Properties

Label 670.2.e.f.431.2
Level $670$
Weight $2$
Character 670.431
Analytic conductor $5.350$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [670,2,Mod(171,670)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(670, 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("670.171");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 670.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: \(5.34997693543\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 431.2
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 670.431
Dual form 670.2.e.f.171.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +3.44949 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.72474 + 2.98735i) q^{6} +(-2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +8.89898 q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +3.44949 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.72474 + 2.98735i) q^{6} +(-2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +8.89898 q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.72474 - 2.98735i) q^{12} +(2.00000 - 3.46410i) q^{13} +4.44949 q^{14} -3.44949 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.22474 + 3.85337i) q^{17} +(-4.44949 + 7.70674i) q^{18} +(3.44949 - 5.97469i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-7.67423 - 13.2922i) q^{21} +(-1.22474 + 2.12132i) q^{23} +3.44949 q^{24} +1.00000 q^{25} +(2.00000 + 3.46410i) q^{26} +20.3485 q^{27} +(-2.22474 + 3.85337i) q^{28} +(3.00000 + 5.19615i) q^{29} +(1.72474 - 2.98735i) q^{30} +(0.275255 + 0.476756i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.22474 - 3.85337i) q^{34} +(2.22474 + 3.85337i) q^{35} +(-4.44949 - 7.70674i) q^{36} +(-2.94949 + 5.10867i) q^{37} +(3.44949 + 5.97469i) q^{38} +(6.89898 - 11.9494i) q^{39} -1.00000 q^{40} +(1.05051 + 1.81954i) q^{41} +15.3485 q^{42} +4.00000 q^{43} -8.89898 q^{45} +(-1.22474 - 2.12132i) q^{46} +(-3.67423 - 6.36396i) q^{47} +(-1.72474 + 2.98735i) q^{48} +(-6.39898 + 11.0834i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-7.67423 + 13.2922i) q^{51} -4.00000 q^{52} -7.00000 q^{53} +(-10.1742 + 17.6223i) q^{54} +(-2.22474 - 3.85337i) q^{56} +(11.8990 - 20.6096i) q^{57} -6.00000 q^{58} -6.89898 q^{59} +(1.72474 + 2.98735i) q^{60} +(-2.22474 + 3.85337i) q^{61} -0.550510 q^{62} +(-19.7980 - 34.2911i) q^{63} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-0.174235 + 8.18350i) q^{67} +4.44949 q^{68} +(-4.22474 + 7.31747i) q^{69} -4.44949 q^{70} +(-0.174235 - 0.301783i) q^{71} +8.89898 q^{72} +(4.22474 - 7.31747i) q^{73} +(-2.94949 - 5.10867i) q^{74} +3.44949 q^{75} -6.89898 q^{76} +(6.89898 + 11.9494i) q^{78} +(-1.00000 - 1.73205i) q^{79} +(0.500000 - 0.866025i) q^{80} +43.4949 q^{81} -2.10102 q^{82} +(-6.17423 + 10.6941i) q^{83} +(-7.67423 + 13.2922i) q^{84} +(2.22474 - 3.85337i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(10.3485 + 17.9241i) q^{87} -2.10102 q^{89} +(4.44949 - 7.70674i) q^{90} -17.7980 q^{91} +2.44949 q^{92} +(0.949490 + 1.64456i) q^{93} +7.34847 q^{94} +(-3.44949 + 5.97469i) q^{95} +(-1.72474 - 2.98735i) q^{96} +(-7.89898 + 13.6814i) q^{97} +(-6.39898 - 11.0834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} + 16 q^{9} + 2 q^{10} - 2 q^{12} + 8 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 8 q^{18} + 4 q^{19} + 2 q^{20} - 16 q^{21} + 4 q^{24} + 4 q^{25} + 8 q^{26} + 52 q^{27} - 4 q^{28} + 12 q^{29} + 2 q^{30} + 6 q^{31} - 2 q^{32} - 4 q^{34} + 4 q^{35} - 8 q^{36} - 2 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} + 14 q^{41} + 32 q^{42} + 16 q^{43} - 16 q^{45} - 2 q^{48} - 6 q^{49} - 2 q^{50} - 16 q^{51} - 16 q^{52} - 28 q^{53} - 26 q^{54} - 4 q^{56} + 28 q^{57} - 24 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 12 q^{62} - 40 q^{63} + 4 q^{64} - 8 q^{65} + 14 q^{67} + 8 q^{68} - 12 q^{69} - 8 q^{70} + 14 q^{71} + 16 q^{72} + 12 q^{73} - 2 q^{74} + 4 q^{75} - 8 q^{76} + 8 q^{78} - 4 q^{79} + 2 q^{80} + 76 q^{81} - 28 q^{82} - 10 q^{83} - 16 q^{84} + 4 q^{85} - 8 q^{86} + 12 q^{87} - 28 q^{89} + 8 q^{90} - 32 q^{91} - 6 q^{93} - 4 q^{95} - 2 q^{96} - 12 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/670\mathbb{Z}\right)^\times\).

\(n\) \(471\) \(537\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 3.44949 1.99156 0.995782 0.0917517i \(-0.0292466\pi\)
0.995782 + 0.0917517i \(0.0292466\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 −0.447214
\(6\) −1.72474 + 2.98735i −0.704124 + 1.21958i
\(7\) −2.22474 3.85337i −0.840875 1.45644i −0.889156 0.457604i \(-0.848708\pi\)
0.0482818 0.998834i \(-0.484625\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.89898 2.96633
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −1.72474 2.98735i −0.497891 0.862372i
\(13\) 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i \(-0.646166\pi\)
0.997927 0.0643593i \(-0.0205004\pi\)
\(14\) 4.44949 1.18918
\(15\) −3.44949 −0.890654
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.22474 + 3.85337i −0.539580 + 0.934580i 0.459347 + 0.888257i \(0.348084\pi\)
−0.998927 + 0.0463227i \(0.985250\pi\)
\(18\) −4.44949 + 7.70674i −1.04875 + 1.81650i
\(19\) 3.44949 5.97469i 0.791367 1.37069i −0.133753 0.991015i \(-0.542703\pi\)
0.925121 0.379674i \(-0.123964\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) −7.67423 13.2922i −1.67466 2.90059i
\(22\) 0 0
\(23\) −1.22474 + 2.12132i −0.255377 + 0.442326i −0.964998 0.262258i \(-0.915533\pi\)
0.709621 + 0.704584i \(0.248866\pi\)
\(24\) 3.44949 0.704124
\(25\) 1.00000 0.200000
\(26\) 2.00000 + 3.46410i 0.392232 + 0.679366i
\(27\) 20.3485 3.91606
\(28\) −2.22474 + 3.85337i −0.420437 + 0.728219i
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 1.72474 2.98735i 0.314894 0.545412i
\(31\) 0.275255 + 0.476756i 0.0494373 + 0.0856279i 0.889685 0.456575i \(-0.150924\pi\)
−0.840248 + 0.542203i \(0.817591\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −2.22474 3.85337i −0.381541 0.660848i
\(35\) 2.22474 + 3.85337i 0.376051 + 0.651339i
\(36\) −4.44949 7.70674i −0.741582 1.28446i
\(37\) −2.94949 + 5.10867i −0.484893 + 0.839860i −0.999849 0.0173569i \(-0.994475\pi\)
0.514956 + 0.857216i \(0.327808\pi\)
\(38\) 3.44949 + 5.97469i 0.559581 + 0.969223i
\(39\) 6.89898 11.9494i 1.10472 1.91343i
\(40\) −1.00000 −0.158114
\(41\) 1.05051 + 1.81954i 0.164062 + 0.284164i 0.936322 0.351143i \(-0.114207\pi\)
−0.772260 + 0.635307i \(0.780874\pi\)
\(42\) 15.3485 2.36832
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) −8.89898 −1.32658
\(46\) −1.22474 2.12132i −0.180579 0.312772i
\(47\) −3.67423 6.36396i −0.535942 0.928279i −0.999117 0.0420122i \(-0.986623\pi\)
0.463175 0.886267i \(-0.346710\pi\)
\(48\) −1.72474 + 2.98735i −0.248945 + 0.431186i
\(49\) −6.39898 + 11.0834i −0.914140 + 1.58334i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) −7.67423 + 13.2922i −1.07461 + 1.86128i
\(52\) −4.00000 −0.554700
\(53\) −7.00000 −0.961524 −0.480762 0.876851i \(-0.659640\pi\)
−0.480762 + 0.876851i \(0.659640\pi\)
\(54\) −10.1742 + 17.6223i −1.38454 + 2.39809i
\(55\) 0 0
\(56\) −2.22474 3.85337i −0.297294 0.514928i
\(57\) 11.8990 20.6096i 1.57606 2.72981i
\(58\) −6.00000 −0.787839
\(59\) −6.89898 −0.898171 −0.449085 0.893489i \(-0.648250\pi\)
−0.449085 + 0.893489i \(0.648250\pi\)
\(60\) 1.72474 + 2.98735i 0.222664 + 0.385665i
\(61\) −2.22474 + 3.85337i −0.284849 + 0.493374i −0.972573 0.232599i \(-0.925277\pi\)
0.687723 + 0.725973i \(0.258610\pi\)
\(62\) −0.550510 −0.0699149
\(63\) −19.7980 34.2911i −2.49431 4.32027i
\(64\) 1.00000 0.125000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 0 0
\(67\) −0.174235 + 8.18350i −0.0212861 + 0.999773i
\(68\) 4.44949 0.539580
\(69\) −4.22474 + 7.31747i −0.508600 + 0.880920i
\(70\) −4.44949 −0.531816
\(71\) −0.174235 0.301783i −0.0206778 0.0358151i 0.855501 0.517801i \(-0.173249\pi\)
−0.876179 + 0.481986i \(0.839916\pi\)
\(72\) 8.89898 1.04875
\(73\) 4.22474 7.31747i 0.494469 0.856445i −0.505511 0.862820i \(-0.668696\pi\)
0.999980 + 0.00637493i \(0.00202922\pi\)
\(74\) −2.94949 5.10867i −0.342871 0.593870i
\(75\) 3.44949 0.398313
\(76\) −6.89898 −0.791367
\(77\) 0 0
\(78\) 6.89898 + 11.9494i 0.781156 + 1.35300i
\(79\) −1.00000 1.73205i −0.112509 0.194871i 0.804272 0.594261i \(-0.202555\pi\)
−0.916781 + 0.399390i \(0.869222\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 43.4949 4.83277
\(82\) −2.10102 −0.232019
\(83\) −6.17423 + 10.6941i −0.677710 + 1.17383i 0.297958 + 0.954579i \(0.403694\pi\)
−0.975669 + 0.219250i \(0.929639\pi\)
\(84\) −7.67423 + 13.2922i −0.837328 + 1.45029i
\(85\) 2.22474 3.85337i 0.241307 0.417957i
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 10.3485 + 17.9241i 1.10947 + 1.92166i
\(88\) 0 0
\(89\) −2.10102 −0.222708 −0.111354 0.993781i \(-0.535519\pi\)
−0.111354 + 0.993781i \(0.535519\pi\)
\(90\) 4.44949 7.70674i 0.469017 0.812362i
\(91\) −17.7980 −1.86573
\(92\) 2.44949 0.255377
\(93\) 0.949490 + 1.64456i 0.0984575 + 0.170533i
\(94\) 7.34847 0.757937
\(95\) −3.44949 + 5.97469i −0.353910 + 0.612990i
\(96\) −1.72474 2.98735i −0.176031 0.304895i
\(97\) −7.89898 + 13.6814i −0.802020 + 1.38914i 0.116265 + 0.993218i \(0.462908\pi\)
−0.918285 + 0.395921i \(0.870425\pi\)
\(98\) −6.39898 11.0834i −0.646395 1.11959i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 6.12372 + 10.6066i 0.609333 + 1.05540i 0.991350 + 0.131241i \(0.0418962\pi\)
−0.382017 + 0.924155i \(0.624770\pi\)
\(102\) −7.67423 13.2922i −0.759862 1.31612i
\(103\) −2.77526 4.80688i −0.273454 0.473636i 0.696290 0.717761i \(-0.254833\pi\)
−0.969744 + 0.244124i \(0.921499\pi\)
\(104\) 2.00000 3.46410i 0.196116 0.339683i
\(105\) 7.67423 + 13.2922i 0.748929 + 1.29718i
\(106\) 3.50000 6.06218i 0.339950 0.588811i
\(107\) 15.4495 1.49356 0.746779 0.665072i \(-0.231599\pi\)
0.746779 + 0.665072i \(0.231599\pi\)
\(108\) −10.1742 17.6223i −0.979016 1.69571i
\(109\) 10.4495 1.00088 0.500440 0.865771i \(-0.333172\pi\)
0.500440 + 0.865771i \(0.333172\pi\)
\(110\) 0 0
\(111\) −10.1742 + 17.6223i −0.965696 + 1.67263i
\(112\) 4.44949 0.420437
\(113\) −2.00000 3.46410i −0.188144 0.325875i 0.756487 0.654008i \(-0.226914\pi\)
−0.944632 + 0.328133i \(0.893581\pi\)
\(114\) 11.8990 + 20.6096i 1.11444 + 1.93027i
\(115\) 1.22474 2.12132i 0.114208 0.197814i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 17.7980 30.8270i 1.64542 2.84995i
\(118\) 3.44949 5.97469i 0.317551 0.550015i
\(119\) 19.7980 1.81488
\(120\) −3.44949 −0.314894
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) −2.22474 3.85337i −0.201419 0.348868i
\(123\) 3.62372 + 6.27647i 0.326740 + 0.565931i
\(124\) 0.275255 0.476756i 0.0247186 0.0428139i
\(125\) −1.00000 −0.0894427
\(126\) 39.5959 3.52748
\(127\) −3.44949 5.97469i −0.306093 0.530168i 0.671411 0.741085i \(-0.265688\pi\)
−0.977504 + 0.210917i \(0.932355\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 13.7980 1.21484
\(130\) −2.00000 3.46410i −0.175412 0.303822i
\(131\) −10.2474 −0.895324 −0.447662 0.894203i \(-0.647743\pi\)
−0.447662 + 0.894203i \(0.647743\pi\)
\(132\) 0 0
\(133\) −30.6969 −2.66176
\(134\) −7.00000 4.24264i −0.604708 0.366508i
\(135\) −20.3485 −1.75132
\(136\) −2.22474 + 3.85337i −0.190770 + 0.330424i
\(137\) −0.449490 −0.0384025 −0.0192013 0.999816i \(-0.506112\pi\)
−0.0192013 + 0.999816i \(0.506112\pi\)
\(138\) −4.22474 7.31747i −0.359634 0.622905i
\(139\) −9.79796 −0.831052 −0.415526 0.909581i \(-0.636402\pi\)
−0.415526 + 0.909581i \(0.636402\pi\)
\(140\) 2.22474 3.85337i 0.188025 0.325669i
\(141\) −12.6742 21.9524i −1.06736 1.84873i
\(142\) 0.348469 0.0292429
\(143\) 0 0
\(144\) −4.44949 + 7.70674i −0.370791 + 0.642229i
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) 4.22474 + 7.31747i 0.349642 + 0.605598i
\(147\) −22.0732 + 38.2319i −1.82057 + 3.15332i
\(148\) 5.89898 0.484893
\(149\) 18.2474 1.49489 0.747445 0.664324i \(-0.231281\pi\)
0.747445 + 0.664324i \(0.231281\pi\)
\(150\) −1.72474 + 2.98735i −0.140825 + 0.243916i
\(151\) −3.27526 + 5.67291i −0.266536 + 0.461655i −0.967965 0.251085i \(-0.919213\pi\)
0.701429 + 0.712740i \(0.252546\pi\)
\(152\) 3.44949 5.97469i 0.279791 0.484611i
\(153\) −19.7980 + 34.2911i −1.60057 + 2.77227i
\(154\) 0 0
\(155\) −0.275255 0.476756i −0.0221090 0.0382940i
\(156\) −13.7980 −1.10472
\(157\) −10.7980 + 18.7026i −0.861771 + 1.49263i 0.00844713 + 0.999964i \(0.497311\pi\)
−0.870218 + 0.492667i \(0.836022\pi\)
\(158\) 2.00000 0.159111
\(159\) −24.1464 −1.91494
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 10.8990 0.858960
\(162\) −21.7474 + 37.6677i −1.70864 + 2.95945i
\(163\) 3.72474 + 6.45145i 0.291745 + 0.505316i 0.974222 0.225590i \(-0.0724310\pi\)
−0.682478 + 0.730906i \(0.739098\pi\)
\(164\) 1.05051 1.81954i 0.0820311 0.142082i
\(165\) 0 0
\(166\) −6.17423 10.6941i −0.479214 0.830022i
\(167\) −7.12372 12.3387i −0.551250 0.954794i −0.998185 0.0602269i \(-0.980818\pi\)
0.446934 0.894567i \(-0.352516\pi\)
\(168\) −7.67423 13.2922i −0.592080 1.02551i
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) 2.22474 + 3.85337i 0.170630 + 0.295540i
\(171\) 30.6969 53.1687i 2.34745 4.06591i
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) −20.6969 −1.56903
\(175\) −2.22474 3.85337i −0.168175 0.291287i
\(176\) 0 0
\(177\) −23.7980 −1.78876
\(178\) 1.05051 1.81954i 0.0787391 0.136380i
\(179\) 12.2474 0.915417 0.457709 0.889102i \(-0.348670\pi\)
0.457709 + 0.889102i \(0.348670\pi\)
\(180\) 4.44949 + 7.70674i 0.331645 + 0.574427i
\(181\) 1.67423 + 2.89986i 0.124445 + 0.215545i 0.921516 0.388341i \(-0.126952\pi\)
−0.797071 + 0.603886i \(0.793618\pi\)
\(182\) 8.89898 15.4135i 0.659636 1.14252i
\(183\) −7.67423 + 13.2922i −0.567296 + 0.982585i
\(184\) −1.22474 + 2.12132i −0.0902894 + 0.156386i
\(185\) 2.94949 5.10867i 0.216851 0.375597i
\(186\) −1.89898 −0.139240
\(187\) 0 0
\(188\) −3.67423 + 6.36396i −0.267971 + 0.464140i
\(189\) −45.2702 78.4102i −3.29292 5.70350i
\(190\) −3.44949 5.97469i −0.250252 0.433450i
\(191\) −9.72474 + 16.8438i −0.703658 + 1.21877i 0.263516 + 0.964655i \(0.415118\pi\)
−0.967174 + 0.254116i \(0.918215\pi\)
\(192\) 3.44949 0.248945
\(193\) −20.4495 −1.47199 −0.735993 0.676989i \(-0.763285\pi\)
−0.735993 + 0.676989i \(0.763285\pi\)
\(194\) −7.89898 13.6814i −0.567114 0.982270i
\(195\) −6.89898 + 11.9494i −0.494046 + 0.855713i
\(196\) 12.7980 0.914140
\(197\) −0.449490 0.778539i −0.0320248 0.0554686i 0.849569 0.527478i \(-0.176862\pi\)
−0.881594 + 0.472009i \(0.843529\pi\)
\(198\) 0 0
\(199\) 6.17423 10.6941i 0.437680 0.758084i −0.559830 0.828607i \(-0.689134\pi\)
0.997510 + 0.0705235i \(0.0224670\pi\)
\(200\) 1.00000 0.0707107
\(201\) −0.601021 + 28.2289i −0.0423927 + 1.99111i
\(202\) −12.2474 −0.861727
\(203\) 13.3485 23.1202i 0.936879 1.62272i
\(204\) 15.3485 1.07461
\(205\) −1.05051 1.81954i −0.0733708 0.127082i
\(206\) 5.55051 0.386722
\(207\) −10.8990 + 18.8776i −0.757531 + 1.31208i
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 0 0
\(210\) −15.3485 −1.05915
\(211\) 7.67423 13.2922i 0.528316 0.915070i −0.471139 0.882059i \(-0.656157\pi\)
0.999455 0.0330113i \(-0.0105097\pi\)
\(212\) 3.50000 + 6.06218i 0.240381 + 0.416352i
\(213\) −0.601021 1.04100i −0.0411812 0.0713280i
\(214\) −7.72474 + 13.3797i −0.528053 + 0.914614i
\(215\) −4.00000 −0.272798
\(216\) 20.3485 1.38454
\(217\) 1.22474 2.12132i 0.0831411 0.144005i
\(218\) −5.22474 + 9.04952i −0.353864 + 0.612911i
\(219\) 14.5732 25.2415i 0.984767 1.70567i
\(220\) 0 0
\(221\) 8.89898 + 15.4135i 0.598610 + 1.03682i
\(222\) −10.1742 17.6223i −0.682850 1.18273i
\(223\) 9.10102 0.609449 0.304725 0.952440i \(-0.401436\pi\)
0.304725 + 0.952440i \(0.401436\pi\)
\(224\) −2.22474 + 3.85337i −0.148647 + 0.257464i
\(225\) 8.89898 0.593265
\(226\) 4.00000 0.266076
\(227\) −11.1742 19.3543i −0.741660 1.28459i −0.951739 0.306908i \(-0.900705\pi\)
0.210079 0.977684i \(-0.432628\pi\)
\(228\) −23.7980 −1.57606
\(229\) −1.12372 + 1.94635i −0.0742578 + 0.128618i −0.900763 0.434310i \(-0.856992\pi\)
0.826505 + 0.562929i \(0.190325\pi\)
\(230\) 1.22474 + 2.12132i 0.0807573 + 0.139876i
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 1.77526 + 3.07483i 0.116301 + 0.201439i 0.918299 0.395888i \(-0.129563\pi\)
−0.801998 + 0.597326i \(0.796230\pi\)
\(234\) 17.7980 + 30.8270i 1.16349 + 2.01522i
\(235\) 3.67423 + 6.36396i 0.239681 + 0.415139i
\(236\) 3.44949 + 5.97469i 0.224543 + 0.388919i
\(237\) −3.44949 5.97469i −0.224068 0.388098i
\(238\) −9.89898 + 17.1455i −0.641656 + 1.11138i
\(239\) 12.8990 + 22.3417i 0.834366 + 1.44516i 0.894546 + 0.446976i \(0.147499\pi\)
−0.0601803 + 0.998188i \(0.519168\pi\)
\(240\) 1.72474 2.98735i 0.111332 0.192832i
\(241\) −27.8990 −1.79713 −0.898566 0.438839i \(-0.855390\pi\)
−0.898566 + 0.438839i \(0.855390\pi\)
\(242\) 5.50000 + 9.52628i 0.353553 + 0.612372i
\(243\) 88.9898 5.70870
\(244\) 4.44949 0.284849
\(245\) 6.39898 11.0834i 0.408816 0.708090i
\(246\) −7.24745 −0.462080
\(247\) −13.7980 23.8988i −0.877943 1.52064i
\(248\) 0.275255 + 0.476756i 0.0174787 + 0.0302740i
\(249\) −21.2980 + 36.8891i −1.34970 + 2.33775i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −6.32577 + 10.9565i −0.399279 + 0.691571i −0.993637 0.112629i \(-0.964073\pi\)
0.594358 + 0.804200i \(0.297406\pi\)
\(252\) −19.7980 + 34.2911i −1.24715 + 2.16013i
\(253\) 0 0
\(254\) 6.89898 0.432880
\(255\) 7.67423 13.2922i 0.480579 0.832388i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.89898 3.28913i −0.118455 0.205170i 0.800701 0.599065i \(-0.204461\pi\)
−0.919156 + 0.393895i \(0.871127\pi\)
\(258\) −6.89898 + 11.9494i −0.429512 + 0.743936i
\(259\) 26.2474 1.63094
\(260\) 4.00000 0.248069
\(261\) 26.6969 + 46.2405i 1.65250 + 2.86221i
\(262\) 5.12372 8.87455i 0.316545 0.548272i
\(263\) −14.8990 −0.918710 −0.459355 0.888253i \(-0.651919\pi\)
−0.459355 + 0.888253i \(0.651919\pi\)
\(264\) 0 0
\(265\) 7.00000 0.430007
\(266\) 15.3485 26.5843i 0.941075 1.62999i
\(267\) −7.24745 −0.443537
\(268\) 7.17423 3.94086i 0.438236 0.240726i
\(269\) −7.59592 −0.463131 −0.231566 0.972819i \(-0.574385\pi\)
−0.231566 + 0.972819i \(0.574385\pi\)
\(270\) 10.1742 17.6223i 0.619184 1.07246i
\(271\) 32.1464 1.95276 0.976378 0.216068i \(-0.0693234\pi\)
0.976378 + 0.216068i \(0.0693234\pi\)
\(272\) −2.22474 3.85337i −0.134895 0.233645i
\(273\) −61.3939 −3.71573
\(274\) 0.224745 0.389270i 0.0135773 0.0235166i
\(275\) 0 0
\(276\) 8.44949 0.508600
\(277\) −16.1010 −0.967417 −0.483708 0.875229i \(-0.660710\pi\)
−0.483708 + 0.875229i \(0.660710\pi\)
\(278\) 4.89898 8.48528i 0.293821 0.508913i
\(279\) 2.44949 + 4.24264i 0.146647 + 0.254000i
\(280\) 2.22474 + 3.85337i 0.132954 + 0.230283i
\(281\) 8.74745 15.1510i 0.521829 0.903834i −0.477849 0.878442i \(-0.658583\pi\)
0.999678 0.0253922i \(-0.00808345\pi\)
\(282\) 25.3485 1.50948
\(283\) 11.7980 0.701316 0.350658 0.936504i \(-0.385958\pi\)
0.350658 + 0.936504i \(0.385958\pi\)
\(284\) −0.174235 + 0.301783i −0.0103389 + 0.0179075i
\(285\) −11.8990 + 20.6096i −0.704835 + 1.22081i
\(286\) 0 0
\(287\) 4.67423 8.09601i 0.275911 0.477892i
\(288\) −4.44949 7.70674i −0.262189 0.454124i
\(289\) −1.39898 2.42310i −0.0822929 0.142536i
\(290\) 6.00000 0.352332
\(291\) −27.2474 + 47.1940i −1.59727 + 2.76656i
\(292\) −8.44949 −0.494469
\(293\) −14.7980 −0.864506 −0.432253 0.901752i \(-0.642281\pi\)
−0.432253 + 0.901752i \(0.642281\pi\)
\(294\) −22.0732 38.2319i −1.28734 2.22973i
\(295\) 6.89898 0.401674
\(296\) −2.94949 + 5.10867i −0.171436 + 0.296935i
\(297\) 0 0
\(298\) −9.12372 + 15.8028i −0.528523 + 0.915429i
\(299\) 4.89898 + 8.48528i 0.283315 + 0.490716i
\(300\) −1.72474 2.98735i −0.0995782 0.172474i
\(301\) −8.89898 15.4135i −0.512929 0.888418i
\(302\) −3.27526 5.67291i −0.188470 0.326439i
\(303\) 21.1237 + 36.5874i 1.21353 + 2.10189i
\(304\) 3.44949 + 5.97469i 0.197842 + 0.342672i
\(305\) 2.22474 3.85337i 0.127389 0.220643i
\(306\) −19.7980 34.2911i −1.13177 1.96029i
\(307\) −2.17423 + 3.76588i −0.124090 + 0.214930i −0.921377 0.388670i \(-0.872935\pi\)
0.797287 + 0.603601i \(0.206268\pi\)
\(308\) 0 0
\(309\) −9.57321 16.5813i −0.544601 0.943277i
\(310\) 0.550510 0.0312669
\(311\) 6.55051 0.371445 0.185723 0.982602i \(-0.440537\pi\)
0.185723 + 0.982602i \(0.440537\pi\)
\(312\) 6.89898 11.9494i 0.390578 0.676501i
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −10.7980 18.7026i −0.609364 1.05545i
\(315\) 19.7980 + 34.2911i 1.11549 + 1.93208i
\(316\) −1.00000 + 1.73205i −0.0562544 + 0.0974355i
\(317\) 13.8485 23.9863i 0.777808 1.34720i −0.155395 0.987852i \(-0.549665\pi\)
0.933203 0.359350i \(-0.117002\pi\)
\(318\) 12.0732 20.9114i 0.677032 1.17265i
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 53.2929 2.97452
\(322\) −5.44949 + 9.43879i −0.303688 + 0.526003i
\(323\) 15.3485 + 26.5843i 0.854012 + 1.47919i
\(324\) −21.7474 37.6677i −1.20819 2.09265i
\(325\) 2.00000 3.46410i 0.110940 0.192154i
\(326\) −7.44949 −0.412589
\(327\) 36.0454 1.99332
\(328\) 1.05051 + 1.81954i 0.0580047 + 0.100467i
\(329\) −16.3485 + 28.3164i −0.901320 + 1.56113i
\(330\) 0 0
\(331\) −1.44949 2.51059i −0.0796712 0.137994i 0.823437 0.567408i \(-0.192054\pi\)
−0.903108 + 0.429413i \(0.858720\pi\)
\(332\) 12.3485 0.677710
\(333\) −26.2474 + 45.4619i −1.43835 + 2.49130i
\(334\) 14.2474 0.779586
\(335\) 0.174235 8.18350i 0.00951945 0.447112i
\(336\) 15.3485 0.837328
\(337\) −0.224745 + 0.389270i −0.0122426 + 0.0212049i −0.872082 0.489360i \(-0.837230\pi\)
0.859839 + 0.510565i \(0.170564\pi\)
\(338\) 3.00000 0.163178
\(339\) −6.89898 11.9494i −0.374701 0.649001i
\(340\) −4.44949 −0.241307
\(341\) 0 0
\(342\) 30.6969 + 53.1687i 1.65990 + 2.87503i
\(343\) 25.7980 1.39296
\(344\) 4.00000 0.215666
\(345\) 4.22474 7.31747i 0.227453 0.393959i
\(346\) 4.50000 + 7.79423i 0.241921 + 0.419020i
\(347\) −9.34847 16.1920i −0.501852 0.869233i −0.999998 0.00213997i \(-0.999319\pi\)
0.498146 0.867093i \(-0.334015\pi\)
\(348\) 10.3485 17.9241i 0.554736 0.960831i
\(349\) 5.79796 0.310358 0.155179 0.987886i \(-0.450405\pi\)
0.155179 + 0.987886i \(0.450405\pi\)
\(350\) 4.44949 0.237835
\(351\) 40.6969 70.4892i 2.17224 3.76243i
\(352\) 0 0
\(353\) −0.224745 + 0.389270i −0.0119620 + 0.0207187i −0.871944 0.489605i \(-0.837141\pi\)
0.859982 + 0.510324i \(0.170474\pi\)
\(354\) 11.8990 20.6096i 0.632424 1.09539i
\(355\) 0.174235 + 0.301783i 0.00924741 + 0.0160170i
\(356\) 1.05051 + 1.81954i 0.0556769 + 0.0964353i
\(357\) 68.2929 3.61444
\(358\) −6.12372 + 10.6066i −0.323649 + 0.560576i
\(359\) 14.1464 0.746620 0.373310 0.927707i \(-0.378223\pi\)
0.373310 + 0.927707i \(0.378223\pi\)
\(360\) −8.89898 −0.469017
\(361\) −14.2980 24.7648i −0.752524 1.30341i
\(362\) −3.34847 −0.175992
\(363\) 18.9722 32.8608i 0.995782 1.72474i
\(364\) 8.89898 + 15.4135i 0.466433 + 0.807886i
\(365\) −4.22474 + 7.31747i −0.221133 + 0.383014i
\(366\) −7.67423 13.2922i −0.401139 0.694793i
\(367\) −3.12372 5.41045i −0.163057 0.282423i 0.772907 0.634520i \(-0.218802\pi\)
−0.935964 + 0.352097i \(0.885469\pi\)
\(368\) −1.22474 2.12132i −0.0638442 0.110581i
\(369\) 9.34847 + 16.1920i 0.486662 + 0.842923i
\(370\) 2.94949 + 5.10867i 0.153337 + 0.265587i
\(371\) 15.5732 + 26.9736i 0.808521 + 1.40040i
\(372\) 0.949490 1.64456i 0.0492287 0.0852667i
\(373\) 7.50000 + 12.9904i 0.388335 + 0.672616i 0.992226 0.124451i \(-0.0397169\pi\)
−0.603890 + 0.797067i \(0.706384\pi\)
\(374\) 0 0
\(375\) −3.44949 −0.178131
\(376\) −3.67423 6.36396i −0.189484 0.328196i
\(377\) 24.0000 1.23606
\(378\) 90.5403 4.65689
\(379\) −6.89898 + 11.9494i −0.354377 + 0.613799i −0.987011 0.160652i \(-0.948640\pi\)
0.632634 + 0.774451i \(0.281974\pi\)
\(380\) 6.89898 0.353910
\(381\) −11.8990 20.6096i −0.609603 1.05586i
\(382\) −9.72474 16.8438i −0.497561 0.861801i
\(383\) 4.34847 7.53177i 0.222196 0.384855i −0.733278 0.679929i \(-0.762011\pi\)
0.955475 + 0.295073i \(0.0953441\pi\)
\(384\) −1.72474 + 2.98735i −0.0880155 + 0.152447i
\(385\) 0 0
\(386\) 10.2247 17.7098i 0.520426 0.901404i
\(387\) 35.5959 1.80944
\(388\) 15.7980 0.802020
\(389\) 9.22474 15.9777i 0.467713 0.810103i −0.531606 0.846992i \(-0.678411\pi\)
0.999319 + 0.0368887i \(0.0117447\pi\)
\(390\) −6.89898 11.9494i −0.349343 0.605081i
\(391\) −5.44949 9.43879i −0.275593 0.477340i
\(392\) −6.39898 + 11.0834i −0.323197 + 0.559794i
\(393\) −35.3485 −1.78309
\(394\) 0.898979 0.0452899
\(395\) 1.00000 + 1.73205i 0.0503155 + 0.0871489i
\(396\) 0 0
\(397\) −7.00000 −0.351320 −0.175660 0.984451i \(-0.556206\pi\)
−0.175660 + 0.984451i \(0.556206\pi\)
\(398\) 6.17423 + 10.6941i 0.309486 + 0.536046i
\(399\) −105.889 −5.30107
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 4.89898 0.244643 0.122322 0.992491i \(-0.460966\pi\)
0.122322 + 0.992491i \(0.460966\pi\)
\(402\) −24.1464 14.6349i −1.20431 0.729925i
\(403\) 2.20204 0.109691
\(404\) 6.12372 10.6066i 0.304667 0.527698i
\(405\) −43.4949 −2.16128
\(406\) 13.3485 + 23.1202i 0.662473 + 1.14744i
\(407\) 0 0
\(408\) −7.67423 + 13.2922i −0.379931 + 0.658060i
\(409\) 18.9495 + 32.8215i 0.936992 + 1.62292i 0.771043 + 0.636783i \(0.219735\pi\)
0.165949 + 0.986134i \(0.446931\pi\)
\(410\) 2.10102 0.103762
\(411\) −1.55051 −0.0764810
\(412\) −2.77526 + 4.80688i −0.136727 + 0.236818i
\(413\) 15.3485 + 26.5843i 0.755249 + 1.30813i
\(414\) −10.8990 18.8776i −0.535656 0.927783i
\(415\) 6.17423 10.6941i 0.303081 0.524952i
\(416\) −4.00000 −0.196116
\(417\) −33.7980 −1.65509
\(418\) 0 0
\(419\) −5.79796 + 10.0424i −0.283249 + 0.490601i −0.972183 0.234223i \(-0.924746\pi\)
0.688934 + 0.724824i \(0.258079\pi\)
\(420\) 7.67423 13.2922i 0.374464 0.648591i
\(421\) −3.89898 + 6.75323i −0.190025 + 0.329132i −0.945258 0.326324i \(-0.894190\pi\)
0.755234 + 0.655456i \(0.227523\pi\)
\(422\) 7.67423 + 13.2922i 0.373576 + 0.647052i
\(423\) −32.6969 56.6328i −1.58978 2.75358i
\(424\) −7.00000 −0.339950
\(425\) −2.22474 + 3.85337i −0.107916 + 0.186916i
\(426\) 1.20204 0.0582391
\(427\) 19.7980 0.958090
\(428\) −7.72474 13.3797i −0.373390 0.646730i
\(429\) 0 0
\(430\) 2.00000 3.46410i 0.0964486 0.167054i
\(431\) −8.17423 14.1582i −0.393739 0.681976i 0.599200 0.800599i \(-0.295485\pi\)
−0.992939 + 0.118623i \(0.962152\pi\)
\(432\) −10.1742 + 17.6223i −0.489508 + 0.847853i
\(433\) −9.02270 15.6278i −0.433603 0.751023i 0.563577 0.826064i \(-0.309425\pi\)
−0.997181 + 0.0750403i \(0.976091\pi\)
\(434\) 1.22474 + 2.12132i 0.0587896 + 0.101827i
\(435\) −10.3485 17.9241i −0.496171 0.859394i
\(436\) −5.22474 9.04952i −0.250220 0.433394i
\(437\) 8.44949 + 14.6349i 0.404194 + 0.700084i
\(438\) 14.5732 + 25.2415i 0.696335 + 1.20609i
\(439\) 0.275255 0.476756i 0.0131372 0.0227543i −0.859382 0.511334i \(-0.829152\pi\)
0.872519 + 0.488580i \(0.162485\pi\)
\(440\) 0 0
\(441\) −56.9444 + 98.6306i −2.71164 + 4.69669i
\(442\) −17.7980 −0.846563
\(443\) −5.62372 9.74058i −0.267191 0.462789i 0.700944 0.713216i \(-0.252762\pi\)
−0.968135 + 0.250427i \(0.919429\pi\)
\(444\) 20.3485 0.965696
\(445\) 2.10102 0.0995979
\(446\) −4.55051 + 7.88171i −0.215473 + 0.373210i
\(447\) 62.9444 2.97717
\(448\) −2.22474 3.85337i −0.105109 0.182055i
\(449\) −2.05051 3.55159i −0.0967696 0.167610i 0.813576 0.581458i \(-0.197518\pi\)
−0.910346 + 0.413849i \(0.864184\pi\)
\(450\) −4.44949 + 7.70674i −0.209751 + 0.363299i
\(451\) 0 0
\(452\) −2.00000 + 3.46410i −0.0940721 + 0.162938i
\(453\) −11.2980 + 19.5686i −0.530824 + 0.919415i
\(454\) 22.3485 1.04887
\(455\) 17.7980 0.834381
\(456\) 11.8990 20.6096i 0.557221 0.965135i
\(457\) −15.7753 27.3235i −0.737935 1.27814i −0.953423 0.301635i \(-0.902468\pi\)
0.215488 0.976506i \(-0.430866\pi\)
\(458\) −1.12372 1.94635i −0.0525082 0.0909469i
\(459\) −45.2702 + 78.4102i −2.11303 + 3.65987i
\(460\) −2.44949 −0.114208
\(461\) −38.7423 −1.80441 −0.902205 0.431306i \(-0.858053\pi\)
−0.902205 + 0.431306i \(0.858053\pi\)
\(462\) 0 0
\(463\) 4.67423 8.09601i 0.217230 0.376254i −0.736730 0.676187i \(-0.763631\pi\)
0.953960 + 0.299933i \(0.0969645\pi\)
\(464\) −6.00000 −0.278543
\(465\) −0.949490 1.64456i −0.0440315 0.0762649i
\(466\) −3.55051 −0.164474
\(467\) −10.9722 + 19.0044i −0.507733 + 0.879419i 0.492227 + 0.870467i \(0.336183\pi\)
−0.999960 + 0.00895193i \(0.997150\pi\)
\(468\) −35.5959 −1.64542
\(469\) 31.9217 17.5348i 1.47401 0.809682i
\(470\) −7.34847 −0.338960
\(471\) −37.2474 + 64.5145i −1.71627 + 2.97267i
\(472\) −6.89898 −0.317551
\(473\) 0 0
\(474\) 6.89898 0.316881
\(475\) 3.44949 5.97469i 0.158273 0.274138i
\(476\) −9.89898 17.1455i −0.453719 0.785864i
\(477\) −62.2929 −2.85219
\(478\) −25.7980 −1.17997
\(479\) 4.65153 8.05669i 0.212534 0.368119i −0.739973 0.672637i \(-0.765162\pi\)
0.952507 + 0.304517i \(0.0984951\pi\)
\(480\) 1.72474 + 2.98735i 0.0787235 + 0.136353i
\(481\) 11.7980 + 20.4347i 0.537941 + 0.931740i
\(482\) 13.9495 24.1612i 0.635382 1.10051i
\(483\) 37.5959 1.71067
\(484\) −11.0000 −0.500000
\(485\) 7.89898 13.6814i 0.358674 0.621242i
\(486\) −44.4949 + 77.0674i −2.01833 + 3.49585i
\(487\) 2.12372 3.67840i 0.0962351 0.166684i −0.813888 0.581021i \(-0.802653\pi\)
0.910123 + 0.414337i \(0.135987\pi\)
\(488\) −2.22474 + 3.85337i −0.100709 + 0.174434i
\(489\) 12.8485 + 22.2542i 0.581028 + 1.00637i
\(490\) 6.39898 + 11.0834i 0.289076 + 0.500695i
\(491\) 13.3485 0.602408 0.301204 0.953560i \(-0.402611\pi\)
0.301204 + 0.953560i \(0.402611\pi\)
\(492\) 3.62372 6.27647i 0.163370 0.282965i
\(493\) −26.6969 −1.20237
\(494\) 27.5959 1.24160
\(495\) 0 0
\(496\) −0.550510 −0.0247186
\(497\) −0.775255 + 1.34278i −0.0347749 + 0.0602320i
\(498\) −21.2980 36.8891i −0.954384 1.65304i
\(499\) 2.89898 5.02118i 0.129776 0.224779i −0.793814 0.608161i \(-0.791907\pi\)
0.923590 + 0.383382i \(0.125241\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) −24.5732 42.5621i −1.09785 1.90153i
\(502\) −6.32577 10.9565i −0.282333 0.489015i
\(503\) 7.79796 + 13.5065i 0.347694 + 0.602223i 0.985839 0.167692i \(-0.0536315\pi\)
−0.638146 + 0.769916i \(0.720298\pi\)
\(504\) −19.7980 34.2911i −0.881871 1.52745i
\(505\) −6.12372 10.6066i −0.272502 0.471988i
\(506\) 0 0
\(507\) −5.17423 8.96204i −0.229796 0.398018i
\(508\) −3.44949 + 5.97469i −0.153046 + 0.265084i
\(509\) 9.55051 0.423319 0.211659 0.977343i \(-0.432113\pi\)
0.211659 + 0.977343i \(0.432113\pi\)
\(510\) 7.67423 + 13.2922i 0.339821 + 0.588587i
\(511\) −37.5959 −1.66315
\(512\) 1.00000 0.0441942
\(513\) 70.1918 121.576i 3.09905 5.36770i
\(514\) 3.79796 0.167521
\(515\) 2.77526 + 4.80688i 0.122292 + 0.211817i
\(516\) −6.89898 11.9494i −0.303711 0.526042i
\(517\) 0 0
\(518\) −13.1237 + 22.7310i −0.576623 + 0.998741i
\(519\) 15.5227 26.8861i 0.681371 1.18017i
\(520\) −2.00000 + 3.46410i −0.0877058 + 0.151911i
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) −53.3939 −2.33699
\(523\) 21.9722 38.0570i 0.960777 1.66411i 0.240220 0.970718i \(-0.422780\pi\)
0.720557 0.693396i \(-0.243886\pi\)
\(524\) 5.12372 + 8.87455i 0.223831 + 0.387687i
\(525\) −7.67423 13.2922i −0.334931 0.580118i
\(526\) 7.44949 12.9029i 0.324813 0.562593i
\(527\) −2.44949 −0.106701
\(528\) 0 0
\(529\) 8.50000 + 14.7224i 0.369565 + 0.640106i
\(530\) −3.50000 + 6.06218i −0.152030 + 0.263324i
\(531\) −61.3939 −2.66427
\(532\) 15.3485 + 26.5843i 0.665441 + 1.15258i
\(533\) 8.40408 0.364021
\(534\) 3.62372 6.27647i 0.156814 0.271610i
\(535\) −15.4495 −0.667940
\(536\) −0.174235 + 8.18350i −0.00752579 + 0.353473i
\(537\) 42.2474 1.82311
\(538\) 3.79796 6.57826i 0.163742 0.283609i
\(539\) 0 0
\(540\) 10.1742 + 17.6223i 0.437829 + 0.758343i
\(541\) 33.5959 1.44440 0.722201 0.691684i \(-0.243131\pi\)
0.722201 + 0.691684i \(0.243131\pi\)
\(542\) −16.0732 + 27.8396i −0.690404 + 1.19581i
\(543\) 5.77526 + 10.0030i 0.247840 + 0.429271i
\(544\) 4.44949 0.190770
\(545\) −10.4495 −0.447607
\(546\) 30.6969 53.1687i 1.31371 2.27541i
\(547\) 22.3207 + 38.6605i 0.954363 + 1.65300i 0.735820 + 0.677177i \(0.236797\pi\)
0.218543 + 0.975827i \(0.429870\pi\)
\(548\) 0.224745 + 0.389270i 0.00960063 + 0.0166288i
\(549\) −19.7980 + 34.2911i −0.844956 + 1.46351i
\(550\) 0 0
\(551\) 41.3939 1.76344
\(552\) −4.22474 + 7.31747i −0.179817 + 0.311452i
\(553\) −4.44949 + 7.70674i −0.189212 + 0.327724i
\(554\) 8.05051 13.9439i 0.342033 0.592419i
\(555\) 10.1742 17.6223i 0.431872 0.748025i
\(556\) 4.89898 + 8.48528i 0.207763 + 0.359856i
\(557\) 19.1969 + 33.2501i 0.813400 + 1.40885i 0.910471 + 0.413573i \(0.135719\pi\)
−0.0970704 + 0.995278i \(0.530947\pi\)
\(558\) −4.89898 −0.207390
\(559\) 8.00000 13.8564i 0.338364 0.586064i
\(560\) −4.44949 −0.188025
\(561\) 0 0
\(562\) 8.74745 + 15.1510i 0.368989 + 0.639107i
\(563\) −27.4495 −1.15686 −0.578429 0.815733i \(-0.696334\pi\)
−0.578429 + 0.815733i \(0.696334\pi\)
\(564\) −12.6742 + 21.9524i −0.533682 + 0.924364i
\(565\) 2.00000 + 3.46410i 0.0841406 + 0.145736i
\(566\) −5.89898 + 10.2173i −0.247953 + 0.429467i
\(567\) −96.7650 167.602i −4.06375 7.03862i
\(568\) −0.174235 0.301783i −0.00731072 0.0126625i
\(569\) 0.949490 + 1.64456i 0.0398047 + 0.0689437i 0.885241 0.465132i \(-0.153993\pi\)
−0.845437 + 0.534076i \(0.820660\pi\)
\(570\) −11.8990 20.6096i −0.498393 0.863243i
\(571\) 14.3485 + 24.8523i 0.600465 + 1.04004i 0.992751 + 0.120192i \(0.0383511\pi\)
−0.392286 + 0.919843i \(0.628316\pi\)
\(572\) 0 0
\(573\) −33.5454 + 58.1024i −1.40138 + 2.42726i
\(574\) 4.67423 + 8.09601i 0.195099 + 0.337921i
\(575\) −1.22474 + 2.12132i −0.0510754 + 0.0884652i
\(576\) 8.89898 0.370791
\(577\) 10.2247 + 17.7098i 0.425662 + 0.737268i 0.996482 0.0838073i \(-0.0267080\pi\)
−0.570820 + 0.821075i \(0.693375\pi\)
\(578\) 2.79796 0.116380
\(579\) −70.5403 −2.93156
\(580\) −3.00000 + 5.19615i −0.124568 + 0.215758i
\(581\) 54.9444 2.27948
\(582\) −27.2474 47.1940i −1.12944 1.95625i
\(583\) 0 0
\(584\) 4.22474 7.31747i 0.174821 0.302799i
\(585\) −17.7980 + 30.8270i −0.735855 + 1.27454i
\(586\) 7.39898 12.8154i 0.305649 0.529400i
\(587\) 5.72474 9.91555i 0.236286 0.409259i −0.723360 0.690471i \(-0.757403\pi\)
0.959645 + 0.281213i \(0.0907366\pi\)
\(588\) 44.1464 1.82057
\(589\) 3.79796 0.156492
\(590\) −3.44949 + 5.97469i −0.142013 + 0.245974i
\(591\) −1.55051 2.68556i −0.0637795 0.110469i
\(592\) −2.94949 5.10867i −0.121223 0.209965i
\(593\) 14.6969 25.4558i 0.603531 1.04535i −0.388751 0.921343i \(-0.627093\pi\)
0.992282 0.124003i \(-0.0395733\pi\)
\(594\) 0 0
\(595\) −19.7980 −0.811637
\(596\) −9.12372 15.8028i −0.373722 0.647306i
\(597\) 21.2980 36.8891i 0.871667 1.50977i
\(598\) −9.79796 −0.400668
\(599\) 15.1464 + 26.2344i 0.618866 + 1.07191i 0.989693 + 0.143206i \(0.0457411\pi\)
−0.370827 + 0.928702i \(0.620926\pi\)
\(600\) 3.44949 0.140825
\(601\) −7.34847 + 12.7279i −0.299750 + 0.519183i −0.976079 0.217417i \(-0.930237\pi\)
0.676328 + 0.736600i \(0.263570\pi\)
\(602\) 17.7980 0.725391
\(603\) −1.55051 + 72.8248i −0.0631417 + 2.96565i
\(604\) 6.55051 0.266536
\(605\) −5.50000 + 9.52628i −0.223607 + 0.387298i
\(606\) −42.2474 −1.71619
\(607\) 8.34847 + 14.4600i 0.338854 + 0.586912i 0.984217 0.176963i \(-0.0566274\pi\)
−0.645364 + 0.763876i \(0.723294\pi\)
\(608\) −6.89898 −0.279791
\(609\) 46.0454 79.7530i 1.86585 3.23175i
\(610\) 2.22474 + 3.85337i 0.0900773 + 0.156018i
\(611\) −29.3939 −1.18915
\(612\) 39.5959 1.60057
\(613\) 14.5000 25.1147i 0.585649 1.01437i −0.409145 0.912470i \(-0.634173\pi\)
0.994794 0.101905i \(-0.0324938\pi\)
\(614\) −2.17423 3.76588i −0.0877450 0.151979i
\(615\) −3.62372 6.27647i −0.146123 0.253092i
\(616\) 0 0
\(617\) −31.3485 −1.26204 −0.631021 0.775766i \(-0.717364\pi\)
−0.631021 + 0.775766i \(0.717364\pi\)
\(618\) 19.1464 0.770182
\(619\) 9.77526 16.9312i 0.392901 0.680524i −0.599930 0.800052i \(-0.704805\pi\)
0.992831 + 0.119528i \(0.0381383\pi\)
\(620\) −0.275255 + 0.476756i −0.0110545 + 0.0191470i
\(621\) −24.9217 + 43.1656i −1.00007 + 1.73218i
\(622\) −3.27526 + 5.67291i −0.131326 + 0.227463i
\(623\) 4.67423 + 8.09601i 0.187269 + 0.324360i
\(624\) 6.89898 + 11.9494i 0.276180 + 0.478358i
\(625\) 1.00000 0.0400000
\(626\) 3.00000 5.19615i 0.119904 0.207680i
\(627\) 0 0
\(628\) 21.5959 0.861771
\(629\) −13.1237 22.7310i −0.523277 0.906343i
\(630\) −39.5959 −1.57754
\(631\) −4.89898 + 8.48528i −0.195025 + 0.337794i −0.946909 0.321502i \(-0.895812\pi\)
0.751884 + 0.659296i \(0.229146\pi\)
\(632\) −1.00000 1.73205i −0.0397779 0.0688973i
\(633\) 26.4722 45.8512i 1.05218 1.82242i
\(634\) 13.8485 + 23.9863i 0.549993 + 0.952616i
\(635\) 3.44949 + 5.97469i 0.136889 + 0.237098i
\(636\) 12.0732 + 20.9114i 0.478734 + 0.829192i
\(637\) 25.5959 + 44.3334i 1.01415 + 1.75655i
\(638\) 0 0
\(639\) −1.55051 2.68556i −0.0613372 0.106239i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −15.3485 26.5843i −0.606228 1.05002i −0.991856 0.127364i \(-0.959349\pi\)
0.385628 0.922654i \(-0.373985\pi\)
\(642\) −26.6464 + 46.1530i −1.05165 + 1.82151i
\(643\) −1.04541 −0.0412269 −0.0206134 0.999788i \(-0.506562\pi\)
−0.0206134 + 0.999788i \(0.506562\pi\)
\(644\) −5.44949 9.43879i −0.214740 0.371941i
\(645\) −13.7980 −0.543294
\(646\) −30.6969 −1.20775
\(647\) −16.3485 + 28.3164i −0.642725 + 1.11323i 0.342097 + 0.939665i \(0.388863\pi\)
−0.984822 + 0.173567i \(0.944471\pi\)
\(648\) 43.4949 1.70864
\(649\) 0 0
\(650\) 2.00000 + 3.46410i 0.0784465 + 0.135873i
\(651\) 4.22474 7.31747i 0.165581 0.286794i
\(652\) 3.72474 6.45145i 0.145872 0.252658i
\(653\) 20.7474 35.9356i 0.811910 1.40627i −0.0996149 0.995026i \(-0.531761\pi\)
0.911525 0.411244i \(-0.134906\pi\)
\(654\) −18.0227 + 31.2162i −0.704743 + 1.22065i
\(655\) 10.2474 0.400401
\(656\) −2.10102 −0.0820311
\(657\) 37.5959 65.1180i 1.46676 2.54050i
\(658\) −16.3485 28.3164i −0.637330 1.10389i
\(659\) −16.8990 29.2699i −0.658291 1.14019i −0.981058 0.193715i \(-0.937946\pi\)
0.322767 0.946478i \(-0.395387\pi\)
\(660\) 0 0
\(661\) −43.1464 −1.67820 −0.839101 0.543976i \(-0.816918\pi\)
−0.839101 + 0.543976i \(0.816918\pi\)
\(662\) 2.89898 0.112672
\(663\) 30.6969 + 53.1687i 1.19217 + 2.06490i
\(664\) −6.17423 + 10.6941i −0.239607 + 0.415011i
\(665\) 30.6969 1.19038
\(666\) −26.2474 45.4619i −1.01707 1.76161i
\(667\) −14.6969 −0.569068
\(668\) −7.12372 + 12.3387i −0.275625 + 0.477397i
\(669\) 31.3939 1.21376
\(670\) 7.00000 + 4.24264i 0.270434 + 0.163908i
\(671\) 0 0
\(672\) −7.67423 + 13.2922i −0.296040 + 0.512756i
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −0.224745 0.389270i −0.00865685 0.0149941i
\(675\) 20.3485 0.783213
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) −14.0505 24.3362i −0.540005 0.935316i −0.998903 0.0468271i \(-0.985089\pi\)
0.458898 0.888489i \(-0.348244\pi\)
\(678\) 13.7980 0.529907
\(679\) 70.2929 2.69759
\(680\) 2.22474 3.85337i 0.0853151 0.147770i
\(681\) −38.5454 66.7626i −1.47706 2.55835i
\(682\) 0 0
\(683\) −5.92679 + 10.2655i −0.226782 + 0.392798i −0.956853 0.290574i \(-0.906154\pi\)
0.730070 + 0.683372i \(0.239487\pi\)
\(684\) −61.3939 −2.34745
\(685\) 0.449490 0.0171741
\(686\) −12.8990 + 22.3417i −0.492485 + 0.853010i
\(687\) −3.87628 + 6.71391i −0.147889 + 0.256152i
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) −14.0000 + 24.2487i −0.533358 + 0.923802i
\(690\) 4.22474 + 7.31747i 0.160833 + 0.278571i
\(691\) 3.24745 + 5.62475i 0.123539 + 0.213975i 0.921161 0.389182i \(-0.127242\pi\)
−0.797622 + 0.603158i \(0.793909\pi\)
\(692\) −9.00000 −0.342129
\(693\) 0 0
\(694\) 18.6969 0.709726
\(695\) 9.79796 0.371658
\(696\) 10.3485 + 17.9241i 0.392258 + 0.679410i
\(697\) −9.34847 −0.354099
\(698\) −2.89898 + 5.02118i −0.109728 + 0.190054i
\(699\) 6.12372 + 10.6066i 0.231621 + 0.401179i
\(700\) −2.22474 + 3.85337i −0.0840875 + 0.145644i
\(701\) 11.7980 + 20.4347i 0.445603 + 0.771807i 0.998094 0.0617121i \(-0.0196561\pi\)
−0.552491 + 0.833519i \(0.686323\pi\)
\(702\) 40.6969 + 70.4892i 1.53601 + 2.66044i
\(703\) 20.3485 + 35.2446i 0.767457 + 1.32927i
\(704\) 0 0
\(705\) 12.6742 + 21.9524i 0.477339 + 0.826776i
\(706\) −0.224745 0.389270i −0.00845838 0.0146504i
\(707\) 27.2474 47.1940i 1.02475 1.77491i
\(708\) 11.8990 + 20.6096i 0.447191 + 0.774558i
\(709\) 13.7980 23.8988i 0.518193 0.897537i −0.481583 0.876400i \(-0.659938\pi\)
0.999777 0.0211367i \(-0.00672853\pi\)
\(710\) −0.348469 −0.0130778
\(711\) −8.89898 15.4135i −0.333738 0.578051i
\(712\) −2.10102 −0.0787391
\(713\) −1.34847 −0.0505006
\(714\) −34.1464 + 59.1433i −1.27790 + 2.21338i
\(715\) 0 0
\(716\) −6.12372 10.6066i −0.228854 0.396387i
\(717\) 44.4949 + 77.0674i 1.66169 + 2.87814i
\(718\) −7.07321 + 12.2512i −0.263970 + 0.457209i
\(719\) −7.82577 + 13.5546i −0.291852 + 0.505502i −0.974248 0.225481i \(-0.927605\pi\)
0.682396 + 0.730983i \(0.260938\pi\)
\(720\) 4.44949 7.70674i 0.165823 0.287213i
\(721\) −12.3485 + 21.3882i −0.459881 + 0.796537i
\(722\) 28.5959 1.06423
\(723\) −96.2372 −3.57910
\(724\) 1.67423 2.89986i 0.0622224 0.107772i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 18.9722 + 32.8608i 0.704124 + 1.21958i
\(727\) −15.2474 + 26.4094i −0.565497 + 0.979469i 0.431507 + 0.902110i \(0.357982\pi\)
−0.997003 + 0.0773591i \(0.975351\pi\)
\(728\) −17.7980 −0.659636
\(729\) 176.485 6.53647
\(730\) −4.22474 7.31747i −0.156365 0.270832i
\(731\) −8.89898 + 15.4135i −0.329141 + 0.570088i
\(732\) 15.3485 0.567296
\(733\) −13.7474 23.8113i −0.507774 0.879490i −0.999960 0.00899957i \(-0.997135\pi\)
0.492186 0.870490i \(-0.336198\pi\)
\(734\) 6.24745 0.230598
\(735\) 22.0732 38.2319i 0.814183 1.41021i
\(736\) 2.44949 0.0902894
\(737\) 0 0
\(738\) −18.6969 −0.688244
\(739\) 23.0454 39.9158i 0.847739 1.46833i −0.0354821 0.999370i \(-0.511297\pi\)
0.883221 0.468957i \(-0.155370\pi\)
\(740\) −5.89898 −0.216851
\(741\) −47.5959 82.4385i −1.74848 3.02846i
\(742\) −31.1464 −1.14342
\(743\) 5.10102 8.83523i 0.187138 0.324133i −0.757157 0.653233i \(-0.773412\pi\)
0.944295 + 0.329100i \(0.106745\pi\)
\(744\) 0.949490 + 1.64456i 0.0348100 + 0.0602927i
\(745\) −18.2474 −0.668535
\(746\) −15.0000 −0.549189
\(747\) −54.9444 + 95.1665i −2.01031 + 3.48196i
\(748\) 0 0
\(749\) −34.3712 59.5326i −1.25590 2.17527i
\(750\) 1.72474 2.98735i 0.0629788 0.109082i
\(751\) 14.3485 0.523583 0.261792 0.965124i \(-0.415687\pi\)
0.261792 + 0.965124i \(0.415687\pi\)
\(752\) 7.34847 0.267971
\(753\) −21.8207 + 37.7945i −0.795189 + 1.37731i
\(754\) −12.0000 + 20.7846i −0.437014 + 0.756931i
\(755\) 3.27526 5.67291i 0.119199 0.206458i
\(756\) −45.2702 + 78.4102i −1.64646 + 2.85175i
\(757\) −22.0505 38.1926i −0.801439 1.38813i −0.918669 0.395029i \(-0.870735\pi\)
0.117229 0.993105i \(-0.462599\pi\)
\(758\) −6.89898 11.9494i −0.250582 0.434021i
\(759\) 0 0
\(760\) −3.44949 + 5.97469i −0.125126 + 0.216725i
\(761\) 25.4949 0.924189 0.462095 0.886831i \(-0.347098\pi\)
0.462095 + 0.886831i \(0.347098\pi\)
\(762\) 23.7980 0.862109
\(763\) −23.2474 40.2658i −0.841614 1.45772i
\(764\) 19.4495 0.703658
\(765\) 19.7980 34.2911i 0.715797 1.23980i
\(766\) 4.34847 + 7.53177i 0.157117 + 0.272134i
\(767\) −13.7980 + 23.8988i −0.498215 + 0.862934i
\(768\) −1.72474 2.98735i −0.0622364 0.107797i
\(769\) −9.14643 15.8421i −0.329829 0.571280i 0.652649 0.757660i \(-0.273658\pi\)
−0.982478 + 0.186380i \(0.940324\pi\)
\(770\) 0 0
\(771\) −6.55051 11.3458i −0.235911 0.408610i
\(772\) 10.2247 + 17.7098i 0.367997 + 0.637389i
\(773\) 8.84847 + 15.3260i 0.318257 + 0.551238i 0.980125 0.198383i \(-0.0635691\pi\)
−0.661867 + 0.749621i \(0.730236\pi\)
\(774\) −17.7980 + 30.8270i −0.639734 + 1.10805i
\(775\) 0.275255 + 0.476756i 0.00988746 + 0.0171256i
\(776\) −7.89898 + 13.6814i −0.283557 + 0.491135i
\(777\) 90.5403 3.24812
\(778\) 9.22474 + 15.9777i 0.330723 + 0.572829i
\(779\) 14.4949 0.519334
\(780\) 13.7980 0.494046
\(781\) 0 0
\(782\) 10.8990 0.389747
\(783\) 61.0454 + 105.734i 2.18158 + 3.77862i
\(784\) −6.39898 11.0834i −0.228535 0.395834i
\(785\) 10.7980 18.7026i 0.385396 0.667525i
\(786\) 17.6742 30.6127i 0.630419 1.09192i
\(787\) 18.4217 31.9073i 0.656662 1.13737i −0.324812 0.945779i \(-0.605301\pi\)
0.981474 0.191594i \(-0.0613656\pi\)
\(788\) −0.449490 + 0.778539i −0.0160124 + 0.0277343i
\(789\) −51.3939 −1.82967
\(790\) −2.00000 −0.0711568
\(791\) −8.89898 + 15.4135i −0.316411 + 0.548040i
\(792\) 0 0
\(793\) 8.89898 + 15.4135i 0.316012 + 0.547349i
\(794\) 3.50000 6.06218i 0.124210 0.215139i
\(795\) 24.1464 0.856386
\(796\) −12.3485 −0.437680
\(797\) −15.1969 26.3219i −0.538303 0.932368i −0.998996 0.0448086i \(-0.985732\pi\)
0.460692 0.887560i \(-0.347601\pi\)
\(798\) 52.9444 91.7024i 1.87421 3.24623i
\(799\) 32.6969 1.15673
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) −18.6969 −0.660624
\(802\) −2.44949 + 4.24264i −0.0864945 + 0.149813i
\(803\) 0 0
\(804\) 24.7474 13.5939i 0.872775 0.479422i
\(805\) −10.8990 −0.384139
\(806\) −1.10102 + 1.90702i −0.0387818 + 0.0671720i
\(807\) −26.2020 −0.922356
\(808\) 6.12372 + 10.6066i 0.215432 + 0.373139i
\(809\) −22.6969 −0.797982 −0.398991 0.916955i \(-0.630640\pi\)
−0.398991 + 0.916955i \(0.630640\pi\)
\(810\) 21.7474 37.6677i 0.764127 1.32351i
\(811\) −11.3712 19.6954i −0.399296 0.691601i 0.594343 0.804211i \(-0.297412\pi\)
−0.993639 + 0.112611i \(0.964079\pi\)
\(812\) −26.6969 −0.936879
\(813\) 110.889 3.88904
\(814\) 0 0
\(815\) −3.72474 6.45145i −0.130472 0.225984i
\(816\) −7.67423 13.2922i −0.268652 0.465319i
\(817\) 13.7980 23.8988i 0.482729 0.836112i
\(818\) −37.8990 −1.32511
\(819\) −158.384 −5.53437
\(820\) −1.05051 + 1.81954i −0.0366854 + 0.0635410i
\(821\) −15.1237 + 26.1951i −0.527822 + 0.914214i 0.471652 + 0.881785i \(0.343658\pi\)
−0.999474 + 0.0324293i \(0.989676\pi\)
\(822\) 0.775255 1.34278i 0.0270401 0.0468349i
\(823\) 12.1464 21.0382i 0.423398 0.733347i −0.572871 0.819645i \(-0.694171\pi\)
0.996269 + 0.0862986i \(0.0275039\pi\)
\(824\) −2.77526 4.80688i −0.0966806 0.167456i
\(825\) 0 0
\(826\) −30.6969 −1.06808
\(827\) 15.1464 26.2344i 0.526693 0.912259i −0.472823 0.881157i \(-0.656765\pi\)
0.999516 0.0311016i \(-0.00990155\pi\)
\(828\) 21.7980 0.757531
\(829\) −19.8434 −0.689189 −0.344594 0.938752i \(-0.611984\pi\)
−0.344594 + 0.938752i \(0.611984\pi\)
\(830\) 6.17423 + 10.6941i 0.214311 + 0.371197i
\(831\) −55.5403 −1.92667
\(832\) 2.00000 3.46410i 0.0693375 0.120096i
\(833\) −28.4722 49.3153i −0.986503 1.70867i
\(834\) 16.8990 29.2699i 0.585164 1.01353i
\(835\) 7.12372 + 12.3387i 0.246527 + 0.426997i
\(836\) 0 0
\(837\) 5.60102 + 9.70125i 0.193600 + 0.335324i
\(838\) −5.79796 10.0424i −0.200287 0.346908i
\(839\) −15.0732 26.1076i −0.520385 0.901334i −0.999719 0.0237009i \(-0.992455\pi\)
0.479334 0.877633i \(-0.340878\pi\)
\(840\) 7.67423 + 13.2922i 0.264786 + 0.458623i
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) −3.89898 6.75323i −0.134368 0.232732i
\(843\) 30.1742 52.2633i 1.03926 1.80004i
\(844\) −15.3485 −0.528316
\(845\) 1.50000 + 2.59808i 0.0516016 + 0.0893765i
\(846\) 65.3939 2.24829
\(847\) −48.9444 −1.68175
\(848\) 3.50000 6.06218i 0.120190 0.208176i
\(849\) 40.6969 1.39672
\(850\) −2.22474 3.85337i −0.0763081 0.132170i
\(851\) −7.22474 12.5136i −0.247661 0.428962i
\(852\) −0.601021 + 1.04100i −0.0205906 + 0.0356640i
\(853\) −4.05051 + 7.01569i −0.138687 + 0.240213i −0.927000 0.375062i \(-0.877621\pi\)
0.788313 + 0.615274i \(0.210955\pi\)
\(854\) −9.89898 + 17.1455i −0.338736 + 0.586708i
\(855\) −30.6969 + 53.1687i −1.04981 + 1.81833i
\(856\) 15.4495 0.528053
\(857\) −53.6413 −1.83235 −0.916176 0.400775i \(-0.868741\pi\)
−0.916176 + 0.400775i \(0.868741\pi\)
\(858\) 0 0
\(859\) −5.44949 9.43879i −0.185934 0.322047i 0.757957 0.652305i \(-0.226198\pi\)
−0.943891 + 0.330257i \(0.892864\pi\)
\(860\) 2.00000 + 3.46410i 0.0681994 + 0.118125i
\(861\) 16.1237 27.9271i 0.549495 0.951753i
\(862\) 16.3485 0.556831
\(863\) 27.7526 0.944708 0.472354 0.881409i \(-0.343404\pi\)
0.472354 + 0.881409i \(0.343404\pi\)
\(864\) −10.1742 17.6223i −0.346134 0.599523i
\(865\) −4.50000 + 7.79423i −0.153005 + 0.265012i
\(866\) 18.0454 0.613208
\(867\) −4.82577 8.35847i −0.163892 0.283869i
\(868\) −2.44949 −0.0831411
\(869\) 0 0
\(870\) 20.6969 0.701692
\(871\) 28.0000 + 16.9706i 0.948744 + 0.575026i
\(872\) 10.4495 0.353864
\(873\) −70.2929 + 121.751i −2.37905 + 4.12064i
\(874\) −16.8990 −0.571617
\(875\) 2.22474 + 3.85337i 0.0752101 + 0.130268i
\(876\) −29.1464 −0.984767
\(877\) −20.0000 + 34.6410i −0.675352 + 1.16974i 0.301014 + 0.953620i \(0.402675\pi\)
−0.976366 + 0.216124i \(0.930658\pi\)
\(878\) 0.275255 + 0.476756i 0.00928941 + 0.0160897i
\(879\) −51.0454 −1.72172
\(880\) 0 0
\(881\) 10.3990 18.0116i 0.350351 0.606825i −0.635960 0.771722i \(-0.719396\pi\)
0.986311 + 0.164897i \(0.0527291\pi\)
\(882\) −56.9444 98.6306i −1.91742 3.32106i
\(883\) −2.89898 5.02118i −0.0975584 0.168976i 0.813115 0.582103i \(-0.197770\pi\)
−0.910674 + 0.413127i \(0.864437\pi\)
\(884\) 8.89898 15.4135i 0.299305 0.518412i
\(885\) 23.7980 0.799960
\(886\) 11.2474 0.377865
\(887\) 8.22474 14.2457i 0.276160 0.478323i −0.694267 0.719717i \(-0.744271\pi\)
0.970427 + 0.241394i \(0.0776047\pi\)
\(888\) −10.1742 + 17.6223i −0.341425 + 0.591365i
\(889\) −15.3485 + 26.5843i −0.514771 + 0.891610i
\(890\) −1.05051 + 1.81954i −0.0352132 + 0.0609910i
\(891\) 0 0
\(892\) −4.55051 7.88171i −0.152362 0.263899i
\(893\) −50.6969 −1.69651
\(894\) −31.4722 + 54.5114i −1.05259 + 1.82314i
\(895\) −12.2474 −0.409387
\(896\) 4.44949 0.148647
\(897\) 16.8990 + 29.2699i 0.564241 + 0.977293i
\(898\) 4.10102 0.136853
\(899\) −1.65153 + 2.86054i −0.0550816 + 0.0954042i
\(900\) −4.44949 7.70674i −0.148316 0.256891i
\(901\) 15.5732 26.9736i 0.518819 0.898621i
\(902\) 0 0
\(903\) −30.6969 53.1687i −1.02153 1.76934i
\(904\) −2.00000 3.46410i −0.0665190 0.115214i
\(905\) −1.67423 2.89986i −0.0556534 0.0963946i
\(906\) −11.2980 19.5686i −0.375350 0.650124i
\(907\) 9.87117 + 17.0974i 0.327767 + 0.567709i 0.982068 0.188525i \(-0.0603706\pi\)
−0.654302 + 0.756234i \(0.727037\pi\)
\(908\) −11.1742 + 19.3543i −0.370830 + 0.642296i
\(909\) 54.4949 + 94.3879i 1.80748 + 3.13065i
\(910\) −8.89898 + 15.4135i −0.294998 + 0.510952i
\(911\) 40.8434 1.35320 0.676601 0.736350i \(-0.263452\pi\)
0.676601 + 0.736350i \(0.263452\pi\)
\(912\) 11.8990 + 20.6096i 0.394015 + 0.682453i
\(913\) 0 0
\(914\) 31.5505 1.04360
\(915\) 7.67423 13.2922i 0.253702 0.439425i
\(916\) 2.24745 0.0742578
\(917\) 22.7980 + 39.4872i 0.752855 + 1.30398i
\(918\) −45.2702 78.4102i −1.49414 2.58792i
\(919\) −7.17423 + 12.4261i −0.236656 + 0.409900i −0.959753 0.280846i \(-0.909385\pi\)
0.723097 + 0.690747i \(0.242718\pi\)
\(920\) 1.22474 2.12132i 0.0403786 0.0699379i
\(921\) −7.50000 + 12.9904i −0.247133 + 0.428048i
\(922\) 19.3712 33.5519i 0.637956 1.10497i
\(923\) −1.39388 −0.0458800
\(924\) 0 0
\(925\) −2.94949 + 5.10867i −0.0969786 + 0.167972i
\(926\) 4.67423 + 8.09601i 0.153605 + 0.266051i
\(927\) −24.6969 42.7764i −0.811154 1.40496i
\(928\) 3.00000 5.19615i 0.0984798 0.170572i
\(929\) −28.8990 −0.948145 −0.474072 0.880486i \(-0.657216\pi\)
−0.474072 + 0.880486i \(0.657216\pi\)
\(930\) 1.89898 0.0622700
\(931\) 44.1464 + 76.4639i 1.44684 + 2.50600i
\(932\) 1.77526 3.07483i 0.0581504 0.100719i
\(933\) 22.5959 0.739757
\(934\) −10.9722 19.0044i −0.359021 0.621843i
\(935\) 0 0
\(936\) 17.7980 30.8270i 0.581744 1.00761i
\(937\) −9.34847 −0.305401 −0.152701 0.988272i \(-0.548797\pi\)
−0.152701 + 0.988272i \(0.548797\pi\)
\(938\) −0.775255 + 36.4124i −0.0253130 + 1.18891i
\(939\) −20.6969 −0.675419
\(940\) 3.67423 6.36396i 0.119840 0.207570i
\(941\) −47.5959 −1.55158 −0.775791 0.630990i \(-0.782649\pi\)
−0.775791 + 0.630990i \(0.782649\pi\)
\(942\) −37.2474 64.5145i −1.21359 2.10200i
\(943\) −5.14643 −0.167591
\(944\) 3.44949 5.97469i 0.112271 0.194460i
\(945\) 45.2702 + 78.4102i 1.47264 + 2.55068i
\(946\) 0 0
\(947\) −24.4949 −0.795977 −0.397989 0.917390i \(-0.630292\pi\)
−0.397989 + 0.917390i \(0.630292\pi\)
\(948\) −3.44949 + 5.97469i −0.112034 + 0.194049i
\(949\) −16.8990 29.2699i −0.548564 0.950141i
\(950\) 3.44949 + 5.97469i 0.111916 + 0.193845i
\(951\) 47.7702 82.7403i 1.54905 2.68304i
\(952\) 19.7980 0.641656
\(953\) 0.202041 0.00654475 0.00327238 0.999995i \(-0.498958\pi\)
0.00327238 + 0.999995i \(0.498958\pi\)
\(954\) 31.1464 53.9472i 1.00840 1.74660i
\(955\) 9.72474 16.8438i 0.314685 0.545051i
\(956\) 12.8990 22.3417i 0.417183 0.722582i
\(957\) 0 0
\(958\) 4.65153 + 8.05669i 0.150284 + 0.260300i
\(959\) 1.00000 + 1.73205i 0.0322917 + 0.0559308i
\(960\) −3.44949 −0.111332
\(961\) 15.3485 26.5843i 0.495112 0.857559i
\(962\) −23.5959 −0.760763
\(963\) 137.485 4.43038
\(964\) 13.9495 + 24.1612i 0.449283 + 0.778181i
\(965\) 20.4495 0.658292
\(966\) −18.7980 + 32.5590i −0.604814 + 1.04757i
\(967\) −8.47219 14.6743i −0.272447 0.471893i 0.697041 0.717032i \(-0.254500\pi\)
−0.969488 + 0.245139i \(0.921166\pi\)
\(968\) 5.50000 9.52628i 0.176777 0.306186i
\(969\) 52.9444 + 91.7024i 1.70082 + 2.94590i
\(970\) 7.89898 + 13.6814i 0.253621 + 0.439284i
\(971\) 3.79796 + 6.57826i 0.121882 + 0.211106i 0.920510 0.390719i \(-0.127774\pi\)
−0.798628 + 0.601825i \(0.794440\pi\)
\(972\) −44.4949 77.0674i −1.42717 2.47194i
\(973\) 21.7980 + 37.7552i 0.698810 + 1.21038i
\(974\) 2.12372 + 3.67840i 0.0680485 + 0.117863i
\(975\) 6.89898 11.9494i 0.220944 0.382687i
\(976\) −2.22474 3.85337i −0.0712123 0.123343i
\(977\) −24.2702 + 42.0371i −0.776471 + 1.34489i 0.157493 + 0.987520i \(0.449659\pi\)
−0.933964 + 0.357367i \(0.883675\pi\)
\(978\) −25.6969 −0.821697
\(979\) 0 0
\(980\) −12.7980 −0.408816
\(981\) 92.9898 2.96894
\(982\) −6.67423 + 11.5601i −0.212983 + 0.368898i
\(983\) −27.1464 −0.865837 −0.432918 0.901433i \(-0.642516\pi\)
−0.432918 + 0.901433i \(0.642516\pi\)
\(984\) 3.62372 + 6.27647i 0.115520 + 0.200087i
\(985\) 0.449490 + 0.778539i 0.0143219 + 0.0248063i
\(986\) 13.3485 23.1202i 0.425102 0.736298i
\(987\) −56.3939 + 97.6771i −1.79504 + 3.10910i
\(988\) −13.7980 + 23.8988i −0.438972 + 0.760321i
\(989\) −4.89898 + 8.48528i −0.155778 + 0.269816i
\(990\) 0 0
\(991\) −49.7423 −1.58012 −0.790059 0.613031i \(-0.789950\pi\)
−0.790059 + 0.613031i \(0.789950\pi\)
\(992\) 0.275255 0.476756i 0.00873936 0.0151370i
\(993\) −5.00000 8.66025i −0.158670 0.274825i
\(994\) −0.775255 1.34278i −0.0245896 0.0425904i
\(995\) −6.17423 + 10.6941i −0.195736 + 0.339025i
\(996\) 42.5959 1.34970
\(997\) −16.3939 −0.519199 −0.259600 0.965716i \(-0.583591\pi\)
−0.259600 + 0.965716i \(0.583591\pi\)
\(998\) 2.89898 + 5.02118i 0.0917656 + 0.158943i
\(999\) −60.0176 + 103.954i −1.89887 + 3.28894i
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 670.2.e.f.431.2 yes 4
67.37 even 3 inner 670.2.e.f.171.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
670.2.e.f.171.2 4 67.37 even 3 inner
670.2.e.f.431.2 yes 4 1.1 even 1 trivial