Properties

Label 1155.2.k.a.769.18
Level $1155$
Weight $2$
Character 1155.769
Analytic conductor $9.223$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 769.18
Character \(\chi\) \(=\) 1155.769
Dual form 1155.2.k.a.769.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.12050 q^{2} -1.00000 q^{3} -0.744486 q^{4} +(-1.27295 - 1.83837i) q^{5} +1.12050 q^{6} +(2.54893 + 0.709189i) q^{7} +3.07519 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.12050 q^{2} -1.00000 q^{3} -0.744486 q^{4} +(-1.27295 - 1.83837i) q^{5} +1.12050 q^{6} +(2.54893 + 0.709189i) q^{7} +3.07519 q^{8} +1.00000 q^{9} +(1.42634 + 2.05989i) q^{10} +(2.57061 - 2.09571i) q^{11} +0.744486 q^{12} -0.476765i q^{13} +(-2.85607 - 0.794644i) q^{14} +(1.27295 + 1.83837i) q^{15} -1.95677 q^{16} +4.13710i q^{17} -1.12050 q^{18} -3.40984 q^{19} +(0.947693 + 1.36864i) q^{20} +(-2.54893 - 0.709189i) q^{21} +(-2.88036 + 2.34823i) q^{22} +2.30034i q^{23} -3.07519 q^{24} +(-1.75920 + 4.68030i) q^{25} +0.534214i q^{26} -1.00000 q^{27} +(-1.89764 - 0.527981i) q^{28} -8.78831i q^{29} +(-1.42634 - 2.05989i) q^{30} +7.12148i q^{31} -3.95782 q^{32} +(-2.57061 + 2.09571i) q^{33} -4.63561i q^{34} +(-1.94091 - 5.58864i) q^{35} -0.744486 q^{36} +4.59966i q^{37} +3.82071 q^{38} +0.476765i q^{39} +(-3.91456 - 5.65333i) q^{40} +6.76000 q^{41} +(2.85607 + 0.794644i) q^{42} +4.78259 q^{43} +(-1.91378 + 1.56022i) q^{44} +(-1.27295 - 1.83837i) q^{45} -2.57752i q^{46} +9.14037 q^{47} +1.95677 q^{48} +(5.99410 + 3.61535i) q^{49} +(1.97118 - 5.24426i) q^{50} -4.13710i q^{51} +0.354945i q^{52} +4.46060i q^{53} +1.12050 q^{54} +(-7.12493 - 2.05799i) q^{55} +(7.83845 + 2.18089i) q^{56} +3.40984 q^{57} +9.84727i q^{58} -10.6711i q^{59} +(-0.947693 - 1.36864i) q^{60} -2.11783 q^{61} -7.97960i q^{62} +(2.54893 + 0.709189i) q^{63} +8.34827 q^{64} +(-0.876470 + 0.606897i) q^{65} +(2.88036 - 2.34823i) q^{66} -11.4547i q^{67} -3.08002i q^{68} -2.30034i q^{69} +(2.17478 + 6.26205i) q^{70} +14.1690 q^{71} +3.07519 q^{72} -9.29571i q^{73} -5.15390i q^{74} +(1.75920 - 4.68030i) q^{75} +2.53858 q^{76} +(8.03855 - 3.51877i) q^{77} -0.534214i q^{78} +0.726204i q^{79} +(2.49087 + 3.59726i) q^{80} +1.00000 q^{81} -7.57456 q^{82} -8.78886i q^{83} +(1.89764 + 0.527981i) q^{84} +(7.60552 - 5.26632i) q^{85} -5.35887 q^{86} +8.78831i q^{87} +(7.90510 - 6.44469i) q^{88} +10.2107i q^{89} +(1.42634 + 2.05989i) q^{90} +(0.338116 - 1.21524i) q^{91} -1.71257i q^{92} -7.12148i q^{93} -10.2418 q^{94} +(4.34055 + 6.26854i) q^{95} +3.95782 q^{96} -4.36785 q^{97} +(-6.71637 - 4.05099i) q^{98} +(2.57061 - 2.09571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12050 −0.792311 −0.396156 0.918183i \(-0.629656\pi\)
−0.396156 + 0.918183i \(0.629656\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.744486 −0.372243
\(5\) −1.27295 1.83837i −0.569280 0.822144i
\(6\) 1.12050 0.457441
\(7\) 2.54893 + 0.709189i 0.963406 + 0.268048i
\(8\) 3.07519 1.08724
\(9\) 1.00000 0.333333
\(10\) 1.42634 + 2.05989i 0.451047 + 0.651394i
\(11\) 2.57061 2.09571i 0.775067 0.631879i
\(12\) 0.744486 0.214915
\(13\) 0.476765i 0.132231i −0.997812 0.0661154i \(-0.978939\pi\)
0.997812 0.0661154i \(-0.0210605\pi\)
\(14\) −2.85607 0.794644i −0.763317 0.212378i
\(15\) 1.27295 + 1.83837i 0.328674 + 0.474665i
\(16\) −1.95677 −0.489192
\(17\) 4.13710i 1.00340i 0.865043 + 0.501698i \(0.167291\pi\)
−0.865043 + 0.501698i \(0.832709\pi\)
\(18\) −1.12050 −0.264104
\(19\) −3.40984 −0.782270 −0.391135 0.920333i \(-0.627918\pi\)
−0.391135 + 0.920333i \(0.627918\pi\)
\(20\) 0.947693 + 1.36864i 0.211911 + 0.306037i
\(21\) −2.54893 0.709189i −0.556222 0.154758i
\(22\) −2.88036 + 2.34823i −0.614094 + 0.500645i
\(23\) 2.30034i 0.479654i 0.970816 + 0.239827i \(0.0770907\pi\)
−0.970816 + 0.239827i \(0.922909\pi\)
\(24\) −3.07519 −0.627720
\(25\) −1.75920 + 4.68030i −0.351840 + 0.936060i
\(26\) 0.534214i 0.104768i
\(27\) −1.00000 −0.192450
\(28\) −1.89764 0.527981i −0.358621 0.0997791i
\(29\) 8.78831i 1.63195i −0.578089 0.815974i \(-0.696201\pi\)
0.578089 0.815974i \(-0.303799\pi\)
\(30\) −1.42634 2.05989i −0.260412 0.376082i
\(31\) 7.12148i 1.27906i 0.768768 + 0.639528i \(0.220870\pi\)
−0.768768 + 0.639528i \(0.779130\pi\)
\(32\) −3.95782 −0.699651
\(33\) −2.57061 + 2.09571i −0.447485 + 0.364816i
\(34\) 4.63561i 0.795001i
\(35\) −1.94091 5.58864i −0.328074 0.944652i
\(36\) −0.744486 −0.124081
\(37\) 4.59966i 0.756179i 0.925769 + 0.378090i \(0.123419\pi\)
−0.925769 + 0.378090i \(0.876581\pi\)
\(38\) 3.82071 0.619802
\(39\) 0.476765i 0.0763435i
\(40\) −3.91456 5.65333i −0.618946 0.893870i
\(41\) 6.76000 1.05573 0.527867 0.849327i \(-0.322992\pi\)
0.527867 + 0.849327i \(0.322992\pi\)
\(42\) 2.85607 + 0.794644i 0.440701 + 0.122616i
\(43\) 4.78259 0.729338 0.364669 0.931137i \(-0.381182\pi\)
0.364669 + 0.931137i \(0.381182\pi\)
\(44\) −1.91378 + 1.56022i −0.288513 + 0.235213i
\(45\) −1.27295 1.83837i −0.189760 0.274048i
\(46\) 2.57752i 0.380035i
\(47\) 9.14037 1.33326 0.666630 0.745389i \(-0.267736\pi\)
0.666630 + 0.745389i \(0.267736\pi\)
\(48\) 1.95677 0.282435
\(49\) 5.99410 + 3.61535i 0.856300 + 0.516478i
\(50\) 1.97118 5.24426i 0.278767 0.741651i
\(51\) 4.13710i 0.579310i
\(52\) 0.354945i 0.0492220i
\(53\) 4.46060i 0.612710i 0.951917 + 0.306355i \(0.0991095\pi\)
−0.951917 + 0.306355i \(0.900891\pi\)
\(54\) 1.12050 0.152480
\(55\) −7.12493 2.05799i −0.960726 0.277500i
\(56\) 7.83845 + 2.18089i 1.04746 + 0.291434i
\(57\) 3.40984 0.451644
\(58\) 9.84727i 1.29301i
\(59\) 10.6711i 1.38926i −0.719368 0.694629i \(-0.755568\pi\)
0.719368 0.694629i \(-0.244432\pi\)
\(60\) −0.947693 1.36864i −0.122347 0.176691i
\(61\) −2.11783 −0.271160 −0.135580 0.990766i \(-0.543290\pi\)
−0.135580 + 0.990766i \(0.543290\pi\)
\(62\) 7.97960i 1.01341i
\(63\) 2.54893 + 0.709189i 0.321135 + 0.0893494i
\(64\) 8.34827 1.04353
\(65\) −0.876470 + 0.606897i −0.108713 + 0.0752763i
\(66\) 2.88036 2.34823i 0.354547 0.289048i
\(67\) 11.4547i 1.39942i −0.714427 0.699710i \(-0.753313\pi\)
0.714427 0.699710i \(-0.246687\pi\)
\(68\) 3.08002i 0.373507i
\(69\) 2.30034i 0.276928i
\(70\) 2.17478 + 6.26205i 0.259936 + 0.748458i
\(71\) 14.1690 1.68155 0.840777 0.541381i \(-0.182098\pi\)
0.840777 + 0.541381i \(0.182098\pi\)
\(72\) 3.07519 0.362414
\(73\) 9.29571i 1.08798i −0.839092 0.543990i \(-0.816913\pi\)
0.839092 0.543990i \(-0.183087\pi\)
\(74\) 5.15390i 0.599129i
\(75\) 1.75920 4.68030i 0.203135 0.540435i
\(76\) 2.53858 0.291195
\(77\) 8.03855 3.51877i 0.916078 0.401001i
\(78\) 0.534214i 0.0604878i
\(79\) 0.726204i 0.0817044i 0.999165 + 0.0408522i \(0.0130073\pi\)
−0.999165 + 0.0408522i \(0.986993\pi\)
\(80\) 2.49087 + 3.59726i 0.278487 + 0.402186i
\(81\) 1.00000 0.111111
\(82\) −7.57456 −0.836470
\(83\) 8.78886i 0.964703i −0.875978 0.482352i \(-0.839783\pi\)
0.875978 0.482352i \(-0.160217\pi\)
\(84\) 1.89764 + 0.527981i 0.207050 + 0.0576075i
\(85\) 7.60552 5.26632i 0.824935 0.571213i
\(86\) −5.35887 −0.577862
\(87\) 8.78831i 0.942205i
\(88\) 7.90510 6.44469i 0.842686 0.687007i
\(89\) 10.2107i 1.08233i 0.840915 + 0.541167i \(0.182017\pi\)
−0.840915 + 0.541167i \(0.817983\pi\)
\(90\) 1.42634 + 2.05989i 0.150349 + 0.217131i
\(91\) 0.338116 1.21524i 0.0354442 0.127392i
\(92\) 1.71257i 0.178548i
\(93\) 7.12148i 0.738463i
\(94\) −10.2418 −1.05636
\(95\) 4.34055 + 6.26854i 0.445331 + 0.643139i
\(96\) 3.95782 0.403944
\(97\) −4.36785 −0.443488 −0.221744 0.975105i \(-0.571175\pi\)
−0.221744 + 0.975105i \(0.571175\pi\)
\(98\) −6.71637 4.05099i −0.678456 0.409211i
\(99\) 2.57061 2.09571i 0.258356 0.210626i
\(100\) 1.30970 3.48442i 0.130970 0.348442i
\(101\) 10.2868 1.02358 0.511788 0.859112i \(-0.328983\pi\)
0.511788 + 0.859112i \(0.328983\pi\)
\(102\) 4.63561i 0.458994i
\(103\) −17.2764 −1.70229 −0.851145 0.524931i \(-0.824091\pi\)
−0.851145 + 0.524931i \(0.824091\pi\)
\(104\) 1.46614i 0.143767i
\(105\) 1.94091 + 5.58864i 0.189413 + 0.545395i
\(106\) 4.99809i 0.485457i
\(107\) −3.72911 −0.360507 −0.180254 0.983620i \(-0.557692\pi\)
−0.180254 + 0.983620i \(0.557692\pi\)
\(108\) 0.744486 0.0716382
\(109\) 11.3168i 1.08395i 0.840393 + 0.541977i \(0.182324\pi\)
−0.840393 + 0.541977i \(0.817676\pi\)
\(110\) 7.98347 + 2.30598i 0.761194 + 0.219866i
\(111\) 4.59966i 0.436580i
\(112\) −4.98767 1.38772i −0.471290 0.131127i
\(113\) 6.26655i 0.589508i 0.955573 + 0.294754i \(0.0952377\pi\)
−0.955573 + 0.294754i \(0.904762\pi\)
\(114\) −3.82071 −0.357843
\(115\) 4.22887 2.92821i 0.394344 0.273057i
\(116\) 6.54277i 0.607481i
\(117\) 0.476765i 0.0440769i
\(118\) 11.9569i 1.10073i
\(119\) −2.93399 + 10.5452i −0.268958 + 0.966676i
\(120\) 3.91456 + 5.65333i 0.357349 + 0.516076i
\(121\) 2.21603 10.7745i 0.201457 0.979497i
\(122\) 2.37302 0.214843
\(123\) −6.76000 −0.609528
\(124\) 5.30185i 0.476120i
\(125\) 10.8435 2.72372i 0.969871 0.243617i
\(126\) −2.85607 0.794644i −0.254439 0.0707925i
\(127\) 8.57420 0.760837 0.380418 0.924814i \(-0.375780\pi\)
0.380418 + 0.924814i \(0.375780\pi\)
\(128\) −1.43856 −0.127152
\(129\) −4.78259 −0.421083
\(130\) 0.982082 0.680027i 0.0861343 0.0596423i
\(131\) 14.2168 1.24213 0.621063 0.783760i \(-0.286701\pi\)
0.621063 + 0.783760i \(0.286701\pi\)
\(132\) 1.91378 1.56022i 0.166573 0.135800i
\(133\) −8.69144 2.41822i −0.753644 0.209686i
\(134\) 12.8350i 1.10878i
\(135\) 1.27295 + 1.83837i 0.109558 + 0.158222i
\(136\) 12.7224i 1.09093i
\(137\) 8.16717i 0.697768i −0.937166 0.348884i \(-0.886561\pi\)
0.937166 0.348884i \(-0.113439\pi\)
\(138\) 2.57752i 0.219413i
\(139\) 5.25987 0.446136 0.223068 0.974803i \(-0.428393\pi\)
0.223068 + 0.974803i \(0.428393\pi\)
\(140\) 1.44498 + 4.16066i 0.122123 + 0.351640i
\(141\) −9.14037 −0.769758
\(142\) −15.8764 −1.33231
\(143\) −0.999159 1.22557i −0.0835539 0.102488i
\(144\) −1.95677 −0.163064
\(145\) −16.1562 + 11.1871i −1.34170 + 0.929035i
\(146\) 10.4158i 0.862019i
\(147\) −5.99410 3.61535i −0.494385 0.298189i
\(148\) 3.42438i 0.281482i
\(149\) 22.3770i 1.83319i −0.399812 0.916597i \(-0.630925\pi\)
0.399812 0.916597i \(-0.369075\pi\)
\(150\) −1.97118 + 5.24426i −0.160946 + 0.428192i
\(151\) 2.40104i 0.195394i −0.995216 0.0976969i \(-0.968852\pi\)
0.995216 0.0976969i \(-0.0311476\pi\)
\(152\) −10.4859 −0.850518
\(153\) 4.13710i 0.334465i
\(154\) −9.00717 + 3.94277i −0.725819 + 0.317717i
\(155\) 13.0919 9.06529i 1.05157 0.728141i
\(156\) 0.354945i 0.0284183i
\(157\) 12.3697 0.987211 0.493605 0.869686i \(-0.335679\pi\)
0.493605 + 0.869686i \(0.335679\pi\)
\(158\) 0.813710i 0.0647353i
\(159\) 4.46060i 0.353748i
\(160\) 5.03811 + 7.27594i 0.398298 + 0.575214i
\(161\) −1.63137 + 5.86341i −0.128570 + 0.462101i
\(162\) −1.12050 −0.0880346
\(163\) 20.8684i 1.63454i 0.576256 + 0.817269i \(0.304513\pi\)
−0.576256 + 0.817269i \(0.695487\pi\)
\(164\) −5.03272 −0.392990
\(165\) 7.12493 + 2.05799i 0.554675 + 0.160215i
\(166\) 9.84790i 0.764345i
\(167\) 11.4710i 0.887654i −0.896113 0.443827i \(-0.853620\pi\)
0.896113 0.443827i \(-0.146380\pi\)
\(168\) −7.83845 2.18089i −0.604749 0.168259i
\(169\) 12.7727 0.982515
\(170\) −8.52197 + 5.90090i −0.653605 + 0.452578i
\(171\) −3.40984 −0.260757
\(172\) −3.56057 −0.271491
\(173\) 21.5558i 1.63886i −0.573183 0.819428i \(-0.694291\pi\)
0.573183 0.819428i \(-0.305709\pi\)
\(174\) 9.84727i 0.746520i
\(175\) −7.80330 + 10.6822i −0.589874 + 0.807495i
\(176\) −5.03008 + 4.10081i −0.379157 + 0.309110i
\(177\) 10.6711i 0.802089i
\(178\) 11.4411i 0.857545i
\(179\) −14.1203 −1.05540 −0.527701 0.849430i \(-0.676946\pi\)
−0.527701 + 0.849430i \(0.676946\pi\)
\(180\) 0.947693 + 1.36864i 0.0706369 + 0.102012i
\(181\) 6.42683i 0.477702i −0.971056 0.238851i \(-0.923229\pi\)
0.971056 0.238851i \(-0.0767708\pi\)
\(182\) −0.378858 + 1.36167i −0.0280828 + 0.100934i
\(183\) 2.11783 0.156554
\(184\) 7.07398i 0.521501i
\(185\) 8.45587 5.85513i 0.621688 0.430478i
\(186\) 7.97960i 0.585093i
\(187\) 8.67016 + 10.6349i 0.634025 + 0.777698i
\(188\) −6.80488 −0.496297
\(189\) −2.54893 0.709189i −0.185407 0.0515859i
\(190\) −4.86357 7.02388i −0.352841 0.509566i
\(191\) 1.65973 0.120094 0.0600469 0.998196i \(-0.480875\pi\)
0.0600469 + 0.998196i \(0.480875\pi\)
\(192\) −8.34827 −0.602484
\(193\) 7.02842 0.505916 0.252958 0.967477i \(-0.418596\pi\)
0.252958 + 0.967477i \(0.418596\pi\)
\(194\) 4.89416 0.351380
\(195\) 0.876470 0.606897i 0.0627653 0.0434608i
\(196\) −4.46253 2.69158i −0.318752 0.192255i
\(197\) 8.04622 0.573269 0.286635 0.958040i \(-0.407463\pi\)
0.286635 + 0.958040i \(0.407463\pi\)
\(198\) −2.88036 + 2.34823i −0.204698 + 0.166882i
\(199\) 22.3264i 1.58268i −0.611379 0.791338i \(-0.709385\pi\)
0.611379 0.791338i \(-0.290615\pi\)
\(200\) −5.40987 + 14.3928i −0.382536 + 1.01773i
\(201\) 11.4547i 0.807955i
\(202\) −11.5263 −0.810990
\(203\) 6.23257 22.4008i 0.437441 1.57223i
\(204\) 3.08002i 0.215644i
\(205\) −8.60513 12.4274i −0.601009 0.867965i
\(206\) 19.3581 1.34874
\(207\) 2.30034i 0.159885i
\(208\) 0.932918i 0.0646862i
\(209\) −8.76535 + 7.14602i −0.606312 + 0.494300i
\(210\) −2.17478 6.26205i −0.150074 0.432123i
\(211\) 14.8136i 1.01981i 0.860231 + 0.509905i \(0.170320\pi\)
−0.860231 + 0.509905i \(0.829680\pi\)
\(212\) 3.32085i 0.228077i
\(213\) −14.1690 −0.970846
\(214\) 4.17846 0.285634
\(215\) −6.08799 8.79216i −0.415197 0.599620i
\(216\) −3.07519 −0.209240
\(217\) −5.05048 + 18.1522i −0.342849 + 1.23225i
\(218\) 12.6805i 0.858829i
\(219\) 9.29571i 0.628146i
\(220\) 5.30441 + 1.53215i 0.357623 + 0.103297i
\(221\) 1.97243 0.132680
\(222\) 5.15390i 0.345907i
\(223\) 3.11670 0.208709 0.104355 0.994540i \(-0.466722\pi\)
0.104355 + 0.994540i \(0.466722\pi\)
\(224\) −10.0882 2.80684i −0.674048 0.187540i
\(225\) −1.75920 + 4.68030i −0.117280 + 0.312020i
\(226\) 7.02166i 0.467074i
\(227\) 13.6688i 0.907232i −0.891197 0.453616i \(-0.850134\pi\)
0.891197 0.453616i \(-0.149866\pi\)
\(228\) −2.53858 −0.168121
\(229\) 5.12695i 0.338798i −0.985548 0.169399i \(-0.945817\pi\)
0.985548 0.169399i \(-0.0541827\pi\)
\(230\) −4.73844 + 3.28106i −0.312443 + 0.216346i
\(231\) −8.03855 + 3.51877i −0.528898 + 0.231518i
\(232\) 27.0257i 1.77432i
\(233\) −7.14633 −0.468171 −0.234086 0.972216i \(-0.575210\pi\)
−0.234086 + 0.972216i \(0.575210\pi\)
\(234\) 0.534214i 0.0349226i
\(235\) −11.6352 16.8034i −0.758999 1.09613i
\(236\) 7.94449i 0.517142i
\(237\) 0.726204i 0.0471720i
\(238\) 3.28752 11.8159i 0.213099 0.765908i
\(239\) 9.42544i 0.609681i 0.952403 + 0.304841i \(0.0986032\pi\)
−0.952403 + 0.304841i \(0.901397\pi\)
\(240\) −2.49087 3.59726i −0.160785 0.232202i
\(241\) 20.5632 1.32459 0.662297 0.749242i \(-0.269582\pi\)
0.662297 + 0.749242i \(0.269582\pi\)
\(242\) −2.48305 + 12.0728i −0.159617 + 0.776067i
\(243\) −1.00000 −0.0641500
\(244\) 1.57669 0.100937
\(245\) −0.983846 15.6215i −0.0628556 0.998023i
\(246\) 7.57456 0.482936
\(247\) 1.62569i 0.103440i
\(248\) 21.8999i 1.39065i
\(249\) 8.78886i 0.556972i
\(250\) −12.1501 + 3.05193i −0.768440 + 0.193021i
\(251\) 21.5112i 1.35778i 0.734242 + 0.678888i \(0.237538\pi\)
−0.734242 + 0.678888i \(0.762462\pi\)
\(252\) −1.89764 0.527981i −0.119540 0.0332597i
\(253\) 4.82084 + 5.91326i 0.303083 + 0.371764i
\(254\) −9.60736 −0.602820
\(255\) −7.60552 + 5.26632i −0.476276 + 0.329790i
\(256\) −15.0846 −0.942789
\(257\) 24.5941 1.53414 0.767068 0.641566i \(-0.221715\pi\)
0.767068 + 0.641566i \(0.221715\pi\)
\(258\) 5.35887 0.333629
\(259\) −3.26203 + 11.7242i −0.202692 + 0.728507i
\(260\) 0.652519 0.451827i 0.0404675 0.0280211i
\(261\) 8.78831i 0.543983i
\(262\) −15.9299 −0.984151
\(263\) −30.0425 −1.85250 −0.926250 0.376910i \(-0.876987\pi\)
−0.926250 + 0.376910i \(0.876987\pi\)
\(264\) −7.90510 + 6.44469i −0.486525 + 0.396643i
\(265\) 8.20022 5.67811i 0.503736 0.348804i
\(266\) 9.73874 + 2.70961i 0.597120 + 0.166137i
\(267\) 10.2107i 0.624885i
\(268\) 8.52790i 0.520924i
\(269\) 11.3709i 0.693294i 0.937996 + 0.346647i \(0.112680\pi\)
−0.937996 + 0.346647i \(0.887320\pi\)
\(270\) −1.42634 2.05989i −0.0868040 0.125361i
\(271\) 9.14710 0.555647 0.277823 0.960632i \(-0.410387\pi\)
0.277823 + 0.960632i \(0.410387\pi\)
\(272\) 8.09535i 0.490853i
\(273\) −0.338116 + 1.21524i −0.0204637 + 0.0735497i
\(274\) 9.15129i 0.552850i
\(275\) 5.28633 + 15.7180i 0.318777 + 0.947830i
\(276\) 1.71257i 0.103085i
\(277\) −10.6798 −0.641688 −0.320844 0.947132i \(-0.603967\pi\)
−0.320844 + 0.947132i \(0.603967\pi\)
\(278\) −5.89367 −0.353479
\(279\) 7.12148i 0.426352i
\(280\) −5.96866 17.1861i −0.356696 1.02707i
\(281\) 26.3350i 1.57101i −0.618854 0.785506i \(-0.712403\pi\)
0.618854 0.785506i \(-0.287597\pi\)
\(282\) 10.2418 0.609888
\(283\) 0.827641i 0.0491981i −0.999697 0.0245991i \(-0.992169\pi\)
0.999697 0.0245991i \(-0.00783092\pi\)
\(284\) −10.5486 −0.625947
\(285\) −4.34055 6.26854i −0.257112 0.371316i
\(286\) 1.11955 + 1.37325i 0.0662007 + 0.0812021i
\(287\) 17.2308 + 4.79411i 1.01710 + 0.282988i
\(288\) −3.95782 −0.233217
\(289\) −0.115630 −0.00680177
\(290\) 18.1029 12.5351i 1.06304 0.736085i
\(291\) 4.36785 0.256048
\(292\) 6.92052i 0.404993i
\(293\) 5.25394i 0.306938i 0.988153 + 0.153469i \(0.0490446\pi\)
−0.988153 + 0.153469i \(0.950955\pi\)
\(294\) 6.71637 + 4.05099i 0.391707 + 0.236258i
\(295\) −19.6174 + 13.5838i −1.14217 + 0.790877i
\(296\) 14.1448i 0.822151i
\(297\) −2.57061 + 2.09571i −0.149162 + 0.121605i
\(298\) 25.0733i 1.45246i
\(299\) 1.09672 0.0634250
\(300\) −1.30970 + 3.48442i −0.0756156 + 0.201173i
\(301\) 12.1905 + 3.39176i 0.702648 + 0.195498i
\(302\) 2.69036i 0.154813i
\(303\) −10.2868 −0.590962
\(304\) 6.67226 0.382680
\(305\) 2.69589 + 3.89335i 0.154366 + 0.222932i
\(306\) 4.63561i 0.265000i
\(307\) 7.14246i 0.407642i 0.979008 + 0.203821i \(0.0653360\pi\)
−0.979008 + 0.203821i \(0.934664\pi\)
\(308\) −5.98459 + 2.61967i −0.341004 + 0.149270i
\(309\) 17.2764 0.982818
\(310\) −14.6695 + 10.1576i −0.833169 + 0.576915i
\(311\) 0.743752i 0.0421743i −0.999778 0.0210872i \(-0.993287\pi\)
0.999778 0.0210872i \(-0.00671275\pi\)
\(312\) 1.46614i 0.0830039i
\(313\) 7.12227 0.402575 0.201287 0.979532i \(-0.435488\pi\)
0.201287 + 0.979532i \(0.435488\pi\)
\(314\) −13.8602 −0.782178
\(315\) −1.94091 5.58864i −0.109358 0.314884i
\(316\) 0.540649i 0.0304139i
\(317\) 33.7483i 1.89550i 0.319020 + 0.947748i \(0.396646\pi\)
−0.319020 + 0.947748i \(0.603354\pi\)
\(318\) 4.99809i 0.280279i
\(319\) −18.4177 22.5913i −1.03119 1.26487i
\(320\) −10.6269 15.3472i −0.594063 0.857934i
\(321\) 3.72911 0.208139
\(322\) 1.82795 6.56993i 0.101868 0.366128i
\(323\) 14.1069i 0.784926i
\(324\) −0.744486 −0.0413603
\(325\) 2.23140 + 0.838725i 0.123776 + 0.0465241i
\(326\) 23.3830i 1.29506i
\(327\) 11.3168i 0.625821i
\(328\) 20.7883 1.14784
\(329\) 23.2982 + 6.48225i 1.28447 + 0.357378i
\(330\) −7.98347 2.30598i −0.439475 0.126940i
\(331\) −23.7696 −1.30650 −0.653248 0.757144i \(-0.726594\pi\)
−0.653248 + 0.757144i \(0.726594\pi\)
\(332\) 6.54319i 0.359104i
\(333\) 4.59966i 0.252060i
\(334\) 12.8532i 0.703298i
\(335\) −21.0580 + 14.5813i −1.15052 + 0.796662i
\(336\) 4.98767 + 1.38772i 0.272100 + 0.0757062i
\(337\) 12.7589 0.695022 0.347511 0.937676i \(-0.387027\pi\)
0.347511 + 0.937676i \(0.387027\pi\)
\(338\) −14.3118 −0.778458
\(339\) 6.26655i 0.340353i
\(340\) −5.66221 + 3.92070i −0.307076 + 0.212630i
\(341\) 14.9245 + 18.3065i 0.808209 + 0.991354i
\(342\) 3.82071 0.206601
\(343\) 12.7146 + 13.4662i 0.686523 + 0.727108i
\(344\) 14.7074 0.792968
\(345\) −4.22887 + 2.92821i −0.227675 + 0.157650i
\(346\) 24.1532i 1.29848i
\(347\) −17.6529 −0.947658 −0.473829 0.880617i \(-0.657129\pi\)
−0.473829 + 0.880617i \(0.657129\pi\)
\(348\) 6.54277i 0.350729i
\(349\) 1.12533 0.0602377 0.0301189 0.999546i \(-0.490411\pi\)
0.0301189 + 0.999546i \(0.490411\pi\)
\(350\) 8.74357 11.9693i 0.467364 0.639788i
\(351\) 0.476765i 0.0254478i
\(352\) −10.1740 + 8.29444i −0.542276 + 0.442095i
\(353\) −26.6713 −1.41957 −0.709784 0.704419i \(-0.751208\pi\)
−0.709784 + 0.704419i \(0.751208\pi\)
\(354\) 11.9569i 0.635504i
\(355\) −18.0365 26.0479i −0.957276 1.38248i
\(356\) 7.60173i 0.402891i
\(357\) 2.93399 10.5452i 0.155283 0.558111i
\(358\) 15.8218 0.836207
\(359\) 30.0463i 1.58578i −0.609362 0.792892i \(-0.708574\pi\)
0.609362 0.792892i \(-0.291426\pi\)
\(360\) −3.91456 5.65333i −0.206315 0.297957i
\(361\) −7.37301 −0.388053
\(362\) 7.20124i 0.378489i
\(363\) −2.21603 + 10.7745i −0.116311 + 0.565513i
\(364\) −0.251723 + 0.904730i −0.0131939 + 0.0474207i
\(365\) −17.0889 + 11.8330i −0.894476 + 0.619365i
\(366\) −2.37302 −0.124040
\(367\) −1.39804 −0.0729769 −0.0364885 0.999334i \(-0.511617\pi\)
−0.0364885 + 0.999334i \(0.511617\pi\)
\(368\) 4.50123i 0.234643i
\(369\) 6.76000 0.351911
\(370\) −9.47478 + 6.56066i −0.492570 + 0.341072i
\(371\) −3.16341 + 11.3698i −0.164236 + 0.590288i
\(372\) 5.30185i 0.274888i
\(373\) −7.28539 −0.377223 −0.188612 0.982052i \(-0.560399\pi\)
−0.188612 + 0.982052i \(0.560399\pi\)
\(374\) −9.71489 11.9163i −0.502345 0.616179i
\(375\) −10.8435 + 2.72372i −0.559956 + 0.140653i
\(376\) 28.1084 1.44958
\(377\) −4.18995 −0.215794
\(378\) 2.85607 + 0.794644i 0.146900 + 0.0408721i
\(379\) −6.68357 −0.343312 −0.171656 0.985157i \(-0.554912\pi\)
−0.171656 + 0.985157i \(0.554912\pi\)
\(380\) −3.23148 4.66684i −0.165771 0.239404i
\(381\) −8.57420 −0.439269
\(382\) −1.85972 −0.0951517
\(383\) 24.6757 1.26087 0.630435 0.776242i \(-0.282877\pi\)
0.630435 + 0.776242i \(0.282877\pi\)
\(384\) 1.43856 0.0734112
\(385\) −16.7015 10.2986i −0.851185 0.524866i
\(386\) −7.87532 −0.400843
\(387\) 4.78259 0.243113
\(388\) 3.25180 0.165085
\(389\) −1.28344 −0.0650728 −0.0325364 0.999471i \(-0.510358\pi\)
−0.0325364 + 0.999471i \(0.510358\pi\)
\(390\) −0.982082 + 0.680027i −0.0497296 + 0.0344345i
\(391\) −9.51674 −0.481282
\(392\) 18.4330 + 11.1179i 0.931007 + 0.561537i
\(393\) −14.2168 −0.717142
\(394\) −9.01576 −0.454208
\(395\) 1.33503 0.924421i 0.0671727 0.0465127i
\(396\) −1.91378 + 1.56022i −0.0961711 + 0.0784042i
\(397\) 10.4696 0.525455 0.262728 0.964870i \(-0.415378\pi\)
0.262728 + 0.964870i \(0.415378\pi\)
\(398\) 25.0167i 1.25397i
\(399\) 8.69144 + 2.41822i 0.435116 + 0.121062i
\(400\) 3.44235 9.15826i 0.172117 0.457913i
\(401\) 10.6984 0.534251 0.267125 0.963662i \(-0.413926\pi\)
0.267125 + 0.963662i \(0.413926\pi\)
\(402\) 12.8350i 0.640152i
\(403\) 3.39527 0.169131
\(404\) −7.65839 −0.381019
\(405\) −1.27295 1.83837i −0.0632534 0.0913493i
\(406\) −6.98358 + 25.1000i −0.346589 + 1.24569i
\(407\) 9.63953 + 11.8239i 0.477814 + 0.586089i
\(408\) 12.7224i 0.629851i
\(409\) 8.76079 0.433193 0.216597 0.976261i \(-0.430504\pi\)
0.216597 + 0.976261i \(0.430504\pi\)
\(410\) 9.64203 + 13.9248i 0.476186 + 0.687698i
\(411\) 8.16717i 0.402857i
\(412\) 12.8620 0.633666
\(413\) 7.56782 27.1999i 0.372388 1.33842i
\(414\) 2.57752i 0.126678i
\(415\) −16.1572 + 11.1878i −0.793124 + 0.549186i
\(416\) 1.88695i 0.0925154i
\(417\) −5.25987 −0.257577
\(418\) 9.82155 8.00709i 0.480388 0.391640i
\(419\) 27.5310i 1.34498i 0.740107 + 0.672489i \(0.234775\pi\)
−0.740107 + 0.672489i \(0.765225\pi\)
\(420\) −1.44498 4.16066i −0.0705078 0.203020i
\(421\) 26.1898 1.27641 0.638207 0.769865i \(-0.279676\pi\)
0.638207 + 0.769865i \(0.279676\pi\)
\(422\) 16.5986i 0.808007i
\(423\) 9.14037 0.444420
\(424\) 13.7172i 0.666165i
\(425\) −19.3629 7.27800i −0.939238 0.353035i
\(426\) 15.8764 0.769212
\(427\) −5.39820 1.50194i −0.261237 0.0726839i
\(428\) 2.77627 0.134196
\(429\) 0.999159 + 1.22557i 0.0482399 + 0.0591713i
\(430\) 6.82158 + 9.85159i 0.328966 + 0.475086i
\(431\) 22.3030i 1.07430i 0.843488 + 0.537149i \(0.180499\pi\)
−0.843488 + 0.537149i \(0.819501\pi\)
\(432\) 1.95677 0.0941451
\(433\) −3.91589 −0.188186 −0.0940928 0.995563i \(-0.529995\pi\)
−0.0940928 + 0.995563i \(0.529995\pi\)
\(434\) 5.65904 20.3395i 0.271643 0.976325i
\(435\) 16.1562 11.1871i 0.774628 0.536379i
\(436\) 8.42521i 0.403494i
\(437\) 7.84378i 0.375219i
\(438\) 10.4158i 0.497687i
\(439\) 7.00412 0.334288 0.167144 0.985932i \(-0.446545\pi\)
0.167144 + 0.985932i \(0.446545\pi\)
\(440\) −21.9105 6.32872i −1.04454 0.301710i
\(441\) 5.99410 + 3.61535i 0.285433 + 0.172159i
\(442\) −2.21010 −0.105124
\(443\) 18.3450i 0.871595i −0.900045 0.435798i \(-0.856466\pi\)
0.900045 0.435798i \(-0.143534\pi\)
\(444\) 3.42438i 0.162514i
\(445\) 18.7711 12.9977i 0.889833 0.616151i
\(446\) −3.49225 −0.165363
\(447\) 22.3770i 1.05840i
\(448\) 21.2792 + 5.92050i 1.00535 + 0.279717i
\(449\) −9.69505 −0.457538 −0.228769 0.973481i \(-0.573470\pi\)
−0.228769 + 0.973481i \(0.573470\pi\)
\(450\) 1.97118 5.24426i 0.0929223 0.247217i
\(451\) 17.3773 14.1670i 0.818265 0.667097i
\(452\) 4.66536i 0.219440i
\(453\) 2.40104i 0.112811i
\(454\) 15.3159i 0.718810i
\(455\) −2.66447 + 0.925357i −0.124912 + 0.0433814i
\(456\) 10.4859 0.491047
\(457\) 25.1070 1.17446 0.587228 0.809422i \(-0.300219\pi\)
0.587228 + 0.809422i \(0.300219\pi\)
\(458\) 5.74473i 0.268434i
\(459\) 4.13710i 0.193103i
\(460\) −3.14834 + 2.18002i −0.146792 + 0.101644i
\(461\) −41.2119 −1.91943 −0.959716 0.280973i \(-0.909343\pi\)
−0.959716 + 0.280973i \(0.909343\pi\)
\(462\) 9.00717 3.94277i 0.419052 0.183434i
\(463\) 0.834251i 0.0387709i 0.999812 + 0.0193855i \(0.00617097\pi\)
−0.999812 + 0.0193855i \(0.993829\pi\)
\(464\) 17.1967i 0.798336i
\(465\) −13.0919 + 9.06529i −0.607123 + 0.420393i
\(466\) 8.00744 0.370937
\(467\) −15.6729 −0.725257 −0.362628 0.931934i \(-0.618121\pi\)
−0.362628 + 0.931934i \(0.618121\pi\)
\(468\) 0.354945i 0.0164073i
\(469\) 8.12357 29.1974i 0.375112 1.34821i
\(470\) 13.0372 + 18.8281i 0.601363 + 0.868477i
\(471\) −12.3697 −0.569966
\(472\) 32.8156i 1.51046i
\(473\) 12.2941 10.0229i 0.565285 0.460853i
\(474\) 0.813710i 0.0373749i
\(475\) 5.99859 15.9591i 0.275234 0.732252i
\(476\) 2.18431 7.85075i 0.100118 0.359839i
\(477\) 4.46060i 0.204237i
\(478\) 10.5612i 0.483057i
\(479\) −0.782115 −0.0357358 −0.0178679 0.999840i \(-0.505688\pi\)
−0.0178679 + 0.999840i \(0.505688\pi\)
\(480\) −5.03811 7.27594i −0.229957 0.332100i
\(481\) 2.19295 0.0999901
\(482\) −23.0410 −1.04949
\(483\) 1.63137 5.86341i 0.0742301 0.266794i
\(484\) −1.64980 + 8.02144i −0.0749910 + 0.364611i
\(485\) 5.56005 + 8.02971i 0.252469 + 0.364610i
\(486\) 1.12050 0.0508268
\(487\) 2.35861i 0.106879i −0.998571 0.0534395i \(-0.982982\pi\)
0.998571 0.0534395i \(-0.0170184\pi\)
\(488\) −6.51272 −0.294817
\(489\) 20.8684i 0.943701i
\(490\) 1.10240 + 17.5039i 0.0498012 + 0.790744i
\(491\) 13.8928i 0.626975i −0.949592 0.313488i \(-0.898503\pi\)
0.949592 0.313488i \(-0.101497\pi\)
\(492\) 5.03272 0.226893
\(493\) 36.3581 1.63749
\(494\) 1.82158i 0.0819568i
\(495\) −7.12493 2.05799i −0.320242 0.0924999i
\(496\) 13.9351i 0.625704i
\(497\) 36.1159 + 10.0485i 1.62002 + 0.450738i
\(498\) 9.84790i 0.441295i
\(499\) 0.751292 0.0336325 0.0168162 0.999859i \(-0.494647\pi\)
0.0168162 + 0.999859i \(0.494647\pi\)
\(500\) −8.07283 + 2.02778i −0.361028 + 0.0906849i
\(501\) 11.4710i 0.512487i
\(502\) 24.1033i 1.07578i
\(503\) 8.81058i 0.392844i −0.980519 0.196422i \(-0.937068\pi\)
0.980519 0.196422i \(-0.0629323\pi\)
\(504\) 7.83845 + 2.18089i 0.349152 + 0.0971445i
\(505\) −13.0946 18.9109i −0.582701 0.841526i
\(506\) −5.40173 6.62580i −0.240136 0.294553i
\(507\) −12.7727 −0.567255
\(508\) −6.38337 −0.283216
\(509\) 18.7722i 0.832065i −0.909350 0.416033i \(-0.863420\pi\)
0.909350 0.416033i \(-0.136580\pi\)
\(510\) 8.52197 5.90090i 0.377359 0.261296i
\(511\) 6.59241 23.6941i 0.291631 1.04817i
\(512\) 19.7794 0.874135
\(513\) 3.40984 0.150548
\(514\) −27.5576 −1.21551
\(515\) 21.9919 + 31.7603i 0.969080 + 1.39953i
\(516\) 3.56057 0.156745
\(517\) 23.4963 19.1555i 1.03337 0.842460i
\(518\) 3.65509 13.1369i 0.160595 0.577204i
\(519\) 21.5558i 0.946193i
\(520\) −2.69531 + 1.86632i −0.118197 + 0.0818437i
\(521\) 25.6661i 1.12445i −0.826983 0.562227i \(-0.809945\pi\)
0.826983 0.562227i \(-0.190055\pi\)
\(522\) 9.84727i 0.431003i
\(523\) 36.1446i 1.58049i 0.612790 + 0.790246i \(0.290047\pi\)
−0.612790 + 0.790246i \(0.709953\pi\)
\(524\) −10.5842 −0.462373
\(525\) 7.80330 10.6822i 0.340564 0.466208i
\(526\) 33.6625 1.46776
\(527\) −29.4623 −1.28340
\(528\) 5.03008 4.10081i 0.218906 0.178465i
\(529\) 17.7084 0.769932
\(530\) −9.18833 + 6.36231i −0.399115 + 0.276361i
\(531\) 10.6711i 0.463086i
\(532\) 6.47066 + 1.80033i 0.280539 + 0.0780542i
\(533\) 3.22293i 0.139601i
\(534\) 11.4411i 0.495104i
\(535\) 4.74697 + 6.85549i 0.205230 + 0.296389i
\(536\) 35.2255i 1.52151i
\(537\) 14.1203 0.609336
\(538\) 12.7410i 0.549304i
\(539\) 22.9852 3.26825i 0.990042 0.140773i
\(540\) −0.947693 1.36864i −0.0407822 0.0588969i
\(541\) 30.0504i 1.29197i −0.763351 0.645984i \(-0.776447\pi\)
0.763351 0.645984i \(-0.223553\pi\)
\(542\) −10.2493 −0.440245
\(543\) 6.42683i 0.275801i
\(544\) 16.3739i 0.702027i
\(545\) 20.8045 14.4057i 0.891166 0.617073i
\(546\) 0.378858 1.36167i 0.0162136 0.0582743i
\(547\) −28.6466 −1.22484 −0.612420 0.790532i \(-0.709804\pi\)
−0.612420 + 0.790532i \(0.709804\pi\)
\(548\) 6.08034i 0.259739i
\(549\) −2.11783 −0.0903867
\(550\) −5.92331 17.6119i −0.252571 0.750976i
\(551\) 29.9667i 1.27662i
\(552\) 7.07398i 0.301088i
\(553\) −0.515016 + 1.85105i −0.0219007 + 0.0787145i
\(554\) 11.9667 0.508416
\(555\) −8.45587 + 5.85513i −0.358932 + 0.248536i
\(556\) −3.91590 −0.166071
\(557\) 15.1173 0.640540 0.320270 0.947326i \(-0.396226\pi\)
0.320270 + 0.947326i \(0.396226\pi\)
\(558\) 7.97960i 0.337804i
\(559\) 2.28017i 0.0964409i
\(560\) 3.79791 + 10.9357i 0.160491 + 0.462116i
\(561\) −8.67016 10.6349i −0.366054 0.449004i
\(562\) 29.5083i 1.24473i
\(563\) 18.8199i 0.793164i 0.917999 + 0.396582i \(0.129804\pi\)
−0.917999 + 0.396582i \(0.870196\pi\)
\(564\) 6.80488 0.286537
\(565\) 11.5202 7.97700i 0.484660 0.335595i
\(566\) 0.927369i 0.0389802i
\(567\) 2.54893 + 0.709189i 0.107045 + 0.0297831i
\(568\) 43.5724 1.82826
\(569\) 9.67129i 0.405442i 0.979237 + 0.202721i \(0.0649784\pi\)
−0.979237 + 0.202721i \(0.935022\pi\)
\(570\) 4.86357 + 7.02388i 0.203713 + 0.294198i
\(571\) 23.8505i 0.998111i 0.866570 + 0.499055i \(0.166320\pi\)
−0.866570 + 0.499055i \(0.833680\pi\)
\(572\) 0.743860 + 0.912423i 0.0311024 + 0.0381503i
\(573\) −1.65973 −0.0693362
\(574\) −19.3070 5.37179i −0.805860 0.224214i
\(575\) −10.7663 4.04676i −0.448985 0.168761i
\(576\) 8.34827 0.347844
\(577\) −34.7774 −1.44780 −0.723902 0.689903i \(-0.757653\pi\)
−0.723902 + 0.689903i \(0.757653\pi\)
\(578\) 0.129563 0.00538912
\(579\) −7.02842 −0.292091
\(580\) 12.0280 8.32862i 0.499437 0.345827i
\(581\) 6.23296 22.4022i 0.258587 0.929400i
\(582\) −4.89416 −0.202869
\(583\) 9.34810 + 11.4664i 0.387159 + 0.474891i
\(584\) 28.5861i 1.18290i
\(585\) −0.876470 + 0.606897i −0.0362376 + 0.0250921i
\(586\) 5.88702i 0.243191i
\(587\) −22.0581 −0.910436 −0.455218 0.890380i \(-0.650439\pi\)
−0.455218 + 0.890380i \(0.650439\pi\)
\(588\) 4.46253 + 2.69158i 0.184031 + 0.110999i
\(589\) 24.2831i 1.00057i
\(590\) 21.9813 15.2206i 0.904954 0.626621i
\(591\) −8.04622 −0.330977
\(592\) 9.00046i 0.369917i
\(593\) 41.1949i 1.69167i 0.533444 + 0.845836i \(0.320898\pi\)
−0.533444 + 0.845836i \(0.679102\pi\)
\(594\) 2.88036 2.34823i 0.118182 0.0963492i
\(595\) 23.1208 8.02974i 0.947859 0.329187i
\(596\) 16.6594i 0.682394i
\(597\) 22.3264i 0.913759i
\(598\) −1.22887 −0.0502523
\(599\) −15.1101 −0.617382 −0.308691 0.951162i \(-0.599891\pi\)
−0.308691 + 0.951162i \(0.599891\pi\)
\(600\) 5.40987 14.3928i 0.220857 0.587584i
\(601\) 15.6214 0.637209 0.318605 0.947888i \(-0.396786\pi\)
0.318605 + 0.947888i \(0.396786\pi\)
\(602\) −13.6594 3.80045i −0.556716 0.154895i
\(603\) 11.4547i 0.466473i
\(604\) 1.78754i 0.0727340i
\(605\) −22.6283 + 9.64148i −0.919973 + 0.391982i
\(606\) 11.5263 0.468226
\(607\) 33.0830i 1.34280i 0.741096 + 0.671399i \(0.234306\pi\)
−0.741096 + 0.671399i \(0.765694\pi\)
\(608\) 13.4955 0.547316
\(609\) −6.23257 + 22.4008i −0.252556 + 0.907726i
\(610\) −3.02073 4.36248i −0.122306 0.176632i
\(611\) 4.35781i 0.176298i
\(612\) 3.08002i 0.124502i
\(613\) 41.6396 1.68181 0.840903 0.541186i \(-0.182024\pi\)
0.840903 + 0.541186i \(0.182024\pi\)
\(614\) 8.00311i 0.322979i
\(615\) 8.60513 + 12.4274i 0.346992 + 0.501120i
\(616\) 24.7201 10.8209i 0.995999 0.435986i
\(617\) 0.241842i 0.00973618i 0.999988 + 0.00486809i \(0.00154957\pi\)
−0.999988 + 0.00486809i \(0.998450\pi\)
\(618\) −19.3581 −0.778697
\(619\) 45.8257i 1.84189i 0.389692 + 0.920945i \(0.372581\pi\)
−0.389692 + 0.920945i \(0.627419\pi\)
\(620\) −9.74675 + 6.74898i −0.391439 + 0.271046i
\(621\) 2.30034i 0.0923094i
\(622\) 0.833372i 0.0334152i
\(623\) −7.24132 + 26.0264i −0.290117 + 1.04273i
\(624\) 0.932918i 0.0373466i
\(625\) −18.8104 16.4672i −0.752417 0.658687i
\(626\) −7.98049 −0.318964
\(627\) 8.76535 7.14602i 0.350054 0.285385i
\(628\) −9.20908 −0.367482
\(629\) −19.0293 −0.758746
\(630\) 2.17478 + 6.26205i 0.0866455 + 0.249486i
\(631\) −5.31291 −0.211504 −0.105752 0.994393i \(-0.533725\pi\)
−0.105752 + 0.994393i \(0.533725\pi\)
\(632\) 2.23322i 0.0888326i
\(633\) 14.8136i 0.588788i
\(634\) 37.8149i 1.50182i
\(635\) −10.9145 15.7625i −0.433129 0.625517i
\(636\) 3.32085i 0.131680i
\(637\) 1.72367 2.85778i 0.0682943 0.113229i
\(638\) 20.6370 + 25.3135i 0.817026 + 1.00217i
\(639\) 14.1690 0.560518
\(640\) 1.83121 + 2.64461i 0.0723851 + 0.104537i
\(641\) −3.41919 −0.135050 −0.0675249 0.997718i \(-0.521510\pi\)
−0.0675249 + 0.997718i \(0.521510\pi\)
\(642\) −4.17846 −0.164911
\(643\) 46.7632 1.84416 0.922080 0.386998i \(-0.126488\pi\)
0.922080 + 0.386998i \(0.126488\pi\)
\(644\) 1.21454 4.36522i 0.0478594 0.172014i
\(645\) 6.08799 + 8.79216i 0.239714 + 0.346191i
\(646\) 15.8067i 0.621906i
\(647\) −15.6538 −0.615415 −0.307708 0.951481i \(-0.599562\pi\)
−0.307708 + 0.951481i \(0.599562\pi\)
\(648\) 3.07519 0.120805
\(649\) −22.3635 27.4312i −0.877844 1.07677i
\(650\) −2.50028 0.939789i −0.0980690 0.0368616i
\(651\) 5.05048 18.1522i 0.197944 0.711440i
\(652\) 15.5362i 0.608445i
\(653\) 34.1748i 1.33736i 0.743548 + 0.668682i \(0.233141\pi\)
−0.743548 + 0.668682i \(0.766859\pi\)
\(654\) 12.6805i 0.495845i
\(655\) −18.0972 26.1357i −0.707118 1.02121i
\(656\) −13.2277 −0.516457
\(657\) 9.29571i 0.362660i
\(658\) −26.1055 7.26334i −1.01770 0.283155i
\(659\) 12.0053i 0.467660i 0.972277 + 0.233830i \(0.0751260\pi\)
−0.972277 + 0.233830i \(0.924874\pi\)
\(660\) −5.30441 1.53215i −0.206474 0.0596388i
\(661\) 8.58426i 0.333889i 0.985966 + 0.166944i \(0.0533900\pi\)
−0.985966 + 0.166944i \(0.946610\pi\)
\(662\) 26.6338 1.03515
\(663\) −1.97243 −0.0766027
\(664\) 27.0274i 1.04887i
\(665\) 6.61819 + 19.0563i 0.256642 + 0.738973i
\(666\) 5.15390i 0.199710i
\(667\) 20.2161 0.782770
\(668\) 8.54001i 0.330423i
\(669\) −3.11670 −0.120498
\(670\) 23.5955 16.3383i 0.911573 0.631204i
\(671\) −5.44410 + 4.43834i −0.210167 + 0.171340i
\(672\) 10.0882 + 2.80684i 0.389162 + 0.108276i
\(673\) −32.3671 −1.24766 −0.623829 0.781561i \(-0.714424\pi\)
−0.623829 + 0.781561i \(0.714424\pi\)
\(674\) −14.2963 −0.550674
\(675\) 1.75920 4.68030i 0.0677117 0.180145i
\(676\) −9.50909 −0.365734
\(677\) 11.9557i 0.459497i −0.973250 0.229748i \(-0.926210\pi\)
0.973250 0.229748i \(-0.0737903\pi\)
\(678\) 7.02166i 0.269665i
\(679\) −11.1333 3.09763i −0.427258 0.118876i
\(680\) 23.3884 16.1949i 0.896905 0.621048i
\(681\) 13.6688i 0.523791i
\(682\) −16.7229 20.5124i −0.640353 0.785461i
\(683\) 7.34339i 0.280987i −0.990082 0.140494i \(-0.955131\pi\)
0.990082 0.140494i \(-0.0448689\pi\)
\(684\) 2.53858 0.0970649
\(685\) −15.0143 + 10.3964i −0.573666 + 0.397226i
\(686\) −14.2467 15.0889i −0.543940 0.576095i
\(687\) 5.12695i 0.195605i
\(688\) −9.35841 −0.356786
\(689\) 2.12666 0.0810191
\(690\) 4.73844 3.28106i 0.180389 0.124908i
\(691\) 7.78297i 0.296078i 0.988982 + 0.148039i \(0.0472961\pi\)
−0.988982 + 0.148039i \(0.952704\pi\)
\(692\) 16.0480i 0.610052i
\(693\) 8.03855 3.51877i 0.305359 0.133667i
\(694\) 19.7800 0.750840
\(695\) −6.69554 9.66958i −0.253976 0.366788i
\(696\) 27.0257i 1.02441i
\(697\) 27.9668i 1.05932i
\(698\) −1.26093 −0.0477270
\(699\) 7.14633 0.270299
\(700\) 5.80945 7.95272i 0.219576 0.300585i
\(701\) 14.4847i 0.547078i 0.961861 + 0.273539i \(0.0881943\pi\)
−0.961861 + 0.273539i \(0.911806\pi\)
\(702\) 0.534214i 0.0201626i
\(703\) 15.6841i 0.591537i
\(704\) 21.4601 17.4955i 0.808808 0.659387i
\(705\) 11.6352 + 16.8034i 0.438208 + 0.632852i
\(706\) 29.8851 1.12474
\(707\) 26.2204 + 7.29529i 0.986118 + 0.274368i
\(708\) 7.94449i 0.298572i
\(709\) 13.2996 0.499476 0.249738 0.968313i \(-0.419655\pi\)
0.249738 + 0.968313i \(0.419655\pi\)
\(710\) 20.2098 + 29.1866i 0.758460 + 1.09535i
\(711\) 0.726204i 0.0272348i
\(712\) 31.3999i 1.17676i
\(713\) −16.3818 −0.613504
\(714\) −3.28752 + 11.8159i −0.123033 + 0.442197i
\(715\) −0.981179 + 3.39692i −0.0366940 + 0.127037i
\(716\) 10.5124 0.392866
\(717\) 9.42544i 0.352000i
\(718\) 33.6668i 1.25643i
\(719\) 21.8590i 0.815203i −0.913160 0.407602i \(-0.866365\pi\)
0.913160 0.407602i \(-0.133635\pi\)
\(720\) 2.49087 + 3.59726i 0.0928291 + 0.134062i
\(721\) −44.0363 12.2522i −1.64000 0.456296i
\(722\) 8.26143 0.307459
\(723\) −20.5632 −0.764754
\(724\) 4.78468i 0.177821i
\(725\) 41.1319 + 15.4604i 1.52760 + 0.574185i
\(726\) 2.48305 12.0728i 0.0921547 0.448062i
\(727\) −6.31100 −0.234062 −0.117031 0.993128i \(-0.537338\pi\)
−0.117031 + 0.993128i \(0.537338\pi\)
\(728\) 1.03977 3.73709i 0.0385365 0.138506i
\(729\) 1.00000 0.0370370
\(730\) 19.1481 13.2588i 0.708703 0.490730i
\(731\) 19.7861i 0.731814i
\(732\) −1.57669 −0.0582762
\(733\) 6.36583i 0.235127i −0.993065 0.117564i \(-0.962492\pi\)
0.993065 0.117564i \(-0.0375084\pi\)
\(734\) 1.56650 0.0578204
\(735\) 0.983846 + 15.6215i 0.0362897 + 0.576209i
\(736\) 9.10434i 0.335590i
\(737\) −24.0058 29.4456i −0.884264 1.08464i
\(738\) −7.57456 −0.278823
\(739\) 42.1815i 1.55167i 0.630935 + 0.775835i \(0.282671\pi\)
−0.630935 + 0.775835i \(0.717329\pi\)
\(740\) −6.29528 + 4.35906i −0.231419 + 0.160242i
\(741\) 1.62569i 0.0597212i
\(742\) 3.54459 12.7398i 0.130126 0.467692i
\(743\) 3.62823 0.133107 0.0665534 0.997783i \(-0.478800\pi\)
0.0665534 + 0.997783i \(0.478800\pi\)
\(744\) 21.8999i 0.802890i
\(745\) −41.1372 + 28.4848i −1.50715 + 1.04360i
\(746\) 8.16326 0.298878
\(747\) 8.78886i 0.321568i
\(748\) −6.45481 7.91751i −0.236011 0.289493i
\(749\) −9.50526 2.64465i −0.347314 0.0966333i
\(750\) 12.1501 3.05193i 0.443659 0.111441i
\(751\) 4.91421 0.179322 0.0896610 0.995972i \(-0.471422\pi\)
0.0896610 + 0.995972i \(0.471422\pi\)
\(752\) −17.8856 −0.652220
\(753\) 21.5112i 0.783912i
\(754\) 4.69483 0.170976
\(755\) −4.41400 + 3.05640i −0.160642 + 0.111234i
\(756\) 1.89764 + 0.527981i 0.0690166 + 0.0192025i
\(757\) 12.5745i 0.457030i 0.973540 + 0.228515i \(0.0733869\pi\)
−0.973540 + 0.228515i \(0.926613\pi\)
\(758\) 7.48893 0.272010
\(759\) −4.82084 5.91326i −0.174985 0.214638i
\(760\) 13.3480 + 19.2769i 0.484183 + 0.699248i
\(761\) 50.2936 1.82314 0.911571 0.411142i \(-0.134870\pi\)
0.911571 + 0.411142i \(0.134870\pi\)
\(762\) 9.60736 0.348038
\(763\) −8.02575 + 28.8458i −0.290552 + 1.04429i
\(764\) −1.23565 −0.0447041
\(765\) 7.60552 5.26632i 0.274978 0.190404i
\(766\) −27.6491 −0.999001
\(767\) −5.08760 −0.183703
\(768\) 15.0846 0.544320
\(769\) 52.8622 1.90626 0.953129 0.302563i \(-0.0978424\pi\)
0.953129 + 0.302563i \(0.0978424\pi\)
\(770\) 18.7139 + 11.5396i 0.674403 + 0.415857i
\(771\) −24.5941 −0.885734
\(772\) −5.23256 −0.188324
\(773\) 50.9018 1.83081 0.915405 0.402534i \(-0.131870\pi\)
0.915405 + 0.402534i \(0.131870\pi\)
\(774\) −5.35887 −0.192621
\(775\) −33.3307 12.5281i −1.19727 0.450023i
\(776\) −13.4320 −0.482179
\(777\) 3.26203 11.7242i 0.117025 0.420604i
\(778\) 1.43809 0.0515579
\(779\) −23.0505 −0.825870
\(780\) −0.652519 + 0.451827i −0.0233639 + 0.0161780i
\(781\) 36.4230 29.6941i 1.30332 1.06254i
\(782\) 10.6635 0.381325
\(783\) 8.78831i 0.314068i
\(784\) −11.7291 7.07440i −0.418895 0.252657i
\(785\) −15.7460 22.7401i −0.562000 0.811629i
\(786\) 15.9299 0.568200
\(787\) 35.5901i 1.26865i −0.773067 0.634324i \(-0.781278\pi\)
0.773067 0.634324i \(-0.218722\pi\)
\(788\) −5.99030 −0.213395
\(789\) 30.0425 1.06954
\(790\) −1.49590 + 1.03581i −0.0532217 + 0.0368525i
\(791\) −4.44417 + 15.9730i −0.158016 + 0.567935i
\(792\) 7.90510 6.44469i 0.280895 0.229002i
\(793\) 1.00971i 0.0358557i
\(794\) −11.7312 −0.416324
\(795\) −8.20022 + 5.67811i −0.290832 + 0.201382i
\(796\) 16.6217i 0.589140i
\(797\) −10.2007 −0.361326 −0.180663 0.983545i \(-0.557824\pi\)
−0.180663 + 0.983545i \(0.557824\pi\)
\(798\) −9.73874 2.70961i −0.344748 0.0959190i
\(799\) 37.8147i 1.33779i
\(800\) 6.96261 18.5238i 0.246165 0.654916i
\(801\) 10.2107i 0.360778i
\(802\) −11.9875 −0.423293
\(803\) −19.4811 23.8956i −0.687472 0.843257i
\(804\) 8.52790i 0.300756i
\(805\) 12.8558 4.46475i 0.453106 0.157362i
\(806\) −3.80439 −0.134004
\(807\) 11.3709i 0.400273i
\(808\) 31.6339 1.11288
\(809\) 30.0386i 1.05610i −0.849213 0.528050i \(-0.822923\pi\)
0.849213 0.528050i \(-0.177077\pi\)
\(810\) 1.42634 + 2.05989i 0.0501163 + 0.0723771i
\(811\) −23.5708 −0.827683 −0.413841 0.910349i \(-0.635813\pi\)
−0.413841 + 0.910349i \(0.635813\pi\)
\(812\) −4.64006 + 16.6771i −0.162834 + 0.585251i
\(813\) −9.14710 −0.320803
\(814\) −10.8011 13.2487i −0.378577 0.464365i
\(815\) 38.3638 26.5644i 1.34382 0.930510i
\(816\) 8.09535i 0.283394i
\(817\) −16.3078 −0.570539
\(818\) −9.81644 −0.343224
\(819\) 0.338116 1.21524i 0.0118147 0.0424639i
\(820\) 6.40640 + 9.25200i 0.223721 + 0.323094i
\(821\) 0.143674i 0.00501425i −0.999997 0.00250713i \(-0.999202\pi\)
0.999997 0.00250713i \(-0.000798044\pi\)
\(822\) 9.15129i 0.319188i
\(823\) 4.96934i 0.173220i −0.996242 0.0866102i \(-0.972397\pi\)
0.996242 0.0866102i \(-0.0276035\pi\)
\(824\) −53.1281 −1.85080
\(825\) −5.28633 15.7180i −0.184046 0.547230i
\(826\) −8.47972 + 30.4774i −0.295047 + 1.06044i
\(827\) −28.6141 −0.995010 −0.497505 0.867461i \(-0.665750\pi\)
−0.497505 + 0.867461i \(0.665750\pi\)
\(828\) 1.71257i 0.0595159i
\(829\) 25.4245i 0.883029i 0.897254 + 0.441515i \(0.145559\pi\)
−0.897254 + 0.441515i \(0.854441\pi\)
\(830\) 18.1041 12.5359i 0.628401 0.435126i
\(831\) 10.6798 0.370479
\(832\) 3.98016i 0.137987i
\(833\) −14.9571 + 24.7982i −0.518232 + 0.859208i
\(834\) 5.89367 0.204081
\(835\) −21.0880 + 14.6020i −0.729779 + 0.505324i
\(836\) 6.52568 5.32011i 0.225695 0.184000i
\(837\) 7.12148i 0.246154i
\(838\) 30.8484i 1.06564i
\(839\) 6.73515i 0.232523i −0.993219 0.116262i \(-0.962909\pi\)
0.993219 0.116262i \(-0.0370911\pi\)
\(840\) 5.96866 + 17.1861i 0.205938 + 0.592977i
\(841\) −48.2343 −1.66325
\(842\) −29.3456 −1.01132
\(843\) 26.3350i 0.907024i
\(844\) 11.0285i 0.379617i
\(845\) −16.2590 23.4809i −0.559326 0.807768i
\(846\) −10.2418 −0.352119
\(847\) 13.2896 25.8918i 0.456637 0.889653i
\(848\) 8.72835i 0.299733i
\(849\) 0.827641i 0.0284046i
\(850\) 21.6961 + 8.15497i 0.744169 + 0.279713i
\(851\) −10.5808 −0.362704
\(852\) 10.5486 0.361391
\(853\) 30.4003i 1.04089i −0.853896 0.520444i \(-0.825767\pi\)
0.853896 0.520444i \(-0.174233\pi\)
\(854\) 6.04866 + 1.68292i 0.206981 + 0.0575883i
\(855\) 4.34055 + 6.26854i 0.148444 + 0.214380i
\(856\) −11.4677 −0.391959
\(857\) 2.21267i 0.0755834i −0.999286 0.0377917i \(-0.987968\pi\)
0.999286 0.0377917i \(-0.0120323\pi\)
\(858\) −1.11955 1.37325i −0.0382210 0.0468821i
\(859\) 26.2514i 0.895687i 0.894112 + 0.447843i \(0.147808\pi\)
−0.894112 + 0.447843i \(0.852192\pi\)
\(860\) 4.53242 + 6.54564i 0.154554 + 0.223204i
\(861\) −17.2308 4.79411i −0.587223 0.163383i
\(862\) 24.9904i 0.851178i
\(863\) 31.5519i 1.07404i 0.843569 + 0.537020i \(0.180450\pi\)
−0.843569 + 0.537020i \(0.819550\pi\)
\(864\) 3.95782 0.134648
\(865\) −39.6275 + 27.4394i −1.34737 + 0.932968i
\(866\) 4.38774 0.149102
\(867\) 0.115630 0.00392700
\(868\) 3.76001 13.5140i 0.127623 0.458696i
\(869\) 1.52191 + 1.86679i 0.0516273 + 0.0633264i
\(870\) −18.1029 + 12.5351i −0.613746 + 0.424979i
\(871\) −5.46122 −0.185046
\(872\) 34.8013i 1.17852i
\(873\) −4.36785 −0.147829
\(874\) 8.78894i 0.297290i
\(875\) 29.5710 + 0.747496i 0.999681 + 0.0252700i
\(876\) 6.92052i 0.233823i
\(877\) −15.5996 −0.526762 −0.263381 0.964692i \(-0.584838\pi\)
−0.263381 + 0.964692i \(0.584838\pi\)
\(878\) −7.84810 −0.264860
\(879\) 5.25394i 0.177211i
\(880\) 13.9418 + 4.02702i 0.469979 + 0.135751i
\(881\) 42.7607i 1.44065i −0.693639 0.720323i \(-0.743994\pi\)
0.693639 0.720323i \(-0.256006\pi\)
\(882\) −6.71637 4.05099i −0.226152 0.136404i
\(883\) 19.1056i 0.642956i −0.946917 0.321478i \(-0.895820\pi\)
0.946917 0.321478i \(-0.104180\pi\)
\(884\) −1.46844 −0.0493891
\(885\) 19.6174 13.5838i 0.659432 0.456613i
\(886\) 20.5555i 0.690574i
\(887\) 51.6117i 1.73295i 0.499221 + 0.866475i \(0.333620\pi\)
−0.499221 + 0.866475i \(0.666380\pi\)
\(888\) 14.1448i 0.474669i
\(889\) 21.8550 + 6.08072i 0.732994 + 0.203941i
\(890\) −21.0329 + 14.5639i −0.705025 + 0.488183i
\(891\) 2.57061 2.09571i 0.0861185 0.0702088i
\(892\) −2.32034 −0.0776906
\(893\) −31.1672 −1.04297
\(894\) 25.0733i 0.838578i
\(895\) 17.9744 + 25.9583i 0.600819 + 0.867692i
\(896\) −3.66679 1.02021i −0.122499 0.0340829i
\(897\) −1.09672 −0.0366184
\(898\) 10.8633 0.362512
\(899\) 62.5858 2.08735
\(900\) 1.30970 3.48442i 0.0436567 0.116147i
\(901\) −18.4540 −0.614790
\(902\) −19.4712 + 15.8741i −0.648320 + 0.528548i
\(903\) −12.1905 3.39176i −0.405674 0.112871i
\(904\) 19.2708i 0.640939i
\(905\) −11.8149 + 8.18102i −0.392740 + 0.271946i
\(906\) 2.69036i 0.0893812i
\(907\) 6.32362i 0.209972i −0.994474 0.104986i \(-0.966520\pi\)
0.994474 0.104986i \(-0.0334798\pi\)
\(908\) 10.1763i 0.337711i
\(909\) 10.2868 0.341192
\(910\) 2.98553 1.03686i 0.0989692 0.0343716i
\(911\) −39.5020 −1.30876 −0.654379 0.756167i \(-0.727070\pi\)
−0.654379 + 0.756167i \(0.727070\pi\)
\(912\) −6.67226 −0.220941
\(913\) −18.4189 22.5927i −0.609576 0.747709i
\(914\) −28.1323 −0.930534
\(915\) −2.69589 3.89335i −0.0891232 0.128710i
\(916\) 3.81694i 0.126115i
\(917\) 36.2376 + 10.0824i 1.19667 + 0.332950i
\(918\) 4.63561i 0.152998i
\(919\) 10.5173i 0.346934i −0.984840 0.173467i \(-0.944503\pi\)
0.984840 0.173467i \(-0.0554969\pi\)
\(920\) 13.0046 9.00481i 0.428748 0.296880i
\(921\) 7.14246i 0.235352i
\(922\) 46.1779 1.52079
\(923\) 6.75529i 0.222353i
\(924\) 5.98459 2.61967i 0.196879 0.0861809i
\(925\) −21.5278 8.09172i −0.707829 0.266054i
\(926\) 0.934776i 0.0307186i
\(927\) −17.2764 −0.567430
\(928\) 34.7826i 1.14179i
\(929\) 36.2241i 1.18847i 0.804290 + 0.594237i \(0.202546\pi\)
−0.804290 + 0.594237i \(0.797454\pi\)
\(930\) 14.6695 10.1576i 0.481030 0.333082i
\(931\) −20.4389 12.3277i −0.669858 0.404026i
\(932\) 5.32034 0.174274
\(933\) 0.743752i 0.0243494i
\(934\) 17.5615 0.574629
\(935\) 8.51413 29.4766i 0.278442 0.963987i
\(936\) 1.46614i 0.0479223i
\(937\) 2.65704i 0.0868018i 0.999058 + 0.0434009i \(0.0138193\pi\)
−0.999058 + 0.0434009i \(0.986181\pi\)
\(938\) −9.10244 + 32.7155i −0.297205 + 1.06820i
\(939\) −7.12227 −0.232427
\(940\) 8.66227 + 12.5099i 0.282532 + 0.408027i
\(941\) −40.6135 −1.32396 −0.661982 0.749520i \(-0.730284\pi\)
−0.661982 + 0.749520i \(0.730284\pi\)
\(942\) 13.8602 0.451591
\(943\) 15.5503i 0.506387i
\(944\) 20.8809i 0.679614i
\(945\) 1.94091 + 5.58864i 0.0631378 + 0.181798i
\(946\) −13.7756 + 11.2306i −0.447882 + 0.365139i
\(947\) 17.3928i 0.565191i −0.959239 0.282595i \(-0.908805\pi\)
0.959239 0.282595i \(-0.0911954\pi\)
\(948\) 0.540649i 0.0175595i
\(949\) −4.43186 −0.143864
\(950\) −6.72140 + 17.8821i −0.218071 + 0.580171i
\(951\) 33.7483i 1.09437i
\(952\) −9.02257 + 32.4285i −0.292423 + 1.05101i
\(953\) −18.0925 −0.586072 −0.293036 0.956101i \(-0.594666\pi\)
−0.293036 + 0.956101i \(0.594666\pi\)
\(954\) 4.99809i 0.161819i
\(955\) −2.11275 3.05120i −0.0683670 0.0987344i
\(956\) 7.01711i 0.226950i
\(957\) 18.4177 + 22.5913i 0.595360 + 0.730272i
\(958\) 0.876358 0.0283138
\(959\) 5.79206 20.8176i 0.187036 0.672234i
\(960\) 10.6269 + 15.3472i 0.342982 + 0.495329i
\(961\) −19.7155 −0.635985
\(962\) −2.45720 −0.0792233
\(963\) −3.72911 −0.120169
\(964\) −15.3090 −0.493071
\(965\) −8.94682 12.9208i −0.288008 0.415936i
\(966\) −1.82795 + 6.56993i −0.0588134 + 0.211384i
\(967\) −50.4552 −1.62253 −0.811265 0.584678i \(-0.801221\pi\)
−0.811265 + 0.584678i \(0.801221\pi\)
\(968\) 6.81470 33.1335i 0.219033 1.06495i
\(969\) 14.1069i 0.453177i
\(970\) −6.23002 8.99727i −0.200034 0.288885i
\(971\) 51.6403i 1.65722i −0.559830 0.828608i \(-0.689133\pi\)
0.559830 0.828608i \(-0.310867\pi\)
\(972\) 0.744486 0.0238794
\(973\) 13.4070 + 3.73024i 0.429810 + 0.119586i
\(974\) 2.64282i 0.0846814i
\(975\) −2.23140 0.838725i −0.0714621 0.0268607i
\(976\) 4.14410 0.132649
\(977\) 46.0339i 1.47275i −0.676571 0.736377i \(-0.736535\pi\)
0.676571 0.736377i \(-0.263465\pi\)
\(978\) 23.3830i 0.747705i
\(979\) 21.3987 + 26.2477i 0.683904 + 0.838881i
\(980\) 0.732460 + 11.6300i 0.0233976 + 0.371507i
\(981\) 11.3168i 0.361318i
\(982\) 15.5669i 0.496760i
\(983\) 10.1938 0.325131 0.162566 0.986698i \(-0.448023\pi\)
0.162566 + 0.986698i \(0.448023\pi\)
\(984\) −20.7883 −0.662706
\(985\) −10.2424 14.7919i −0.326351 0.471310i
\(986\) −40.7392 −1.29740
\(987\) −23.2982 6.48225i −0.741589 0.206332i
\(988\) 1.21030i 0.0385049i
\(989\) 11.0016i 0.349830i
\(990\) 7.98347 + 2.30598i 0.253731 + 0.0732887i
\(991\) −26.8543 −0.853056 −0.426528 0.904474i \(-0.640263\pi\)
−0.426528 + 0.904474i \(0.640263\pi\)
\(992\) 28.1856i 0.894893i
\(993\) 23.7696 0.754305
\(994\) −40.4678 11.2593i −1.28356 0.357124i
\(995\) −41.0442 + 28.4204i −1.30119 + 0.900986i
\(996\) 6.54319i 0.207329i
\(997\) 43.7961i 1.38704i −0.720439 0.693519i \(-0.756060\pi\)
0.720439 0.693519i \(-0.243940\pi\)
\(998\) −0.841821 −0.0266474
\(999\) 4.59966i 0.145527i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1155.2.k.a.769.18 yes 48
5.4 even 2 1155.2.k.b.769.31 yes 48
7.6 odd 2 1155.2.k.b.769.17 yes 48
11.10 odd 2 inner 1155.2.k.a.769.31 yes 48
35.34 odd 2 inner 1155.2.k.a.769.32 yes 48
55.54 odd 2 1155.2.k.b.769.18 yes 48
77.76 even 2 1155.2.k.b.769.32 yes 48
385.384 even 2 inner 1155.2.k.a.769.17 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.k.a.769.17 48 385.384 even 2 inner
1155.2.k.a.769.18 yes 48 1.1 even 1 trivial
1155.2.k.a.769.31 yes 48 11.10 odd 2 inner
1155.2.k.a.769.32 yes 48 35.34 odd 2 inner
1155.2.k.b.769.17 yes 48 7.6 odd 2
1155.2.k.b.769.18 yes 48 55.54 odd 2
1155.2.k.b.769.31 yes 48 5.4 even 2
1155.2.k.b.769.32 yes 48 77.76 even 2