Properties

Label 273.2.t.d.4.1
Level $273$
Weight $2$
Character 273.4
Analytic conductor $2.180$
Analytic rank $0$
Dimension $20$
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] = [273,2,Mod(4,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.t (of order \(6\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + 27166 x^{4} + 6435 x^{2} + 576 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.1
Root \(-2.50900i\) of defining polynomial
Character \(\chi\) \(=\) 273.4
Dual form 273.2.t.d.205.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.50900i q^{2} +(0.500000 + 0.866025i) q^{3} -4.29509 q^{4} +(-2.97008 + 1.71478i) q^{5} +(2.17286 - 1.25450i) q^{6} +(-0.0473512 + 2.64533i) q^{7} +5.75840i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q-2.50900i q^{2} +(0.500000 + 0.866025i) q^{3} -4.29509 q^{4} +(-2.97008 + 1.71478i) q^{5} +(2.17286 - 1.25450i) q^{6} +(-0.0473512 + 2.64533i) q^{7} +5.75840i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.30238 + 7.45195i) q^{10} +(-4.35178 + 2.51250i) q^{11} +(-2.14755 - 3.71966i) q^{12} +(0.135561 - 3.60300i) q^{13} +(6.63713 + 0.118804i) q^{14} +(-2.97008 - 1.71478i) q^{15} +5.85764 q^{16} +0.199310 q^{17} +(2.17286 + 1.25450i) q^{18} +(3.99823 + 2.30838i) q^{19} +(12.7568 - 7.36513i) q^{20} +(-2.31460 + 1.28166i) q^{21} +(6.30387 + 10.9186i) q^{22} -7.52372 q^{23} +(-4.98692 + 2.87920i) q^{24} +(3.38093 - 5.85594i) q^{25} +(-9.03994 - 0.340122i) q^{26} -1.00000 q^{27} +(0.203378 - 11.3619i) q^{28} +(1.58334 - 2.74243i) q^{29} +(-4.30238 + 7.45195i) q^{30} +(-3.65876 - 2.11239i) q^{31} -3.18005i q^{32} +(-4.35178 - 2.51250i) q^{33} -0.500070i q^{34} +(-4.39551 - 7.93804i) q^{35} +(2.14755 - 3.71966i) q^{36} +9.11903i q^{37} +(5.79173 - 10.0316i) q^{38} +(3.18807 - 1.68410i) q^{39} +(-9.87437 - 17.1029i) q^{40} +(4.67486 + 2.69903i) q^{41} +(3.21568 + 5.80733i) q^{42} +(1.27860 + 2.21461i) q^{43} +(18.6913 - 10.7914i) q^{44} -3.42956i q^{45} +18.8770i q^{46} +(6.19804 - 3.57844i) q^{47} +(2.92882 + 5.07287i) q^{48} +(-6.99552 - 0.250519i) q^{49} +(-14.6926 - 8.48276i) q^{50} +(0.0996552 + 0.172608i) q^{51} +(-0.582245 + 15.4752i) q^{52} +(-0.215922 + 0.373988i) q^{53} +2.50900i q^{54} +(8.61676 - 14.9247i) q^{55} +(-15.2328 - 0.272667i) q^{56} +4.61676i q^{57} +(-6.88077 - 3.97261i) q^{58} +0.838256i q^{59} +(12.7568 + 7.36513i) q^{60} +(1.33262 - 2.30816i) q^{61} +(-5.29999 + 9.17985i) q^{62} +(-2.26725 - 1.36367i) q^{63} +3.73654 q^{64} +(5.77572 + 10.9337i) q^{65} +(-6.30387 + 10.9186i) q^{66} +(-9.67775 + 5.58745i) q^{67} -0.856057 q^{68} +(-3.76186 - 6.51573i) q^{69} +(-19.9166 + 11.0284i) q^{70} +(-4.95582 + 2.86124i) q^{71} +(-4.98692 - 2.87920i) q^{72} +(2.73161 + 1.57710i) q^{73} +22.8797 q^{74} +6.76186 q^{75} +(-17.1728 - 9.91470i) q^{76} +(-6.44032 - 11.6308i) q^{77} +(-4.22542 - 7.99888i) q^{78} +(2.25566 + 3.90692i) q^{79} +(-17.3977 + 10.0446i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.77187 - 11.7292i) q^{82} +14.7167i q^{83} +(9.94141 - 5.50483i) q^{84} +(-0.591968 + 0.341773i) q^{85} +(5.55645 - 3.20802i) q^{86} +3.16669 q^{87} +(-14.4680 - 25.0593i) q^{88} -2.34608i q^{89} -8.60477 q^{90} +(9.52470 + 0.529209i) q^{91} +32.3151 q^{92} -4.22478i q^{93} +(-8.97832 - 15.5509i) q^{94} -15.8334 q^{95} +(2.75400 - 1.59002i) q^{96} +(-5.02047 + 2.89857i) q^{97} +(-0.628552 + 17.5518i) q^{98} -5.02500i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.50900i 1.77413i −0.461642 0.887066i \(-0.652740\pi\)
0.461642 0.887066i \(-0.347260\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −4.29509 −2.14755
\(5\) −2.97008 + 1.71478i −1.32826 + 0.766872i −0.985031 0.172379i \(-0.944855\pi\)
−0.343231 + 0.939251i \(0.611521\pi\)
\(6\) 2.17286 1.25450i 0.887066 0.512148i
\(7\) −0.0473512 + 2.64533i −0.0178971 + 0.999840i
\(8\) 5.75840i 2.03590i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 4.30238 + 7.45195i 1.36053 + 2.35651i
\(11\) −4.35178 + 2.51250i −1.31211 + 0.757547i −0.982445 0.186551i \(-0.940269\pi\)
−0.329665 + 0.944098i \(0.606936\pi\)
\(12\) −2.14755 3.71966i −0.619943 1.07377i
\(13\) 0.135561 3.60300i 0.0375977 0.999293i
\(14\) 6.63713 + 0.118804i 1.77385 + 0.0317518i
\(15\) −2.97008 1.71478i −0.766872 0.442754i
\(16\) 5.85764 1.46441
\(17\) 0.199310 0.0483399 0.0241699 0.999708i \(-0.492306\pi\)
0.0241699 + 0.999708i \(0.492306\pi\)
\(18\) 2.17286 + 1.25450i 0.512148 + 0.295689i
\(19\) 3.99823 + 2.30838i 0.917256 + 0.529578i 0.882759 0.469827i \(-0.155684\pi\)
0.0344977 + 0.999405i \(0.489017\pi\)
\(20\) 12.7568 7.36513i 2.85250 1.64689i
\(21\) −2.31460 + 1.28166i −0.505086 + 0.279680i
\(22\) 6.30387 + 10.9186i 1.34399 + 2.32786i
\(23\) −7.52372 −1.56880 −0.784402 0.620253i \(-0.787030\pi\)
−0.784402 + 0.620253i \(0.787030\pi\)
\(24\) −4.98692 + 2.87920i −1.01795 + 0.587714i
\(25\) 3.38093 5.85594i 0.676186 1.17119i
\(26\) −9.03994 0.340122i −1.77288 0.0667034i
\(27\) −1.00000 −0.192450
\(28\) 0.203378 11.3619i 0.0384348 2.14720i
\(29\) 1.58334 2.74243i 0.294020 0.509257i −0.680737 0.732528i \(-0.738340\pi\)
0.974756 + 0.223271i \(0.0716736\pi\)
\(30\) −4.30238 + 7.45195i −0.785504 + 1.36053i
\(31\) −3.65876 2.11239i −0.657133 0.379396i 0.134051 0.990974i \(-0.457202\pi\)
−0.791184 + 0.611578i \(0.790535\pi\)
\(32\) 3.18005i 0.562158i
\(33\) −4.35178 2.51250i −0.757547 0.437370i
\(34\) 0.500070i 0.0857613i
\(35\) −4.39551 7.93804i −0.742977 1.34177i
\(36\) 2.14755 3.71966i 0.357924 0.619943i
\(37\) 9.11903i 1.49916i 0.661914 + 0.749580i \(0.269744\pi\)
−0.661914 + 0.749580i \(0.730256\pi\)
\(38\) 5.79173 10.0316i 0.939542 1.62733i
\(39\) 3.18807 1.68410i 0.510500 0.269672i
\(40\) −9.87437 17.1029i −1.56128 2.70421i
\(41\) 4.67486 + 2.69903i 0.730090 + 0.421517i 0.818455 0.574571i \(-0.194831\pi\)
−0.0883653 + 0.996088i \(0.528164\pi\)
\(42\) 3.21568 + 5.80733i 0.496190 + 0.896090i
\(43\) 1.27860 + 2.21461i 0.194985 + 0.337724i 0.946896 0.321541i \(-0.104201\pi\)
−0.751910 + 0.659265i \(0.770867\pi\)
\(44\) 18.6913 10.7914i 2.81782 1.62687i
\(45\) 3.42956i 0.511248i
\(46\) 18.8770i 2.78327i
\(47\) 6.19804 3.57844i 0.904077 0.521969i 0.0255566 0.999673i \(-0.491864\pi\)
0.878521 + 0.477704i \(0.158531\pi\)
\(48\) 2.92882 + 5.07287i 0.422739 + 0.732205i
\(49\) −6.99552 0.250519i −0.999359 0.0357884i
\(50\) −14.6926 8.48276i −2.07784 1.19964i
\(51\) 0.0996552 + 0.172608i 0.0139545 + 0.0241699i
\(52\) −0.582245 + 15.4752i −0.0807429 + 2.14603i
\(53\) −0.215922 + 0.373988i −0.0296592 + 0.0513712i −0.880474 0.474094i \(-0.842776\pi\)
0.850815 + 0.525466i \(0.176109\pi\)
\(54\) 2.50900i 0.341432i
\(55\) 8.61676 14.9247i 1.16188 2.01244i
\(56\) −15.2328 0.272667i −2.03557 0.0364366i
\(57\) 4.61676i 0.611504i
\(58\) −6.88077 3.97261i −0.903489 0.521630i
\(59\) 0.838256i 0.109132i 0.998510 + 0.0545658i \(0.0173775\pi\)
−0.998510 + 0.0545658i \(0.982623\pi\)
\(60\) 12.7568 + 7.36513i 1.64689 + 0.950835i
\(61\) 1.33262 2.30816i 0.170624 0.295530i −0.768014 0.640433i \(-0.778755\pi\)
0.938638 + 0.344903i \(0.112088\pi\)
\(62\) −5.29999 + 9.17985i −0.673099 + 1.16584i
\(63\) −2.26725 1.36367i −0.285646 0.171806i
\(64\) 3.73654 0.467068
\(65\) 5.77572 + 10.9337i 0.716390 + 1.35616i
\(66\) −6.30387 + 10.9186i −0.775952 + 1.34399i
\(67\) −9.67775 + 5.58745i −1.18233 + 0.682616i −0.956551 0.291564i \(-0.905824\pi\)
−0.225774 + 0.974180i \(0.572491\pi\)
\(68\) −0.856057 −0.103812
\(69\) −3.76186 6.51573i −0.452875 0.784402i
\(70\) −19.9166 + 11.0284i −2.38048 + 1.31814i
\(71\) −4.95582 + 2.86124i −0.588148 + 0.339567i −0.764365 0.644784i \(-0.776947\pi\)
0.176217 + 0.984351i \(0.443614\pi\)
\(72\) −4.98692 2.87920i −0.587714 0.339317i
\(73\) 2.73161 + 1.57710i 0.319711 + 0.184585i 0.651264 0.758851i \(-0.274239\pi\)
−0.331553 + 0.943437i \(0.607573\pi\)
\(74\) 22.8797 2.65971
\(75\) 6.76186 0.780792
\(76\) −17.1728 9.91470i −1.96985 1.13729i
\(77\) −6.44032 11.6308i −0.733943 1.32546i
\(78\) −4.22542 7.99888i −0.478434 0.905695i
\(79\) 2.25566 + 3.90692i 0.253782 + 0.439563i 0.964564 0.263849i \(-0.0849921\pi\)
−0.710782 + 0.703412i \(0.751659\pi\)
\(80\) −17.3977 + 10.0446i −1.94512 + 1.12302i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 6.77187 11.7292i 0.747828 1.29528i
\(83\) 14.7167i 1.61537i 0.589613 + 0.807686i \(0.299280\pi\)
−0.589613 + 0.807686i \(0.700720\pi\)
\(84\) 9.94141 5.50483i 1.08470 0.600627i
\(85\) −0.591968 + 0.341773i −0.0642080 + 0.0370705i
\(86\) 5.55645 3.20802i 0.599168 0.345930i
\(87\) 3.16669 0.339505
\(88\) −14.4680 25.0593i −1.54229 2.67133i
\(89\) 2.34608i 0.248684i −0.992239 0.124342i \(-0.960318\pi\)
0.992239 0.124342i \(-0.0396820\pi\)
\(90\) −8.60477 −0.907022
\(91\) 9.52470 + 0.529209i 0.998460 + 0.0554761i
\(92\) 32.3151 3.36908
\(93\) 4.22478i 0.438089i
\(94\) −8.97832 15.5509i −0.926043 1.60395i
\(95\) −15.8334 −1.62448
\(96\) 2.75400 1.59002i 0.281079 0.162281i
\(97\) −5.02047 + 2.89857i −0.509751 + 0.294305i −0.732731 0.680518i \(-0.761755\pi\)
0.222980 + 0.974823i \(0.428421\pi\)
\(98\) −0.628552 + 17.5518i −0.0634934 + 1.77300i
\(99\) 5.02500i 0.505031i
\(100\) −14.5214 + 25.1518i −1.45214 + 2.51518i
\(101\) 2.10772 + 3.65067i 0.209726 + 0.363256i 0.951628 0.307252i \(-0.0994095\pi\)
−0.741902 + 0.670508i \(0.766076\pi\)
\(102\) 0.433074 0.250035i 0.0428807 0.0247572i
\(103\) −2.11287 3.65960i −0.208187 0.360591i 0.742956 0.669340i \(-0.233423\pi\)
−0.951144 + 0.308749i \(0.900090\pi\)
\(104\) 20.7475 + 0.780612i 2.03446 + 0.0765453i
\(105\) 4.67679 7.77565i 0.456408 0.758825i
\(106\) 0.938336 + 0.541749i 0.0911393 + 0.0526193i
\(107\) 4.65458 0.449975 0.224988 0.974362i \(-0.427766\pi\)
0.224988 + 0.974362i \(0.427766\pi\)
\(108\) 4.29509 0.413296
\(109\) −0.524968 0.303090i −0.0502828 0.0290308i 0.474648 0.880176i \(-0.342575\pi\)
−0.524931 + 0.851145i \(0.675909\pi\)
\(110\) −37.4460 21.6195i −3.57034 2.06134i
\(111\) −7.89731 + 4.55951i −0.749580 + 0.432770i
\(112\) −0.277366 + 15.4954i −0.0262086 + 1.46418i
\(113\) −4.15517 7.19697i −0.390886 0.677034i 0.601681 0.798737i \(-0.294498\pi\)
−0.992567 + 0.121703i \(0.961165\pi\)
\(114\) 11.5835 1.08489
\(115\) 22.3461 12.9015i 2.08378 1.20307i
\(116\) −6.80061 + 11.7790i −0.631421 + 1.09365i
\(117\) 3.05251 + 1.91890i 0.282205 + 0.177402i
\(118\) 2.10319 0.193614
\(119\) −0.00943758 + 0.527241i −0.000865142 + 0.0483321i
\(120\) 9.87437 17.1029i 0.901403 1.56128i
\(121\) 7.12531 12.3414i 0.647755 1.12195i
\(122\) −5.79118 3.34354i −0.524309 0.302710i
\(123\) 5.39806i 0.486726i
\(124\) 15.7147 + 9.07290i 1.41122 + 0.814771i
\(125\) 6.04239i 0.540448i
\(126\) −3.42145 + 5.68852i −0.304807 + 0.506774i
\(127\) 5.03862 8.72715i 0.447105 0.774409i −0.551091 0.834445i \(-0.685788\pi\)
0.998196 + 0.0600359i \(0.0191215\pi\)
\(128\) 15.7351i 1.39080i
\(129\) −1.27860 + 2.21461i −0.112575 + 0.194985i
\(130\) 27.4326 14.4913i 2.40600 1.27097i
\(131\) 5.52188 + 9.56417i 0.482449 + 0.835626i 0.999797 0.0201493i \(-0.00641417\pi\)
−0.517348 + 0.855775i \(0.673081\pi\)
\(132\) 18.6913 + 10.7914i 1.62687 + 0.939273i
\(133\) −6.29574 + 10.4673i −0.545910 + 0.907632i
\(134\) 14.0189 + 24.2815i 1.21105 + 2.09760i
\(135\) 2.97008 1.71478i 0.255624 0.147585i
\(136\) 1.14771i 0.0984151i
\(137\) 11.3738i 0.971730i −0.874034 0.485865i \(-0.838505\pi\)
0.874034 0.485865i \(-0.161495\pi\)
\(138\) −16.3480 + 9.43851i −1.39163 + 0.803459i
\(139\) 8.76143 + 15.1752i 0.743135 + 1.28715i 0.951061 + 0.309003i \(0.0999954\pi\)
−0.207926 + 0.978145i \(0.566671\pi\)
\(140\) 18.8791 + 34.0946i 1.59558 + 2.88152i
\(141\) 6.19804 + 3.57844i 0.521969 + 0.301359i
\(142\) 7.17887 + 12.4342i 0.602437 + 1.04345i
\(143\) 8.46261 + 16.0201i 0.707679 + 1.33966i
\(144\) −2.92882 + 5.07287i −0.244068 + 0.422739i
\(145\) 10.8603i 0.901902i
\(146\) 3.95694 6.85362i 0.327479 0.567209i
\(147\) −3.28080 6.18355i −0.270596 0.510011i
\(148\) 39.1671i 3.21951i
\(149\) 10.2864 + 5.93887i 0.842696 + 0.486531i 0.858180 0.513349i \(-0.171595\pi\)
−0.0154836 + 0.999880i \(0.504929\pi\)
\(150\) 16.9655i 1.38523i
\(151\) −11.5380 6.66145i −0.938946 0.542101i −0.0493164 0.998783i \(-0.515704\pi\)
−0.889630 + 0.456682i \(0.849038\pi\)
\(152\) −13.2926 + 23.0234i −1.07817 + 1.86744i
\(153\) −0.0996552 + 0.172608i −0.00805664 + 0.0139545i
\(154\) −29.1818 + 16.1588i −2.35154 + 1.30211i
\(155\) 14.4891 1.16379
\(156\) −13.6931 + 7.23338i −1.09632 + 0.579134i
\(157\) 5.62062 9.73519i 0.448574 0.776953i −0.549719 0.835349i \(-0.685265\pi\)
0.998293 + 0.0583963i \(0.0185987\pi\)
\(158\) 9.80248 5.65947i 0.779844 0.450243i
\(159\) −0.431844 −0.0342474
\(160\) 5.45307 + 9.44500i 0.431103 + 0.746693i
\(161\) 0.356257 19.9027i 0.0280770 1.56855i
\(162\) −2.17286 + 1.25450i −0.170716 + 0.0985629i
\(163\) 3.14511 + 1.81583i 0.246344 + 0.142227i 0.618089 0.786108i \(-0.287907\pi\)
−0.371745 + 0.928335i \(0.621240\pi\)
\(164\) −20.0789 11.5926i −1.56790 0.905228i
\(165\) 17.2335 1.34163
\(166\) 36.9243 2.86588
\(167\) −8.95880 5.17237i −0.693253 0.400250i 0.111577 0.993756i \(-0.464410\pi\)
−0.804829 + 0.593506i \(0.797743\pi\)
\(168\) −7.38028 13.3284i −0.569401 1.02831i
\(169\) −12.9632 0.976850i −0.997173 0.0751423i
\(170\) 0.857510 + 1.48525i 0.0657680 + 0.113913i
\(171\) −3.99823 + 2.30838i −0.305752 + 0.176526i
\(172\) −5.49172 9.51194i −0.418740 0.725279i
\(173\) 2.29902 3.98202i 0.174791 0.302747i −0.765298 0.643676i \(-0.777408\pi\)
0.940089 + 0.340929i \(0.110742\pi\)
\(174\) 7.94523i 0.602326i
\(175\) 15.3308 + 9.22095i 1.15890 + 0.697038i
\(176\) −25.4911 + 14.7173i −1.92147 + 1.10936i
\(177\) −0.725951 + 0.419128i −0.0545658 + 0.0315036i
\(178\) −5.88633 −0.441199
\(179\) −0.453209 0.784982i −0.0338745 0.0586723i 0.848591 0.529049i \(-0.177451\pi\)
−0.882466 + 0.470377i \(0.844118\pi\)
\(180\) 14.7303i 1.09793i
\(181\) −18.9155 −1.40598 −0.702991 0.711199i \(-0.748152\pi\)
−0.702991 + 0.711199i \(0.748152\pi\)
\(182\) 1.32779 23.8975i 0.0984220 1.77140i
\(183\) 2.66523 0.197020
\(184\) 43.3245i 3.19393i
\(185\) −15.6371 27.0843i −1.14966 1.99128i
\(186\) −10.6000 −0.777228
\(187\) −0.867354 + 0.500767i −0.0634272 + 0.0366197i
\(188\) −26.6212 + 15.3697i −1.94155 + 1.12095i
\(189\) 0.0473512 2.64533i 0.00344429 0.192419i
\(190\) 39.7261i 2.88203i
\(191\) −7.70584 + 13.3469i −0.557575 + 0.965749i 0.440123 + 0.897938i \(0.354935\pi\)
−0.997698 + 0.0678112i \(0.978398\pi\)
\(192\) 1.86827 + 3.23594i 0.134831 + 0.233534i
\(193\) 6.89839 3.98279i 0.496557 0.286688i −0.230733 0.973017i \(-0.574113\pi\)
0.727291 + 0.686330i \(0.240779\pi\)
\(194\) 7.27252 + 12.5964i 0.522136 + 0.904366i
\(195\) −6.58098 + 10.4688i −0.471273 + 0.749683i
\(196\) 30.0464 + 1.07600i 2.14617 + 0.0768573i
\(197\) −11.3638 6.56087i −0.809634 0.467443i 0.0371945 0.999308i \(-0.488158\pi\)
−0.846829 + 0.531865i \(0.821491\pi\)
\(198\) −12.6077 −0.895993
\(199\) 19.5203 1.38375 0.691877 0.722015i \(-0.256784\pi\)
0.691877 + 0.722015i \(0.256784\pi\)
\(200\) 33.7208 + 19.4687i 2.38442 + 1.37665i
\(201\) −9.67775 5.58745i −0.682616 0.394108i
\(202\) 9.15955 5.28827i 0.644464 0.372081i
\(203\) 7.17966 + 4.31832i 0.503913 + 0.303087i
\(204\) −0.428028 0.741367i −0.0299680 0.0519061i
\(205\) −18.5129 −1.29300
\(206\) −9.18195 + 5.30120i −0.639737 + 0.369352i
\(207\) 3.76186 6.51573i 0.261467 0.452875i
\(208\) 0.794065 21.1051i 0.0550585 1.46337i
\(209\) −23.1992 −1.60472
\(210\) −19.5091 11.7341i −1.34626 0.809728i
\(211\) −11.9554 + 20.7074i −0.823046 + 1.42556i 0.0803582 + 0.996766i \(0.474394\pi\)
−0.903404 + 0.428791i \(0.858940\pi\)
\(212\) 0.927405 1.60631i 0.0636944 0.110322i
\(213\) −4.95582 2.86124i −0.339567 0.196049i
\(214\) 11.6784i 0.798316i
\(215\) −7.59512 4.38504i −0.517983 0.299057i
\(216\) 5.75840i 0.391809i
\(217\) 5.76120 9.57860i 0.391096 0.650238i
\(218\) −0.760454 + 1.31715i −0.0515045 + 0.0892083i
\(219\) 3.15419i 0.213141i
\(220\) −37.0098 + 64.1028i −2.49520 + 4.32181i
\(221\) 0.0270186 0.718116i 0.00181747 0.0483057i
\(222\) 11.4398 + 19.8144i 0.767791 + 1.32985i
\(223\) 9.03870 + 5.21849i 0.605276 + 0.349456i 0.771114 0.636697i \(-0.219700\pi\)
−0.165838 + 0.986153i \(0.553033\pi\)
\(224\) 8.41226 + 0.150579i 0.562068 + 0.0100610i
\(225\) 3.38093 + 5.85594i 0.225395 + 0.390396i
\(226\) −18.0572 + 10.4253i −1.20115 + 0.693483i
\(227\) 9.90050i 0.657119i 0.944483 + 0.328560i \(0.106563\pi\)
−0.944483 + 0.328560i \(0.893437\pi\)
\(228\) 19.8294i 1.31323i
\(229\) −13.6564 + 7.88453i −0.902441 + 0.521025i −0.877991 0.478676i \(-0.841117\pi\)
−0.0244498 + 0.999701i \(0.507783\pi\)
\(230\) −32.3699 56.0663i −2.13441 3.69690i
\(231\) 6.85245 11.3929i 0.450858 0.749598i
\(232\) 15.7920 + 9.11752i 1.03680 + 0.598595i
\(233\) −0.952488 1.64976i −0.0623996 0.108079i 0.833138 0.553065i \(-0.186542\pi\)
−0.895538 + 0.444986i \(0.853209\pi\)
\(234\) 4.81452 7.65876i 0.314735 0.500669i
\(235\) −12.2725 + 21.2565i −0.800567 + 1.38662i
\(236\) 3.60039i 0.234365i
\(237\) −2.25566 + 3.90692i −0.146521 + 0.253782i
\(238\) 1.32285 + 0.0236789i 0.0857476 + 0.00153488i
\(239\) 26.3087i 1.70177i 0.525352 + 0.850885i \(0.323934\pi\)
−0.525352 + 0.850885i \(0.676066\pi\)
\(240\) −17.3977 10.0446i −1.12302 0.648373i
\(241\) 22.5867i 1.45494i 0.686139 + 0.727470i \(0.259304\pi\)
−0.686139 + 0.727470i \(0.740696\pi\)
\(242\) −30.9646 17.8774i −1.99048 1.14920i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.72371 + 9.91376i −0.366423 + 0.634664i
\(245\) 21.2068 11.2517i 1.35486 0.718845i
\(246\) 13.5437 0.863517
\(247\) 8.85909 14.0927i 0.563691 0.896697i
\(248\) 12.1640 21.0686i 0.772412 1.33786i
\(249\) −12.7451 + 7.35837i −0.807686 + 0.466318i
\(250\) 15.1604 0.958827
\(251\) 14.4466 + 25.0222i 0.911859 + 1.57939i 0.811436 + 0.584442i \(0.198686\pi\)
0.100424 + 0.994945i \(0.467980\pi\)
\(252\) 9.73803 + 5.85709i 0.613438 + 0.368962i
\(253\) 32.7415 18.9033i 2.05844 1.18844i
\(254\) −21.8964 12.6419i −1.37390 0.793224i
\(255\) −0.591968 0.341773i −0.0370705 0.0214027i
\(256\) −32.0063 −2.00039
\(257\) 16.0503 1.00119 0.500595 0.865682i \(-0.333115\pi\)
0.500595 + 0.865682i \(0.333115\pi\)
\(258\) 5.55645 + 3.20802i 0.345930 + 0.199723i
\(259\) −24.1228 0.431797i −1.49892 0.0268305i
\(260\) −24.8073 46.9611i −1.53848 2.91241i
\(261\) 1.58334 + 2.74243i 0.0980065 + 0.169752i
\(262\) 23.9965 13.8544i 1.48251 0.855928i
\(263\) −7.23551 12.5323i −0.446161 0.772773i 0.551972 0.833863i \(-0.313876\pi\)
−0.998132 + 0.0610900i \(0.980542\pi\)
\(264\) 14.4680 25.0593i 0.890442 1.54229i
\(265\) 1.48103i 0.0909791i
\(266\) 26.2625 + 15.7960i 1.61026 + 0.968516i
\(267\) 2.03177 1.17304i 0.124342 0.0717890i
\(268\) 41.5668 23.9986i 2.53910 1.46595i
\(269\) 16.2953 0.993542 0.496771 0.867882i \(-0.334519\pi\)
0.496771 + 0.867882i \(0.334519\pi\)
\(270\) −4.30238 7.45195i −0.261835 0.453511i
\(271\) 11.2296i 0.682153i −0.940036 0.341076i \(-0.889209\pi\)
0.940036 0.341076i \(-0.110791\pi\)
\(272\) 1.16749 0.0707894
\(273\) 4.30404 + 8.51324i 0.260493 + 0.515245i
\(274\) −28.5369 −1.72398
\(275\) 33.9783i 2.04897i
\(276\) 16.1575 + 27.9857i 0.972569 + 1.68454i
\(277\) −19.2059 −1.15397 −0.576984 0.816755i \(-0.695771\pi\)
−0.576984 + 0.816755i \(0.695771\pi\)
\(278\) 38.0747 21.9825i 2.28357 1.31842i
\(279\) 3.65876 2.11239i 0.219044 0.126465i
\(280\) 45.7104 25.3111i 2.73172 1.51263i
\(281\) 21.4527i 1.27976i 0.768474 + 0.639881i \(0.221016\pi\)
−0.768474 + 0.639881i \(0.778984\pi\)
\(282\) 8.97832 15.5509i 0.534651 0.926043i
\(283\) −4.10738 7.11419i −0.244159 0.422895i 0.717736 0.696315i \(-0.245178\pi\)
−0.961895 + 0.273420i \(0.911845\pi\)
\(284\) 21.2857 12.2893i 1.26307 0.729236i
\(285\) −7.91671 13.7121i −0.468946 0.812238i
\(286\) 40.1944 21.2327i 2.37674 1.25552i
\(287\) −7.36118 + 12.2387i −0.434516 + 0.722429i
\(288\) 2.75400 + 1.59002i 0.162281 + 0.0936930i
\(289\) −16.9603 −0.997663
\(290\) 27.2486 1.60009
\(291\) −5.02047 2.89857i −0.294305 0.169917i
\(292\) −11.7325 6.77378i −0.686594 0.396405i
\(293\) 8.05762 4.65207i 0.470731 0.271777i −0.245815 0.969317i \(-0.579055\pi\)
0.716546 + 0.697540i \(0.245722\pi\)
\(294\) −15.5146 + 8.23154i −0.904827 + 0.480073i
\(295\) −1.43742 2.48969i −0.0836901 0.144955i
\(296\) −52.5110 −3.05214
\(297\) 4.35178 2.51250i 0.252516 0.145790i
\(298\) 14.9006 25.8086i 0.863170 1.49505i
\(299\) −1.01992 + 27.1080i −0.0589835 + 1.56769i
\(300\) −29.0428 −1.67679
\(301\) −5.91890 + 3.27746i −0.341160 + 0.188910i
\(302\) −16.7136 + 28.9488i −0.961759 + 1.66582i
\(303\) −2.10772 + 3.65067i −0.121085 + 0.209726i
\(304\) 23.4202 + 13.5216i 1.34324 + 0.775520i
\(305\) 9.14057i 0.523388i
\(306\) 0.433074 + 0.250035i 0.0247572 + 0.0142936i
\(307\) 17.3759i 0.991695i −0.868410 0.495848i \(-0.834857\pi\)
0.868410 0.495848i \(-0.165143\pi\)
\(308\) 27.6618 + 49.9556i 1.57618 + 2.84648i
\(309\) 2.11287 3.65960i 0.120197 0.208187i
\(310\) 36.3532i 2.06472i
\(311\) −2.53895 + 4.39760i −0.143971 + 0.249365i −0.928988 0.370109i \(-0.879320\pi\)
0.785018 + 0.619473i \(0.212654\pi\)
\(312\) 9.69773 + 18.3582i 0.549026 + 1.03933i
\(313\) −3.64621 6.31543i −0.206096 0.356969i 0.744385 0.667750i \(-0.232743\pi\)
−0.950481 + 0.310781i \(0.899409\pi\)
\(314\) −24.4256 14.1021i −1.37842 0.795830i
\(315\) 9.07230 + 0.162394i 0.511166 + 0.00914984i
\(316\) −9.68829 16.7806i −0.545009 0.943983i
\(317\) −20.5617 + 11.8713i −1.15486 + 0.666757i −0.950066 0.312048i \(-0.898985\pi\)
−0.204791 + 0.978806i \(0.565652\pi\)
\(318\) 1.08350i 0.0607595i
\(319\) 15.9126i 0.890935i
\(320\) −11.0978 + 6.40734i −0.620388 + 0.358181i
\(321\) 2.32729 + 4.03099i 0.129897 + 0.224988i
\(322\) −49.9359 0.893849i −2.78282 0.0498123i
\(323\) 0.796888 + 0.460084i 0.0443401 + 0.0255997i
\(324\) 2.14755 + 3.71966i 0.119308 + 0.206648i
\(325\) −20.6406 12.9753i −1.14494 0.719742i
\(326\) 4.55593 7.89110i 0.252330 0.437048i
\(327\) 0.606180i 0.0335219i
\(328\) −15.5421 + 26.9197i −0.858167 + 1.48639i
\(329\) 9.17266 + 16.5653i 0.505705 + 0.913274i
\(330\) 43.2389i 2.38023i
\(331\) −0.0199341 0.0115089i −0.00109568 0.000632589i 0.499452 0.866342i \(-0.333535\pi\)
−0.500548 + 0.865709i \(0.666868\pi\)
\(332\) 63.2097i 3.46909i
\(333\) −7.89731 4.55951i −0.432770 0.249860i
\(334\) −12.9775 + 22.4777i −0.710096 + 1.22992i
\(335\) 19.1625 33.1904i 1.04696 1.81338i
\(336\) −13.5581 + 7.50748i −0.739654 + 0.409567i
\(337\) 12.3103 0.670583 0.335291 0.942114i \(-0.391165\pi\)
0.335291 + 0.942114i \(0.391165\pi\)
\(338\) −2.45092 + 32.5248i −0.133312 + 1.76912i
\(339\) 4.15517 7.19697i 0.225678 0.390886i
\(340\) 2.54256 1.46795i 0.137890 0.0796106i
\(341\) 21.2295 1.14964
\(342\) 5.79173 + 10.0316i 0.313181 + 0.542445i
\(343\) 0.993950 18.4936i 0.0536683 0.998559i
\(344\) −12.7526 + 7.36270i −0.687573 + 0.396970i
\(345\) 22.3461 + 12.9015i 1.20307 + 0.694594i
\(346\) −9.99089 5.76824i −0.537114 0.310103i
\(347\) 31.5302 1.69263 0.846315 0.532683i \(-0.178816\pi\)
0.846315 + 0.532683i \(0.178816\pi\)
\(348\) −13.6012 −0.729102
\(349\) 1.69290 + 0.977398i 0.0906191 + 0.0523189i 0.544625 0.838680i \(-0.316672\pi\)
−0.454006 + 0.890999i \(0.650005\pi\)
\(350\) 23.1354 38.4650i 1.23664 2.05604i
\(351\) −0.135561 + 3.60300i −0.00723569 + 0.192314i
\(352\) 7.98986 + 13.8388i 0.425861 + 0.737613i
\(353\) −14.1302 + 8.15806i −0.752073 + 0.434210i −0.826442 0.563021i \(-0.809639\pi\)
0.0743694 + 0.997231i \(0.476306\pi\)
\(354\) 1.05159 + 1.82141i 0.0558916 + 0.0968070i
\(355\) 9.81280 16.9963i 0.520809 0.902068i
\(356\) 10.0766i 0.534061i
\(357\) −0.461323 + 0.255447i −0.0244158 + 0.0135197i
\(358\) −1.96952 + 1.13710i −0.104092 + 0.0600978i
\(359\) 19.2335 11.1044i 1.01510 0.586070i 0.102421 0.994741i \(-0.467341\pi\)
0.912682 + 0.408671i \(0.134008\pi\)
\(360\) 19.7487 1.04085
\(361\) 1.15722 + 2.00436i 0.0609062 + 0.105493i
\(362\) 47.4592i 2.49440i
\(363\) 14.2506 0.747963
\(364\) −40.9095 2.27300i −2.14424 0.119138i
\(365\) −10.8175 −0.566213
\(366\) 6.68708i 0.349539i
\(367\) 4.00293 + 6.93327i 0.208951 + 0.361914i 0.951384 0.308006i \(-0.0996617\pi\)
−0.742433 + 0.669920i \(0.766328\pi\)
\(368\) −44.0712 −2.29737
\(369\) −4.67486 + 2.69903i −0.243363 + 0.140506i
\(370\) −67.9545 + 39.2336i −3.53279 + 2.03966i
\(371\) −0.979096 0.588893i −0.0508321 0.0305738i
\(372\) 18.1458i 0.940816i
\(373\) −14.9023 + 25.8116i −0.771614 + 1.33647i 0.165065 + 0.986283i \(0.447217\pi\)
−0.936678 + 0.350191i \(0.886117\pi\)
\(374\) 1.25643 + 2.17619i 0.0649683 + 0.112528i
\(375\) −5.23287 + 3.02120i −0.270224 + 0.156014i
\(376\) 20.6061 + 35.6908i 1.06268 + 1.84061i
\(377\) −9.66635 6.07656i −0.497842 0.312959i
\(378\) −6.63713 0.118804i −0.341377 0.00611063i
\(379\) 9.17101 + 5.29489i 0.471083 + 0.271980i 0.716693 0.697389i \(-0.245655\pi\)
−0.245610 + 0.969369i \(0.578988\pi\)
\(380\) 68.0060 3.48864
\(381\) 10.0772 0.516273
\(382\) 33.4874 + 19.3340i 1.71337 + 0.989213i
\(383\) −24.0899 13.9083i −1.23094 0.710681i −0.263711 0.964602i \(-0.584947\pi\)
−0.967225 + 0.253920i \(0.918280\pi\)
\(384\) 13.6270 7.86754i 0.695399 0.401489i
\(385\) 39.0726 + 23.5009i 1.99132 + 1.19771i
\(386\) −9.99283 17.3081i −0.508622 0.880959i
\(387\) −2.55721 −0.129990
\(388\) 21.5634 12.4496i 1.09471 0.632034i
\(389\) −10.2034 + 17.6728i −0.517331 + 0.896044i 0.482466 + 0.875915i \(0.339741\pi\)
−0.999797 + 0.0201295i \(0.993592\pi\)
\(390\) 26.2661 + 16.5117i 1.33004 + 0.836102i
\(391\) −1.49955 −0.0758357
\(392\) 1.44259 40.2829i 0.0728616 2.03460i
\(393\) −5.52188 + 9.56417i −0.278542 + 0.482449i
\(394\) −16.4612 + 28.5117i −0.829305 + 1.43640i
\(395\) −13.3990 7.73593i −0.674178 0.389237i
\(396\) 21.5828i 1.08458i
\(397\) −12.1438 7.01122i −0.609479 0.351883i 0.163282 0.986579i \(-0.447792\pi\)
−0.772762 + 0.634696i \(0.781125\pi\)
\(398\) 48.9764i 2.45496i
\(399\) −12.2128 0.218609i −0.611406 0.0109441i
\(400\) 19.8043 34.3020i 0.990213 1.71510i
\(401\) 5.30040i 0.264689i −0.991204 0.132345i \(-0.957749\pi\)
0.991204 0.132345i \(-0.0422506\pi\)
\(402\) −14.0189 + 24.2815i −0.699201 + 1.21105i
\(403\) −8.10692 + 12.8962i −0.403835 + 0.642404i
\(404\) −9.05284 15.6800i −0.450396 0.780108i
\(405\) 2.97008 + 1.71478i 0.147585 + 0.0852080i
\(406\) 10.8347 18.0138i 0.537716 0.894009i
\(407\) −22.9116 39.6840i −1.13568 1.96706i
\(408\) −0.993944 + 0.573854i −0.0492076 + 0.0284100i
\(409\) 29.0175i 1.43482i −0.696649 0.717412i \(-0.745327\pi\)
0.696649 0.717412i \(-0.254673\pi\)
\(410\) 46.4490i 2.29395i
\(411\) 9.85001 5.68690i 0.485865 0.280514i
\(412\) 9.07498 + 15.7183i 0.447092 + 0.774387i
\(413\) −2.21746 0.0396924i −0.109114 0.00195314i
\(414\) −16.3480 9.43851i −0.803459 0.463878i
\(415\) −25.2359 43.7099i −1.23878 2.14564i
\(416\) −11.4577 0.431089i −0.561760 0.0211359i
\(417\) −8.76143 + 15.1752i −0.429049 + 0.743135i
\(418\) 58.2068i 2.84699i
\(419\) −6.43099 + 11.1388i −0.314174 + 0.544166i −0.979262 0.202600i \(-0.935061\pi\)
0.665087 + 0.746766i \(0.268394\pi\)
\(420\) −20.0872 + 33.3971i −0.980157 + 1.62961i
\(421\) 5.25836i 0.256277i −0.991756 0.128138i \(-0.959100\pi\)
0.991756 0.128138i \(-0.0409002\pi\)
\(422\) 51.9549 + 29.9962i 2.52913 + 1.46019i
\(423\) 7.15688i 0.347980i
\(424\) −2.15357 1.24336i −0.104587 0.0603831i
\(425\) 0.673854 1.16715i 0.0326867 0.0566151i
\(426\) −7.17887 + 12.4342i −0.347817 + 0.602437i
\(427\) 6.04274 + 3.63450i 0.292429 + 0.175886i
\(428\) −19.9919 −0.966343
\(429\) −9.64247 + 15.3389i −0.465543 + 0.740567i
\(430\) −11.0021 + 19.0562i −0.530568 + 0.918970i
\(431\) 21.4053 12.3584i 1.03106 0.595281i 0.113770 0.993507i \(-0.463707\pi\)
0.917287 + 0.398226i \(0.130374\pi\)
\(432\) −5.85764 −0.281826
\(433\) 10.8239 + 18.7476i 0.520166 + 0.900953i 0.999725 + 0.0234439i \(0.00746310\pi\)
−0.479560 + 0.877509i \(0.659204\pi\)
\(434\) −24.0327 14.4549i −1.15361 0.693856i
\(435\) −9.40533 + 5.43017i −0.450951 + 0.260357i
\(436\) 2.25479 + 1.30180i 0.107985 + 0.0623450i
\(437\) −30.0815 17.3676i −1.43899 0.830804i
\(438\) 7.91388 0.378140
\(439\) −7.75058 −0.369915 −0.184957 0.982747i \(-0.559215\pi\)
−0.184957 + 0.982747i \(0.559215\pi\)
\(440\) 85.9421 + 49.6187i 4.09713 + 2.36548i
\(441\) 3.71471 5.93303i 0.176891 0.282525i
\(442\) −1.80175 0.0677898i −0.0857007 0.00322443i
\(443\) 3.55156 + 6.15148i 0.168740 + 0.292265i 0.937977 0.346698i \(-0.112697\pi\)
−0.769237 + 0.638963i \(0.779364\pi\)
\(444\) 33.9197 19.5835i 1.60976 0.929394i
\(445\) 4.02301 + 6.96806i 0.190709 + 0.330318i
\(446\) 13.0932 22.6781i 0.619982 1.07384i
\(447\) 11.8777i 0.561797i
\(448\) −0.176930 + 9.88437i −0.00835914 + 0.466993i
\(449\) 25.1353 14.5119i 1.18621 0.684858i 0.228767 0.973481i \(-0.426531\pi\)
0.957443 + 0.288623i \(0.0931974\pi\)
\(450\) 14.6926 8.48276i 0.692614 0.399881i
\(451\) −27.1252 −1.27728
\(452\) 17.8469 + 30.9117i 0.839445 + 1.45396i
\(453\) 13.3229i 0.625964i
\(454\) 24.8404 1.16582
\(455\) −29.1966 + 14.7610i −1.36876 + 0.692004i
\(456\) −26.5851 −1.24496
\(457\) 27.0304i 1.26443i −0.774794 0.632213i \(-0.782147\pi\)
0.774794 0.632213i \(-0.217853\pi\)
\(458\) 19.7823 + 34.2640i 0.924367 + 1.60105i
\(459\) −0.199310 −0.00930301
\(460\) −95.9784 + 55.4132i −4.47502 + 2.58365i
\(461\) 2.16474 1.24981i 0.100822 0.0582096i −0.448741 0.893662i \(-0.648127\pi\)
0.549563 + 0.835452i \(0.314794\pi\)
\(462\) −28.5848 17.1928i −1.32989 0.799882i
\(463\) 28.9351i 1.34473i −0.740222 0.672363i \(-0.765279\pi\)
0.740222 0.672363i \(-0.234721\pi\)
\(464\) 9.27466 16.0642i 0.430565 0.745761i
\(465\) 7.24455 + 12.5479i 0.335958 + 0.581897i
\(466\) −4.13925 + 2.38979i −0.191747 + 0.110705i
\(467\) −4.23383 7.33321i −0.195918 0.339340i 0.751283 0.659980i \(-0.229435\pi\)
−0.947201 + 0.320640i \(0.896102\pi\)
\(468\) −13.1108 8.24185i −0.606048 0.380980i
\(469\) −14.3224 25.8654i −0.661346 1.19435i
\(470\) 53.3327 + 30.7917i 2.46005 + 1.42031i
\(471\) 11.2412 0.517969
\(472\) −4.82701 −0.222181
\(473\) −11.1284 6.42498i −0.511684 0.295421i
\(474\) 9.80248 + 5.65947i 0.450243 + 0.259948i
\(475\) 27.0355 15.6089i 1.24047 0.716187i
\(476\) 0.0405353 2.26455i 0.00185793 0.103795i
\(477\) −0.215922 0.373988i −0.00988639 0.0171237i
\(478\) 66.0087 3.01917
\(479\) 20.7557 11.9833i 0.948351 0.547531i 0.0557827 0.998443i \(-0.482235\pi\)
0.892568 + 0.450912i \(0.148901\pi\)
\(480\) −5.45307 + 9.44500i −0.248898 + 0.431103i
\(481\) 32.8559 + 1.23618i 1.49810 + 0.0563650i
\(482\) 56.6702 2.58126
\(483\) 17.4144 9.64282i 0.792381 0.438763i
\(484\) −30.6039 + 53.0075i −1.39108 + 2.40943i
\(485\) 9.94081 17.2180i 0.451389 0.781828i
\(486\) −2.17286 1.25450i −0.0985629 0.0569053i
\(487\) 36.7256i 1.66420i 0.554628 + 0.832099i \(0.312861\pi\)
−0.554628 + 0.832099i \(0.687139\pi\)
\(488\) 13.2913 + 7.67373i 0.601669 + 0.347374i
\(489\) 3.63167i 0.164230i
\(490\) −28.2305 53.2080i −1.27533 2.40369i
\(491\) 4.83577 8.37579i 0.218235 0.377994i −0.736033 0.676945i \(-0.763303\pi\)
0.954268 + 0.298951i \(0.0966367\pi\)
\(492\) 23.1852i 1.04527i
\(493\) 0.315577 0.546595i 0.0142129 0.0246174i
\(494\) −35.3586 22.2275i −1.59086 1.00006i
\(495\) 8.61676 + 14.9247i 0.387295 + 0.670814i
\(496\) −21.4317 12.3736i −0.962313 0.555591i
\(497\) −7.33426 13.2453i −0.328987 0.594131i
\(498\) 18.4622 + 31.9774i 0.827309 + 1.43294i
\(499\) −24.0357 + 13.8770i −1.07599 + 0.621221i −0.929811 0.368037i \(-0.880030\pi\)
−0.146176 + 0.989259i \(0.546697\pi\)
\(500\) 25.9526i 1.16064i
\(501\) 10.3447i 0.462169i
\(502\) 62.7807 36.2465i 2.80204 1.61776i
\(503\) 6.56936 + 11.3785i 0.292913 + 0.507341i 0.974497 0.224399i \(-0.0720419\pi\)
−0.681584 + 0.731740i \(0.738709\pi\)
\(504\) 7.85256 13.0557i 0.349781 0.581547i
\(505\) −12.5202 7.22854i −0.557141 0.321666i
\(506\) −47.4285 82.1486i −2.10845 3.65195i
\(507\) −5.63565 11.7149i −0.250288 0.520278i
\(508\) −21.6414 + 37.4839i −0.960180 + 1.66308i
\(509\) 29.1555i 1.29230i −0.763212 0.646148i \(-0.776379\pi\)
0.763212 0.646148i \(-0.223621\pi\)
\(510\) −0.857510 + 1.48525i −0.0379712 + 0.0657680i
\(511\) −4.30128 + 7.15133i −0.190277 + 0.316356i
\(512\) 48.8337i 2.15816i
\(513\) −3.99823 2.30838i −0.176526 0.101917i
\(514\) 40.2702i 1.77624i
\(515\) 12.5508 + 7.24621i 0.553055 + 0.319306i
\(516\) 5.49172 9.51194i 0.241760 0.418740i
\(517\) −17.9817 + 31.1452i −0.790833 + 1.36976i
\(518\) −1.08338 + 60.5242i −0.0476010 + 2.65928i
\(519\) 4.59804 0.201831
\(520\) −62.9604 + 33.2589i −2.76100 + 1.45850i
\(521\) 7.62747 13.2112i 0.334166 0.578792i −0.649159 0.760653i \(-0.724879\pi\)
0.983324 + 0.181861i \(0.0582122\pi\)
\(522\) 6.88077 3.97261i 0.301163 0.173877i
\(523\) −24.9370 −1.09042 −0.545209 0.838300i \(-0.683550\pi\)
−0.545209 + 0.838300i \(0.683550\pi\)
\(524\) −23.7170 41.0790i −1.03608 1.79454i
\(525\) −0.320182 + 17.8873i −0.0139739 + 0.780667i
\(526\) −31.4435 + 18.1539i −1.37100 + 0.791548i
\(527\) −0.729229 0.421021i −0.0317657 0.0183400i
\(528\) −25.4911 14.7173i −1.10936 0.640489i
\(529\) 33.6063 1.46114
\(530\) −3.71592 −0.161409
\(531\) −0.725951 0.419128i −0.0315036 0.0181886i
\(532\) 27.0408 44.9581i 1.17237 1.94918i
\(533\) 10.3583 16.4776i 0.448669 0.713725i
\(534\) −2.94316 5.09771i −0.127363 0.220600i
\(535\) −13.8245 + 7.98158i −0.597685 + 0.345074i
\(536\) −32.1748 55.7283i −1.38974 2.40710i
\(537\) 0.453209 0.784982i 0.0195574 0.0338745i
\(538\) 40.8849i 1.76267i
\(539\) 31.0724 16.4860i 1.33838 0.710104i
\(540\) −12.7568 + 7.36513i −0.548965 + 0.316945i
\(541\) −21.8817 + 12.6334i −0.940767 + 0.543152i −0.890201 0.455569i \(-0.849436\pi\)
−0.0505664 + 0.998721i \(0.516103\pi\)
\(542\) −28.1752 −1.21023
\(543\) −9.45777 16.3813i −0.405872 0.702991i
\(544\) 0.633816i 0.0271746i
\(545\) 2.07893 0.0890516
\(546\) 21.3597 10.7989i 0.914112 0.462148i
\(547\) 31.0477 1.32750 0.663752 0.747953i \(-0.268963\pi\)
0.663752 + 0.747953i \(0.268963\pi\)
\(548\) 48.8516i 2.08684i
\(549\) 1.33262 + 2.30816i 0.0568747 + 0.0985099i
\(550\) 85.2517 3.63515
\(551\) 12.6611 7.30991i 0.539383 0.311413i
\(552\) 37.5201 21.6623i 1.59696 0.922007i
\(553\) −10.4419 + 5.78197i −0.444035 + 0.245874i
\(554\) 48.1876i 2.04729i
\(555\) 15.6371 27.0843i 0.663759 1.14966i
\(556\) −37.6312 65.1791i −1.59592 2.76421i
\(557\) 22.2174 12.8272i 0.941380 0.543506i 0.0509872 0.998699i \(-0.483763\pi\)
0.890393 + 0.455193i \(0.150430\pi\)
\(558\) −5.29999 9.17985i −0.224366 0.388614i
\(559\) 8.15256 4.30660i 0.344816 0.182150i
\(560\) −25.7473 46.4982i −1.08802 1.96491i
\(561\) −0.867354 0.500767i −0.0366197 0.0211424i
\(562\) 53.8249 2.27047
\(563\) 9.04397 0.381158 0.190579 0.981672i \(-0.438964\pi\)
0.190579 + 0.981672i \(0.438964\pi\)
\(564\) −26.6212 15.3697i −1.12095 0.647183i
\(565\) 24.6824 + 14.2504i 1.03840 + 0.599519i
\(566\) −17.8495 + 10.3054i −0.750272 + 0.433170i
\(567\) 2.31460 1.28166i 0.0972039 0.0538245i
\(568\) −16.4762 28.5376i −0.691325 1.19741i
\(569\) 43.9957 1.84440 0.922198 0.386719i \(-0.126391\pi\)
0.922198 + 0.386719i \(0.126391\pi\)
\(570\) −34.4038 + 19.8631i −1.44102 + 0.831972i
\(571\) −8.12709 + 14.0765i −0.340108 + 0.589085i −0.984453 0.175651i \(-0.943797\pi\)
0.644344 + 0.764735i \(0.277130\pi\)
\(572\) −36.3477 68.8076i −1.51977 2.87699i
\(573\) −15.4117 −0.643833
\(574\) 30.7070 + 18.4692i 1.28168 + 0.770890i
\(575\) −25.4372 + 44.0584i −1.06080 + 1.83736i
\(576\) −1.86827 + 3.23594i −0.0778446 + 0.134831i
\(577\) 2.00627 + 1.15832i 0.0835222 + 0.0482216i 0.541179 0.840907i \(-0.317978\pi\)
−0.457657 + 0.889129i \(0.651311\pi\)
\(578\) 42.5534i 1.76999i
\(579\) 6.89839 + 3.98279i 0.286688 + 0.165519i
\(580\) 46.6462i 1.93688i
\(581\) −38.9306 0.696855i −1.61511 0.0289104i
\(582\) −7.27252 + 12.5964i −0.301455 + 0.522136i
\(583\) 2.17001i 0.0898728i
\(584\) −9.08154 + 15.7297i −0.375797 + 0.650899i
\(585\) −12.3567 0.464913i −0.510887 0.0192218i
\(586\) −11.6720 20.2166i −0.482168 0.835139i
\(587\) −29.7041 17.1497i −1.22602 0.707843i −0.259825 0.965656i \(-0.583665\pi\)
−0.966195 + 0.257813i \(0.916998\pi\)
\(588\) 14.0914 + 26.5589i 0.581118 + 1.09527i
\(589\) −9.75238 16.8916i −0.401840 0.696007i
\(590\) −6.24664 + 3.60650i −0.257170 + 0.148477i
\(591\) 13.1217i 0.539756i
\(592\) 53.4160i 2.19538i
\(593\) −21.2551 + 12.2717i −0.872844 + 0.503937i −0.868292 0.496053i \(-0.834782\pi\)
−0.00455184 + 0.999990i \(0.501449\pi\)
\(594\) −6.30387 10.9186i −0.258651 0.447996i
\(595\) −0.876071 1.58213i −0.0359154 0.0648612i
\(596\) −44.1811 25.5080i −1.80973 1.04485i
\(597\) 9.76013 + 16.9050i 0.399456 + 0.691877i
\(598\) 68.0140 + 2.55898i 2.78130 + 0.104644i
\(599\) 8.47361 14.6767i 0.346222 0.599675i −0.639353 0.768914i \(-0.720798\pi\)
0.985575 + 0.169239i \(0.0541309\pi\)
\(600\) 38.9375i 1.58961i
\(601\) 20.0508 34.7290i 0.817888 1.41662i −0.0893467 0.996001i \(-0.528478\pi\)
0.907235 0.420624i \(-0.138189\pi\)
\(602\) 8.22316 + 14.8505i 0.335151 + 0.605263i
\(603\) 11.1749i 0.455077i
\(604\) 49.5566 + 28.6115i 2.01643 + 1.16419i
\(605\) 48.8733i 1.98698i
\(606\) 9.15955 + 5.28827i 0.372081 + 0.214821i
\(607\) 21.9043 37.9393i 0.889067 1.53991i 0.0480874 0.998843i \(-0.484687\pi\)
0.840980 0.541066i \(-0.181979\pi\)
\(608\) 7.34075 12.7145i 0.297707 0.515643i
\(609\) −0.149946 + 8.37693i −0.00607614 + 0.339450i
\(610\) 22.9337 0.928559
\(611\) −12.0529 22.8167i −0.487609 0.923063i
\(612\) 0.428028 0.741367i 0.0173020 0.0299680i
\(613\) −8.91783 + 5.14871i −0.360188 + 0.207954i −0.669163 0.743116i \(-0.733347\pi\)
0.308975 + 0.951070i \(0.400014\pi\)
\(614\) −43.5962 −1.75940
\(615\) −9.25647 16.0327i −0.373257 0.646500i
\(616\) 66.9750 37.0859i 2.69850 1.49423i
\(617\) 12.1246 7.00015i 0.488119 0.281815i −0.235675 0.971832i \(-0.575730\pi\)
0.723794 + 0.690017i \(0.242397\pi\)
\(618\) −9.18195 5.30120i −0.369352 0.213246i
\(619\) 25.0425 + 14.4583i 1.00654 + 0.581127i 0.910177 0.414219i \(-0.135945\pi\)
0.0963641 + 0.995346i \(0.469279\pi\)
\(620\) −62.2321 −2.49930
\(621\) 7.52372 0.301916
\(622\) 11.0336 + 6.37024i 0.442406 + 0.255423i
\(623\) 6.20616 + 0.111090i 0.248645 + 0.00445072i
\(624\) 18.6746 9.86487i 0.747581 0.394911i
\(625\) 6.54328 + 11.3333i 0.261731 + 0.453332i
\(626\) −15.8454 + 9.14836i −0.633310 + 0.365642i
\(627\) −11.5996 20.0911i −0.463243 0.802361i
\(628\) −24.1411 + 41.8136i −0.963334 + 1.66854i
\(629\) 1.81752i 0.0724692i
\(630\) 0.407446 22.7624i 0.0162330 0.906877i
\(631\) −36.5812 + 21.1202i −1.45628 + 0.840782i −0.998825 0.0484534i \(-0.984571\pi\)
−0.457451 + 0.889235i \(0.651237\pi\)
\(632\) −22.4976 + 12.9890i −0.894907 + 0.516675i
\(633\) −23.9109 −0.950371
\(634\) 29.7851 + 51.5892i 1.18292 + 2.04887i
\(635\) 34.5605i 1.37149i
\(636\) 1.85481 0.0735480
\(637\) −1.85094 + 25.1709i −0.0733368 + 0.997307i
\(638\) 39.9248 1.58064
\(639\) 5.72249i 0.226378i
\(640\) 26.9822 + 46.7345i 1.06656 + 1.84734i
\(641\) −22.6364 −0.894086 −0.447043 0.894512i \(-0.647523\pi\)
−0.447043 + 0.894512i \(0.647523\pi\)
\(642\) 10.1138 5.83918i 0.399158 0.230454i
\(643\) 21.1425 12.2066i 0.833778 0.481382i −0.0213662 0.999772i \(-0.506802\pi\)
0.855145 + 0.518389i \(0.173468\pi\)
\(644\) −1.53016 + 85.4839i −0.0602966 + 3.36854i
\(645\) 8.77009i 0.345322i
\(646\) 1.15435 1.99939i 0.0454173 0.0786651i
\(647\) 13.1968 + 22.8574i 0.518818 + 0.898619i 0.999761 + 0.0218670i \(0.00696104\pi\)
−0.480943 + 0.876752i \(0.659706\pi\)
\(648\) 4.98692 2.87920i 0.195905 0.113106i
\(649\) −2.10612 3.64790i −0.0826724 0.143193i
\(650\) −32.5551 + 51.7874i −1.27692 + 2.03127i
\(651\) 11.1759 + 0.200048i 0.438019 + 0.00784050i
\(652\) −13.5086 7.79917i −0.529036 0.305439i
\(653\) 15.9908 0.625766 0.312883 0.949792i \(-0.398705\pi\)
0.312883 + 0.949792i \(0.398705\pi\)
\(654\) −1.52091 −0.0594722
\(655\) −32.8009 18.9376i −1.28164 0.739953i
\(656\) 27.3836 + 15.8099i 1.06915 + 0.617275i
\(657\) −2.73161 + 1.57710i −0.106570 + 0.0615284i
\(658\) 41.5624 23.0142i 1.62027 0.897188i
\(659\) 1.71887 + 2.97717i 0.0669576 + 0.115974i 0.897561 0.440891i \(-0.145337\pi\)
−0.830603 + 0.556865i \(0.812004\pi\)
\(660\) −74.0196 −2.88121
\(661\) 7.12554 4.11393i 0.277151 0.160013i −0.354982 0.934873i \(-0.615513\pi\)
0.632133 + 0.774860i \(0.282180\pi\)
\(662\) −0.0288760 + 0.0500147i −0.00112230 + 0.00194388i
\(663\) 0.635416 0.335659i 0.0246775 0.0130359i
\(664\) −84.7448 −3.28873
\(665\) 0.749731 41.8846i 0.0290733 1.62422i
\(666\) −11.4398 + 19.8144i −0.443285 + 0.767791i
\(667\) −11.9126 + 20.6333i −0.461259 + 0.798924i
\(668\) 38.4789 + 22.2158i 1.48879 + 0.859555i
\(669\) 10.4370i 0.403517i
\(670\) −83.2748 48.0787i −3.21719 1.85744i
\(671\) 13.3928i 0.517023i
\(672\) 4.07573 + 7.36052i 0.157225 + 0.283938i
\(673\) −12.6425 + 21.8974i −0.487332 + 0.844084i −0.999894 0.0145663i \(-0.995363\pi\)
0.512562 + 0.858650i \(0.328697\pi\)
\(674\) 30.8865i 1.18970i
\(675\) −3.38093 + 5.85594i −0.130132 + 0.225395i
\(676\) 55.6784 + 4.19566i 2.14148 + 0.161372i
\(677\) 3.17568 + 5.50044i 0.122051 + 0.211399i 0.920576 0.390562i \(-0.127719\pi\)
−0.798525 + 0.601961i \(0.794386\pi\)
\(678\) −18.0572 10.4253i −0.693483 0.400383i
\(679\) −7.42994 13.4180i −0.285135 0.514937i
\(680\) −1.96806 3.40879i −0.0754718 0.130721i
\(681\) −8.57408 + 4.95025i −0.328560 + 0.189694i
\(682\) 53.2649i 2.03962i
\(683\) 47.9352i 1.83419i −0.398671 0.917094i \(-0.630529\pi\)
0.398671 0.917094i \(-0.369471\pi\)
\(684\) 17.1728 9.91470i 0.656617 0.379098i
\(685\) 19.5036 + 33.7812i 0.745193 + 1.29071i
\(686\) −46.4004 2.49382i −1.77158 0.0952146i
\(687\) −13.6564 7.88453i −0.521025 0.300814i
\(688\) 7.48960 + 12.9724i 0.285538 + 0.494567i
\(689\) 1.31821 + 0.828665i 0.0502197 + 0.0315696i
\(690\) 32.3699 56.0663i 1.23230 2.13441i
\(691\) 25.5592i 0.972317i 0.873871 + 0.486159i \(0.161602\pi\)
−0.873871 + 0.486159i \(0.838398\pi\)
\(692\) −9.87450 + 17.1031i −0.375372 + 0.650164i
\(693\) 13.2928 + 0.237940i 0.504951 + 0.00903858i
\(694\) 79.1094i 3.00295i
\(695\) −52.0444 30.0478i −1.97416 1.13978i
\(696\) 18.2350i 0.691198i
\(697\) 0.931747 + 0.537944i 0.0352924 + 0.0203761i
\(698\) 2.45230 4.24750i 0.0928207 0.160770i
\(699\) 0.952488 1.64976i 0.0360264 0.0623996i
\(700\) −65.8472 39.6048i −2.48879 1.49692i
\(701\) −14.6478 −0.553238 −0.276619 0.960980i \(-0.589214\pi\)
−0.276619 + 0.960980i \(0.589214\pi\)
\(702\) 9.03994 + 0.340122i 0.341191 + 0.0128371i
\(703\) −21.0502 + 36.4600i −0.793922 + 1.37511i
\(704\) −16.2606 + 9.38806i −0.612844 + 0.353826i
\(705\) −24.5449 −0.924416
\(706\) 20.4686 + 35.4526i 0.770345 + 1.33428i
\(707\) −9.75703 + 5.40274i −0.366951 + 0.203191i
\(708\) 3.11803 1.80019i 0.117183 0.0676555i
\(709\) 16.2182 + 9.36357i 0.609087 + 0.351656i 0.772608 0.634883i \(-0.218952\pi\)
−0.163521 + 0.986540i \(0.552285\pi\)
\(710\) −42.6437 24.6203i −1.60039 0.923985i
\(711\) −4.51133 −0.169188
\(712\) 13.5097 0.506297
\(713\) 27.5275 + 15.8930i 1.03091 + 0.595198i
\(714\) 0.640918 + 1.15746i 0.0239858 + 0.0433169i
\(715\) −52.6055 33.0694i −1.96733 1.23673i
\(716\) 1.94658 + 3.37157i 0.0727470 + 0.126001i
\(717\) −22.7840 + 13.1544i −0.850885 + 0.491259i
\(718\) −27.8611 48.2568i −1.03977 1.80093i
\(719\) −8.57680 + 14.8555i −0.319861 + 0.554015i −0.980459 0.196725i \(-0.936969\pi\)
0.660598 + 0.750740i \(0.270303\pi\)
\(720\) 20.0891i 0.748677i
\(721\) 9.78089 5.41595i 0.364259 0.201701i
\(722\) 5.02895 2.90346i 0.187158 0.108056i
\(723\) −19.5607 + 11.2934i −0.727470 + 0.420005i
\(724\) 81.2440 3.01941
\(725\) −10.7063 18.5439i −0.397624 0.688705i
\(726\) 35.7548i 1.32699i
\(727\) 7.13494 0.264620 0.132310 0.991208i \(-0.457760\pi\)
0.132310 + 0.991208i \(0.457760\pi\)
\(728\) −3.04739 + 54.8470i −0.112944 + 2.03276i
\(729\) 1.00000 0.0370370
\(730\) 27.1411i 1.00454i
\(731\) 0.254839 + 0.441394i 0.00942556 + 0.0163255i
\(732\) −11.4474 −0.423109
\(733\) 17.0588 9.84891i 0.630082 0.363778i −0.150702 0.988579i \(-0.548153\pi\)
0.780784 + 0.624801i \(0.214820\pi\)
\(734\) 17.3956 10.0434i 0.642083 0.370707i
\(735\) 20.3477 + 12.7398i 0.750535 + 0.469915i
\(736\) 23.9258i 0.881915i
\(737\) 28.0769 48.6307i 1.03423 1.79133i
\(738\) 6.77187 + 11.7292i 0.249276 + 0.431759i
\(739\) 9.67092 5.58351i 0.355751 0.205393i −0.311464 0.950258i \(-0.600819\pi\)
0.667215 + 0.744865i \(0.267486\pi\)
\(740\) 67.1629 + 116.329i 2.46896 + 4.27636i
\(741\) 16.6342 + 0.625850i 0.611072 + 0.0229912i
\(742\) −1.47753 + 2.45655i −0.0542420 + 0.0901829i
\(743\) −19.2388 11.1075i −0.705802 0.407495i 0.103703 0.994608i \(-0.466931\pi\)
−0.809505 + 0.587114i \(0.800264\pi\)
\(744\) 24.3279 0.891905
\(745\) −40.7354 −1.49243
\(746\) 64.7614 + 37.3900i 2.37108 + 1.36895i
\(747\) −12.7451 7.35837i −0.466318 0.269229i
\(748\) 3.72537 2.15084i 0.136213 0.0786426i
\(749\) −0.220400 + 12.3129i −0.00805324 + 0.449903i
\(750\) 7.58019 + 13.1293i 0.276789 + 0.479413i
\(751\) −29.2653 −1.06791 −0.533954 0.845514i \(-0.679294\pi\)
−0.533954 + 0.845514i \(0.679294\pi\)
\(752\) 36.3059 20.9612i 1.32394 0.764377i
\(753\) −14.4466 + 25.0222i −0.526462 + 0.911859i
\(754\) −15.2461 + 24.2529i −0.555230 + 0.883238i
\(755\) 45.6916 1.66289
\(756\) −0.203378 + 11.3619i −0.00739678 + 0.413229i
\(757\) 26.6911 46.2303i 0.970104 1.68027i 0.274878 0.961479i \(-0.411363\pi\)
0.695226 0.718791i \(-0.255304\pi\)
\(758\) 13.2849 23.0101i 0.482529 0.835764i
\(759\) 32.7415 + 18.9033i 1.18844 + 0.686148i
\(760\) 91.1751i 3.30727i
\(761\) −8.96431 5.17555i −0.324956 0.187613i 0.328644 0.944454i \(-0.393409\pi\)
−0.653599 + 0.756841i \(0.726742\pi\)
\(762\) 25.2838i 0.915937i
\(763\) 0.826631 1.37436i 0.0299260 0.0497552i
\(764\) 33.0973 57.3262i 1.19742 2.07399i
\(765\) 0.683546i 0.0247137i
\(766\) −34.8960 + 60.4416i −1.26084 + 2.18384i
\(767\) 3.02024 + 0.113635i 0.109055 + 0.00410311i
\(768\) −16.0031 27.7182i −0.577463 1.00020i
\(769\) 11.0010 + 6.35144i 0.396707 + 0.229039i 0.685062 0.728485i \(-0.259775\pi\)
−0.288355 + 0.957523i \(0.593108\pi\)
\(770\) 58.9637 98.0333i 2.12490 3.53287i
\(771\) 8.02514 + 13.9000i 0.289018 + 0.500595i
\(772\) −29.6292 + 17.1065i −1.06638 + 0.615675i
\(773\) 52.0546i 1.87227i 0.351637 + 0.936137i \(0.385625\pi\)
−0.351637 + 0.936137i \(0.614375\pi\)
\(774\) 6.41604i 0.230620i
\(775\) −24.7400 + 14.2837i −0.888688 + 0.513085i
\(776\) −16.6911 28.9098i −0.599176 1.03780i
\(777\) −11.6875 21.1069i −0.419285 0.757205i
\(778\) 44.3410 + 25.6003i 1.58970 + 0.917814i
\(779\) 12.4608 + 21.5827i 0.446453 + 0.773279i
\(780\) 28.2659 44.9643i 1.01208 1.60998i
\(781\) 14.3777 24.9030i 0.514476 0.891099i
\(782\) 3.76239i 0.134543i
\(783\) −1.58334 + 2.74243i −0.0565841 + 0.0980065i
\(784\) −40.9772 1.46745i −1.46347 0.0524089i
\(785\) 38.5524i 1.37600i
\(786\) 23.9965 + 13.8544i 0.855928 + 0.494170i
\(787\) 28.6226i 1.02028i −0.860090 0.510142i \(-0.829593\pi\)
0.860090 0.510142i \(-0.170407\pi\)
\(788\) 48.8084 + 28.1795i 1.73873 + 1.00385i
\(789\) 7.23551 12.5323i 0.257591 0.446161i
\(790\) −19.4095 + 33.6182i −0.690558 + 1.19608i
\(791\) 19.2351 10.6510i 0.683921 0.378706i
\(792\) 28.9359 1.02819
\(793\) −8.13566 5.11432i −0.288906 0.181615i
\(794\) −17.5912 + 30.4688i −0.624287 + 1.08130i
\(795\) 1.28261 0.740516i 0.0454896 0.0262634i
\(796\) −83.8414 −2.97168
\(797\) −7.72007 13.3715i −0.273459 0.473644i 0.696286 0.717764i \(-0.254834\pi\)
−0.969745 + 0.244120i \(0.921501\pi\)
\(798\) −0.548490 + 30.6420i −0.0194163 + 1.08472i
\(799\) 1.23533 0.713220i 0.0437030 0.0252319i
\(800\) −18.6222 10.7515i −0.658393 0.380123i
\(801\) 2.03177 + 1.17304i 0.0717890 + 0.0414474i
\(802\) −13.2987 −0.469594
\(803\) −15.8498 −0.559328
\(804\) 41.5668 + 23.9986i 1.46595 + 0.846366i
\(805\) 33.0706 + 59.7236i 1.16559 + 2.10498i
\(806\) 32.3565 + 20.3403i 1.13971 + 0.716456i
\(807\) 8.14765 + 14.1121i 0.286811 + 0.496771i
\(808\) −21.0220 + 12.1371i −0.739552 + 0.426981i
\(809\) −1.85814 3.21840i −0.0653289 0.113153i 0.831511 0.555508i \(-0.187476\pi\)
−0.896840 + 0.442355i \(0.854143\pi\)
\(810\) 4.30238 7.45195i 0.151170 0.261835i
\(811\) 22.6432i 0.795111i −0.917578 0.397555i \(-0.869859\pi\)
0.917578 0.397555i \(-0.130141\pi\)
\(812\) −30.8373 18.5476i −1.08218 0.650893i
\(813\) 9.72516 5.61482i 0.341076 0.196920i
\(814\) −99.5672 + 57.4852i −3.48983 + 2.01485i
\(815\) −12.4550 −0.436280
\(816\) 0.583744 + 1.01107i 0.0204351 + 0.0353947i
\(817\) 11.8060i 0.413040i
\(818\) −72.8050 −2.54557
\(819\) −5.22066 + 7.98403i −0.182425 + 0.278985i
\(820\) 79.5148 2.77678
\(821\) 0.279111i 0.00974104i 0.999988 + 0.00487052i \(0.00155034\pi\)
−0.999988 + 0.00487052i \(0.998450\pi\)
\(822\) −14.2685 24.7137i −0.497669 0.861989i
\(823\) 12.0751 0.420913 0.210456 0.977603i \(-0.432505\pi\)
0.210456 + 0.977603i \(0.432505\pi\)
\(824\) 21.0734 12.1668i 0.734128 0.423849i
\(825\) −29.4261 + 16.9892i −1.02449 + 0.591487i
\(826\) −0.0995884 + 5.56362i −0.00346512 + 0.193583i
\(827\) 8.62027i 0.299756i 0.988704 + 0.149878i \(0.0478881\pi\)
−0.988704 + 0.149878i \(0.952112\pi\)
\(828\) −16.1575 + 27.9857i −0.561513 + 0.972569i
\(829\) −6.28936 10.8935i −0.218438 0.378346i 0.735892 0.677099i \(-0.236763\pi\)
−0.954331 + 0.298752i \(0.903430\pi\)
\(830\) −109.668 + 63.3170i −3.80664 + 2.19777i
\(831\) −9.60293 16.6328i −0.333122 0.576984i
\(832\) 0.506528 13.4628i 0.0175607 0.466737i
\(833\) −1.39428 0.0499310i −0.0483089 0.00173001i
\(834\) 38.0747 + 21.9825i 1.31842 + 0.761190i
\(835\) 35.4778 1.22776
\(836\) 99.6427 3.44622
\(837\) 3.65876 + 2.11239i 0.126465 + 0.0730148i
\(838\) 27.9473 + 16.1354i 0.965423 + 0.557387i
\(839\) −21.7367 + 12.5497i −0.750435 + 0.433264i −0.825851 0.563888i \(-0.809305\pi\)
0.0754160 + 0.997152i \(0.475972\pi\)
\(840\) 44.7752 + 26.9308i 1.54489 + 0.929201i
\(841\) 9.48604 + 16.4303i 0.327105 + 0.566562i
\(842\) −13.1932 −0.454669
\(843\) −18.5786 + 10.7264i −0.639881 + 0.369435i
\(844\) 51.3497 88.9403i 1.76753 3.06145i
\(845\) 40.1770 19.3278i 1.38213 0.664895i
\(846\) 17.9566 0.617362
\(847\) 32.3096 + 19.4332i 1.11017 + 0.667731i
\(848\) −1.26479 + 2.19069i −0.0434332 + 0.0752285i
\(849\) 4.10738 7.11419i 0.140965 0.244159i
\(850\) −2.92838 1.69070i −0.100443 0.0579906i
\(851\) 68.6090i 2.35189i
\(852\) 21.2857 + 12.2893i 0.729236 + 0.421025i
\(853\) 41.0459i 1.40538i 0.711494 + 0.702692i \(0.248019\pi\)
−0.711494 + 0.702692i \(0.751981\pi\)
\(854\) 9.11898 15.1612i 0.312045 0.518807i
\(855\) 7.91671 13.7121i 0.270746 0.468946i
\(856\) 26.8029i 0.916105i
\(857\) 5.36867 9.29880i 0.183390 0.317641i −0.759643 0.650341i \(-0.774626\pi\)
0.943033 + 0.332700i \(0.107959\pi\)
\(858\) 38.4853 + 24.1930i 1.31386 + 0.825935i
\(859\) 26.1491 + 45.2917i 0.892197 + 1.54533i 0.837235 + 0.546843i \(0.184171\pi\)
0.0549622 + 0.998488i \(0.482496\pi\)
\(860\) 32.6217 + 18.8342i 1.11239 + 0.642240i
\(861\) −14.2796 0.255604i −0.486649 0.00871098i
\(862\) −31.0072 53.7060i −1.05611 1.82923i
\(863\) −37.4567 + 21.6256i −1.27504 + 0.736145i −0.975932 0.218073i \(-0.930023\pi\)
−0.299109 + 0.954219i \(0.596689\pi\)
\(864\) 3.18005i 0.108187i
\(865\) 15.7692i 0.536170i
\(866\) 47.0378 27.1573i 1.59841 0.922843i
\(867\) −8.48014 14.6880i −0.288001 0.498832i
\(868\) −24.7449 + 41.1410i −0.839897 + 1.39642i
\(869\) −19.6323 11.3347i −0.665980 0.384504i
\(870\) 13.6243 + 23.5980i 0.461907 + 0.800047i
\(871\) 18.8197 + 35.6264i 0.637680 + 1.20715i
\(872\) 1.74531 3.02297i 0.0591038 0.102371i
\(873\) 5.79714i 0.196203i
\(874\) −43.5753 + 75.4746i −1.47396 + 2.55297i
\(875\) −15.9841 0.286115i −0.540362 0.00967244i
\(876\) 13.5476i 0.457729i
\(877\) −30.7866 17.7747i −1.03959 0.600208i −0.119873 0.992789i \(-0.538249\pi\)
−0.919717 + 0.392582i \(0.871582\pi\)
\(878\) 19.4462i 0.656278i
\(879\) 8.05762 + 4.65207i 0.271777 + 0.156910i
\(880\) 50.4739 87.4233i 1.70147 2.94704i
\(881\) 16.3098 28.2494i 0.549491 0.951746i −0.448819 0.893623i \(-0.648155\pi\)
0.998309 0.0581231i \(-0.0185116\pi\)
\(882\) −14.8860 9.32023i −0.501238 0.313828i
\(883\) 26.9860 0.908151 0.454075 0.890963i \(-0.349970\pi\)
0.454075 + 0.890963i \(0.349970\pi\)
\(884\) −0.116048 + 3.08437i −0.00390310 + 0.103739i
\(885\) 1.43742 2.48969i 0.0483185 0.0836901i
\(886\) 15.4341 8.91086i 0.518518 0.299366i
\(887\) 28.8798 0.969687 0.484844 0.874601i \(-0.338877\pi\)
0.484844 + 0.874601i \(0.338877\pi\)
\(888\) −26.2555 45.4758i −0.881076 1.52607i
\(889\) 22.8476 + 13.7420i 0.766283 + 0.460893i
\(890\) 17.4829 10.0937i 0.586028 0.338343i
\(891\) 4.35178 + 2.51250i 0.145790 + 0.0841719i
\(892\) −38.8220 22.4139i −1.29986 0.750473i
\(893\) 33.0416 1.10569
\(894\) 29.8013 0.996703
\(895\) 2.69214 + 1.55431i 0.0899883 + 0.0519548i
\(896\) 41.6244 + 0.745075i 1.39057 + 0.0248912i
\(897\) −23.9861 + 12.6707i −0.800874 + 0.423063i
\(898\) −36.4104 63.0646i −1.21503 2.10449i
\(899\) −11.5862 + 6.68927i −0.386420 + 0.223100i
\(900\) −14.5214 25.1518i −0.484047 0.838394i
\(901\) −0.0430355 + 0.0745396i −0.00143372 + 0.00248328i
\(902\) 68.0573i 2.26606i
\(903\) −5.79782 3.48719i −0.192939 0.116046i
\(904\) 41.4430 23.9271i 1.37837 0.795804i
\(905\) 56.1807 32.4360i 1.86751 1.07821i
\(906\) −33.4272 −1.11054
\(907\) 0.289244 + 0.500985i 0.00960418 + 0.0166349i 0.870788 0.491659i \(-0.163610\pi\)
−0.861183 + 0.508294i \(0.830276\pi\)
\(908\) 42.5236i 1.41119i
\(909\) −4.21544 −0.139817
\(910\) 37.0353 + 73.2544i 1.22771 + 2.42836i
\(911\) −46.6019 −1.54399 −0.771994 0.635629i \(-0.780741\pi\)
−0.771994 + 0.635629i \(0.780741\pi\)
\(912\) 27.0433i 0.895493i
\(913\) −36.9758 64.0439i −1.22372 2.11955i
\(914\) −67.8192 −2.24326
\(915\) −7.91597 + 4.57029i −0.261694 + 0.151089i
\(916\) 58.6556 33.8648i 1.93803 1.11892i
\(917\) −25.5618 + 14.1543i −0.844126 + 0.467416i
\(918\) 0.500070i 0.0165048i
\(919\) 7.80769 13.5233i 0.257552 0.446093i −0.708034 0.706179i \(-0.750417\pi\)
0.965586 + 0.260086i \(0.0837508\pi\)
\(920\) 74.2920 + 128.677i 2.44933 + 4.24237i
\(921\) 15.0480 8.68795i 0.495848 0.286278i
\(922\) −3.13579 5.43134i −0.103272 0.178872i
\(923\) 9.63725 + 18.2437i 0.317214 + 0.600499i
\(924\) −29.4319 + 48.9336i −0.968238 + 1.60980i
\(925\) 53.4005 + 30.8308i 1.75580 + 1.01371i
\(926\) −72.5981 −2.38572
\(927\) 4.22574 0.138792
\(928\) −8.72106 5.03511i −0.286283 0.165285i
\(929\) 9.06186 + 5.23187i 0.297310 + 0.171652i 0.641234 0.767346i \(-0.278423\pi\)
−0.343924 + 0.938998i \(0.611756\pi\)
\(930\) 31.4828 18.1766i 1.03236 0.596034i
\(931\) −27.3914 17.1499i −0.897716 0.562066i
\(932\) 4.09102 + 7.08586i 0.134006 + 0.232105i
\(933\) −5.07791 −0.166243
\(934\) −18.3990 + 10.6227i −0.602035 + 0.347585i
\(935\) 1.71741 2.97464i 0.0561653 0.0972812i
\(936\) −11.0498 + 17.5776i −0.361173 + 0.574541i
\(937\) −37.2603 −1.21724 −0.608621 0.793461i \(-0.708277\pi\)
−0.608621 + 0.793461i \(0.708277\pi\)
\(938\) −64.8963 + 35.9349i −2.11894 + 1.17332i
\(939\) 3.64621 6.31543i 0.118990 0.206096i
\(940\) 52.7114 91.2988i 1.71926 2.97784i
\(941\) 9.05253 + 5.22648i 0.295104 + 0.170378i 0.640241 0.768174i \(-0.278834\pi\)
−0.345137 + 0.938552i \(0.612168\pi\)
\(942\) 28.2043i 0.918945i
\(943\) −35.1723 20.3067i −1.14537 0.661278i
\(944\) 4.91020i 0.159814i
\(945\) 4.39551 + 7.93804i 0.142986 + 0.258224i
\(946\) −16.1203 + 27.9212i −0.524116 + 0.907796i
\(947\) 10.7568i 0.349549i −0.984609 0.174774i \(-0.944080\pi\)
0.984609 0.174774i \(-0.0559196\pi\)
\(948\) 9.68829 16.7806i 0.314661 0.545009i
\(949\) 6.05258 9.62821i 0.196475 0.312545i
\(950\) −39.1628 67.8320i −1.27061 2.20076i
\(951\) −20.5617 11.8713i −0.666757 0.384953i
\(952\) −3.03606 0.0543453i −0.0983994 0.00176134i
\(953\) −22.9984 39.8344i −0.744992 1.29036i −0.950199 0.311645i \(-0.899120\pi\)
0.205207 0.978719i \(-0.434213\pi\)
\(954\) −0.938336 + 0.541749i −0.0303798 + 0.0175398i
\(955\) 52.8553i 1.71036i
\(956\) 112.998i 3.65463i
\(957\) −13.7807 + 7.95630i −0.445467 + 0.257191i
\(958\) −30.0661 52.0760i −0.971392 1.68250i
\(959\) 30.0874 + 0.538563i 0.971574 + 0.0173911i
\(960\) −11.0978 6.40734i −0.358181 0.206796i
\(961\) −6.57564 11.3893i −0.212117 0.367398i
\(962\) 3.10158 82.4355i 0.0999990 2.65783i
\(963\) −2.32729 + 4.03099i −0.0749959 + 0.129897i
\(964\) 97.0122i 3.12455i
\(965\) −13.6592 + 23.6584i −0.439705 + 0.761592i
\(966\) −24.1939 43.6927i −0.778425 1.40579i
\(967\) 54.8212i 1.76293i 0.472250 + 0.881465i \(0.343442\pi\)
−0.472250 + 0.881465i \(0.656558\pi\)
\(968\) 71.0666 + 41.0303i 2.28417 + 1.31877i
\(969\) 0.920167i 0.0295600i
\(970\) −43.2000 24.9415i −1.38707 0.800823i
\(971\) −18.9408 + 32.8064i −0.607838 + 1.05281i 0.383758 + 0.923434i \(0.374630\pi\)
−0.991596 + 0.129373i \(0.958704\pi\)
\(972\) −2.14755 + 3.71966i −0.0688826 + 0.119308i
\(973\) −40.5584 + 22.4583i −1.30024 + 0.719980i
\(974\) 92.1447 2.95251
\(975\) 0.916642 24.3630i 0.0293560 0.780240i
\(976\) 7.80599 13.5204i 0.249864 0.432777i
\(977\) −45.3003 + 26.1541i −1.44928 + 0.836745i −0.998439 0.0558573i \(-0.982211\pi\)
−0.450846 + 0.892602i \(0.648877\pi\)
\(978\) 9.11186 0.291365
\(979\) 5.89453 + 10.2096i 0.188390 + 0.326301i
\(980\) −91.0854 + 48.3271i −2.90962 + 1.54375i
\(981\) 0.524968 0.303090i 0.0167609 0.00967693i
\(982\) −21.0149 12.1330i −0.670612 0.387178i
\(983\) −29.7363 17.1683i −0.948442 0.547583i −0.0558452 0.998439i \(-0.517785\pi\)
−0.892597 + 0.450856i \(0.851119\pi\)
\(984\) −31.0841 −0.990926
\(985\) 45.0018 1.43388
\(986\) −1.37141 0.791783i −0.0436746 0.0252155i
\(987\) −9.75963 + 16.2264i −0.310653 + 0.516492i
\(988\) −38.0506 + 60.5295i −1.21055 + 1.92570i
\(989\) −9.61985 16.6621i −0.305893 0.529823i
\(990\) 37.4460 21.6195i 1.19011 0.687112i
\(991\) 16.2263 + 28.1048i 0.515446 + 0.892778i 0.999839 + 0.0179281i \(0.00570701\pi\)
−0.484393 + 0.874850i \(0.660960\pi\)
\(992\) −6.71749 + 11.6350i −0.213280 + 0.369413i
\(993\) 0.0230179i 0.000730451i
\(994\) −33.2324 + 18.4017i −1.05407 + 0.583666i
\(995\) −57.9768 + 33.4729i −1.83799 + 1.06116i
\(996\) 54.7412 31.6049i 1.73454 1.00144i
\(997\) −2.32191 −0.0735355 −0.0367677 0.999324i \(-0.511706\pi\)
−0.0367677 + 0.999324i \(0.511706\pi\)
\(998\) 34.8175 + 60.3057i 1.10213 + 1.90894i
\(999\) 9.11903i 0.288513i
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 273.2.t.d.4.1 20
3.2 odd 2 819.2.bm.g.550.10 20
7.2 even 3 273.2.bl.d.121.1 yes 20
13.10 even 6 273.2.bl.d.88.1 yes 20
21.2 odd 6 819.2.do.g.667.10 20
39.23 odd 6 819.2.do.g.361.10 20
91.23 even 6 inner 273.2.t.d.205.10 yes 20
273.23 odd 6 819.2.bm.g.478.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.t.d.4.1 20 1.1 even 1 trivial
273.2.t.d.205.10 yes 20 91.23 even 6 inner
273.2.bl.d.88.1 yes 20 13.10 even 6
273.2.bl.d.121.1 yes 20 7.2 even 3
819.2.bm.g.478.1 20 273.23 odd 6
819.2.bm.g.550.10 20 3.2 odd 2
819.2.do.g.361.10 20 39.23 odd 6
819.2.do.g.667.10 20 21.2 odd 6