Properties

Label 136.2.h.a.101.16
Level $136$
Weight $2$
Character 136.101
Analytic conductor $1.086$
Analytic rank $0$
Dimension $16$
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] = [136,2,Mod(101,136)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(136, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("136.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.h (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: \(1.08596546749\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 8x^{14} + 20x^{12} + 36x^{10} + 240x^{8} - 156x^{6} + 268x^{4} + 136x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{11} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 101.16
Root \(-1.32216 - 1.07919i\) of defining polynomial
Character \(\chi\) \(=\) 136.101
Dual form 136.2.h.a.101.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.09558 + 0.894257i) q^{2} +1.88797 q^{3} +(0.400610 + 1.95947i) q^{4} -2.41361 q^{5} +(2.06843 + 1.68833i) q^{6} -2.57100i q^{7} +(-1.31336 + 2.50501i) q^{8} +0.564439 q^{9} +O(q^{10})\) \(q+(1.09558 + 0.894257i) q^{2} +1.88797 q^{3} +(0.400610 + 1.95947i) q^{4} -2.41361 q^{5} +(2.06843 + 1.68833i) q^{6} -2.57100i q^{7} +(-1.31336 + 2.50501i) q^{8} +0.564439 q^{9} +(-2.64431 - 2.15839i) q^{10} -0.736213 q^{11} +(0.756340 + 3.69942i) q^{12} -4.07497i q^{13} +(2.29914 - 2.81675i) q^{14} -4.55683 q^{15} +(-3.67902 + 1.56996i) q^{16} +(3.99239 + 1.02997i) q^{17} +(0.618390 + 0.504753i) q^{18} -0.853468i q^{19} +(-0.966916 - 4.72939i) q^{20} -4.85398i q^{21} +(-0.806583 - 0.658363i) q^{22} +8.20450i q^{23} +(-2.47960 + 4.72939i) q^{24} +0.825510 q^{25} +(3.64407 - 4.46448i) q^{26} -4.59827 q^{27} +(5.03779 - 1.02997i) q^{28} +5.86012 q^{29} +(-4.99239 - 4.07497i) q^{30} +3.51111i q^{31} +(-5.43463 - 1.56996i) q^{32} -1.38995 q^{33} +(3.45294 + 4.69864i) q^{34} +6.20539i q^{35} +(0.226120 + 1.10600i) q^{36} -4.38770 q^{37} +(0.763219 - 0.935046i) q^{38} -7.69344i q^{39} +(3.16995 - 6.04611i) q^{40} -11.7156i q^{41} +(4.34070 - 5.31794i) q^{42} -1.09108i q^{43} +(-0.294934 - 1.44258i) q^{44} -1.36234 q^{45} +(-7.33693 + 8.98872i) q^{46} -5.42795 q^{47} +(-6.94589 + 2.96405i) q^{48} +0.389949 q^{49} +(0.904416 + 0.738218i) q^{50} +(7.53752 + 1.94455i) q^{51} +(7.98478 - 1.63247i) q^{52} +4.66811i q^{53} +(-5.03779 - 4.11204i) q^{54} +1.77693 q^{55} +(6.44038 + 3.37666i) q^{56} -1.61132i q^{57} +(6.42026 + 5.24045i) q^{58} +12.5060i q^{59} +(-1.82551 - 8.92895i) q^{60} +8.16364 q^{61} +(-3.13983 + 3.84672i) q^{62} -1.45117i q^{63} +(-4.55015 - 6.57998i) q^{64} +9.83539i q^{65} +(-1.52281 - 1.24297i) q^{66} -10.5614i q^{67} +(-0.418800 + 8.23557i) q^{68} +15.4899i q^{69} +(-5.54922 + 6.79853i) q^{70} +0.511064i q^{71} +(-0.741314 + 1.41392i) q^{72} +13.3269i q^{73} +(-4.80709 - 3.92373i) q^{74} +1.55854 q^{75} +(1.67234 - 0.341908i) q^{76} +1.89280i q^{77} +(6.87991 - 8.42881i) q^{78} -1.45117i q^{79} +(8.87973 - 3.78928i) q^{80} -10.3747 q^{81} +(10.4768 - 12.8354i) q^{82} +4.35603i q^{83} +(9.51121 - 1.94455i) q^{84} +(-9.63607 - 2.48594i) q^{85} +(0.975710 - 1.19538i) q^{86} +11.0637 q^{87} +(0.966916 - 1.84422i) q^{88} +5.72371 q^{89} +(-1.49255 - 1.21828i) q^{90} -10.4768 q^{91} +(-16.0765 + 3.28680i) q^{92} +6.62888i q^{93} +(-5.94678 - 4.85398i) q^{94} +2.05994i q^{95} +(-10.2604 - 2.96405i) q^{96} -11.8953i q^{97} +(0.427222 + 0.348714i) q^{98} -0.415547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} - 8 q^{15} - 14 q^{16} - 2 q^{18} - 16 q^{30} - 2 q^{32} - 8 q^{33} + 18 q^{34} - 22 q^{36} + 36 q^{38} - 24 q^{47} - 8 q^{49} + 34 q^{50} - 8 q^{55} - 16 q^{60} - 30 q^{64} - 32 q^{66} + 38 q^{68} + 40 q^{70} + 70 q^{72} + 4 q^{76} - 24 q^{81} + 72 q^{84} + 4 q^{86} - 40 q^{87} - 24 q^{89} - 16 q^{94} + 34 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09558 + 0.894257i 0.774695 + 0.632335i
\(3\) 1.88797 1.09002 0.545011 0.838429i \(-0.316526\pi\)
0.545011 + 0.838429i \(0.316526\pi\)
\(4\) 0.400610 + 1.95947i 0.200305 + 0.979734i
\(5\) −2.41361 −1.07940 −0.539699 0.841858i \(-0.681462\pi\)
−0.539699 + 0.841858i \(0.681462\pi\)
\(6\) 2.06843 + 1.68833i 0.844434 + 0.689259i
\(7\) 2.57100i 0.971747i −0.874029 0.485874i \(-0.838501\pi\)
0.874029 0.485874i \(-0.161499\pi\)
\(8\) −1.31336 + 2.50501i −0.464345 + 0.885655i
\(9\) 0.564439 0.188146
\(10\) −2.64431 2.15839i −0.836205 0.682542i
\(11\) −0.736213 −0.221976 −0.110988 0.993822i \(-0.535402\pi\)
−0.110988 + 0.993822i \(0.535402\pi\)
\(12\) 0.756340 + 3.69942i 0.218337 + 1.06793i
\(13\) 4.07497i 1.13019i −0.825024 0.565097i \(-0.808839\pi\)
0.825024 0.565097i \(-0.191161\pi\)
\(14\) 2.29914 2.81675i 0.614470 0.752808i
\(15\) −4.55683 −1.17657
\(16\) −3.67902 + 1.56996i −0.919756 + 0.392491i
\(17\) 3.99239 + 1.02997i 0.968296 + 0.249804i
\(18\) 0.618390 + 0.504753i 0.145756 + 0.118971i
\(19\) 0.853468i 0.195799i −0.995196 0.0978995i \(-0.968788\pi\)
0.995196 0.0978995i \(-0.0312124\pi\)
\(20\) −0.966916 4.72939i −0.216209 1.05752i
\(21\) 4.85398i 1.05923i
\(22\) −0.806583 0.658363i −0.171964 0.140363i
\(23\) 8.20450i 1.71076i 0.518004 + 0.855378i \(0.326675\pi\)
−0.518004 + 0.855378i \(0.673325\pi\)
\(24\) −2.47960 + 4.72939i −0.506145 + 0.965382i
\(25\) 0.825510 0.165102
\(26\) 3.64407 4.46448i 0.714661 0.875556i
\(27\) −4.59827 −0.884938
\(28\) 5.03779 1.02997i 0.952054 0.194646i
\(29\) 5.86012 1.08820 0.544099 0.839021i \(-0.316872\pi\)
0.544099 + 0.839021i \(0.316872\pi\)
\(30\) −4.99239 4.07497i −0.911481 0.743985i
\(31\) 3.51111i 0.630614i 0.948990 + 0.315307i \(0.102108\pi\)
−0.948990 + 0.315307i \(0.897892\pi\)
\(32\) −5.43463 1.56996i −0.960716 0.277533i
\(33\) −1.38995 −0.241959
\(34\) 3.45294 + 4.69864i 0.592175 + 0.805810i
\(35\) 6.20539i 1.04890i
\(36\) 0.226120 + 1.10600i 0.0376866 + 0.184333i
\(37\) −4.38770 −0.721333 −0.360666 0.932695i \(-0.617451\pi\)
−0.360666 + 0.932695i \(0.617451\pi\)
\(38\) 0.763219 0.935046i 0.123811 0.151684i
\(39\) 7.69344i 1.23194i
\(40\) 3.16995 6.04611i 0.501213 0.955975i
\(41\) 11.7156i 1.82967i −0.403827 0.914836i \(-0.632320\pi\)
0.403827 0.914836i \(-0.367680\pi\)
\(42\) 4.34070 5.31794i 0.669785 0.820577i
\(43\) 1.09108i 0.166389i −0.996533 0.0831944i \(-0.973488\pi\)
0.996533 0.0831944i \(-0.0265123\pi\)
\(44\) −0.294934 1.44258i −0.0444630 0.217478i
\(45\) −1.36234 −0.203085
\(46\) −7.33693 + 8.98872i −1.08177 + 1.32531i
\(47\) −5.42795 −0.791748 −0.395874 0.918305i \(-0.629558\pi\)
−0.395874 + 0.918305i \(0.629558\pi\)
\(48\) −6.94589 + 2.96405i −1.00255 + 0.427823i
\(49\) 0.389949 0.0557070
\(50\) 0.904416 + 0.738218i 0.127904 + 0.104400i
\(51\) 7.53752 + 1.94455i 1.05546 + 0.272292i
\(52\) 7.98478 1.63247i 1.10729 0.226383i
\(53\) 4.66811i 0.641214i 0.947212 + 0.320607i \(0.103887\pi\)
−0.947212 + 0.320607i \(0.896113\pi\)
\(54\) −5.03779 4.11204i −0.685557 0.559577i
\(55\) 1.77693 0.239601
\(56\) 6.44038 + 3.37666i 0.860633 + 0.451226i
\(57\) 1.61132i 0.213425i
\(58\) 6.42026 + 5.24045i 0.843021 + 0.688105i
\(59\) 12.5060i 1.62814i 0.580767 + 0.814070i \(0.302753\pi\)
−0.580767 + 0.814070i \(0.697247\pi\)
\(60\) −1.82551 8.92895i −0.235672 1.15272i
\(61\) 8.16364 1.04525 0.522624 0.852564i \(-0.324953\pi\)
0.522624 + 0.852564i \(0.324953\pi\)
\(62\) −3.13983 + 3.84672i −0.398759 + 0.488534i
\(63\) 1.45117i 0.182831i
\(64\) −4.55015 6.57998i −0.568768 0.822498i
\(65\) 9.83539i 1.21993i
\(66\) −1.52281 1.24297i −0.187444 0.152999i
\(67\) 10.5614i 1.29028i −0.764063 0.645142i \(-0.776798\pi\)
0.764063 0.645142i \(-0.223202\pi\)
\(68\) −0.418800 + 8.23557i −0.0507869 + 0.998710i
\(69\) 15.4899i 1.86476i
\(70\) −5.54922 + 6.79853i −0.663258 + 0.812580i
\(71\) 0.511064i 0.0606522i 0.999540 + 0.0303261i \(0.00965458\pi\)
−0.999540 + 0.0303261i \(0.990345\pi\)
\(72\) −0.741314 + 1.41392i −0.0873647 + 0.166633i
\(73\) 13.3269i 1.55980i 0.625904 + 0.779900i \(0.284730\pi\)
−0.625904 + 0.779900i \(0.715270\pi\)
\(74\) −4.80709 3.92373i −0.558813 0.456124i
\(75\) 1.55854 0.179965
\(76\) 1.67234 0.341908i 0.191831 0.0392195i
\(77\) 1.89280i 0.215705i
\(78\) 6.87991 8.42881i 0.778996 0.954375i
\(79\) 1.45117i 0.163270i −0.996662 0.0816349i \(-0.973986\pi\)
0.996662 0.0816349i \(-0.0260141\pi\)
\(80\) 8.87973 3.78928i 0.992783 0.423654i
\(81\) −10.3747 −1.15275
\(82\) 10.4768 12.8354i 1.15697 1.41744i
\(83\) 4.35603i 0.478137i 0.971003 + 0.239068i \(0.0768420\pi\)
−0.971003 + 0.239068i \(0.923158\pi\)
\(84\) 9.51121 1.94455i 1.03776 0.212168i
\(85\) −9.63607 2.48594i −1.04518 0.269638i
\(86\) 0.975710 1.19538i 0.105213 0.128901i
\(87\) 11.0637 1.18616
\(88\) 0.966916 1.84422i 0.103074 0.196594i
\(89\) 5.72371 0.606712 0.303356 0.952877i \(-0.401893\pi\)
0.303356 + 0.952877i \(0.401893\pi\)
\(90\) −1.49255 1.21828i −0.157329 0.128418i
\(91\) −10.4768 −1.09826
\(92\) −16.0765 + 3.28680i −1.67609 + 0.342673i
\(93\) 6.62888i 0.687383i
\(94\) −5.94678 4.85398i −0.613363 0.500650i
\(95\) 2.05994i 0.211345i
\(96\) −10.2604 2.96405i −1.04720 0.302517i
\(97\) 11.8953i 1.20779i −0.797065 0.603894i \(-0.793615\pi\)
0.797065 0.603894i \(-0.206385\pi\)
\(98\) 0.427222 + 0.348714i 0.0431559 + 0.0352255i
\(99\) −0.415547 −0.0417640
\(100\) 0.330707 + 1.61756i 0.0330707 + 0.161756i
\(101\) 8.33582i 0.829445i −0.909948 0.414722i \(-0.863879\pi\)
0.909948 0.414722i \(-0.136121\pi\)
\(102\) 6.51906 + 8.87090i 0.645483 + 0.878350i
\(103\) 15.5446 1.53165 0.765826 0.643048i \(-0.222330\pi\)
0.765826 + 0.643048i \(0.222330\pi\)
\(104\) 10.2078 + 5.35193i 1.00096 + 0.524800i
\(105\) 11.7156i 1.14333i
\(106\) −4.17449 + 5.11431i −0.405462 + 0.496746i
\(107\) 14.9889 1.44903 0.724517 0.689257i \(-0.242063\pi\)
0.724517 + 0.689257i \(0.242063\pi\)
\(108\) −1.84211 9.01016i −0.177257 0.867003i
\(109\) 0.941184 0.0901491 0.0450745 0.998984i \(-0.485647\pi\)
0.0450745 + 0.998984i \(0.485647\pi\)
\(110\) 1.94678 + 1.58903i 0.185618 + 0.151508i
\(111\) −8.28385 −0.786268
\(112\) 4.03638 + 9.45878i 0.381402 + 0.893770i
\(113\) 9.83539i 0.925236i −0.886558 0.462618i \(-0.846910\pi\)
0.886558 0.462618i \(-0.153090\pi\)
\(114\) 1.44094 1.76534i 0.134956 0.165339i
\(115\) 19.8025i 1.84659i
\(116\) 2.34762 + 11.4827i 0.217971 + 1.06614i
\(117\) 2.30007i 0.212642i
\(118\) −11.1836 + 13.7014i −1.02953 + 1.26131i
\(119\) 2.64805 10.2644i 0.242747 0.940940i
\(120\) 5.98478 11.4149i 0.546333 1.04203i
\(121\) −10.4580 −0.950726
\(122\) 8.94396 + 7.30039i 0.809748 + 0.660946i
\(123\) 22.1187i 1.99438i
\(124\) −6.87991 + 1.40659i −0.617834 + 0.126315i
\(125\) 10.0756 0.901188
\(126\) 1.29772 1.58988i 0.115610 0.141638i
\(127\) −11.0984 −0.984827 −0.492413 0.870362i \(-0.663885\pi\)
−0.492413 + 0.870362i \(0.663885\pi\)
\(128\) 0.899126 11.2779i 0.0794722 0.996837i
\(129\) 2.05994i 0.181367i
\(130\) −8.79537 + 10.7755i −0.771405 + 0.945074i
\(131\) −18.4354 −1.61071 −0.805356 0.592792i \(-0.798026\pi\)
−0.805356 + 0.592792i \(0.798026\pi\)
\(132\) −0.556827 2.72356i −0.0484656 0.237055i
\(133\) −2.19427 −0.190267
\(134\) 9.44463 11.5709i 0.815892 0.999577i
\(135\) 11.0984 0.955201
\(136\) −7.82354 + 8.64825i −0.670863 + 0.741581i
\(137\) −13.5340 −1.15629 −0.578143 0.815935i \(-0.696223\pi\)
−0.578143 + 0.815935i \(0.696223\pi\)
\(138\) −13.8519 + 16.9705i −1.17915 + 1.44462i
\(139\) 2.71030 0.229885 0.114942 0.993372i \(-0.463332\pi\)
0.114942 + 0.993372i \(0.463332\pi\)
\(140\) −12.1593 + 2.48594i −1.02765 + 0.210100i
\(141\) −10.2478 −0.863022
\(142\) −0.457023 + 0.559914i −0.0383525 + 0.0469870i
\(143\) 3.00005i 0.250876i
\(144\) −2.07658 + 0.886149i −0.173049 + 0.0738457i
\(145\) −14.1440 −1.17460
\(146\) −11.9177 + 14.6008i −0.986316 + 1.20837i
\(147\) 0.736213 0.0607218
\(148\) −1.75775 8.59755i −0.144487 0.706714i
\(149\) 1.70694i 0.139838i 0.997553 + 0.0699188i \(0.0222740\pi\)
−0.997553 + 0.0699188i \(0.977726\pi\)
\(150\) 1.70751 + 1.39373i 0.139418 + 0.113798i
\(151\) 3.47786 0.283024 0.141512 0.989937i \(-0.454804\pi\)
0.141512 + 0.989937i \(0.454804\pi\)
\(152\) 2.13794 + 1.12091i 0.173410 + 0.0909182i
\(153\) 2.25346 + 0.581354i 0.182181 + 0.0469997i
\(154\) −1.69265 + 2.07373i −0.136398 + 0.167106i
\(155\) 8.47445i 0.680684i
\(156\) 15.0750 3.08207i 1.20697 0.246763i
\(157\) 22.0508i 1.75984i −0.475118 0.879922i \(-0.657595\pi\)
0.475118 0.879922i \(-0.342405\pi\)
\(158\) 1.29772 1.58988i 0.103241 0.126484i
\(159\) 8.81326i 0.698937i
\(160\) 13.1171 + 3.78928i 1.03700 + 0.299569i
\(161\) 21.0938 1.66242
\(162\) −11.3664 9.27767i −0.893028 0.728922i
\(163\) −6.94414 −0.543907 −0.271953 0.962310i \(-0.587670\pi\)
−0.271953 + 0.962310i \(0.587670\pi\)
\(164\) 22.9564 4.69339i 1.79259 0.366492i
\(165\) 3.35479 0.261170
\(166\) −3.89541 + 4.77240i −0.302343 + 0.370410i
\(167\) 11.3843i 0.880941i −0.897767 0.440470i \(-0.854812\pi\)
0.897767 0.440470i \(-0.145188\pi\)
\(168\) 12.1593 + 6.37505i 0.938108 + 0.491846i
\(169\) −3.60541 −0.277339
\(170\) −8.33405 11.3407i −0.639193 0.869790i
\(171\) 0.481730i 0.0368388i
\(172\) 2.13794 0.437099i 0.163017 0.0333285i
\(173\) −5.68789 −0.432442 −0.216221 0.976344i \(-0.569373\pi\)
−0.216221 + 0.976344i \(0.569373\pi\)
\(174\) 12.1213 + 9.89383i 0.918911 + 0.750049i
\(175\) 2.12239i 0.160437i
\(176\) 2.70854 1.15583i 0.204164 0.0871237i
\(177\) 23.6109i 1.77471i
\(178\) 6.27080 + 5.11846i 0.470016 + 0.383645i
\(179\) 16.5292i 1.23545i 0.786394 + 0.617725i \(0.211946\pi\)
−0.786394 + 0.617725i \(0.788054\pi\)
\(180\) −0.545765 2.66945i −0.0406789 0.198969i
\(181\) 20.6345 1.53375 0.766874 0.641798i \(-0.221811\pi\)
0.766874 + 0.641798i \(0.221811\pi\)
\(182\) −11.4782 9.36892i −0.850819 0.694470i
\(183\) 15.4127 1.13934
\(184\) −20.5524 10.7755i −1.51514 0.794381i
\(185\) 10.5902 0.778606
\(186\) −5.92792 + 7.26250i −0.434656 + 0.532512i
\(187\) −2.93925 0.758276i −0.214939 0.0554506i
\(188\) −2.17449 10.6359i −0.158591 0.775702i
\(189\) 11.8222i 0.859936i
\(190\) −1.84211 + 2.25684i −0.133641 + 0.163728i
\(191\) −17.3215 −1.25334 −0.626670 0.779285i \(-0.715583\pi\)
−0.626670 + 0.779285i \(0.715583\pi\)
\(192\) −8.59055 12.4228i −0.619969 0.896540i
\(193\) 12.3439i 0.888537i −0.895894 0.444268i \(-0.853464\pi\)
0.895894 0.444268i \(-0.146536\pi\)
\(194\) 10.6375 13.0323i 0.763727 0.935667i
\(195\) 18.5689i 1.32975i
\(196\) 0.156217 + 0.764092i 0.0111584 + 0.0545780i
\(197\) −5.96937 −0.425300 −0.212650 0.977128i \(-0.568209\pi\)
−0.212650 + 0.977128i \(0.568209\pi\)
\(198\) −0.455267 0.371606i −0.0323544 0.0264089i
\(199\) 12.8979i 0.914307i 0.889388 + 0.457154i \(0.151131\pi\)
−0.889388 + 0.457154i \(0.848869\pi\)
\(200\) −1.08420 + 2.06791i −0.0766642 + 0.146223i
\(201\) 19.9397i 1.40644i
\(202\) 7.45436 9.13259i 0.524487 0.642567i
\(203\) 15.0664i 1.05745i
\(204\) −0.790682 + 15.5485i −0.0553588 + 1.08861i
\(205\) 28.2769i 1.97495i
\(206\) 17.0304 + 13.9008i 1.18656 + 0.968517i
\(207\) 4.63094i 0.321873i
\(208\) 6.39756 + 14.9919i 0.443591 + 1.03950i
\(209\) 0.628334i 0.0434627i
\(210\) −10.4768 + 12.8354i −0.722965 + 0.885730i
\(211\) 4.31995 0.297398 0.148699 0.988883i \(-0.452491\pi\)
0.148699 + 0.988883i \(0.452491\pi\)
\(212\) −9.14701 + 1.87009i −0.628219 + 0.128438i
\(213\) 0.964875i 0.0661122i
\(214\) 16.4216 + 13.4039i 1.12256 + 0.916275i
\(215\) 2.63345i 0.179600i
\(216\) 6.03921 11.5187i 0.410916 0.783749i
\(217\) 9.02707 0.612798
\(218\) 1.03115 + 0.841660i 0.0698381 + 0.0570044i
\(219\) 25.1609i 1.70021i
\(220\) 0.711855 + 3.48184i 0.0479933 + 0.234745i
\(221\) 4.19710 16.2689i 0.282327 1.09436i
\(222\) −9.07565 7.40789i −0.609118 0.497185i
\(223\) 15.5793 1.04326 0.521632 0.853171i \(-0.325323\pi\)
0.521632 + 0.853171i \(0.325323\pi\)
\(224\) −4.03638 + 13.9724i −0.269692 + 0.933573i
\(225\) 0.465950 0.0310633
\(226\) 8.79537 10.7755i 0.585059 0.716776i
\(227\) 5.47171 0.363170 0.181585 0.983375i \(-0.441877\pi\)
0.181585 + 0.983375i \(0.441877\pi\)
\(228\) 3.15733 0.645512i 0.209100 0.0427501i
\(229\) 2.88870i 0.190890i 0.995435 + 0.0954452i \(0.0304275\pi\)
−0.995435 + 0.0954452i \(0.969573\pi\)
\(230\) 17.7085 21.6953i 1.16766 1.43054i
\(231\) 3.57356i 0.235123i
\(232\) −7.69648 + 14.6797i −0.505298 + 0.963767i
\(233\) 8.67268i 0.568166i 0.958800 + 0.284083i \(0.0916892\pi\)
−0.958800 + 0.284083i \(0.908311\pi\)
\(234\) 2.05686 2.51992i 0.134461 0.164733i
\(235\) 13.1009 0.854612
\(236\) −24.5051 + 5.01002i −1.59514 + 0.326124i
\(237\) 2.73978i 0.177968i
\(238\) 12.0802 8.87752i 0.783043 0.575444i
\(239\) −16.1107 −1.04211 −0.521057 0.853522i \(-0.674462\pi\)
−0.521057 + 0.853522i \(0.674462\pi\)
\(240\) 16.7647 7.15405i 1.08216 0.461792i
\(241\) 9.65567i 0.621977i −0.950414 0.310988i \(-0.899340\pi\)
0.950414 0.310988i \(-0.100660\pi\)
\(242\) −11.4576 9.35213i −0.736523 0.601178i
\(243\) −5.79238 −0.371581
\(244\) 3.27043 + 15.9964i 0.209368 + 1.02406i
\(245\) −0.941184 −0.0601301
\(246\) 19.7798 24.2330i 1.26112 1.54504i
\(247\) −3.47786 −0.221291
\(248\) −8.79537 4.61137i −0.558506 0.292822i
\(249\) 8.22407i 0.521179i
\(250\) 11.0387 + 9.01016i 0.698146 + 0.569853i
\(251\) 19.7073i 1.24391i 0.783052 + 0.621956i \(0.213662\pi\)
−0.783052 + 0.621956i \(0.786338\pi\)
\(252\) 2.84353 0.581354i 0.179125 0.0366219i
\(253\) 6.04026i 0.379748i
\(254\) −12.1593 9.92485i −0.762940 0.622740i
\(255\) −18.1926 4.69339i −1.13927 0.293911i
\(256\) 11.0704 11.5519i 0.691902 0.721992i
\(257\) 6.33840 0.395379 0.197689 0.980265i \(-0.436656\pi\)
0.197689 + 0.980265i \(0.436656\pi\)
\(258\) 1.84211 2.25684i 0.114685 0.140504i
\(259\) 11.2808i 0.700953i
\(260\) −19.2721 + 3.94016i −1.19521 + 0.244358i
\(261\) 3.30768 0.204740
\(262\) −20.1976 16.4860i −1.24781 1.01851i
\(263\) −15.5446 −0.958519 −0.479260 0.877673i \(-0.659095\pi\)
−0.479260 + 0.877673i \(0.659095\pi\)
\(264\) 1.82551 3.48184i 0.112352 0.214292i
\(265\) 11.2670i 0.692126i
\(266\) −2.40400 1.96224i −0.147399 0.120313i
\(267\) 10.8062 0.661329
\(268\) 20.6948 4.23101i 1.26413 0.258450i
\(269\) −22.8463 −1.39296 −0.696481 0.717575i \(-0.745252\pi\)
−0.696481 + 0.717575i \(0.745252\pi\)
\(270\) 12.1593 + 9.92485i 0.739989 + 0.604007i
\(271\) 7.17019 0.435558 0.217779 0.975998i \(-0.430119\pi\)
0.217779 + 0.975998i \(0.430119\pi\)
\(272\) −16.3051 + 2.47863i −0.988642 + 0.150289i
\(273\) −19.7798 −1.19713
\(274\) −14.8276 12.1029i −0.895770 0.731161i
\(275\) −0.607751 −0.0366488
\(276\) −30.3519 + 6.20539i −1.82697 + 0.373521i
\(277\) −6.61070 −0.397199 −0.198599 0.980081i \(-0.563639\pi\)
−0.198599 + 0.980081i \(0.563639\pi\)
\(278\) 2.96936 + 2.42370i 0.178090 + 0.145364i
\(279\) 1.98181i 0.118648i
\(280\) −15.5446 8.14995i −0.928966 0.487052i
\(281\) 14.8479 0.885754 0.442877 0.896582i \(-0.353958\pi\)
0.442877 + 0.896582i \(0.353958\pi\)
\(282\) −11.2273 9.16418i −0.668579 0.545719i
\(283\) −14.3388 −0.852355 −0.426177 0.904640i \(-0.640140\pi\)
−0.426177 + 0.904640i \(0.640140\pi\)
\(284\) −1.00141 + 0.204737i −0.0594230 + 0.0121489i
\(285\) 3.88910i 0.230371i
\(286\) −2.68281 + 3.28680i −0.158638 + 0.194353i
\(287\) −30.1209 −1.77798
\(288\) −3.06752 0.886149i −0.180755 0.0522168i
\(289\) 14.8783 + 8.22407i 0.875196 + 0.483769i
\(290\) −15.4960 12.6484i −0.909956 0.742740i
\(291\) 22.4581i 1.31651i
\(292\) −26.1137 + 5.33890i −1.52819 + 0.312436i
\(293\) 19.5648i 1.14299i −0.820605 0.571495i \(-0.806364\pi\)
0.820605 0.571495i \(-0.193636\pi\)
\(294\) 0.806583 + 0.658363i 0.0470409 + 0.0383965i
\(295\) 30.1846i 1.75741i
\(296\) 5.76265 10.9912i 0.334947 0.638852i
\(297\) 3.38531 0.196435
\(298\) −1.52644 + 1.87009i −0.0884242 + 0.108331i
\(299\) 33.4331 1.93349
\(300\) 0.624366 + 3.05391i 0.0360478 + 0.176317i
\(301\) −2.80518 −0.161688
\(302\) 3.81029 + 3.11010i 0.219257 + 0.178966i
\(303\) 15.7378i 0.904112i
\(304\) 1.33991 + 3.13993i 0.0768493 + 0.180087i
\(305\) −19.7038 −1.12824
\(306\) 1.94897 + 2.65209i 0.111415 + 0.151610i
\(307\) 10.6087i 0.605468i 0.953075 + 0.302734i \(0.0978994\pi\)
−0.953075 + 0.302734i \(0.902101\pi\)
\(308\) −3.70889 + 0.758276i −0.211333 + 0.0432068i
\(309\) 29.3477 1.66953
\(310\) 7.57833 9.28447i 0.430420 0.527323i
\(311\) 15.2696i 0.865860i 0.901428 + 0.432930i \(0.142520\pi\)
−0.901428 + 0.432930i \(0.857480\pi\)
\(312\) 19.2721 + 10.1043i 1.09107 + 0.572043i
\(313\) 13.1472i 0.743125i 0.928408 + 0.371562i \(0.121178\pi\)
−0.928408 + 0.371562i \(0.878822\pi\)
\(314\) 19.7191 24.1585i 1.11281 1.36334i
\(315\) 3.50257i 0.197347i
\(316\) 2.84353 0.581354i 0.159961 0.0327037i
\(317\) −25.7911 −1.44857 −0.724287 0.689499i \(-0.757831\pi\)
−0.724287 + 0.689499i \(0.757831\pi\)
\(318\) −7.88132 + 9.65567i −0.441963 + 0.541463i
\(319\) −4.31429 −0.241554
\(320\) 10.9823 + 15.8815i 0.613928 + 0.887803i
\(321\) 28.2987 1.57948
\(322\) 23.1100 + 18.8633i 1.28787 + 1.05121i
\(323\) 0.879045 3.40737i 0.0489114 0.189591i
\(324\) −4.15622 20.3289i −0.230901 1.12939i
\(325\) 3.36393i 0.186597i
\(326\) −7.60789 6.20984i −0.421362 0.343931i
\(327\) 1.77693 0.0982644
\(328\) 29.3477 + 15.3869i 1.62046 + 0.849598i
\(329\) 13.9553i 0.769379i
\(330\) 3.67546 + 3.00005i 0.202327 + 0.165147i
\(331\) 17.4779i 0.960670i 0.877085 + 0.480335i \(0.159485\pi\)
−0.877085 + 0.480335i \(0.840515\pi\)
\(332\) −8.53551 + 1.74507i −0.468447 + 0.0957732i
\(333\) −2.47659 −0.135716
\(334\) 10.1805 12.4724i 0.557050 0.682461i
\(335\) 25.4912i 1.39273i
\(336\) 7.62057 + 17.8579i 0.415736 + 0.974229i
\(337\) 26.1195i 1.42282i 0.702777 + 0.711410i \(0.251943\pi\)
−0.702777 + 0.711410i \(0.748057\pi\)
\(338\) −3.95003 3.22416i −0.214853 0.175371i
\(339\) 18.5689i 1.00853i
\(340\) 1.01082 19.8774i 0.0548194 1.07801i
\(341\) 2.58492i 0.139981i
\(342\) 0.430791 0.527776i 0.0232945 0.0285389i
\(343\) 18.9996i 1.02588i
\(344\) 2.73318 + 1.43299i 0.147363 + 0.0772618i
\(345\) 37.3865i 2.01282i
\(346\) −6.23157 5.08644i −0.335011 0.273448i
\(347\) −17.9138 −0.961663 −0.480832 0.876813i \(-0.659665\pi\)
−0.480832 + 0.876813i \(0.659665\pi\)
\(348\) 4.43225 + 21.6790i 0.237593 + 1.16212i
\(349\) 22.5260i 1.20579i 0.797820 + 0.602895i \(0.205986\pi\)
−0.797820 + 0.602895i \(0.794014\pi\)
\(350\) 1.89796 2.32525i 0.101450 0.124290i
\(351\) 18.7378i 1.00015i
\(352\) 4.00104 + 1.15583i 0.213256 + 0.0616058i
\(353\) 5.56775 0.296342 0.148171 0.988962i \(-0.452661\pi\)
0.148171 + 0.988962i \(0.452661\pi\)
\(354\) −21.1142 + 25.8678i −1.12221 + 1.37486i
\(355\) 1.23351i 0.0654679i
\(356\) 2.29297 + 11.2154i 0.121527 + 0.594416i
\(357\) 4.99945 19.3790i 0.264599 1.02564i
\(358\) −14.7814 + 18.1091i −0.781219 + 0.957098i
\(359\) 22.1622 1.16967 0.584837 0.811150i \(-0.301158\pi\)
0.584837 + 0.811150i \(0.301158\pi\)
\(360\) 1.78924 3.41266i 0.0943014 0.179863i
\(361\) 18.2716 0.961663
\(362\) 22.6068 + 18.4525i 1.18819 + 0.969842i
\(363\) −19.7444 −1.03631
\(364\) −4.19710 20.5289i −0.219988 1.07601i
\(365\) 32.1660i 1.68365i
\(366\) 16.8859 + 13.7829i 0.882642 + 0.720445i
\(367\) 2.12239i 0.110788i 0.998465 + 0.0553939i \(0.0176414\pi\)
−0.998465 + 0.0553939i \(0.982359\pi\)
\(368\) −12.8808 30.1846i −0.671456 1.57348i
\(369\) 6.61275i 0.344246i
\(370\) 11.6024 + 9.47034i 0.603182 + 0.492340i
\(371\) 12.0017 0.623098
\(372\) −12.9891 + 2.65559i −0.673452 + 0.137686i
\(373\) 17.6720i 0.915023i 0.889204 + 0.457512i \(0.151259\pi\)
−0.889204 + 0.457512i \(0.848741\pi\)
\(374\) −2.54210 3.45920i −0.131449 0.178871i
\(375\) 19.0224 0.982314
\(376\) 7.12888 13.5971i 0.367644 0.701215i
\(377\) 23.8798i 1.22987i
\(378\) −10.5721 + 12.9522i −0.543768 + 0.666188i
\(379\) −3.23194 −0.166013 −0.0830067 0.996549i \(-0.526452\pi\)
−0.0830067 + 0.996549i \(0.526452\pi\)
\(380\) −4.03638 + 0.825231i −0.207062 + 0.0423335i
\(381\) −20.9535 −1.07348
\(382\) −18.9772 15.4899i −0.970956 0.792531i
\(383\) 7.92400 0.404897 0.202449 0.979293i \(-0.435110\pi\)
0.202449 + 0.979293i \(0.435110\pi\)
\(384\) 1.69752 21.2924i 0.0866264 1.08657i
\(385\) 4.56849i 0.232832i
\(386\) 11.0387 13.5238i 0.561853 0.688345i
\(387\) 0.615851i 0.0313054i
\(388\) 23.3085 4.76539i 1.18331 0.241926i
\(389\) 4.78602i 0.242661i −0.992612 0.121330i \(-0.961284\pi\)
0.992612 0.121330i \(-0.0387160\pi\)
\(390\) −16.6054 + 20.3438i −0.840848 + 1.03015i
\(391\) −8.45038 + 32.7556i −0.427354 + 1.65652i
\(392\) −0.512145 + 0.976826i −0.0258672 + 0.0493371i
\(393\) −34.8056 −1.75571
\(394\) −6.53995 5.33815i −0.329478 0.268932i
\(395\) 3.50257i 0.176233i
\(396\) −0.166472 0.814251i −0.00836554 0.0409176i
\(397\) 5.00982 0.251436 0.125718 0.992066i \(-0.459877\pi\)
0.125718 + 0.992066i \(0.459877\pi\)
\(398\) −11.5340 + 14.1307i −0.578148 + 0.708309i
\(399\) −4.14272 −0.207395
\(400\) −3.03707 + 1.29602i −0.151854 + 0.0648010i
\(401\) 7.61142i 0.380096i 0.981775 + 0.190048i \(0.0608644\pi\)
−0.981775 + 0.190048i \(0.939136\pi\)
\(402\) 17.8312 21.8456i 0.889339 1.08956i
\(403\) 14.3077 0.712717
\(404\) 16.3338 3.33941i 0.812635 0.166142i
\(405\) 25.0405 1.24427
\(406\) 13.4732 16.5065i 0.668664 0.819203i
\(407\) 3.23028 0.160119
\(408\) −14.7706 + 16.3276i −0.731255 + 0.808339i
\(409\) −18.6582 −0.922590 −0.461295 0.887247i \(-0.652615\pi\)
−0.461295 + 0.887247i \(0.652615\pi\)
\(410\) −25.2868 + 30.9797i −1.24883 + 1.52998i
\(411\) −25.5518 −1.26038
\(412\) 6.22731 + 30.4591i 0.306797 + 1.50061i
\(413\) 32.1529 1.58214
\(414\) −4.14125 + 5.07358i −0.203531 + 0.249353i
\(415\) 10.5138i 0.516100i
\(416\) −6.39756 + 22.1460i −0.313666 + 1.08580i
\(417\) 5.11697 0.250579
\(418\) −0.561892 + 0.688392i −0.0274830 + 0.0336704i
\(419\) −1.05688 −0.0516319 −0.0258159 0.999667i \(-0.508218\pi\)
−0.0258159 + 0.999667i \(0.508218\pi\)
\(420\) −22.9564 + 4.69339i −1.12016 + 0.229014i
\(421\) 1.37215i 0.0668743i 0.999441 + 0.0334371i \(0.0106454\pi\)
−0.999441 + 0.0334371i \(0.989355\pi\)
\(422\) 4.73287 + 3.86315i 0.230393 + 0.188055i
\(423\) −3.06375 −0.148964
\(424\) −11.6937 6.13093i −0.567895 0.297744i
\(425\) 3.29576 + 0.850249i 0.159868 + 0.0412432i
\(426\) −0.862846 + 1.05710i −0.0418050 + 0.0512168i
\(427\) 20.9887i 1.01572i
\(428\) 6.00471 + 29.3703i 0.290249 + 1.41967i
\(429\) 5.66400i 0.273461i
\(430\) −2.35498 + 2.88517i −0.113567 + 0.139135i
\(431\) 14.9578i 0.720493i −0.932857 0.360247i \(-0.882693\pi\)
0.932857 0.360247i \(-0.117307\pi\)
\(432\) 16.9171 7.21912i 0.813927 0.347330i
\(433\) −1.48117 −0.0711806 −0.0355903 0.999366i \(-0.511331\pi\)
−0.0355903 + 0.999366i \(0.511331\pi\)
\(434\) 9.88992 + 8.07252i 0.474731 + 0.387493i
\(435\) −26.7036 −1.28034
\(436\) 0.377048 + 1.84422i 0.0180573 + 0.0883221i
\(437\) 7.00228 0.334964
\(438\) −22.5003 + 27.5659i −1.07511 + 1.31715i
\(439\) 19.6083i 0.935855i 0.883767 + 0.467927i \(0.154999\pi\)
−0.883767 + 0.467927i \(0.845001\pi\)
\(440\) −2.33376 + 4.45123i −0.111257 + 0.212204i
\(441\) 0.220102 0.0104811
\(442\) 19.1468 14.0706i 0.910721 0.669272i
\(443\) 32.3084i 1.53502i −0.641037 0.767510i \(-0.721495\pi\)
0.641037 0.767510i \(-0.278505\pi\)
\(444\) −3.31859 16.2319i −0.157493 0.770333i
\(445\) −13.8148 −0.654884
\(446\) 17.0684 + 13.9319i 0.808212 + 0.659692i
\(447\) 3.22265i 0.152426i
\(448\) −16.9171 + 11.6984i −0.799260 + 0.552699i
\(449\) 17.4468i 0.823366i −0.911327 0.411683i \(-0.864941\pi\)
0.911327 0.411683i \(-0.135059\pi\)
\(450\) 0.510487 + 0.416679i 0.0240646 + 0.0196424i
\(451\) 8.62518i 0.406144i
\(452\) 19.2721 3.94016i 0.906485 0.185329i
\(453\) 6.56610 0.308502
\(454\) 5.99472 + 4.89312i 0.281346 + 0.229645i
\(455\) 25.2868 1.18546
\(456\) 4.03638 + 2.11626i 0.189021 + 0.0991027i
\(457\) −2.35230 −0.110036 −0.0550179 0.998485i \(-0.517522\pi\)
−0.0550179 + 0.998485i \(0.517522\pi\)
\(458\) −2.58324 + 3.16481i −0.120707 + 0.147882i
\(459\) −18.3581 4.73608i −0.856882 0.221061i
\(460\) 38.8023 7.93306i 1.80917 0.369881i
\(461\) 4.32881i 0.201613i −0.994906 0.100806i \(-0.967858\pi\)
0.994906 0.100806i \(-0.0321422\pi\)
\(462\) −3.19568 + 3.91514i −0.148677 + 0.182149i
\(463\) 5.29610 0.246131 0.123065 0.992399i \(-0.460728\pi\)
0.123065 + 0.992399i \(0.460728\pi\)
\(464\) −21.5595 + 9.20018i −1.00088 + 0.427108i
\(465\) 15.9995i 0.741960i
\(466\) −7.75561 + 9.50166i −0.359272 + 0.440156i
\(467\) 4.40327i 0.203759i −0.994797 0.101879i \(-0.967514\pi\)
0.994797 0.101879i \(-0.0324856\pi\)
\(468\) 4.50692 0.921432i 0.208332 0.0425932i
\(469\) −27.1535 −1.25383
\(470\) 14.3532 + 11.7156i 0.662063 + 0.540401i
\(471\) 41.6313i 1.91827i
\(472\) −31.3276 16.4249i −1.44197 0.756018i
\(473\) 0.803270i 0.0369344i
\(474\) 2.45006 3.00165i 0.112535 0.137871i
\(475\) 0.704546i 0.0323268i
\(476\) 21.1737 + 1.07674i 0.970493 + 0.0493521i
\(477\) 2.63486i 0.120642i
\(478\) −17.6506 14.4071i −0.807320 0.658965i
\(479\) 16.4286i 0.750641i −0.926895 0.375320i \(-0.877533\pi\)
0.926895 0.375320i \(-0.122467\pi\)
\(480\) 24.7647 + 7.15405i 1.13035 + 0.326536i
\(481\) 17.8797i 0.815246i
\(482\) 8.63465 10.5786i 0.393298 0.481842i
\(483\) 39.8245 1.81208
\(484\) −4.18957 20.4921i −0.190435 0.931459i
\(485\) 28.7107i 1.30368i
\(486\) −6.34604 5.17987i −0.287862 0.234964i
\(487\) 4.75584i 0.215508i −0.994178 0.107754i \(-0.965634\pi\)
0.994178 0.107754i \(-0.0343658\pi\)
\(488\) −10.7218 + 20.4500i −0.485355 + 0.925728i
\(489\) −13.1103 −0.592870
\(490\) −1.03115 0.841660i −0.0465825 0.0380223i
\(491\) 1.89082i 0.0853316i 0.999089 + 0.0426658i \(0.0135851\pi\)
−0.999089 + 0.0426658i \(0.986415\pi\)
\(492\) 43.3410 8.86099i 1.95396 0.399484i
\(493\) 23.3959 + 6.03574i 1.05370 + 0.271836i
\(494\) −3.81029 3.11010i −0.171433 0.139930i
\(495\) 1.00297 0.0450801
\(496\) −5.51232 12.9175i −0.247510 0.580011i
\(497\) 1.31395 0.0589386
\(498\) −7.35443 + 9.01016i −0.329560 + 0.403755i
\(499\) 36.9132 1.65246 0.826231 0.563331i \(-0.190480\pi\)
0.826231 + 0.563331i \(0.190480\pi\)
\(500\) 4.03638 + 19.7428i 0.180512 + 0.882924i
\(501\) 21.4932i 0.960244i
\(502\) −17.6234 + 21.5910i −0.786569 + 0.963652i
\(503\) 17.3295i 0.772686i −0.922355 0.386343i \(-0.873738\pi\)
0.922355 0.386343i \(-0.126262\pi\)
\(504\) 3.63520 + 1.90592i 0.161925 + 0.0848964i
\(505\) 20.1194i 0.895302i
\(506\) 5.40154 6.61761i 0.240128 0.294189i
\(507\) −6.80691 −0.302305
\(508\) −4.44614 21.7470i −0.197266 0.964868i
\(509\) 10.2701i 0.455213i 0.973753 + 0.227607i \(0.0730900\pi\)
−0.973753 + 0.227607i \(0.926910\pi\)
\(510\) −15.7345 21.4109i −0.696733 0.948090i
\(511\) 34.2636 1.51573
\(512\) 22.4589 2.75624i 0.992553 0.121810i
\(513\) 3.92448i 0.173270i
\(514\) 6.94425 + 5.66816i 0.306298 + 0.250012i
\(515\) −37.5185 −1.65326
\(516\) 4.03638 0.825231i 0.177692 0.0363288i
\(517\) 3.99612 0.175749
\(518\) −10.0879 + 12.3590i −0.443237 + 0.543025i
\(519\) −10.7386 −0.471371
\(520\) −24.6378 12.9175i −1.08044 0.566468i
\(521\) 26.1195i 1.14432i 0.820143 + 0.572158i \(0.193894\pi\)
−0.820143 + 0.572158i \(0.806106\pi\)
\(522\) 3.62384 + 2.95792i 0.158611 + 0.129464i
\(523\) 14.8223i 0.648133i −0.946034 0.324066i \(-0.894950\pi\)
0.946034 0.324066i \(-0.105050\pi\)
\(524\) −7.38542 36.1236i −0.322633 1.57807i
\(525\) 4.00701i 0.174880i
\(526\) −17.0304 13.9008i −0.742560 0.606105i
\(527\) −3.61633 + 14.0177i −0.157530 + 0.610621i
\(528\) 5.11365 2.18217i 0.222543 0.0949667i
\(529\) −44.3138 −1.92669
\(530\) 10.0756 12.3439i 0.437656 0.536187i
\(531\) 7.05886i 0.306329i
\(532\) −0.879045 4.29959i −0.0381114 0.186411i
\(533\) −47.7408 −2.06788
\(534\) 11.8391 + 9.66351i 0.512328 + 0.418181i
\(535\) −36.1774 −1.56409
\(536\) 26.4565 + 13.8710i 1.14275 + 0.599136i
\(537\) 31.2067i 1.34667i
\(538\) −25.0300 20.4304i −1.07912 0.880818i
\(539\) −0.287085 −0.0123656
\(540\) 4.44614 + 21.7470i 0.191331 + 0.935842i
\(541\) −9.11519 −0.391893 −0.195946 0.980615i \(-0.562778\pi\)
−0.195946 + 0.980615i \(0.562778\pi\)
\(542\) 7.85555 + 6.41199i 0.337425 + 0.275419i
\(543\) 38.9573 1.67182
\(544\) −20.0801 11.8654i −0.860929 0.508725i
\(545\) −2.27165 −0.0973068
\(546\) −21.6705 17.6883i −0.927411 0.756987i
\(547\) 26.1596 1.11850 0.559251 0.828999i \(-0.311089\pi\)
0.559251 + 0.828999i \(0.311089\pi\)
\(548\) −5.42185 26.5194i −0.231610 1.13285i
\(549\) 4.60788 0.196659
\(550\) −0.665842 0.543485i −0.0283916 0.0231743i
\(551\) 5.00142i 0.213068i
\(552\) −38.8023 20.3438i −1.65153 0.865892i
\(553\) −3.73097 −0.158657
\(554\) −7.24258 5.91167i −0.307708 0.251163i
\(555\) 19.9940 0.848697
\(556\) 1.08577 + 5.31074i 0.0460470 + 0.225226i
\(557\) 41.3488i 1.75200i 0.482307 + 0.876002i \(0.339799\pi\)
−0.482307 + 0.876002i \(0.660201\pi\)
\(558\) −1.77224 + 2.17124i −0.0750251 + 0.0919158i
\(559\) −4.44614 −0.188052
\(560\) −9.74224 22.8298i −0.411685 0.964735i
\(561\) −5.54922 1.43160i −0.234288 0.0604424i
\(562\) 16.2672 + 13.2779i 0.686189 + 0.560093i
\(563\) 37.5179i 1.58119i −0.612338 0.790596i \(-0.709771\pi\)
0.612338 0.790596i \(-0.290229\pi\)
\(564\) −4.10538 20.0803i −0.172868 0.845532i
\(565\) 23.7388i 0.998699i
\(566\) −15.7094 12.8226i −0.660315 0.538974i
\(567\) 26.6734i 1.12018i
\(568\) −1.28022 0.671214i −0.0537169 0.0281635i
\(569\) 18.1288 0.760000 0.380000 0.924987i \(-0.375924\pi\)
0.380000 + 0.924987i \(0.375924\pi\)
\(570\) −3.47786 + 4.26084i −0.145671 + 0.178467i
\(571\) 15.4181 0.645226 0.322613 0.946531i \(-0.395439\pi\)
0.322613 + 0.946531i \(0.395439\pi\)
\(572\) −5.87849 + 1.20185i −0.245792 + 0.0502518i
\(573\) −32.7025 −1.36617
\(574\) −32.9999 26.9358i −1.37739 1.12428i
\(575\) 6.77290i 0.282449i
\(576\) −2.56828 3.71400i −0.107012 0.154750i
\(577\) 18.4051 0.766215 0.383107 0.923704i \(-0.374854\pi\)
0.383107 + 0.923704i \(0.374854\pi\)
\(578\) 8.94603 + 22.3152i 0.372106 + 0.928190i
\(579\) 23.3050i 0.968524i
\(580\) −5.66624 27.7148i −0.235278 1.15079i
\(581\) 11.1994 0.464628
\(582\) 20.0833 24.6047i 0.832478 1.01990i
\(583\) 3.43672i 0.142334i
\(584\) −33.3841 17.5031i −1.38144 0.724285i
\(585\) 5.55148i 0.229525i
\(586\) 17.4960 21.4349i 0.722753 0.885469i
\(587\) 28.5683i 1.17914i 0.807718 + 0.589569i \(0.200702\pi\)
−0.807718 + 0.589569i \(0.799298\pi\)
\(588\) 0.294934 + 1.44258i 0.0121629 + 0.0594912i
\(589\) 2.99662 0.123474
\(590\) 26.9927 33.0697i 1.11127 1.36146i
\(591\) −11.2700 −0.463586
\(592\) 16.1424 6.88852i 0.663450 0.283117i
\(593\) −21.7131 −0.891651 −0.445826 0.895120i \(-0.647090\pi\)
−0.445826 + 0.895120i \(0.647090\pi\)
\(594\) 3.70889 + 3.02733i 0.152177 + 0.124213i
\(595\) −6.39136 + 24.7743i −0.262020 + 1.01565i
\(596\) −3.34468 + 0.683815i −0.137004 + 0.0280102i
\(597\) 24.3509i 0.996614i
\(598\) 36.6288 + 29.8978i 1.49786 + 1.22261i
\(599\) 4.44614 0.181664 0.0908322 0.995866i \(-0.471047\pi\)
0.0908322 + 0.995866i \(0.471047\pi\)
\(600\) −2.04693 + 3.90416i −0.0835656 + 0.159387i
\(601\) 31.5661i 1.28761i 0.765190 + 0.643804i \(0.222645\pi\)
−0.765190 + 0.643804i \(0.777355\pi\)
\(602\) −3.07331 2.50855i −0.125259 0.102241i
\(603\) 5.96128i 0.242762i
\(604\) 1.39326 + 6.81475i 0.0566911 + 0.277288i
\(605\) 25.2415 1.02621
\(606\) 14.0736 17.2421i 0.571702 0.700411i
\(607\) 32.8533i 1.33347i −0.745294 0.666736i \(-0.767691\pi\)
0.745294 0.666736i \(-0.232309\pi\)
\(608\) −1.33991 + 4.63828i −0.0543407 + 0.188107i
\(609\) 28.4449i 1.15265i
\(610\) −21.5872 17.6203i −0.874041 0.713425i
\(611\) 22.1187i 0.894829i
\(612\) −0.236387 + 4.64848i −0.00955538 + 0.187904i
\(613\) 32.7902i 1.32438i 0.749335 + 0.662191i \(0.230373\pi\)
−0.749335 + 0.662191i \(0.769627\pi\)
\(614\) −9.48687 + 11.6227i −0.382859 + 0.469053i
\(615\) 53.3860i 2.15273i
\(616\) −4.74149 2.48594i −0.191040 0.100161i
\(617\) 33.4463i 1.34650i −0.739415 0.673249i \(-0.764898\pi\)
0.739415 0.673249i \(-0.235102\pi\)
\(618\) 32.1529 + 26.2444i 1.29338 + 1.05570i
\(619\) −29.0694 −1.16840 −0.584199 0.811610i \(-0.698591\pi\)
−0.584199 + 0.811610i \(0.698591\pi\)
\(620\) 16.6054 3.39495i 0.666889 0.136344i
\(621\) 37.7265i 1.51391i
\(622\) −13.6549 + 16.7291i −0.547513 + 0.670777i
\(623\) 14.7157i 0.589570i
\(624\) 12.0784 + 28.3043i 0.483524 + 1.13308i
\(625\) −28.4461 −1.13784
\(626\) −11.7570 + 14.4039i −0.469904 + 0.575695i
\(627\) 1.18628i 0.0473753i
\(628\) 43.2078 8.83376i 1.72418 0.352505i
\(629\) −17.5174 4.51919i −0.698464 0.180192i
\(630\) −3.13219 + 3.83736i −0.124790 + 0.152884i
\(631\) −35.3823 −1.40855 −0.704273 0.709929i \(-0.748727\pi\)
−0.704273 + 0.709929i \(0.748727\pi\)
\(632\) 3.63520 + 1.90592i 0.144601 + 0.0758134i
\(633\) 8.15595 0.324170
\(634\) −28.2563 23.0639i −1.12220 0.915984i
\(635\) 26.7873 1.06302
\(636\) −17.2693 + 3.53068i −0.684772 + 0.140001i
\(637\) 1.58903i 0.0629597i
\(638\) −4.72667 3.85809i −0.187131 0.152743i
\(639\) 0.288465i 0.0114115i
\(640\) −2.17014 + 27.2205i −0.0857823 + 1.07598i
\(641\) 3.40578i 0.134520i −0.997735 0.0672601i \(-0.978574\pi\)
0.997735 0.0672601i \(-0.0214257\pi\)
\(642\) 31.0036 + 25.3063i 1.22361 + 0.998759i
\(643\) −39.7622 −1.56807 −0.784033 0.620719i \(-0.786841\pi\)
−0.784033 + 0.620719i \(0.786841\pi\)
\(644\) 8.45038 + 41.3326i 0.332992 + 1.62873i
\(645\) 4.97188i 0.195768i
\(646\) 4.01014 2.94697i 0.157777 0.115947i
\(647\) 19.5885 0.770105 0.385053 0.922895i \(-0.374183\pi\)
0.385053 + 0.922895i \(0.374183\pi\)
\(648\) 13.6258 25.9888i 0.535272 1.02094i
\(649\) 9.20706i 0.361409i
\(650\) 3.00822 3.68547i 0.117992 0.144556i
\(651\) 17.0429 0.667962
\(652\) −2.78189 13.6068i −0.108947 0.532884i
\(653\) 47.0453 1.84103 0.920513 0.390712i \(-0.127771\pi\)
0.920513 + 0.390712i \(0.127771\pi\)
\(654\) 1.94678 + 1.58903i 0.0761250 + 0.0621360i
\(655\) 44.4959 1.73860
\(656\) 18.3931 + 43.1020i 0.718129 + 1.68285i
\(657\) 7.52224i 0.293471i
\(658\) −12.4796 + 15.2892i −0.486505 + 0.596034i
\(659\) 26.4748i 1.03131i 0.856796 + 0.515656i \(0.172452\pi\)
−0.856796 + 0.515656i \(0.827548\pi\)
\(660\) 1.34396 + 6.57361i 0.0523137 + 0.255877i
\(661\) 34.0089i 1.32279i −0.750037 0.661396i \(-0.769964\pi\)
0.750037 0.661396i \(-0.230036\pi\)
\(662\) −15.6297 + 19.1485i −0.607465 + 0.744227i
\(663\) 7.92400 30.7152i 0.307743 1.19288i
\(664\) −10.9119 5.72106i −0.423464 0.222020i
\(665\) 5.29610 0.205374
\(666\) −2.71331 2.21470i −0.105139 0.0858180i
\(667\) 48.0794i 1.86164i
\(668\) 22.3071 4.56065i 0.863088 0.176457i
\(669\) 29.4132 1.13718
\(670\) −22.7956 + 27.9277i −0.880672 + 1.07894i
\(671\) −6.01017 −0.232020
\(672\) −7.62057 + 26.3796i −0.293970 + 1.01761i
\(673\) 14.2242i 0.548301i −0.961687 0.274151i \(-0.911603\pi\)
0.961687 0.274151i \(-0.0883967\pi\)
\(674\) −23.3575 + 28.6161i −0.899699 + 1.10225i
\(675\) −3.79592 −0.146105
\(676\) −1.44436 7.06468i −0.0555524 0.271718i
\(677\) 16.1654 0.621288 0.310644 0.950526i \(-0.399455\pi\)
0.310644 + 0.950526i \(0.399455\pi\)
\(678\) 16.6054 20.3438i 0.637727 0.781301i
\(679\) −30.5829 −1.17366
\(680\) 18.8830 20.8735i 0.724129 0.800462i
\(681\) 10.3304 0.395863
\(682\) 2.31159 2.83200i 0.0885152 0.108443i
\(683\) −15.6478 −0.598746 −0.299373 0.954136i \(-0.596777\pi\)
−0.299373 + 0.954136i \(0.596777\pi\)
\(684\) 0.943935 0.192986i 0.0360923 0.00737900i
\(685\) 32.6658 1.24809
\(686\) 16.9905 20.8156i 0.648700 0.794745i
\(687\) 5.45378i 0.208075i
\(688\) 1.71296 + 4.01413i 0.0653061 + 0.153037i
\(689\) 19.0224 0.724697
\(690\) 33.4331 40.9601i 1.27278 1.55932i
\(691\) 2.33710 0.0889075 0.0444537 0.999011i \(-0.485845\pi\)
0.0444537 + 0.999011i \(0.485845\pi\)
\(692\) −2.27863 11.1452i −0.0866203 0.423678i
\(693\) 1.06837i 0.0405841i
\(694\) −19.6261 16.0195i −0.744996 0.608093i
\(695\) −6.54160 −0.248137
\(696\) −14.5307 + 27.7148i −0.550786 + 1.05053i
\(697\) 12.0667 46.7733i 0.457059 1.77166i
\(698\) −20.1440 + 24.6792i −0.762463 + 0.934120i
\(699\) 16.3738i 0.619314i
\(700\) 4.15875 0.850249i 0.157186 0.0321364i
\(701\) 30.6904i 1.15916i 0.814916 + 0.579580i \(0.196783\pi\)
−0.814916 + 0.579580i \(0.803217\pi\)
\(702\) −16.7564 + 20.5289i −0.632431 + 0.774813i
\(703\) 3.74476i 0.141236i
\(704\) 3.34987 + 4.84427i 0.126253 + 0.182575i
\(705\) 24.7342 0.931545
\(706\) 6.09994 + 4.97900i 0.229574 + 0.187387i
\(707\) −21.4314 −0.806011
\(708\) −46.2649 + 9.45878i −1.73874 + 0.355483i
\(709\) −11.4092 −0.428481 −0.214240 0.976781i \(-0.568728\pi\)
−0.214240 + 0.976781i \(0.568728\pi\)
\(710\) 1.10307 1.35141i 0.0413977 0.0507177i
\(711\) 0.819099i 0.0307186i
\(712\) −7.51731 + 14.3379i −0.281723 + 0.537337i
\(713\) −28.8069 −1.07883
\(714\) 22.8071 16.7605i 0.853534 0.627246i
\(715\) 7.24094i 0.270796i
\(716\) −32.3884 + 6.62176i −1.21041 + 0.247467i
\(717\) −30.4165 −1.13593
\(718\) 24.2805 + 19.8187i 0.906141 + 0.739626i
\(719\) 7.71301i 0.287647i 0.989603 + 0.143823i \(0.0459397\pi\)
−0.989603 + 0.143823i \(0.954060\pi\)
\(720\) 5.01206 2.13882i 0.186789 0.0797090i
\(721\) 39.9651i 1.48838i
\(722\) 20.0181 + 16.3395i 0.744995 + 0.608093i
\(723\) 18.2296i 0.677968i
\(724\) 8.26637 + 40.4326i 0.307217 + 1.50266i
\(725\) 4.83759 0.179664
\(726\) −21.6317 17.6566i −0.802826 0.655296i
\(727\) −13.2911 −0.492938 −0.246469 0.969151i \(-0.579270\pi\)
−0.246469 + 0.969151i \(0.579270\pi\)
\(728\) 13.7598 26.2444i 0.509973 0.972682i
\(729\) 20.1883 0.747716
\(730\) 28.7647 35.2406i 1.06463 1.30431i
\(731\) 1.12378 4.35603i 0.0415646 0.161114i
\(732\) 6.17449 + 30.2007i 0.228216 + 1.11625i
\(733\) 4.51326i 0.166701i −0.996520 0.0833505i \(-0.973438\pi\)
0.996520 0.0833505i \(-0.0265621\pi\)
\(734\) −1.89796 + 2.32525i −0.0700550 + 0.0858267i
\(735\) −1.77693 −0.0655430
\(736\) 12.8808 44.5884i 0.474791 1.64355i
\(737\) 7.77546i 0.286413i
\(738\) 5.91349 7.24482i 0.217679 0.266686i
\(739\) 14.4505i 0.531571i −0.964032 0.265786i \(-0.914369\pi\)
0.964032 0.265786i \(-0.0856314\pi\)
\(740\) 4.24253 + 20.7511i 0.155959 + 0.762826i
\(741\) −6.56610 −0.241212
\(742\) 13.1489 + 10.7326i 0.482711 + 0.394007i
\(743\) 17.2867i 0.634186i 0.948394 + 0.317093i \(0.102707\pi\)
−0.948394 + 0.317093i \(0.897293\pi\)
\(744\) −16.6054 8.70614i −0.608784 0.319182i
\(745\) 4.11988i 0.150941i
\(746\) −15.8033 + 19.3612i −0.578601 + 0.708864i
\(747\) 2.45871i 0.0899597i
\(748\) 0.308326 6.06313i 0.0112735 0.221690i
\(749\) 38.5365i 1.40809i
\(750\) 20.8407 + 17.0109i 0.760994 + 0.621152i
\(751\) 27.5979i 1.00706i 0.863978 + 0.503530i \(0.167966\pi\)
−0.863978 + 0.503530i \(0.832034\pi\)
\(752\) 19.9696 8.52168i 0.728215 0.310754i
\(753\) 37.2068i 1.35589i
\(754\) 21.3547 26.1624i 0.777692 0.952778i
\(755\) −8.39419 −0.305496
\(756\) −23.1651 + 4.73608i −0.842508 + 0.172249i
\(757\) 29.2683i 1.06377i −0.846815 0.531887i \(-0.821483\pi\)
0.846815 0.531887i \(-0.178517\pi\)
\(758\) −3.54086 2.89018i −0.128610 0.104976i
\(759\) 11.4038i 0.413933i
\(760\) −5.16016 2.70545i −0.187179 0.0981370i
\(761\) 5.48844 0.198956 0.0994779 0.995040i \(-0.468283\pi\)
0.0994779 + 0.995040i \(0.468283\pi\)
\(762\) −22.9564 18.7378i −0.831621 0.678800i
\(763\) 2.41979i 0.0876021i
\(764\) −6.93916 33.9409i −0.251050 1.22794i
\(765\) −5.43897 1.40316i −0.196646 0.0507314i
\(766\) 8.68141 + 7.08609i 0.313672 + 0.256031i
\(767\) 50.9615 1.84011
\(768\) 20.9007 21.8096i 0.754188 0.786986i
\(769\) 41.5703 1.49906 0.749531 0.661969i \(-0.230279\pi\)
0.749531 + 0.661969i \(0.230279\pi\)
\(770\) 4.08540 5.00517i 0.147228 0.180374i
\(771\) 11.9667 0.430971
\(772\) 24.1876 4.94511i 0.870529 0.177978i
\(773\) 24.0984i 0.866761i −0.901211 0.433380i \(-0.857321\pi\)
0.901211 0.433380i \(-0.142679\pi\)
\(774\) 0.550729 0.674716i 0.0197955 0.0242522i
\(775\) 2.89846i 0.104116i
\(776\) 29.7979 + 15.6229i 1.06968 + 0.560830i
\(777\) 21.2978i 0.764054i
\(778\) 4.27993 5.24348i 0.153443 0.187988i
\(779\) −9.99890 −0.358248
\(780\) −36.3852 + 7.43890i −1.30280 + 0.266356i
\(781\) 0.376252i 0.0134634i
\(782\) −38.5500 + 28.3297i −1.37854 + 1.01307i
\(783\) −26.9464 −0.962987
\(784\) −1.43463 + 0.612206i −0.0512368 + 0.0218645i
\(785\) 53.2220i 1.89957i
\(786\) −38.1325 31.1251i −1.36014 1.11020i
\(787\) −14.1491 −0.504360 −0.252180 0.967680i \(-0.581147\pi\)
−0.252180 + 0.967680i \(0.581147\pi\)
\(788\) −2.39139 11.6968i −0.0851897 0.416681i
\(789\) −29.3477 −1.04481
\(790\) −3.13219 + 3.83736i −0.111438 + 0.136527i
\(791\) −25.2868 −0.899096
\(792\) 0.545765 1.04095i 0.0193929 0.0369885i
\(793\) 33.2666i 1.18133i
\(794\) 5.48868 + 4.48006i 0.194786 + 0.158991i
\(795\) 21.2718i 0.754432i
\(796\) −25.2730 + 5.16702i −0.895777 + 0.183140i
\(797\) 19.0896i 0.676189i −0.941112 0.338094i \(-0.890218\pi\)
0.941112 0.338094i \(-0.109782\pi\)
\(798\) −4.53869 3.70465i −0.160668 0.131143i
\(799\) −21.6705 5.59062i −0.766647 0.197782i
\(800\) −4.48634 1.29602i −0.158616 0.0458213i
\(801\) 3.23068 0.114151
\(802\) −6.80656 + 8.33895i −0.240348 + 0.294458i
\(803\) 9.81146i 0.346239i
\(804\) 39.0712 7.98803i 1.37793 0.281716i
\(805\) −50.9122 −1.79442
\(806\) 15.6753 + 12.7947i 0.552138 + 0.450676i
\(807\) −43.1331 −1.51836
\(808\) 20.8813 + 10.9480i 0.734601 + 0.385148i
\(809\) 24.7737i 0.870995i 0.900190 + 0.435498i \(0.143428\pi\)
−0.900190 + 0.435498i \(0.856572\pi\)
\(810\) 27.4340 + 22.3927i 0.963933 + 0.786798i
\(811\) 28.7575 1.00981 0.504906 0.863174i \(-0.331527\pi\)
0.504906 + 0.863174i \(0.331527\pi\)
\(812\) 29.5221 6.03574i 1.03602 0.211813i
\(813\) 13.5371 0.474768
\(814\) 3.53904 + 2.88870i 0.124043 + 0.101249i
\(815\) 16.7604 0.587092
\(816\) −30.7836 + 4.67958i −1.07764 + 0.163818i
\(817\) −0.931205 −0.0325788
\(818\) −20.4417 16.6852i −0.714726 0.583386i
\(819\) −5.91349 −0.206634
\(820\) −55.4077 + 11.3280i −1.93492 + 0.395591i
\(821\) −28.6880 −1.00122 −0.500609 0.865673i \(-0.666891\pi\)
−0.500609 + 0.865673i \(0.666891\pi\)
\(822\) −27.9942 22.8499i −0.976408 0.796981i
\(823\) 35.5415i 1.23890i 0.785036 + 0.619450i \(0.212644\pi\)
−0.785036 + 0.619450i \(0.787356\pi\)
\(824\) −20.4157 + 38.9393i −0.711214 + 1.35651i
\(825\) −1.14742 −0.0399479
\(826\) 35.2262 + 28.7529i 1.22568 + 1.00044i
\(827\) 35.4846 1.23392 0.616959 0.786995i \(-0.288364\pi\)
0.616959 + 0.786995i \(0.288364\pi\)
\(828\) −9.07417 + 1.85520i −0.315349 + 0.0644727i
\(829\) 54.8280i 1.90425i −0.305703 0.952127i \(-0.598891\pi\)
0.305703 0.952127i \(-0.401109\pi\)
\(830\) 9.40200 11.5187i 0.326348 0.399820i
\(831\) −12.4808 −0.432955
\(832\) −26.8133 + 18.5417i −0.929582 + 0.642819i
\(833\) 1.55683 + 0.401635i 0.0539409 + 0.0139158i
\(834\) 5.60607 + 4.57588i 0.194122 + 0.158450i
\(835\) 27.4772i 0.950887i
\(836\) −1.23120 + 0.251717i −0.0425819 + 0.00870580i
\(837\) 16.1450i 0.558054i
\(838\) −1.15790 0.945120i −0.0399990 0.0326486i
\(839\) 2.66018i 0.0918395i 0.998945 + 0.0459198i \(0.0146219\pi\)
−0.998945 + 0.0459198i \(0.985378\pi\)
\(840\) −29.3477 15.3869i −1.01259 0.530898i
\(841\) 5.34102 0.184173
\(842\) −1.22705 + 1.50330i −0.0422869 + 0.0518072i
\(843\) 28.0325 0.965490
\(844\) 1.73062 + 8.46481i 0.0595703 + 0.291371i
\(845\) 8.70205 0.299359
\(846\) −3.35659 2.73978i −0.115402 0.0941954i
\(847\) 26.8875i 0.923866i
\(848\) −7.32877 17.1741i −0.251671 0.589761i
\(849\) −27.0713 −0.929085
\(850\) 2.85044 + 3.87877i 0.0977692 + 0.133041i
\(851\) 35.9989i 1.23402i
\(852\) −1.89064 + 0.386539i −0.0647723 + 0.0132426i
\(853\) 3.49362 0.119619 0.0598097 0.998210i \(-0.480951\pi\)
0.0598097 + 0.998210i \(0.480951\pi\)
\(854\) 18.7693 22.9949i 0.642273 0.786870i
\(855\) 1.16271i 0.0397638i
\(856\) −19.6859 + 37.5474i −0.672851 + 1.28334i
\(857\) 32.6540i 1.11544i −0.830030 0.557719i \(-0.811677\pi\)
0.830030 0.557719i \(-0.188323\pi\)
\(858\) −5.06507 + 6.20539i −0.172919 + 0.211849i
\(859\) 44.7174i 1.52574i −0.646553 0.762869i \(-0.723790\pi\)
0.646553 0.762869i \(-0.276210\pi\)
\(860\) −5.16016 + 1.05499i −0.175960 + 0.0359748i
\(861\) −56.8673 −1.93803
\(862\) 13.3761 16.3876i 0.455593 0.558163i
\(863\) −2.12167 −0.0722225 −0.0361113 0.999348i \(-0.511497\pi\)
−0.0361113 + 0.999348i \(0.511497\pi\)
\(864\) 24.9899 + 7.21912i 0.850174 + 0.245599i
\(865\) 13.7283 0.466778
\(866\) −1.62275 1.32455i −0.0551433 0.0450100i
\(867\) 28.0899 + 15.5268i 0.953982 + 0.527318i
\(868\) 3.61633 + 17.6883i 0.122746 + 0.600378i
\(869\) 1.06837i 0.0362420i
\(870\) −29.2560 23.8798i −0.991871 0.809602i
\(871\) −43.0375 −1.45827
\(872\) −1.23612 + 2.35768i −0.0418602 + 0.0798410i
\(873\) 6.71419i 0.227241i
\(874\) 7.67158 + 6.26183i 0.259495 + 0.211810i
\(875\) 25.9044i 0.875727i
\(876\) −49.3019 + 10.0797i −1.66576 + 0.340561i
\(877\) 48.3375 1.63224 0.816121 0.577881i \(-0.196120\pi\)
0.816121 + 0.577881i \(0.196120\pi\)
\(878\) −17.5349 + 21.4826i −0.591774 + 0.725002i
\(879\) 36.9379i 1.24588i
\(880\) −6.53737 + 2.78971i −0.220375 + 0.0940413i
\(881\) 12.6986i 0.427827i −0.976853 0.213913i \(-0.931379\pi\)
0.976853 0.213913i \(-0.0686210\pi\)
\(882\) 0.241141 + 0.196828i 0.00811963 + 0.00662754i
\(883\) 33.2423i 1.11869i 0.828934 + 0.559346i \(0.188948\pi\)
−0.828934 + 0.559346i \(0.811052\pi\)
\(884\) 33.5597 + 1.70660i 1.12874 + 0.0573991i
\(885\) 56.9876i 1.91562i
\(886\) 28.8920 35.3966i 0.970647 1.18917i
\(887\) 39.5909i 1.32933i −0.747140 0.664666i \(-0.768574\pi\)
0.747140 0.664666i \(-0.231426\pi\)
\(888\) 10.8797 20.7511i 0.365099 0.696362i
\(889\) 28.5341i 0.957003i
\(890\) −15.1353 12.3540i −0.507335 0.414106i
\(891\) 7.63800 0.255883
\(892\) 6.24120 + 30.5270i 0.208971 + 1.02212i
\(893\) 4.63258i 0.155023i
\(894\) −2.88187 + 3.53068i −0.0963843 + 0.118084i
\(895\) 39.8950i 1.33354i
\(896\) −28.9956 2.31165i −0.968674 0.0772269i
\(897\) 63.1208 2.10754
\(898\) 15.6019 19.1145i 0.520643 0.637857i
\(899\) 20.5755i 0.686233i
\(900\) 0.186664 + 0.913014i 0.00622214 + 0.0304338i
\(901\) −4.80801 + 18.6369i −0.160178 + 0.620886i
\(902\) −7.71313 + 9.44961i −0.256819 + 0.314638i
\(903\) −5.29610 −0.176243
\(904\) 24.6378 + 12.9175i 0.819440 + 0.429628i
\(905\) −49.8035 −1.65553
\(906\) 7.19371 + 5.87178i 0.238995 + 0.195077i
\(907\) −52.1980 −1.73321 −0.866603 0.498998i \(-0.833701\pi\)
−0.866603 + 0.498998i \(0.833701\pi\)
\(908\) 2.19202 + 10.7216i 0.0727448 + 0.355810i
\(909\) 4.70506i 0.156057i
\(910\) 27.7038 + 22.6129i 0.918373 + 0.749611i
\(911\) 33.2042i 1.10010i −0.835131 0.550052i \(-0.814608\pi\)
0.835131 0.550052i \(-0.185392\pi\)
\(912\) 2.52972 + 5.92810i 0.0837674 + 0.196299i
\(913\) 3.20697i 0.106135i
\(914\) −2.57714 2.10356i −0.0852441 0.0695794i
\(915\) −37.2003 −1.22980
\(916\) −5.66031 + 1.15724i −0.187022 + 0.0382363i
\(917\) 47.3975i 1.56520i
\(918\) −15.8776 21.6056i −0.524038 0.713091i
\(919\) 2.50268 0.0825558 0.0412779 0.999148i \(-0.486857\pi\)
0.0412779 + 0.999148i \(0.486857\pi\)
\(920\) 49.6053 + 26.0079i 1.63544 + 0.857454i
\(921\) 20.0289i 0.659973i
\(922\) 3.87106 4.74257i 0.127487 0.156188i
\(923\) 2.08257 0.0685488
\(924\) −7.00228 + 1.43160i −0.230358 + 0.0470963i
\(925\) −3.62209 −0.119093
\(926\) 5.80233 + 4.73608i 0.190676 + 0.155637i
\(927\) 8.77396 0.288175
\(928\) −31.8476 9.20018i −1.04545 0.302011i
\(929\) 20.2991i 0.665993i −0.942928 0.332996i \(-0.891940\pi\)
0.942928 0.332996i \(-0.108060\pi\)
\(930\) 14.3077 17.5288i 0.469167 0.574793i
\(931\) 0.332809i 0.0109074i
\(932\) −16.9938 + 3.47436i −0.556652 + 0.113807i
\(933\) 28.8286i 0.943806i
\(934\) 3.93765 4.82415i 0.128844 0.157851i
\(935\) 7.09419 + 1.83018i 0.232005 + 0.0598533i
\(936\) 5.76171 + 3.02084i 0.188327 + 0.0987391i
\(937\) 36.2874 1.18546 0.592729 0.805402i \(-0.298051\pi\)
0.592729 + 0.805402i \(0.298051\pi\)
\(938\) −29.7489 24.2822i −0.971336 0.792841i
\(939\) 24.8216i 0.810022i
\(940\) 5.24837 + 25.6709i 0.171183 + 0.837292i
\(941\) −13.6402 −0.444658 −0.222329 0.974972i \(-0.571366\pi\)
−0.222329 + 0.974972i \(0.571366\pi\)
\(942\) 37.2290 45.6106i 1.21299 1.48607i
\(943\) 96.1207 3.13012
\(944\) −19.6339 46.0098i −0.639030 1.49749i
\(945\) 28.5341i 0.928214i
\(946\) −0.718330 + 0.880050i −0.0233549 + 0.0286129i
\(947\) −9.92155 −0.322407 −0.161203 0.986921i \(-0.551538\pi\)
−0.161203 + 0.986921i \(0.551538\pi\)
\(948\) 5.36850 1.09758i 0.174361 0.0356478i
\(949\) 54.3069 1.76288
\(950\) 0.630045 0.771890i 0.0204414 0.0250434i
\(951\) −48.6929 −1.57898
\(952\) 22.2347 + 20.1143i 0.720629 + 0.651910i
\(953\) 4.30663 0.139505 0.0697526 0.997564i \(-0.477779\pi\)
0.0697526 + 0.997564i \(0.477779\pi\)
\(954\) −2.35624 + 2.88672i −0.0762862 + 0.0934609i
\(955\) 41.8073 1.35285
\(956\) −6.45410 31.5684i −0.208741 1.02099i
\(957\) −8.14527 −0.263299
\(958\) 14.6914 17.9989i 0.474656 0.581518i
\(959\) 34.7959i 1.12362i
\(960\) 20.7342 + 29.9838i 0.669194 + 0.967724i
\(961\) 18.6721 0.602326
\(962\) −15.9891 + 19.5888i −0.515509 + 0.631567i
\(963\) 8.46033 0.272630
\(964\) 18.9200 3.86816i 0.609371 0.124585i
\(965\) 29.7935i 0.959085i
\(966\) 43.6311 + 35.6133i 1.40381 + 1.14584i
\(967\) −17.6400 −0.567265 −0.283633 0.958933i \(-0.591540\pi\)
−0.283633 + 0.958933i \(0.591540\pi\)
\(968\) 13.7352 26.1974i 0.441465 0.842015i
\(969\) 1.65961 6.43303i 0.0533144 0.206659i
\(970\) −25.6747 + 31.4550i −0.824366 + 1.00996i
\(971\) 10.5762i 0.339407i 0.985495 + 0.169704i \(0.0542811\pi\)
−0.985495 + 0.169704i \(0.945719\pi\)
\(972\) −2.32048 11.3500i −0.0744296 0.364051i
\(973\) 6.96819i 0.223390i
\(974\) 4.25294 5.21042i 0.136273 0.166953i
\(975\) 6.35101i 0.203395i
\(976\) −30.0342 + 12.8166i −0.961372 + 0.410250i
\(977\) −40.2041 −1.28624 −0.643122 0.765764i \(-0.722361\pi\)
−0.643122 + 0.765764i \(0.722361\pi\)
\(978\) −14.3635 11.7240i −0.459293 0.374892i
\(979\) −4.21386 −0.134676
\(980\) −0.377048 1.84422i −0.0120443 0.0589114i
\(981\) 0.531241 0.0169612
\(982\) −1.69088 + 2.07156i −0.0539582 + 0.0661060i
\(983\) 20.5056i 0.654026i 0.945020 + 0.327013i \(0.106042\pi\)
−0.945020 + 0.327013i \(0.893958\pi\)
\(984\) 55.4077 + 29.0500i 1.76633 + 0.926080i
\(985\) 14.4077 0.459069
\(986\) 20.2347 + 27.5346i 0.644403 + 0.876880i
\(987\) 26.3472i 0.838639i
\(988\) −1.39326 6.81475i −0.0443256 0.216806i
\(989\) 8.95180 0.284651
\(990\) 1.09884 + 0.896911i 0.0349233 + 0.0285057i
\(991\) 4.64662i 0.147605i −0.997273 0.0738024i \(-0.976487\pi\)
0.997273 0.0738024i \(-0.0235134\pi\)
\(992\) 5.51232 19.0816i 0.175016 0.605841i
\(993\) 32.9977i 1.04715i
\(994\) 1.43954 + 1.17501i 0.0456595 + 0.0372689i
\(995\) 31.1305i 0.986902i
\(996\) −16.1148 + 3.29464i −0.510617 + 0.104395i
\(997\) 32.7934 1.03858 0.519289 0.854599i \(-0.326197\pi\)
0.519289 + 0.854599i \(0.326197\pi\)
\(998\) 40.4415 + 33.0099i 1.28015 + 1.04491i
\(999\) 20.1758 0.638335
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 136.2.h.a.101.16 yes 16
3.2 odd 2 1224.2.l.b.1189.2 16
4.3 odd 2 544.2.h.a.305.4 16
8.3 odd 2 544.2.h.a.305.14 16
8.5 even 2 inner 136.2.h.a.101.13 16
12.11 even 2 4896.2.l.b.3025.14 16
17.16 even 2 inner 136.2.h.a.101.15 yes 16
24.5 odd 2 1224.2.l.b.1189.3 16
24.11 even 2 4896.2.l.b.3025.4 16
51.50 odd 2 1224.2.l.b.1189.1 16
68.67 odd 2 544.2.h.a.305.13 16
136.67 odd 2 544.2.h.a.305.3 16
136.101 even 2 inner 136.2.h.a.101.14 yes 16
204.203 even 2 4896.2.l.b.3025.3 16
408.101 odd 2 1224.2.l.b.1189.4 16
408.203 even 2 4896.2.l.b.3025.13 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
136.2.h.a.101.13 16 8.5 even 2 inner
136.2.h.a.101.14 yes 16 136.101 even 2 inner
136.2.h.a.101.15 yes 16 17.16 even 2 inner
136.2.h.a.101.16 yes 16 1.1 even 1 trivial
544.2.h.a.305.3 16 136.67 odd 2
544.2.h.a.305.4 16 4.3 odd 2
544.2.h.a.305.13 16 68.67 odd 2
544.2.h.a.305.14 16 8.3 odd 2
1224.2.l.b.1189.1 16 51.50 odd 2
1224.2.l.b.1189.2 16 3.2 odd 2
1224.2.l.b.1189.3 16 24.5 odd 2
1224.2.l.b.1189.4 16 408.101 odd 2
4896.2.l.b.3025.3 16 204.203 even 2
4896.2.l.b.3025.4 16 24.11 even 2
4896.2.l.b.3025.13 16 408.203 even 2
4896.2.l.b.3025.14 16 12.11 even 2