Properties

Label 201.2.e.b.163.2
Level $201$
Weight $2$
Character 201.163
Analytic conductor $1.605$
Analytic rank $0$
Dimension $10$
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] = [201,2,Mod(37,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 49x^{6} - 39x^{5} + 128x^{4} - 14x^{3} + 119x^{2} - 49x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.2
Root \(0.947050 - 1.64034i\) of defining polynomial
Character \(\chi\) \(=\) 201.163
Dual form 201.2.e.b.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.947050 + 1.64034i) q^{2} -1.00000 q^{3} +(-0.793808 - 1.37492i) q^{4} +1.30648 q^{5} +(0.947050 - 1.64034i) q^{6} +(2.53710 + 4.39438i) q^{7} -0.781096 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.947050 + 1.64034i) q^{2} -1.00000 q^{3} +(-0.793808 - 1.37492i) q^{4} +1.30648 q^{5} +(0.947050 - 1.64034i) q^{6} +(2.53710 + 4.39438i) q^{7} -0.781096 q^{8} +1.00000 q^{9} +(-1.23731 + 2.14308i) q^{10} +(-1.88386 - 3.26293i) q^{11} +(0.793808 + 1.37492i) q^{12} +(-2.77440 + 4.80541i) q^{13} -9.61104 q^{14} -1.30648 q^{15} +(2.32735 - 4.03109i) q^{16} +(-2.28465 + 3.95713i) q^{17} +(-0.947050 + 1.64034i) q^{18} +(0.737306 - 1.27705i) q^{19} +(-1.03710 - 1.79631i) q^{20} +(-2.53710 - 4.39438i) q^{21} +7.13642 q^{22} +(1.39410 - 2.41465i) q^{23} +0.781096 q^{24} -3.29310 q^{25} +(-5.25500 - 9.10193i) q^{26} -1.00000 q^{27} +(4.02794 - 6.97659i) q^{28} +(2.62785 + 4.55158i) q^{29} +(1.23731 - 2.14308i) q^{30} +(0.883856 + 1.53088i) q^{31} +(3.62715 + 6.28240i) q^{32} +(1.88386 + 3.26293i) q^{33} +(-4.32735 - 7.49520i) q^{34} +(3.31468 + 5.74119i) q^{35} +(-0.793808 - 1.37492i) q^{36} +(3.48841 - 6.04210i) q^{37} +(1.39653 + 2.41886i) q^{38} +(2.77440 - 4.80541i) q^{39} -1.02049 q^{40} +(4.25612 + 7.37182i) q^{41} +9.61104 q^{42} +8.89927 q^{43} +(-2.99084 + 5.18029i) q^{44} +1.30648 q^{45} +(2.64057 + 4.57359i) q^{46} +(-2.59431 - 4.49347i) q^{47} +(-2.32735 + 4.03109i) q^{48} +(-9.37373 + 16.2358i) q^{49} +(3.11873 - 5.40180i) q^{50} +(2.28465 - 3.95713i) q^{51} +8.80938 q^{52} -2.37365 q^{53} +(0.947050 - 1.64034i) q^{54} +(-2.46123 - 4.26297i) q^{55} +(-1.98172 - 3.43243i) q^{56} +(-0.737306 + 1.27705i) q^{57} -9.95484 q^{58} +10.8348 q^{59} +(1.03710 + 1.79631i) q^{60} +(6.21229 - 10.7600i) q^{61} -3.34822 q^{62} +(2.53710 + 4.39438i) q^{63} -4.43094 q^{64} +(-3.62471 + 6.27819i) q^{65} -7.13642 q^{66} +(8.01183 - 1.67649i) q^{67} +7.25429 q^{68} +(-1.39410 + 2.41465i) q^{69} -12.5567 q^{70} +(-4.98658 - 8.63701i) q^{71} -0.781096 q^{72} +(2.00845 - 3.47874i) q^{73} +(6.60740 + 11.4443i) q^{74} +3.29310 q^{75} -2.34112 q^{76} +(9.55905 - 16.5568i) q^{77} +(5.25500 + 9.10193i) q^{78} +(-0.880303 - 1.52473i) q^{79} +(3.04065 - 5.26656i) q^{80} +1.00000 q^{81} -16.1230 q^{82} +(1.08406 - 1.87765i) q^{83} +(-4.02794 + 6.97659i) q^{84} +(-2.98486 + 5.16992i) q^{85} +(-8.42806 + 14.5978i) q^{86} +(-2.62785 - 4.55158i) q^{87} +(1.47147 + 2.54866i) q^{88} +7.24943 q^{89} +(-1.23731 + 2.14308i) q^{90} -28.1557 q^{91} -4.42659 q^{92} +(-0.883856 - 1.53088i) q^{93} +9.82776 q^{94} +(0.963278 - 1.66845i) q^{95} +(-3.62715 - 6.28240i) q^{96} +(-2.81823 + 4.88132i) q^{97} +(-17.7548 - 30.7522i) q^{98} +(-1.88386 - 3.26293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + 3 q^{13} - 22 q^{14} - 2 q^{15} + 2 q^{17} - 2 q^{18} + 3 q^{19} + 16 q^{20} + q^{21} + 6 q^{22} - q^{23} - 12 q^{24} + 7 q^{26} - 10 q^{27} - 9 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 9 q^{32} - 2 q^{33} - 20 q^{34} + 19 q^{35} - 6 q^{36} + 27 q^{37} - 16 q^{38} - 3 q^{39} - 22 q^{40} - 7 q^{41} + 22 q^{42} + 12 q^{43} - 7 q^{44} + 2 q^{45} + 30 q^{46} - 33 q^{47} - 24 q^{49} + 21 q^{50} - 2 q^{51} - 32 q^{52} - 24 q^{53} + 2 q^{54} + 6 q^{55} - q^{56} - 3 q^{57} + 44 q^{58} + 24 q^{59} - 16 q^{60} + q^{61} + 2 q^{62} - q^{63} - 8 q^{64} - 6 q^{65} - 6 q^{66} + 2 q^{67} - 18 q^{68} + q^{69} + 42 q^{70} - q^{71} + 12 q^{72} + 12 q^{73} + 43 q^{74} + 2 q^{76} + 40 q^{77} - 7 q^{78} + 7 q^{79} - q^{80} + 10 q^{81} - 74 q^{82} + 12 q^{83} + 9 q^{84} - 27 q^{85} - 27 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} - 80 q^{91} - 28 q^{92} + 12 q^{93} + 30 q^{94} - 12 q^{95} + 9 q^{96} - 9 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.947050 + 1.64034i −0.669666 + 1.15989i 0.308332 + 0.951279i \(0.400229\pi\)
−0.977998 + 0.208616i \(0.933104\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.793808 1.37492i −0.396904 0.687458i
\(5\) 1.30648 0.584277 0.292139 0.956376i \(-0.405633\pi\)
0.292139 + 0.956376i \(0.405633\pi\)
\(6\) 0.947050 1.64034i 0.386632 0.669666i
\(7\) 2.53710 + 4.39438i 0.958933 + 1.66092i 0.725100 + 0.688643i \(0.241793\pi\)
0.233833 + 0.972277i \(0.424873\pi\)
\(8\) −0.781096 −0.276159
\(9\) 1.00000 0.333333
\(10\) −1.23731 + 2.14308i −0.391271 + 0.677700i
\(11\) −1.88386 3.26293i −0.568004 0.983812i −0.996763 0.0803928i \(-0.974383\pi\)
0.428759 0.903419i \(-0.358951\pi\)
\(12\) 0.793808 + 1.37492i 0.229153 + 0.396904i
\(13\) −2.77440 + 4.80541i −0.769481 + 1.33278i 0.168363 + 0.985725i \(0.446152\pi\)
−0.937845 + 0.347055i \(0.887182\pi\)
\(14\) −9.61104 −2.56866
\(15\) −1.30648 −0.337333
\(16\) 2.32735 4.03109i 0.581838 1.00777i
\(17\) −2.28465 + 3.95713i −0.554109 + 0.959744i 0.443864 + 0.896094i \(0.353607\pi\)
−0.997972 + 0.0636500i \(0.979726\pi\)
\(18\) −0.947050 + 1.64034i −0.223222 + 0.386632i
\(19\) 0.737306 1.27705i 0.169150 0.292976i −0.768972 0.639283i \(-0.779231\pi\)
0.938121 + 0.346307i \(0.112565\pi\)
\(20\) −1.03710 1.79631i −0.231902 0.401666i
\(21\) −2.53710 4.39438i −0.553640 0.958933i
\(22\) 7.13642 1.52149
\(23\) 1.39410 2.41465i 0.290690 0.503490i −0.683283 0.730154i \(-0.739448\pi\)
0.973973 + 0.226664i \(0.0727818\pi\)
\(24\) 0.781096 0.159441
\(25\) −3.29310 −0.658620
\(26\) −5.25500 9.10193i −1.03059 1.78503i
\(27\) −1.00000 −0.192450
\(28\) 4.02794 6.97659i 0.761209 1.31845i
\(29\) 2.62785 + 4.55158i 0.487980 + 0.845207i 0.999904 0.0138241i \(-0.00440048\pi\)
−0.511924 + 0.859031i \(0.671067\pi\)
\(30\) 1.23731 2.14308i 0.225900 0.391271i
\(31\) 0.883856 + 1.53088i 0.158745 + 0.274955i 0.934416 0.356182i \(-0.115922\pi\)
−0.775671 + 0.631137i \(0.782589\pi\)
\(32\) 3.62715 + 6.28240i 0.641195 + 1.11058i
\(33\) 1.88386 + 3.26293i 0.327937 + 0.568004i
\(34\) −4.32735 7.49520i −0.742135 1.28542i
\(35\) 3.31468 + 5.74119i 0.560283 + 0.970438i
\(36\) −0.793808 1.37492i −0.132301 0.229153i
\(37\) 3.48841 6.04210i 0.573491 0.993315i −0.422713 0.906264i \(-0.638922\pi\)
0.996204 0.0870517i \(-0.0277445\pi\)
\(38\) 1.39653 + 2.41886i 0.226547 + 0.392391i
\(39\) 2.77440 4.80541i 0.444260 0.769481i
\(40\) −1.02049 −0.161354
\(41\) 4.25612 + 7.37182i 0.664694 + 1.15128i 0.979368 + 0.202084i \(0.0647716\pi\)
−0.314674 + 0.949200i \(0.601895\pi\)
\(42\) 9.61104 1.48302
\(43\) 8.89927 1.35713 0.678563 0.734542i \(-0.262603\pi\)
0.678563 + 0.734542i \(0.262603\pi\)
\(44\) −2.99084 + 5.18029i −0.450886 + 0.780958i
\(45\) 1.30648 0.194759
\(46\) 2.64057 + 4.57359i 0.389330 + 0.674340i
\(47\) −2.59431 4.49347i −0.378419 0.655441i 0.612414 0.790538i \(-0.290199\pi\)
−0.990832 + 0.135097i \(0.956865\pi\)
\(48\) −2.32735 + 4.03109i −0.335925 + 0.581838i
\(49\) −9.37373 + 16.2358i −1.33910 + 2.31940i
\(50\) 3.11873 5.40180i 0.441055 0.763930i
\(51\) 2.28465 3.95713i 0.319915 0.554109i
\(52\) 8.80938 1.22164
\(53\) −2.37365 −0.326046 −0.163023 0.986622i \(-0.552124\pi\)
−0.163023 + 0.986622i \(0.552124\pi\)
\(54\) 0.947050 1.64034i 0.128877 0.223222i
\(55\) −2.46123 4.26297i −0.331872 0.574819i
\(56\) −1.98172 3.43243i −0.264818 0.458678i
\(57\) −0.737306 + 1.27705i −0.0976586 + 0.169150i
\(58\) −9.95484 −1.30713
\(59\) 10.8348 1.41057 0.705286 0.708923i \(-0.250819\pi\)
0.705286 + 0.708923i \(0.250819\pi\)
\(60\) 1.03710 + 1.79631i 0.133889 + 0.231902i
\(61\) 6.21229 10.7600i 0.795403 1.37768i −0.127180 0.991880i \(-0.540593\pi\)
0.922583 0.385798i \(-0.126074\pi\)
\(62\) −3.34822 −0.425225
\(63\) 2.53710 + 4.39438i 0.319644 + 0.553640i
\(64\) −4.43094 −0.553868
\(65\) −3.62471 + 6.27819i −0.449590 + 0.778714i
\(66\) −7.13642 −0.878433
\(67\) 8.01183 1.67649i 0.978801 0.204815i
\(68\) 7.25429 0.879712
\(69\) −1.39410 + 2.41465i −0.167830 + 0.290690i
\(70\) −12.5567 −1.50081
\(71\) −4.98658 8.63701i −0.591798 1.02502i −0.993990 0.109469i \(-0.965085\pi\)
0.402192 0.915555i \(-0.368248\pi\)
\(72\) −0.781096 −0.0920530
\(73\) 2.00845 3.47874i 0.235071 0.407156i −0.724222 0.689567i \(-0.757801\pi\)
0.959293 + 0.282411i \(0.0911343\pi\)
\(74\) 6.60740 + 11.4443i 0.768094 + 1.33038i
\(75\) 3.29310 0.380254
\(76\) −2.34112 −0.268545
\(77\) 9.55905 16.5568i 1.08936 1.88682i
\(78\) 5.25500 + 9.10193i 0.595011 + 1.03059i
\(79\) −0.880303 1.52473i −0.0990419 0.171546i 0.812246 0.583314i \(-0.198244\pi\)
−0.911288 + 0.411769i \(0.864911\pi\)
\(80\) 3.04065 5.26656i 0.339955 0.588819i
\(81\) 1.00000 0.111111
\(82\) −16.1230 −1.78049
\(83\) 1.08406 1.87765i 0.118991 0.206099i −0.800377 0.599497i \(-0.795367\pi\)
0.919368 + 0.393398i \(0.128701\pi\)
\(84\) −4.02794 + 6.97659i −0.439484 + 0.761209i
\(85\) −2.98486 + 5.16992i −0.323753 + 0.560757i
\(86\) −8.42806 + 14.5978i −0.908821 + 1.57412i
\(87\) −2.62785 4.55158i −0.281736 0.487980i
\(88\) 1.47147 + 2.54866i 0.156859 + 0.271689i
\(89\) 7.24943 0.768438 0.384219 0.923242i \(-0.374471\pi\)
0.384219 + 0.923242i \(0.374471\pi\)
\(90\) −1.23731 + 2.14308i −0.130424 + 0.225900i
\(91\) −28.1557 −2.95152
\(92\) −4.42659 −0.461504
\(93\) −0.883856 1.53088i −0.0916516 0.158745i
\(94\) 9.82776 1.01366
\(95\) 0.963278 1.66845i 0.0988303 0.171179i
\(96\) −3.62715 6.28240i −0.370194 0.641195i
\(97\) −2.81823 + 4.88132i −0.286148 + 0.495623i −0.972887 0.231281i \(-0.925708\pi\)
0.686739 + 0.726904i \(0.259042\pi\)
\(98\) −17.7548 30.7522i −1.79350 3.10644i
\(99\) −1.88386 3.26293i −0.189335 0.327937i
\(100\) 2.61409 + 4.52774i 0.261409 + 0.452774i
\(101\) 2.45278 + 4.24833i 0.244060 + 0.422725i 0.961867 0.273518i \(-0.0881872\pi\)
−0.717807 + 0.696242i \(0.754854\pi\)
\(102\) 4.32735 + 7.49520i 0.428472 + 0.742135i
\(103\) −1.83199 3.17310i −0.180511 0.312655i 0.761543 0.648114i \(-0.224442\pi\)
−0.942055 + 0.335459i \(0.891109\pi\)
\(104\) 2.16708 3.75348i 0.212499 0.368059i
\(105\) −3.31468 5.74119i −0.323479 0.560283i
\(106\) 2.24796 3.89359i 0.218341 0.378179i
\(107\) −11.8927 −1.14971 −0.574855 0.818256i \(-0.694941\pi\)
−0.574855 + 0.818256i \(0.694941\pi\)
\(108\) 0.793808 + 1.37492i 0.0763842 + 0.132301i
\(109\) −2.84549 −0.272549 −0.136274 0.990671i \(-0.543513\pi\)
−0.136274 + 0.990671i \(0.543513\pi\)
\(110\) 9.32362 0.888973
\(111\) −3.48841 + 6.04210i −0.331105 + 0.573491i
\(112\) 23.6189 2.23178
\(113\) 7.73768 + 13.4021i 0.727900 + 1.26076i 0.957769 + 0.287538i \(0.0928368\pi\)
−0.229869 + 0.973222i \(0.573830\pi\)
\(114\) −1.39653 2.41886i −0.130797 0.226547i
\(115\) 1.82137 3.15471i 0.169844 0.294178i
\(116\) 4.17202 7.22616i 0.387363 0.670932i
\(117\) −2.77440 + 4.80541i −0.256494 + 0.444260i
\(118\) −10.2611 + 17.7727i −0.944611 + 1.63611i
\(119\) −23.1855 −2.12541
\(120\) 1.02049 0.0931575
\(121\) −1.59782 + 2.76751i −0.145257 + 0.251592i
\(122\) 11.7667 + 20.3805i 1.06531 + 1.84517i
\(123\) −4.25612 7.37182i −0.383761 0.664694i
\(124\) 1.40322 2.43045i 0.126013 0.218261i
\(125\) −10.8348 −0.969094
\(126\) −9.61104 −0.856219
\(127\) −0.232407 0.402541i −0.0206228 0.0357198i 0.855530 0.517754i \(-0.173232\pi\)
−0.876153 + 0.482034i \(0.839898\pi\)
\(128\) −3.05797 + 5.29655i −0.270289 + 0.468154i
\(129\) −8.89927 −0.783537
\(130\) −6.86557 11.8915i −0.602151 1.04296i
\(131\) 5.79113 0.505973 0.252987 0.967470i \(-0.418587\pi\)
0.252987 + 0.967470i \(0.418587\pi\)
\(132\) 2.99084 5.18029i 0.260319 0.450886i
\(133\) 7.48247 0.648812
\(134\) −4.83760 + 14.7298i −0.417905 + 1.27246i
\(135\) −1.30648 −0.112444
\(136\) 1.78453 3.09090i 0.153022 0.265042i
\(137\) 10.9296 0.933775 0.466888 0.884317i \(-0.345375\pi\)
0.466888 + 0.884317i \(0.345375\pi\)
\(138\) −2.64057 4.57359i −0.224780 0.389330i
\(139\) −1.23335 −0.104611 −0.0523057 0.998631i \(-0.516657\pi\)
−0.0523057 + 0.998631i \(0.516657\pi\)
\(140\) 5.26244 9.11481i 0.444757 0.770342i
\(141\) 2.59431 + 4.49347i 0.218480 + 0.378419i
\(142\) 18.8902 1.58523
\(143\) 20.9063 1.74827
\(144\) 2.32735 4.03109i 0.193946 0.335925i
\(145\) 3.43325 + 5.94656i 0.285116 + 0.493835i
\(146\) 3.80421 + 6.58908i 0.314838 + 0.545316i
\(147\) 9.37373 16.2358i 0.773132 1.33910i
\(148\) −11.0765 −0.910484
\(149\) −9.27620 −0.759936 −0.379968 0.925000i \(-0.624065\pi\)
−0.379968 + 0.925000i \(0.624065\pi\)
\(150\) −3.11873 + 5.40180i −0.254643 + 0.441055i
\(151\) −1.05893 + 1.83413i −0.0861748 + 0.149259i −0.905891 0.423510i \(-0.860798\pi\)
0.819716 + 0.572770i \(0.194131\pi\)
\(152\) −0.575907 + 0.997500i −0.0467122 + 0.0809079i
\(153\) −2.28465 + 3.95713i −0.184703 + 0.319915i
\(154\) 18.1058 + 31.3602i 1.45901 + 2.52707i
\(155\) 1.15474 + 2.00007i 0.0927512 + 0.160650i
\(156\) −8.80938 −0.705315
\(157\) 3.57954 6.19995i 0.285679 0.494810i −0.687095 0.726568i \(-0.741114\pi\)
0.972773 + 0.231758i \(0.0744477\pi\)
\(158\) 3.33477 0.265300
\(159\) 2.37365 0.188242
\(160\) 4.73881 + 8.20786i 0.374636 + 0.648888i
\(161\) 14.1479 1.11501
\(162\) −0.947050 + 1.64034i −0.0744073 + 0.128877i
\(163\) −4.15131 7.19028i −0.325156 0.563186i 0.656388 0.754423i \(-0.272083\pi\)
−0.981544 + 0.191237i \(0.938750\pi\)
\(164\) 6.75709 11.7036i 0.527640 0.913899i
\(165\) 2.46123 + 4.26297i 0.191606 + 0.331872i
\(166\) 2.05333 + 3.55646i 0.159369 + 0.276035i
\(167\) 3.39055 + 5.87260i 0.262368 + 0.454436i 0.966871 0.255266i \(-0.0821631\pi\)
−0.704502 + 0.709702i \(0.748830\pi\)
\(168\) 1.98172 + 3.43243i 0.152893 + 0.264818i
\(169\) −8.89463 15.4060i −0.684202 1.18507i
\(170\) −5.65362 9.79235i −0.433613 0.751039i
\(171\) 0.737306 1.27705i 0.0563832 0.0976586i
\(172\) −7.06432 12.2358i −0.538649 0.932967i
\(173\) 6.56276 11.3670i 0.498957 0.864220i −0.501042 0.865423i \(-0.667050\pi\)
0.999999 + 0.00120350i \(0.000383085\pi\)
\(174\) 9.95484 0.754674
\(175\) −8.35492 14.4711i −0.631572 1.09392i
\(176\) −17.5376 −1.32195
\(177\) −10.8348 −0.814394
\(178\) −6.86557 + 11.8915i −0.514596 + 0.891307i
\(179\) −7.19424 −0.537723 −0.268861 0.963179i \(-0.586647\pi\)
−0.268861 + 0.963179i \(0.586647\pi\)
\(180\) −1.03710 1.79631i −0.0773007 0.133889i
\(181\) 12.8219 + 22.2081i 0.953042 + 1.65072i 0.738787 + 0.673939i \(0.235399\pi\)
0.214255 + 0.976778i \(0.431268\pi\)
\(182\) 26.6649 46.1849i 1.97653 3.42346i
\(183\) −6.21229 + 10.7600i −0.459226 + 0.795403i
\(184\) −1.08893 + 1.88608i −0.0802767 + 0.139043i
\(185\) 4.55755 7.89391i 0.335078 0.580372i
\(186\) 3.34822 0.245504
\(187\) 17.2158 1.25894
\(188\) −4.11877 + 7.13391i −0.300392 + 0.520294i
\(189\) −2.53710 4.39438i −0.184547 0.319644i
\(190\) 1.82455 + 3.16021i 0.132366 + 0.229265i
\(191\) 1.62654 2.81726i 0.117693 0.203850i −0.801160 0.598450i \(-0.795784\pi\)
0.918853 + 0.394600i \(0.129117\pi\)
\(192\) 4.43094 0.319776
\(193\) −21.0010 −1.51168 −0.755842 0.654754i \(-0.772772\pi\)
−0.755842 + 0.654754i \(0.772772\pi\)
\(194\) −5.33801 9.24571i −0.383247 0.663803i
\(195\) 3.62471 6.27819i 0.259571 0.449590i
\(196\) 29.7638 2.12598
\(197\) 0.543826 + 0.941935i 0.0387460 + 0.0671101i 0.884748 0.466070i \(-0.154330\pi\)
−0.846002 + 0.533180i \(0.820997\pi\)
\(198\) 7.13642 0.507164
\(199\) 3.69988 6.40838i 0.262278 0.454278i −0.704569 0.709635i \(-0.748860\pi\)
0.966847 + 0.255357i \(0.0821931\pi\)
\(200\) 2.57223 0.181884
\(201\) −8.01183 + 1.67649i −0.565111 + 0.118250i
\(202\) −9.29161 −0.653755
\(203\) −13.3342 + 23.0956i −0.935880 + 1.62099i
\(204\) −7.25429 −0.507902
\(205\) 5.56055 + 9.63116i 0.388366 + 0.672669i
\(206\) 6.93995 0.483529
\(207\) 1.39410 2.41465i 0.0968967 0.167830i
\(208\) 12.9140 + 22.3678i 0.895427 + 1.55093i
\(209\) −5.55591 −0.384310
\(210\) 12.5567 0.866492
\(211\) 3.51731 6.09217i 0.242142 0.419402i −0.719182 0.694821i \(-0.755483\pi\)
0.961324 + 0.275419i \(0.0888167\pi\)
\(212\) 1.88422 + 3.26357i 0.129409 + 0.224143i
\(213\) 4.98658 + 8.63701i 0.341675 + 0.591798i
\(214\) 11.2630 19.5080i 0.769921 1.33354i
\(215\) 11.6268 0.792938
\(216\) 0.781096 0.0531468
\(217\) −4.48486 + 7.76800i −0.304452 + 0.527326i
\(218\) 2.69483 4.66758i 0.182517 0.316128i
\(219\) −2.00845 + 3.47874i −0.135719 + 0.235071i
\(220\) −3.90748 + 6.76796i −0.263443 + 0.456296i
\(221\) −12.6771 21.9573i −0.852752 1.47701i
\(222\) −6.60740 11.4443i −0.443459 0.768094i
\(223\) −14.3934 −0.963854 −0.481927 0.876211i \(-0.660063\pi\)
−0.481927 + 0.876211i \(0.660063\pi\)
\(224\) −18.4048 + 31.8781i −1.22973 + 2.12995i
\(225\) −3.29310 −0.219540
\(226\) −29.3119 −1.94980
\(227\) 12.5810 + 21.7909i 0.835031 + 1.44632i 0.894005 + 0.448056i \(0.147884\pi\)
−0.0589747 + 0.998259i \(0.518783\pi\)
\(228\) 2.34112 0.155044
\(229\) 8.38027 14.5150i 0.553784 0.959181i −0.444213 0.895921i \(-0.646517\pi\)
0.997997 0.0632604i \(-0.0201499\pi\)
\(230\) 3.44986 + 5.97533i 0.227477 + 0.394001i
\(231\) −9.55905 + 16.5568i −0.628939 + 1.08936i
\(232\) −2.05261 3.55522i −0.134760 0.233412i
\(233\) −13.2071 22.8754i −0.865226 1.49862i −0.866823 0.498617i \(-0.833841\pi\)
0.00159640 0.999999i \(-0.499492\pi\)
\(234\) −5.25500 9.10193i −0.343530 0.595011i
\(235\) −3.38942 5.87065i −0.221102 0.382959i
\(236\) −8.60075 14.8969i −0.559861 0.969708i
\(237\) 0.880303 + 1.52473i 0.0571818 + 0.0990419i
\(238\) 21.9578 38.0321i 1.42332 2.46525i
\(239\) −0.221715 0.384022i −0.0143416 0.0248403i 0.858766 0.512369i \(-0.171232\pi\)
−0.873107 + 0.487528i \(0.837899\pi\)
\(240\) −3.04065 + 5.26656i −0.196273 + 0.339955i
\(241\) −21.3462 −1.37503 −0.687515 0.726170i \(-0.741299\pi\)
−0.687515 + 0.726170i \(0.741299\pi\)
\(242\) −3.02644 5.24195i −0.194547 0.336965i
\(243\) −1.00000 −0.0641500
\(244\) −19.7255 −1.26279
\(245\) −12.2466 + 21.2118i −0.782408 + 1.35517i
\(246\) 16.1230 1.02797
\(247\) 4.09117 + 7.08611i 0.260315 + 0.450879i
\(248\) −0.690376 1.19577i −0.0438389 0.0759313i
\(249\) −1.08406 + 1.87765i −0.0686998 + 0.118991i
\(250\) 10.2611 17.7727i 0.648969 1.12405i
\(251\) 9.72392 16.8423i 0.613768 1.06308i −0.376831 0.926282i \(-0.622986\pi\)
0.990599 0.136796i \(-0.0436805\pi\)
\(252\) 4.02794 6.97659i 0.253736 0.439484i
\(253\) −10.5051 −0.660452
\(254\) 0.880406 0.0552416
\(255\) 2.98486 5.16992i 0.186919 0.323753i
\(256\) −10.2230 17.7068i −0.638940 1.10668i
\(257\) −2.60822 4.51758i −0.162697 0.281799i 0.773138 0.634237i \(-0.218686\pi\)
−0.935835 + 0.352439i \(0.885352\pi\)
\(258\) 8.42806 14.5978i 0.524708 0.908821i
\(259\) 35.4017 2.19976
\(260\) 11.5093 0.713777
\(261\) 2.62785 + 4.55158i 0.162660 + 0.281736i
\(262\) −5.48449 + 9.49942i −0.338833 + 0.586876i
\(263\) 13.6157 0.839578 0.419789 0.907622i \(-0.362104\pi\)
0.419789 + 0.907622i \(0.362104\pi\)
\(264\) −1.47147 2.54866i −0.0905628 0.156859i
\(265\) −3.10113 −0.190501
\(266\) −7.08627 + 12.2738i −0.434487 + 0.752554i
\(267\) −7.24943 −0.443658
\(268\) −8.66488 9.68478i −0.529292 0.591592i
\(269\) −19.0352 −1.16060 −0.580298 0.814405i \(-0.697064\pi\)
−0.580298 + 0.814405i \(0.697064\pi\)
\(270\) 1.23731 2.14308i 0.0753000 0.130424i
\(271\) 10.4679 0.635883 0.317941 0.948110i \(-0.397009\pi\)
0.317941 + 0.948110i \(0.397009\pi\)
\(272\) 10.6344 + 18.4193i 0.644803 + 1.11683i
\(273\) 28.1557 1.70406
\(274\) −10.3508 + 17.9282i −0.625317 + 1.08308i
\(275\) 6.20372 + 10.7452i 0.374099 + 0.647958i
\(276\) 4.42659 0.266450
\(277\) 7.44098 0.447085 0.223542 0.974694i \(-0.428238\pi\)
0.223542 + 0.974694i \(0.428238\pi\)
\(278\) 1.16805 2.02311i 0.0700547 0.121338i
\(279\) 0.883856 + 1.53088i 0.0529151 + 0.0916516i
\(280\) −2.58908 4.48442i −0.154727 0.267995i
\(281\) −9.72183 + 16.8387i −0.579956 + 1.00451i 0.415528 + 0.909581i \(0.363597\pi\)
−0.995484 + 0.0949327i \(0.969736\pi\)
\(282\) −9.82776 −0.585235
\(283\) −28.0749 −1.66888 −0.834441 0.551097i \(-0.814209\pi\)
−0.834441 + 0.551097i \(0.814209\pi\)
\(284\) −7.91677 + 13.7123i −0.469774 + 0.813673i
\(285\) −0.963278 + 1.66845i −0.0570597 + 0.0988303i
\(286\) −19.7993 + 34.2934i −1.17076 + 2.02781i
\(287\) −21.5964 + 37.4060i −1.27479 + 2.20801i
\(288\) 3.62715 + 6.28240i 0.213732 + 0.370194i
\(289\) −1.93924 3.35886i −0.114073 0.197580i
\(290\) −13.0058 −0.763729
\(291\) 2.81823 4.88132i 0.165208 0.286148i
\(292\) −6.37730 −0.373203
\(293\) −15.9270 −0.930467 −0.465234 0.885188i \(-0.654030\pi\)
−0.465234 + 0.885188i \(0.654030\pi\)
\(294\) 17.7548 + 30.7522i 1.03548 + 1.79350i
\(295\) 14.1555 0.824165
\(296\) −2.72478 + 4.71946i −0.158375 + 0.274313i
\(297\) 1.88386 + 3.26293i 0.109312 + 0.189335i
\(298\) 8.78502 15.2161i 0.508903 0.881446i
\(299\) 7.73559 + 13.3984i 0.447361 + 0.774852i
\(300\) −2.61409 4.52774i −0.150925 0.261409i
\(301\) 22.5783 + 39.1068i 1.30139 + 2.25408i
\(302\) −2.00573 3.47402i −0.115417 0.199907i
\(303\) −2.45278 4.24833i −0.140908 0.244060i
\(304\) −3.43194 5.94430i −0.196835 0.340929i
\(305\) 8.11626 14.0578i 0.464736 0.804946i
\(306\) −4.32735 7.49520i −0.247378 0.428472i
\(307\) 6.60681 11.4433i 0.377070 0.653105i −0.613564 0.789645i \(-0.710265\pi\)
0.990635 + 0.136540i \(0.0435981\pi\)
\(308\) −30.3522 −1.72948
\(309\) 1.83199 + 3.17310i 0.104218 + 0.180511i
\(310\) −4.37440 −0.248449
\(311\) 7.96043 0.451395 0.225697 0.974197i \(-0.427534\pi\)
0.225697 + 0.974197i \(0.427534\pi\)
\(312\) −2.16708 + 3.75348i −0.122686 + 0.212499i
\(313\) 15.3567 0.868015 0.434007 0.900909i \(-0.357099\pi\)
0.434007 + 0.900909i \(0.357099\pi\)
\(314\) 6.78001 + 11.7433i 0.382618 + 0.662714i
\(315\) 3.31468 + 5.74119i 0.186761 + 0.323479i
\(316\) −1.39758 + 2.42069i −0.0786202 + 0.136174i
\(317\) −6.42765 + 11.1330i −0.361013 + 0.625292i −0.988128 0.153634i \(-0.950902\pi\)
0.627115 + 0.778927i \(0.284236\pi\)
\(318\) −2.24796 + 3.89359i −0.126060 + 0.218341i
\(319\) 9.90100 17.1490i 0.554349 0.960161i
\(320\) −5.78895 −0.323612
\(321\) 11.8927 0.663785
\(322\) −13.3987 + 23.2073i −0.746683 + 1.29329i
\(323\) 3.36897 + 5.83523i 0.187454 + 0.324681i
\(324\) −0.793808 1.37492i −0.0441005 0.0763842i
\(325\) 9.13639 15.8247i 0.506796 0.877796i
\(326\) 15.7260 0.870982
\(327\) 2.84549 0.157356
\(328\) −3.32444 5.75810i −0.183561 0.317938i
\(329\) 13.1640 22.8008i 0.725756 1.25705i
\(330\) −9.32362 −0.513249
\(331\) −8.64872 14.9800i −0.475377 0.823376i 0.524226 0.851579i \(-0.324355\pi\)
−0.999602 + 0.0282030i \(0.991022\pi\)
\(332\) −3.44216 −0.188913
\(333\) 3.48841 6.04210i 0.191164 0.331105i
\(334\) −12.8441 −0.702797
\(335\) 10.4673 2.19030i 0.571891 0.119669i
\(336\) −23.6189 −1.28852
\(337\) 10.5384 18.2531i 0.574064 0.994307i −0.422079 0.906559i \(-0.638700\pi\)
0.996143 0.0877484i \(-0.0279671\pi\)
\(338\) 33.6947 1.83275
\(339\) −7.73768 13.4021i −0.420253 0.727900i
\(340\) 9.47761 0.513996
\(341\) 3.33011 5.76793i 0.180336 0.312351i
\(342\) 1.39653 + 2.41886i 0.0755158 + 0.130797i
\(343\) −59.6089 −3.21858
\(344\) −6.95119 −0.374783
\(345\) −1.82137 + 3.15471i −0.0980593 + 0.169844i
\(346\) 12.4305 + 21.5303i 0.668269 + 1.15748i
\(347\) −4.91238 8.50850i −0.263711 0.456760i 0.703514 0.710681i \(-0.251613\pi\)
−0.967225 + 0.253921i \(0.918280\pi\)
\(348\) −4.17202 + 7.22616i −0.223644 + 0.387363i
\(349\) −21.7712 −1.16538 −0.582692 0.812693i \(-0.698000\pi\)
−0.582692 + 0.812693i \(0.698000\pi\)
\(350\) 31.6501 1.69177
\(351\) 2.77440 4.80541i 0.148087 0.256494i
\(352\) 13.6660 23.6703i 0.728402 1.26163i
\(353\) 2.19536 3.80247i 0.116847 0.202385i −0.801670 0.597767i \(-0.796055\pi\)
0.918517 + 0.395382i \(0.129388\pi\)
\(354\) 10.2611 17.7727i 0.545371 0.944611i
\(355\) −6.51489 11.2841i −0.345774 0.598899i
\(356\) −5.75466 9.96736i −0.304996 0.528269i
\(357\) 23.1855 1.22711
\(358\) 6.81331 11.8010i 0.360094 0.623702i
\(359\) −26.4848 −1.39781 −0.698907 0.715212i \(-0.746330\pi\)
−0.698907 + 0.715212i \(0.746330\pi\)
\(360\) −1.02049 −0.0537845
\(361\) 8.41276 + 14.5713i 0.442777 + 0.766912i
\(362\) −48.5718 −2.55288
\(363\) 1.59782 2.76751i 0.0838640 0.145257i
\(364\) 22.3503 + 38.7118i 1.17147 + 2.02905i
\(365\) 2.62401 4.54492i 0.137347 0.237892i
\(366\) −11.7667 20.3805i −0.615056 1.06531i
\(367\) 1.03235 + 1.78809i 0.0538885 + 0.0933375i 0.891711 0.452605i \(-0.149505\pi\)
−0.837823 + 0.545942i \(0.816172\pi\)
\(368\) −6.48913 11.2395i −0.338269 0.585899i
\(369\) 4.25612 + 7.37182i 0.221565 + 0.383761i
\(370\) 8.63246 + 14.9519i 0.448780 + 0.777310i
\(371\) −6.02218 10.4307i −0.312656 0.541536i
\(372\) −1.40322 + 2.43045i −0.0727538 + 0.126013i
\(373\) −0.0539160 0.0933852i −0.00279166 0.00483530i 0.864626 0.502416i \(-0.167555\pi\)
−0.867418 + 0.497580i \(0.834222\pi\)
\(374\) −16.3042 + 28.2397i −0.843071 + 1.46024i
\(375\) 10.8348 0.559507
\(376\) 2.02640 + 3.50983i 0.104504 + 0.181006i
\(377\) −29.1629 −1.50197
\(378\) 9.61104 0.494338
\(379\) 1.97499 3.42078i 0.101448 0.175714i −0.810833 0.585277i \(-0.800986\pi\)
0.912282 + 0.409564i \(0.134319\pi\)
\(380\) −3.05863 −0.156905
\(381\) 0.232407 + 0.402541i 0.0119066 + 0.0206228i
\(382\) 3.08084 + 5.33617i 0.157629 + 0.273022i
\(383\) 2.53694 4.39411i 0.129632 0.224529i −0.793902 0.608045i \(-0.791954\pi\)
0.923534 + 0.383517i \(0.125287\pi\)
\(384\) 3.05797 5.29655i 0.156051 0.270289i
\(385\) 12.4887 21.6311i 0.636486 1.10243i
\(386\) 19.8890 34.4487i 1.01232 1.75339i
\(387\) 8.89927 0.452375
\(388\) 8.94854 0.454293
\(389\) 3.47440 6.01784i 0.176159 0.305117i −0.764403 0.644739i \(-0.776966\pi\)
0.940562 + 0.339623i \(0.110299\pi\)
\(390\) 6.86557 + 11.8915i 0.347652 + 0.602151i
\(391\) 6.37006 + 11.0333i 0.322148 + 0.557976i
\(392\) 7.32178 12.6817i 0.369806 0.640523i
\(393\) −5.79113 −0.292124
\(394\) −2.06012 −0.103788
\(395\) −1.15010 1.99204i −0.0578679 0.100230i
\(396\) −2.99084 + 5.18029i −0.150295 + 0.260319i
\(397\) −22.0237 −1.10534 −0.552668 0.833402i \(-0.686390\pi\)
−0.552668 + 0.833402i \(0.686390\pi\)
\(398\) 7.00794 + 12.1381i 0.351276 + 0.608429i
\(399\) −7.48247 −0.374592
\(400\) −7.66421 + 13.2748i −0.383210 + 0.663740i
\(401\) 4.46178 0.222810 0.111405 0.993775i \(-0.464465\pi\)
0.111405 + 0.993775i \(0.464465\pi\)
\(402\) 4.83760 14.7298i 0.241277 0.734657i
\(403\) −9.80869 −0.488606
\(404\) 3.89407 6.74472i 0.193737 0.335563i
\(405\) 1.30648 0.0649197
\(406\) −25.2564 43.7454i −1.25345 2.17105i
\(407\) −26.2866 −1.30298
\(408\) −1.78453 + 3.09090i −0.0883474 + 0.153022i
\(409\) 0.523372 + 0.906507i 0.0258791 + 0.0448239i 0.878675 0.477421i \(-0.158428\pi\)
−0.852796 + 0.522244i \(0.825095\pi\)
\(410\) −21.0645 −1.04030
\(411\) −10.9296 −0.539115
\(412\) −2.90850 + 5.03767i −0.143291 + 0.248188i
\(413\) 27.4890 + 47.6123i 1.35264 + 2.34285i
\(414\) 2.64057 + 4.57359i 0.129777 + 0.224780i
\(415\) 1.41631 2.45312i 0.0695240 0.120419i
\(416\) −40.2527 −1.97355
\(417\) 1.23335 0.0603975
\(418\) 5.26173 9.11358i 0.257360 0.445760i
\(419\) 7.75058 13.4244i 0.378641 0.655825i −0.612224 0.790684i \(-0.709725\pi\)
0.990865 + 0.134859i \(0.0430583\pi\)
\(420\) −5.26244 + 9.11481i −0.256781 + 0.444757i
\(421\) 9.60643 16.6388i 0.468189 0.810927i −0.531150 0.847278i \(-0.678240\pi\)
0.999339 + 0.0363508i \(0.0115734\pi\)
\(422\) 6.66214 + 11.5392i 0.324308 + 0.561718i
\(423\) −2.59431 4.49347i −0.126140 0.218480i
\(424\) 1.85405 0.0900405
\(425\) 7.52357 13.0312i 0.364947 0.632107i
\(426\) −18.8902 −0.915231
\(427\) 63.0448 3.05095
\(428\) 9.44051 + 16.3514i 0.456324 + 0.790377i
\(429\) −20.9063 −1.00937
\(430\) −11.0111 + 19.0718i −0.531004 + 0.919725i
\(431\) 17.0369 + 29.5088i 0.820638 + 1.42139i 0.905208 + 0.424969i \(0.139715\pi\)
−0.0845698 + 0.996418i \(0.526952\pi\)
\(432\) −2.32735 + 4.03109i −0.111975 + 0.193946i
\(433\) 5.43994 + 9.42226i 0.261427 + 0.452805i 0.966621 0.256209i \(-0.0824736\pi\)
−0.705194 + 0.709014i \(0.749140\pi\)
\(434\) −8.49477 14.7134i −0.407762 0.706264i
\(435\) −3.43325 5.94656i −0.164612 0.285116i
\(436\) 2.25878 + 3.91232i 0.108176 + 0.187366i
\(437\) −2.05576 3.56068i −0.0983402 0.170330i
\(438\) −3.80421 6.58908i −0.181772 0.314838i
\(439\) −2.66780 + 4.62076i −0.127327 + 0.220537i −0.922640 0.385662i \(-0.873973\pi\)
0.795313 + 0.606199i \(0.207306\pi\)
\(440\) 1.92245 + 3.32979i 0.0916494 + 0.158741i
\(441\) −9.37373 + 16.2358i −0.446368 + 0.773132i
\(442\) 48.0233 2.28424
\(443\) 14.4937 + 25.1038i 0.688615 + 1.19272i 0.972286 + 0.233794i \(0.0751142\pi\)
−0.283671 + 0.958922i \(0.591552\pi\)
\(444\) 11.0765 0.525668
\(445\) 9.47126 0.448981
\(446\) 13.6313 23.6101i 0.645460 1.11797i
\(447\) 9.27620 0.438749
\(448\) −11.2417 19.4712i −0.531122 0.919930i
\(449\) −18.5754 32.1735i −0.876626 1.51836i −0.855021 0.518594i \(-0.826456\pi\)
−0.0216050 0.999767i \(-0.506878\pi\)
\(450\) 3.11873 5.40180i 0.147018 0.254643i
\(451\) 16.0358 27.7749i 0.755098 1.30787i
\(452\) 12.2845 21.2773i 0.577813 1.00080i
\(453\) 1.05893 1.83413i 0.0497530 0.0861748i
\(454\) −47.6594 −2.23677
\(455\) −36.7850 −1.72451
\(456\) 0.575907 0.997500i 0.0269693 0.0467122i
\(457\) 11.0230 + 19.0923i 0.515633 + 0.893102i 0.999835 + 0.0181464i \(0.00577648\pi\)
−0.484202 + 0.874956i \(0.660890\pi\)
\(458\) 15.8731 + 27.4930i 0.741700 + 1.28466i
\(459\) 2.28465 3.95713i 0.106638 0.184703i
\(460\) −5.78327 −0.269647
\(461\) 34.2504 1.59520 0.797601 0.603186i \(-0.206102\pi\)
0.797601 + 0.603186i \(0.206102\pi\)
\(462\) −18.1058 31.3602i −0.842358 1.45901i
\(463\) −6.00012 + 10.3925i −0.278849 + 0.482981i −0.971099 0.238677i \(-0.923286\pi\)
0.692250 + 0.721658i \(0.256620\pi\)
\(464\) 24.4638 1.13570
\(465\) −1.15474 2.00007i −0.0535499 0.0927512i
\(466\) 50.0312 2.31765
\(467\) 4.53905 7.86186i 0.210042 0.363803i −0.741685 0.670748i \(-0.765973\pi\)
0.951727 + 0.306944i \(0.0993066\pi\)
\(468\) 8.80938 0.407214
\(469\) 27.6939 + 30.9536i 1.27879 + 1.42931i
\(470\) 12.8398 0.592256
\(471\) −3.57954 + 6.19995i −0.164937 + 0.285679i
\(472\) −8.46302 −0.389542
\(473\) −16.7649 29.0377i −0.770853 1.33516i
\(474\) −3.33477 −0.153171
\(475\) −2.42802 + 4.20546i −0.111405 + 0.192960i
\(476\) 18.4048 + 31.8781i 0.843585 + 1.46113i
\(477\) −2.37365 −0.108682
\(478\) 0.839902 0.0384162
\(479\) 5.28318 9.15074i 0.241395 0.418108i −0.719717 0.694268i \(-0.755728\pi\)
0.961112 + 0.276159i \(0.0890618\pi\)
\(480\) −4.73881 8.20786i −0.216296 0.374636i
\(481\) 19.3565 + 33.5265i 0.882581 + 1.52867i
\(482\) 20.2159 35.0150i 0.920811 1.59489i
\(483\) −14.1479 −0.643751
\(484\) 5.07347 0.230612
\(485\) −3.68197 + 6.37736i −0.167190 + 0.289581i
\(486\) 0.947050 1.64034i 0.0429591 0.0744073i
\(487\) −10.8033 + 18.7119i −0.489545 + 0.847916i −0.999928 0.0120311i \(-0.996170\pi\)
0.510383 + 0.859947i \(0.329504\pi\)
\(488\) −4.85240 + 8.40460i −0.219658 + 0.380458i
\(489\) 4.15131 + 7.19028i 0.187729 + 0.325156i
\(490\) −23.1963 40.1772i −1.04790 1.81502i
\(491\) −16.9759 −0.766113 −0.383056 0.923725i \(-0.625128\pi\)
−0.383056 + 0.923725i \(0.625128\pi\)
\(492\) −6.75709 + 11.7036i −0.304633 + 0.527640i
\(493\) −24.0149 −1.08158
\(494\) −15.4982 −0.697296
\(495\) −2.46123 4.26297i −0.110624 0.191606i
\(496\) 8.22818 0.369456
\(497\) 25.3029 43.8259i 1.13499 1.96586i
\(498\) −2.05333 3.55646i −0.0920117 0.159369i
\(499\) −0.759399 + 1.31532i −0.0339954 + 0.0588817i −0.882523 0.470270i \(-0.844156\pi\)
0.848527 + 0.529152i \(0.177490\pi\)
\(500\) 8.60075 + 14.8969i 0.384637 + 0.666212i
\(501\) −3.39055 5.87260i −0.151479 0.262368i
\(502\) 18.4181 + 31.9011i 0.822039 + 1.42381i
\(503\) −12.9835 22.4881i −0.578905 1.00269i −0.995605 0.0936493i \(-0.970147\pi\)
0.416700 0.909044i \(-0.363187\pi\)
\(504\) −1.98172 3.43243i −0.0882727 0.152893i
\(505\) 3.20451 + 5.55038i 0.142599 + 0.246989i
\(506\) 9.94889 17.2320i 0.442282 0.766055i
\(507\) 8.89463 + 15.4060i 0.395024 + 0.684202i
\(508\) −0.368974 + 0.639081i −0.0163706 + 0.0283546i
\(509\) 14.0774 0.623971 0.311986 0.950087i \(-0.399006\pi\)
0.311986 + 0.950087i \(0.399006\pi\)
\(510\) 5.65362 + 9.79235i 0.250346 + 0.433613i
\(511\) 20.3825 0.901671
\(512\) 26.4951 1.17093
\(513\) −0.737306 + 1.27705i −0.0325529 + 0.0563832i
\(514\) 9.88048 0.435809
\(515\) −2.39347 4.14561i −0.105469 0.182677i
\(516\) 7.06432 + 12.2358i 0.310989 + 0.538649i
\(517\) −9.77461 + 16.9301i −0.429887 + 0.744586i
\(518\) −33.5272 + 58.0709i −1.47310 + 2.55149i
\(519\) −6.56276 + 11.3670i −0.288073 + 0.498957i
\(520\) 2.83125 4.90387i 0.124159 0.215049i
\(521\) 41.5898 1.82208 0.911042 0.412314i \(-0.135279\pi\)
0.911042 + 0.412314i \(0.135279\pi\)
\(522\) −9.95484 −0.435711
\(523\) 2.16181 3.74437i 0.0945294 0.163730i −0.814883 0.579626i \(-0.803199\pi\)
0.909412 + 0.415896i \(0.136532\pi\)
\(524\) −4.59705 7.96232i −0.200823 0.347836i
\(525\) 8.35492 + 14.4711i 0.364638 + 0.631572i
\(526\) −12.8947 + 22.3343i −0.562236 + 0.973822i
\(527\) −8.07720 −0.351848
\(528\) 17.5376 0.763226
\(529\) 7.61297 + 13.1860i 0.330999 + 0.573306i
\(530\) 2.93693 5.08691i 0.127572 0.220961i
\(531\) 10.8348 0.470190
\(532\) −5.93965 10.2878i −0.257516 0.446031i
\(533\) −47.2328 −2.04588
\(534\) 6.86557 11.8915i 0.297102 0.514596i
\(535\) −15.5376 −0.671749
\(536\) −6.25801 + 1.30950i −0.270305 + 0.0565616i
\(537\) 7.19424 0.310454
\(538\) 18.0273 31.2241i 0.777211 1.34617i
\(539\) 70.6350 3.04247
\(540\) 1.03710 + 1.79631i 0.0446296 + 0.0773007i
\(541\) −31.6753 −1.36183 −0.680914 0.732363i \(-0.738417\pi\)
−0.680914 + 0.732363i \(0.738417\pi\)
\(542\) −9.91367 + 17.1710i −0.425829 + 0.737557i
\(543\) −12.8219 22.2081i −0.550239 0.953042i
\(544\) −33.1470 −1.42117
\(545\) −3.71759 −0.159244
\(546\) −26.6649 + 46.1849i −1.14115 + 1.97653i
\(547\) 21.0146 + 36.3983i 0.898518 + 1.55628i 0.829389 + 0.558671i \(0.188689\pi\)
0.0691286 + 0.997608i \(0.477978\pi\)
\(548\) −8.67597 15.0272i −0.370619 0.641931i
\(549\) 6.21229 10.7600i 0.265134 0.459226i
\(550\) −23.5010 −1.00208
\(551\) 7.75013 0.330167
\(552\) 1.08893 1.88608i 0.0463478 0.0802767i
\(553\) 4.46683 7.73678i 0.189949 0.329001i
\(554\) −7.04698 + 12.2057i −0.299397 + 0.518571i
\(555\) −4.55755 + 7.89391i −0.193457 + 0.335078i
\(556\) 0.979044 + 1.69575i 0.0415207 + 0.0719160i
\(557\) −13.9900 24.2315i −0.592777 1.02672i −0.993856 0.110677i \(-0.964698\pi\)
0.401079 0.916043i \(-0.368635\pi\)
\(558\) −3.34822 −0.141742
\(559\) −24.6902 + 42.7646i −1.04428 + 1.80875i
\(560\) 30.8577 1.30398
\(561\) −17.2158 −0.726851
\(562\) −18.4141 31.8942i −0.776753 1.34538i
\(563\) −10.1948 −0.429661 −0.214830 0.976651i \(-0.568920\pi\)
−0.214830 + 0.976651i \(0.568920\pi\)
\(564\) 4.11877 7.13391i 0.173431 0.300392i
\(565\) 10.1092 + 17.5096i 0.425295 + 0.736633i
\(566\) 26.5884 46.0524i 1.11759 1.93573i
\(567\) 2.53710 + 4.39438i 0.106548 + 0.184547i
\(568\) 3.89500 + 6.74633i 0.163430 + 0.283070i
\(569\) −6.73089 11.6582i −0.282173 0.488739i 0.689746 0.724051i \(-0.257722\pi\)
−0.971920 + 0.235312i \(0.924389\pi\)
\(570\) −1.82455 3.16021i −0.0764218 0.132366i
\(571\) −0.0508949 0.0881525i −0.00212988 0.00368907i 0.864958 0.501843i \(-0.167345\pi\)
−0.867088 + 0.498154i \(0.834011\pi\)
\(572\) −16.5956 28.7444i −0.693897 1.20186i
\(573\) −1.62654 + 2.81726i −0.0679499 + 0.117693i
\(574\) −40.9057 70.8508i −1.70737 2.95726i
\(575\) −4.59091 + 7.95169i −0.191454 + 0.331608i
\(576\) −4.43094 −0.184623
\(577\) −11.6556 20.1881i −0.485228 0.840440i 0.514628 0.857414i \(-0.327930\pi\)
−0.999856 + 0.0169740i \(0.994597\pi\)
\(578\) 7.34622 0.305562
\(579\) 21.0010 0.872771
\(580\) 5.45068 9.44086i 0.226327 0.392010i
\(581\) 11.0015 0.456419
\(582\) 5.33801 + 9.24571i 0.221268 + 0.383247i
\(583\) 4.47161 + 7.74505i 0.185195 + 0.320767i
\(584\) −1.56879 + 2.71723i −0.0649171 + 0.112440i
\(585\) −3.62471 + 6.27819i −0.149863 + 0.259571i
\(586\) 15.0837 26.1257i 0.623102 1.07924i
\(587\) −20.8906 + 36.1835i −0.862246 + 1.49345i 0.00750931 + 0.999972i \(0.497610\pi\)
−0.869756 + 0.493483i \(0.835724\pi\)
\(588\) −29.7638 −1.22744
\(589\) 2.60669 0.107407
\(590\) −13.4060 + 23.2198i −0.551915 + 0.955945i
\(591\) −0.543826 0.941935i −0.0223700 0.0387460i
\(592\) −16.2375 28.1242i −0.667358 1.15590i
\(593\) −21.8783 + 37.8943i −0.898433 + 1.55613i −0.0689346 + 0.997621i \(0.521960\pi\)
−0.829498 + 0.558510i \(0.811373\pi\)
\(594\) −7.13642 −0.292811
\(595\) −30.2915 −1.24183
\(596\) 7.36352 + 12.7540i 0.301622 + 0.522424i
\(597\) −3.69988 + 6.40838i −0.151426 + 0.262278i
\(598\) −29.3040 −1.19833
\(599\) −18.0305 31.2298i −0.736708 1.27602i −0.953970 0.299902i \(-0.903046\pi\)
0.217262 0.976113i \(-0.430287\pi\)
\(600\) −2.57223 −0.105011
\(601\) −20.2419 + 35.0600i −0.825684 + 1.43013i 0.0757120 + 0.997130i \(0.475877\pi\)
−0.901396 + 0.432996i \(0.857456\pi\)
\(602\) −85.5312 −3.48599
\(603\) 8.01183 1.67649i 0.326267 0.0682718i
\(604\) 3.36236 0.136812
\(605\) −2.08753 + 3.61571i −0.0848703 + 0.147000i
\(606\) 9.29161 0.377446
\(607\) −7.43613 12.8798i −0.301823 0.522773i 0.674726 0.738069i \(-0.264262\pi\)
−0.976549 + 0.215295i \(0.930929\pi\)
\(608\) 10.6973 0.433831
\(609\) 13.3342 23.0956i 0.540331 0.935880i
\(610\) 15.3730 + 26.6268i 0.622435 + 1.07809i
\(611\) 28.7906 1.16474
\(612\) 7.25429 0.293237
\(613\) 16.4986 28.5764i 0.666372 1.15419i −0.312539 0.949905i \(-0.601180\pi\)
0.978911 0.204286i \(-0.0654871\pi\)
\(614\) 12.5140 + 21.6748i 0.505022 + 0.874724i
\(615\) −5.56055 9.63116i −0.224223 0.388366i
\(616\) −7.46654 + 12.9324i −0.300835 + 0.521062i
\(617\) −3.38641 −0.136332 −0.0681659 0.997674i \(-0.521715\pi\)
−0.0681659 + 0.997674i \(0.521715\pi\)
\(618\) −6.93995 −0.279166
\(619\) −7.66331 + 13.2732i −0.308015 + 0.533497i −0.977928 0.208942i \(-0.932998\pi\)
0.669913 + 0.742439i \(0.266331\pi\)
\(620\) 1.83329 3.17535i 0.0736267 0.127525i
\(621\) −1.39410 + 2.41465i −0.0559433 + 0.0968967i
\(622\) −7.53893 + 13.0578i −0.302283 + 0.523570i
\(623\) 18.3925 + 31.8568i 0.736880 + 1.27631i
\(624\) −12.9140 22.3678i −0.516975 0.895427i
\(625\) 2.31000 0.0924001
\(626\) −14.5436 + 25.1903i −0.581280 + 1.00681i
\(627\) 5.55591 0.221882
\(628\) −11.3659 −0.453548
\(629\) 15.9396 + 27.6082i 0.635553 + 1.10081i
\(630\) −12.5567 −0.500269
\(631\) −10.6274 + 18.4072i −0.423069 + 0.732777i −0.996238 0.0866599i \(-0.972381\pi\)
0.573169 + 0.819437i \(0.305714\pi\)
\(632\) 0.687601 + 1.19096i 0.0273513 + 0.0473739i
\(633\) −3.51731 + 6.09217i −0.139801 + 0.242142i
\(634\) −12.1746 21.0870i −0.483515 0.837473i
\(635\) −0.303636 0.525914i −0.0120494 0.0208703i
\(636\) −1.88422 3.26357i −0.0747142 0.129409i
\(637\) −52.0130 90.0892i −2.06083 3.56946i
\(638\) 18.7535 + 32.4820i 0.742457 + 1.28597i
\(639\) −4.98658 8.63701i −0.197266 0.341675i
\(640\) −3.99519 + 6.91986i −0.157924 + 0.273532i
\(641\) 15.3831 + 26.6443i 0.607595 + 1.05239i 0.991636 + 0.129070i \(0.0411991\pi\)
−0.384040 + 0.923316i \(0.625468\pi\)
\(642\) −11.2630 + 19.5080i −0.444514 + 0.769921i
\(643\) 26.8566 1.05912 0.529560 0.848272i \(-0.322357\pi\)
0.529560 + 0.848272i \(0.322357\pi\)
\(644\) −11.2307 19.4521i −0.442552 0.766522i
\(645\) −11.6268 −0.457803
\(646\) −12.7623 −0.502127
\(647\) 1.93564 3.35262i 0.0760978 0.131805i −0.825465 0.564453i \(-0.809087\pi\)
0.901563 + 0.432648i \(0.142421\pi\)
\(648\) −0.781096 −0.0306843
\(649\) −20.4112 35.3532i −0.801210 1.38774i
\(650\) 17.3052 + 29.9735i 0.678767 + 1.17566i
\(651\) 4.48486 7.76800i 0.175775 0.304452i
\(652\) −6.59069 + 11.4154i −0.258111 + 0.447062i
\(653\) 12.6197 21.8580i 0.493847 0.855369i −0.506128 0.862459i \(-0.668923\pi\)
0.999975 + 0.00708998i \(0.00225683\pi\)
\(654\) −2.69483 + 4.66758i −0.105376 + 0.182517i
\(655\) 7.56602 0.295629
\(656\) 39.6220 1.54698
\(657\) 2.00845 3.47874i 0.0783571 0.135719i
\(658\) 24.9340 + 43.1869i 0.972028 + 1.68360i
\(659\) −16.5882 28.7317i −0.646186 1.11923i −0.984026 0.178024i \(-0.943030\pi\)
0.337840 0.941204i \(-0.390304\pi\)
\(660\) 3.90748 6.76796i 0.152099 0.263443i
\(661\) 11.6142 0.451739 0.225869 0.974158i \(-0.427478\pi\)
0.225869 + 0.974158i \(0.427478\pi\)
\(662\) 32.7631 1.27337
\(663\) 12.6771 + 21.9573i 0.492337 + 0.852752i
\(664\) −0.846758 + 1.46663i −0.0328606 + 0.0569162i
\(665\) 9.77573 0.379086
\(666\) 6.60740 + 11.4443i 0.256031 + 0.443459i
\(667\) 14.6540 0.567404
\(668\) 5.38289 9.32344i 0.208270 0.360735i
\(669\) 14.3934 0.556481
\(670\) −6.32024 + 19.2443i −0.244172 + 0.743472i
\(671\) −46.8123 −1.80717
\(672\) 18.4048 31.8781i 0.709982 1.22973i
\(673\) −47.1987 −1.81938 −0.909688 0.415292i \(-0.863679\pi\)
−0.909688 + 0.415292i \(0.863679\pi\)
\(674\) 19.9608 + 34.5731i 0.768861 + 1.33171i
\(675\) 3.29310 0.126751
\(676\) −14.1213 + 24.4587i −0.543126 + 0.940721i
\(677\) −9.48232 16.4239i −0.364435 0.631220i 0.624250 0.781224i \(-0.285405\pi\)
−0.988685 + 0.150004i \(0.952071\pi\)
\(678\) 29.3119 1.12572
\(679\) −28.6005 −1.09759
\(680\) 2.33146 4.03821i 0.0894074 0.154858i
\(681\) −12.5810 21.7909i −0.482105 0.835031i
\(682\) 6.30757 + 10.9250i 0.241529 + 0.418341i
\(683\) −8.95805 + 15.5158i −0.342770 + 0.593696i −0.984946 0.172862i \(-0.944699\pi\)
0.642176 + 0.766557i \(0.278032\pi\)
\(684\) −2.34112 −0.0895149
\(685\) 14.2793 0.545584
\(686\) 56.4526 97.7788i 2.15537 3.73321i
\(687\) −8.38027 + 14.5150i −0.319727 + 0.553784i
\(688\) 20.7118 35.8738i 0.789628 1.36768i
\(689\) 6.58546 11.4063i 0.250886 0.434547i
\(690\) −3.44986 5.97533i −0.131334 0.227477i
\(691\) 16.9922 + 29.4314i 0.646414 + 1.11962i 0.983973 + 0.178318i \(0.0570655\pi\)
−0.337559 + 0.941304i \(0.609601\pi\)
\(692\) −20.8383 −0.792153
\(693\) 9.55905 16.5568i 0.363118 0.628939i
\(694\) 18.6091 0.706392
\(695\) −1.61135 −0.0611221
\(696\) 2.05261 + 3.55522i 0.0778038 + 0.134760i
\(697\) −38.8950 −1.47325
\(698\) 20.6184 35.7121i 0.780417 1.35172i
\(699\) 13.2071 + 22.8754i 0.499539 + 0.865226i
\(700\) −13.2644 + 22.9746i −0.501347 + 0.868359i
\(701\) −18.2611 31.6291i −0.689712 1.19462i −0.971931 0.235266i \(-0.924404\pi\)
0.282220 0.959350i \(-0.408929\pi\)
\(702\) 5.25500 + 9.10193i 0.198337 + 0.343530i
\(703\) −5.14405 8.90976i −0.194012 0.336038i
\(704\) 8.34725 + 14.4579i 0.314599 + 0.544901i
\(705\) 3.38942 + 5.87065i 0.127653 + 0.221102i
\(706\) 4.15823 + 7.20226i 0.156497 + 0.271061i
\(707\) −12.4459 + 21.5569i −0.468075 + 0.810730i
\(708\) 8.60075 + 14.8969i 0.323236 + 0.559861i
\(709\) 2.58582 4.47877i 0.0971126 0.168204i −0.813376 0.581739i \(-0.802373\pi\)
0.910488 + 0.413535i \(0.135706\pi\)
\(710\) 24.6797 0.926212
\(711\) −0.880303 1.52473i −0.0330140 0.0571818i
\(712\) −5.66250 −0.212211
\(713\) 4.92873 0.184583
\(714\) −21.9578 + 38.0321i −0.821751 + 1.42332i
\(715\) 27.3138 1.02148
\(716\) 5.71085 + 9.89148i 0.213424 + 0.369662i
\(717\) 0.221715 + 0.384022i 0.00828011 + 0.0143416i
\(718\) 25.0824 43.4441i 0.936069 1.62132i
\(719\) 1.11728 1.93519i 0.0416675 0.0721703i −0.844440 0.535651i \(-0.820066\pi\)
0.886107 + 0.463481i \(0.153400\pi\)
\(720\) 3.04065 5.26656i 0.113318 0.196273i
\(721\) 9.29588 16.1009i 0.346197 0.599630i
\(722\) −31.8692 −1.18605
\(723\) 21.3462 0.793874
\(724\) 20.3562 35.2580i 0.756532 1.31035i
\(725\) −8.65378 14.9888i −0.321393 0.556670i
\(726\) 3.02644 + 5.24195i 0.112322 + 0.194547i
\(727\) −1.05448 + 1.82642i −0.0391086 + 0.0677380i −0.884917 0.465748i \(-0.845785\pi\)
0.845809 + 0.533487i \(0.179118\pi\)
\(728\) 21.9923 0.815090
\(729\) 1.00000 0.0370370
\(730\) 4.97014 + 8.60853i 0.183953 + 0.318616i
\(731\) −20.3317 + 35.2156i −0.751995 + 1.30249i
\(732\) 19.7255 0.729075
\(733\) 8.03807 + 13.9223i 0.296893 + 0.514233i 0.975423 0.220339i \(-0.0707163\pi\)
−0.678531 + 0.734572i \(0.737383\pi\)
\(734\) −3.91077 −0.144349
\(735\) 12.2466 21.2118i 0.451724 0.782408i
\(736\) 20.2264 0.745556
\(737\) −20.5634 22.9838i −0.757462 0.846619i
\(738\) −16.1230 −0.593497
\(739\) −5.54518 + 9.60454i −0.203983 + 0.353309i −0.949808 0.312833i \(-0.898722\pi\)
0.745825 + 0.666142i \(0.232055\pi\)
\(740\) −14.4713 −0.531975
\(741\) −4.09117 7.08611i −0.150293 0.260315i
\(742\) 22.8132 0.837499
\(743\) 20.1297 34.8657i 0.738488 1.27910i −0.214688 0.976683i \(-0.568873\pi\)
0.953176 0.302416i \(-0.0977933\pi\)
\(744\) 0.690376 + 1.19577i 0.0253104 + 0.0438389i
\(745\) −12.1192 −0.444013
\(746\) 0.204244 0.00747792
\(747\) 1.08406 1.87765i 0.0396638 0.0686998i
\(748\) −13.6660 23.6703i −0.499680 0.865471i
\(749\) −30.1729 52.2610i −1.10249 1.90958i
\(750\) −10.2611 + 17.7727i −0.374682 + 0.648969i
\(751\) 45.1172 1.64635 0.823174 0.567789i \(-0.192201\pi\)
0.823174 + 0.567789i \(0.192201\pi\)
\(752\) −24.1515 −0.880714
\(753\) −9.72392 + 16.8423i −0.354359 + 0.613768i
\(754\) 27.6187 47.8371i 1.00582 1.74212i
\(755\) −1.38348 + 2.39626i −0.0503500 + 0.0872087i
\(756\) −4.02794 + 6.97659i −0.146495 + 0.253736i
\(757\) −10.0985 17.4911i −0.367036 0.635725i 0.622065 0.782966i \(-0.286294\pi\)
−0.989101 + 0.147241i \(0.952961\pi\)
\(758\) 3.74083 + 6.47930i 0.135873 + 0.235339i
\(759\) 10.5051 0.381312
\(760\) −0.752413 + 1.30322i −0.0272929 + 0.0472727i
\(761\) 53.1019 1.92494 0.962471 0.271386i \(-0.0874820\pi\)
0.962471 + 0.271386i \(0.0874820\pi\)
\(762\) −0.880406 −0.0318937
\(763\) −7.21930 12.5042i −0.261356 0.452682i
\(764\) −5.16466 −0.186851
\(765\) −2.98486 + 5.16992i −0.107918 + 0.186919i
\(766\) 4.80522 + 8.32289i 0.173620 + 0.300718i
\(767\) −30.0601 + 52.0656i −1.08541 + 1.87998i
\(768\) 10.2230 + 17.7068i 0.368892 + 0.638940i
\(769\) 20.8702 + 36.1483i 0.752600 + 1.30354i 0.946559 + 0.322531i \(0.104534\pi\)
−0.193959 + 0.981010i \(0.562133\pi\)
\(770\) 23.6549 + 40.9716i 0.852465 + 1.47651i
\(771\) 2.60822 + 4.51758i 0.0939329 + 0.162697i
\(772\) 16.6708 + 28.8746i 0.599994 + 1.03922i
\(773\) 23.8426 + 41.2965i 0.857557 + 1.48533i 0.874252 + 0.485472i \(0.161352\pi\)
−0.0166951 + 0.999861i \(0.505314\pi\)
\(774\) −8.42806 + 14.5978i −0.302940 + 0.524708i
\(775\) −2.91062 5.04135i −0.104553 0.181091i
\(776\) 2.20131 3.81278i 0.0790224 0.136871i
\(777\) −35.4017 −1.27003
\(778\) 6.58087 + 11.3984i 0.235935 + 0.408652i
\(779\) 12.5523 0.449731
\(780\) −11.5093 −0.412099
\(781\) −18.7880 + 32.5418i −0.672287 + 1.16444i
\(782\) −24.1311 −0.862925
\(783\) −2.62785 4.55158i −0.0939118 0.162660i
\(784\) 43.6320 + 75.5728i 1.55828 + 2.69903i
\(785\) 4.67661 8.10013i 0.166916 0.289106i
\(786\) 5.48449 9.49942i 0.195625 0.338833i
\(787\) 17.8793 30.9679i 0.637328 1.10388i −0.348689 0.937239i \(-0.613373\pi\)
0.986017 0.166646i \(-0.0532937\pi\)
\(788\) 0.863388 1.49543i 0.0307569 0.0532725i
\(789\) −13.6157 −0.484730
\(790\) 4.35682 0.155009
\(791\) −39.2625 + 68.0047i −1.39601 + 2.41797i
\(792\) 1.47147 + 2.54866i 0.0522865 + 0.0905628i
\(793\) 34.4708 + 59.7052i 1.22409 + 2.12019i
\(794\) 20.8575 36.1263i 0.740205 1.28207i
\(795\) 3.10113 0.109986
\(796\) −11.7480 −0.416396
\(797\) −1.46925 2.54481i −0.0520434 0.0901417i 0.838830 0.544393i \(-0.183240\pi\)
−0.890873 + 0.454252i \(0.849907\pi\)
\(798\) 7.08627 12.2738i 0.250851 0.434487i
\(799\) 23.7083 0.838741
\(800\) −11.9446 20.6886i −0.422304 0.731451i
\(801\) 7.24943 0.256146
\(802\) −4.22553 + 7.31882i −0.149208 + 0.258437i
\(803\) −15.1345 −0.534086
\(804\) 8.66488 + 9.68478i 0.305587 + 0.341556i
\(805\) 18.4840 0.651474
\(806\) 9.28932 16.0896i 0.327202 0.566731i
\(807\) 19.0352 0.670070
\(808\) −1.91585 3.31836i −0.0673995 0.116739i
\(809\) 47.7915 1.68026 0.840130 0.542384i \(-0.182478\pi\)
0.840130 + 0.542384i \(0.182478\pi\)
\(810\) −1.23731 + 2.14308i −0.0434745 + 0.0753000i
\(811\) −16.1468 27.9670i −0.566989 0.982054i −0.996862 0.0791643i \(-0.974775\pi\)
0.429872 0.902890i \(-0.358559\pi\)
\(812\) 42.3393 1.48582
\(813\) −10.4679 −0.367127
\(814\) 24.8948 43.1190i 0.872561 1.51132i
\(815\) −5.42362 9.39399i −0.189981 0.329057i
\(816\) −10.6344 18.4193i −0.372277 0.644803i
\(817\) 6.56149 11.3648i 0.229557 0.397605i
\(818\) −1.98264 −0.0693213
\(819\) −28.1557 −0.983841
\(820\) 8.82803 15.2906i 0.308288 0.533971i
\(821\) −2.73257 + 4.73296i −0.0953675 + 0.165181i −0.909762 0.415130i \(-0.863736\pi\)
0.814394 + 0.580312i \(0.197069\pi\)
\(822\) 10.3508 17.9282i 0.361027 0.625317i
\(823\) −11.0975 + 19.2214i −0.386833 + 0.670015i −0.992022 0.126067i \(-0.959764\pi\)
0.605188 + 0.796082i \(0.293098\pi\)
\(824\) 1.43096 + 2.47850i 0.0498499 + 0.0863425i
\(825\) −6.20372 10.7452i −0.215986 0.374099i
\(826\) −104.134 −3.62327
\(827\) 14.5565 25.2127i 0.506181 0.876731i −0.493794 0.869579i \(-0.664390\pi\)
0.999974 0.00715162i \(-0.00227645\pi\)
\(828\) −4.42659 −0.153835
\(829\) 28.8657 1.00255 0.501274 0.865289i \(-0.332865\pi\)
0.501274 + 0.865289i \(0.332865\pi\)
\(830\) 2.68264 + 4.64646i 0.0931157 + 0.161281i
\(831\) −7.44098 −0.258125
\(832\) 12.2932 21.2925i 0.426191 0.738184i
\(833\) −42.8314 74.1861i −1.48402 2.57040i
\(834\) −1.16805 + 2.02311i −0.0404461 + 0.0700547i
\(835\) 4.42970 + 7.67246i 0.153296 + 0.265516i
\(836\) 4.41033 + 7.63891i 0.152534 + 0.264197i
\(837\) −0.883856 1.53088i −0.0305505 0.0529151i
\(838\) 14.6804 + 25.4272i 0.507125 + 0.878367i
\(839\) −17.3078 29.9780i −0.597532 1.03496i −0.993184 0.116555i \(-0.962815\pi\)
0.395652 0.918400i \(-0.370519\pi\)
\(840\) 2.58908 + 4.48442i 0.0893318 + 0.154727i
\(841\) 0.688767 1.19298i 0.0237506 0.0411372i
\(842\) 18.1955 + 31.5156i 0.627060 + 1.08610i
\(843\) 9.72183 16.8387i 0.334838 0.579956i
\(844\) −11.1683 −0.384428
\(845\) −11.6207 20.1276i −0.399764 0.692412i
\(846\) 9.82776 0.337885
\(847\) −16.2153 −0.557166
\(848\) −5.52432 + 9.56840i −0.189706 + 0.328580i
\(849\) 28.0749 0.963530
\(850\) 14.2504 + 24.6824i 0.488785 + 0.846600i
\(851\) −9.72639 16.8466i −0.333416 0.577494i
\(852\) 7.91677 13.7123i 0.271224 0.469774i
\(853\) 21.8097 37.7756i 0.746751 1.29341i −0.202622 0.979257i \(-0.564946\pi\)
0.949372 0.314153i \(-0.101721\pi\)
\(854\) −59.7066 + 103.415i −2.04312 + 3.53878i
\(855\) 0.963278 1.66845i 0.0329434 0.0570597i
\(856\) 9.28933 0.317503
\(857\) 14.3293 0.489480 0.244740 0.969589i \(-0.421297\pi\)
0.244740 + 0.969589i \(0.421297\pi\)
\(858\) 19.7993 34.2934i 0.675938 1.17076i
\(859\) −1.29747 2.24728i −0.0442690 0.0766762i 0.843042 0.537848i \(-0.180763\pi\)
−0.887311 + 0.461172i \(0.847429\pi\)
\(860\) −9.22942 15.9858i −0.314720 0.545112i
\(861\) 21.5964 37.4060i 0.736003 1.27479i
\(862\) −64.5392 −2.19821
\(863\) −8.33860 −0.283849 −0.141925 0.989877i \(-0.545329\pi\)
−0.141925 + 0.989877i \(0.545329\pi\)
\(864\) −3.62715 6.28240i −0.123398 0.213732i
\(865\) 8.57414 14.8508i 0.291530 0.504944i
\(866\) −20.6076 −0.700274
\(867\) 1.93924 + 3.35886i 0.0658599 + 0.114073i
\(868\) 14.2405 0.483353
\(869\) −3.31673 + 5.74474i −0.112512 + 0.194877i
\(870\) 13.0058 0.440939
\(871\) −14.1718 + 43.1514i −0.480195 + 1.46213i
\(872\) 2.22260 0.0752669
\(873\) −2.81823 + 4.88132i −0.0953826 + 0.165208i
\(874\) 7.78762 0.263420
\(875\) −27.4890 47.6123i −0.929296 1.60959i
\(876\) 6.37730 0.215469
\(877\) 18.2965 31.6905i 0.617830 1.07011i −0.372051 0.928212i \(-0.621345\pi\)
0.989881 0.141900i \(-0.0453212\pi\)
\(878\) −5.05308 8.75219i −0.170533 0.295372i
\(879\) 15.9270 0.537205
\(880\) −22.9126 −0.772383
\(881\) 2.96911 5.14265i 0.100032 0.173260i −0.811666 0.584122i \(-0.801439\pi\)
0.911698 + 0.410862i \(0.134772\pi\)
\(882\) −17.7548 30.7522i −0.597835 1.03548i
\(883\) −18.1563 31.4477i −0.611009 1.05830i −0.991071 0.133337i \(-0.957431\pi\)
0.380062 0.924961i \(-0.375903\pi\)
\(884\) −20.1263 + 34.8598i −0.676922 + 1.17246i
\(885\) −14.1555 −0.475832
\(886\) −54.9049 −1.84457
\(887\) −2.14151 + 3.70921i −0.0719049 + 0.124543i −0.899736 0.436434i \(-0.856241\pi\)
0.827831 + 0.560977i \(0.189574\pi\)
\(888\) 2.72478 4.71946i 0.0914377 0.158375i
\(889\) 1.17928 2.04257i 0.0395518 0.0685057i
\(890\) −8.96976 + 15.5361i −0.300667 + 0.520771i
\(891\) −1.88386 3.26293i −0.0631115 0.109312i
\(892\) 11.4256 + 19.7897i 0.382558 + 0.662609i
\(893\) −7.65120 −0.256038
\(894\) −8.78502 + 15.2161i −0.293815 + 0.508903i
\(895\) −9.39916 −0.314179
\(896\) −31.0334 −1.03675
\(897\) −7.73559 13.3984i −0.258284 0.447361i
\(898\) 70.3672 2.34818
\(899\) −4.64529 + 8.04587i −0.154929 + 0.268345i
\(900\) 2.61409 + 4.52774i 0.0871363 + 0.150925i
\(901\) 5.42295 9.39282i 0.180665 0.312920i
\(902\) 30.3735 + 52.6084i 1.01133 + 1.75167i
\(903\) −22.5783 39.1068i −0.751360 1.30139i
\(904\) −6.04387 10.4683i −0.201016 0.348170i
\(905\) 16.7516 + 29.0146i 0.556841 + 0.964476i
\(906\) 2.00573 + 3.47402i 0.0666358 + 0.115417i
\(907\) −21.1344 36.6059i −0.701757 1.21548i −0.967849 0.251531i \(-0.919066\pi\)
0.266092 0.963948i \(-0.414267\pi\)
\(908\) 19.9738 34.5957i 0.662854 1.14810i
\(909\) 2.45278 + 4.24833i 0.0813535 + 0.140908i
\(910\) 34.8373 60.3399i 1.15484 2.00025i
\(911\) −22.1085 −0.732488 −0.366244 0.930519i \(-0.619356\pi\)
−0.366244 + 0.930519i \(0.619356\pi\)
\(912\) 3.43194 + 5.94430i 0.113643 + 0.196835i
\(913\) −8.16888 −0.270350
\(914\) −41.7572 −1.38121
\(915\) −8.11626 + 14.0578i −0.268315 + 0.464736i
\(916\) −26.6093 −0.879196
\(917\) 14.6927 + 25.4484i 0.485195 + 0.840382i
\(918\) 4.32735 + 7.49520i 0.142824 + 0.247378i
\(919\) 12.7249 22.0402i 0.419756 0.727038i −0.576159 0.817338i \(-0.695449\pi\)
0.995915 + 0.0902993i \(0.0287824\pi\)
\(920\) −1.42266 + 2.46413i −0.0469039 + 0.0812399i
\(921\) −6.60681 + 11.4433i −0.217702 + 0.377070i
\(922\) −32.4369 + 56.1823i −1.06825 + 1.85027i
\(923\) 55.3391 1.82151
\(924\) 30.3522 0.998515
\(925\) −11.4877 + 19.8972i −0.377713 + 0.654217i
\(926\) −11.3648 19.6845i −0.373471 0.646871i
\(927\) −1.83199 3.17310i −0.0601705 0.104218i
\(928\) −19.0632 + 33.0185i −0.625781 + 1.08388i
\(929\) −46.8292 −1.53642 −0.768208 0.640200i \(-0.778851\pi\)
−0.768208 + 0.640200i \(0.778851\pi\)
\(930\) 4.37440 0.143442
\(931\) 13.8226 + 23.9415i 0.453018 + 0.784650i
\(932\) −20.9678 + 36.3173i −0.686824 + 1.18961i
\(933\) −7.96043 −0.260613
\(934\) 8.59741 + 14.8912i 0.281316 + 0.487253i
\(935\) 22.4922 0.735572
\(936\) 2.16708 3.75348i 0.0708331 0.122686i
\(937\) 23.0724 0.753743 0.376872 0.926266i \(-0.377000\pi\)
0.376872 + 0.926266i \(0.377000\pi\)
\(938\) −77.0020 + 16.1128i −2.51420 + 0.526101i
\(939\) −15.3567 −0.501148
\(940\) −5.38110 + 9.32034i −0.175512 + 0.303996i
\(941\) −40.1417 −1.30858 −0.654291 0.756243i \(-0.727033\pi\)
−0.654291 + 0.756243i \(0.727033\pi\)
\(942\) −6.78001 11.7433i −0.220905 0.382618i
\(943\) 23.7338 0.772880
\(944\) 25.2164 43.6761i 0.820724 1.42154i
\(945\) −3.31468 5.74119i −0.107826 0.186761i
\(946\) 63.5090 2.06486
\(947\) −2.23315 −0.0725675 −0.0362838 0.999342i \(-0.511552\pi\)
−0.0362838 + 0.999342i \(0.511552\pi\)
\(948\) 1.39758 2.42069i 0.0453914 0.0786202i
\(949\) 11.1445 + 19.3029i 0.361766 + 0.626597i
\(950\) −4.59892 7.96556i −0.149209 0.258437i
\(951\) 6.42765 11.1330i 0.208431 0.361013i
\(952\) 18.1101 0.586952
\(953\) −9.44942 −0.306097 −0.153048 0.988219i \(-0.548909\pi\)
−0.153048 + 0.988219i \(0.548909\pi\)
\(954\) 2.24796 3.89359i 0.0727805 0.126060i
\(955\) 2.12505 3.68070i 0.0687651 0.119105i
\(956\) −0.351999 + 0.609680i −0.0113845 + 0.0197184i
\(957\) −9.90100 + 17.1490i −0.320054 + 0.554349i
\(958\) 10.0069 + 17.3324i 0.323308 + 0.559985i
\(959\) 27.7294 + 48.0287i 0.895428 + 1.55093i
\(960\) 5.78895 0.186838
\(961\) 13.9376 24.1406i 0.449600 0.778730i
\(962\) −73.3263 −2.36414
\(963\) −11.8927 −0.383236
\(964\) 16.9448 + 29.3493i 0.545755 + 0.945276i
\(965\) −27.4375 −0.883243
\(966\) 13.3987 23.2073i 0.431098 0.746683i
\(967\) −4.79203 8.30003i −0.154101 0.266911i 0.778630 0.627483i \(-0.215915\pi\)
−0.932731 + 0.360572i \(0.882582\pi\)
\(968\) 1.24805 2.16169i 0.0401140 0.0694795i
\(969\) −3.36897 5.83523i −0.108227 0.187454i
\(970\) −6.97403 12.0794i −0.223922 0.387845i
\(971\) −21.2948 36.8837i −0.683384 1.18366i −0.973942 0.226798i \(-0.927174\pi\)
0.290558 0.956857i \(-0.406159\pi\)
\(972\) 0.793808 + 1.37492i 0.0254614 + 0.0441005i
\(973\) −3.12913 5.41982i −0.100315 0.173751i
\(974\) −20.4625 35.4422i −0.655662 1.13564i
\(975\) −9.13639 + 15.8247i −0.292599 + 0.506796i
\(976\) −28.9164 50.0847i −0.925592 1.60317i
\(977\) −19.6324 + 34.0043i −0.628096 + 1.08789i 0.359837 + 0.933015i \(0.382832\pi\)
−0.987933 + 0.154879i \(0.950501\pi\)
\(978\) −15.7260 −0.502862
\(979\) −13.6569 23.6544i −0.436476 0.755998i
\(980\) 38.8859 1.24216
\(981\) −2.84549 −0.0908496
\(982\) 16.0771 27.8463i 0.513039 0.888610i
\(983\) 31.2624 0.997115 0.498558 0.866856i \(-0.333863\pi\)
0.498558 + 0.866856i \(0.333863\pi\)
\(984\) 3.32444 + 5.75810i 0.105979 + 0.183561i
\(985\) 0.710500 + 1.23062i 0.0226384 + 0.0392109i
\(986\) 22.7433 39.3926i 0.724294 1.25451i
\(987\) −13.1640 + 22.8008i −0.419016 + 0.725756i
\(988\) 6.49521 11.2500i 0.206640 0.357911i
\(989\) 12.4065 21.4887i 0.394503 0.683299i
\(990\) 9.32362 0.296324
\(991\) −25.9571 −0.824555 −0.412277 0.911058i \(-0.635267\pi\)
−0.412277 + 0.911058i \(0.635267\pi\)
\(992\) −6.41175 + 11.1055i −0.203573 + 0.352599i
\(993\) 8.64872 + 14.9800i 0.274459 + 0.475377i
\(994\) 47.9262 + 83.0106i 1.52013 + 2.63294i
\(995\) 4.83383 8.37245i 0.153243 0.265424i
\(996\) 3.44216 0.109069
\(997\) −2.89021 −0.0915337 −0.0457669 0.998952i \(-0.514573\pi\)
−0.0457669 + 0.998952i \(0.514573\pi\)
\(998\) −1.43838 2.49134i −0.0455311 0.0788621i
\(999\) −3.48841 + 6.04210i −0.110368 + 0.191164i
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 201.2.e.b.163.2 yes 10
3.2 odd 2 603.2.g.g.163.4 10
67.37 even 3 inner 201.2.e.b.37.2 10
201.104 odd 6 603.2.g.g.37.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.e.b.37.2 10 67.37 even 3 inner
201.2.e.b.163.2 yes 10 1.1 even 1 trivial
603.2.g.g.37.4 10 201.104 odd 6
603.2.g.g.163.4 10 3.2 odd 2