Properties

Label 637.2.r.f.324.8
Level $637$
Weight $2$
Character 637.324
Analytic conductor $5.086$
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] = [637,2,Mod(116,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.116");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.r (of order \(6\), degree \(2\), not 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 324.8
Root \(-1.97871 + 1.14241i\) of defining polynomial
Character \(\chi\) \(=\) 637.324
Dual form 637.2.r.f.116.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.97871 + 1.14241i) q^{2} +(1.57521 + 2.72835i) q^{3} +(1.61019 + 2.78892i) q^{4} +(-1.84030 - 1.06250i) q^{5} +7.19813i q^{6} +2.78832i q^{8} +(-3.46258 + 5.99736i) q^{9} +O(q^{10})\) \(q+(1.97871 + 1.14241i) q^{2} +(1.57521 + 2.72835i) q^{3} +(1.61019 + 2.78892i) q^{4} +(-1.84030 - 1.06250i) q^{5} +7.19813i q^{6} +2.78832i q^{8} +(-3.46258 + 5.99736i) q^{9} +(-2.42760 - 4.20473i) q^{10} +(0.267139 - 0.154233i) q^{11} +(-5.07276 + 8.78629i) q^{12} +(3.22037 - 1.62148i) q^{13} -6.69462i q^{15} +(0.0349749 - 0.0605784i) q^{16} +(0.887368 + 1.53697i) q^{17} +(-13.7029 + 7.91135i) q^{18} +(-1.54266 - 0.890653i) q^{19} -6.84326i q^{20} +0.704786 q^{22} +(0.575211 - 0.996294i) q^{23} +(-7.60750 + 4.39219i) q^{24} +(-0.242207 - 0.419515i) q^{25} +(8.22456 + 0.470536i) q^{26} -12.3659 q^{27} +2.01052 q^{29} +(7.64798 - 13.2467i) q^{30} +(-3.98791 + 2.30242i) q^{31} +(4.96792 - 2.86823i) q^{32} +(0.841600 + 0.485898i) q^{33} +4.05494i q^{34} -22.3016 q^{36} +(4.79901 + 2.77071i) q^{37} +(-2.03497 - 3.52468i) q^{38} +(9.49673 + 6.23211i) q^{39} +(2.96258 - 5.13134i) q^{40} -6.72984i q^{41} -1.52611 q^{43} +(0.860286 + 0.496686i) q^{44} +(12.7443 - 7.35795i) q^{45} +(2.27635 - 1.31425i) q^{46} +(8.24297 + 4.75908i) q^{47} +0.220372 q^{48} -1.10680i q^{50} +(-2.79558 + 4.84209i) q^{51} +(9.70759 + 6.37048i) q^{52} +(-3.72037 - 6.44387i) q^{53} +(-24.4685 - 14.1269i) q^{54} -0.655486 q^{55} -5.61186i q^{57} +(3.97823 + 2.29683i) q^{58} +(7.03304 - 4.06053i) q^{59} +(18.6708 - 10.7796i) q^{60} +(-1.72037 + 2.97977i) q^{61} -10.5212 q^{62} +12.9669 q^{64} +(-7.64926 - 0.437622i) q^{65} +(1.11019 + 1.92290i) q^{66} +(-10.9249 + 6.30747i) q^{67} +(-2.85765 + 4.94960i) q^{68} +3.62431 q^{69} +1.35070i q^{71} +(-16.7226 - 9.65478i) q^{72} +(-10.2894 + 5.94059i) q^{73} +(6.33056 + 10.9648i) q^{74} +(0.763054 - 1.32165i) q^{75} -5.73646i q^{76} +(11.6716 + 23.1806i) q^{78} +(3.96258 - 6.86339i) q^{79} +(-0.128728 + 0.0743214i) q^{80} +(-9.09116 - 15.7464i) q^{81} +(7.68821 - 13.3164i) q^{82} -11.2290i q^{83} -3.77130i q^{85} +(-3.01972 - 1.74344i) q^{86} +(3.16700 + 5.48540i) q^{87} +(0.430050 + 0.744869i) q^{88} +(-1.43688 - 0.829583i) q^{89} +33.6231 q^{90} +3.70479 q^{92} +(-12.5636 - 7.25360i) q^{93} +(10.8736 + 18.8336i) q^{94} +(1.89263 + 3.27813i) q^{95} +(15.6511 + 9.03614i) q^{96} -7.66641i q^{97} +2.13617i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.97871 + 1.14241i 1.39916 + 0.807803i 0.994304 0.106579i \(-0.0339896\pi\)
0.404852 + 0.914382i \(0.367323\pi\)
\(3\) 1.57521 + 2.72835i 0.909448 + 1.57521i 0.814832 + 0.579697i \(0.196829\pi\)
0.0946163 + 0.995514i \(0.469838\pi\)
\(4\) 1.61019 + 2.78892i 0.805093 + 1.39446i
\(5\) −1.84030 1.06250i −0.823005 0.475162i 0.0284464 0.999595i \(-0.490944\pi\)
−0.851452 + 0.524433i \(0.824277\pi\)
\(6\) 7.19813i 2.93862i
\(7\) 0 0
\(8\) 2.78832i 0.985820i
\(9\) −3.46258 + 5.99736i −1.15419 + 1.99912i
\(10\) −2.42760 4.20473i −0.767676 1.32965i
\(11\) 0.267139 0.154233i 0.0805454 0.0465029i −0.459186 0.888340i \(-0.651859\pi\)
0.539732 + 0.841837i \(0.318526\pi\)
\(12\) −5.07276 + 8.78629i −1.46438 + 2.53638i
\(13\) 3.22037 1.62148i 0.893170 0.449718i
\(14\) 0 0
\(15\) 6.69462i 1.72854i
\(16\) 0.0349749 0.0605784i 0.00874373 0.0151446i
\(17\) 0.887368 + 1.53697i 0.215218 + 0.372769i 0.953340 0.301898i \(-0.0976204\pi\)
−0.738122 + 0.674667i \(0.764287\pi\)
\(18\) −13.7029 + 7.91135i −3.22979 + 1.86472i
\(19\) −1.54266 0.890653i −0.353909 0.204330i 0.312496 0.949919i \(-0.398835\pi\)
−0.666406 + 0.745589i \(0.732168\pi\)
\(20\) 6.84326i 1.53020i
\(21\) 0 0
\(22\) 0.704786 0.150261
\(23\) 0.575211 0.996294i 0.119940 0.207742i −0.799804 0.600261i \(-0.795063\pi\)
0.919744 + 0.392520i \(0.128397\pi\)
\(24\) −7.60750 + 4.39219i −1.55288 + 0.896553i
\(25\) −0.242207 0.419515i −0.0484414 0.0839029i
\(26\) 8.22456 + 0.470536i 1.61297 + 0.0922796i
\(27\) −12.3659 −2.37982
\(28\) 0 0
\(29\) 2.01052 0.373345 0.186672 0.982422i \(-0.440230\pi\)
0.186672 + 0.982422i \(0.440230\pi\)
\(30\) 7.64798 13.2467i 1.39632 2.41850i
\(31\) −3.98791 + 2.30242i −0.716251 + 0.413527i −0.813371 0.581745i \(-0.802370\pi\)
0.0971205 + 0.995273i \(0.469037\pi\)
\(32\) 4.96792 2.86823i 0.878213 0.507037i
\(33\) 0.841600 + 0.485898i 0.146504 + 0.0845840i
\(34\) 4.05494i 0.695416i
\(35\) 0 0
\(36\) −22.3016 −3.71693
\(37\) 4.79901 + 2.77071i 0.788953 + 0.455502i 0.839594 0.543215i \(-0.182793\pi\)
−0.0506410 + 0.998717i \(0.516126\pi\)
\(38\) −2.03497 3.52468i −0.330117 0.571779i
\(39\) 9.49673 + 6.23211i 1.52069 + 0.997936i
\(40\) 2.96258 5.13134i 0.468425 0.811336i
\(41\) 6.72984i 1.05102i −0.850786 0.525512i \(-0.823874\pi\)
0.850786 0.525512i \(-0.176126\pi\)
\(42\) 0 0
\(43\) −1.52611 −0.232729 −0.116365 0.993207i \(-0.537124\pi\)
−0.116365 + 0.993207i \(0.537124\pi\)
\(44\) 0.860286 + 0.496686i 0.129693 + 0.0748783i
\(45\) 12.7443 7.35795i 1.89981 1.09686i
\(46\) 2.27635 1.31425i 0.335629 0.193776i
\(47\) 8.24297 + 4.75908i 1.20236 + 0.694183i 0.961079 0.276272i \(-0.0890991\pi\)
0.241281 + 0.970455i \(0.422432\pi\)
\(48\) 0.220372 0.0318079
\(49\) 0 0
\(50\) 1.10680i 0.156524i
\(51\) −2.79558 + 4.84209i −0.391460 + 0.678028i
\(52\) 9.70759 + 6.37048i 1.34620 + 0.883427i
\(53\) −3.72037 6.44387i −0.511032 0.885134i −0.999918 0.0127862i \(-0.995930\pi\)
0.488886 0.872348i \(-0.337403\pi\)
\(54\) −24.4685 14.1269i −3.32974 1.92243i
\(55\) −0.655486 −0.0883857
\(56\) 0 0
\(57\) 5.61186i 0.743309i
\(58\) 3.97823 + 2.29683i 0.522368 + 0.301589i
\(59\) 7.03304 4.06053i 0.915624 0.528636i 0.0333877 0.999442i \(-0.489370\pi\)
0.882236 + 0.470807i \(0.156037\pi\)
\(60\) 18.6708 10.7796i 2.41039 1.39164i
\(61\) −1.72037 + 2.97977i −0.220271 + 0.381521i −0.954890 0.296959i \(-0.904028\pi\)
0.734619 + 0.678480i \(0.237361\pi\)
\(62\) −10.5212 −1.33620
\(63\) 0 0
\(64\) 12.9669 1.62086
\(65\) −7.64926 0.437622i −0.948773 0.0542803i
\(66\) 1.11019 + 1.92290i 0.136654 + 0.236692i
\(67\) −10.9249 + 6.30747i −1.33468 + 0.770580i −0.986014 0.166665i \(-0.946700\pi\)
−0.348671 + 0.937245i \(0.613367\pi\)
\(68\) −2.85765 + 4.94960i −0.346541 + 0.600227i
\(69\) 3.62431 0.436316
\(70\) 0 0
\(71\) 1.35070i 0.160299i 0.996783 + 0.0801494i \(0.0255397\pi\)
−0.996783 + 0.0801494i \(0.974460\pi\)
\(72\) −16.7226 9.65478i −1.97077 1.13783i
\(73\) −10.2894 + 5.94059i −1.20428 + 0.695293i −0.961505 0.274789i \(-0.911392\pi\)
−0.242778 + 0.970082i \(0.578059\pi\)
\(74\) 6.33056 + 10.9648i 0.735912 + 1.27464i
\(75\) 0.763054 1.32165i 0.0881099 0.152611i
\(76\) 5.73646i 0.658018i
\(77\) 0 0
\(78\) 11.6716 + 23.1806i 1.32155 + 2.62469i
\(79\) 3.96258 6.86339i 0.445825 0.772191i −0.552284 0.833656i \(-0.686244\pi\)
0.998109 + 0.0614644i \(0.0195771\pi\)
\(80\) −0.128728 + 0.0743214i −0.0143923 + 0.00830939i
\(81\) −9.09116 15.7464i −1.01013 1.74960i
\(82\) 7.68821 13.3164i 0.849021 1.47055i
\(83\) 11.2290i 1.23255i −0.787533 0.616273i \(-0.788642\pi\)
0.787533 0.616273i \(-0.211358\pi\)
\(84\) 0 0
\(85\) 3.77130i 0.409055i
\(86\) −3.01972 1.74344i −0.325625 0.188000i
\(87\) 3.16700 + 5.48540i 0.339538 + 0.588096i
\(88\) 0.430050 + 0.744869i 0.0458435 + 0.0794033i
\(89\) −1.43688 0.829583i −0.152309 0.0879357i 0.421909 0.906638i \(-0.361360\pi\)
−0.574218 + 0.818703i \(0.694694\pi\)
\(90\) 33.6231 3.54418
\(91\) 0 0
\(92\) 3.70479 0.386251
\(93\) −12.5636 7.25360i −1.30279 0.752164i
\(94\) 10.8736 + 18.8336i 1.12153 + 1.94254i
\(95\) 1.89263 + 3.27813i 0.194180 + 0.336329i
\(96\) 15.6511 + 9.03614i 1.59738 + 0.922247i
\(97\) 7.66641i 0.778406i −0.921152 0.389203i \(-0.872750\pi\)
0.921152 0.389203i \(-0.127250\pi\)
\(98\) 0 0
\(99\) 2.13617i 0.214693i
\(100\) 0.779996 1.35099i 0.0779996 0.135099i
\(101\) −4.55864 7.89579i −0.453601 0.785660i 0.545005 0.838433i \(-0.316528\pi\)
−0.998607 + 0.0527721i \(0.983194\pi\)
\(102\) −11.0633 + 6.38738i −1.09543 + 0.632445i
\(103\) −3.02085 + 5.23226i −0.297653 + 0.515550i −0.975599 0.219562i \(-0.929537\pi\)
0.677946 + 0.735112i \(0.262870\pi\)
\(104\) 4.52122 + 8.97943i 0.443342 + 0.880506i
\(105\) 0 0
\(106\) 17.0007i 1.65125i
\(107\) −6.04305 + 10.4669i −0.584204 + 1.01187i 0.410770 + 0.911739i \(0.365260\pi\)
−0.994974 + 0.100132i \(0.968074\pi\)
\(108\) −19.9114 34.4876i −1.91598 3.31857i
\(109\) −1.17942 + 0.680941i −0.112968 + 0.0652223i −0.555420 0.831570i \(-0.687442\pi\)
0.442451 + 0.896793i \(0.354109\pi\)
\(110\) −1.29701 0.748831i −0.123665 0.0713983i
\(111\) 17.4578i 1.65702i
\(112\) 0 0
\(113\) −9.42009 −0.886168 −0.443084 0.896480i \(-0.646116\pi\)
−0.443084 + 0.896480i \(0.646116\pi\)
\(114\) 6.41103 11.1042i 0.600448 1.04001i
\(115\) −2.11712 + 1.22232i −0.197422 + 0.113982i
\(116\) 3.23731 + 5.60719i 0.300577 + 0.520615i
\(117\) −1.42617 + 24.9282i −0.131849 + 2.30462i
\(118\) 18.5551 1.70814
\(119\) 0 0
\(120\) 18.6667 1.70403
\(121\) −5.45242 + 9.44388i −0.495675 + 0.858534i
\(122\) −6.80822 + 3.93073i −0.616387 + 0.355871i
\(123\) 18.3613 10.6009i 1.65558 0.955852i
\(124\) −12.8426 7.41466i −1.15330 0.665856i
\(125\) 11.6543i 1.04239i
\(126\) 0 0
\(127\) 13.3998 1.18904 0.594519 0.804081i \(-0.297342\pi\)
0.594519 + 0.804081i \(0.297342\pi\)
\(128\) 15.7217 + 9.07695i 1.38962 + 0.802297i
\(129\) −2.40394 4.16375i −0.211655 0.366598i
\(130\) −14.6357 9.60448i −1.28363 0.842369i
\(131\) 6.69854 11.6022i 0.585254 1.01369i −0.409590 0.912270i \(-0.634328\pi\)
0.994844 0.101420i \(-0.0323385\pi\)
\(132\) 3.12954i 0.272392i
\(133\) 0 0
\(134\) −28.8228 −2.48991
\(135\) 22.7569 + 13.1387i 1.95860 + 1.13080i
\(136\) −4.28555 + 2.47427i −0.367483 + 0.212167i
\(137\) 0.433917 0.250522i 0.0370720 0.0214036i −0.481349 0.876529i \(-0.659853\pi\)
0.518421 + 0.855125i \(0.326520\pi\)
\(138\) 7.17145 + 4.14044i 0.610475 + 0.352458i
\(139\) −1.41936 −0.120388 −0.0601941 0.998187i \(-0.519172\pi\)
−0.0601941 + 0.998187i \(0.519172\pi\)
\(140\) 0 0
\(141\) 29.9862i 2.52529i
\(142\) −1.54305 + 2.67264i −0.129490 + 0.224283i
\(143\) 0.610200 0.929847i 0.0510275 0.0777577i
\(144\) 0.242207 + 0.419515i 0.0201839 + 0.0349596i
\(145\) −3.69996 2.13617i −0.307265 0.177399i
\(146\) −27.1463 −2.24664
\(147\) 0 0
\(148\) 17.8454i 1.46689i
\(149\) −18.2652 10.5454i −1.49635 0.863916i −0.496355 0.868120i \(-0.665328\pi\)
−0.999991 + 0.00420426i \(0.998662\pi\)
\(150\) 3.01972 1.74344i 0.246559 0.142351i
\(151\) −15.1591 + 8.75211i −1.23363 + 0.712236i −0.967785 0.251779i \(-0.918984\pi\)
−0.265845 + 0.964016i \(0.585651\pi\)
\(152\) 2.48343 4.30142i 0.201432 0.348891i
\(153\) −12.2903 −0.993614
\(154\) 0 0
\(155\) 9.78526 0.785971
\(156\) −2.08937 + 36.5205i −0.167284 + 2.92398i
\(157\) 0.0377894 + 0.0654532i 0.00301593 + 0.00522374i 0.867529 0.497386i \(-0.165707\pi\)
−0.864514 + 0.502610i \(0.832373\pi\)
\(158\) 15.6816 9.05375i 1.24756 0.720278i
\(159\) 11.7207 20.3009i 0.929515 1.60997i
\(160\) −12.1899 −0.963699
\(161\) 0 0
\(162\) 41.5432i 3.26394i
\(163\) 8.73102 + 5.04086i 0.683866 + 0.394830i 0.801310 0.598249i \(-0.204137\pi\)
−0.117444 + 0.993080i \(0.537470\pi\)
\(164\) 18.7690 10.8363i 1.46561 0.846172i
\(165\) −1.03253 1.78839i −0.0803822 0.139226i
\(166\) 12.8281 22.2189i 0.995655 1.72452i
\(167\) 5.84989i 0.452678i 0.974049 + 0.226339i \(0.0726757\pi\)
−0.974049 + 0.226339i \(0.927324\pi\)
\(168\) 0 0
\(169\) 7.74159 10.4436i 0.595507 0.803350i
\(170\) 4.30835 7.46229i 0.330436 0.572331i
\(171\) 10.6831 6.16791i 0.816960 0.471672i
\(172\) −2.45732 4.25620i −0.187369 0.324532i
\(173\) −8.49511 + 14.7140i −0.645871 + 1.11868i 0.338229 + 0.941064i \(0.390172\pi\)
−0.984100 + 0.177617i \(0.943161\pi\)
\(174\) 14.4720i 1.09712i
\(175\) 0 0
\(176\) 0.0215771i 0.00162644i
\(177\) 22.1570 + 12.7924i 1.66543 + 0.961534i
\(178\) −1.89544 3.28300i −0.142069 0.246072i
\(179\) −7.65079 13.2516i −0.571847 0.990468i −0.996376 0.0850537i \(-0.972894\pi\)
0.424529 0.905414i \(-0.360440\pi\)
\(180\) 41.0415 + 23.6953i 3.05905 + 1.76615i
\(181\) 5.84958 0.434796 0.217398 0.976083i \(-0.430243\pi\)
0.217398 + 0.976083i \(0.430243\pi\)
\(182\) 0 0
\(183\) −10.8398 −0.801301
\(184\) 2.77799 + 1.60387i 0.204796 + 0.118239i
\(185\) −5.88774 10.1979i −0.432875 0.749761i
\(186\) −16.5731 28.7055i −1.21520 2.10479i
\(187\) 0.474101 + 0.273722i 0.0346697 + 0.0200165i
\(188\) 30.6520i 2.23553i
\(189\) 0 0
\(190\) 8.64861i 0.627436i
\(191\) 13.4090 23.2250i 0.970238 1.68050i 0.275407 0.961328i \(-0.411188\pi\)
0.694831 0.719173i \(-0.255479\pi\)
\(192\) 20.4255 + 35.3780i 1.47409 + 2.55319i
\(193\) −0.185315 + 0.106992i −0.0133393 + 0.00770145i −0.506655 0.862149i \(-0.669118\pi\)
0.493316 + 0.869850i \(0.335785\pi\)
\(194\) 8.75816 15.1696i 0.628799 1.08911i
\(195\) −10.8552 21.5592i −0.777358 1.54388i
\(196\) 0 0
\(197\) 11.2290i 0.800035i −0.916508 0.400017i \(-0.869004\pi\)
0.916508 0.400017i \(-0.130996\pi\)
\(198\) −2.44038 + 4.22685i −0.173430 + 0.300389i
\(199\) −10.2100 17.6843i −0.723771 1.25361i −0.959478 0.281784i \(-0.909074\pi\)
0.235707 0.971824i \(-0.424259\pi\)
\(200\) 1.16974 0.675351i 0.0827132 0.0477545i
\(201\) −34.4179 19.8712i −2.42765 1.40161i
\(202\) 20.8313i 1.46568i
\(203\) 0 0
\(204\) −18.0056 −1.26065
\(205\) −7.15042 + 12.3849i −0.499407 + 0.864999i
\(206\) −11.9547 + 6.90207i −0.832926 + 0.480890i
\(207\) 3.98343 + 6.89950i 0.276867 + 0.479548i
\(208\) 0.0144055 0.251796i 0.000998842 0.0174589i
\(209\) −0.549471 −0.0380077
\(210\) 0 0
\(211\) 8.41738 0.579476 0.289738 0.957106i \(-0.406432\pi\)
0.289738 + 0.957106i \(0.406432\pi\)
\(212\) 11.9810 20.7517i 0.822857 1.42523i
\(213\) −3.68518 + 2.12764i −0.252504 + 0.145783i
\(214\) −23.9148 + 13.8072i −1.63479 + 0.943844i
\(215\) 2.80849 + 1.62148i 0.191537 + 0.110584i
\(216\) 34.4801i 2.34607i
\(217\) 0 0
\(218\) −3.11164 −0.210747
\(219\) −32.4159 18.7154i −2.19047 1.26467i
\(220\) −1.05545 1.82810i −0.0711587 0.123250i
\(221\) 5.34982 + 3.51075i 0.359868 + 0.236159i
\(222\) −19.9439 + 34.5439i −1.33855 + 2.31843i
\(223\) 13.6091i 0.911333i 0.890151 + 0.455666i \(0.150599\pi\)
−0.890151 + 0.455666i \(0.849401\pi\)
\(224\) 0 0
\(225\) 3.35464 0.223643
\(226\) −18.6396 10.7616i −1.23989 0.715849i
\(227\) −3.12008 + 1.80138i −0.207087 + 0.119562i −0.599957 0.800032i \(-0.704816\pi\)
0.392870 + 0.919594i \(0.371482\pi\)
\(228\) 15.6511 9.03614i 1.03652 0.598433i
\(229\) −15.9212 9.19208i −1.05210 0.607430i −0.128863 0.991662i \(-0.541133\pi\)
−0.923236 + 0.384232i \(0.874466\pi\)
\(230\) −5.58554 −0.368299
\(231\) 0 0
\(232\) 5.60598i 0.368051i
\(233\) 10.1348 17.5541i 0.663955 1.15000i −0.315612 0.948888i \(-0.602210\pi\)
0.979567 0.201116i \(-0.0644568\pi\)
\(234\) −31.3002 + 47.6964i −2.04616 + 3.11801i
\(235\) −10.1130 17.5162i −0.659699 1.14263i
\(236\) 22.6490 + 13.0764i 1.47432 + 0.851202i
\(237\) 24.9676 1.62182
\(238\) 0 0
\(239\) 20.8097i 1.34607i 0.739612 + 0.673033i \(0.235009\pi\)
−0.739612 + 0.673033i \(0.764991\pi\)
\(240\) −0.405549 0.234144i −0.0261781 0.0151139i
\(241\) −11.0113 + 6.35736i −0.709299 + 0.409514i −0.810801 0.585322i \(-0.800968\pi\)
0.101503 + 0.994835i \(0.467635\pi\)
\(242\) −21.5775 + 12.4578i −1.38705 + 0.800816i
\(243\) 10.0922 17.4801i 0.647412 1.12135i
\(244\) −11.0805 −0.709355
\(245\) 0 0
\(246\) 48.4422 3.08856
\(247\) −6.41210 0.366843i −0.407992 0.0233417i
\(248\) −6.41990 11.1196i −0.407664 0.706094i
\(249\) 30.6367 17.6881i 1.94152 1.12094i
\(250\) −13.3140 + 23.0605i −0.842050 + 1.45847i
\(251\) 13.7436 0.867486 0.433743 0.901037i \(-0.357193\pi\)
0.433743 + 0.901037i \(0.357193\pi\)
\(252\) 0 0
\(253\) 0.354865i 0.0223102i
\(254\) 26.5142 + 15.3080i 1.66365 + 0.960510i
\(255\) 10.2894 5.94059i 0.644347 0.372014i
\(256\) 7.77229 + 13.4620i 0.485768 + 0.841375i
\(257\) 3.66736 6.35206i 0.228764 0.396231i −0.728678 0.684856i \(-0.759865\pi\)
0.957442 + 0.288626i \(0.0931983\pi\)
\(258\) 10.9851i 0.683904i
\(259\) 0 0
\(260\) −11.0962 22.0378i −0.688159 1.36673i
\(261\) −6.96159 + 12.0578i −0.430912 + 0.746361i
\(262\) 26.5089 15.3049i 1.63772 0.945540i
\(263\) 3.33942 + 5.78405i 0.205918 + 0.356660i 0.950425 0.310955i \(-0.100649\pi\)
−0.744507 + 0.667615i \(0.767315\pi\)
\(264\) −1.35484 + 2.34665i −0.0833846 + 0.144426i
\(265\) 15.8115i 0.971293i
\(266\) 0 0
\(267\) 5.22708i 0.319892i
\(268\) −35.1821 20.3124i −2.14909 1.24078i
\(269\) 8.11263 + 14.0515i 0.494636 + 0.856735i 0.999981 0.00618287i \(-0.00196808\pi\)
−0.505345 + 0.862917i \(0.668635\pi\)
\(270\) 30.0195 + 51.9953i 1.82693 + 3.16433i
\(271\) 16.2277 + 9.36904i 0.985760 + 0.569129i 0.904004 0.427524i \(-0.140614\pi\)
0.0817555 + 0.996652i \(0.473947\pi\)
\(272\) 0.124143 0.00752725
\(273\) 0 0
\(274\) 1.14479 0.0691595
\(275\) −0.129406 0.0747124i −0.00780346 0.00450533i
\(276\) 5.83582 + 10.1079i 0.351275 + 0.608426i
\(277\) 15.0163 + 26.0090i 0.902243 + 1.56273i 0.824575 + 0.565752i \(0.191414\pi\)
0.0776679 + 0.996979i \(0.475253\pi\)
\(278\) −2.80849 1.62148i −0.168442 0.0972501i
\(279\) 31.8893i 1.90916i
\(280\) 0 0
\(281\) 2.23065i 0.133070i −0.997784 0.0665348i \(-0.978806\pi\)
0.997784 0.0665348i \(-0.0211943\pi\)
\(282\) −34.2565 + 59.3339i −2.03994 + 3.53328i
\(283\) −6.88774 11.9299i −0.409433 0.709159i 0.585393 0.810750i \(-0.300940\pi\)
−0.994826 + 0.101590i \(0.967607\pi\)
\(284\) −3.76700 + 2.17488i −0.223531 + 0.129055i
\(285\) −5.96258 + 10.3275i −0.353193 + 0.611748i
\(286\) 2.26967 1.14280i 0.134208 0.0675750i
\(287\) 0 0
\(288\) 39.7259i 2.34087i
\(289\) 6.92516 11.9947i 0.407362 0.705572i
\(290\) −4.88075 8.45371i −0.286608 0.496419i
\(291\) 20.9166 12.0762i 1.22615 0.707920i
\(292\) −33.1357 19.1309i −1.93912 1.11955i
\(293\) 1.01231i 0.0591400i −0.999563 0.0295700i \(-0.990586\pi\)
0.999563 0.0295700i \(-0.00941380\pi\)
\(294\) 0 0
\(295\) −17.2572 −1.00475
\(296\) −7.72563 + 13.3812i −0.449043 + 0.777766i
\(297\) −3.30341 + 1.90723i −0.191683 + 0.110668i
\(298\) −24.0943 41.7326i −1.39575 2.41751i
\(299\) 0.236918 4.14113i 0.0137013 0.239488i
\(300\) 4.91464 0.283747
\(301\) 0 0
\(302\) −39.9939 −2.30139
\(303\) 14.3616 24.8751i 0.825054 1.42904i
\(304\) −0.107909 + 0.0623010i −0.00618898 + 0.00357321i
\(305\) 6.33199 3.65577i 0.362568 0.209329i
\(306\) −24.3189 14.0405i −1.39022 0.802645i
\(307\) 24.0527i 1.37276i 0.727244 + 0.686379i \(0.240801\pi\)
−0.727244 + 0.686379i \(0.759199\pi\)
\(308\) 0 0
\(309\) −19.0339 −1.08280
\(310\) 19.3622 + 11.1787i 1.09970 + 0.634910i
\(311\) 4.49548 + 7.78639i 0.254915 + 0.441526i 0.964872 0.262719i \(-0.0846192\pi\)
−0.709957 + 0.704245i \(0.751286\pi\)
\(312\) −17.3771 + 26.4799i −0.983786 + 1.49913i
\(313\) −7.61806 + 13.1949i −0.430598 + 0.745818i −0.996925 0.0783626i \(-0.975031\pi\)
0.566326 + 0.824181i \(0.308364\pi\)
\(314\) 0.172684i 0.00974510i
\(315\) 0 0
\(316\) 25.5220 1.43572
\(317\) −5.91972 3.41775i −0.332484 0.191960i 0.324459 0.945900i \(-0.394818\pi\)
−0.656944 + 0.753940i \(0.728151\pi\)
\(318\) 46.3838 26.7797i 2.60107 1.50173i
\(319\) 0.537088 0.310088i 0.0300712 0.0173616i
\(320\) −23.8628 13.7772i −1.33397 0.770170i
\(321\) −38.0763 −2.12521
\(322\) 0 0
\(323\) 3.16135i 0.175902i
\(324\) 29.2769 50.7091i 1.62650 2.81717i
\(325\) −1.46023 0.958259i −0.0809991 0.0531546i
\(326\) 11.5174 + 19.9487i 0.637890 + 1.10486i
\(327\) −3.71568 2.14525i −0.205478 0.118633i
\(328\) 18.7649 1.03612
\(329\) 0 0
\(330\) 4.71827i 0.259732i
\(331\) −11.9637 6.90727i −0.657587 0.379658i 0.133770 0.991012i \(-0.457292\pi\)
−0.791357 + 0.611354i \(0.790625\pi\)
\(332\) 31.3169 18.0808i 1.71874 0.992314i
\(333\) −33.2339 + 19.1876i −1.82121 + 1.05147i
\(334\) −6.68295 + 11.5752i −0.365675 + 0.633367i
\(335\) 26.8066 1.46460
\(336\) 0 0
\(337\) −27.0432 −1.47314 −0.736568 0.676364i \(-0.763555\pi\)
−0.736568 + 0.676364i \(0.763555\pi\)
\(338\) 27.2491 11.8207i 1.48216 0.642961i
\(339\) −14.8386 25.7013i −0.805924 1.39590i
\(340\) 10.5179 6.07249i 0.570411 0.329327i
\(341\) −0.710218 + 1.23013i −0.0384604 + 0.0666154i
\(342\) 28.1850 1.52407
\(343\) 0 0
\(344\) 4.25528i 0.229429i
\(345\) −6.66981 3.85082i −0.359091 0.207321i
\(346\) −33.6186 + 19.4097i −1.80735 + 1.04347i
\(347\) 9.65568 + 16.7241i 0.518344 + 0.897799i 0.999773 + 0.0213132i \(0.00678472\pi\)
−0.481429 + 0.876485i \(0.659882\pi\)
\(348\) −10.1989 + 17.6650i −0.546719 + 0.946944i
\(349\) 14.1573i 0.757821i −0.925433 0.378911i \(-0.876299\pi\)
0.925433 0.378911i \(-0.123701\pi\)
\(350\) 0 0
\(351\) −39.8228 + 20.0511i −2.12558 + 1.07025i
\(352\) 0.884750 1.53243i 0.0471573 0.0816789i
\(353\) 14.6919 8.48235i 0.781969 0.451470i −0.0551585 0.998478i \(-0.517566\pi\)
0.837128 + 0.547008i \(0.184233\pi\)
\(354\) 29.2282 + 50.6247i 1.55346 + 2.69067i
\(355\) 1.43511 2.48569i 0.0761680 0.131927i
\(356\) 5.34313i 0.283186i
\(357\) 0 0
\(358\) 34.9613i 1.84776i
\(359\) 19.7136 + 11.3816i 1.04044 + 0.600700i 0.919959 0.392016i \(-0.128222\pi\)
0.120484 + 0.992715i \(0.461555\pi\)
\(360\) 20.5163 + 35.5353i 1.08131 + 1.87288i
\(361\) −7.91348 13.7065i −0.416499 0.721397i
\(362\) 11.5746 + 6.68260i 0.608347 + 0.351229i
\(363\) −34.3549 −1.80316
\(364\) 0 0
\(365\) 25.2474 1.32151
\(366\) −21.4488 12.3835i −1.12114 0.647293i
\(367\) 8.29168 + 14.3616i 0.432822 + 0.749670i 0.997115 0.0759048i \(-0.0241845\pi\)
−0.564293 + 0.825575i \(0.690851\pi\)
\(368\) −0.0402359 0.0696907i −0.00209744 0.00363288i
\(369\) 40.3613 + 23.3026i 2.10112 + 1.21308i
\(370\) 26.9048i 1.39871i
\(371\) 0 0
\(372\) 46.7186i 2.42225i
\(373\) −13.8230 + 23.9422i −0.715730 + 1.23968i 0.246947 + 0.969029i \(0.420573\pi\)
−0.962677 + 0.270652i \(0.912761\pi\)
\(374\) 0.625404 + 1.08323i 0.0323389 + 0.0560126i
\(375\) −31.7970 + 18.3580i −1.64199 + 0.948004i
\(376\) −13.2698 + 22.9840i −0.684340 + 1.18531i
\(377\) 6.47463 3.26003i 0.333460 0.167900i
\(378\) 0 0
\(379\) 9.24228i 0.474744i 0.971419 + 0.237372i \(0.0762860\pi\)
−0.971419 + 0.237372i \(0.923714\pi\)
\(380\) −6.09497 + 10.5568i −0.312665 + 0.541552i
\(381\) 21.1075 + 36.5592i 1.08137 + 1.87299i
\(382\) 53.0648 30.6369i 2.71503 1.56752i
\(383\) −6.62358 3.82413i −0.338449 0.195404i 0.321137 0.947033i \(-0.395935\pi\)
−0.659586 + 0.751629i \(0.729268\pi\)
\(384\) 57.1925i 2.91859i
\(385\) 0 0
\(386\) −0.488913 −0.0248850
\(387\) 5.28427 9.15262i 0.268614 0.465254i
\(388\) 21.3810 12.3443i 1.08546 0.626689i
\(389\) 3.26868 + 5.66153i 0.165729 + 0.287051i 0.936914 0.349560i \(-0.113669\pi\)
−0.771185 + 0.636611i \(0.780336\pi\)
\(390\) 3.15006 55.0603i 0.159509 2.78809i
\(391\) 2.04169 0.103253
\(392\) 0 0
\(393\) 42.2064 2.12903
\(394\) 12.8281 22.2189i 0.646271 1.11937i
\(395\) −14.5846 + 8.42044i −0.733833 + 0.423678i
\(396\) −5.95762 + 3.43963i −0.299381 + 0.172848i
\(397\) 25.0548 + 14.4654i 1.25746 + 0.725996i 0.972581 0.232566i \(-0.0747123\pi\)
0.284882 + 0.958563i \(0.408046\pi\)
\(398\) 46.6561i 2.33866i
\(399\) 0 0
\(400\) −0.0338847 −0.00169423
\(401\) −23.1603 13.3716i −1.15657 0.667747i −0.206092 0.978533i \(-0.566075\pi\)
−0.950480 + 0.310786i \(0.899408\pi\)
\(402\) −45.4020 78.6385i −2.26444 3.92213i
\(403\) −9.10923 + 13.8810i −0.453763 + 0.691462i
\(404\) 14.6805 25.4274i 0.730382 1.26506i
\(405\) 38.6373i 1.91990i
\(406\) 0 0
\(407\) 1.70934 0.0847287
\(408\) −13.5013 7.79498i −0.668414 0.385909i
\(409\) −30.1138 + 17.3862i −1.48903 + 0.859694i −0.999922 0.0125273i \(-0.996012\pi\)
−0.489112 + 0.872221i \(0.662679\pi\)
\(410\) −28.2972 + 16.3374i −1.39750 + 0.806846i
\(411\) 1.36702 + 0.789250i 0.0674302 + 0.0389309i
\(412\) −19.4565 −0.958553
\(413\) 0 0
\(414\) 18.2028i 0.894617i
\(415\) −11.9308 + 20.6647i −0.585659 + 1.01439i
\(416\) 11.3478 17.2922i 0.556370 0.847819i
\(417\) −2.23579 3.87250i −0.109487 0.189637i
\(418\) −1.08724 0.627719i −0.0531787 0.0307027i
\(419\) 4.19246 0.204815 0.102407 0.994743i \(-0.467345\pi\)
0.102407 + 0.994743i \(0.467345\pi\)
\(420\) 0 0
\(421\) 20.9526i 1.02117i 0.859828 + 0.510584i \(0.170571\pi\)
−0.859828 + 0.510584i \(0.829429\pi\)
\(422\) 16.6555 + 9.61607i 0.810778 + 0.468103i
\(423\) −57.0838 + 32.9574i −2.77551 + 1.60244i
\(424\) 17.9676 10.3736i 0.872583 0.503786i
\(425\) 0.429853 0.744528i 0.0208509 0.0361149i
\(426\) −9.72252 −0.471058
\(427\) 0 0
\(428\) −38.9217 −1.88135
\(429\) 3.49814 + 0.200132i 0.168892 + 0.00966247i
\(430\) 3.70479 + 6.41688i 0.178661 + 0.309449i
\(431\) −14.6309 + 8.44713i −0.704744 + 0.406884i −0.809112 0.587655i \(-0.800051\pi\)
0.104368 + 0.994539i \(0.466718\pi\)
\(432\) −0.432497 + 0.749106i −0.0208085 + 0.0360414i
\(433\) −3.42241 −0.164471 −0.0822353 0.996613i \(-0.526206\pi\)
−0.0822353 + 0.996613i \(0.526206\pi\)
\(434\) 0 0
\(435\) 13.4597i 0.645342i
\(436\) −3.79818 2.19288i −0.181900 0.105020i
\(437\) −1.77470 + 1.02463i −0.0848956 + 0.0490145i
\(438\) −42.7611 74.0644i −2.04320 3.53893i
\(439\) −9.03253 + 15.6448i −0.431099 + 0.746685i −0.996968 0.0778096i \(-0.975207\pi\)
0.565869 + 0.824495i \(0.308541\pi\)
\(440\) 1.82771i 0.0871324i
\(441\) 0 0
\(442\) 6.57501 + 13.0584i 0.312742 + 0.621125i
\(443\) −3.22173 + 5.58020i −0.153069 + 0.265123i −0.932354 0.361546i \(-0.882249\pi\)
0.779285 + 0.626669i \(0.215582\pi\)
\(444\) −48.6885 + 28.1103i −2.31065 + 1.33406i
\(445\) 1.76286 + 3.05336i 0.0835674 + 0.144743i
\(446\) −15.5471 + 26.9284i −0.736178 + 1.27510i
\(447\) 66.4451i 3.14275i
\(448\) 0 0
\(449\) 1.75306i 0.0827322i 0.999144 + 0.0413661i \(0.0131710\pi\)
−0.999144 + 0.0413661i \(0.986829\pi\)
\(450\) 6.63785 + 3.83237i 0.312911 + 0.180659i
\(451\) −1.03796 1.79780i −0.0488757 0.0846551i
\(452\) −15.1681 26.2719i −0.713447 1.23573i
\(453\) −47.7575 27.5728i −2.24385 1.29548i
\(454\) −8.23163 −0.386330
\(455\) 0 0
\(456\) 15.6477 0.732770
\(457\) 28.3277 + 16.3550i 1.32511 + 0.765054i 0.984539 0.175164i \(-0.0560455\pi\)
0.340573 + 0.940218i \(0.389379\pi\)
\(458\) −21.0022 36.3769i −0.981368 1.69978i
\(459\) −10.9731 19.0060i −0.512180 0.887123i
\(460\) −6.81790 3.93632i −0.317886 0.183532i
\(461\) 7.66641i 0.357060i 0.983934 + 0.178530i \(0.0571342\pi\)
−0.983934 + 0.178530i \(0.942866\pi\)
\(462\) 0 0
\(463\) 14.4720i 0.672570i −0.941760 0.336285i \(-0.890829\pi\)
0.941760 0.336285i \(-0.109171\pi\)
\(464\) 0.0703179 0.121794i 0.00326443 0.00565415i
\(465\) 15.4138 + 26.6976i 0.714800 + 1.23807i
\(466\) 40.1077 23.1562i 1.85795 1.07269i
\(467\) 1.68801 2.92373i 0.0781120 0.135294i −0.824323 0.566119i \(-0.808444\pi\)
0.902435 + 0.430825i \(0.141777\pi\)
\(468\) −71.8194 + 36.1616i −3.31985 + 1.67157i
\(469\) 0 0
\(470\) 46.2126i 2.13163i
\(471\) −0.119053 + 0.206205i −0.00548566 + 0.00950144i
\(472\) 11.3221 + 19.6104i 0.521140 + 0.902641i
\(473\) −0.407683 + 0.235376i −0.0187453 + 0.0108226i
\(474\) 49.4035 + 28.5231i 2.26918 + 1.31011i
\(475\) 0.862889i 0.0395921i
\(476\) 0 0
\(477\) 51.5283 2.35932
\(478\) −23.7731 + 41.1763i −1.08736 + 1.88336i
\(479\) −0.125768 + 0.0726124i −0.00574651 + 0.00331775i −0.502871 0.864362i \(-0.667723\pi\)
0.497124 + 0.867680i \(0.334389\pi\)
\(480\) −19.2017 33.2584i −0.876435 1.51803i
\(481\) 19.9473 + 1.14120i 0.909517 + 0.0520344i
\(482\) −29.0508 −1.32323
\(483\) 0 0
\(484\) −35.1177 −1.59626
\(485\) −8.14553 + 14.1085i −0.369869 + 0.640633i
\(486\) 39.9388 23.0587i 1.81166 1.04596i
\(487\) 14.2214 8.21073i 0.644433 0.372064i −0.141887 0.989883i \(-0.545317\pi\)
0.786320 + 0.617819i \(0.211984\pi\)
\(488\) −8.30856 4.79695i −0.376111 0.217148i
\(489\) 31.7616i 1.43631i
\(490\) 0 0
\(491\) −18.2077 −0.821701 −0.410850 0.911703i \(-0.634768\pi\)
−0.410850 + 0.911703i \(0.634768\pi\)
\(492\) 59.1303 + 34.1389i 2.66580 + 1.53910i
\(493\) 1.78407 + 3.09010i 0.0803506 + 0.139171i
\(494\) −12.2686 8.05110i −0.551990 0.362236i
\(495\) 2.26967 3.93119i 0.102014 0.176694i
\(496\) 0.322108i 0.0144631i
\(497\) 0 0
\(498\) 80.8279 3.62199
\(499\) 32.5383 + 18.7860i 1.45661 + 0.840976i 0.998843 0.0480945i \(-0.0153148\pi\)
0.457770 + 0.889070i \(0.348648\pi\)
\(500\) −32.5030 + 18.7656i −1.45358 + 0.839225i
\(501\) −15.9605 + 9.21481i −0.713063 + 0.411687i
\(502\) 27.1945 + 15.7007i 1.21375 + 0.700758i
\(503\) 4.20535 0.187507 0.0937537 0.995595i \(-0.470113\pi\)
0.0937537 + 0.995595i \(0.470113\pi\)
\(504\) 0 0
\(505\) 19.3741i 0.862137i
\(506\) 0.405400 0.702174i 0.0180222 0.0312154i
\(507\) 40.6883 + 4.67092i 1.80703 + 0.207443i
\(508\) 21.5761 + 37.3710i 0.957287 + 1.65807i
\(509\) 7.30705 + 4.21873i 0.323879 + 0.186992i 0.653120 0.757254i \(-0.273460\pi\)
−0.329241 + 0.944246i \(0.606793\pi\)
\(510\) 27.1463 1.20206
\(511\) 0 0
\(512\) 0.791350i 0.0349731i
\(513\) 19.0763 + 11.0137i 0.842240 + 0.486268i
\(514\) 14.5133 8.37924i 0.640153 0.369593i
\(515\) 11.1185 6.41927i 0.489940 0.282867i
\(516\) 7.74159 13.4088i 0.340804 0.590290i
\(517\) 2.93602 0.129126
\(518\) 0 0
\(519\) −53.5263 −2.34955
\(520\) 1.22023 21.3286i 0.0535106 0.935320i
\(521\) 12.9140 + 22.3677i 0.565773 + 0.979948i 0.996977 + 0.0776936i \(0.0247556\pi\)
−0.431204 + 0.902254i \(0.641911\pi\)
\(522\) −27.5499 + 15.9059i −1.20583 + 0.696184i
\(523\) −0.378202 + 0.655065i −0.0165376 + 0.0286440i −0.874176 0.485610i \(-0.838598\pi\)
0.857638 + 0.514254i \(0.171931\pi\)
\(524\) 43.1436 1.88473
\(525\) 0 0
\(526\) 15.2599i 0.665364i
\(527\) −7.07749 4.08619i −0.308300 0.177997i
\(528\) 0.0588698 0.0339885i 0.00256198 0.00147916i
\(529\) 10.8383 + 18.7724i 0.471229 + 0.816192i
\(530\) −18.0632 + 31.2863i −0.784614 + 1.35899i
\(531\) 56.2396i 2.44059i
\(532\) 0 0
\(533\) −10.9123 21.6726i −0.472665 0.938744i
\(534\) 5.97145 10.3428i 0.258410 0.447579i
\(535\) 22.2420 12.8414i 0.961606 0.555183i
\(536\) −17.5873 30.4620i −0.759654 1.31576i
\(537\) 24.1032 41.7480i 1.04013 1.80156i
\(538\) 37.0717i 1.59827i
\(539\) 0 0
\(540\) 84.6231i 3.64160i
\(541\) −19.4099 11.2063i −0.834496 0.481797i 0.0208936 0.999782i \(-0.493349\pi\)
−0.855390 + 0.517985i \(0.826682\pi\)
\(542\) 21.4065 + 37.0772i 0.919488 + 1.59260i
\(543\) 9.21432 + 15.9597i 0.395424 + 0.684895i
\(544\) 8.81675 + 5.09035i 0.378015 + 0.218247i
\(545\) 2.89398 0.123965
\(546\) 0 0
\(547\) −11.8059 −0.504784 −0.252392 0.967625i \(-0.581217\pi\)
−0.252392 + 0.967625i \(0.581217\pi\)
\(548\) 1.39737 + 0.806774i 0.0596929 + 0.0344637i
\(549\) −11.9138 20.6354i −0.508470 0.880697i
\(550\) −0.170704 0.295668i −0.00727884 0.0126073i
\(551\) −3.10154 1.79068i −0.132130 0.0762854i
\(552\) 10.1058i 0.430129i
\(553\) 0 0
\(554\) 68.6190i 2.91534i
\(555\) 18.5489 32.1276i 0.787355 1.36374i
\(556\) −2.28543 3.95848i −0.0969238 0.167877i
\(557\) 7.59273 4.38366i 0.321714 0.185742i −0.330442 0.943826i \(-0.607198\pi\)
0.652156 + 0.758084i \(0.273865\pi\)
\(558\) 36.4305 63.0995i 1.54223 2.67122i
\(559\) −4.91464 + 2.47456i −0.207867 + 0.104663i
\(560\) 0 0
\(561\) 1.72468i 0.0728161i
\(562\) 2.54831 4.41380i 0.107494 0.186185i
\(563\) −18.3879 31.8488i −0.774958 1.34227i −0.934818 0.355127i \(-0.884438\pi\)
0.159860 0.987140i \(-0.448896\pi\)
\(564\) −83.6293 + 48.2834i −3.52143 + 2.03310i
\(565\) 17.3358 + 10.0088i 0.729321 + 0.421074i
\(566\) 31.4744i 1.32297i
\(567\) 0 0
\(568\) −3.76619 −0.158026
\(569\) −17.8918 + 30.9896i −0.750065 + 1.29915i 0.197726 + 0.980257i \(0.436644\pi\)
−0.947791 + 0.318893i \(0.896689\pi\)
\(570\) −23.5964 + 13.6234i −0.988344 + 0.570621i
\(571\) 7.46920 + 12.9370i 0.312576 + 0.541398i 0.978919 0.204248i \(-0.0654747\pi\)
−0.666343 + 0.745645i \(0.732141\pi\)
\(572\) 3.57581 + 0.204576i 0.149512 + 0.00855374i
\(573\) 84.4877 3.52952
\(574\) 0 0
\(575\) −0.557280 −0.0232402
\(576\) −44.8987 + 77.7669i −1.87078 + 3.24029i
\(577\) 14.5892 8.42309i 0.607357 0.350658i −0.164573 0.986365i \(-0.552625\pi\)
0.771930 + 0.635707i \(0.219291\pi\)
\(578\) 27.4057 15.8227i 1.13993 0.658137i
\(579\) −0.583822 0.337070i −0.0242628 0.0140081i
\(580\) 13.7585i 0.571292i
\(581\) 0 0
\(582\) 55.1838 2.28744
\(583\) −1.98771 1.14761i −0.0823226 0.0475290i
\(584\) −16.5643 28.6901i −0.685434 1.18721i
\(585\) 29.1107 44.3601i 1.20358 1.83406i
\(586\) 1.15647 2.00307i 0.0477735 0.0827461i
\(587\) 36.8833i 1.52234i −0.648555 0.761168i \(-0.724626\pi\)
0.648555 0.761168i \(-0.275374\pi\)
\(588\) 0 0
\(589\) 8.20264 0.337984
\(590\) −34.1469 19.7147i −1.40580 0.811642i
\(591\) 30.6367 17.6881i 1.26022 0.727590i
\(592\) 0.335690 0.193811i 0.0137968 0.00796558i
\(593\) −13.9894 8.07676i −0.574474 0.331673i 0.184460 0.982840i \(-0.440946\pi\)
−0.758934 + 0.651167i \(0.774280\pi\)
\(594\) −8.71531 −0.357593
\(595\) 0 0
\(596\) 67.9204i 2.78213i
\(597\) 32.1660 55.7131i 1.31646 2.28018i
\(598\) 5.19965 7.92343i 0.212629 0.324013i
\(599\) 1.24238 + 2.15186i 0.0507622 + 0.0879227i 0.890290 0.455394i \(-0.150502\pi\)
−0.839528 + 0.543317i \(0.817168\pi\)
\(600\) 3.68518 + 2.12764i 0.150447 + 0.0868605i
\(601\) −9.55999 −0.389960 −0.194980 0.980807i \(-0.562464\pi\)
−0.194980 + 0.980807i \(0.562464\pi\)
\(602\) 0 0
\(603\) 87.3605i 3.55759i
\(604\) −48.8179 28.1850i −1.98637 1.14683i
\(605\) 20.0682 11.5864i 0.815886 0.471052i
\(606\) 56.8349 32.8136i 2.30876 1.33296i
\(607\) −9.74294 + 16.8753i −0.395454 + 0.684946i −0.993159 0.116770i \(-0.962746\pi\)
0.597705 + 0.801716i \(0.296079\pi\)
\(608\) −10.2184 −0.414411
\(609\) 0 0
\(610\) 16.7055 0.676387
\(611\) 34.2622 + 1.96017i 1.38610 + 0.0793002i
\(612\) −19.7897 34.2768i −0.799951 1.38556i
\(613\) −12.7896 + 7.38409i −0.516568 + 0.298241i −0.735529 0.677493i \(-0.763066\pi\)
0.218962 + 0.975733i \(0.429733\pi\)
\(614\) −27.4779 + 47.5931i −1.10892 + 1.92070i
\(615\) −45.0537 −1.81674
\(616\) 0 0
\(617\) 30.9478i 1.24591i 0.782257 + 0.622955i \(0.214068\pi\)
−0.782257 + 0.622955i \(0.785932\pi\)
\(618\) −37.6625 21.7444i −1.51501 0.874689i
\(619\) 11.3297 6.54123i 0.455380 0.262914i −0.254719 0.967015i \(-0.581983\pi\)
0.710100 + 0.704101i \(0.248650\pi\)
\(620\) 15.7561 + 27.2903i 0.632780 + 1.09601i
\(621\) −7.11300 + 12.3201i −0.285435 + 0.494388i
\(622\) 20.5426i 0.823685i
\(623\) 0 0
\(624\) 0.709679 0.357329i 0.0284099 0.0143046i
\(625\) 11.1716 19.3498i 0.446865 0.773994i
\(626\) −30.1478 + 17.4059i −1.20495 + 0.695678i
\(627\) −0.865532 1.49915i −0.0345660 0.0598701i
\(628\) −0.121696 + 0.210784i −0.00485620 + 0.00841119i
\(629\) 9.83456i 0.392130i
\(630\) 0 0
\(631\) 35.3591i 1.40762i −0.710387 0.703812i \(-0.751480\pi\)
0.710387 0.703812i \(-0.248520\pi\)
\(632\) 19.1373 + 11.0489i 0.761242 + 0.439503i
\(633\) 13.2591 + 22.9655i 0.527004 + 0.912797i
\(634\) −7.80892 13.5254i −0.310132 0.537164i
\(635\) −24.6596 14.2372i −0.978585 0.564986i
\(636\) 75.4903 2.99338
\(637\) 0 0
\(638\) 1.41699 0.0560990
\(639\) −8.10065 4.67691i −0.320457 0.185016i
\(640\) −19.2884 33.4086i −0.762443 1.32059i
\(641\) −10.6188 18.3923i −0.419417 0.726452i 0.576464 0.817123i \(-0.304432\pi\)
−0.995881 + 0.0906706i \(0.971099\pi\)
\(642\) −75.3418 43.4986i −2.97351 1.71675i
\(643\) 25.4808i 1.00486i 0.864617 + 0.502432i \(0.167561\pi\)
−0.864617 + 0.502432i \(0.832439\pi\)
\(644\) 0 0
\(645\) 10.2167i 0.402283i
\(646\) 3.61154 6.25537i 0.142094 0.246114i
\(647\) −11.3928 19.7329i −0.447897 0.775781i 0.550352 0.834933i \(-0.314494\pi\)
−0.998249 + 0.0591522i \(0.981160\pi\)
\(648\) 43.9059 25.3491i 1.72479 0.995806i
\(649\) 1.25253 2.16945i 0.0491662 0.0851583i
\(650\) −1.79465 3.56429i −0.0703919 0.139803i
\(651\) 0 0
\(652\) 32.4669i 1.27150i
\(653\) −8.13928 + 14.0976i −0.318515 + 0.551684i −0.980178 0.198117i \(-0.936517\pi\)
0.661664 + 0.749801i \(0.269851\pi\)
\(654\) −4.90150 8.48964i −0.191664 0.331971i
\(655\) −24.6546 + 14.2343i −0.963334 + 0.556181i
\(656\) −0.407683 0.235376i −0.0159173 0.00918988i
\(657\) 82.2790i 3.21001i
\(658\) 0 0
\(659\) 20.5596 0.800888 0.400444 0.916321i \(-0.368856\pi\)
0.400444 + 0.916321i \(0.368856\pi\)
\(660\) 3.32513 5.75929i 0.129430 0.224180i
\(661\) 24.0518 13.8863i 0.935507 0.540115i 0.0469576 0.998897i \(-0.485047\pi\)
0.888549 + 0.458782i \(0.151714\pi\)
\(662\) −15.7818 27.3349i −0.613378 1.06240i
\(663\) −1.15145 + 20.1263i −0.0447185 + 0.781642i
\(664\) 31.3101 1.21507
\(665\) 0 0
\(666\) −87.6802 −3.39754
\(667\) 1.15647 2.00307i 0.0447789 0.0775593i
\(668\) −16.3149 + 9.41941i −0.631242 + 0.364448i
\(669\) −37.1303 + 21.4372i −1.43554 + 0.828810i
\(670\) 53.0425 + 30.6241i 2.04921 + 1.18311i
\(671\) 1.06135i 0.0409730i
\(672\) 0 0
\(673\) 5.20337 0.200575 0.100288 0.994958i \(-0.468024\pi\)
0.100288 + 0.994958i \(0.468024\pi\)
\(674\) −53.5105 30.8943i −2.06115 1.19000i
\(675\) 2.99511 + 5.18768i 0.115282 + 0.199674i
\(676\) 41.5917 + 4.77463i 1.59968 + 0.183640i
\(677\) 22.4239 38.8394i 0.861821 1.49272i −0.00834820 0.999965i \(-0.502657\pi\)
0.870169 0.492753i \(-0.164009\pi\)
\(678\) 67.8070i 2.60411i
\(679\) 0 0
\(680\) 10.5156 0.403254
\(681\) −9.82957 5.67510i −0.376670 0.217470i
\(682\) −2.81062 + 1.62271i −0.107624 + 0.0621370i
\(683\) 16.4318 9.48691i 0.628745 0.363006i −0.151521 0.988454i \(-0.548417\pi\)
0.780266 + 0.625448i \(0.215084\pi\)
\(684\) 34.4037 + 19.8630i 1.31546 + 0.759479i
\(685\) −1.06471 −0.0406807
\(686\) 0 0
\(687\) 57.9179i 2.20970i
\(688\) −0.0533755 + 0.0924491i −0.00203492 + 0.00352459i
\(689\) −22.4296 14.7191i −0.854500 0.560755i
\(690\) −8.79840 15.2393i −0.334949 0.580149i
\(691\) −32.4085 18.7111i −1.23288 0.711803i −0.265250 0.964180i \(-0.585455\pi\)
−0.967629 + 0.252376i \(0.918788\pi\)
\(692\) −54.7148 −2.07994
\(693\) 0 0
\(694\) 44.1229i 1.67488i
\(695\) 2.61204 + 1.50806i 0.0990802 + 0.0572040i
\(696\) −15.2951 + 8.83060i −0.579757 + 0.334723i
\(697\) 10.3435 5.97184i 0.391789 0.226200i
\(698\) 16.1734 28.0131i 0.612171 1.06031i
\(699\) 63.8580 2.41533
\(700\) 0 0
\(701\) 42.5513 1.60714 0.803570 0.595210i \(-0.202931\pi\)
0.803570 + 0.595210i \(0.202931\pi\)
\(702\) −101.704 5.81860i −3.83857 0.219609i
\(703\) −4.93548 8.54851i −0.186145 0.322413i
\(704\) 3.46395 1.99991i 0.130552 0.0753745i
\(705\) 31.8602 55.1835i 1.19993 2.07833i
\(706\) 38.7612 1.45880
\(707\) 0 0
\(708\) 82.3924i 3.09650i
\(709\) 43.5889 + 25.1661i 1.63702 + 0.945131i 0.981853 + 0.189644i \(0.0607333\pi\)
0.655163 + 0.755488i \(0.272600\pi\)
\(710\) 5.67934 3.27897i 0.213142 0.123057i
\(711\) 27.4415 + 47.5300i 1.02914 + 1.78252i
\(712\) 2.31315 4.00648i 0.0866888 0.150149i
\(713\) 5.29752i 0.198394i
\(714\) 0 0
\(715\) −2.11091 + 1.06286i −0.0789435 + 0.0397487i
\(716\) 24.6384 42.6749i 0.920780 1.59484i
\(717\) −56.7760 + 32.7796i −2.12034 + 1.22418i
\(718\) 26.0049 + 45.0418i 0.970495 + 1.68095i
\(719\) −14.4616 + 25.0482i −0.539326 + 0.934141i 0.459614 + 0.888119i \(0.347988\pi\)
−0.998940 + 0.0460219i \(0.985346\pi\)
\(720\) 1.02938i 0.0383625i
\(721\) 0 0
\(722\) 36.1616i 1.34580i
\(723\) −34.6902 20.0284i −1.29014 0.744863i
\(724\) 9.41891 + 16.3140i 0.350051 + 0.606306i
\(725\) −0.486962 0.843444i −0.0180853 0.0313247i
\(726\) −67.9782 39.2472i −2.52291 1.45660i
\(727\) −19.8593 −0.736539 −0.368269 0.929719i \(-0.620050\pi\)
−0.368269 + 0.929719i \(0.620050\pi\)
\(728\) 0 0
\(729\) 9.04209 0.334892
\(730\) 49.9572 + 28.8428i 1.84900 + 1.06752i
\(731\) −1.35422 2.34558i −0.0500876 0.0867543i
\(732\) −17.4541 30.2314i −0.645121 1.11738i
\(733\) −17.6237 10.1751i −0.650947 0.375824i 0.137872 0.990450i \(-0.455974\pi\)
−0.788819 + 0.614626i \(0.789307\pi\)
\(734\) 37.8899i 1.39854i
\(735\) 0 0
\(736\) 6.59935i 0.243255i
\(737\) −1.94564 + 3.36994i −0.0716684 + 0.124133i
\(738\) 53.2421 + 92.2180i 1.95987 + 3.39459i
\(739\) 16.4554 9.50055i 0.605323 0.349483i −0.165810 0.986158i \(-0.553024\pi\)
0.771133 + 0.636674i \(0.219690\pi\)
\(740\) 18.9607 32.8409i 0.697009 1.20726i
\(741\) −9.09954 18.0723i −0.334280 0.663902i
\(742\) 0 0
\(743\) 8.15098i 0.299030i −0.988759 0.149515i \(-0.952229\pi\)
0.988759 0.149515i \(-0.0477713\pi\)
\(744\) 20.2254 35.0314i 0.741498 1.28431i
\(745\) 22.4090 + 38.8134i 0.821000 + 1.42201i
\(746\) −54.7035 + 31.5831i −2.00284 + 1.15634i
\(747\) 67.3445 + 38.8814i 2.46401 + 1.42260i
\(748\) 1.76297i 0.0644607i
\(749\) 0 0
\(750\) −83.8893 −3.06320
\(751\) 18.3713 31.8201i 0.670379 1.16113i −0.307417 0.951575i \(-0.599465\pi\)
0.977797 0.209556i \(-0.0672020\pi\)
\(752\) 0.576595 0.332897i 0.0210262 0.0121395i
\(753\) 21.6490 + 37.4972i 0.788934 + 1.36647i
\(754\) 16.5357 + 0.946022i 0.602193 + 0.0344521i
\(755\) 37.1963 1.35371
\(756\) 0 0
\(757\) 38.3971 1.39557 0.697783 0.716310i \(-0.254170\pi\)
0.697783 + 0.716310i \(0.254170\pi\)
\(758\) −10.5584 + 18.2878i −0.383500 + 0.664241i
\(759\) 0.968195 0.558987i 0.0351432 0.0202900i
\(760\) −9.14048 + 5.27726i −0.331560 + 0.191426i
\(761\) 10.7922 + 6.23089i 0.391218 + 0.225870i 0.682688 0.730710i \(-0.260811\pi\)
−0.291470 + 0.956580i \(0.594144\pi\)
\(762\) 96.4533i 3.49414i
\(763\) 0 0
\(764\) 86.3636 3.12453
\(765\) 22.6178 + 13.0584i 0.817749 + 0.472128i
\(766\) −8.73742 15.1336i −0.315696 0.546801i
\(767\) 16.0649 24.4804i 0.580071 0.883935i
\(768\) −24.4860 + 42.4110i −0.883562 + 1.53037i
\(769\) 4.81390i 0.173594i 0.996226 + 0.0867969i \(0.0276631\pi\)
−0.996226 + 0.0867969i \(0.972337\pi\)
\(770\) 0 0
\(771\) 23.1075 0.832196
\(772\) −0.596785 0.344554i −0.0214787 0.0124008i
\(773\) 24.4863 14.1372i 0.880713 0.508480i 0.00981931 0.999952i \(-0.496874\pi\)
0.870893 + 0.491472i \(0.163541\pi\)
\(774\) 20.9120 12.0736i 0.751668 0.433975i
\(775\) 1.93180 + 1.11533i 0.0693923 + 0.0400637i
\(776\) 21.3764 0.767369
\(777\) 0 0
\(778\) 14.9367i 0.535505i
\(779\) −5.99395 + 10.3818i −0.214755 + 0.371967i
\(780\) 42.6479 64.9886i 1.52704 2.32696i
\(781\) 0.208322 + 0.360825i 0.00745436 + 0.0129113i
\(782\) 4.03991 + 2.33244i 0.144467 + 0.0834081i
\(783\) −24.8619 −0.888492
\(784\) 0 0
\(785\) 0.160604i 0.00573222i
\(786\) 83.5141 + 48.2169i 2.97885 + 1.71984i
\(787\) 43.0053 24.8291i 1.53297 0.885062i 0.533749 0.845643i \(-0.320783\pi\)
0.999223 0.0394193i \(-0.0125508\pi\)
\(788\) 31.3169 18.0808i 1.11562 0.644102i
\(789\) −10.5206 + 18.2222i −0.374543 + 0.648728i
\(790\) −38.4783 −1.36900
\(791\) 0 0
\(792\) −5.95633 −0.211649
\(793\) −0.708588 + 12.3855i −0.0251627 + 0.439823i
\(794\) 33.0507 + 57.2455i 1.17292 + 2.03157i
\(795\) −43.1393 + 24.9065i −1.52999 + 0.883341i
\(796\) 32.8801 56.9501i 1.16541 2.01854i
\(797\) 5.37263 0.190308 0.0951542 0.995463i \(-0.469666\pi\)
0.0951542 + 0.995463i \(0.469666\pi\)
\(798\) 0 0
\(799\) 16.8922i 0.597604i
\(800\) −2.40653 1.38941i −0.0850837 0.0491231i
\(801\) 9.95062 5.74500i 0.351588 0.202989i
\(802\) −30.5517 52.9170i −1.07882 1.86857i
\(803\) −1.83246 + 3.17392i −0.0646663 + 0.112005i
\(804\) 127.985i 4.51369i
\(805\) 0 0
\(806\) −33.8822 + 17.0600i −1.19345 + 0.600912i
\(807\) −25.5582 + 44.2681i −0.899692 + 1.55831i
\(808\) 22.0160 12.7109i 0.774520 0.447169i
\(809\) −20.6184 35.7122i −0.724905 1.25557i −0.959013 0.283362i \(-0.908550\pi\)
0.234107 0.972211i \(-0.424783\pi\)
\(810\) −44.1395 + 76.4518i −1.55090 + 2.68624i
\(811\) 19.4366i 0.682512i 0.939970 + 0.341256i \(0.110852\pi\)
−0.939970 + 0.341256i \(0.889148\pi\)
\(812\) 0 0
\(813\) 59.0328i 2.07037i
\(814\) 3.38227 + 1.95276i 0.118549 + 0.0684441i
\(815\) −10.7118 18.5533i −0.375217 0.649895i
\(816\) 0.195551 + 0.338704i 0.00684564 + 0.0118570i
\(817\) 2.35426 + 1.35923i 0.0823651 + 0.0475535i
\(818\) −79.4486 −2.77785
\(819\) 0 0
\(820\) −46.0540 −1.60828
\(821\) −17.4856 10.0953i −0.610251 0.352329i 0.162813 0.986657i \(-0.447943\pi\)
−0.773064 + 0.634328i \(0.781277\pi\)
\(822\) 1.80329 + 3.12339i 0.0628970 + 0.108941i
\(823\) −21.4049 37.0743i −0.746127 1.29233i −0.949666 0.313263i \(-0.898578\pi\)
0.203539 0.979067i \(-0.434756\pi\)
\(824\) −14.5892 8.42309i −0.508240 0.293432i
\(825\) 0.470751i 0.0163895i
\(826\) 0 0
\(827\) 33.5376i 1.16622i 0.812394 + 0.583109i \(0.198164\pi\)
−0.812394 + 0.583109i \(0.801836\pi\)
\(828\) −12.8281 + 22.2189i −0.445808 + 0.772162i
\(829\) 19.8949 + 34.4590i 0.690978 + 1.19681i 0.971518 + 0.236967i \(0.0761533\pi\)
−0.280540 + 0.959842i \(0.590513\pi\)
\(830\) −47.2150 + 27.2596i −1.63886 + 0.946195i
\(831\) −47.3077 + 81.9394i −1.64109 + 2.84245i
\(832\) 41.7581 21.0255i 1.44770 0.728929i
\(833\) 0 0
\(834\) 10.2167i 0.353776i
\(835\) 6.21548 10.7655i 0.215096 0.372556i
\(836\) −0.884750 1.53243i −0.0305997 0.0530003i
\(837\) 49.3142 28.4715i 1.70455 0.984120i
\(838\) 8.29564 + 4.78949i 0.286568 + 0.165450i
\(839\) 36.7098i 1.26736i 0.773594 + 0.633682i \(0.218457\pi\)
−0.773594 + 0.633682i \(0.781543\pi\)
\(840\) 0 0
\(841\) −24.9578 −0.860614
\(842\) −23.9364 + 41.4591i −0.824903 + 1.42877i
\(843\) 6.08599 3.51375i 0.209613 0.121020i
\(844\) 13.5535 + 23.4754i 0.466532 + 0.808058i
\(845\) −25.3430 + 10.9938i −0.871827 + 0.378199i
\(846\) −150.603 −5.17783
\(847\) 0 0
\(848\) −0.520479 −0.0178733
\(849\) 21.6993 37.5842i 0.744717 1.28989i
\(850\) 1.70111 0.982134i 0.0583475 0.0336869i
\(851\) 5.52089 3.18749i 0.189254 0.109266i
\(852\) −11.8676 6.85179i −0.406579 0.234738i
\(853\) 11.7156i 0.401136i −0.979680 0.200568i \(-0.935721\pi\)
0.979680 0.200568i \(-0.0642788\pi\)
\(854\) 0 0
\(855\) −26.2135 −0.896483
\(856\) −29.1850 16.8500i −0.997523 0.575920i
\(857\) 13.8453 + 23.9807i 0.472945 + 0.819164i 0.999521 0.0309639i \(-0.00985769\pi\)
−0.526576 + 0.850128i \(0.676524\pi\)
\(858\) 6.69316 + 4.39230i 0.228501 + 0.149951i
\(859\) −19.2819 + 33.3972i −0.657890 + 1.13950i 0.323271 + 0.946306i \(0.395217\pi\)
−0.981161 + 0.193192i \(0.938116\pi\)
\(860\) 10.4436i 0.356122i
\(861\) 0 0
\(862\) −38.6002 −1.31473
\(863\) −15.4613 8.92660i −0.526310 0.303865i 0.213203 0.977008i \(-0.431611\pi\)
−0.739512 + 0.673143i \(0.764944\pi\)
\(864\) −61.4329 + 35.4683i −2.08999 + 1.20666i
\(865\) 31.2670 18.0520i 1.06311 0.613787i
\(866\) −6.77195 3.90979i −0.230120 0.132860i
\(867\) 43.6343 1.48190
\(868\) 0 0
\(869\) 2.44464i 0.0829286i
\(870\) 15.3764 26.6327i 0.521310 0.902935i
\(871\) −24.9547 + 38.0269i −0.845556 + 1.28849i
\(872\) −1.89868 3.28861i −0.0642975 0.111366i
\(873\) 45.9783 + 26.5456i 1.55613 + 0.898431i
\(874\) −4.68216 −0.158376
\(875\) 0 0
\(876\) 120.541i 4.07270i
\(877\) 7.72524 + 4.46017i 0.260863 + 0.150609i 0.624728 0.780842i \(-0.285210\pi\)
−0.363865 + 0.931452i \(0.618543\pi\)
\(878\) −35.7454 + 20.6376i −1.20635 + 0.696487i
\(879\) 2.76194 1.59461i 0.0931580 0.0537848i
\(880\) −0.0229256 + 0.0397083i −0.000772821 + 0.00133857i
\(881\) −54.6144 −1.84001 −0.920003 0.391911i \(-0.871814\pi\)
−0.920003 + 0.391911i \(0.871814\pi\)
\(882\) 0 0
\(883\) −7.51632 −0.252944 −0.126472 0.991970i \(-0.540365\pi\)
−0.126472 + 0.991970i \(0.540365\pi\)
\(884\) −1.17701 + 20.5732i −0.0395872 + 0.691951i
\(885\) −27.1837 47.0835i −0.913770 1.58270i
\(886\) −12.7497 + 7.36105i −0.428335 + 0.247299i
\(887\) 22.5391 39.0389i 0.756790 1.31080i −0.187689 0.982229i \(-0.560100\pi\)
0.944479 0.328571i \(-0.106567\pi\)
\(888\) −48.6780 −1.63353
\(889\) 0 0
\(890\) 8.05560i 0.270024i
\(891\) −4.85720 2.80431i −0.162722 0.0939479i
\(892\) −37.9547 + 21.9132i −1.27082 + 0.733708i
\(893\) −8.47737 14.6832i −0.283684 0.491356i
\(894\) 75.9074 131.475i 2.53872 4.39720i
\(895\) 32.5157i 1.08688i
\(896\) 0 0
\(897\) 11.6716 5.87676i 0.389705 0.196219i
\(898\) −2.00271 + 3.46880i −0.0668314 + 0.115755i
\(899\) −8.01779 + 4.62907i −0.267408 + 0.154388i
\(900\) 5.40160 + 9.35584i 0.180053 + 0.311861i
\(901\) 6.60268 11.4362i 0.219967 0.380994i
\(902\) 4.74309i 0.157928i
\(903\) 0 0
\(904\) 26.2662i 0.873602i
\(905\) −10.7650 6.21515i −0.357839 0.206599i
\(906\) −62.9988 109.117i −2.09299 3.62517i
\(907\) 3.18295 + 5.51303i 0.105688 + 0.183057i 0.914019 0.405671i \(-0.132962\pi\)
−0.808331 + 0.588728i \(0.799629\pi\)
\(908\) −10.0478 5.80111i −0.333449 0.192517i
\(909\) 63.1385 2.09417
\(910\) 0 0
\(911\) 20.9161 0.692982 0.346491 0.938053i \(-0.387373\pi\)
0.346491 + 0.938053i \(0.387373\pi\)
\(912\) −0.339958 0.196275i −0.0112571 0.00649930i
\(913\) −1.73188 2.99971i −0.0573169 0.0992758i
\(914\) 37.3681 + 64.7234i 1.23603 + 2.14086i
\(915\) 19.9484 + 11.5172i 0.659475 + 0.380748i
\(916\) 59.2038i 1.95615i
\(917\) 0 0
\(918\) 50.1430i 1.65496i
\(919\) −2.44326 + 4.23185i −0.0805957 + 0.139596i −0.903506 0.428576i \(-0.859016\pi\)
0.822910 + 0.568171i \(0.192349\pi\)
\(920\) −3.40821 5.90320i −0.112366 0.194623i
\(921\) −65.6239 + 37.8880i −2.16238 + 1.24845i
\(922\) −8.75816 + 15.1696i −0.288435 + 0.499584i
\(923\) 2.19014 + 4.34976i 0.0720893 + 0.143174i
\(924\) 0 0
\(925\) 2.68434i 0.0882606i
\(926\) 16.5329 28.6358i 0.543305 0.941031i
\(927\) −20.9198 36.2342i −0.687098 1.19009i
\(928\) 9.98812 5.76664i 0.327876 0.189299i
\(929\) 44.6306 + 25.7675i 1.46428 + 0.845404i 0.999205 0.0398663i \(-0.0126932\pi\)
0.465077 + 0.885270i \(0.346027\pi\)
\(930\) 70.4355i 2.30967i
\(931\) 0 0
\(932\) 65.2759 2.13818
\(933\) −14.1626 + 24.5304i −0.463664 + 0.803090i
\(934\) 6.68017 3.85680i 0.218582 0.126198i
\(935\) −0.581657 1.00746i −0.0190222 0.0329474i
\(936\) −69.5080 3.97662i −2.27194 0.129980i
\(937\) −20.3565 −0.665016 −0.332508 0.943100i \(-0.607895\pi\)
−0.332508 + 0.943100i \(0.607895\pi\)
\(938\) 0 0
\(939\) −48.0002 −1.56643
\(940\) 32.5676 56.4088i 1.06224 1.83985i
\(941\) −29.6730 + 17.1317i −0.967314 + 0.558479i −0.898416 0.439145i \(-0.855281\pi\)
−0.0688974 + 0.997624i \(0.521948\pi\)
\(942\) −0.471141 + 0.272013i −0.0153506 + 0.00886267i
\(943\) −6.70490 3.87108i −0.218342 0.126060i
\(944\) 0.568067i 0.0184890i
\(945\) 0 0
\(946\) −1.07558 −0.0349701
\(947\) 47.9046 + 27.6578i 1.55669 + 0.898756i 0.997570 + 0.0696707i \(0.0221949\pi\)
0.559122 + 0.829086i \(0.311138\pi\)
\(948\) 40.2025 + 69.6327i 1.30572 + 2.26156i
\(949\) −23.5031 + 35.8150i −0.762944 + 1.16260i
\(950\) −0.985770 + 1.70740i −0.0319826 + 0.0553955i
\(951\) 21.5347i 0.698311i
\(952\) 0 0
\(953\) −14.8378 −0.480644 −0.240322 0.970693i \(-0.577253\pi\)
−0.240322 + 0.970693i \(0.577253\pi\)
\(954\) 101.959 + 58.8663i 3.30106 + 1.90587i
\(955\) −49.3529 + 28.4939i −1.59702 + 0.922041i
\(956\) −58.0366 + 33.5075i −1.87704 + 1.08371i
\(957\) 1.69205 + 0.976908i 0.0546964 + 0.0315790i
\(958\) −0.331812 −0.0107203
\(959\) 0 0
\(960\) 86.8081i 2.80172i
\(961\) −4.89769 + 8.48305i −0.157990 + 0.273647i
\(962\) 38.1661 + 25.0460i 1.23052 + 0.807515i
\(963\) −41.8491 72.4847i −1.34857 2.33579i
\(964\) −35.4604 20.4731i −1.14210 0.659393i
\(965\) 0.454714 0.0146378
\(966\) 0 0
\(967\) 3.09473i 0.0995199i 0.998761 + 0.0497600i \(0.0158456\pi\)
−0.998761 + 0.0497600i \(0.984154\pi\)
\(968\) −26.3326 15.2031i −0.846361 0.488647i
\(969\) 8.62524 4.97979i 0.277083 0.159974i
\(970\) −32.2352 + 18.6110i −1.03501 + 0.597564i
\(971\) 27.4506 47.5459i 0.880933 1.52582i 0.0306280 0.999531i \(-0.490249\pi\)
0.850305 0.526290i \(-0.176417\pi\)
\(972\) 65.0010 2.08491
\(973\) 0 0
\(974\) 37.5200 1.20222
\(975\) 0.314287 5.49348i 0.0100653 0.175932i
\(976\) 0.120340 + 0.208435i 0.00385198 + 0.00667183i
\(977\) −37.4196 + 21.6042i −1.19716 + 0.691181i −0.959921 0.280270i \(-0.909576\pi\)
−0.237239 + 0.971451i \(0.576243\pi\)
\(978\) −36.2847 + 62.8470i −1.16026 + 2.00962i
\(979\) −0.511795 −0.0163570
\(980\) 0 0
\(981\) 9.43124i 0.301116i
\(982\) −36.0276 20.8006i −1.14969 0.663773i
\(983\) 21.5498 12.4418i 0.687332 0.396831i −0.115280 0.993333i \(-0.536776\pi\)
0.802612 + 0.596502i \(0.203443\pi\)
\(984\) 29.5588 + 51.1973i 0.942299 + 1.63211i
\(985\) −11.9308 + 20.6647i −0.380146 + 0.658433i
\(986\) 8.15254i 0.259630i
\(987\) 0 0
\(988\) −9.30158 18.4735i −0.295923 0.587722i
\(989\) −0.877834 + 1.52045i −0.0279135 + 0.0483476i
\(990\) 8.98203 5.18578i 0.285468 0.164815i
\(991\) −2.39164 4.14244i −0.0759730 0.131589i 0.825536 0.564349i \(-0.190873\pi\)
−0.901509 + 0.432760i \(0.857540\pi\)
\(992\) −13.2078 + 22.8765i −0.419347 + 0.726331i
\(993\) 43.5216i 1.38112i
\(994\) 0 0
\(995\) 43.3925i 1.37564i
\(996\) 98.6614 + 56.9622i 3.12621 + 1.80492i
\(997\) 1.72037 + 2.97977i 0.0544847 + 0.0943703i 0.891981 0.452072i \(-0.149315\pi\)
−0.837497 + 0.546442i \(0.815982\pi\)
\(998\) 42.9225 + 74.3439i 1.35869 + 2.35331i
\(999\) −59.3441 34.2623i −1.87756 1.08401i
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 637.2.r.f.324.8 16
7.2 even 3 637.2.c.e.246.1 8
7.3 odd 6 91.2.r.a.25.1 16
7.4 even 3 inner 637.2.r.f.116.1 16
7.5 odd 6 637.2.c.f.246.1 8
7.6 odd 2 91.2.r.a.51.8 yes 16
13.12 even 2 inner 637.2.r.f.324.1 16
21.17 even 6 819.2.dl.e.298.8 16
21.20 even 2 819.2.dl.e.415.1 16
91.5 even 12 8281.2.a.ck.1.1 8
91.12 odd 6 637.2.c.f.246.8 8
91.25 even 6 inner 637.2.r.f.116.8 16
91.31 even 12 1183.2.e.i.508.8 16
91.34 even 4 1183.2.e.i.170.1 16
91.38 odd 6 91.2.r.a.25.8 yes 16
91.44 odd 12 8281.2.a.cj.1.1 8
91.47 even 12 8281.2.a.ck.1.8 8
91.51 even 6 637.2.c.e.246.8 8
91.73 even 12 1183.2.e.i.508.1 16
91.83 even 4 1183.2.e.i.170.8 16
91.86 odd 12 8281.2.a.cj.1.8 8
91.90 odd 2 91.2.r.a.51.1 yes 16
273.38 even 6 819.2.dl.e.298.1 16
273.272 even 2 819.2.dl.e.415.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.r.a.25.1 16 7.3 odd 6
91.2.r.a.25.8 yes 16 91.38 odd 6
91.2.r.a.51.1 yes 16 91.90 odd 2
91.2.r.a.51.8 yes 16 7.6 odd 2
637.2.c.e.246.1 8 7.2 even 3
637.2.c.e.246.8 8 91.51 even 6
637.2.c.f.246.1 8 7.5 odd 6
637.2.c.f.246.8 8 91.12 odd 6
637.2.r.f.116.1 16 7.4 even 3 inner
637.2.r.f.116.8 16 91.25 even 6 inner
637.2.r.f.324.1 16 13.12 even 2 inner
637.2.r.f.324.8 16 1.1 even 1 trivial
819.2.dl.e.298.1 16 273.38 even 6
819.2.dl.e.298.8 16 21.17 even 6
819.2.dl.e.415.1 16 21.20 even 2
819.2.dl.e.415.8 16 273.272 even 2
1183.2.e.i.170.1 16 91.34 even 4
1183.2.e.i.170.8 16 91.83 even 4
1183.2.e.i.508.1 16 91.73 even 12
1183.2.e.i.508.8 16 91.31 even 12
8281.2.a.cj.1.1 8 91.44 odd 12
8281.2.a.cj.1.8 8 91.86 odd 12
8281.2.a.ck.1.1 8 91.5 even 12
8281.2.a.ck.1.8 8 91.47 even 12