.376333 −0.188166 0.982137i \(-0.560254\pi\)
−0.188166 + 0.982137i \(0.560254\pi\)
\(954\) 21.8915i 0.708762i
\(955\) 18.8420 + 30.1416i 0.609712 + 0.975359i
\(956\) 13.3054i 0.430327i
\(957\) 3.86129 2.70195i 0.124818 0.0873418i
\(958\) 22.2139 0.717697
\(959\) 21.4491 + 27.9651i 0.692627 + 0.903039i
\(960\) −19.2402 30.7787i −0.620976 0.993377i
\(961\) 30.6955 0.990176
\(962\) 13.7607 0.443663
\(963\) 16.4098 0.528798
\(964\) 5.20740 0.167719
\(965\) −9.86473 15.7806i −0.317557 0.507997i
\(966\) 31.4503 + 41.0046i 1.01190 + 1.31930i
\(967\) 36.8220 1.18412 0.592058 0.805895i \(-0.298316\pi\)
0.592058 + 0.805895i \(0.298316\pi\)
\(968\) 31.1366 85.3857i 1.00077 2.74440i
\(969\) 4.12424i 0.132490i
\(970\) −58.0897 92.9263i −1.86515 2.98368i
\(971\) 19.0710i 0.612019i 0.952029 + 0.306009i \(0.0989939\pi\)
−0.952029 + 0.306009i \(0.901006\pi\)
\(972\) −5.10065 −0.163604
\(973\) −11.7875 + 9.04098i −0.377891 + 0.289841i
\(974\) 16.1309i 0.516866i
\(975\) 3.88718 + 1.89420i 0.124489 + 0.0606629i
\(976\) 82.2175 2.63172
\(977\) 23.1779i 0.741527i −0.928727 0.370764i \(-0.879096\pi\)
0.928727 0.370764i \(-0.120904\pi\)
\(978\) 9.36651i 0.299508i
\(979\) −20.4194 + 14.2886i −0.652608 + 0.456666i
\(980\) 76.3550 23.3240i 2.43907 0.745057i
\(981\) 11.4582i 0.365832i
\(982\) 67.6076i 2.15744i
\(983\) 11.1133 0.354459 0.177230 0.984170i \(-0.443286\pi\)
0.177230 + 0.984170i \(0.443286\pi\)
\(984\) 5.01774 0.159960
\(985\) −15.6839 25.0895i −0.499730 0.799419i
\(986\) 5.82067 0.185368
\(987\) 17.5830 13.4861i 0.559672 0.429266i
\(988\) 11.8346i 0.376510i
\(989\) 6.03482i 0.191896i
\(990\) 7.72392 18.1900i 0.245482 0.578117i
\(991\) −21.0898 −0.669939 −0.334969 0.942229i \(-0.608726\pi\)
−0.334969 + 0.942229i \(0.608726\pi\)
\(992\) 8.25552i 0.262113i
\(993\) 5.20944 0.165317
\(994\) 24.5393 18.8215i 0.778340 0.596983i
\(995\) 7.27016 4.54469i 0.230479 0.144076i
\(996\) 67.0430i 2.12434i
\(997\) 32.2736i 1.02212i 0.859546 + 0.511058i \(0.170746\pi\)
−0.859546 + 0.511058i \(0.829254\pi\)
\(998\) −83.9772 −2.65825
\(999\) 5.97120i 0.188921i
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 1155.2.k.a.769.2 yes 48
5.4 even 2 1155.2.k.b.769.47 yes 48
7.6 odd 2 1155.2.k.b.769.1 yes 48
11.10 odd 2 inner 1155.2.k.a.769.47 yes 48
35.34 odd 2 inner 1155.2.k.a.769.48 yes 48
55.54 odd 2 1155.2.k.b.769.2 yes 48
77.76 even 2 1155.2.k.b.769.48 yes 48
385.384 even 2 inner 1155.2.k.a.769.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.k.a.769.1 48 385.384 even 2 inner
1155.2.k.a.769.2 yes 48 1.1 even 1 trivial
1155.2.k.a.769.47 yes 48 11.10 odd 2 inner
1155.2.k.a.769.48 yes 48 35.34 odd 2 inner
1155.2.k.b.769.1 yes 48 7.6 odd 2
1155.2.k.b.769.2 yes 48 55.54 odd 2
1155.2.k.b.769.47 yes 48 5.4 even 2
1155.2.k.b.769.48 yes 48 77.76 even 2