Properties

Label 950.2.l.j.351.3
Level $950$
Weight $2$
Character 950.351
Analytic conductor $7.586$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 351.3
Character \(\chi\) \(=\) 950.351
Dual form 950.2.l.j.701.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.173648 - 0.984808i) q^{2} +(0.654394 - 0.549102i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.654394 - 0.549102i) q^{6} +(-1.39086 + 2.40903i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.394226 + 2.23577i) q^{9} +O(q^{10})\) \(q+(-0.173648 - 0.984808i) q^{2} +(0.654394 - 0.549102i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.654394 - 0.549102i) q^{6} +(-1.39086 + 2.40903i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.394226 + 2.23577i) q^{9} +(-1.58300 - 2.74184i) q^{11} +(-0.427125 + 0.739803i) q^{12} +(-3.68105 - 3.08877i) q^{13} +(2.61395 + 0.951401i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.235648 + 1.33642i) q^{17} +2.27026 q^{18} +(4.15700 + 1.31125i) q^{19} +(0.412636 + 2.34018i) q^{21} +(-2.42530 + 2.03507i) q^{22} +(-5.66623 + 2.06234i) q^{23} +(0.802733 + 0.292171i) q^{24} +(-2.40263 + 4.16148i) q^{26} +(2.25106 + 3.89895i) q^{27} +(0.483039 - 2.73945i) q^{28} +(-1.81040 + 10.2673i) q^{29} +(-3.80232 + 6.58582i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-2.54146 - 0.925014i) q^{33} +(1.27520 - 0.464135i) q^{34} +(-0.394226 - 2.23577i) q^{36} -10.9693 q^{37} +(0.569469 - 4.32154i) q^{38} -4.10490 q^{39} +(2.86803 - 2.40656i) q^{41} +(2.23297 - 0.812735i) q^{42} +(-1.44447 - 0.525743i) q^{43} +(2.42530 + 2.03507i) q^{44} +(3.01494 + 5.22203i) q^{46} +(-0.516096 + 2.92693i) q^{47} +(0.148339 - 0.841273i) q^{48} +(-0.368957 - 0.639053i) q^{49} +(0.888040 + 0.745154i) q^{51} +(4.51548 + 1.64350i) q^{52} +(4.04911 - 1.47376i) q^{53} +(3.44882 - 2.89391i) q^{54} -2.78171 q^{56} +(3.44032 - 1.42454i) q^{57} +10.4257 q^{58} +(0.714103 + 4.04988i) q^{59} +(3.98274 - 1.44960i) q^{61} +(7.14603 + 2.60094i) q^{62} +(-4.83772 - 4.05933i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.469642 + 2.66347i) q^{66} +(0.992825 - 5.63059i) q^{67} +(-0.678520 - 1.17523i) q^{68} +(-2.57551 + 4.46092i) q^{69} +(-0.844623 - 0.307418i) q^{71} +(-2.13334 + 0.776473i) q^{72} +(8.01712 - 6.72716i) q^{73} +(1.90480 + 10.8027i) q^{74} +(-4.35477 + 0.189610i) q^{76} +8.80690 q^{77} +(0.712809 + 4.04254i) q^{78} +(-1.71509 + 1.43913i) q^{79} +(-2.78603 - 1.01403i) q^{81} +(-2.86803 - 2.40656i) q^{82} +(-4.16812 + 7.21939i) q^{83} +(-1.18814 - 2.05792i) q^{84} +(-0.266927 + 1.51382i) q^{86} +(4.45307 + 7.71295i) q^{87} +(1.58300 - 2.74184i) q^{88} +(-7.26679 - 6.09756i) q^{89} +(12.5607 - 4.57174i) q^{91} +(4.61915 - 3.87593i) q^{92} +(1.12807 + 6.39758i) q^{93} +2.97208 q^{94} -0.854251 q^{96} +(-0.456661 - 2.58985i) q^{97} +(-0.565276 + 0.474323i) q^{98} +(6.75417 - 2.45832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.173648 0.984808i −0.122788 0.696364i
\(3\) 0.654394 0.549102i 0.377815 0.317024i −0.434029 0.900899i \(-0.642909\pi\)
0.811844 + 0.583875i \(0.198464\pi\)
\(4\) −0.939693 + 0.342020i −0.469846 + 0.171010i
\(5\) 0 0
\(6\) −0.654394 0.549102i −0.267155 0.224170i
\(7\) −1.39086 + 2.40903i −0.525694 + 0.910529i 0.473858 + 0.880601i \(0.342861\pi\)
−0.999552 + 0.0299274i \(0.990472\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) −0.394226 + 2.23577i −0.131409 + 0.745255i
\(10\) 0 0
\(11\) −1.58300 2.74184i −0.477293 0.826695i 0.522368 0.852720i \(-0.325049\pi\)
−0.999661 + 0.0260244i \(0.991715\pi\)
\(12\) −0.427125 + 0.739803i −0.123300 + 0.213563i
\(13\) −3.68105 3.08877i −1.02094 0.856670i −0.0311941 0.999513i \(-0.509931\pi\)
−0.989745 + 0.142844i \(0.954375\pi\)
\(14\) 2.61395 + 0.951401i 0.698608 + 0.254273i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) 0.235648 + 1.33642i 0.0571530 + 0.324131i 0.999958 0.00921543i \(-0.00293340\pi\)
−0.942805 + 0.333346i \(0.891822\pi\)
\(18\) 2.27026 0.535104
\(19\) 4.15700 + 1.31125i 0.953681 + 0.300820i
\(20\) 0 0
\(21\) 0.412636 + 2.34018i 0.0900447 + 0.510669i
\(22\) −2.42530 + 2.03507i −0.517075 + 0.433878i
\(23\) −5.66623 + 2.06234i −1.18149 + 0.430027i −0.856728 0.515768i \(-0.827507\pi\)
−0.324762 + 0.945796i \(0.605284\pi\)
\(24\) 0.802733 + 0.292171i 0.163857 + 0.0596392i
\(25\) 0 0
\(26\) −2.40263 + 4.16148i −0.471195 + 0.816134i
\(27\) 2.25106 + 3.89895i 0.433217 + 0.750353i
\(28\) 0.483039 2.73945i 0.0912858 0.517707i
\(29\) −1.81040 + 10.2673i −0.336183 + 1.90659i 0.0790458 + 0.996871i \(0.474813\pi\)
−0.415229 + 0.909717i \(0.636298\pi\)
\(30\) 0 0
\(31\) −3.80232 + 6.58582i −0.682917 + 1.18285i 0.291169 + 0.956672i \(0.405956\pi\)
−0.974086 + 0.226176i \(0.927378\pi\)
\(32\) −0.766044 0.642788i −0.135419 0.113630i
\(33\) −2.54146 0.925014i −0.442411 0.161024i
\(34\) 1.27520 0.464135i 0.218695 0.0795986i
\(35\) 0 0
\(36\) −0.394226 2.23577i −0.0657043 0.372628i
\(37\) −10.9693 −1.80335 −0.901673 0.432419i \(-0.857660\pi\)
−0.901673 + 0.432419i \(0.857660\pi\)
\(38\) 0.569469 4.32154i 0.0923801 0.701046i
\(39\) −4.10490 −0.657311
\(40\) 0 0
\(41\) 2.86803 2.40656i 0.447910 0.375841i −0.390749 0.920497i \(-0.627784\pi\)
0.838660 + 0.544656i \(0.183340\pi\)
\(42\) 2.23297 0.812735i 0.344555 0.125408i
\(43\) −1.44447 0.525743i −0.220279 0.0801750i 0.229523 0.973303i \(-0.426283\pi\)
−0.449802 + 0.893128i \(0.648506\pi\)
\(44\) 2.42530 + 2.03507i 0.365628 + 0.306798i
\(45\) 0 0
\(46\) 3.01494 + 5.22203i 0.444528 + 0.769946i
\(47\) −0.516096 + 2.92693i −0.0752804 + 0.426936i 0.923753 + 0.382988i \(0.125105\pi\)
−0.999034 + 0.0439484i \(0.986006\pi\)
\(48\) 0.148339 0.841273i 0.0214109 0.121427i
\(49\) −0.368957 0.639053i −0.0527082 0.0912933i
\(50\) 0 0
\(51\) 0.888040 + 0.745154i 0.124350 + 0.104342i
\(52\) 4.51548 + 1.64350i 0.626184 + 0.227912i
\(53\) 4.04911 1.47376i 0.556188 0.202436i −0.0486055 0.998818i \(-0.515478\pi\)
0.604794 + 0.796382i \(0.293255\pi\)
\(54\) 3.44882 2.89391i 0.469326 0.393811i
\(55\) 0 0
\(56\) −2.78171 −0.371722
\(57\) 3.44032 1.42454i 0.455682 0.188686i
\(58\) 10.4257 1.36896
\(59\) 0.714103 + 4.04988i 0.0929682 + 0.527249i 0.995351 + 0.0963137i \(0.0307052\pi\)
−0.902383 + 0.430935i \(0.858184\pi\)
\(60\) 0 0
\(61\) 3.98274 1.44960i 0.509937 0.185602i −0.0742210 0.997242i \(-0.523647\pi\)
0.584158 + 0.811640i \(0.301425\pi\)
\(62\) 7.14603 + 2.60094i 0.907547 + 0.330320i
\(63\) −4.83772 4.05933i −0.609495 0.511427i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −0.469642 + 2.66347i −0.0578089 + 0.327851i
\(67\) 0.992825 5.63059i 0.121293 0.687886i −0.862148 0.506657i \(-0.830881\pi\)
0.983441 0.181230i \(-0.0580077\pi\)
\(68\) −0.678520 1.17523i −0.0822827 0.142518i
\(69\) −2.57551 + 4.46092i −0.310055 + 0.537032i
\(70\) 0 0
\(71\) −0.844623 0.307418i −0.100238 0.0364838i 0.291414 0.956597i \(-0.405874\pi\)
−0.391652 + 0.920113i \(0.628096\pi\)
\(72\) −2.13334 + 0.776473i −0.251417 + 0.0915082i
\(73\) 8.01712 6.72716i 0.938333 0.787355i −0.0389612 0.999241i \(-0.512405\pi\)
0.977294 + 0.211886i \(0.0679604\pi\)
\(74\) 1.90480 + 10.8027i 0.221429 + 1.25579i
\(75\) 0 0
\(76\) −4.35477 + 0.189610i −0.499527 + 0.0217497i
\(77\) 8.80690 1.00364
\(78\) 0.712809 + 4.04254i 0.0807097 + 0.457728i
\(79\) −1.71509 + 1.43913i −0.192963 + 0.161915i −0.734151 0.678987i \(-0.762419\pi\)
0.541187 + 0.840902i \(0.317975\pi\)
\(80\) 0 0
\(81\) −2.78603 1.01403i −0.309558 0.112670i
\(82\) −2.86803 2.40656i −0.316720 0.265760i
\(83\) −4.16812 + 7.21939i −0.457510 + 0.792431i −0.998829 0.0483869i \(-0.984592\pi\)
0.541319 + 0.840818i \(0.317925\pi\)
\(84\) −1.18814 2.05792i −0.129637 0.224537i
\(85\) 0 0
\(86\) −0.266927 + 1.51382i −0.0287834 + 0.163239i
\(87\) 4.45307 + 7.71295i 0.477420 + 0.826915i
\(88\) 1.58300 2.74184i 0.168748 0.292281i
\(89\) −7.26679 6.09756i −0.770278 0.646340i 0.170502 0.985357i \(-0.445461\pi\)
−0.940780 + 0.339017i \(0.889906\pi\)
\(90\) 0 0
\(91\) 12.5607 4.57174i 1.31672 0.479248i
\(92\) 4.61915 3.87593i 0.481580 0.404094i
\(93\) 1.12807 + 6.39758i 0.116975 + 0.663398i
\(94\) 2.97208 0.306547
\(95\) 0 0
\(96\) −0.854251 −0.0871866
\(97\) −0.456661 2.58985i −0.0463669 0.262960i 0.952808 0.303573i \(-0.0981798\pi\)
−0.999175 + 0.0406138i \(0.987069\pi\)
\(98\) −0.565276 + 0.474323i −0.0571015 + 0.0479138i
\(99\) 6.75417 2.45832i 0.678819 0.247070i
\(100\) 0 0
\(101\) 13.2133 + 11.0873i 1.31477 + 1.10323i 0.987386 + 0.158335i \(0.0506125\pi\)
0.327387 + 0.944890i \(0.393832\pi\)
\(102\) 0.579627 1.00394i 0.0573916 0.0994051i
\(103\) −6.08058 10.5319i −0.599137 1.03774i −0.992949 0.118545i \(-0.962177\pi\)
0.393811 0.919191i \(-0.371156\pi\)
\(104\) 0.834426 4.73227i 0.0818222 0.464037i
\(105\) 0 0
\(106\) −2.15449 3.73168i −0.209262 0.362453i
\(107\) −6.97556 + 12.0820i −0.674353 + 1.16801i 0.302305 + 0.953211i \(0.402244\pi\)
−0.976658 + 0.214802i \(0.931090\pi\)
\(108\) −3.44882 2.89391i −0.331863 0.278466i
\(109\) −15.9616 5.80955i −1.52884 0.556454i −0.565506 0.824744i \(-0.691319\pi\)
−0.963338 + 0.268291i \(0.913541\pi\)
\(110\) 0 0
\(111\) −7.17826 + 6.02328i −0.681330 + 0.571704i
\(112\) 0.483039 + 2.73945i 0.0456429 + 0.258854i
\(113\) −0.218859 −0.0205885 −0.0102943 0.999947i \(-0.503277\pi\)
−0.0102943 + 0.999947i \(0.503277\pi\)
\(114\) −2.00031 3.14069i −0.187346 0.294152i
\(115\) 0 0
\(116\) −1.81040 10.2673i −0.168091 0.953294i
\(117\) 8.35692 7.01229i 0.772598 0.648286i
\(118\) 3.86435 1.40651i 0.355742 0.129480i
\(119\) −3.54724 1.29109i −0.325175 0.118354i
\(120\) 0 0
\(121\) 0.488214 0.845612i 0.0443831 0.0768738i
\(122\) −2.11917 3.67051i −0.191861 0.332312i
\(123\) 0.555373 3.14968i 0.0500763 0.283997i
\(124\) 1.32053 7.48911i 0.118587 0.672542i
\(125\) 0 0
\(126\) −3.15760 + 5.46912i −0.281301 + 0.487228i
\(127\) −9.62855 8.07931i −0.854396 0.716923i 0.106357 0.994328i \(-0.466081\pi\)
−0.960753 + 0.277405i \(0.910526\pi\)
\(128\) 0.939693 + 0.342020i 0.0830579 + 0.0302306i
\(129\) −1.23394 + 0.449116i −0.108642 + 0.0395425i
\(130\) 0 0
\(131\) −2.41452 13.6934i −0.210958 1.19640i −0.887785 0.460259i \(-0.847756\pi\)
0.676827 0.736143i \(-0.263355\pi\)
\(132\) 2.70456 0.235402
\(133\) −8.94062 + 8.19059i −0.775250 + 0.710214i
\(134\) −5.71745 −0.493913
\(135\) 0 0
\(136\) −1.03955 + 0.872289i −0.0891410 + 0.0747982i
\(137\) −5.81017 + 2.11473i −0.496397 + 0.180674i −0.578073 0.815985i \(-0.696195\pi\)
0.0816760 + 0.996659i \(0.473973\pi\)
\(138\) 4.84038 + 1.76175i 0.412041 + 0.149971i
\(139\) 6.72241 + 5.64077i 0.570188 + 0.478444i 0.881708 0.471795i \(-0.156394\pi\)
−0.311521 + 0.950239i \(0.600838\pi\)
\(140\) 0 0
\(141\) 1.26945 + 2.19875i 0.106907 + 0.185168i
\(142\) −0.156080 + 0.885174i −0.0130979 + 0.0742822i
\(143\) −2.64180 + 14.9824i −0.220918 + 1.25289i
\(144\) 1.13513 + 1.96610i 0.0945940 + 0.163842i
\(145\) 0 0
\(146\) −8.01712 6.72716i −0.663502 0.556744i
\(147\) −0.592349 0.215597i −0.0488561 0.0177822i
\(148\) 10.3078 3.75173i 0.847295 0.308390i
\(149\) 12.6163 10.5864i 1.03357 0.867268i 0.0422987 0.999105i \(-0.486532\pi\)
0.991271 + 0.131837i \(0.0420875\pi\)
\(150\) 0 0
\(151\) 14.7347 1.19909 0.599547 0.800340i \(-0.295347\pi\)
0.599547 + 0.800340i \(0.295347\pi\)
\(152\) 0.942928 + 4.25569i 0.0764815 + 0.345182i
\(153\) −3.08083 −0.249070
\(154\) −1.52930 8.67311i −0.123235 0.698899i
\(155\) 0 0
\(156\) 3.85735 1.40396i 0.308835 0.112407i
\(157\) 8.62832 + 3.14045i 0.688615 + 0.250635i 0.662542 0.749025i \(-0.269478\pi\)
0.0260727 + 0.999660i \(0.491700\pi\)
\(158\) 1.71509 + 1.43913i 0.136446 + 0.114491i
\(159\) 1.84047 3.18779i 0.145959 0.252808i
\(160\) 0 0
\(161\) 2.91267 16.5185i 0.229550 1.30184i
\(162\) −0.514837 + 2.91978i −0.0404494 + 0.229400i
\(163\) 8.18335 + 14.1740i 0.640970 + 1.11019i 0.985217 + 0.171313i \(0.0548010\pi\)
−0.344247 + 0.938879i \(0.611866\pi\)
\(164\) −1.87197 + 3.24235i −0.146176 + 0.253185i
\(165\) 0 0
\(166\) 7.83349 + 2.85116i 0.607997 + 0.221293i
\(167\) −12.3025 + 4.47774i −0.951994 + 0.346498i −0.770891 0.636967i \(-0.780189\pi\)
−0.181103 + 0.983464i \(0.557967\pi\)
\(168\) −1.82034 + 1.52744i −0.140442 + 0.117845i
\(169\) 1.75222 + 9.93731i 0.134786 + 0.764408i
\(170\) 0 0
\(171\) −4.57043 + 8.77715i −0.349510 + 0.671205i
\(172\) 1.53717 0.117208
\(173\) 2.98366 + 16.9212i 0.226843 + 1.28649i 0.859130 + 0.511758i \(0.171006\pi\)
−0.632286 + 0.774735i \(0.717883\pi\)
\(174\) 6.82250 5.72476i 0.517213 0.433993i
\(175\) 0 0
\(176\) −2.97507 1.08284i −0.224254 0.0816219i
\(177\) 2.69110 + 2.25810i 0.202275 + 0.169729i
\(178\) −4.74306 + 8.21522i −0.355507 + 0.615757i
\(179\) 0.234505 + 0.406174i 0.0175277 + 0.0303589i 0.874656 0.484744i \(-0.161087\pi\)
−0.857129 + 0.515103i \(0.827754\pi\)
\(180\) 0 0
\(181\) 2.91687 16.5424i 0.216809 1.22958i −0.660931 0.750447i \(-0.729838\pi\)
0.877740 0.479138i \(-0.159051\pi\)
\(182\) −6.68343 11.5760i −0.495409 0.858074i
\(183\) 1.81030 3.13554i 0.133821 0.231785i
\(184\) −4.61915 3.87593i −0.340528 0.285737i
\(185\) 0 0
\(186\) 6.10450 2.22186i 0.447604 0.162914i
\(187\) 3.29123 2.76167i 0.240679 0.201953i
\(188\) −0.516096 2.92693i −0.0376402 0.213468i
\(189\) −12.5236 −0.910958
\(190\) 0 0
\(191\) −18.1568 −1.31378 −0.656891 0.753985i \(-0.728129\pi\)
−0.656891 + 0.753985i \(0.728129\pi\)
\(192\) 0.148339 + 0.841273i 0.0107055 + 0.0607136i
\(193\) 3.41781 2.86788i 0.246019 0.206435i −0.511437 0.859321i \(-0.670887\pi\)
0.757456 + 0.652886i \(0.226442\pi\)
\(194\) −2.47121 + 0.899446i −0.177422 + 0.0645765i
\(195\) 0 0
\(196\) 0.565276 + 0.474323i 0.0403768 + 0.0338802i
\(197\) 10.2342 17.7262i 0.729160 1.26294i −0.228079 0.973643i \(-0.573244\pi\)
0.957239 0.289299i \(-0.0934223\pi\)
\(198\) −3.59382 6.22467i −0.255401 0.442368i
\(199\) 1.40764 7.98310i 0.0997847 0.565907i −0.893391 0.449280i \(-0.851681\pi\)
0.993176 0.116627i \(-0.0372083\pi\)
\(200\) 0 0
\(201\) −2.44207 4.22979i −0.172250 0.298346i
\(202\) 8.62437 14.9378i 0.606808 1.05102i
\(203\) −22.2162 18.6416i −1.55927 1.30839i
\(204\) −1.08934 0.396488i −0.0762692 0.0277597i
\(205\) 0 0
\(206\) −9.31599 + 7.81704i −0.649076 + 0.544639i
\(207\) −2.37713 13.4814i −0.165222 0.937021i
\(208\) −4.80527 −0.333185
\(209\) −2.98531 13.4735i −0.206498 0.931983i
\(210\) 0 0
\(211\) 4.24189 + 24.0570i 0.292024 + 1.65615i 0.679059 + 0.734084i \(0.262388\pi\)
−0.387035 + 0.922065i \(0.626501\pi\)
\(212\) −3.30087 + 2.76976i −0.226704 + 0.190228i
\(213\) −0.721520 + 0.262612i −0.0494377 + 0.0179939i
\(214\) 13.1098 + 4.77156i 0.896165 + 0.326177i
\(215\) 0 0
\(216\) −2.25106 + 3.89895i −0.153165 + 0.265290i
\(217\) −10.5770 18.3198i −0.718011 1.24363i
\(218\) −2.94958 + 16.7279i −0.199771 + 1.13296i
\(219\) 1.55246 8.80443i 0.104905 0.594949i
\(220\) 0 0
\(221\) 3.26047 5.64730i 0.219323 0.379879i
\(222\) 7.17826 + 6.02328i 0.481773 + 0.404256i
\(223\) 23.3511 + 8.49912i 1.56371 + 0.569143i 0.971582 0.236703i \(-0.0760667\pi\)
0.592126 + 0.805846i \(0.298289\pi\)
\(224\) 2.61395 0.951401i 0.174652 0.0635682i
\(225\) 0 0
\(226\) 0.0380045 + 0.215534i 0.00252802 + 0.0143371i
\(227\) −8.33013 −0.552890 −0.276445 0.961030i \(-0.589156\pi\)
−0.276445 + 0.961030i \(0.589156\pi\)
\(228\) −2.74562 + 2.51529i −0.181833 + 0.166579i
\(229\) 0.699318 0.0462123 0.0231061 0.999733i \(-0.492644\pi\)
0.0231061 + 0.999733i \(0.492644\pi\)
\(230\) 0 0
\(231\) 5.76319 4.83589i 0.379190 0.318178i
\(232\) −9.79693 + 3.56579i −0.643200 + 0.234106i
\(233\) −2.41623 0.879436i −0.158293 0.0576138i 0.261659 0.965160i \(-0.415731\pi\)
−0.419951 + 0.907547i \(0.637953\pi\)
\(234\) −8.35692 7.01229i −0.546309 0.458408i
\(235\) 0 0
\(236\) −2.05618 3.56140i −0.133846 0.231828i
\(237\) −0.332116 + 1.88352i −0.0215732 + 0.122348i
\(238\) −0.655504 + 3.71755i −0.0424900 + 0.240973i
\(239\) −8.86697 15.3580i −0.573557 0.993430i −0.996197 0.0871319i \(-0.972230\pi\)
0.422640 0.906298i \(-0.361104\pi\)
\(240\) 0 0
\(241\) −6.92980 5.81479i −0.446387 0.374564i 0.391706 0.920091i \(-0.371885\pi\)
−0.838093 + 0.545527i \(0.816330\pi\)
\(242\) −0.917543 0.333958i −0.0589819 0.0214676i
\(243\) −15.0718 + 5.48568i −0.966856 + 0.351907i
\(244\) −3.24676 + 2.72435i −0.207852 + 0.174409i
\(245\) 0 0
\(246\) −3.19827 −0.203914
\(247\) −11.2520 17.6668i −0.715947 1.12411i
\(248\) −7.60465 −0.482896
\(249\) 1.23659 + 7.01304i 0.0783656 + 0.444434i
\(250\) 0 0
\(251\) 6.34305 2.30868i 0.400370 0.145723i −0.133984 0.990983i \(-0.542777\pi\)
0.534354 + 0.845261i \(0.320555\pi\)
\(252\) 5.93434 + 2.15992i 0.373828 + 0.136062i
\(253\) 14.6242 + 12.2712i 0.919419 + 0.771484i
\(254\) −6.28459 + 10.8852i −0.394330 + 0.683000i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −0.561448 + 3.18413i −0.0350222 + 0.198621i −0.997299 0.0734526i \(-0.976598\pi\)
0.962277 + 0.272073i \(0.0877093\pi\)
\(258\) 0.656564 + 1.13720i 0.0408759 + 0.0707991i
\(259\) 15.2567 26.4255i 0.948008 1.64200i
\(260\) 0 0
\(261\) −22.2415 8.09526i −1.37672 0.501084i
\(262\) −13.0661 + 4.75568i −0.807228 + 0.293807i
\(263\) 0.784511 0.658282i 0.0483750 0.0405914i −0.618280 0.785958i \(-0.712170\pi\)
0.666655 + 0.745367i \(0.267726\pi\)
\(264\) −0.469642 2.66347i −0.0289045 0.163925i
\(265\) 0 0
\(266\) 9.61868 + 7.38251i 0.589759 + 0.452650i
\(267\) −8.10353 −0.495928
\(268\) 0.992825 + 5.63059i 0.0606465 + 0.343943i
\(269\) −7.15929 + 6.00736i −0.436509 + 0.366275i −0.834401 0.551157i \(-0.814186\pi\)
0.397892 + 0.917432i \(0.369742\pi\)
\(270\) 0 0
\(271\) −9.09509 3.31034i −0.552487 0.201089i 0.0506640 0.998716i \(-0.483866\pi\)
−0.603151 + 0.797627i \(0.706088\pi\)
\(272\) 1.03955 + 0.872289i 0.0630322 + 0.0528903i
\(273\) 5.70933 9.88885i 0.345544 0.598500i
\(274\) 3.09153 + 5.35468i 0.186766 + 0.323488i
\(275\) 0 0
\(276\) 0.894466 5.07277i 0.0538405 0.305345i
\(277\) 1.30482 + 2.26001i 0.0783990 + 0.135791i 0.902559 0.430566i \(-0.141686\pi\)
−0.824160 + 0.566357i \(0.808353\pi\)
\(278\) 4.38774 7.59980i 0.263159 0.455805i
\(279\) −13.2254 11.0974i −0.791782 0.664384i
\(280\) 0 0
\(281\) −28.4175 + 10.3431i −1.69524 + 0.617018i −0.995270 0.0971504i \(-0.969027\pi\)
−0.699974 + 0.714169i \(0.746805\pi\)
\(282\) 1.94491 1.63197i 0.115818 0.0971827i
\(283\) 3.30904 + 18.7665i 0.196702 + 1.11555i 0.909974 + 0.414665i \(0.136101\pi\)
−0.713272 + 0.700887i \(0.752788\pi\)
\(284\) 0.898829 0.0533357
\(285\) 0 0
\(286\) 15.2135 0.899593
\(287\) 1.80847 + 10.2563i 0.106751 + 0.605413i
\(288\) 1.73912 1.45929i 0.102478 0.0859896i
\(289\) 14.2443 5.18449i 0.837898 0.304970i
\(290\) 0 0
\(291\) −1.72093 1.44403i −0.100883 0.0846506i
\(292\) −5.23281 + 9.06348i −0.306227 + 0.530400i
\(293\) −0.314058 0.543964i −0.0183474 0.0317787i 0.856706 0.515805i \(-0.172507\pi\)
−0.875053 + 0.484026i \(0.839174\pi\)
\(294\) −0.109462 + 0.620788i −0.00638393 + 0.0362051i
\(295\) 0 0
\(296\) −5.48466 9.49971i −0.318789 0.552160i
\(297\) 7.12686 12.3441i 0.413542 0.716277i
\(298\) −12.6163 10.5864i −0.730844 0.613251i
\(299\) 27.2278 + 9.91009i 1.57462 + 0.573115i
\(300\) 0 0
\(301\) 3.27558 2.74853i 0.188801 0.158423i
\(302\) −2.55866 14.5109i −0.147234 0.835006i
\(303\) 14.7347 0.846489
\(304\) 4.02730 1.66760i 0.230981 0.0956431i
\(305\) 0 0
\(306\) 0.534980 + 3.03402i 0.0305828 + 0.173444i
\(307\) −16.3205 + 13.6945i −0.931460 + 0.781588i −0.976079 0.217417i \(-0.930237\pi\)
0.0446192 + 0.999004i \(0.485793\pi\)
\(308\) −8.27578 + 3.01214i −0.471556 + 0.171633i
\(309\) −9.76217 3.55314i −0.555350 0.202131i
\(310\) 0 0
\(311\) −16.4799 + 28.5440i −0.934490 + 1.61858i −0.158950 + 0.987287i \(0.550811\pi\)
−0.775541 + 0.631298i \(0.782523\pi\)
\(312\) −2.05245 3.55495i −0.116197 0.201259i
\(313\) 4.95291 28.0894i 0.279955 1.58770i −0.442813 0.896614i \(-0.646020\pi\)
0.722768 0.691090i \(-0.242869\pi\)
\(314\) 1.59445 9.04257i 0.0899799 0.510302i
\(315\) 0 0
\(316\) 1.11945 1.93894i 0.0629739 0.109074i
\(317\) 23.4843 + 19.7057i 1.31901 + 1.10678i 0.986514 + 0.163674i \(0.0523346\pi\)
0.332494 + 0.943105i \(0.392110\pi\)
\(318\) −3.45896 1.25896i −0.193969 0.0705988i
\(319\) 31.0171 11.2893i 1.73663 0.632080i
\(320\) 0 0
\(321\) 2.06950 + 11.7367i 0.115508 + 0.655078i
\(322\) −16.7734 −0.934743
\(323\) −0.772793 + 5.86451i −0.0429993 + 0.326310i
\(324\) 2.96483 0.164713
\(325\) 0 0
\(326\) 12.5376 10.5203i 0.694395 0.582666i
\(327\) −13.6352 + 4.96281i −0.754029 + 0.274444i
\(328\) 3.51815 + 1.28050i 0.194258 + 0.0707040i
\(329\) −6.33325 5.31422i −0.349163 0.292983i
\(330\) 0 0
\(331\) −3.90181 6.75813i −0.214463 0.371460i 0.738644 0.674096i \(-0.235467\pi\)
−0.953106 + 0.302636i \(0.902133\pi\)
\(332\) 1.44757 8.20958i 0.0794458 0.450559i
\(333\) 4.32439 24.5248i 0.236975 1.34395i
\(334\) 6.54601 + 11.3380i 0.358182 + 0.620389i
\(335\) 0 0
\(336\) 1.82034 + 1.52744i 0.0993074 + 0.0833288i
\(337\) 3.37565 + 1.22864i 0.183883 + 0.0669280i 0.432321 0.901720i \(-0.357695\pi\)
−0.248437 + 0.968648i \(0.579917\pi\)
\(338\) 9.48207 3.45119i 0.515756 0.187720i
\(339\) −0.143220 + 0.120176i −0.00777865 + 0.00652706i
\(340\) 0 0
\(341\) 24.0763 1.30381
\(342\) 9.43745 + 2.97686i 0.510319 + 0.160970i
\(343\) −17.4193 −0.940554
\(344\) −0.266927 1.51382i −0.0143917 0.0816195i
\(345\) 0 0
\(346\) 16.1460 5.87666i 0.868014 0.315931i
\(347\) 14.4497 + 5.25926i 0.775701 + 0.282332i 0.699379 0.714751i \(-0.253460\pi\)
0.0763220 + 0.997083i \(0.475682\pi\)
\(348\) −6.82250 5.72476i −0.365725 0.306879i
\(349\) −16.4988 + 28.5767i −0.883159 + 1.52968i −0.0353493 + 0.999375i \(0.511254\pi\)
−0.847809 + 0.530301i \(0.822079\pi\)
\(350\) 0 0
\(351\) 3.75669 21.3052i 0.200517 1.13719i
\(352\) −0.549771 + 3.11790i −0.0293029 + 0.166185i
\(353\) 2.92362 + 5.06386i 0.155608 + 0.269522i 0.933280 0.359149i \(-0.116933\pi\)
−0.777672 + 0.628670i \(0.783600\pi\)
\(354\) 1.75649 3.04233i 0.0933564 0.161698i
\(355\) 0 0
\(356\) 8.91404 + 3.24444i 0.472443 + 0.171955i
\(357\) −3.03023 + 1.10291i −0.160377 + 0.0583724i
\(358\) 0.359282 0.301474i 0.0189887 0.0159334i
\(359\) 2.72021 + 15.4271i 0.143567 + 0.814209i 0.968507 + 0.248988i \(0.0800980\pi\)
−0.824940 + 0.565221i \(0.808791\pi\)
\(360\) 0 0
\(361\) 15.5613 + 10.9017i 0.819014 + 0.573773i
\(362\) −16.7976 −0.882860
\(363\) −0.144843 0.821443i −0.00760226 0.0431146i
\(364\) −10.2396 + 8.59206i −0.536702 + 0.450346i
\(365\) 0 0
\(366\) −3.40226 1.23832i −0.177839 0.0647280i
\(367\) 10.7857 + 9.05031i 0.563011 + 0.472423i 0.879318 0.476234i \(-0.157999\pi\)
−0.316307 + 0.948657i \(0.602443\pi\)
\(368\) −3.01494 + 5.22203i −0.157164 + 0.272217i
\(369\) 4.24985 + 7.36096i 0.221238 + 0.383196i
\(370\) 0 0
\(371\) −2.08140 + 11.8042i −0.108061 + 0.612845i
\(372\) −3.24814 5.62594i −0.168408 0.291691i
\(373\) 1.70094 2.94612i 0.0880714 0.152544i −0.818624 0.574329i \(-0.805263\pi\)
0.906696 + 0.421785i \(0.138596\pi\)
\(374\) −3.29123 2.76167i −0.170185 0.142803i
\(375\) 0 0
\(376\) −2.79284 + 1.01651i −0.144030 + 0.0524226i
\(377\) 38.3774 32.2025i 1.97654 1.65851i
\(378\) 2.17470 + 12.3333i 0.111854 + 0.634358i
\(379\) 3.36412 0.172803 0.0864016 0.996260i \(-0.472463\pi\)
0.0864016 + 0.996260i \(0.472463\pi\)
\(380\) 0 0
\(381\) −10.7372 −0.550085
\(382\) 3.15290 + 17.8810i 0.161316 + 0.914871i
\(383\) 1.33818 1.12286i 0.0683776 0.0573756i −0.607958 0.793969i \(-0.708011\pi\)
0.676336 + 0.736593i \(0.263567\pi\)
\(384\) 0.802733 0.292171i 0.0409643 0.0149098i
\(385\) 0 0
\(386\) −3.41781 2.86788i −0.173962 0.145971i
\(387\) 1.74488 3.02223i 0.0886974 0.153628i
\(388\) 1.31490 + 2.27748i 0.0667540 + 0.115621i
\(389\) −0.512989 + 2.90930i −0.0260096 + 0.147508i −0.995047 0.0994067i \(-0.968306\pi\)
0.969037 + 0.246914i \(0.0794166\pi\)
\(390\) 0 0
\(391\) −4.09139 7.08650i −0.206911 0.358380i
\(392\) 0.368957 0.639053i 0.0186352 0.0322771i
\(393\) −9.09915 7.63509i −0.458991 0.385139i
\(394\) −19.2341 7.00064i −0.969000 0.352687i
\(395\) 0 0
\(396\) −5.50605 + 4.62012i −0.276689 + 0.232170i
\(397\) −0.330922 1.87675i −0.0166085 0.0941914i 0.975377 0.220545i \(-0.0707837\pi\)
−0.991985 + 0.126354i \(0.959673\pi\)
\(398\) −8.10626 −0.406330
\(399\) −1.35322 + 10.2692i −0.0677456 + 0.514102i
\(400\) 0 0
\(401\) 0.443767 + 2.51673i 0.0221607 + 0.125679i 0.993881 0.110455i \(-0.0352307\pi\)
−0.971721 + 0.236134i \(0.924120\pi\)
\(402\) −3.74147 + 3.13946i −0.186607 + 0.156582i
\(403\) 34.3386 12.4982i 1.71053 0.622581i
\(404\) −16.2085 5.89942i −0.806404 0.293507i
\(405\) 0 0
\(406\) −14.5006 + 25.1158i −0.719653 + 1.24648i
\(407\) 17.3645 + 30.0761i 0.860724 + 1.49082i
\(408\) −0.201302 + 1.14164i −0.00996594 + 0.0565197i
\(409\) −0.172527 + 0.978451i −0.00853092 + 0.0483813i −0.988776 0.149405i \(-0.952264\pi\)
0.980245 + 0.197786i \(0.0633752\pi\)
\(410\) 0 0
\(411\) −2.64094 + 4.57424i −0.130268 + 0.225631i
\(412\) 9.31599 + 7.81704i 0.458966 + 0.385118i
\(413\) −10.7495 3.91250i −0.528948 0.192521i
\(414\) −12.8638 + 4.68204i −0.632221 + 0.230110i
\(415\) 0 0
\(416\) 0.834426 + 4.73227i 0.0409111 + 0.232018i
\(417\) 7.49647 0.367104
\(418\) −12.7504 + 5.27961i −0.623644 + 0.258234i
\(419\) −14.8657 −0.726238 −0.363119 0.931743i \(-0.618288\pi\)
−0.363119 + 0.931743i \(0.618288\pi\)
\(420\) 0 0
\(421\) 29.8436 25.0418i 1.45449 1.22046i 0.525269 0.850936i \(-0.323965\pi\)
0.929221 0.369526i \(-0.120480\pi\)
\(422\) 22.9549 8.35489i 1.11743 0.406710i
\(423\) −6.34046 2.30774i −0.308284 0.112206i
\(424\) 3.30087 + 2.76976i 0.160304 + 0.134511i
\(425\) 0 0
\(426\) 0.383913 + 0.664957i 0.0186006 + 0.0322173i
\(427\) −2.04728 + 11.6107i −0.0990750 + 0.561882i
\(428\) 2.42259 13.7392i 0.117100 0.664108i
\(429\) 6.49807 + 11.2550i 0.313730 + 0.543396i
\(430\) 0 0
\(431\) −20.8535 17.4982i −1.00448 0.842857i −0.0168797 0.999858i \(-0.505373\pi\)
−0.987599 + 0.157000i \(0.949818\pi\)
\(432\) 4.23061 + 1.53982i 0.203545 + 0.0740844i
\(433\) 31.3746 11.4194i 1.50777 0.548782i 0.549709 0.835356i \(-0.314739\pi\)
0.958058 + 0.286574i \(0.0925165\pi\)
\(434\) −16.2048 + 13.5975i −0.777858 + 0.652700i
\(435\) 0 0
\(436\) 16.9860 0.813481
\(437\) −26.2587 + 1.14332i −1.25613 + 0.0546926i
\(438\) −8.94026 −0.427182
\(439\) 3.21620 + 18.2400i 0.153501 + 0.870546i 0.960144 + 0.279507i \(0.0901710\pi\)
−0.806643 + 0.591039i \(0.798718\pi\)
\(440\) 0 0
\(441\) 1.57423 0.572971i 0.0749631 0.0272843i
\(442\) −6.12768 2.23029i −0.291464 0.106084i
\(443\) 10.4056 + 8.73132i 0.494384 + 0.414838i 0.855594 0.517647i \(-0.173192\pi\)
−0.361210 + 0.932484i \(0.617636\pi\)
\(444\) 4.68528 8.11514i 0.222353 0.385127i
\(445\) 0 0
\(446\) 4.31512 24.4722i 0.204327 1.15879i
\(447\) 2.44306 13.8553i 0.115553 0.655333i
\(448\) −1.39086 2.40903i −0.0657117 0.113816i
\(449\) −1.40297 + 2.43001i −0.0662101 + 0.114679i −0.897230 0.441563i \(-0.854424\pi\)
0.831020 + 0.556242i \(0.187757\pi\)
\(450\) 0 0
\(451\) −11.1385 4.05408i −0.524491 0.190899i
\(452\) 0.205660 0.0748542i 0.00967345 0.00352085i
\(453\) 9.64231 8.09086i 0.453035 0.380142i
\(454\) 1.44651 + 8.20357i 0.0678881 + 0.385013i
\(455\) 0 0
\(456\) 2.95385 + 2.26713i 0.138327 + 0.106168i
\(457\) 18.8826 0.883289 0.441644 0.897190i \(-0.354395\pi\)
0.441644 + 0.897190i \(0.354395\pi\)
\(458\) −0.121435 0.688694i −0.00567430 0.0321806i
\(459\) −4.68020 + 3.92715i −0.218453 + 0.183304i
\(460\) 0 0
\(461\) −5.14272 1.87180i −0.239521 0.0871784i 0.219471 0.975619i \(-0.429567\pi\)
−0.458991 + 0.888441i \(0.651789\pi\)
\(462\) −5.76319 4.83589i −0.268128 0.224986i
\(463\) 3.52956 6.11338i 0.164033 0.284113i −0.772279 0.635284i \(-0.780883\pi\)
0.936311 + 0.351171i \(0.114216\pi\)
\(464\) 5.21284 + 9.02890i 0.242000 + 0.419156i
\(465\) 0 0
\(466\) −0.446501 + 2.53223i −0.0206838 + 0.117304i
\(467\) 4.75442 + 8.23490i 0.220008 + 0.381066i 0.954810 0.297216i \(-0.0960582\pi\)
−0.734802 + 0.678282i \(0.762725\pi\)
\(468\) −5.45459 + 9.44763i −0.252139 + 0.436717i
\(469\) 12.1834 + 10.2231i 0.562577 + 0.472058i
\(470\) 0 0
\(471\) 7.37075 2.68273i 0.339626 0.123614i
\(472\) −3.15025 + 2.64337i −0.145002 + 0.121671i
\(473\) 0.845090 + 4.79274i 0.0388573 + 0.220371i
\(474\) 1.91258 0.0878477
\(475\) 0 0
\(476\) 3.77490 0.173022
\(477\) 1.69871 + 9.63386i 0.0777786 + 0.441104i
\(478\) −13.5850 + 11.3992i −0.621363 + 0.521386i
\(479\) −28.7966 + 10.4811i −1.31575 + 0.478894i −0.902094 0.431539i \(-0.857971\pi\)
−0.413657 + 0.910433i \(0.635749\pi\)
\(480\) 0 0
\(481\) 40.3786 + 33.8817i 1.84111 + 1.54487i
\(482\) −4.52310 + 7.83425i −0.206022 + 0.356840i
\(483\) −7.16433 12.4090i −0.325988 0.564628i
\(484\) −0.169555 + 0.961594i −0.00770705 + 0.0437088i
\(485\) 0 0
\(486\) 8.01953 + 13.8902i 0.363773 + 0.630074i
\(487\) −14.4610 + 25.0472i −0.655292 + 1.13500i 0.326529 + 0.945187i \(0.394121\pi\)
−0.981821 + 0.189811i \(0.939212\pi\)
\(488\) 3.24676 + 2.72435i 0.146974 + 0.123326i
\(489\) 13.1381 + 4.78188i 0.594125 + 0.216244i
\(490\) 0 0
\(491\) −30.3092 + 25.4325i −1.36784 + 1.14775i −0.394361 + 0.918955i \(0.629034\pi\)
−0.973475 + 0.228795i \(0.926521\pi\)
\(492\) 0.555373 + 3.14968i 0.0250381 + 0.141998i
\(493\) −14.1481 −0.637197
\(494\) −15.4445 + 14.1488i −0.694880 + 0.636587i
\(495\) 0 0
\(496\) 1.32053 + 7.48911i 0.0592937 + 0.336271i
\(497\) 1.91533 1.60715i 0.0859142 0.0720906i
\(498\) 6.69177 2.43560i 0.299865 0.109142i
\(499\) −2.87074 1.04486i −0.128512 0.0467745i 0.276964 0.960880i \(-0.410672\pi\)
−0.405476 + 0.914106i \(0.632894\pi\)
\(500\) 0 0
\(501\) −5.59194 + 9.68552i −0.249829 + 0.432717i
\(502\) −3.37507 5.84579i −0.150637 0.260910i
\(503\) −5.70366 + 32.3470i −0.254313 + 1.44228i 0.543515 + 0.839399i \(0.317093\pi\)
−0.797829 + 0.602884i \(0.794018\pi\)
\(504\) 1.09662 6.21925i 0.0488474 0.277028i
\(505\) 0 0
\(506\) 9.54530 16.5329i 0.424340 0.734979i
\(507\) 6.60323 + 5.54077i 0.293260 + 0.246074i
\(508\) 11.8112 + 4.29891i 0.524036 + 0.190733i
\(509\) 19.0237 6.92408i 0.843213 0.306904i 0.115943 0.993256i \(-0.463011\pi\)
0.727270 + 0.686352i \(0.240789\pi\)
\(510\) 0 0
\(511\) 5.05530 + 28.6700i 0.223633 + 1.26829i
\(512\) −1.00000 −0.0441942
\(513\) 4.24517 + 19.1596i 0.187429 + 0.845918i
\(514\) 3.23325 0.142613
\(515\) 0 0
\(516\) 1.00591 0.844062i 0.0442829 0.0371578i
\(517\) 8.84214 3.21828i 0.388877 0.141540i
\(518\) −28.6733 10.4362i −1.25983 0.458541i
\(519\) 11.2439 + 9.43478i 0.493554 + 0.414141i
\(520\) 0 0
\(521\) 7.47243 + 12.9426i 0.327373 + 0.567027i 0.981990 0.188934i \(-0.0605032\pi\)
−0.654617 + 0.755961i \(0.727170\pi\)
\(522\) −4.11007 + 23.3094i −0.179893 + 1.02022i
\(523\) 4.90745 27.8315i 0.214588 1.21699i −0.667032 0.745029i \(-0.732436\pi\)
0.881620 0.471960i \(-0.156453\pi\)
\(524\) 6.95234 + 12.0418i 0.303715 + 0.526049i
\(525\) 0 0
\(526\) −0.784511 0.658282i −0.0342063 0.0287025i
\(527\) −9.69745 3.52958i −0.422428 0.153751i
\(528\) −2.54146 + 0.925014i −0.110603 + 0.0402561i
\(529\) 10.2339 8.58726i 0.444952 0.373359i
\(530\) 0 0
\(531\) −9.33609 −0.405152
\(532\) 5.60008 10.7545i 0.242794 0.466267i
\(533\) −17.9906 −0.779261
\(534\) 1.40716 + 7.98042i 0.0608939 + 0.345346i
\(535\) 0 0
\(536\) 5.37265 1.95548i 0.232063 0.0844640i
\(537\) 0.376490 + 0.137031i 0.0162467 + 0.00591333i
\(538\) 7.15929 + 6.00736i 0.308659 + 0.258995i
\(539\) −1.16812 + 2.02324i −0.0503145 + 0.0871473i
\(540\) 0 0
\(541\) 3.81672 21.6457i 0.164093 0.930620i −0.785901 0.618353i \(-0.787800\pi\)
0.949994 0.312267i \(-0.101088\pi\)
\(542\) −1.68070 + 9.53175i −0.0721924 + 0.409424i
\(543\) −7.17466 12.4269i −0.307894 0.533289i
\(544\) 0.678520 1.17523i 0.0290913 0.0503877i
\(545\) 0 0
\(546\) −10.7300 3.90541i −0.459203 0.167136i
\(547\) −26.1305 + 9.51074i −1.11726 + 0.406650i −0.833652 0.552290i \(-0.813754\pi\)
−0.283609 + 0.958940i \(0.591532\pi\)
\(548\) 4.73650 3.97439i 0.202333 0.169778i
\(549\) 1.67086 + 9.47593i 0.0713107 + 0.404423i
\(550\) 0 0
\(551\) −20.9888 + 40.3072i −0.894151 + 1.71715i
\(552\) −5.15103 −0.219242
\(553\) −1.08147 6.13335i −0.0459890 0.260816i
\(554\) 1.99910 1.67744i 0.0849336 0.0712677i
\(555\) 0 0
\(556\) −8.24626 3.00139i −0.349719 0.127287i
\(557\) −11.9805 10.0528i −0.507630 0.425952i 0.352664 0.935750i \(-0.385276\pi\)
−0.860294 + 0.509798i \(0.829720\pi\)
\(558\) −8.63224 + 14.9515i −0.365432 + 0.632947i
\(559\) 3.69325 + 6.39690i 0.156208 + 0.270560i
\(560\) 0 0
\(561\) 0.637323 3.61444i 0.0269078 0.152602i
\(562\) 15.1206 + 26.1897i 0.637825 + 1.10474i
\(563\) 15.9429 27.6140i 0.671914 1.16379i −0.305446 0.952209i \(-0.598806\pi\)
0.977361 0.211580i \(-0.0678610\pi\)
\(564\) −1.94491 1.63197i −0.0818955 0.0687185i
\(565\) 0 0
\(566\) 17.9068 6.51754i 0.752679 0.273953i
\(567\) 6.31779 5.30126i 0.265322 0.222632i
\(568\) −0.156080 0.885174i −0.00654897 0.0371411i
\(569\) 16.2946 0.683104 0.341552 0.939863i \(-0.389047\pi\)
0.341552 + 0.939863i \(0.389047\pi\)
\(570\) 0 0
\(571\) 45.9474 1.92284 0.961418 0.275090i \(-0.0887077\pi\)
0.961418 + 0.275090i \(0.0887077\pi\)
\(572\) −2.64180 14.9824i −0.110459 0.626444i
\(573\) −11.8817 + 9.96995i −0.496366 + 0.416501i
\(574\) 9.78649 3.56199i 0.408480 0.148675i
\(575\) 0 0
\(576\) −1.73912 1.45929i −0.0724632 0.0608038i
\(577\) 21.0732 36.4998i 0.877288 1.51951i 0.0229826 0.999736i \(-0.492684\pi\)
0.854305 0.519771i \(-0.173983\pi\)
\(578\) −7.57922 13.1276i −0.315254 0.546036i
\(579\) 0.661834 3.75345i 0.0275049 0.155988i
\(580\) 0 0
\(581\) −11.5945 20.0822i −0.481021 0.833152i
\(582\) −1.12326 + 1.94554i −0.0465605 + 0.0806451i
\(583\) −10.4506 8.76906i −0.432818 0.363177i
\(584\) 9.83446 + 3.57945i 0.406953 + 0.148119i
\(585\) 0 0
\(586\) −0.481164 + 0.403745i −0.0198767 + 0.0166785i
\(587\) 3.63466 + 20.6132i 0.150019 + 0.850797i 0.963200 + 0.268787i \(0.0866227\pi\)
−0.813181 + 0.582011i \(0.802266\pi\)
\(588\) 0.630364 0.0259958
\(589\) −24.4419 + 22.3915i −1.00711 + 0.922624i
\(590\) 0 0
\(591\) −3.03628 17.2196i −0.124896 0.708319i
\(592\) −8.40299 + 7.05094i −0.345361 + 0.289792i
\(593\) 32.4706 11.8183i 1.33341 0.485320i 0.425676 0.904875i \(-0.360036\pi\)
0.907730 + 0.419555i \(0.137814\pi\)
\(594\) −13.3941 4.87506i −0.549567 0.200026i
\(595\) 0 0
\(596\) −8.23473 + 14.2630i −0.337307 + 0.584234i
\(597\) −3.46239 5.99703i −0.141706 0.245442i
\(598\) 5.03149 28.5350i 0.205753 1.16688i
\(599\) −0.508878 + 2.88599i −0.0207922 + 0.117918i −0.993437 0.114378i \(-0.963513\pi\)
0.972645 + 0.232296i \(0.0746238\pi\)
\(600\) 0 0
\(601\) −16.1662 + 28.0006i −0.659432 + 1.14217i 0.321331 + 0.946967i \(0.395870\pi\)
−0.980763 + 0.195202i \(0.937464\pi\)
\(602\) −3.27558 2.74853i −0.133502 0.112022i
\(603\) 12.1973 + 4.43945i 0.496712 + 0.180788i
\(604\) −13.8461 + 5.03957i −0.563390 + 0.205057i
\(605\) 0 0
\(606\) −2.55866 14.5109i −0.103939 0.589465i
\(607\) −12.3695 −0.502063 −0.251031 0.967979i \(-0.580770\pi\)
−0.251031 + 0.967979i \(0.580770\pi\)
\(608\) −2.34159 3.67654i −0.0949642 0.149103i
\(609\) −24.7743 −1.00391
\(610\) 0 0
\(611\) 10.9404 9.18006i 0.442600 0.371385i
\(612\) 2.89503 1.05371i 0.117025 0.0425935i
\(613\) 14.5146 + 5.28288i 0.586239 + 0.213373i 0.618074 0.786120i \(-0.287913\pi\)
−0.0318356 + 0.999493i \(0.510135\pi\)
\(614\) 16.3205 + 13.6945i 0.658641 + 0.552666i
\(615\) 0 0
\(616\) 4.40345 + 7.62700i 0.177420 + 0.307301i
\(617\) −7.72363 + 43.8029i −0.310942 + 1.76344i 0.283185 + 0.959065i \(0.408609\pi\)
−0.594126 + 0.804372i \(0.702502\pi\)
\(618\) −1.80398 + 10.2309i −0.0725666 + 0.411545i
\(619\) 1.83161 + 3.17245i 0.0736187 + 0.127511i 0.900485 0.434888i \(-0.143212\pi\)
−0.826866 + 0.562399i \(0.809879\pi\)
\(620\) 0 0
\(621\) −20.7960 17.4499i −0.834514 0.700240i
\(622\) 30.9721 + 11.2729i 1.24187 + 0.452003i
\(623\) 24.7963 9.02511i 0.993442 0.361583i
\(624\) −3.14454 + 2.63858i −0.125882 + 0.105628i
\(625\) 0 0
\(626\) −28.5227 −1.14000
\(627\) −9.35191 7.17775i −0.373479 0.286652i
\(628\) −9.18206 −0.366404
\(629\) −2.58490 14.6597i −0.103067 0.584519i
\(630\) 0 0
\(631\) −13.5764 + 4.94141i −0.540468 + 0.196714i −0.597807 0.801640i \(-0.703961\pi\)
0.0573381 + 0.998355i \(0.481739\pi\)
\(632\) −2.10387 0.765748i −0.0836876 0.0304598i
\(633\) 15.9856 + 13.4135i 0.635370 + 0.533139i
\(634\) 15.3283 26.5494i 0.608764 1.05441i
\(635\) 0 0
\(636\) −0.639190 + 3.62502i −0.0253455 + 0.143742i
\(637\) −0.615736 + 3.49201i −0.0243963 + 0.138358i
\(638\) −16.5039 28.5855i −0.653394 1.13171i
\(639\) 1.02029 1.76719i 0.0403619 0.0699089i
\(640\) 0 0
\(641\) −3.70070 1.34695i −0.146169 0.0532011i 0.267900 0.963447i \(-0.413670\pi\)
−0.414069 + 0.910246i \(0.635893\pi\)
\(642\) 11.1990 4.07611i 0.441990 0.160871i
\(643\) −32.0655 + 26.9061i −1.26454 + 1.06107i −0.269355 + 0.963041i \(0.586811\pi\)
−0.995183 + 0.0980331i \(0.968745\pi\)
\(644\) 2.91267 + 16.5185i 0.114775 + 0.650922i
\(645\) 0 0
\(646\) 5.90961 0.257308i 0.232510 0.0101237i
\(647\) 37.3768 1.46943 0.734716 0.678375i \(-0.237315\pi\)
0.734716 + 0.678375i \(0.237315\pi\)
\(648\) −0.514837 2.91978i −0.0202247 0.114700i
\(649\) 9.97368 8.36891i 0.391501 0.328509i
\(650\) 0 0
\(651\) −16.9810 6.18056i −0.665536 0.242235i
\(652\) −12.5376 10.5203i −0.491011 0.412007i
\(653\) −15.4098 + 26.6905i −0.603031 + 1.04448i 0.389328 + 0.921099i \(0.372707\pi\)
−0.992359 + 0.123381i \(0.960626\pi\)
\(654\) 7.25514 + 12.5663i 0.283698 + 0.491380i
\(655\) 0 0
\(656\) 0.650129 3.68706i 0.0253833 0.143956i
\(657\) 11.8798 + 20.5764i 0.463475 + 0.802763i
\(658\) −4.13373 + 7.15983i −0.161150 + 0.279119i
\(659\) −5.21609 4.37682i −0.203190 0.170497i 0.535514 0.844526i \(-0.320118\pi\)
−0.738705 + 0.674029i \(0.764562\pi\)
\(660\) 0 0
\(661\) 33.9368 12.3520i 1.31999 0.480437i 0.416535 0.909120i \(-0.363244\pi\)
0.903455 + 0.428683i \(0.141022\pi\)
\(662\) −5.97791 + 5.01606i −0.232338 + 0.194955i
\(663\) −0.967311 5.48589i −0.0375673 0.213054i
\(664\) −8.33623 −0.323508
\(665\) 0 0
\(666\) −24.9032 −0.964978
\(667\) −10.9165 61.9105i −0.422688 2.39718i
\(668\) 10.0291 8.41539i 0.388036 0.325601i
\(669\) 19.9477 7.26038i 0.771224 0.280702i
\(670\) 0 0
\(671\) −10.2792 8.62530i −0.396826 0.332976i
\(672\) 1.18814 2.05792i 0.0458335 0.0793859i
\(673\) 1.30856 + 2.26649i 0.0504412 + 0.0873667i 0.890144 0.455680i \(-0.150604\pi\)
−0.839702 + 0.543047i \(0.817271\pi\)
\(674\) 0.623795 3.53771i 0.0240277 0.136268i
\(675\) 0 0
\(676\) −5.04530 8.73872i −0.194050 0.336105i
\(677\) 0.634426 1.09886i 0.0243830 0.0422325i −0.853576 0.520968i \(-0.825571\pi\)
0.877959 + 0.478735i \(0.158905\pi\)
\(678\) 0.143220 + 0.120176i 0.00550034 + 0.00461533i
\(679\) 6.87418 + 2.50200i 0.263807 + 0.0960179i
\(680\) 0 0
\(681\) −5.45119 + 4.57409i −0.208890 + 0.175279i
\(682\) −4.18081 23.7106i −0.160092 0.907924i
\(683\) 16.3670 0.626264 0.313132 0.949710i \(-0.398622\pi\)
0.313132 + 0.949710i \(0.398622\pi\)
\(684\) 1.29284 9.81100i 0.0494330 0.375133i
\(685\) 0 0
\(686\) 3.02483 + 17.1547i 0.115489 + 0.654968i
\(687\) 0.457630 0.383997i 0.0174597 0.0146504i
\(688\) −1.44447 + 0.525743i −0.0550698 + 0.0200438i
\(689\) −19.4571 7.08180i −0.741255 0.269795i
\(690\) 0 0
\(691\) 8.07725 13.9902i 0.307273 0.532213i −0.670492 0.741917i \(-0.733917\pi\)
0.977765 + 0.209704i \(0.0672501\pi\)
\(692\) −8.59110 14.8802i −0.326585 0.565661i
\(693\) −3.47191 + 19.6902i −0.131887 + 0.747968i
\(694\) 2.67020 15.1434i 0.101359 0.574837i
\(695\) 0 0
\(696\) −4.45307 + 7.71295i −0.168793 + 0.292359i
\(697\) 3.89203 + 3.26580i 0.147421 + 0.123701i
\(698\) 31.0075 + 11.2858i 1.17365 + 0.427175i
\(699\) −2.06407 + 0.751259i −0.0780702 + 0.0284152i
\(700\) 0 0
\(701\) 3.90435 + 22.1427i 0.147465 + 0.836317i 0.965355 + 0.260942i \(0.0840331\pi\)
−0.817889 + 0.575376i \(0.804856\pi\)
\(702\) −21.6339 −0.816519
\(703\) −45.5995 14.3835i −1.71982 0.542483i
\(704\) 3.16600 0.119323
\(705\) 0 0
\(706\) 4.47924 3.75853i 0.168579 0.141454i
\(707\) −45.0874 + 16.4105i −1.69569 + 0.617179i
\(708\) −3.30112 1.20151i −0.124064 0.0451555i
\(709\) 30.7633 + 25.8135i 1.15534 + 0.969447i 0.999831 0.0183876i \(-0.00585328\pi\)
0.155511 + 0.987834i \(0.450298\pi\)
\(710\) 0 0
\(711\) −2.54143 4.40189i −0.0953112 0.165084i
\(712\) 1.64725 9.34201i 0.0617332 0.350106i
\(713\) 7.96265 45.1584i 0.298204 1.69120i
\(714\) 1.61235 + 2.79268i 0.0603408 + 0.104513i
\(715\) 0 0
\(716\) −0.359282 0.301474i −0.0134270 0.0112666i
\(717\) −14.2356 5.18134i −0.531639 0.193501i
\(718\) 14.7203 5.35776i 0.549358 0.199950i
\(719\) 8.60668 7.22186i 0.320975 0.269330i −0.468036 0.883710i \(-0.655038\pi\)
0.789011 + 0.614380i \(0.210594\pi\)
\(720\) 0 0
\(721\) 33.8288 1.25985
\(722\) 8.03388 17.2179i 0.298990 0.640785i
\(723\) −7.72773 −0.287397
\(724\) 2.91687 + 16.5424i 0.108404 + 0.614792i
\(725\) 0 0
\(726\) −0.783812 + 0.285284i −0.0290900 + 0.0105879i
\(727\) 4.30407 + 1.56655i 0.159629 + 0.0581003i 0.420599 0.907247i \(-0.361820\pi\)
−0.260970 + 0.965347i \(0.584042\pi\)
\(728\) 10.2396 + 8.59206i 0.379505 + 0.318443i
\(729\) −2.40345 + 4.16290i −0.0890167 + 0.154182i
\(730\) 0 0
\(731\) 0.362230 2.05431i 0.0133976 0.0759814i
\(732\) −0.628711 + 3.56560i −0.0232378 + 0.131788i
\(733\) 1.77436 + 3.07329i 0.0655376 + 0.113514i 0.896932 0.442168i \(-0.145790\pi\)
−0.831395 + 0.555682i \(0.812457\pi\)
\(734\) 7.03989 12.1935i 0.259847 0.450069i
\(735\) 0 0
\(736\) 5.66623 + 2.06234i 0.208860 + 0.0760188i
\(737\) −17.0098 + 6.19107i −0.626565 + 0.228051i
\(738\) 6.51115 5.46351i 0.239679 0.201114i
\(739\) −8.11900 46.0451i −0.298662 1.69380i −0.651934 0.758276i \(-0.726042\pi\)
0.353271 0.935521i \(-0.385069\pi\)
\(740\) 0 0
\(741\) −17.0641 5.38254i −0.626865 0.197732i
\(742\) 11.9863 0.440032
\(743\) 5.46514 + 30.9943i 0.200496 + 1.13707i 0.904371 + 0.426747i \(0.140341\pi\)
−0.703874 + 0.710324i \(0.748548\pi\)
\(744\) −4.97644 + 4.17573i −0.182445 + 0.153090i
\(745\) 0 0
\(746\) −3.19672 1.16351i −0.117040 0.0425992i
\(747\) −14.4977 12.1650i −0.530442 0.445094i
\(748\) −2.14820 + 3.72079i −0.0785459 + 0.136045i
\(749\) −19.4040 33.6087i −0.709006 1.22803i
\(750\) 0 0
\(751\) 1.07418 6.09197i 0.0391974 0.222299i −0.958917 0.283688i \(-0.908442\pi\)
0.998114 + 0.0613890i \(0.0195530\pi\)
\(752\) 1.48604 + 2.57390i 0.0541903 + 0.0938603i
\(753\) 2.88315 4.99377i 0.105068 0.181983i
\(754\) −38.3774 32.2025i −1.39762 1.17275i
\(755\) 0 0
\(756\) 11.7683 4.28332i 0.428010 0.155783i
\(757\) −32.5924 + 27.3483i −1.18459 + 0.993990i −0.184653 + 0.982804i \(0.559116\pi\)
−0.999937 + 0.0111858i \(0.996439\pi\)
\(758\) −0.584173 3.31301i −0.0212181 0.120334i
\(759\) 16.3082 0.591949
\(760\) 0 0
\(761\) 9.05719 0.328323 0.164161 0.986433i \(-0.447508\pi\)
0.164161 + 0.986433i \(0.447508\pi\)
\(762\) 1.86450 + 10.5741i 0.0675437 + 0.383060i
\(763\) 36.1957 30.3718i 1.31037 1.09953i
\(764\) 17.0618 6.21000i 0.617276 0.224670i
\(765\) 0 0
\(766\) −1.33818 1.12286i −0.0483503 0.0405707i
\(767\) 9.88048 17.1135i 0.356763 0.617932i
\(768\) −0.427125 0.739803i −0.0154126 0.0266953i
\(769\) −2.77743 + 15.7516i −0.100157 + 0.568017i 0.892888 + 0.450279i \(0.148676\pi\)
−0.993045 + 0.117738i \(0.962436\pi\)
\(770\) 0 0
\(771\) 1.38100 + 2.39197i 0.0497357 + 0.0861447i
\(772\) −2.23082 + 3.86389i −0.0802888 + 0.139064i
\(773\) −33.0004 27.6907i −1.18694 0.995964i −0.999907 0.0136105i \(-0.995667\pi\)
−0.187036 0.982353i \(-0.559888\pi\)
\(774\) −3.27931 1.19357i −0.117872 0.0429020i
\(775\) 0 0
\(776\) 2.01455 1.69041i 0.0723180 0.0606820i
\(777\) −4.52634 25.6702i −0.162382 0.920912i
\(778\) 2.95418 0.105913
\(779\) 15.0780 6.24338i 0.540224 0.223692i
\(780\) 0 0
\(781\) 0.494150 + 2.80246i 0.0176821 + 0.100280i
\(782\) −6.26838 + 5.25979i −0.224157 + 0.188090i
\(783\) −44.1070 + 16.0536i −1.57625 + 0.573710i
\(784\) −0.693413 0.252382i −0.0247648 0.00901364i
\(785\) 0 0
\(786\) −5.93905 + 10.2867i −0.211839 + 0.366915i
\(787\) −0.505079 0.874822i −0.0180041 0.0311840i 0.856883 0.515511i \(-0.172398\pi\)
−0.874887 + 0.484327i \(0.839065\pi\)
\(788\) −3.55432 + 20.1575i −0.126617 + 0.718082i
\(789\) 0.151915 0.861552i 0.00540831 0.0306721i
\(790\) 0 0
\(791\) 0.304401 0.527239i 0.0108233 0.0187465i
\(792\) 5.50605 + 4.62012i 0.195649 + 0.164169i
\(793\) −19.1381 6.96570i −0.679614 0.247359i
\(794\) −1.79077 + 0.651789i −0.0635522 + 0.0231311i
\(795\) 0 0
\(796\) 1.40764 + 7.98310i 0.0498924 + 0.282954i
\(797\) 38.3494 1.35841 0.679203 0.733951i \(-0.262326\pi\)
0.679203 + 0.733951i \(0.262326\pi\)
\(798\) 10.3482 0.450566i 0.366321 0.0159499i
\(799\) −4.03323 −0.142686
\(800\) 0 0
\(801\) 16.4975 13.8430i 0.582909 0.489119i
\(802\) 2.40143 0.874050i 0.0847975 0.0308638i
\(803\) −31.1359 11.3325i −1.09876 0.399917i
\(804\) 3.74147 + 3.13946i 0.131951 + 0.110720i
\(805\) 0 0
\(806\) −18.2712 31.6466i −0.643575 1.11470i
\(807\) −1.38635 + 7.86236i −0.0488017 + 0.276768i
\(808\) −2.99521 + 16.9867i −0.105371 + 0.597590i
\(809\) −26.9094 46.6085i −0.946086 1.63867i −0.753563 0.657376i \(-0.771667\pi\)
−0.192522 0.981293i \(-0.561667\pi\)
\(810\) 0 0
\(811\) −33.3848 28.0132i −1.17230 0.983676i −0.172300 0.985044i \(-0.555120\pi\)
−0.999999 + 0.00136831i \(0.999564\pi\)
\(812\) 27.2522 + 9.91900i 0.956366 + 0.348089i
\(813\) −7.76949 + 2.82786i −0.272488 + 0.0991774i
\(814\) 26.6039 22.3233i 0.932466 0.782432i
\(815\) 0 0
\(816\) 1.15925 0.0405820
\(817\) −5.31527 4.07956i −0.185958 0.142726i
\(818\) 0.993545 0.0347385
\(819\) 5.26956 + 29.8852i 0.184133 + 1.04427i
\(820\) 0 0
\(821\) 22.1270 8.05358i 0.772239 0.281072i 0.0743065 0.997235i \(-0.476326\pi\)
0.697933 + 0.716163i \(0.254103\pi\)
\(822\) 4.96335 + 1.80651i 0.173117 + 0.0630093i
\(823\) 19.5518 + 16.4059i 0.681534 + 0.571875i 0.916454 0.400140i \(-0.131038\pi\)
−0.234920 + 0.972015i \(0.575483\pi\)
\(824\) 6.08058 10.5319i 0.211827 0.366895i
\(825\) 0 0
\(826\) −1.98643 + 11.2656i −0.0691166 + 0.391980i
\(827\) 1.04161 5.90726i 0.0362203 0.205416i −0.961327 0.275409i \(-0.911187\pi\)
0.997547 + 0.0699935i \(0.0222978\pi\)
\(828\) 6.84468 + 11.8553i 0.237869 + 0.412001i
\(829\) 4.83910 8.38157i 0.168069 0.291104i −0.769672 0.638440i \(-0.779580\pi\)
0.937741 + 0.347336i \(0.112914\pi\)
\(830\) 0 0
\(831\) 2.09484 + 0.762460i 0.0726693 + 0.0264495i
\(832\) 4.51548 1.64350i 0.156546 0.0569781i
\(833\) 0.767102 0.643675i 0.0265785 0.0223020i
\(834\) −1.30175 7.38258i −0.0450758 0.255638i
\(835\) 0 0
\(836\) 7.41349 + 11.6399i 0.256401 + 0.402575i
\(837\) −34.2370 −1.18340
\(838\) 2.58141 + 14.6399i 0.0891732 + 0.505726i
\(839\) 23.9478 20.0946i 0.826768 0.693741i −0.127778 0.991803i \(-0.540785\pi\)
0.954547 + 0.298062i \(0.0963402\pi\)
\(840\) 0 0
\(841\) −74.8886 27.2572i −2.58237 0.939904i
\(842\) −29.8436 25.0418i −1.02848 0.862997i
\(843\) −12.9168 + 22.3725i −0.444878 + 0.770551i
\(844\) −12.2140 21.1553i −0.420424 0.728197i
\(845\) 0 0
\(846\) −1.17167 + 6.64487i −0.0402829 + 0.228455i
\(847\) 1.35807 + 2.35225i 0.0466639 + 0.0808242i
\(848\) 2.15449 3.73168i 0.0739854 0.128147i
\(849\) 12.4701 + 10.4637i 0.427974 + 0.359113i
\(850\) 0 0
\(851\) 62.1547 22.6225i 2.13064 0.775488i
\(852\) 0.588189 0.493549i 0.0201510 0.0169087i
\(853\) 7.36275 + 41.7562i 0.252096 + 1.42971i 0.803419 + 0.595414i \(0.203012\pi\)
−0.551324 + 0.834292i \(0.685877\pi\)
\(854\) 11.7898 0.403440
\(855\) 0 0
\(856\) −13.9511 −0.476839
\(857\) −6.27056 35.5621i −0.214198 1.21478i −0.882292 0.470702i \(-0.844001\pi\)
0.668094 0.744077i \(-0.267110\pi\)
\(858\) 9.95562 8.35376i 0.339879 0.285193i
\(859\) −24.3549 + 8.86444i −0.830977 + 0.302451i −0.722260 0.691622i \(-0.756897\pi\)
−0.108717 + 0.994073i \(0.534674\pi\)
\(860\) 0 0
\(861\) 6.81523 + 5.71866i 0.232262 + 0.194891i
\(862\) −13.6112 + 23.5752i −0.463598 + 0.802975i
\(863\) 22.7413 + 39.3891i 0.774124 + 1.34082i 0.935286 + 0.353894i \(0.115143\pi\)
−0.161162 + 0.986928i \(0.551524\pi\)
\(864\) 0.781785 4.43372i 0.0265969 0.150838i
\(865\) 0 0
\(866\) −16.6941 28.9150i −0.567288 0.982571i
\(867\) 6.47455 11.2143i 0.219887 0.380856i
\(868\) 16.2048 + 13.5975i 0.550028 + 0.461529i
\(869\) 6.66087 + 2.42436i 0.225955 + 0.0822407i
\(870\) 0 0
\(871\) −21.0462 + 17.6599i −0.713124 + 0.598382i
\(872\) −2.94958 16.7279i −0.0998855 0.566479i
\(873\) 5.97033 0.202065
\(874\) 5.68574 + 25.6613i 0.192323 + 0.868006i
\(875\) 0 0
\(876\) 1.55246 + 8.80443i 0.0524527 + 0.297474i
\(877\) −20.6745 + 17.3479i −0.698127 + 0.585798i −0.921240 0.388995i \(-0.872822\pi\)
0.223113 + 0.974793i \(0.428378\pi\)
\(878\) 17.4044 6.33467i 0.587369 0.213785i
\(879\) −0.504209 0.183517i −0.0170065 0.00618988i
\(880\) 0 0
\(881\) −24.0249 + 41.6123i −0.809419 + 1.40196i 0.103847 + 0.994593i \(0.466885\pi\)
−0.913267 + 0.407362i \(0.866449\pi\)
\(882\) −0.837628 1.45081i −0.0282044 0.0488514i
\(883\) −3.54171 + 20.0861i −0.119188 + 0.675949i 0.865403 + 0.501077i \(0.167063\pi\)
−0.984591 + 0.174873i \(0.944049\pi\)
\(884\) −1.13235 + 6.42188i −0.0380851 + 0.215991i
\(885\) 0 0
\(886\) 6.79176 11.7637i 0.228174 0.395208i
\(887\) −20.0250 16.8029i −0.672372 0.564187i 0.241394 0.970427i \(-0.422395\pi\)
−0.913767 + 0.406240i \(0.866840\pi\)
\(888\) −8.80544 3.20492i −0.295491 0.107550i
\(889\) 32.8553 11.9583i 1.10193 0.401070i
\(890\) 0 0
\(891\) 1.62997 + 9.24405i 0.0546062 + 0.309687i
\(892\) −24.8498 −0.832031
\(893\) −5.98333 + 11.4905i −0.200224 + 0.384515i
\(894\) −14.0690 −0.470539
\(895\) 0 0
\(896\) −2.13091 + 1.78805i −0.0711888 + 0.0597345i
\(897\) 23.2593 8.46570i 0.776606 0.282662i
\(898\) 2.63671 + 0.959686i 0.0879883 + 0.0320251i
\(899\) −60.7348 50.9625i −2.02562 1.69970i
\(900\) 0 0
\(901\) 2.92373 + 5.06405i 0.0974035 + 0.168708i
\(902\) −2.05831 + 11.6733i −0.0685342 + 0.388677i
\(903\) 0.634292 3.59725i 0.0211079 0.119709i
\(904\) −0.109430 0.189538i −0.00363957 0.00630393i
\(905\) 0 0
\(906\) −9.64231 8.09086i −0.320344 0.268801i
\(907\) 7.18433 + 2.61488i 0.238552 + 0.0868258i 0.458530 0.888679i \(-0.348376\pi\)
−0.219978 + 0.975505i \(0.570598\pi\)
\(908\) 7.82776 2.84907i 0.259773 0.0945497i
\(909\) −29.9976 + 25.1709i −0.994956 + 0.834868i
\(910\) 0 0
\(911\) 25.2731 0.837335 0.418668 0.908140i \(-0.362497\pi\)
0.418668 + 0.908140i \(0.362497\pi\)
\(912\) 1.71976 3.30266i 0.0569470 0.109362i
\(913\) 26.3925 0.873465
\(914\) −3.27892 18.5957i −0.108457 0.615091i
\(915\) 0 0
\(916\) −0.657144 + 0.239181i −0.0217127 + 0.00790276i
\(917\) 36.3462 + 13.2289i 1.20026 + 0.436858i
\(918\) 4.68020 + 3.92715i 0.154469 + 0.129615i
\(919\) −9.50216 + 16.4582i −0.313447 + 0.542907i −0.979106 0.203349i \(-0.934817\pi\)
0.665659 + 0.746256i \(0.268151\pi\)
\(920\) 0 0
\(921\) −3.16035 + 17.9232i −0.104137 + 0.590590i
\(922\) −0.950337 + 5.38963i −0.0312977 + 0.177498i
\(923\) 2.15956 + 3.74046i 0.0710827 + 0.123119i
\(924\) −3.76165 + 6.51537i −0.123749 + 0.214340i
\(925\) 0 0
\(926\) −6.63341 2.41436i −0.217987 0.0793409i
\(927\) 25.9439 9.44282i 0.852110 0.310143i
\(928\) 7.98653 6.70150i 0.262171 0.219987i
\(929\) 1.18404 + 6.71501i 0.0388470 + 0.220312i 0.998051 0.0624023i \(-0.0198762\pi\)
−0.959204 + 0.282715i \(0.908765\pi\)
\(930\) 0 0
\(931\) −0.695800 3.14034i −0.0228039 0.102920i
\(932\) 2.57130 0.0842257
\(933\) 4.88923 + 27.7282i 0.160066 + 0.907781i
\(934\) 7.28419 6.11216i 0.238346 0.199996i
\(935\) 0 0
\(936\) 10.2513 + 3.73116i 0.335074 + 0.121957i
\(937\) 1.49929 + 1.25805i 0.0489796 + 0.0410988i 0.666949 0.745104i \(-0.267600\pi\)
−0.617969 + 0.786202i \(0.712044\pi\)
\(938\) 7.95215 13.7735i 0.259647 0.449722i
\(939\) −12.1828 21.1012i −0.397569 0.688610i
\(940\) 0 0
\(941\) −1.30211 + 7.38466i −0.0424477 + 0.240733i −0.998648 0.0519798i \(-0.983447\pi\)
0.956200 + 0.292713i \(0.0945580\pi\)
\(942\) −3.92189 6.79292i −0.127782 0.221325i
\(943\) −11.2878 + 19.5510i −0.367580 + 0.636667i
\(944\) 3.15025 + 2.64337i 0.102532 + 0.0860343i
\(945\) 0 0
\(946\) 4.57318 1.66450i 0.148687 0.0541177i
\(947\) 0.549732 0.461280i 0.0178639 0.0149896i −0.633812 0.773487i \(-0.718511\pi\)
0.651676 + 0.758498i \(0.274066\pi\)
\(948\) −0.332116 1.88352i −0.0107866 0.0611740i
\(949\) −50.2901 −1.63248
\(950\) 0 0
\(951\) 26.1884 0.849217
\(952\) −0.655504 3.71755i −0.0212450 0.120486i
\(953\) −37.5256 + 31.4877i −1.21557 + 1.01999i −0.216528 + 0.976277i \(0.569473\pi\)
−0.999044 + 0.0437094i \(0.986082\pi\)
\(954\) 9.19252 3.34580i 0.297619 0.108324i
\(955\) 0 0
\(956\) 13.5850 + 11.3992i 0.439370 + 0.368675i
\(957\) 14.0984 24.4192i 0.455738 0.789361i
\(958\) 15.3224 + 26.5391i 0.495043 + 0.857440i
\(959\) 2.98666 16.9382i 0.0964442 0.546962i
\(960\) 0 0
\(961\) −13.4153 23.2360i −0.432752 0.749549i
\(962\) 26.3553 45.6487i 0.849728 1.47177i
\(963\) −24.2626 20.3587i −0.781852 0.656052i
\(964\) 8.50065 + 3.09399i 0.273788 + 0.0996506i
\(965\) 0 0
\(966\) −10.9764 + 9.21029i −0.353160 + 0.296336i
\(967\) −0.906194 5.13928i −0.0291412 0.165268i 0.966764 0.255670i \(-0.0822960\pi\)
−0.995905 + 0.0904018i \(0.971185\pi\)
\(968\) 0.976429 0.0313836
\(969\) 2.71450 + 4.26204i 0.0872023 + 0.136916i
\(970\) 0 0
\(971\) 0.747673 + 4.24027i 0.0239940 + 0.136077i 0.994452 0.105195i \(-0.0335467\pi\)
−0.970458 + 0.241272i \(0.922436\pi\)
\(972\) 12.2866 10.3097i 0.394094 0.330684i
\(973\) −22.9387 + 8.34901i −0.735381 + 0.267657i
\(974\) 27.1778 + 9.89193i 0.870834 + 0.316958i
\(975\) 0 0
\(976\) 2.11917 3.67051i 0.0678330 0.117490i
\(977\) 10.0224 + 17.3593i 0.320645 + 0.555374i 0.980621 0.195913i \(-0.0627669\pi\)
−0.659976 + 0.751287i \(0.729434\pi\)
\(978\) 2.42782 13.7689i 0.0776332 0.440280i
\(979\) −5.21519 + 29.5768i −0.166678 + 0.945279i
\(980\) 0 0
\(981\) 19.2813 33.3961i 0.615603 1.06626i
\(982\) 30.3092 + 25.4325i 0.967206 + 0.811582i
\(983\) −29.9674 10.9072i −0.955812 0.347887i −0.183421 0.983034i \(-0.558717\pi\)
−0.772391 + 0.635147i \(0.780939\pi\)
\(984\) 3.00539 1.09387i 0.0958082 0.0348713i
\(985\) 0 0
\(986\) 2.45679 + 13.9331i 0.0782400 + 0.443721i
\(987\) −7.06249 −0.224801
\(988\) 16.6158 + 12.7529i 0.528619 + 0.405724i
\(989\) 9.26894 0.294735
\(990\) 0 0
\(991\) 28.4508 23.8730i 0.903768 0.758352i −0.0671549 0.997743i \(-0.521392\pi\)
0.970923 + 0.239391i \(0.0769477\pi\)
\(992\) 7.14603 2.60094i 0.226887 0.0825800i
\(993\) −6.26422 2.27999i −0.198789 0.0723533i
\(994\) −1.91533 1.60715i −0.0607505 0.0509757i
\(995\) 0 0
\(996\) −3.56062 6.16717i −0.112822 0.195414i
\(997\) 9.74265 55.2533i 0.308553 1.74989i −0.297738 0.954648i \(-0.596232\pi\)
0.606291 0.795243i \(-0.292657\pi\)
\(998\) −0.530491 + 3.00856i −0.0167924 + 0.0952344i
\(999\) −24.6926 42.7688i −0.781239 1.35315i
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 950.2.l.j.351.3 24
5.2 odd 4 950.2.u.h.199.6 48
5.3 odd 4 950.2.u.h.199.3 48
5.4 even 2 950.2.l.k.351.2 yes 24
19.17 even 9 inner 950.2.l.j.701.3 yes 24
95.17 odd 36 950.2.u.h.549.3 48
95.74 even 18 950.2.l.k.701.2 yes 24
95.93 odd 36 950.2.u.h.549.6 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.l.j.351.3 24 1.1 even 1 trivial
950.2.l.j.701.3 yes 24 19.17 even 9 inner
950.2.l.k.351.2 yes 24 5.4 even 2
950.2.l.k.701.2 yes 24 95.74 even 18
950.2.u.h.199.3 48 5.3 odd 4
950.2.u.h.199.6 48 5.2 odd 4
950.2.u.h.549.3 48 95.17 odd 36
950.2.u.h.549.6 48 95.93 odd 36