Properties

Label 99.3.l.a.26.5
Level $99$
Weight $3$
Character 99.26
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
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] = [99,3,Mod(26,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.26");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 26.5
Character \(\chi\) \(=\) 99.26
Dual form 99.3.l.a.80.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.480038 - 0.660715i) q^{2} +(1.02996 + 3.16989i) q^{4} +(0.615389 + 0.847011i) q^{5} +(2.11067 + 6.49597i) q^{7} +(5.69568 + 1.85064i) q^{8} +O(q^{10})\) \(q+(0.480038 - 0.660715i) q^{2} +(1.02996 + 3.16989i) q^{4} +(0.615389 + 0.847011i) q^{5} +(2.11067 + 6.49597i) q^{7} +(5.69568 + 1.85064i) q^{8} +0.855043 q^{10} +(2.57144 - 10.6952i) q^{11} +(6.23315 + 4.52865i) q^{13} +(5.30519 + 1.72376i) q^{14} +(-6.82898 + 4.96155i) q^{16} +(-5.52104 - 7.59906i) q^{17} +(2.91103 - 8.95922i) q^{19} +(-2.05110 + 2.82310i) q^{20} +(-5.83211 - 6.83310i) q^{22} +4.82409i q^{23} +(7.38670 - 22.7339i) q^{25} +(5.98430 - 1.94442i) q^{26} +(-18.4176 + 13.3812i) q^{28} +(-44.4675 + 14.4484i) q^{29} +(-15.3643 - 11.1628i) q^{31} +30.8489i q^{32} -7.67113 q^{34} +(-4.20328 + 5.78531i) q^{35} +(-14.5803 - 44.8737i) q^{37} +(-4.52209 - 6.22413i) q^{38} +(1.93755 + 5.96317i) q^{40} +(7.22871 + 2.34875i) q^{41} +50.6851 q^{43} +(36.5511 - 2.86447i) q^{44} +(3.18735 + 2.31575i) q^{46} +(-62.9091 - 20.4404i) q^{47} +(1.89907 - 1.37976i) q^{49} +(-11.4748 - 15.7937i) q^{50} +(-7.93542 + 24.4227i) q^{52} +(22.5774 - 31.0751i) q^{53} +(10.6414 - 4.40369i) q^{55} +40.9051i q^{56} +(-11.7998 + 36.3161i) q^{58} +(111.526 - 36.2371i) q^{59} +(-65.8779 + 47.8631i) q^{61} +(-14.7509 + 4.79287i) q^{62} +(-6.93357 - 5.03753i) q^{64} +8.06643i q^{65} +70.1488 q^{67} +(18.4017 - 25.3278i) q^{68} +(1.80471 + 5.55434i) q^{70} +(25.4295 + 35.0007i) q^{71} +(14.1852 + 43.6575i) q^{73} +(-36.6478 - 11.9076i) q^{74} +31.3980 q^{76} +(74.9033 - 5.87008i) q^{77} +(69.3955 + 50.4188i) q^{79} +(-8.40497 - 2.73094i) q^{80} +(5.02191 - 3.64863i) q^{82} +(-93.5371 - 128.743i) q^{83} +(3.03890 - 9.35276i) q^{85} +(24.3308 - 33.4884i) q^{86} +(34.4391 - 56.1578i) q^{88} +154.015i q^{89} +(-16.2619 + 50.0489i) q^{91} +(-15.2918 + 4.96862i) q^{92} +(-43.7040 + 31.7528i) q^{94} +(9.37997 - 3.04774i) q^{95} +(-124.151 - 90.2007i) q^{97} -1.91708i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.480038 0.660715i 0.240019 0.330358i −0.671966 0.740582i \(-0.734550\pi\)
0.911984 + 0.410225i \(0.134550\pi\)
\(3\) 0 0
\(4\) 1.02996 + 3.16989i 0.257490 + 0.792472i
\(5\) 0.615389 + 0.847011i 0.123078 + 0.169402i 0.866110 0.499854i \(-0.166613\pi\)
−0.743032 + 0.669256i \(0.766613\pi\)
\(6\) 0 0
\(7\) 2.11067 + 6.49597i 0.301524 + 0.927996i 0.980951 + 0.194253i \(0.0622284\pi\)
−0.679427 + 0.733743i \(0.737772\pi\)
\(8\) 5.69568 + 1.85064i 0.711961 + 0.231330i
\(9\) 0 0
\(10\) 0.855043 0.0855043
\(11\) 2.57144 10.6952i 0.233767 0.972293i
\(12\) 0 0
\(13\) 6.23315 + 4.52865i 0.479473 + 0.348358i 0.801122 0.598502i \(-0.204237\pi\)
−0.321649 + 0.946859i \(0.604237\pi\)
\(14\) 5.30519 + 1.72376i 0.378942 + 0.123126i
\(15\) 0 0
\(16\) −6.82898 + 4.96155i −0.426812 + 0.310097i
\(17\) −5.52104 7.59906i −0.324767 0.447004i 0.615148 0.788412i \(-0.289096\pi\)
−0.939915 + 0.341408i \(0.889096\pi\)
\(18\) 0 0
\(19\) 2.91103 8.95922i 0.153212 0.471538i −0.844763 0.535140i \(-0.820259\pi\)
0.997975 + 0.0636020i \(0.0202588\pi\)
\(20\) −2.05110 + 2.82310i −0.102555 + 0.141155i
\(21\) 0 0
\(22\) −5.83211 6.83310i −0.265096 0.310595i
\(23\) 4.82409i 0.209743i 0.994486 + 0.104872i \(0.0334431\pi\)
−0.994486 + 0.104872i \(0.966557\pi\)
\(24\) 0 0
\(25\) 7.38670 22.7339i 0.295468 0.909357i
\(26\) 5.98430 1.94442i 0.230165 0.0747852i
\(27\) 0 0
\(28\) −18.4176 + 13.3812i −0.657772 + 0.477899i
\(29\) −44.4675 + 14.4484i −1.53336 + 0.498220i −0.949536 0.313658i \(-0.898445\pi\)
−0.583827 + 0.811878i \(0.698445\pi\)
\(30\) 0 0
\(31\) −15.3643 11.1628i −0.495624 0.360092i 0.311719 0.950174i \(-0.399095\pi\)
−0.807343 + 0.590082i \(0.799095\pi\)
\(32\) 30.8489i 0.964029i
\(33\) 0 0
\(34\) −7.67113 −0.225621
\(35\) −4.20328 + 5.78531i −0.120094 + 0.165295i
\(36\) 0 0
\(37\) −14.5803 44.8737i −0.394063 1.21280i −0.929689 0.368346i \(-0.879924\pi\)
0.535626 0.844455i \(-0.320076\pi\)
\(38\) −4.52209 6.22413i −0.119002 0.163793i
\(39\) 0 0
\(40\) 1.93755 + 5.96317i 0.0484388 + 0.149079i
\(41\) 7.22871 + 2.34875i 0.176310 + 0.0572866i 0.395842 0.918319i \(-0.370453\pi\)
−0.219532 + 0.975605i \(0.570453\pi\)
\(42\) 0 0
\(43\) 50.6851 1.17872 0.589362 0.807869i \(-0.299379\pi\)
0.589362 + 0.807869i \(0.299379\pi\)
\(44\) 36.5511 2.86447i 0.830708 0.0651015i
\(45\) 0 0
\(46\) 3.18735 + 2.31575i 0.0692903 + 0.0503423i
\(47\) −62.9091 20.4404i −1.33849 0.434902i −0.449686 0.893187i \(-0.648464\pi\)
−0.888805 + 0.458285i \(0.848464\pi\)
\(48\) 0 0
\(49\) 1.89907 1.37976i 0.0387566 0.0281583i
\(50\) −11.4748 15.7937i −0.229495 0.315873i
\(51\) 0 0
\(52\) −7.93542 + 24.4227i −0.152604 + 0.469668i
\(53\) 22.5774 31.0751i 0.425988 0.586322i −0.541039 0.840998i \(-0.681969\pi\)
0.967026 + 0.254676i \(0.0819688\pi\)
\(54\) 0 0
\(55\) 10.6414 4.40369i 0.193480 0.0800671i
\(56\) 40.9051i 0.730448i
\(57\) 0 0
\(58\) −11.7998 + 36.3161i −0.203445 + 0.626140i
\(59\) 111.526 36.2371i 1.89028 0.614188i 0.910720 0.413025i \(-0.135528\pi\)
0.979558 0.201164i \(-0.0644723\pi\)
\(60\) 0 0
\(61\) −65.8779 + 47.8631i −1.07997 + 0.784641i −0.977677 0.210114i \(-0.932616\pi\)
−0.102288 + 0.994755i \(0.532616\pi\)
\(62\) −14.7509 + 4.79287i −0.237918 + 0.0773043i
\(63\) 0 0
\(64\) −6.93357 5.03753i −0.108337 0.0787115i
\(65\) 8.06643i 0.124099i
\(66\) 0 0
\(67\) 70.1488 1.04700 0.523499 0.852027i \(-0.324627\pi\)
0.523499 + 0.852027i \(0.324627\pi\)
\(68\) 18.4017 25.3278i 0.270614 0.372468i
\(69\) 0 0
\(70\) 1.80471 + 5.55434i 0.0257816 + 0.0793477i
\(71\) 25.4295 + 35.0007i 0.358162 + 0.492968i 0.949636 0.313356i \(-0.101453\pi\)
−0.591473 + 0.806325i \(0.701453\pi\)
\(72\) 0 0
\(73\) 14.1852 + 43.6575i 0.194318 + 0.598048i 0.999984 + 0.00567825i \(0.00180745\pi\)
−0.805666 + 0.592370i \(0.798193\pi\)
\(74\) −36.6478 11.9076i −0.495241 0.160914i
\(75\) 0 0
\(76\) 31.3980 0.413131
\(77\) 74.9033 5.87008i 0.972771 0.0762348i
\(78\) 0 0
\(79\) 69.3955 + 50.4188i 0.878424 + 0.638212i 0.932834 0.360306i \(-0.117328\pi\)
−0.0544101 + 0.998519i \(0.517328\pi\)
\(80\) −8.40497 2.73094i −0.105062 0.0341367i
\(81\) 0 0
\(82\) 5.02191 3.64863i 0.0612428 0.0444955i
\(83\) −93.5371 128.743i −1.12695 1.55112i −0.793731 0.608269i \(-0.791864\pi\)
−0.333222 0.942848i \(-0.608136\pi\)
\(84\) 0 0
\(85\) 3.03890 9.35276i 0.0357517 0.110033i
\(86\) 24.3308 33.4884i 0.282916 0.389400i
\(87\) 0 0
\(88\) 34.4391 56.1578i 0.391353 0.638157i
\(89\) 154.015i 1.73051i 0.501335 + 0.865253i \(0.332842\pi\)
−0.501335 + 0.865253i \(0.667158\pi\)
\(90\) 0 0
\(91\) −16.2619 + 50.0489i −0.178702 + 0.549987i
\(92\) −15.2918 + 4.96862i −0.166216 + 0.0540067i
\(93\) 0 0
\(94\) −43.7040 + 31.7528i −0.464936 + 0.337796i
\(95\) 9.37997 3.04774i 0.0987366 0.0320815i
\(96\) 0 0
\(97\) −124.151 90.2007i −1.27990 0.929904i −0.280353 0.959897i \(-0.590451\pi\)
−0.999550 + 0.0299934i \(0.990451\pi\)
\(98\) 1.91708i 0.0195621i
\(99\) 0 0
\(100\) 79.6720 0.796720
\(101\) −92.2112 + 126.918i −0.912982 + 1.25661i 0.0531554 + 0.998586i \(0.483072\pi\)
−0.966138 + 0.258026i \(0.916928\pi\)
\(102\) 0 0
\(103\) −19.5863 60.2804i −0.190158 0.585246i 0.809841 0.586649i \(-0.199553\pi\)
−0.999999 + 0.00140322i \(0.999553\pi\)
\(104\) 27.1212 + 37.3291i 0.260780 + 0.358933i
\(105\) 0 0
\(106\) −9.69379 29.8344i −0.0914508 0.281457i
\(107\) 48.9872 + 15.9169i 0.457824 + 0.148756i 0.528844 0.848719i \(-0.322626\pi\)
−0.0710204 + 0.997475i \(0.522626\pi\)
\(108\) 0 0
\(109\) −63.0507 −0.578446 −0.289223 0.957262i \(-0.593397\pi\)
−0.289223 + 0.957262i \(0.593397\pi\)
\(110\) 2.19869 9.14487i 0.0199881 0.0831352i
\(111\) 0 0
\(112\) −46.6438 33.8887i −0.416463 0.302578i
\(113\) −82.5291 26.8153i −0.730346 0.237304i −0.0798430 0.996807i \(-0.525442\pi\)
−0.650503 + 0.759504i \(0.725442\pi\)
\(114\) 0 0
\(115\) −4.08606 + 2.96869i −0.0355309 + 0.0258147i
\(116\) −91.5995 126.076i −0.789651 1.08686i
\(117\) 0 0
\(118\) 29.5945 91.0824i 0.250801 0.771885i
\(119\) 37.7102 51.9037i 0.316893 0.436165i
\(120\) 0 0
\(121\) −107.775 55.0042i −0.890706 0.454580i
\(122\) 66.5026i 0.545103i
\(123\) 0 0
\(124\) 19.5603 60.2005i 0.157745 0.485488i
\(125\) 48.6946 15.8218i 0.389557 0.126575i
\(126\) 0 0
\(127\) −61.2042 + 44.4675i −0.481923 + 0.350138i −0.802070 0.597230i \(-0.796268\pi\)
0.320147 + 0.947368i \(0.396268\pi\)
\(128\) −124.013 + 40.2943i −0.968852 + 0.314799i
\(129\) 0 0
\(130\) 5.32961 + 3.87219i 0.0409970 + 0.0297861i
\(131\) 124.201i 0.948097i 0.880499 + 0.474049i \(0.157208\pi\)
−0.880499 + 0.474049i \(0.842792\pi\)
\(132\) 0 0
\(133\) 64.3431 0.483783
\(134\) 33.6741 46.3484i 0.251299 0.345884i
\(135\) 0 0
\(136\) −17.3830 53.4993i −0.127816 0.393377i
\(137\) −31.2464 43.0070i −0.228076 0.313920i 0.679607 0.733577i \(-0.262150\pi\)
−0.907683 + 0.419657i \(0.862150\pi\)
\(138\) 0 0
\(139\) 24.4299 + 75.1874i 0.175754 + 0.540917i 0.999667 0.0258002i \(-0.00821337\pi\)
−0.823913 + 0.566717i \(0.808213\pi\)
\(140\) −22.6680 7.36528i −0.161914 0.0526092i
\(141\) 0 0
\(142\) 35.3327 0.248822
\(143\) 64.4630 55.0198i 0.450790 0.384754i
\(144\) 0 0
\(145\) −39.6028 28.7731i −0.273123 0.198435i
\(146\) 35.6546 + 11.5849i 0.244210 + 0.0793485i
\(147\) 0 0
\(148\) 127.227 92.4361i 0.859644 0.624568i
\(149\) 12.7700 + 17.5764i 0.0857045 + 0.117962i 0.849716 0.527240i \(-0.176773\pi\)
−0.764012 + 0.645202i \(0.776773\pi\)
\(150\) 0 0
\(151\) −38.3457 + 118.016i −0.253945 + 0.781563i 0.740091 + 0.672507i \(0.234783\pi\)
−0.994036 + 0.109055i \(0.965217\pi\)
\(152\) 33.1606 45.6416i 0.218162 0.300274i
\(153\) 0 0
\(154\) 32.0780 52.3076i 0.208299 0.339660i
\(155\) 19.8833i 0.128279i
\(156\) 0 0
\(157\) −55.9981 + 172.344i −0.356676 + 1.09774i 0.598356 + 0.801231i \(0.295821\pi\)
−0.955031 + 0.296505i \(0.904179\pi\)
\(158\) 66.6249 21.6478i 0.421677 0.137011i
\(159\) 0 0
\(160\) −26.1294 + 18.9841i −0.163309 + 0.118651i
\(161\) −31.3372 + 10.1821i −0.194641 + 0.0632426i
\(162\) 0 0
\(163\) 223.913 + 162.683i 1.37370 + 0.998053i 0.997438 + 0.0715405i \(0.0227915\pi\)
0.376264 + 0.926512i \(0.377208\pi\)
\(164\) 25.3333i 0.154472i
\(165\) 0 0
\(166\) −129.964 −0.782914
\(167\) −32.0565 + 44.1220i −0.191955 + 0.264204i −0.894136 0.447795i \(-0.852210\pi\)
0.702181 + 0.711998i \(0.252210\pi\)
\(168\) 0 0
\(169\) −33.8804 104.273i −0.200476 0.617000i
\(170\) −4.72073 6.49753i −0.0277690 0.0382208i
\(171\) 0 0
\(172\) 52.2036 + 160.666i 0.303509 + 0.934106i
\(173\) 95.8015 + 31.1278i 0.553766 + 0.179929i 0.572514 0.819895i \(-0.305968\pi\)
−0.0187484 + 0.999824i \(0.505968\pi\)
\(174\) 0 0
\(175\) 163.270 0.932971
\(176\) 35.5045 + 85.7958i 0.201730 + 0.487476i
\(177\) 0 0
\(178\) 101.760 + 73.9331i 0.571686 + 0.415354i
\(179\) 77.8279 + 25.2878i 0.434793 + 0.141273i 0.518232 0.855240i \(-0.326590\pi\)
−0.0834391 + 0.996513i \(0.526590\pi\)
\(180\) 0 0
\(181\) −164.876 + 119.789i −0.910915 + 0.661818i −0.941246 0.337722i \(-0.890344\pi\)
0.0303313 + 0.999540i \(0.490344\pi\)
\(182\) 25.2617 + 34.7698i 0.138801 + 0.191043i
\(183\) 0 0
\(184\) −8.92766 + 27.4765i −0.0485199 + 0.149329i
\(185\) 29.0359 39.9645i 0.156951 0.216024i
\(186\) 0 0
\(187\) −95.4707 + 39.5082i −0.510538 + 0.211274i
\(188\) 220.468i 1.17270i
\(189\) 0 0
\(190\) 2.48905 7.66052i 0.0131003 0.0403185i
\(191\) 191.865 62.3406i 1.00453 0.326390i 0.239854 0.970809i \(-0.422901\pi\)
0.764673 + 0.644419i \(0.222901\pi\)
\(192\) 0 0
\(193\) 184.461 134.019i 0.955755 0.694397i 0.00359389 0.999994i \(-0.498856\pi\)
0.952161 + 0.305597i \(0.0988560\pi\)
\(194\) −119.194 + 38.7285i −0.614402 + 0.199631i
\(195\) 0 0
\(196\) 6.32964 + 4.59875i 0.0322941 + 0.0234630i
\(197\) 170.096i 0.863429i 0.902010 + 0.431715i \(0.142091\pi\)
−0.902010 + 0.431715i \(0.857909\pi\)
\(198\) 0 0
\(199\) 143.997 0.723602 0.361801 0.932255i \(-0.382162\pi\)
0.361801 + 0.932255i \(0.382162\pi\)
\(200\) 84.1446 115.815i 0.420723 0.579076i
\(201\) 0 0
\(202\) 39.5917 + 121.851i 0.195999 + 0.603222i
\(203\) −187.713 258.364i −0.924692 1.27273i
\(204\) 0 0
\(205\) 2.45905 + 7.56819i 0.0119954 + 0.0369180i
\(206\) −49.2303 15.9959i −0.238982 0.0776500i
\(207\) 0 0
\(208\) −65.0352 −0.312669
\(209\) −88.3353 54.1722i −0.422657 0.259197i
\(210\) 0 0
\(211\) −97.3640 70.7391i −0.461441 0.335256i 0.332655 0.943048i \(-0.392055\pi\)
−0.794096 + 0.607792i \(0.792055\pi\)
\(212\) 121.758 + 39.5617i 0.574331 + 0.186612i
\(213\) 0 0
\(214\) 34.0322 24.7259i 0.159029 0.115541i
\(215\) 31.1911 + 42.9308i 0.145075 + 0.199678i
\(216\) 0 0
\(217\) 40.0845 123.367i 0.184721 0.568514i
\(218\) −30.2667 + 41.6585i −0.138838 + 0.191094i
\(219\) 0 0
\(220\) 24.9194 + 29.1964i 0.113270 + 0.132711i
\(221\) 72.3689i 0.327461i
\(222\) 0 0
\(223\) 33.5784 103.344i 0.150576 0.463424i −0.847110 0.531417i \(-0.821660\pi\)
0.997686 + 0.0679933i \(0.0216597\pi\)
\(224\) −200.394 + 65.1119i −0.894616 + 0.290678i
\(225\) 0 0
\(226\) −57.3344 + 41.6559i −0.253692 + 0.184318i
\(227\) 201.524 65.4790i 0.887770 0.288454i 0.170590 0.985342i \(-0.445433\pi\)
0.717180 + 0.696888i \(0.245433\pi\)
\(228\) 0 0
\(229\) −225.228 163.638i −0.983528 0.714575i −0.0250334 0.999687i \(-0.507969\pi\)
−0.958494 + 0.285112i \(0.907969\pi\)
\(230\) 4.12481i 0.0179339i
\(231\) 0 0
\(232\) −280.012 −1.20695
\(233\) −111.143 + 152.976i −0.477010 + 0.656548i −0.977927 0.208948i \(-0.932996\pi\)
0.500917 + 0.865495i \(0.332996\pi\)
\(234\) 0 0
\(235\) −21.4003 65.8635i −0.0910653 0.280270i
\(236\) 229.735 + 316.203i 0.973455 + 1.33985i
\(237\) 0 0
\(238\) −16.1912 49.8315i −0.0680303 0.209376i
\(239\) −84.4525 27.4403i −0.353358 0.114813i 0.126959 0.991908i \(-0.459478\pi\)
−0.480317 + 0.877095i \(0.659478\pi\)
\(240\) 0 0
\(241\) −155.144 −0.643750 −0.321875 0.946782i \(-0.604313\pi\)
−0.321875 + 0.946782i \(0.604313\pi\)
\(242\) −88.0784 + 44.8048i −0.363960 + 0.185144i
\(243\) 0 0
\(244\) −219.572 159.529i −0.899886 0.653805i
\(245\) 2.33734 + 0.759447i 0.00954015 + 0.00309978i
\(246\) 0 0
\(247\) 58.7180 42.6611i 0.237725 0.172717i
\(248\) −66.8520 92.0139i −0.269565 0.371024i
\(249\) 0 0
\(250\) 12.9215 39.7684i 0.0516861 0.159073i
\(251\) −176.164 + 242.469i −0.701848 + 0.966011i 0.298086 + 0.954539i \(0.403652\pi\)
−0.999934 + 0.0114720i \(0.996348\pi\)
\(252\) 0 0
\(253\) 51.5947 + 12.4049i 0.203932 + 0.0490310i
\(254\) 61.7847i 0.243247i
\(255\) 0 0
\(256\) −22.3144 + 68.6765i −0.0871655 + 0.268268i
\(257\) −352.243 + 114.451i −1.37060 + 0.445334i −0.899567 0.436784i \(-0.856118\pi\)
−0.471030 + 0.882117i \(0.656118\pi\)
\(258\) 0 0
\(259\) 260.724 189.427i 1.00666 0.731378i
\(260\) −25.5697 + 8.30809i −0.0983449 + 0.0319542i
\(261\) 0 0
\(262\) 82.0613 + 59.6210i 0.313211 + 0.227561i
\(263\) 351.921i 1.33810i −0.743217 0.669050i \(-0.766701\pi\)
0.743217 0.669050i \(-0.233299\pi\)
\(264\) 0 0
\(265\) 40.2148 0.151754
\(266\) 30.8871 42.5125i 0.116117 0.159821i
\(267\) 0 0
\(268\) 72.2504 + 222.364i 0.269591 + 0.829716i
\(269\) −90.0689 123.969i −0.334828 0.460852i 0.608094 0.793865i \(-0.291935\pi\)
−0.942922 + 0.333013i \(0.891935\pi\)
\(270\) 0 0
\(271\) −112.596 346.534i −0.415482 1.27872i −0.911819 0.410592i \(-0.865322\pi\)
0.496337 0.868130i \(-0.334678\pi\)
\(272\) 75.4062 + 24.5010i 0.277229 + 0.0900771i
\(273\) 0 0
\(274\) −43.4148 −0.158448
\(275\) −224.150 137.461i −0.815091 0.499859i
\(276\) 0 0
\(277\) 169.024 + 122.803i 0.610196 + 0.443333i 0.849483 0.527616i \(-0.176914\pi\)
−0.239287 + 0.970949i \(0.576914\pi\)
\(278\) 61.4047 + 19.9516i 0.220880 + 0.0717684i
\(279\) 0 0
\(280\) −34.6471 + 25.1726i −0.123740 + 0.0899020i
\(281\) 278.880 + 383.845i 0.992456 + 1.36600i 0.929842 + 0.367960i \(0.119944\pi\)
0.0626142 + 0.998038i \(0.480056\pi\)
\(282\) 0 0
\(283\) 53.4233 164.420i 0.188775 0.580989i −0.811218 0.584744i \(-0.801195\pi\)
0.999993 + 0.00375459i \(0.00119513\pi\)
\(284\) −84.7571 + 116.658i −0.298440 + 0.410768i
\(285\) 0 0
\(286\) −5.40770 69.0033i −0.0189081 0.241270i
\(287\) 51.9150i 0.180888i
\(288\) 0 0
\(289\) 62.0421 190.946i 0.214678 0.660712i
\(290\) −38.0217 + 12.3540i −0.131109 + 0.0425999i
\(291\) 0 0
\(292\) −123.779 + 89.9309i −0.423902 + 0.307983i
\(293\) 361.681 117.517i 1.23441 0.401083i 0.382098 0.924122i \(-0.375202\pi\)
0.852309 + 0.523039i \(0.175202\pi\)
\(294\) 0 0
\(295\) 99.3254 + 72.1641i 0.336696 + 0.244624i
\(296\) 282.569i 0.954625i
\(297\) 0 0
\(298\) 17.7430 0.0595404
\(299\) −21.8466 + 30.0693i −0.0730656 + 0.100566i
\(300\) 0 0
\(301\) 106.980 + 329.249i 0.355414 + 1.09385i
\(302\) 59.5676 + 81.9877i 0.197244 + 0.271483i
\(303\) 0 0
\(304\) 24.5722 + 75.6256i 0.0808298 + 0.248768i
\(305\) −81.0811 26.3448i −0.265840 0.0863765i
\(306\) 0 0
\(307\) −343.458 −1.11876 −0.559378 0.828912i \(-0.688960\pi\)
−0.559378 + 0.828912i \(0.688960\pi\)
\(308\) 95.7549 + 231.389i 0.310893 + 0.751264i
\(309\) 0 0
\(310\) −13.1372 9.54472i −0.0423780 0.0307894i
\(311\) −173.651 56.4225i −0.558362 0.181423i 0.0162221 0.999868i \(-0.494836\pi\)
−0.574584 + 0.818446i \(0.694836\pi\)
\(312\) 0 0
\(313\) 50.5840 36.7514i 0.161610 0.117417i −0.504041 0.863680i \(-0.668154\pi\)
0.665651 + 0.746263i \(0.268154\pi\)
\(314\) 86.9894 + 119.731i 0.277036 + 0.381308i
\(315\) 0 0
\(316\) −88.3474 + 271.905i −0.279580 + 0.860460i
\(317\) 114.353 157.393i 0.360734 0.496508i −0.589619 0.807681i \(-0.700722\pi\)
0.950353 + 0.311174i \(0.100722\pi\)
\(318\) 0 0
\(319\) 40.1830 + 512.743i 0.125966 + 1.60734i
\(320\) 8.97285i 0.0280402i
\(321\) 0 0
\(322\) −8.31558 + 25.5927i −0.0258248 + 0.0794805i
\(323\) −84.1536 + 27.3432i −0.260537 + 0.0846538i
\(324\) 0 0
\(325\) 148.996 108.252i 0.458450 0.333084i
\(326\) 214.974 69.8492i 0.659429 0.214261i
\(327\) 0 0
\(328\) 36.8258 + 26.7555i 0.112274 + 0.0815716i
\(329\) 451.799i 1.37325i
\(330\) 0 0
\(331\) −17.6498 −0.0533226 −0.0266613 0.999645i \(-0.508488\pi\)
−0.0266613 + 0.999645i \(0.508488\pi\)
\(332\) 311.761 429.102i 0.939039 1.29248i
\(333\) 0 0
\(334\) 13.7637 + 42.3605i 0.0412088 + 0.126828i
\(335\) 43.1688 + 59.4168i 0.128862 + 0.177364i
\(336\) 0 0
\(337\) −135.935 418.364i −0.403367 1.24144i −0.922251 0.386592i \(-0.873652\pi\)
0.518884 0.854845i \(-0.326348\pi\)
\(338\) −85.1587 27.6697i −0.251949 0.0818631i
\(339\) 0 0
\(340\) 32.7772 0.0964034
\(341\) −158.898 + 135.620i −0.465975 + 0.397714i
\(342\) 0 0
\(343\) 283.736 + 206.146i 0.827218 + 0.601009i
\(344\) 288.686 + 93.7999i 0.839205 + 0.272674i
\(345\) 0 0
\(346\) 66.5550 48.3550i 0.192355 0.139754i
\(347\) 239.758 + 329.998i 0.690944 + 0.951003i 1.00000 4.11136e-5i \(-1.30869e-5\pi\)
−0.309056 + 0.951044i \(0.600013\pi\)
\(348\) 0 0
\(349\) −147.852 + 455.042i −0.423645 + 1.30385i 0.480640 + 0.876918i \(0.340404\pi\)
−0.904286 + 0.426928i \(0.859596\pi\)
\(350\) 78.3757 107.875i 0.223931 0.308214i
\(351\) 0 0
\(352\) 329.936 + 79.3261i 0.937318 + 0.225358i
\(353\) 551.674i 1.56282i −0.624020 0.781409i \(-0.714502\pi\)
0.624020 0.781409i \(-0.285498\pi\)
\(354\) 0 0
\(355\) −13.9969 + 43.0782i −0.0394280 + 0.121347i
\(356\) −488.211 + 158.629i −1.37138 + 0.445588i
\(357\) 0 0
\(358\) 54.0684 39.2830i 0.151029 0.109729i
\(359\) 340.459 110.622i 0.948354 0.308139i 0.206308 0.978487i \(-0.433855\pi\)
0.742047 + 0.670348i \(0.233855\pi\)
\(360\) 0 0
\(361\) 220.262 + 160.029i 0.610143 + 0.443295i
\(362\) 166.439i 0.459777i
\(363\) 0 0
\(364\) −175.398 −0.481864
\(365\) −28.2490 + 38.8814i −0.0773944 + 0.106524i
\(366\) 0 0
\(367\) −32.6507 100.489i −0.0889666 0.273811i 0.896668 0.442704i \(-0.145981\pi\)
−0.985634 + 0.168893i \(0.945981\pi\)
\(368\) −23.9350 32.9436i −0.0650407 0.0895208i
\(369\) 0 0
\(370\) −12.4668 38.3689i −0.0336941 0.103700i
\(371\) 249.516 + 81.0727i 0.672550 + 0.218525i
\(372\) 0 0
\(373\) 483.127 1.29525 0.647623 0.761961i \(-0.275763\pi\)
0.647623 + 0.761961i \(0.275763\pi\)
\(374\) −19.7258 + 82.0444i −0.0527429 + 0.219370i
\(375\) 0 0
\(376\) −320.482 232.844i −0.852347 0.619266i
\(377\) −342.604 111.319i −0.908765 0.295276i
\(378\) 0 0
\(379\) −362.665 + 263.492i −0.956901 + 0.695229i −0.952429 0.304761i \(-0.901423\pi\)
−0.00447174 + 0.999990i \(0.501423\pi\)
\(380\) 19.3220 + 26.5944i 0.0508473 + 0.0699853i
\(381\) 0 0
\(382\) 50.9129 156.694i 0.133280 0.410193i
\(383\) −281.976 + 388.106i −0.736229 + 1.01333i 0.262598 + 0.964905i \(0.415421\pi\)
−0.998827 + 0.0484270i \(0.984579\pi\)
\(384\) 0 0
\(385\) 51.0667 + 59.8315i 0.132641 + 0.155407i
\(386\) 186.210i 0.482409i
\(387\) 0 0
\(388\) 158.056 486.447i 0.407361 1.25373i
\(389\) 289.807 94.1639i 0.745005 0.242067i 0.0881743 0.996105i \(-0.471897\pi\)
0.656830 + 0.754038i \(0.271897\pi\)
\(390\) 0 0
\(391\) 36.6586 26.6340i 0.0937560 0.0681177i
\(392\) 13.3699 4.34416i 0.0341070 0.0110820i
\(393\) 0 0
\(394\) 112.385 + 81.6523i 0.285241 + 0.207239i
\(395\) 89.8059i 0.227357i
\(396\) 0 0
\(397\) −433.795 −1.09268 −0.546342 0.837562i \(-0.683980\pi\)
−0.546342 + 0.837562i \(0.683980\pi\)
\(398\) 69.1239 95.1409i 0.173678 0.239048i
\(399\) 0 0
\(400\) 62.3518 + 191.899i 0.155880 + 0.479748i
\(401\) −31.3201 43.1084i −0.0781050 0.107502i 0.768177 0.640238i \(-0.221164\pi\)
−0.846282 + 0.532735i \(0.821164\pi\)
\(402\) 0 0
\(403\) −45.2156 139.159i −0.112198 0.345309i
\(404\) −497.289 161.579i −1.23091 0.399948i
\(405\) 0 0
\(406\) −260.814 −0.642400
\(407\) −517.426 + 40.5500i −1.27132 + 0.0996315i
\(408\) 0 0
\(409\) 96.8500 + 70.3657i 0.236797 + 0.172043i 0.699855 0.714285i \(-0.253248\pi\)
−0.463058 + 0.886328i \(0.653248\pi\)
\(410\) 6.18086 + 2.00828i 0.0150753 + 0.00489825i
\(411\) 0 0
\(412\) 170.909 124.173i 0.414828 0.301390i
\(413\) 470.791 + 647.988i 1.13993 + 1.56898i
\(414\) 0 0
\(415\) 51.4848 158.454i 0.124060 0.381816i
\(416\) −139.704 + 192.286i −0.335827 + 0.462226i
\(417\) 0 0
\(418\) −78.1967 + 32.3598i −0.187073 + 0.0774158i
\(419\) 165.561i 0.395133i 0.980289 + 0.197566i \(0.0633038\pi\)
−0.980289 + 0.197566i \(0.936696\pi\)
\(420\) 0 0
\(421\) −1.17216 + 3.60755i −0.00278424 + 0.00856901i −0.952439 0.304729i \(-0.901434\pi\)
0.949655 + 0.313298i \(0.101434\pi\)
\(422\) −93.4768 + 30.3725i −0.221509 + 0.0719726i
\(423\) 0 0
\(424\) 186.102 135.211i 0.438920 0.318894i
\(425\) −213.539 + 69.3830i −0.502444 + 0.163254i
\(426\) 0 0
\(427\) −449.964 326.918i −1.05378 0.765615i
\(428\) 171.678i 0.401116i
\(429\) 0 0
\(430\) 43.3380 0.100786
\(431\) −90.8780 + 125.083i −0.210854 + 0.290215i −0.901324 0.433145i \(-0.857404\pi\)
0.690470 + 0.723361i \(0.257404\pi\)
\(432\) 0 0
\(433\) −82.0387 252.489i −0.189466 0.583116i 0.810531 0.585696i \(-0.199179\pi\)
−0.999997 + 0.00258002i \(0.999179\pi\)
\(434\) −62.2687 85.7055i −0.143476 0.197478i
\(435\) 0 0
\(436\) −64.9396 199.864i −0.148944 0.458403i
\(437\) 43.2201 + 14.0431i 0.0989019 + 0.0321352i
\(438\) 0 0
\(439\) −716.385 −1.63186 −0.815928 0.578153i \(-0.803774\pi\)
−0.815928 + 0.578153i \(0.803774\pi\)
\(440\) 68.7597 5.38861i 0.156272 0.0122469i
\(441\) 0 0
\(442\) −47.8153 34.7398i −0.108179 0.0785969i
\(443\) 39.7219 + 12.9064i 0.0896657 + 0.0291342i 0.353506 0.935432i \(-0.384989\pi\)
−0.263841 + 0.964566i \(0.584989\pi\)
\(444\) 0 0
\(445\) −130.452 + 94.7793i −0.293152 + 0.212987i
\(446\) −52.1618 71.7945i −0.116955 0.160974i
\(447\) 0 0
\(448\) 18.0892 55.6729i 0.0403777 0.124270i
\(449\) −156.198 + 214.988i −0.347880 + 0.478815i −0.946722 0.322052i \(-0.895628\pi\)
0.598843 + 0.800867i \(0.295628\pi\)
\(450\) 0 0
\(451\) 43.7086 71.2730i 0.0969148 0.158033i
\(452\) 289.227i 0.639882i
\(453\) 0 0
\(454\) 53.4760 164.582i 0.117789 0.362516i
\(455\) −52.3993 + 17.0256i −0.115163 + 0.0374188i
\(456\) 0 0
\(457\) 346.228 251.549i 0.757609 0.550435i −0.140567 0.990071i \(-0.544892\pi\)
0.898176 + 0.439636i \(0.144892\pi\)
\(458\) −216.236 + 70.2593i −0.472130 + 0.153404i
\(459\) 0 0
\(460\) −13.6189 9.89471i −0.0296063 0.0215102i
\(461\) 313.392i 0.679809i −0.940460 0.339904i \(-0.889605\pi\)
0.940460 0.339904i \(-0.110395\pi\)
\(462\) 0 0
\(463\) −529.774 −1.14422 −0.572110 0.820177i \(-0.693875\pi\)
−0.572110 + 0.820177i \(0.693875\pi\)
\(464\) 231.982 319.295i 0.499961 0.688137i
\(465\) 0 0
\(466\) 47.7204 + 146.868i 0.102404 + 0.315168i
\(467\) −40.7515 56.0896i −0.0872623 0.120106i 0.763154 0.646217i \(-0.223650\pi\)
−0.850416 + 0.526111i \(0.823650\pi\)
\(468\) 0 0
\(469\) 148.061 + 455.685i 0.315695 + 0.971610i
\(470\) −53.7900 17.4774i −0.114447 0.0371860i
\(471\) 0 0
\(472\) 702.281 1.48788
\(473\) 130.334 542.088i 0.275547 1.14606i
\(474\) 0 0
\(475\) −182.175 132.358i −0.383527 0.278649i
\(476\) 203.369 + 66.0786i 0.427246 + 0.138820i
\(477\) 0 0
\(478\) −58.6706 + 42.6267i −0.122742 + 0.0891772i
\(479\) 12.2496 + 16.8601i 0.0255732 + 0.0351985i 0.821612 0.570047i \(-0.193075\pi\)
−0.796039 + 0.605245i \(0.793075\pi\)
\(480\) 0 0
\(481\) 112.336 345.733i 0.233546 0.718780i
\(482\) −74.4749 + 102.506i −0.154512 + 0.212668i
\(483\) 0 0
\(484\) 63.3529 398.288i 0.130894 0.822909i
\(485\) 160.665i 0.331269i
\(486\) 0 0
\(487\) 25.7159 79.1453i 0.0528047 0.162516i −0.921176 0.389145i \(-0.872770\pi\)
0.973981 + 0.226629i \(0.0727705\pi\)
\(488\) −463.797 + 150.697i −0.950403 + 0.308805i
\(489\) 0 0
\(490\) 1.62379 1.17975i 0.00331385 0.00240766i
\(491\) 92.5446 30.0696i 0.188482 0.0612415i −0.213255 0.976997i \(-0.568407\pi\)
0.401737 + 0.915755i \(0.368407\pi\)
\(492\) 0 0
\(493\) 355.301 + 258.141i 0.720692 + 0.523613i
\(494\) 59.2749i 0.119990i
\(495\) 0 0
\(496\) 160.308 0.323201
\(497\) −173.691 + 239.065i −0.349478 + 0.481015i
\(498\) 0 0
\(499\) 94.0553 + 289.473i 0.188488 + 0.580105i 0.999991 0.00424242i \(-0.00135041\pi\)
−0.811503 + 0.584348i \(0.801350\pi\)
\(500\) 100.307 + 138.061i 0.200614 + 0.276121i
\(501\) 0 0
\(502\) 75.6375 + 232.788i 0.150672 + 0.463722i
\(503\) 675.460 + 219.470i 1.34286 + 0.436323i 0.890286 0.455402i \(-0.150505\pi\)
0.452577 + 0.891725i \(0.350505\pi\)
\(504\) 0 0
\(505\) −164.247 −0.325241
\(506\) 32.9635 28.1346i 0.0651452 0.0556020i
\(507\) 0 0
\(508\) −203.995 148.211i −0.401565 0.291754i
\(509\) 720.939 + 234.247i 1.41638 + 0.460211i 0.914451 0.404696i \(-0.132623\pi\)
0.501933 + 0.864907i \(0.332623\pi\)
\(510\) 0 0
\(511\) −253.658 + 184.293i −0.496395 + 0.360652i
\(512\) −271.913 374.257i −0.531081 0.730970i
\(513\) 0 0
\(514\) −93.4707 + 287.673i −0.181850 + 0.559676i
\(515\) 39.0049 53.6857i 0.0757377 0.104244i
\(516\) 0 0
\(517\) −380.381 + 620.265i −0.735747 + 1.19974i
\(518\) 263.196i 0.508101i
\(519\) 0 0
\(520\) −14.9281 + 45.9438i −0.0287078 + 0.0883535i
\(521\) 257.644 83.7137i 0.494519 0.160679i −0.0511313 0.998692i \(-0.516283\pi\)
0.545650 + 0.838013i \(0.316283\pi\)
\(522\) 0 0
\(523\) −245.189 + 178.141i −0.468814 + 0.340613i −0.796979 0.604007i \(-0.793570\pi\)
0.328165 + 0.944620i \(0.393570\pi\)
\(524\) −393.702 + 127.922i −0.751341 + 0.244125i
\(525\) 0 0
\(526\) −232.519 168.935i −0.442052 0.321170i
\(527\) 178.385i 0.338492i
\(528\) 0 0
\(529\) 505.728 0.956008
\(530\) 19.3046 26.5705i 0.0364238 0.0501331i
\(531\) 0 0
\(532\) 66.2708 + 203.961i 0.124569 + 0.383384i
\(533\) 34.4210 + 47.3764i 0.0645797 + 0.0888863i
\(534\) 0 0
\(535\) 16.6644 + 51.2877i 0.0311484 + 0.0958649i
\(536\) 399.545 + 129.820i 0.745421 + 0.242202i
\(537\) 0 0
\(538\) −125.145 −0.232611
\(539\) −9.87345 23.8589i −0.0183181 0.0442652i
\(540\) 0 0
\(541\) 840.309 + 610.520i 1.55325 + 1.12850i 0.941282 + 0.337622i \(0.109622\pi\)
0.611969 + 0.790881i \(0.290378\pi\)
\(542\) −283.010 91.9556i −0.522159 0.169660i
\(543\) 0 0
\(544\) 234.423 170.318i 0.430925 0.313085i
\(545\) −38.8007 53.4046i −0.0711939 0.0979901i
\(546\) 0 0
\(547\) 91.8203 282.594i 0.167862 0.516625i −0.831374 0.555713i \(-0.812445\pi\)
0.999236 + 0.0390882i \(0.0124453\pi\)
\(548\) 104.145 143.343i 0.190045 0.261575i
\(549\) 0 0
\(550\) −198.423 + 82.1127i −0.360770 + 0.149296i
\(551\) 440.454i 0.799372i
\(552\) 0 0
\(553\) −181.048 + 557.209i −0.327393 + 1.00761i
\(554\) 162.276 52.7267i 0.292917 0.0951745i
\(555\) 0 0
\(556\) −213.174 + 154.880i −0.383406 + 0.278561i
\(557\) 507.507 164.899i 0.911144 0.296049i 0.184315 0.982867i \(-0.440993\pi\)
0.726829 + 0.686819i \(0.240993\pi\)
\(558\) 0 0
\(559\) 315.928 + 229.535i 0.565166 + 0.410617i
\(560\) 60.3626i 0.107790i
\(561\) 0 0
\(562\) 387.486 0.689476
\(563\) −124.319 + 171.110i −0.220814 + 0.303925i −0.905024 0.425360i \(-0.860147\pi\)
0.684210 + 0.729285i \(0.260147\pi\)
\(564\) 0 0
\(565\) −28.0747 86.4049i −0.0496897 0.152929i
\(566\) −82.9896 114.225i −0.146625 0.201812i
\(567\) 0 0
\(568\) 80.0648 + 246.414i 0.140959 + 0.433828i
\(569\) −686.408 223.027i −1.20634 0.391964i −0.364250 0.931301i \(-0.618675\pi\)
−0.842090 + 0.539337i \(0.818675\pi\)
\(570\) 0 0
\(571\) 798.387 1.39823 0.699113 0.715011i \(-0.253578\pi\)
0.699113 + 0.715011i \(0.253578\pi\)
\(572\) 240.801 + 147.673i 0.420980 + 0.258169i
\(573\) 0 0
\(574\) 34.3010 + 24.9211i 0.0597579 + 0.0434166i
\(575\) 109.671 + 35.6341i 0.190731 + 0.0619724i
\(576\) 0 0
\(577\) 476.899 346.488i 0.826515 0.600498i −0.0920561 0.995754i \(-0.529344\pi\)
0.918571 + 0.395255i \(0.129344\pi\)
\(578\) −96.3783 132.653i −0.166745 0.229504i
\(579\) 0 0
\(580\) 50.4183 155.172i 0.0869281 0.267537i
\(581\) 638.884 879.348i 1.09963 1.51351i
\(582\) 0 0
\(583\) −274.298 321.377i −0.470494 0.551247i
\(584\) 274.911i 0.470738i
\(585\) 0 0
\(586\) 95.9752 295.381i 0.163780 0.504063i
\(587\) 120.102 39.0236i 0.204604 0.0664798i −0.204922 0.978778i \(-0.565694\pi\)
0.409526 + 0.912298i \(0.365694\pi\)
\(588\) 0 0
\(589\) −144.736 + 105.157i −0.245733 + 0.178535i
\(590\) 95.3599 30.9843i 0.161627 0.0525158i
\(591\) 0 0
\(592\) 322.212 + 234.100i 0.544276 + 0.395440i
\(593\) 447.206i 0.754141i 0.926185 + 0.377071i \(0.123069\pi\)
−0.926185 + 0.377071i \(0.876931\pi\)
\(594\) 0 0
\(595\) 67.1694 0.112890
\(596\) −42.5626 + 58.5823i −0.0714137 + 0.0982925i
\(597\) 0 0
\(598\) 9.38004 + 28.8688i 0.0156857 + 0.0482756i
\(599\) −385.750 530.940i −0.643990 0.886377i 0.354830 0.934931i \(-0.384539\pi\)
−0.998821 + 0.0485540i \(0.984539\pi\)
\(600\) 0 0
\(601\) −61.9808 190.757i −0.103129 0.317400i 0.886157 0.463384i \(-0.153365\pi\)
−0.989287 + 0.145985i \(0.953365\pi\)
\(602\) 268.894 + 87.3690i 0.446668 + 0.145131i
\(603\) 0 0
\(604\) −413.592 −0.684755
\(605\) −19.7347 125.136i −0.0326193 0.206836i
\(606\) 0 0
\(607\) −734.383 533.561i −1.20986 0.879013i −0.214640 0.976693i \(-0.568858\pi\)
−0.995218 + 0.0976805i \(0.968858\pi\)
\(608\) 276.382 + 89.8021i 0.454576 + 0.147701i
\(609\) 0 0
\(610\) −56.3284 + 40.9250i −0.0923417 + 0.0670902i
\(611\) −299.554 412.301i −0.490269 0.674797i
\(612\) 0 0
\(613\) −240.068 + 738.852i −0.391627 + 1.20531i 0.539930 + 0.841710i \(0.318451\pi\)
−0.931557 + 0.363595i \(0.881549\pi\)
\(614\) −164.873 + 226.928i −0.268523 + 0.369590i
\(615\) 0 0
\(616\) 437.489 + 105.185i 0.710210 + 0.170755i
\(617\) 490.222i 0.794525i 0.917705 + 0.397263i \(0.130040\pi\)
−0.917705 + 0.397263i \(0.869960\pi\)
\(618\) 0 0
\(619\) −92.4231 + 284.449i −0.149310 + 0.459530i −0.997540 0.0700985i \(-0.977669\pi\)
0.848230 + 0.529628i \(0.177669\pi\)
\(620\) 63.0277 20.4790i 0.101658 0.0330306i
\(621\) 0 0
\(622\) −120.638 + 87.6487i −0.193952 + 0.140914i
\(623\) −1000.48 + 325.075i −1.60590 + 0.521790i
\(624\) 0 0
\(625\) −440.098 319.750i −0.704158 0.511600i
\(626\) 51.0637i 0.0815714i
\(627\) 0 0
\(628\) −603.989 −0.961765
\(629\) −260.499 + 358.546i −0.414148 + 0.570026i
\(630\) 0 0
\(631\) −260.825 802.738i −0.413353 1.27217i −0.913716 0.406353i \(-0.866800\pi\)
0.500364 0.865815i \(-0.333200\pi\)
\(632\) 301.948 + 415.596i 0.477766 + 0.657588i
\(633\) 0 0
\(634\) −49.0983 151.109i −0.0774421 0.238342i
\(635\) −75.3289 24.4758i −0.118628 0.0385446i
\(636\) 0 0
\(637\) 18.0856 0.0283919
\(638\) 358.067 + 219.586i 0.561233 + 0.344179i
\(639\) 0 0
\(640\) −110.446 80.2437i −0.172572 0.125381i
\(641\) −915.198 297.366i −1.42777 0.463909i −0.509705 0.860349i \(-0.670246\pi\)
−0.918061 + 0.396440i \(0.870246\pi\)
\(642\) 0 0
\(643\) −21.2668 + 15.4512i −0.0330743 + 0.0240299i −0.604200 0.796833i \(-0.706507\pi\)
0.571125 + 0.820863i \(0.306507\pi\)
\(644\) −64.5520 88.8483i −0.100236 0.137963i
\(645\) 0 0
\(646\) −22.3309 + 68.7273i −0.0345679 + 0.106389i
\(647\) 172.665 237.653i 0.266870 0.367315i −0.654460 0.756097i \(-0.727104\pi\)
0.921330 + 0.388781i \(0.127104\pi\)
\(648\) 0 0
\(649\) −100.781 1285.98i −0.155286 1.98148i
\(650\) 150.409i 0.231399i
\(651\) 0 0
\(652\) −285.064 + 877.337i −0.437215 + 1.34561i
\(653\) 570.706 185.433i 0.873975 0.283972i 0.162522 0.986705i \(-0.448037\pi\)
0.711453 + 0.702733i \(0.248037\pi\)
\(654\) 0 0
\(655\) −105.199 + 76.4318i −0.160610 + 0.116690i
\(656\) −61.0182 + 19.8260i −0.0930155 + 0.0302226i
\(657\) 0 0
\(658\) −298.510 216.880i −0.453663 0.329606i
\(659\) 19.2417i 0.0291983i −0.999893 0.0145992i \(-0.995353\pi\)
0.999893 0.0145992i \(-0.00464722\pi\)
\(660\) 0 0
\(661\) 543.444 0.822154 0.411077 0.911601i \(-0.365153\pi\)
0.411077 + 0.911601i \(0.365153\pi\)
\(662\) −8.47256 + 11.6615i −0.0127984 + 0.0176155i
\(663\) 0 0
\(664\) −294.501 906.382i −0.443526 1.36503i
\(665\) 39.5961 + 54.4993i 0.0595429 + 0.0819538i
\(666\) 0 0
\(667\) −69.7003 214.515i −0.104498 0.321612i
\(668\) −172.879 56.1717i −0.258801 0.0840894i
\(669\) 0 0
\(670\) 59.9803 0.0895228
\(671\) 342.505 + 827.655i 0.510440 + 1.23347i
\(672\) 0 0
\(673\) −1.17118 0.850910i −0.00174023 0.00126435i 0.586915 0.809649i \(-0.300342\pi\)
−0.588655 + 0.808384i \(0.700342\pi\)
\(674\) −341.673 111.016i −0.506934 0.164713i
\(675\) 0 0
\(676\) 295.639 214.794i 0.437335 0.317743i
\(677\) −616.765 848.904i −0.911026 1.25392i −0.966815 0.255477i \(-0.917767\pi\)
0.0557889 0.998443i \(-0.482233\pi\)
\(678\) 0 0
\(679\) 323.900 996.863i 0.477026 1.46813i
\(680\) 34.6172 47.6465i 0.0509077 0.0700684i
\(681\) 0 0
\(682\) 13.3297 + 170.089i 0.0195450 + 0.249397i
\(683\) 810.057i 1.18603i 0.805192 + 0.593014i \(0.202062\pi\)
−0.805192 + 0.593014i \(0.797938\pi\)
\(684\) 0 0
\(685\) 17.1987 52.9321i 0.0251076 0.0772731i
\(686\) 272.408 88.5106i 0.397096 0.129024i
\(687\) 0 0
\(688\) −346.128 + 251.477i −0.503093 + 0.365518i
\(689\) 281.456 91.4506i 0.408499 0.132729i
\(690\) 0 0
\(691\) 86.1504 + 62.5919i 0.124675 + 0.0905817i 0.648375 0.761321i \(-0.275449\pi\)
−0.523700 + 0.851903i \(0.675449\pi\)
\(692\) 335.740i 0.485174i
\(693\) 0 0
\(694\) 333.127 0.480011
\(695\) −48.6507 + 66.9619i −0.0700010 + 0.0963480i
\(696\) 0 0
\(697\) −22.0617 67.8990i −0.0316524 0.0974160i
\(698\) 229.679 + 316.126i 0.329053 + 0.452902i
\(699\) 0 0
\(700\) 168.161 + 517.548i 0.240231 + 0.739354i
\(701\) −1035.58 336.481i −1.47729 0.480002i −0.543990 0.839092i \(-0.683087\pi\)
−0.933303 + 0.359090i \(0.883087\pi\)
\(702\) 0 0
\(703\) −444.477 −0.632257
\(704\) −71.7068 + 61.2023i −0.101856 + 0.0869351i
\(705\) 0 0
\(706\) −364.500 264.825i −0.516289 0.375106i
\(707\) −1019.08 331.120i −1.44142 0.468345i
\(708\) 0 0
\(709\) −47.5479 + 34.5456i −0.0670633 + 0.0487243i −0.620812 0.783960i \(-0.713197\pi\)
0.553749 + 0.832684i \(0.313197\pi\)
\(710\) 21.7433 + 29.9271i 0.0306244 + 0.0421509i
\(711\) 0 0
\(712\) −285.027 + 877.221i −0.400318 + 1.23205i
\(713\) 53.8506 74.1190i 0.0755268 0.103954i
\(714\) 0 0
\(715\) 86.2722 + 20.7423i 0.120660 + 0.0290102i
\(716\) 272.751i 0.380938i
\(717\) 0 0
\(718\) 90.3437 278.049i 0.125827 0.387255i
\(719\) 692.977 225.162i 0.963806 0.313160i 0.215493 0.976505i \(-0.430864\pi\)
0.748313 + 0.663346i \(0.230864\pi\)
\(720\) 0 0
\(721\) 350.240 254.464i 0.485769 0.352932i
\(722\) 211.468 68.7100i 0.292892 0.0951663i
\(723\) 0 0
\(724\) −549.533 399.259i −0.759024 0.551463i
\(725\) 1117.65i 1.54158i
\(726\) 0 0
\(727\) 1161.64 1.59785 0.798925 0.601431i \(-0.205403\pi\)
0.798925 + 0.601431i \(0.205403\pi\)
\(728\) −185.245 + 254.968i −0.254457 + 0.350230i
\(729\) 0 0
\(730\) 12.1289 + 37.3290i 0.0166150 + 0.0511357i
\(731\) −279.835 385.159i −0.382811 0.526894i
\(732\) 0 0
\(733\) 72.2285 + 222.296i 0.0985382 + 0.303269i 0.988160 0.153429i \(-0.0490317\pi\)
−0.889621 + 0.456699i \(0.849032\pi\)
\(734\) −82.0680 26.6655i −0.111809 0.0363290i
\(735\) 0 0
\(736\) −148.818 −0.202198
\(737\) 180.383 750.257i 0.244753 1.01799i
\(738\) 0 0
\(739\) 606.715 + 440.804i 0.820995 + 0.596487i 0.916997 0.398894i \(-0.130606\pi\)
−0.0960026 + 0.995381i \(0.530606\pi\)
\(740\) 156.589 + 50.8788i 0.211606 + 0.0687551i
\(741\) 0 0
\(742\) 173.343 125.941i 0.233616 0.169732i
\(743\) −313.977 432.152i −0.422580 0.581631i 0.543650 0.839312i \(-0.317042\pi\)
−0.966230 + 0.257680i \(0.917042\pi\)
\(744\) 0 0
\(745\) −7.02886 + 21.6326i −0.00943471 + 0.0290371i
\(746\) 231.919 319.209i 0.310884 0.427895i
\(747\) 0 0
\(748\) −223.568 261.940i −0.298887 0.350187i
\(749\) 351.815i 0.469712i
\(750\) 0 0
\(751\) −367.303 + 1130.44i −0.489086 + 1.50525i 0.336889 + 0.941544i \(0.390625\pi\)
−0.825975 + 0.563707i \(0.809375\pi\)
\(752\) 531.021 172.539i 0.706145 0.229440i
\(753\) 0 0
\(754\) −238.013 + 172.927i −0.315667 + 0.229346i
\(755\) −123.558 + 40.1465i −0.163653 + 0.0531742i
\(756\) 0 0
\(757\) −120.025 87.2036i −0.158554 0.115196i 0.505679 0.862722i \(-0.331242\pi\)
−0.664233 + 0.747525i \(0.731242\pi\)
\(758\) 366.105i 0.482988i
\(759\) 0 0
\(760\) 59.0656 0.0777179
\(761\) 115.997 159.657i 0.152427 0.209798i −0.725974 0.687722i \(-0.758611\pi\)
0.878401 + 0.477924i \(0.158611\pi\)
\(762\) 0 0
\(763\) −133.079 409.575i −0.174416 0.536796i
\(764\) 395.225 + 543.981i 0.517311 + 0.712017i
\(765\) 0 0
\(766\) 121.069 + 372.611i 0.158053 + 0.486438i
\(767\) 859.266 + 279.192i 1.12029 + 0.364006i
\(768\) 0 0
\(769\) 1174.93 1.52787 0.763934 0.645294i \(-0.223265\pi\)
0.763934 + 0.645294i \(0.223265\pi\)
\(770\) 64.0456 5.01917i 0.0831761 0.00651841i
\(771\) 0 0
\(772\) 614.811 + 446.686i 0.796387 + 0.578609i
\(773\) 681.055 + 221.288i 0.881055 + 0.286272i 0.714395 0.699742i \(-0.246702\pi\)
0.166660 + 0.986014i \(0.446702\pi\)
\(774\) 0 0
\(775\) −367.267 + 266.835i −0.473893 + 0.344304i
\(776\) −540.193 743.512i −0.696126 0.958135i
\(777\) 0 0
\(778\) 76.9027 236.682i 0.0988466 0.304219i
\(779\) 42.0860 57.9263i 0.0540256 0.0743599i
\(780\) 0 0
\(781\) 439.731 181.972i 0.563036 0.232999i
\(782\) 37.0062i 0.0473225i
\(783\) 0 0
\(784\) −6.12300 + 18.8447i −0.00780996 + 0.0240366i
\(785\) −180.438 + 58.6279i −0.229858 + 0.0746853i
\(786\) 0 0
\(787\) −529.623 + 384.793i −0.672964 + 0.488937i −0.871016 0.491255i \(-0.836538\pi\)
0.198052 + 0.980192i \(0.436538\pi\)
\(788\) −539.184 + 175.192i −0.684244 + 0.222324i
\(789\) 0 0
\(790\) 59.3361 + 43.1102i 0.0751090 + 0.0545699i
\(791\) 592.705i 0.749311i
\(792\) 0 0
\(793\) −627.382 −0.791149
\(794\) −208.238 + 286.615i −0.262265 + 0.360976i
\(795\) 0 0
\(796\) 148.311 + 456.454i 0.186320 + 0.573435i
\(797\) 305.358 + 420.289i 0.383134 + 0.527338i 0.956411 0.292023i \(-0.0943283\pi\)
−0.573278 + 0.819361i \(0.694328\pi\)
\(798\) 0 0
\(799\) 191.996 + 590.902i 0.240295 + 0.739552i
\(800\) 701.318 + 227.872i 0.876647 + 0.284840i
\(801\) 0 0
\(802\) −43.5172 −0.0542609
\(803\) 503.403 39.4511i 0.626903 0.0491296i
\(804\) 0 0
\(805\) −27.9089 20.2770i −0.0346694 0.0251888i
\(806\) −113.650 36.9271i −0.141005 0.0458153i
\(807\) 0 0
\(808\) −760.085 + 552.234i −0.940700 + 0.683458i
\(809\) −561.893 773.379i −0.694552 0.955969i −0.999993 0.00375802i \(-0.998804\pi\)
0.305441 0.952211i \(-0.401196\pi\)
\(810\) 0 0
\(811\) −93.2508 + 286.996i −0.114982 + 0.353880i −0.991943 0.126682i \(-0.959567\pi\)
0.876961 + 0.480562i \(0.159567\pi\)
\(812\) 625.649 861.133i 0.770504 1.06051i
\(813\) 0 0
\(814\) −221.592 + 361.337i −0.272226 + 0.443903i
\(815\) 289.770i 0.355546i
\(816\) 0 0
\(817\) 147.546 454.099i 0.180595 0.555813i
\(818\) 92.9834 30.2121i 0.113672 0.0369341i
\(819\) 0 0
\(820\) −21.4576 + 15.5899i −0.0261678 + 0.0190120i
\(821\) 219.376 71.2794i 0.267205 0.0868203i −0.172350 0.985036i \(-0.555136\pi\)
0.439555 + 0.898215i \(0.355136\pi\)
\(822\) 0 0
\(823\) 103.804 + 75.4178i 0.126128 + 0.0916376i 0.649061 0.760736i \(-0.275162\pi\)
−0.522933 + 0.852374i \(0.675162\pi\)
\(824\) 379.585i 0.460661i
\(825\) 0 0
\(826\) 654.133 0.791929
\(827\) 387.612 533.503i 0.468697 0.645106i −0.507587 0.861601i \(-0.669462\pi\)
0.976284 + 0.216495i \(0.0694624\pi\)
\(828\) 0 0
\(829\) 124.935 + 384.512i 0.150706 + 0.463826i 0.997701 0.0677757i \(-0.0215902\pi\)
−0.846994 + 0.531602i \(0.821590\pi\)
\(830\) −79.9783 110.081i −0.0963593 0.132627i
\(831\) 0 0
\(832\) −20.4048 62.7994i −0.0245250 0.0754800i
\(833\) −20.9697 6.81347i −0.0251737 0.00817944i
\(834\) 0 0
\(835\) −57.0990 −0.0683821
\(836\) 80.7380 335.808i 0.0965765 0.401685i
\(837\) 0 0
\(838\) 109.389 + 79.4754i 0.130535 + 0.0948394i
\(839\) 443.025 + 143.947i 0.528039 + 0.171570i 0.560891 0.827890i \(-0.310459\pi\)
−0.0328515 + 0.999460i \(0.510459\pi\)
\(840\) 0 0
\(841\) 1088.22 790.639i 1.29396 0.940118i
\(842\) 1.82088 + 2.50623i 0.00216257 + 0.00297652i
\(843\) 0 0
\(844\) 123.954 381.491i 0.146865 0.452004i
\(845\) 67.4708 92.8656i 0.0798471 0.109900i
\(846\) 0 0
\(847\) 129.827 816.202i 0.153279 0.963639i
\(848\) 324.230i 0.382346i
\(849\) 0 0
\(850\) −56.6643 + 174.395i −0.0666639 + 0.205170i
\(851\) 216.475 70.3369i 0.254377 0.0826520i
\(852\) 0 0
\(853\) −1188.83 + 863.733i −1.39370 + 1.01258i −0.398252 + 0.917276i \(0.630383\pi\)
−0.995448 + 0.0953067i \(0.969617\pi\)
\(854\) −431.999 + 140.365i −0.505854 + 0.164362i
\(855\) 0 0
\(856\) 249.559 + 181.315i 0.291541 + 0.211817i
\(857\) 297.274i 0.346877i 0.984845 + 0.173439i \(0.0554878\pi\)
−0.984845 + 0.173439i \(0.944512\pi\)
\(858\) 0 0
\(859\) 38.4367 0.0447459 0.0223729 0.999750i \(-0.492878\pi\)
0.0223729 + 0.999750i \(0.492878\pi\)
\(860\) −103.960 + 143.089i −0.120884 + 0.166383i
\(861\) 0 0
\(862\) 39.0193 + 120.089i 0.0452660 + 0.139314i
\(863\) −585.706 806.155i −0.678686 0.934131i 0.321232 0.947001i \(-0.395903\pi\)
−0.999917 + 0.0128701i \(0.995903\pi\)
\(864\) 0 0
\(865\) 32.5896 + 100.301i 0.0376759 + 0.115954i
\(866\) −206.205 67.0001i −0.238112 0.0773674i
\(867\) 0 0
\(868\) 432.347 0.498095
\(869\) 717.686 612.551i 0.825876 0.704892i
\(870\) 0 0
\(871\) 437.248 + 317.679i 0.502007 + 0.364729i
\(872\) −359.117 116.684i −0.411831 0.133812i
\(873\) 0 0
\(874\) 30.0258 21.8150i 0.0343544 0.0249599i
\(875\) 205.556 + 282.924i 0.234922 + 0.323342i
\(876\) 0 0
\(877\) 161.707 497.683i 0.184386 0.567483i −0.815551 0.578685i \(-0.803566\pi\)
0.999937 + 0.0112024i \(0.00356592\pi\)
\(878\) −343.892 + 473.327i −0.391676 + 0.539096i
\(879\) 0 0
\(880\) −50.8209 + 82.8705i −0.0577510 + 0.0941711i
\(881\) 360.136i 0.408780i 0.978889 + 0.204390i \(0.0655211\pi\)
−0.978889 + 0.204390i \(0.934479\pi\)
\(882\) 0 0
\(883\) 331.290 1019.61i 0.375187 1.15471i −0.568166 0.822914i \(-0.692347\pi\)
0.943353 0.331792i \(-0.107653\pi\)
\(884\) 229.402 74.5371i 0.259504 0.0843180i
\(885\) 0 0
\(886\) 27.5955 20.0493i 0.0311462 0.0226290i
\(887\) −1044.69 + 339.442i −1.17778 + 0.382685i −0.831543 0.555461i \(-0.812542\pi\)
−0.346240 + 0.938146i \(0.612542\pi\)
\(888\) 0 0
\(889\) −418.042 303.725i −0.470238 0.341648i
\(890\) 131.690i 0.147966i
\(891\) 0 0
\(892\) 362.172 0.406022
\(893\) −366.260 + 504.114i −0.410146 + 0.564517i
\(894\) 0 0
\(895\) 26.4754 + 81.4829i 0.0295815 + 0.0910424i
\(896\) −523.501 720.538i −0.584265 0.804172i
\(897\) 0 0
\(898\) 67.0650 + 206.405i 0.0746826 + 0.229849i
\(899\) 844.499 + 274.394i 0.939376 + 0.305222i
\(900\) 0 0
\(901\) −360.792 −0.400435
\(902\) −26.1094 63.0927i −0.0289461 0.0699475i
\(903\) 0 0
\(904\) −420.434 305.463i −0.465082 0.337902i
\(905\) −202.925 65.9344i −0.224227 0.0728557i
\(906\) 0 0
\(907\) −550.128 + 399.691i −0.606536 + 0.440674i −0.848193 0.529688i \(-0.822309\pi\)
0.241657 + 0.970362i \(0.422309\pi\)
\(908\) 415.122 + 571.367i 0.457183 + 0.629259i
\(909\) 0 0
\(910\) −13.9046 + 42.7939i −0.0152798 + 0.0470263i
\(911\) −18.2955 + 25.1817i −0.0200829 + 0.0276418i −0.818940 0.573879i \(-0.805438\pi\)
0.798857 + 0.601520i \(0.205438\pi\)
\(912\) 0 0
\(913\) −1617.46 + 669.346i −1.77158 + 0.733128i
\(914\) 349.511i 0.382397i
\(915\) 0 0
\(916\) 286.738 882.487i 0.313032 0.963414i
\(917\) −806.805 + 262.147i −0.879831 + 0.285874i
\(918\) 0 0
\(919\) 51.8578 37.6769i 0.0564285 0.0409977i −0.559213 0.829024i \(-0.688897\pi\)
0.615642 + 0.788026i \(0.288897\pi\)
\(920\) −28.7669 + 9.34693i −0.0312683 + 0.0101597i
\(921\) 0 0
\(922\) −207.063 150.440i −0.224580 0.163167i
\(923\) 333.326i 0.361133i
\(924\) 0 0
\(925\) −1127.86 −1.21930
\(926\) −254.312 + 350.030i −0.274634 + 0.378002i
\(927\) 0 0
\(928\) −445.717 1371.78i −0.480298 1.47821i
\(929\) 924.026 + 1271.81i 0.994646 + 1.36901i 0.928553 + 0.371199i \(0.121053\pi\)
0.0660924 + 0.997814i \(0.478947\pi\)
\(930\) 0 0
\(931\) −6.83329 21.0307i −0.00733974 0.0225894i
\(932\) −599.389 194.753i −0.643121 0.208963i
\(933\) 0 0
\(934\) −56.6215 −0.0606226
\(935\) −92.2155 56.5517i −0.0986262 0.0604831i
\(936\) 0 0
\(937\) −158.579 115.214i −0.169241 0.122961i 0.499941 0.866060i \(-0.333355\pi\)
−0.669182 + 0.743099i \(0.733355\pi\)
\(938\) 372.153 + 120.920i 0.396751 + 0.128912i
\(939\) 0 0
\(940\) 186.738 135.673i 0.198658 0.144333i
\(941\) 280.415 + 385.958i 0.297997 + 0.410157i 0.931591 0.363508i \(-0.118421\pi\)
−0.633594 + 0.773665i \(0.718421\pi\)
\(942\) 0 0
\(943\) −11.3306 + 34.8720i −0.0120155 + 0.0369798i
\(944\) −581.820 + 800.806i −0.616334 + 0.848312i
\(945\) 0 0
\(946\) −295.601 346.336i −0.312475 0.366106i
\(947\) 151.161i 0.159621i 0.996810 + 0.0798106i \(0.0254316\pi\)
−0.996810 + 0.0798106i \(0.974568\pi\)
\(948\) 0 0
\(949\) −109.291 + 336.363i −0.115164 + 0.354440i
\(950\) −174.902 + 56.8292i −0.184108 + 0.0598202i
\(951\) 0 0
\(952\) 310.841 225.839i 0.326513 0.237226i
\(953\) −1728.32 + 561.565i −1.81356 + 0.589260i −0.813586 + 0.581445i \(0.802488\pi\)
−0.999969 + 0.00781532i \(0.997512\pi\)
\(954\) 0 0
\(955\) 170.875 + 124.148i 0.178926 + 0.129998i
\(956\) 295.967i 0.309589i
\(957\) 0 0
\(958\) 17.0200 0.0177662
\(959\) 213.421 293.749i 0.222546 0.306308i
\(960\) 0 0
\(961\) −185.512 570.946i −0.193040 0.594116i
\(962\) −174.506 240.187i −0.181399 0.249675i
\(963\) 0 0
\(964\) −159.792 491.789i −0.165759 0.510154i
\(965\) 227.030 + 73.7666i 0.235265 + 0.0764421i
\(966\) 0 0
\(967\) 1457.23 1.50696 0.753480 0.657471i \(-0.228374\pi\)
0.753480 + 0.657471i \(0.228374\pi\)
\(968\) −512.062 512.740i −0.528989 0.529690i
\(969\) 0 0
\(970\) −106.154 77.1255i −0.109437 0.0795108i
\(971\) −476.422 154.799i −0.490651 0.159422i 0.0532339 0.998582i \(-0.483047\pi\)
−0.543885 + 0.839160i \(0.683047\pi\)
\(972\) 0 0
\(973\) −436.852 + 317.392i −0.448974 + 0.326199i
\(974\) −39.9479 54.9836i −0.0410143 0.0564514i
\(975\) 0 0
\(976\) 212.404 653.712i 0.217627 0.669787i
\(977\) −149.082 + 205.194i −0.152592 + 0.210025i −0.878469 0.477800i \(-0.841434\pi\)
0.725877 + 0.687825i \(0.241434\pi\)
\(978\) 0 0
\(979\) 1647.23 + 396.040i 1.68256 + 0.404536i
\(980\) 8.19130i 0.00835847i
\(981\) 0 0
\(982\) 24.5575 75.5802i 0.0250076 0.0769656i
\(983\) 627.861 204.005i 0.638720 0.207533i 0.0282858 0.999600i \(-0.490995\pi\)
0.610434 + 0.792067i \(0.290995\pi\)
\(984\) 0 0
\(985\) −144.073 + 104.675i −0.146267 + 0.106269i
\(986\) 341.116 110.835i 0.345959 0.112409i
\(987\) 0 0
\(988\) 195.708 + 142.190i 0.198085 + 0.143917i
\(989\) 244.510i 0.247229i
\(990\) 0 0
\(991\) 33.5854 0.0338905 0.0169452 0.999856i \(-0.494606\pi\)
0.0169452 + 0.999856i \(0.494606\pi\)
\(992\) 344.362 473.974i 0.347139 0.477796i
\(993\) 0 0
\(994\) 74.5756 + 229.520i 0.0750257 + 0.230906i
\(995\) 88.6141 + 121.967i 0.0890594 + 0.122580i
\(996\) 0 0
\(997\) −369.277 1136.52i −0.370388 1.13994i −0.946538 0.322593i \(-0.895445\pi\)
0.576149 0.817344i \(-0.304555\pi\)
\(998\) 236.409 + 76.8140i 0.236883 + 0.0769679i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 99.3.l.a.26.5 yes 32
3.2 odd 2 inner 99.3.l.a.26.4 32
11.3 even 5 inner 99.3.l.a.80.4 yes 32
11.5 even 5 1089.3.b.i.485.10 16
11.6 odd 10 1089.3.b.j.485.7 16
33.5 odd 10 1089.3.b.i.485.7 16
33.14 odd 10 inner 99.3.l.a.80.5 yes 32
33.17 even 10 1089.3.b.j.485.10 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.3.l.a.26.4 32 3.2 odd 2 inner
99.3.l.a.26.5 yes 32 1.1 even 1 trivial
99.3.l.a.80.4 yes 32 11.3 even 5 inner
99.3.l.a.80.5 yes 32 33.14 odd 10 inner
1089.3.b.i.485.7 16 33.5 odd 10
1089.3.b.i.485.10 16 11.5 even 5
1089.3.b.j.485.7 16 11.6 odd 10
1089.3.b.j.485.10 16 33.17 even 10