Properties

Label 45.3.k.a.13.6
Level $45$
Weight $3$
Character 45.13
Analytic conductor $1.226$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,3,Mod(7,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.k (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.22616118962\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 45.13
Dual form 45.3.k.a.7.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.183646 - 0.0492077i) q^{2} +(-1.82902 - 2.37796i) q^{3} +(-3.43280 - 1.98193i) q^{4} +(-1.61810 - 4.73094i) q^{5} +(0.218877 + 0.526704i) q^{6} +(8.70492 + 2.33248i) q^{7} +(1.07064 + 1.07064i) q^{8} +(-2.30940 + 8.69866i) q^{9} +O(q^{10})\) \(q+(-0.183646 - 0.0492077i) q^{2} +(-1.82902 - 2.37796i) q^{3} +(-3.43280 - 1.98193i) q^{4} +(-1.61810 - 4.73094i) q^{5} +(0.218877 + 0.526704i) q^{6} +(8.70492 + 2.33248i) q^{7} +(1.07064 + 1.07064i) q^{8} +(-2.30940 + 8.69866i) q^{9} +(0.0643587 + 0.948439i) q^{10} +(-7.04110 - 12.1955i) q^{11} +(1.56570 + 11.7880i) q^{12} +(12.9444 - 3.46845i) q^{13} +(-1.48385 - 0.856699i) q^{14} +(-8.29045 + 12.5007i) q^{15} +(7.78377 + 13.4819i) q^{16} +(-0.740694 + 0.740694i) q^{17} +(0.852153 - 1.48383i) q^{18} -7.09073i q^{19} +(-3.82175 + 19.4473i) q^{20} +(-10.3749 - 24.9661i) q^{21} +(0.692953 + 2.58614i) q^{22} +(19.0499 - 5.10441i) q^{23} +(0.587726 - 4.50418i) q^{24} +(-19.7635 + 15.3103i) q^{25} -2.54786 q^{26} +(24.9090 - 10.4183i) q^{27} +(-25.2594 - 25.2594i) q^{28} +(6.18301 - 3.56976i) q^{29} +(2.13764 - 1.88775i) q^{30} +(13.0783 - 22.6522i) q^{31} +(-2.33357 - 8.70902i) q^{32} +(-16.1223 + 39.0493i) q^{33} +(0.172473 - 0.0995774i) q^{34} +(-3.05064 - 44.9566i) q^{35} +(25.1678 - 25.2837i) q^{36} +(-23.0151 + 23.0151i) q^{37} +(-0.348919 + 1.30218i) q^{38} +(-31.9234 - 24.4375i) q^{39} +(3.33274 - 6.79756i) q^{40} +(-36.0387 + 62.4209i) q^{41} +(0.676780 + 5.09544i) q^{42} +(3.22835 - 12.0484i) q^{43} +55.8198i q^{44} +(44.8896 - 3.14967i) q^{45} -3.74961 q^{46} +(51.8935 + 13.9048i) q^{47} +(17.8228 - 43.1681i) q^{48} +(27.9000 + 16.1081i) q^{49} +(4.38286 - 1.83915i) q^{50} +(3.11608 + 0.406601i) q^{51} +(-51.3098 - 13.7484i) q^{52} +(17.2907 + 17.2907i) q^{53} +(-5.08709 + 0.687563i) q^{54} +(-46.3031 + 53.0446i) q^{55} +(6.82262 + 11.8171i) q^{56} +(-16.8615 + 12.9691i) q^{57} +(-1.31114 + 0.351320i) q^{58} +(27.5407 + 15.9006i) q^{59} +(53.2350 - 26.4814i) q^{60} +(40.7317 + 70.5494i) q^{61} +(-3.51643 + 3.51643i) q^{62} +(-40.3926 + 70.3345i) q^{63} -60.5560i q^{64} +(-37.3544 - 55.6269i) q^{65} +(4.88231 - 6.37790i) q^{66} +(-17.1864 - 64.1404i) q^{67} +(4.01065 - 1.07465i) q^{68} +(-46.9807 - 35.9639i) q^{69} +(-1.65197 + 8.40620i) q^{70} -36.3928 q^{71} +(-11.7857 + 6.84062i) q^{72} +(2.90991 + 2.90991i) q^{73} +(5.35915 - 3.09411i) q^{74} +(72.5550 + 18.9941i) q^{75} +(-14.0533 + 24.3410i) q^{76} +(-32.8464 - 122.584i) q^{77} +(4.66008 + 6.05872i) q^{78} +(71.8823 - 41.5012i) q^{79} +(51.1870 - 58.6396i) q^{80} +(-70.3333 - 40.1774i) q^{81} +(9.68994 - 9.68994i) q^{82} +(-13.7671 + 51.3796i) q^{83} +(-13.8661 + 106.266i) q^{84} +(4.70269 + 2.30566i) q^{85} +(-1.18574 + 2.05377i) q^{86} +(-19.7976 - 8.17381i) q^{87} +(5.51857 - 20.5956i) q^{88} -22.5436i q^{89} +(-8.39878 - 1.63049i) q^{90} +120.770 q^{91} +(-75.5111 - 20.2331i) q^{92} +(-77.7864 + 10.3316i) q^{93} +(-8.84580 - 5.10712i) q^{94} +(-33.5458 + 11.4735i) q^{95} +(-16.4416 + 21.4781i) q^{96} +(33.7192 + 9.03502i) q^{97} +(-4.33107 - 4.33107i) q^{98} +(122.346 - 33.0837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23} - 8 q^{25} - 112 q^{26} - 198 q^{27} - 88 q^{28} + 162 q^{30} - 4 q^{31} - 14 q^{32} + 96 q^{33} + 352 q^{35} + 264 q^{36} - 92 q^{37} + 330 q^{38} + 30 q^{40} - 28 q^{41} + 498 q^{42} - 2 q^{43} - 72 q^{45} - 136 q^{46} + 64 q^{47} - 510 q^{48} - 458 q^{50} - 396 q^{51} - 74 q^{52} - 608 q^{53} + 224 q^{55} - 192 q^{56} - 114 q^{57} + 30 q^{58} - 798 q^{60} + 92 q^{61} - 100 q^{62} + 24 q^{63} - 326 q^{65} + 588 q^{66} - 80 q^{67} + 626 q^{68} - 102 q^{70} + 248 q^{71} - 162 q^{72} - 8 q^{73} + 810 q^{75} - 96 q^{76} + 338 q^{77} + 1062 q^{78} + 1444 q^{80} + 204 q^{81} + 104 q^{82} + 370 q^{83} - 98 q^{85} - 328 q^{86} + 534 q^{87} - 210 q^{88} + 462 q^{90} + 152 q^{91} + 388 q^{92} - 1062 q^{93} - 360 q^{95} - 876 q^{96} + 292 q^{97} - 1876 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.183646 0.0492077i −0.0918228 0.0246039i 0.212615 0.977136i \(-0.431802\pi\)
−0.304438 + 0.952532i \(0.598469\pi\)
\(3\) −1.82902 2.37796i −0.609672 0.792654i
\(4\) −3.43280 1.98193i −0.858199 0.495482i
\(5\) −1.61810 4.73094i −0.323620 0.946187i
\(6\) 0.218877 + 0.526704i 0.0364795 + 0.0877840i
\(7\) 8.70492 + 2.33248i 1.24356 + 0.333211i 0.819846 0.572585i \(-0.194059\pi\)
0.423715 + 0.905796i \(0.360726\pi\)
\(8\) 1.07064 + 1.07064i 0.133831 + 0.133831i
\(9\) −2.30940 + 8.69866i −0.256600 + 0.966518i
\(10\) 0.0643587 + 0.948439i 0.00643587 + 0.0948439i
\(11\) −7.04110 12.1955i −0.640100 1.10869i −0.985410 0.170197i \(-0.945560\pi\)
0.345310 0.938489i \(-0.387774\pi\)
\(12\) 1.56570 + 11.7880i 0.130475 + 0.982336i
\(13\) 12.9444 3.46845i 0.995725 0.266804i 0.276071 0.961137i \(-0.410967\pi\)
0.719653 + 0.694333i \(0.244301\pi\)
\(14\) −1.48385 0.856699i −0.105989 0.0611928i
\(15\) −8.29045 + 12.5007i −0.552697 + 0.833382i
\(16\) 7.78377 + 13.4819i 0.486486 + 0.842618i
\(17\) −0.740694 + 0.740694i −0.0435702 + 0.0435702i −0.728556 0.684986i \(-0.759808\pi\)
0.684986 + 0.728556i \(0.259808\pi\)
\(18\) 0.852153 1.48383i 0.0473418 0.0824350i
\(19\) 7.09073i 0.373196i −0.982436 0.186598i \(-0.940254\pi\)
0.982436 0.186598i \(-0.0597463\pi\)
\(20\) −3.82175 + 19.4473i −0.191088 + 0.972365i
\(21\) −10.3749 24.9661i −0.494043 1.18886i
\(22\) 0.692953 + 2.58614i 0.0314979 + 0.117552i
\(23\) 19.0499 5.10441i 0.828257 0.221931i 0.180304 0.983611i \(-0.442292\pi\)
0.647953 + 0.761680i \(0.275625\pi\)
\(24\) 0.587726 4.50418i 0.0244886 0.187674i
\(25\) −19.7635 + 15.3103i −0.790540 + 0.612410i
\(26\) −2.54786 −0.0979947
\(27\) 24.9090 10.4183i 0.922556 0.385863i
\(28\) −25.2594 25.2594i −0.902123 0.902123i
\(29\) 6.18301 3.56976i 0.213207 0.123095i −0.389594 0.920987i \(-0.627385\pi\)
0.602801 + 0.797892i \(0.294051\pi\)
\(30\) 2.13764 1.88775i 0.0712546 0.0629251i
\(31\) 13.0783 22.6522i 0.421879 0.730716i −0.574244 0.818684i \(-0.694704\pi\)
0.996123 + 0.0879678i \(0.0280373\pi\)
\(32\) −2.33357 8.70902i −0.0729242 0.272157i
\(33\) −16.1223 + 39.0493i −0.488553 + 1.18331i
\(34\) 0.172473 0.0995774i 0.00507274 0.00292875i
\(35\) −3.05064 44.9566i −0.0871612 1.28447i
\(36\) 25.1678 25.2837i 0.699106 0.702324i
\(37\) −23.0151 + 23.0151i −0.622031 + 0.622031i −0.946050 0.324020i \(-0.894966\pi\)
0.324020 + 0.946050i \(0.394966\pi\)
\(38\) −0.348919 + 1.30218i −0.00918207 + 0.0342680i
\(39\) −31.9234 24.4375i −0.818548 0.626602i
\(40\) 3.33274 6.79756i 0.0833185 0.169939i
\(41\) −36.0387 + 62.4209i −0.878993 + 1.52246i −0.0265459 + 0.999648i \(0.508451\pi\)
−0.852447 + 0.522813i \(0.824883\pi\)
\(42\) 0.676780 + 5.09544i 0.0161138 + 0.121320i
\(43\) 3.22835 12.0484i 0.0750779 0.280195i −0.918173 0.396180i \(-0.870336\pi\)
0.993251 + 0.115985i \(0.0370025\pi\)
\(44\) 55.8198i 1.26863i
\(45\) 44.8896 3.14967i 0.997548 0.0699926i
\(46\) −3.74961 −0.0815133
\(47\) 51.8935 + 13.9048i 1.10412 + 0.295847i 0.764440 0.644695i \(-0.223015\pi\)
0.339677 + 0.940542i \(0.389682\pi\)
\(48\) 17.8228 43.1681i 0.371308 0.899335i
\(49\) 27.9000 + 16.1081i 0.569388 + 0.328736i
\(50\) 4.38286 1.83915i 0.0876573 0.0367829i
\(51\) 3.11608 + 0.406601i 0.0610997 + 0.00797257i
\(52\) −51.3098 13.7484i −0.986727 0.264393i
\(53\) 17.2907 + 17.2907i 0.326240 + 0.326240i 0.851155 0.524915i \(-0.175903\pi\)
−0.524915 + 0.851155i \(0.675903\pi\)
\(54\) −5.08709 + 0.687563i −0.0942054 + 0.0127326i
\(55\) −46.3031 + 53.0446i −0.841875 + 0.964447i
\(56\) 6.82262 + 11.8171i 0.121833 + 0.211020i
\(57\) −16.8615 + 12.9691i −0.295816 + 0.227527i
\(58\) −1.31114 + 0.351320i −0.0226059 + 0.00605724i
\(59\) 27.5407 + 15.9006i 0.466792 + 0.269502i 0.714896 0.699231i \(-0.246474\pi\)
−0.248104 + 0.968733i \(0.579807\pi\)
\(60\) 53.2350 26.4814i 0.887250 0.441357i
\(61\) 40.7317 + 70.5494i 0.667733 + 1.15655i 0.978537 + 0.206073i \(0.0660684\pi\)
−0.310804 + 0.950474i \(0.600598\pi\)
\(62\) −3.51643 + 3.51643i −0.0567166 + 0.0567166i
\(63\) −40.3926 + 70.3345i −0.641152 + 1.11642i
\(64\) 60.5560i 0.946187i
\(65\) −37.3544 55.6269i −0.574683 0.855799i
\(66\) 4.88231 6.37790i 0.0739744 0.0966348i
\(67\) −17.1864 64.1404i −0.256513 0.957319i −0.967243 0.253854i \(-0.918302\pi\)
0.710730 0.703465i \(-0.248365\pi\)
\(68\) 4.01065 1.07465i 0.0589802 0.0158037i
\(69\) −46.9807 35.9639i −0.680880 0.521216i
\(70\) −1.65197 + 8.40620i −0.0235996 + 0.120089i
\(71\) −36.3928 −0.512574 −0.256287 0.966601i \(-0.582499\pi\)
−0.256287 + 0.966601i \(0.582499\pi\)
\(72\) −11.7857 + 6.84062i −0.163691 + 0.0950086i
\(73\) 2.90991 + 2.90991i 0.0398617 + 0.0398617i 0.726757 0.686895i \(-0.241027\pi\)
−0.686895 + 0.726757i \(0.741027\pi\)
\(74\) 5.35915 3.09411i 0.0724210 0.0418123i
\(75\) 72.5550 + 18.9941i 0.967400 + 0.253255i
\(76\) −14.0533 + 24.3410i −0.184912 + 0.320277i
\(77\) −32.8464 122.584i −0.426577 1.59201i
\(78\) 4.66008 + 6.05872i 0.0597446 + 0.0776759i
\(79\) 71.8823 41.5012i 0.909902 0.525332i 0.0295025 0.999565i \(-0.490608\pi\)
0.880400 + 0.474232i \(0.157274\pi\)
\(80\) 51.1870 58.6396i 0.639838 0.732995i
\(81\) −70.3333 40.1774i −0.868313 0.496017i
\(82\) 9.68994 9.68994i 0.118170 0.118170i
\(83\) −13.7671 + 51.3796i −0.165869 + 0.619031i 0.832059 + 0.554687i \(0.187162\pi\)
−0.997928 + 0.0643438i \(0.979505\pi\)
\(84\) −13.8661 + 106.266i −0.165072 + 1.26507i
\(85\) 4.70269 + 2.30566i 0.0553258 + 0.0271254i
\(86\) −1.18574 + 2.05377i −0.0137877 + 0.0238811i
\(87\) −19.7976 8.17381i −0.227558 0.0939518i
\(88\) 5.51857 20.5956i 0.0627111 0.234041i
\(89\) 22.5436i 0.253299i −0.991948 0.126650i \(-0.959578\pi\)
0.991948 0.126650i \(-0.0404224\pi\)
\(90\) −8.39878 1.63049i −0.0933197 0.0181166i
\(91\) 120.770 1.32715
\(92\) −75.5111 20.2331i −0.820773 0.219925i
\(93\) −77.7864 + 10.3316i −0.836413 + 0.111093i
\(94\) −8.84580 5.10712i −0.0941042 0.0543311i
\(95\) −33.5458 + 11.4735i −0.353114 + 0.120774i
\(96\) −16.4416 + 21.4781i −0.171266 + 0.223730i
\(97\) 33.7192 + 9.03502i 0.347620 + 0.0931446i 0.428405 0.903587i \(-0.359076\pi\)
−0.0807843 + 0.996732i \(0.525742\pi\)
\(98\) −4.33107 4.33107i −0.0441946 0.0441946i
\(99\) 122.346 33.0837i 1.23581 0.334179i
\(100\) 98.1879 13.3872i 0.981879 0.133872i
\(101\) −29.7283 51.4909i −0.294340 0.509811i 0.680491 0.732756i \(-0.261766\pi\)
−0.974831 + 0.222945i \(0.928433\pi\)
\(102\) −0.552247 0.228006i −0.00541419 0.00223535i
\(103\) −76.0184 + 20.3691i −0.738043 + 0.197758i −0.608208 0.793778i \(-0.708111\pi\)
−0.129835 + 0.991536i \(0.541445\pi\)
\(104\) 17.5723 + 10.1454i 0.168965 + 0.0975519i
\(105\) −101.325 + 89.4807i −0.965004 + 0.852197i
\(106\) −2.32453 4.02620i −0.0219295 0.0379830i
\(107\) −50.6865 + 50.6865i −0.473706 + 0.473706i −0.903112 0.429406i \(-0.858723\pi\)
0.429406 + 0.903112i \(0.358723\pi\)
\(108\) −106.156 13.6039i −0.982925 0.125962i
\(109\) 47.8364i 0.438866i 0.975628 + 0.219433i \(0.0704208\pi\)
−0.975628 + 0.219433i \(0.929579\pi\)
\(110\) 11.1136 7.46294i 0.101032 0.0678449i
\(111\) 96.8241 + 12.6341i 0.872289 + 0.113820i
\(112\) 36.3109 + 135.514i 0.324205 + 1.20995i
\(113\) 168.318 45.1005i 1.48954 0.399120i 0.579955 0.814648i \(-0.303070\pi\)
0.909580 + 0.415529i \(0.136403\pi\)
\(114\) 3.73472 1.55200i 0.0327607 0.0136140i
\(115\) −54.9733 81.8645i −0.478029 0.711865i
\(116\) −28.3000 −0.243966
\(117\) 0.276954 + 120.609i 0.00236713 + 1.03085i
\(118\) −4.27530 4.27530i −0.0362313 0.0362313i
\(119\) −8.17534 + 4.72003i −0.0687003 + 0.0396641i
\(120\) −22.2600 + 4.50772i −0.185500 + 0.0375643i
\(121\) −38.6542 + 66.9510i −0.319456 + 0.553314i
\(122\) −4.00863 14.9604i −0.0328576 0.122626i
\(123\) 214.350 28.4701i 1.74268 0.231464i
\(124\) −89.7900 + 51.8403i −0.724113 + 0.418067i
\(125\) 104.411 + 68.7263i 0.835289 + 0.549810i
\(126\) 10.8789 10.9290i 0.0863407 0.0867381i
\(127\) 16.3333 16.3333i 0.128608 0.128608i −0.639873 0.768481i \(-0.721013\pi\)
0.768481 + 0.639873i \(0.221013\pi\)
\(128\) −12.3141 + 45.9569i −0.0962041 + 0.359038i
\(129\) −34.5553 + 14.3598i −0.267870 + 0.111316i
\(130\) 4.12270 + 12.0538i 0.0317130 + 0.0927213i
\(131\) −27.6049 + 47.8130i −0.210724 + 0.364985i −0.951941 0.306280i \(-0.900916\pi\)
0.741217 + 0.671265i \(0.234249\pi\)
\(132\) 132.737 102.095i 1.00559 0.773449i
\(133\) 16.5390 61.7243i 0.124353 0.464092i
\(134\) 12.6248i 0.0942150i
\(135\) −89.5936 100.985i −0.663657 0.748037i
\(136\) −1.58604 −0.0116621
\(137\) 189.371 + 50.7417i 1.38227 + 0.370377i 0.871944 0.489606i \(-0.162859\pi\)
0.510323 + 0.859983i \(0.329526\pi\)
\(138\) 6.85810 + 8.91643i 0.0496964 + 0.0646118i
\(139\) −82.5364 47.6524i −0.593787 0.342823i 0.172806 0.984956i \(-0.444717\pi\)
−0.766594 + 0.642133i \(0.778050\pi\)
\(140\) −78.6285 + 160.373i −0.561632 + 1.14552i
\(141\) −61.8489 148.833i −0.438645 1.05555i
\(142\) 6.68338 + 1.79081i 0.0470660 + 0.0126113i
\(143\) −133.443 133.443i −0.933165 0.933165i
\(144\) −135.250 + 36.5733i −0.939237 + 0.253981i
\(145\) −26.8931 23.4752i −0.185469 0.161898i
\(146\) −0.391202 0.677581i −0.00267946 0.00464097i
\(147\) −12.7252 95.8070i −0.0865657 0.651748i
\(148\) 124.621 33.3920i 0.842031 0.225622i
\(149\) −225.341 130.101i −1.51235 0.873158i −0.999896 0.0144460i \(-0.995402\pi\)
−0.512458 0.858712i \(-0.671265\pi\)
\(150\) −12.3897 7.05846i −0.0825983 0.0470564i
\(151\) −128.914 223.285i −0.853735 1.47871i −0.877814 0.479002i \(-0.840999\pi\)
0.0240792 0.999710i \(-0.492335\pi\)
\(152\) 7.59165 7.59165i 0.0499451 0.0499451i
\(153\) −4.73248 8.15361i −0.0309313 0.0532915i
\(154\) 24.1284i 0.156678i
\(155\) −128.328 25.2188i −0.827923 0.162702i
\(156\) 61.1532 + 147.159i 0.392008 + 0.943325i
\(157\) −12.0301 44.8971i −0.0766251 0.285969i 0.916972 0.398952i \(-0.130626\pi\)
−0.993597 + 0.112983i \(0.963959\pi\)
\(158\) −15.2431 + 4.08436i −0.0964750 + 0.0258504i
\(159\) 9.49166 72.7416i 0.0596960 0.457494i
\(160\) −37.4259 + 25.1321i −0.233912 + 0.157075i
\(161\) 177.734 1.10394
\(162\) 10.9394 + 10.8393i 0.0675270 + 0.0669096i
\(163\) 76.8331 + 76.8331i 0.471369 + 0.471369i 0.902357 0.430989i \(-0.141835\pi\)
−0.430989 + 0.902357i \(0.641835\pi\)
\(164\) 247.427 142.852i 1.50870 0.871050i
\(165\) 210.827 + 13.0876i 1.27774 + 0.0793189i
\(166\) 5.05654 8.75819i 0.0304611 0.0527602i
\(167\) 80.7212 + 301.256i 0.483360 + 1.80393i 0.587333 + 0.809346i \(0.300178\pi\)
−0.103972 + 0.994580i \(0.533155\pi\)
\(168\) 15.6220 37.8376i 0.0929881 0.225224i
\(169\) 9.16964 5.29409i 0.0542582 0.0313260i
\(170\) −0.750173 0.654833i −0.00441278 0.00385196i
\(171\) 61.6799 + 16.3754i 0.360701 + 0.0957623i
\(172\) −34.9612 + 34.9612i −0.203263 + 0.203263i
\(173\) −51.6158 + 192.633i −0.298357 + 1.11348i 0.640157 + 0.768244i \(0.278869\pi\)
−0.938514 + 0.345240i \(0.887797\pi\)
\(174\) 3.23353 + 2.47528i 0.0185835 + 0.0142257i
\(175\) −207.751 + 87.1767i −1.18715 + 0.498153i
\(176\) 109.613 189.855i 0.622799 1.07872i
\(177\) −12.5613 94.5733i −0.0709677 0.534312i
\(178\) −1.10932 + 4.14004i −0.00623214 + 0.0232587i
\(179\) 254.120i 1.41967i 0.704370 + 0.709833i \(0.251230\pi\)
−0.704370 + 0.709833i \(0.748770\pi\)
\(180\) −160.339 78.1558i −0.890775 0.434199i
\(181\) −236.998 −1.30938 −0.654691 0.755896i \(-0.727201\pi\)
−0.654691 + 0.755896i \(0.727201\pi\)
\(182\) −22.1789 5.94283i −0.121862 0.0326529i
\(183\) 93.2648 225.894i 0.509644 1.23440i
\(184\) 25.8607 + 14.9307i 0.140547 + 0.0811450i
\(185\) 146.124 + 71.6423i 0.789859 + 0.387256i
\(186\) 14.7935 + 1.93033i 0.0795351 + 0.0103781i
\(187\) 14.2485 + 3.81787i 0.0761950 + 0.0204164i
\(188\) −150.582 150.582i −0.800966 0.800966i
\(189\) 241.131 32.5909i 1.27583 0.172439i
\(190\) 6.72513 0.456350i 0.0353954 0.00240184i
\(191\) 27.2962 + 47.2784i 0.142912 + 0.247531i 0.928592 0.371102i \(-0.121020\pi\)
−0.785680 + 0.618633i \(0.787687\pi\)
\(192\) −144.000 + 110.758i −0.749999 + 0.576864i
\(193\) −193.408 + 51.8234i −1.00211 + 0.268515i −0.722330 0.691548i \(-0.756929\pi\)
−0.279782 + 0.960063i \(0.590262\pi\)
\(194\) −5.74779 3.31849i −0.0296278 0.0171056i
\(195\) −63.9570 + 190.570i −0.327984 + 0.977281i
\(196\) −63.8500 110.591i −0.325765 0.564242i
\(197\) 18.5367 18.5367i 0.0940948 0.0940948i −0.658492 0.752587i \(-0.728806\pi\)
0.752587 + 0.658492i \(0.228806\pi\)
\(198\) −24.0962 + 0.0553320i −0.121698 + 0.000279454i
\(199\) 206.081i 1.03558i 0.855507 + 0.517792i \(0.173246\pi\)
−0.855507 + 0.517792i \(0.826754\pi\)
\(200\) −37.5515 4.76784i −0.187758 0.0238392i
\(201\) −121.089 + 158.182i −0.602434 + 0.786977i
\(202\) 2.92572 + 10.9190i 0.0144838 + 0.0540542i
\(203\) 62.1490 16.6528i 0.306153 0.0820334i
\(204\) −9.89103 7.57163i −0.0484854 0.0371158i
\(205\) 353.623 + 69.4936i 1.72499 + 0.338993i
\(206\) 14.9628 0.0726348
\(207\) 0.407585 + 177.497i 0.00196901 + 0.857473i
\(208\) 147.518 + 147.518i 0.709219 + 0.709219i
\(209\) −86.4753 + 49.9266i −0.413758 + 0.238883i
\(210\) 23.0111 11.4467i 0.109577 0.0545083i
\(211\) 121.373 210.225i 0.575230 0.996327i −0.420787 0.907159i \(-0.638246\pi\)
0.996017 0.0891675i \(-0.0284206\pi\)
\(212\) −25.0866 93.6244i −0.118333 0.441625i
\(213\) 66.5630 + 86.5406i 0.312502 + 0.406294i
\(214\) 11.8025 6.81419i 0.0551520 0.0318420i
\(215\) −62.2238 + 4.22235i −0.289413 + 0.0196389i
\(216\) 37.8230 + 15.5144i 0.175106 + 0.0718258i
\(217\) 166.681 166.681i 0.768115 0.768115i
\(218\) 2.35392 8.78496i 0.0107978 0.0402980i
\(219\) 1.59738 12.2419i 0.00729397 0.0558991i
\(220\) 264.080 90.3220i 1.20036 0.410555i
\(221\) −7.01880 + 12.1569i −0.0317593 + 0.0550087i
\(222\) −17.1596 7.08468i −0.0772957 0.0319130i
\(223\) −53.2572 + 198.758i −0.238821 + 0.891293i 0.737568 + 0.675273i \(0.235974\pi\)
−0.976389 + 0.216020i \(0.930692\pi\)
\(224\) 81.2544i 0.362743i
\(225\) −87.5368 207.273i −0.389053 0.921216i
\(226\) −33.1301 −0.146593
\(227\) −179.821 48.1829i −0.792163 0.212259i −0.160022 0.987113i \(-0.551157\pi\)
−0.632140 + 0.774854i \(0.717823\pi\)
\(228\) 83.5858 11.1019i 0.366604 0.0486927i
\(229\) 156.704 + 90.4733i 0.684298 + 0.395080i 0.801473 0.598031i \(-0.204050\pi\)
−0.117174 + 0.993111i \(0.537384\pi\)
\(230\) 6.06725 + 17.7392i 0.0263793 + 0.0771268i
\(231\) −231.425 + 302.316i −1.00184 + 1.30873i
\(232\) 10.4417 + 2.79786i 0.0450075 + 0.0120597i
\(233\) −120.230 120.230i −0.516010 0.516010i 0.400351 0.916362i \(-0.368888\pi\)
−0.916362 + 0.400351i \(0.868888\pi\)
\(234\) 5.88404 22.1630i 0.0251455 0.0947136i
\(235\) −18.1861 268.004i −0.0773877 1.14044i
\(236\) −63.0278 109.167i −0.267067 0.462573i
\(237\) −230.162 95.0268i −0.971148 0.400957i
\(238\) 1.73363 0.464524i 0.00728415 0.00195178i
\(239\) −332.123 191.751i −1.38963 0.802306i −0.396360 0.918095i \(-0.629727\pi\)
−0.993274 + 0.115790i \(0.963060\pi\)
\(240\) −233.064 14.4681i −0.971102 0.0602836i
\(241\) 162.944 + 282.226i 0.676114 + 1.17106i 0.976142 + 0.217134i \(0.0696708\pi\)
−0.300028 + 0.953931i \(0.596996\pi\)
\(242\) 10.3932 10.3932i 0.0429470 0.0429470i
\(243\) 33.1004 + 240.735i 0.136216 + 0.990679i
\(244\) 322.909i 1.32340i
\(245\) 31.0612 158.058i 0.126781 0.645133i
\(246\) −40.7654 5.31925i −0.165713 0.0216230i
\(247\) −24.5938 91.7854i −0.0995702 0.371601i
\(248\) 38.2546 10.2503i 0.154252 0.0413318i
\(249\) 147.359 61.2364i 0.591803 0.245929i
\(250\) −15.7928 17.7591i −0.0631712 0.0710365i
\(251\) 428.941 1.70893 0.854465 0.519509i \(-0.173885\pi\)
0.854465 + 0.519509i \(0.173885\pi\)
\(252\) 278.057 161.389i 1.10340 0.640433i
\(253\) −196.383 196.383i −0.776219 0.776219i
\(254\) −3.80325 + 2.19581i −0.0149734 + 0.00864492i
\(255\) −3.11853 15.3999i −0.0122295 0.0603918i
\(256\) −116.589 + 201.938i −0.455426 + 0.788821i
\(257\) −95.3527 355.861i −0.371022 1.38467i −0.859070 0.511857i \(-0.828958\pi\)
0.488048 0.872817i \(-0.337709\pi\)
\(258\) 7.05253 0.936723i 0.0273354 0.00363071i
\(259\) −254.027 + 146.663i −0.980800 + 0.566265i
\(260\) 17.9815 + 264.990i 0.0691597 + 1.01919i
\(261\) 16.7731 + 62.0279i 0.0642647 + 0.237655i
\(262\) 7.42228 7.42228i 0.0283293 0.0283293i
\(263\) 17.0763 63.7296i 0.0649289 0.242318i −0.925833 0.377934i \(-0.876635\pi\)
0.990761 + 0.135616i \(0.0433013\pi\)
\(264\) −59.0691 + 24.5467i −0.223747 + 0.0929800i
\(265\) 53.8231 109.779i 0.203106 0.414262i
\(266\) −6.07462 + 10.5216i −0.0228369 + 0.0395547i
\(267\) −53.6079 + 41.2327i −0.200779 + 0.154429i
\(268\) −68.1242 + 254.243i −0.254195 + 0.948668i
\(269\) 146.927i 0.546197i −0.961986 0.273099i \(-0.911951\pi\)
0.961986 0.273099i \(-0.0880485\pi\)
\(270\) 11.4842 + 22.9542i 0.0425342 + 0.0850154i
\(271\) −45.0155 −0.166109 −0.0830544 0.996545i \(-0.526468\pi\)
−0.0830544 + 0.996545i \(0.526468\pi\)
\(272\) −15.7513 4.22056i −0.0579094 0.0155168i
\(273\) −220.891 287.187i −0.809124 1.05197i
\(274\) −32.2802 18.6370i −0.117811 0.0680182i
\(275\) 325.874 + 133.226i 1.18500 + 0.484457i
\(276\) 89.9973 + 216.569i 0.326077 + 0.784671i
\(277\) 153.339 + 41.0870i 0.553570 + 0.148329i 0.524751 0.851256i \(-0.324159\pi\)
0.0288193 + 0.999585i \(0.490825\pi\)
\(278\) 12.8126 + 12.8126i 0.0460885 + 0.0460885i
\(279\) 166.841 + 166.076i 0.597996 + 0.595256i
\(280\) 44.8664 51.3987i 0.160237 0.183567i
\(281\) −33.0937 57.3199i −0.117771 0.203986i 0.801113 0.598513i \(-0.204242\pi\)
−0.918884 + 0.394528i \(0.870908\pi\)
\(282\) 4.03456 + 30.3760i 0.0143069 + 0.107716i
\(283\) 388.793 104.177i 1.37383 0.368116i 0.504952 0.863148i \(-0.331510\pi\)
0.868875 + 0.495032i \(0.164844\pi\)
\(284\) 124.929 + 72.1278i 0.439891 + 0.253971i
\(285\) 88.6394 + 58.7854i 0.311015 + 0.206264i
\(286\) 17.9397 + 31.0726i 0.0627264 + 0.108645i
\(287\) −459.310 + 459.310i −1.60038 + 1.60038i
\(288\) 81.1460 0.186335i 0.281757 0.000646996i
\(289\) 287.903i 0.996203i
\(290\) 3.78363 + 5.63446i 0.0130470 + 0.0194292i
\(291\) −40.1880 96.7081i −0.138103 0.332330i
\(292\) −4.22190 15.7563i −0.0144586 0.0539600i
\(293\) −209.736 + 56.1985i −0.715821 + 0.191804i −0.598306 0.801267i \(-0.704159\pi\)
−0.117515 + 0.993071i \(0.537493\pi\)
\(294\) −2.37752 + 18.2207i −0.00808682 + 0.0619752i
\(295\) 30.6612 156.022i 0.103936 0.528889i
\(296\) −49.2820 −0.166493
\(297\) −302.444 230.423i −1.01833 0.775833i
\(298\) 34.9809 + 34.9809i 0.117386 + 0.117386i
\(299\) 228.886 132.147i 0.765504 0.441964i
\(300\) −211.421 209.002i −0.704738 0.696672i
\(301\) 56.2051 97.3500i 0.186728 0.323422i
\(302\) 12.6871 + 47.3490i 0.0420103 + 0.156785i
\(303\) −68.0699 + 164.871i −0.224653 + 0.544127i
\(304\) 95.5965 55.1926i 0.314462 0.181555i
\(305\) 267.857 306.855i 0.878218 1.00608i
\(306\) 0.467880 + 1.73025i 0.00152902 + 0.00565441i
\(307\) −219.096 + 219.096i −0.713666 + 0.713666i −0.967300 0.253634i \(-0.918374\pi\)
0.253634 + 0.967300i \(0.418374\pi\)
\(308\) −130.198 + 485.907i −0.422722 + 1.57762i
\(309\) 187.476 + 143.513i 0.606717 + 0.464445i
\(310\) 22.3259 + 10.9461i 0.0720191 + 0.0353099i
\(311\) −68.8478 + 119.248i −0.221376 + 0.383434i −0.955226 0.295877i \(-0.904388\pi\)
0.733850 + 0.679311i \(0.237721\pi\)
\(312\) −8.01473 60.3424i −0.0256882 0.193405i
\(313\) 1.70804 6.37451i 0.00545701 0.0203658i −0.963144 0.268988i \(-0.913311\pi\)
0.968601 + 0.248622i \(0.0799776\pi\)
\(314\) 8.83713i 0.0281437i
\(315\) 398.107 + 77.2864i 1.26383 + 0.245354i
\(316\) −329.010 −1.04117
\(317\) 427.280 + 114.489i 1.34789 + 0.361165i 0.859354 0.511381i \(-0.170866\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(318\) −5.32255 + 12.8916i −0.0167376 + 0.0405397i
\(319\) −87.0704 50.2701i −0.272948 0.157587i
\(320\) −286.486 + 97.9856i −0.895270 + 0.306205i
\(321\) 213.237 + 27.8241i 0.664290 + 0.0866796i
\(322\) −32.6401 8.74588i −0.101367 0.0271611i
\(323\) 5.25206 + 5.25206i 0.0162603 + 0.0162603i
\(324\) 161.811 + 277.316i 0.499418 + 0.855915i
\(325\) −202.724 + 266.731i −0.623767 + 0.820711i
\(326\) −10.3293 17.8909i −0.0316849 0.0548799i
\(327\) 113.753 87.4936i 0.347869 0.267565i
\(328\) −105.415 + 28.2459i −0.321388 + 0.0861156i
\(329\) 419.296 + 242.081i 1.27446 + 0.735808i
\(330\) −38.0735 12.7778i −0.115374 0.0387206i
\(331\) −130.851 226.641i −0.395321 0.684716i 0.597821 0.801630i \(-0.296033\pi\)
−0.993142 + 0.116913i \(0.962700\pi\)
\(332\) 149.090 149.090i 0.449067 0.449067i
\(333\) −147.050 253.352i −0.441590 0.760817i
\(334\) 59.2964i 0.177534i
\(335\) −275.635 + 185.093i −0.822791 + 0.552517i
\(336\) 255.834 334.204i 0.761412 0.994654i
\(337\) −37.7355 140.831i −0.111975 0.417895i 0.887068 0.461639i \(-0.152738\pi\)
−0.999043 + 0.0437433i \(0.986072\pi\)
\(338\) −1.94447 + 0.521020i −0.00575288 + 0.00154148i
\(339\) −415.103 317.763i −1.22449 0.937354i
\(340\) −11.5737 17.2352i −0.0340404 0.0506919i
\(341\) −368.341 −1.08018
\(342\) −10.5214 6.04239i −0.0307645 0.0176678i
\(343\) −106.954 106.954i −0.311820 0.311820i
\(344\) 16.3559 9.44310i 0.0475463 0.0274509i
\(345\) −94.1235 + 280.456i −0.272822 + 0.812916i
\(346\) 18.9580 32.8363i 0.0547920 0.0949025i
\(347\) −2.62052 9.77990i −0.00755192 0.0281842i 0.962047 0.272884i \(-0.0879774\pi\)
−0.969599 + 0.244699i \(0.921311\pi\)
\(348\) 51.7612 + 67.2964i 0.148739 + 0.193380i
\(349\) 94.1070 54.3327i 0.269648 0.155681i −0.359080 0.933307i \(-0.616909\pi\)
0.628727 + 0.777626i \(0.283576\pi\)
\(350\) 42.4423 5.78670i 0.121264 0.0165334i
\(351\) 286.297 221.255i 0.815662 0.630355i
\(352\) −89.7803 + 89.7803i −0.255058 + 0.255058i
\(353\) 125.168 467.133i 0.354583 1.32332i −0.526425 0.850221i \(-0.676468\pi\)
0.881008 0.473101i \(-0.156865\pi\)
\(354\) −2.34691 + 17.9861i −0.00662968 + 0.0508082i
\(355\) 58.8872 + 172.172i 0.165879 + 0.484991i
\(356\) −44.6798 + 77.3877i −0.125505 + 0.217381i
\(357\) 26.1769 + 10.8076i 0.0733246 + 0.0302735i
\(358\) 12.5047 46.6681i 0.0349293 0.130358i
\(359\) 279.063i 0.777333i −0.921378 0.388667i \(-0.872936\pi\)
0.921378 0.388667i \(-0.127064\pi\)
\(360\) 51.4330 + 44.6887i 0.142869 + 0.124135i
\(361\) 310.722 0.860724
\(362\) 43.5237 + 11.6621i 0.120231 + 0.0322159i
\(363\) 229.906 30.5363i 0.633350 0.0841220i
\(364\) −414.580 239.358i −1.13896 0.657576i
\(365\) 9.05805 18.4751i 0.0248166 0.0506167i
\(366\) −28.2434 + 36.8952i −0.0771678 + 0.100806i
\(367\) −172.547 46.2339i −0.470156 0.125978i 0.0159593 0.999873i \(-0.494920\pi\)
−0.486115 + 0.873895i \(0.661586\pi\)
\(368\) 217.097 + 217.097i 0.589938 + 0.589938i
\(369\) −459.750 457.643i −1.24594 1.24023i
\(370\) −23.3097 20.3472i −0.0629991 0.0549925i
\(371\) 110.184 + 190.844i 0.296992 + 0.514406i
\(372\) 287.502 + 118.701i 0.772854 + 0.319087i
\(373\) 84.7938 22.7204i 0.227329 0.0609127i −0.143356 0.989671i \(-0.545789\pi\)
0.370685 + 0.928758i \(0.379123\pi\)
\(374\) −2.42880 1.40227i −0.00649412 0.00374938i
\(375\) −27.5412 373.987i −0.0734432 0.997299i
\(376\) 40.6724 + 70.4466i 0.108171 + 0.187358i
\(377\) 67.6540 67.6540i 0.179453 0.179453i
\(378\) −45.8865 5.88035i −0.121393 0.0155565i
\(379\) 10.3793i 0.0273860i −0.999906 0.0136930i \(-0.995641\pi\)
0.999906 0.0136930i \(-0.00435875\pi\)
\(380\) 137.896 + 27.0990i 0.362883 + 0.0713133i
\(381\) −68.7136 8.96607i −0.180351 0.0235330i
\(382\) −2.68637 10.0257i −0.00703238 0.0262452i
\(383\) 124.435 33.3422i 0.324895 0.0870554i −0.0926850 0.995695i \(-0.529545\pi\)
0.417580 + 0.908640i \(0.362878\pi\)
\(384\) 131.807 54.7734i 0.343246 0.142639i
\(385\) −526.790 + 353.748i −1.36829 + 0.918827i
\(386\) 38.0686 0.0986233
\(387\) 97.3490 + 55.9068i 0.251548 + 0.144462i
\(388\) −97.8443 97.8443i −0.252176 0.252176i
\(389\) −635.357 + 366.824i −1.63331 + 0.942991i −0.650245 + 0.759724i \(0.725334\pi\)
−0.983063 + 0.183267i \(0.941333\pi\)
\(390\) 21.1229 31.8501i 0.0541613 0.0816670i
\(391\) −10.3294 + 17.8910i −0.0264178 + 0.0457570i
\(392\) 12.6250 + 47.1170i 0.0322065 + 0.120196i
\(393\) 164.187 21.8075i 0.417779 0.0554898i
\(394\) −4.31633 + 2.49203i −0.0109552 + 0.00632496i
\(395\) −312.652 272.917i −0.791525 0.690930i
\(396\) −485.557 128.910i −1.22615 0.325531i
\(397\) 151.257 151.257i 0.381000 0.381000i −0.490463 0.871462i \(-0.663172\pi\)
0.871462 + 0.490463i \(0.163172\pi\)
\(398\) 10.1408 37.8459i 0.0254794 0.0950903i
\(399\) −177.028 + 73.5656i −0.443679 + 0.184375i
\(400\) −360.246 147.278i −0.900614 0.368194i
\(401\) −3.27254 + 5.66821i −0.00816096 + 0.0141352i −0.870077 0.492916i \(-0.835931\pi\)
0.861916 + 0.507051i \(0.169264\pi\)
\(402\) 30.0213 23.0910i 0.0746799 0.0574402i
\(403\) 90.7225 338.581i 0.225118 0.840151i
\(404\) 235.677i 0.583360i
\(405\) −76.2704 + 397.753i −0.188322 + 0.982107i
\(406\) −12.2328 −0.0301302
\(407\) 442.734 + 118.630i 1.08780 + 0.291475i
\(408\) 2.90089 + 3.77154i 0.00711003 + 0.00924397i
\(409\) 639.259 + 369.076i 1.56298 + 0.902387i 0.996953 + 0.0779993i \(0.0248532\pi\)
0.566026 + 0.824387i \(0.308480\pi\)
\(410\) −61.5218 30.1632i −0.150053 0.0735688i
\(411\) −225.700 543.123i −0.549148 1.32147i
\(412\) 301.326 + 80.7400i 0.731373 + 0.195971i
\(413\) 202.652 + 202.652i 0.490683 + 0.490683i
\(414\) 8.65937 32.6166i 0.0209163 0.0787840i
\(415\) 265.350 18.0060i 0.639398 0.0433879i
\(416\) −60.4136 104.639i −0.145225 0.251537i
\(417\) 37.6448 + 283.426i 0.0902753 + 0.679678i
\(418\) 18.3376 4.91354i 0.0438698 0.0117549i
\(419\) −235.376 135.894i −0.561756 0.324330i 0.192094 0.981377i \(-0.438472\pi\)
−0.753850 + 0.657047i \(0.771805\pi\)
\(420\) 525.174 106.349i 1.25041 0.253213i
\(421\) 102.996 + 178.395i 0.244647 + 0.423741i 0.962032 0.272936i \(-0.0879947\pi\)
−0.717386 + 0.696676i \(0.754661\pi\)
\(422\) −32.6344 + 32.6344i −0.0773327 + 0.0773327i
\(423\) −240.796 + 419.292i −0.569259 + 0.991235i
\(424\) 37.0244i 0.0873217i
\(425\) 3.29849 25.9789i 0.00776115 0.0611269i
\(426\) −7.96553 19.1682i −0.0186984 0.0449958i
\(427\) 190.011 + 709.133i 0.444992 + 1.66073i
\(428\) 274.453 73.5396i 0.641246 0.171821i
\(429\) −73.2528 + 561.390i −0.170752 + 1.30860i
\(430\) 11.6349 + 2.28648i 0.0270579 + 0.00531738i
\(431\) −238.470 −0.553294 −0.276647 0.960972i \(-0.589223\pi\)
−0.276647 + 0.960972i \(0.589223\pi\)
\(432\) 334.345 + 254.727i 0.773946 + 0.589645i
\(433\) 79.6977 + 79.6977i 0.184059 + 0.184059i 0.793122 0.609063i \(-0.208454\pi\)
−0.609063 + 0.793122i \(0.708454\pi\)
\(434\) −38.8122 + 22.4083i −0.0894291 + 0.0516319i
\(435\) −6.63528 + 106.887i −0.0152535 + 0.245718i
\(436\) 94.8083 164.213i 0.217450 0.376635i
\(437\) −36.1940 135.078i −0.0828238 0.309103i
\(438\) −0.895748 + 2.16957i −0.00204509 + 0.00495336i
\(439\) 280.123 161.729i 0.638094 0.368404i −0.145786 0.989316i \(-0.546571\pi\)
0.783880 + 0.620912i \(0.213238\pi\)
\(440\) −106.366 + 7.21774i −0.241741 + 0.0164039i
\(441\) −204.551 + 205.492i −0.463834 + 0.465969i
\(442\) 1.88719 1.88719i 0.00426965 0.00426965i
\(443\) 195.518 729.682i 0.441349 1.64714i −0.284051 0.958809i \(-0.591678\pi\)
0.725400 0.688328i \(-0.241655\pi\)
\(444\) −307.338 235.268i −0.692202 0.529884i
\(445\) −106.653 + 36.4779i −0.239669 + 0.0819728i
\(446\) 19.5609 33.8805i 0.0438585 0.0759652i
\(447\) 102.778 + 773.808i 0.229928 + 1.73111i
\(448\) 141.245 527.135i 0.315280 1.17664i
\(449\) 514.733i 1.14640i 0.819416 + 0.573199i \(0.194298\pi\)
−0.819416 + 0.573199i \(0.805702\pi\)
\(450\) 5.87631 + 42.3724i 0.0130585 + 0.0941608i
\(451\) 1015.01 2.25057
\(452\) −667.186 178.772i −1.47607 0.395513i
\(453\) −295.179 + 714.945i −0.651609 + 1.57825i
\(454\) 30.6524 + 17.6972i 0.0675162 + 0.0389805i
\(455\) −195.418 571.356i −0.429491 1.25573i
\(456\) −31.9379 4.16741i −0.0700393 0.00913905i
\(457\) −550.455 147.494i −1.20450 0.322744i −0.399897 0.916560i \(-0.630954\pi\)
−0.804601 + 0.593816i \(0.797621\pi\)
\(458\) −24.3261 24.3261i −0.0531137 0.0531137i
\(459\) −10.7332 + 26.1667i −0.0233838 + 0.0570081i
\(460\) 26.4629 + 389.977i 0.0575280 + 0.847777i
\(461\) −119.334 206.693i −0.258860 0.448358i 0.707077 0.707137i \(-0.250013\pi\)
−0.965937 + 0.258778i \(0.916680\pi\)
\(462\) 57.3764 44.1312i 0.124191 0.0955222i
\(463\) −796.822 + 213.508i −1.72100 + 0.461140i −0.978078 0.208239i \(-0.933227\pi\)
−0.742921 + 0.669380i \(0.766560\pi\)
\(464\) 96.2543 + 55.5724i 0.207445 + 0.119768i
\(465\) 174.745 + 351.285i 0.375795 + 0.755451i
\(466\) 16.1635 + 27.9961i 0.0346857 + 0.0600774i
\(467\) 489.265 489.265i 1.04768 1.04768i 0.0488707 0.998805i \(-0.484438\pi\)
0.998805 0.0488707i \(-0.0155622\pi\)
\(468\) 238.088 414.576i 0.508734 0.885845i
\(469\) 598.424i 1.27596i
\(470\) −9.84808 + 50.1127i −0.0209534 + 0.106623i
\(471\) −84.7602 + 110.725i −0.179958 + 0.235084i
\(472\) 12.4624 + 46.5102i 0.0264033 + 0.0985386i
\(473\) −169.667 + 45.4623i −0.358705 + 0.0961147i
\(474\) 37.5922 + 28.7770i 0.0793085 + 0.0607110i
\(475\) 108.561 + 140.138i 0.228549 + 0.295027i
\(476\) 37.4190 0.0786114
\(477\) −190.337 + 110.475i −0.399030 + 0.231603i
\(478\) 51.5572 + 51.5572i 0.107860 + 0.107860i
\(479\) 142.795 82.4426i 0.298110 0.172114i −0.343483 0.939159i \(-0.611607\pi\)
0.641594 + 0.767045i \(0.278274\pi\)
\(480\) 128.216 + 43.0303i 0.267116 + 0.0896465i
\(481\) −218.091 + 377.744i −0.453411 + 0.785331i
\(482\) −16.0362 59.8478i −0.0332700 0.124165i
\(483\) −325.078 422.645i −0.673040 0.875041i
\(484\) 265.384 153.220i 0.548314 0.316569i
\(485\) −11.8169 174.143i −0.0243647 0.359057i
\(486\) 5.76728 45.8387i 0.0118668 0.0943184i
\(487\) 326.960 326.960i 0.671376 0.671376i −0.286657 0.958033i \(-0.592544\pi\)
0.958033 + 0.286657i \(0.0925441\pi\)
\(488\) −31.9241 + 119.142i −0.0654183 + 0.244144i
\(489\) 42.1772 323.235i 0.0862520 0.661013i
\(490\) −13.4819 + 27.4981i −0.0275141 + 0.0561186i
\(491\) −182.011 + 315.253i −0.370695 + 0.642063i −0.989673 0.143346i \(-0.954214\pi\)
0.618977 + 0.785409i \(0.287547\pi\)
\(492\) −792.245 327.094i −1.61025 0.664824i
\(493\) −1.93562 + 7.22382i −0.00392620 + 0.0146528i
\(494\) 18.0662i 0.0365713i
\(495\) −354.484 525.276i −0.716130 1.06116i
\(496\) 407.193 0.820953
\(497\) −316.796 84.8853i −0.637417 0.170795i
\(498\) −30.0751 + 3.99460i −0.0603918 + 0.00802129i
\(499\) −353.578 204.138i −0.708573 0.409095i 0.101960 0.994789i \(-0.467489\pi\)
−0.810532 + 0.585694i \(0.800822\pi\)
\(500\) −222.212 442.859i −0.444424 0.885717i
\(501\) 568.734 742.953i 1.13520 1.48294i
\(502\) −78.7732 21.1072i −0.156919 0.0420463i
\(503\) 555.921 + 555.921i 1.10521 + 1.10521i 0.993771 + 0.111440i \(0.0355462\pi\)
0.111440 + 0.993771i \(0.464454\pi\)
\(504\) −118.549 + 32.0571i −0.235217 + 0.0636055i
\(505\) −195.497 + 223.960i −0.387123 + 0.443486i
\(506\) 26.4014 + 45.7286i 0.0521767 + 0.0903726i
\(507\) −29.3606 12.1221i −0.0579104 0.0239094i
\(508\) −88.4400 + 23.6974i −0.174095 + 0.0466485i
\(509\) 453.968 + 262.098i 0.891882 + 0.514928i 0.874558 0.484922i \(-0.161152\pi\)
0.0173243 + 0.999850i \(0.494485\pi\)
\(510\) −0.185089 + 2.98158i −0.000362920 + 0.00584624i
\(511\) 18.5432 + 32.1178i 0.0362881 + 0.0628528i
\(512\) 165.919 165.919i 0.324061 0.324061i
\(513\) −73.8735 176.623i −0.144003 0.344295i
\(514\) 70.0445i 0.136273i
\(515\) 219.370 + 326.679i 0.425961 + 0.634328i
\(516\) 147.081 + 19.1918i 0.285041 + 0.0371935i
\(517\) −195.811 730.775i −0.378744 1.41349i
\(518\) 53.8679 14.4339i 0.103992 0.0278646i
\(519\) 552.479 229.588i 1.06451 0.442366i
\(520\) 19.5634 99.5499i 0.0376219 0.191442i
\(521\) −694.042 −1.33213 −0.666067 0.745892i \(-0.732023\pi\)
−0.666067 + 0.745892i \(0.732023\pi\)
\(522\) −0.0280527 12.2165i −5.37408e−5 0.0234033i
\(523\) 244.233 + 244.233i 0.466985 + 0.466985i 0.900936 0.433951i \(-0.142881\pi\)
−0.433951 + 0.900936i \(0.642881\pi\)
\(524\) 189.524 109.422i 0.361687 0.208820i
\(525\) 587.282 + 334.575i 1.11863 + 0.637286i
\(526\) −6.27198 + 10.8634i −0.0119239 + 0.0206528i
\(527\) 7.09137 + 26.4653i 0.0134561 + 0.0502189i
\(528\) −651.950 + 86.5925i −1.23475 + 0.164001i
\(529\) −121.283 + 70.0227i −0.229268 + 0.132368i
\(530\) −15.2864 + 17.5120i −0.0288422 + 0.0330415i
\(531\) −201.917 + 202.846i −0.380258 + 0.382008i
\(532\) −179.108 + 179.108i −0.336669 + 0.336669i
\(533\) −249.997 + 933.001i −0.469037 + 1.75047i
\(534\) 11.8738 4.93428i 0.0222356 0.00924022i
\(535\) 321.810 + 157.779i 0.601515 + 0.294913i
\(536\) 50.2711 87.0720i 0.0937893 0.162448i
\(537\) 604.288 464.790i 1.12530 0.865531i
\(538\) −7.22994 + 26.9825i −0.0134386 + 0.0501534i
\(539\) 453.674i 0.841696i
\(540\) 107.412 + 524.229i 0.198911 + 0.970795i
\(541\) −682.588 −1.26172 −0.630858 0.775899i \(-0.717297\pi\)
−0.630858 + 0.775899i \(0.717297\pi\)
\(542\) 8.26689 + 2.21511i 0.0152526 + 0.00408691i
\(543\) 433.474 + 563.573i 0.798294 + 1.03789i
\(544\) 8.17918 + 4.72225i 0.0150353 + 0.00868061i
\(545\) 226.311 77.4042i 0.415250 0.142026i
\(546\) 26.4338 + 63.6102i 0.0484136 + 0.116502i
\(547\) 62.4694 + 16.7386i 0.114204 + 0.0306008i 0.315468 0.948936i \(-0.397838\pi\)
−0.201265 + 0.979537i \(0.564505\pi\)
\(548\) −549.504 549.504i −1.00275 1.00275i
\(549\) −707.751 + 191.384i −1.28916 + 0.348605i
\(550\) −53.2896 40.5018i −0.0968901 0.0736396i
\(551\) −25.3122 43.8421i −0.0459387 0.0795682i
\(552\) −11.7950 88.8042i −0.0213678 0.160877i
\(553\) 722.530 193.601i 1.30656 0.350093i
\(554\) −26.1382 15.0909i −0.0471809 0.0272399i
\(555\) −96.9003 478.512i −0.174595 0.862184i
\(556\) 188.887 + 327.162i 0.339725 + 0.588421i
\(557\) −66.9124 + 66.9124i −0.120130 + 0.120130i −0.764616 0.644486i \(-0.777071\pi\)
0.644486 + 0.764616i \(0.277071\pi\)
\(558\) −22.4674 38.7091i −0.0402641 0.0693711i
\(559\) 167.156i 0.299028i
\(560\) 582.354 391.060i 1.03992 0.698322i
\(561\) −16.9819 40.8652i −0.0302708 0.0728436i
\(562\) 3.25693 + 12.1550i 0.00579525 + 0.0216282i
\(563\) −137.436 + 36.8258i −0.244113 + 0.0654099i −0.378801 0.925478i \(-0.623663\pi\)
0.134688 + 0.990888i \(0.456997\pi\)
\(564\) −82.6612 + 633.493i −0.146562 + 1.12322i
\(565\) −485.722 723.322i −0.859686 1.28022i
\(566\) −76.5264 −0.135206
\(567\) −518.533 513.792i −0.914521 0.906159i
\(568\) −38.9637 38.9637i −0.0685981 0.0685981i
\(569\) 276.828 159.827i 0.486517 0.280891i −0.236611 0.971604i \(-0.576037\pi\)
0.723128 + 0.690714i \(0.242703\pi\)
\(570\) −13.3855 15.1574i −0.0234834 0.0265920i
\(571\) −324.309 + 561.720i −0.567967 + 0.983748i 0.428800 + 0.903400i \(0.358937\pi\)
−0.996767 + 0.0803483i \(0.974397\pi\)
\(572\) 193.608 + 722.555i 0.338475 + 1.26321i
\(573\) 62.5011 151.382i 0.109077 0.264193i
\(574\) 106.952 61.7486i 0.186327 0.107576i
\(575\) −298.343 + 392.540i −0.518858 + 0.682679i
\(576\) 526.756 + 139.848i 0.914506 + 0.242792i
\(577\) −519.616 + 519.616i −0.900548 + 0.900548i −0.995483 0.0949353i \(-0.969736\pi\)
0.0949353 + 0.995483i \(0.469736\pi\)
\(578\) 14.1670 52.8721i 0.0245104 0.0914742i
\(579\) 476.980 + 365.130i 0.823800 + 0.630622i
\(580\) 45.7923 + 133.886i 0.0789522 + 0.230837i
\(581\) −239.683 + 415.144i −0.412536 + 0.714533i
\(582\) 2.62156 + 19.7376i 0.00450440 + 0.0339134i
\(583\) 89.1240 332.615i 0.152871 0.570523i
\(584\) 6.23095i 0.0106694i
\(585\) 570.146 196.468i 0.974608 0.335843i
\(586\) 41.2824 0.0704478
\(587\) −797.684 213.739i −1.35892 0.364120i −0.495498 0.868609i \(-0.665014\pi\)
−0.863418 + 0.504489i \(0.831681\pi\)
\(588\) −146.200 + 354.106i −0.248639 + 0.602222i
\(589\) −160.621 92.7344i −0.272701 0.157444i
\(590\) −13.3083 + 27.1440i −0.0225564 + 0.0460068i
\(591\) −77.9834 10.1756i −0.131952 0.0172177i
\(592\) −489.432 131.143i −0.826743 0.221525i
\(593\) 329.014 + 329.014i 0.554829 + 0.554829i 0.927831 0.373002i \(-0.121671\pi\)
−0.373002 + 0.927831i \(0.621671\pi\)
\(594\) 44.2039 + 57.1987i 0.0744174 + 0.0962941i
\(595\) 35.5587 + 31.0395i 0.0597625 + 0.0521672i
\(596\) 515.699 + 893.218i 0.865267 + 1.49869i
\(597\) 490.053 376.926i 0.820860 0.631366i
\(598\) −48.5366 + 13.0053i −0.0811648 + 0.0217480i
\(599\) 445.587 + 257.260i 0.743885 + 0.429482i 0.823480 0.567345i \(-0.192029\pi\)
−0.0795952 + 0.996827i \(0.525363\pi\)
\(600\) 57.3446 + 98.0165i 0.0955743 + 0.163361i
\(601\) −19.7478 34.2041i −0.0328582 0.0569121i 0.849129 0.528186i \(-0.177128\pi\)
−0.881987 + 0.471274i \(0.843794\pi\)
\(602\) −15.1122 + 15.1122i −0.0251033 + 0.0251033i
\(603\) 597.626 1.37232i 0.991087 0.00227583i
\(604\) 1021.99i 1.69204i
\(605\) 379.287 + 74.5370i 0.626921 + 0.123202i
\(606\) 20.6137 26.9282i 0.0340159 0.0444360i
\(607\) 104.659 + 390.594i 0.172421 + 0.643483i 0.996977 + 0.0777026i \(0.0247585\pi\)
−0.824556 + 0.565781i \(0.808575\pi\)
\(608\) −61.7533 + 16.5468i −0.101568 + 0.0272151i
\(609\) −153.271 117.330i −0.251677 0.192660i
\(610\) −64.2903 + 43.1720i −0.105394 + 0.0707738i
\(611\) 719.960 1.17833
\(612\) 0.0858104 + 37.3691i 0.000140213 + 0.0610606i
\(613\) −559.593 559.593i −0.912876 0.912876i 0.0836213 0.996498i \(-0.473351\pi\)
−0.996498 + 0.0836213i \(0.973351\pi\)
\(614\) 51.0172 29.4548i 0.0830898 0.0479719i
\(615\) −481.530 968.008i −0.782975 1.57400i
\(616\) 96.0775 166.411i 0.155970 0.270148i
\(617\) 90.4285 + 337.484i 0.146562 + 0.546976i 0.999681 + 0.0252596i \(0.00804123\pi\)
−0.853119 + 0.521716i \(0.825292\pi\)
\(618\) −27.3671 35.5809i −0.0442834 0.0575742i
\(619\) −384.591 + 222.044i −0.621311 + 0.358714i −0.777379 0.629032i \(-0.783451\pi\)
0.156068 + 0.987746i \(0.450118\pi\)
\(620\) 390.542 + 340.908i 0.629907 + 0.549852i
\(621\) 421.335 325.614i 0.678479 0.524338i
\(622\) 18.5115 18.5115i 0.0297613 0.0297613i
\(623\) 52.5825 196.241i 0.0844021 0.314993i
\(624\) 80.9792 620.603i 0.129774 0.994557i
\(625\) 156.192 605.169i 0.249907 0.968270i
\(626\) −0.627350 + 1.08660i −0.00100216 + 0.00173579i
\(627\) 276.888 + 114.319i 0.441608 + 0.182326i
\(628\) −47.6857 + 177.965i −0.0759326 + 0.283384i
\(629\) 34.0943i 0.0542040i
\(630\) −69.3076 33.7833i −0.110012 0.0536242i
\(631\) −181.428 −0.287524 −0.143762 0.989612i \(-0.545920\pi\)
−0.143762 + 0.989612i \(0.545920\pi\)
\(632\) 121.393 + 32.5273i 0.192078 + 0.0514672i
\(633\) −721.901 + 95.8834i −1.14044 + 0.151475i
\(634\) −72.8343 42.0509i −0.114881 0.0663264i
\(635\) −103.700 50.8427i −0.163308 0.0800673i
\(636\) −176.751 + 230.895i −0.277911 + 0.363043i
\(637\) 417.019 + 111.740i 0.654661 + 0.175416i
\(638\) 13.5164 + 13.5164i 0.0211856 + 0.0211856i
\(639\) 84.0456 316.568i 0.131527 0.495412i
\(640\) 237.345 16.1056i 0.370851 0.0251650i
\(641\) 44.3645 + 76.8416i 0.0692114 + 0.119878i 0.898554 0.438862i \(-0.144618\pi\)
−0.829343 + 0.558740i \(0.811285\pi\)
\(642\) −37.7909 15.6027i −0.0588643 0.0243032i
\(643\) −414.879 + 111.166i −0.645224 + 0.172887i −0.566568 0.824015i \(-0.691729\pi\)
−0.0786553 + 0.996902i \(0.525063\pi\)
\(644\) −610.125 352.256i −0.947399 0.546981i
\(645\) 123.849 + 140.243i 0.192014 + 0.217431i
\(646\) −0.706077 1.22296i −0.00109300 0.00189313i
\(647\) 237.290 237.290i 0.366755 0.366755i −0.499537 0.866292i \(-0.666497\pi\)
0.866292 + 0.499537i \(0.166497\pi\)
\(648\) −32.2862 118.318i −0.0498244 0.182589i
\(649\) 447.832i 0.690034i
\(650\) 50.3547 39.0084i 0.0774687 0.0600130i
\(651\) −701.223 91.4988i −1.07715 0.140551i
\(652\) −111.475 416.030i −0.170974 0.638083i
\(653\) −777.291 + 208.275i −1.19034 + 0.318950i −0.799020 0.601305i \(-0.794648\pi\)
−0.391319 + 0.920255i \(0.627981\pi\)
\(654\) −25.1956 + 10.4703i −0.0385255 + 0.0160096i
\(655\) 270.868 + 53.2305i 0.413539 + 0.0812680i
\(656\) −1122.07 −1.71047
\(657\) −32.0324 + 18.5921i −0.0487556 + 0.0282985i
\(658\) −65.0897 65.0897i −0.0989206 0.0989206i
\(659\) −407.245 + 235.123i −0.617974 + 0.356787i −0.776080 0.630635i \(-0.782795\pi\)
0.158106 + 0.987422i \(0.449461\pi\)
\(660\) −697.788 462.771i −1.05725 0.701168i
\(661\) 379.580 657.451i 0.574251 0.994631i −0.421872 0.906655i \(-0.638627\pi\)
0.996123 0.0879760i \(-0.0280399\pi\)
\(662\) 12.8778 + 48.0606i 0.0194528 + 0.0725990i
\(663\) 41.7462 5.54476i 0.0629656 0.00836313i
\(664\) −69.7489 + 40.2696i −0.105044 + 0.0606469i
\(665\) −318.775 + 21.6313i −0.479361 + 0.0325283i
\(666\) 14.5381 + 53.7630i 0.0218290 + 0.0807252i
\(667\) 99.5643 99.5643i 0.149272 0.149272i
\(668\) 319.967 1194.13i 0.478992 1.78762i
\(669\) 570.048 236.889i 0.852090 0.354094i
\(670\) 59.7272 20.4282i 0.0891450 0.0304899i
\(671\) 573.592 993.490i 0.854832 1.48061i
\(672\) −193.220 + 148.616i −0.287529 + 0.221154i
\(673\) −326.337 + 1217.91i −0.484899 + 1.80967i 0.0956152 + 0.995418i \(0.469518\pi\)
−0.580514 + 0.814250i \(0.697148\pi\)
\(674\) 27.7198i 0.0411273i
\(675\) −332.782 + 587.266i −0.493011 + 0.870023i
\(676\) −41.9700 −0.0620858
\(677\) −96.3967 25.8294i −0.142388 0.0381528i 0.186921 0.982375i \(-0.440149\pi\)
−0.329309 + 0.944222i \(0.606816\pi\)
\(678\) 60.5954 + 78.7820i 0.0893738 + 0.116198i
\(679\) 272.449 + 157.298i 0.401250 + 0.231662i
\(680\) 2.56637 + 7.50345i 0.00377408 + 0.0110345i
\(681\) 214.318 + 515.734i 0.314711 + 0.757319i
\(682\) 67.6443 + 18.1252i 0.0991852 + 0.0265766i
\(683\) 366.381 + 366.381i 0.536430 + 0.536430i 0.922478 0.386049i \(-0.126160\pi\)
−0.386049 + 0.922478i \(0.626160\pi\)
\(684\) −179.280 178.458i −0.262105 0.260904i
\(685\) −66.3650 978.005i −0.0968832 1.42774i
\(686\) 14.3787 + 24.9047i 0.0209602 + 0.0363042i
\(687\) −71.4727 538.114i −0.104036 0.783281i
\(688\) 187.563 50.2575i 0.272621 0.0730486i
\(689\) 283.790 + 163.846i 0.411887 + 0.237803i
\(690\) 31.0860 46.8729i 0.0450521 0.0679318i
\(691\) −298.133 516.381i −0.431451 0.747296i 0.565547 0.824716i \(-0.308665\pi\)
−0.996999 + 0.0774204i \(0.975332\pi\)
\(692\) 558.971 558.971i 0.807761 0.807761i
\(693\) 1142.18 2.62277i 1.64816 0.00378466i
\(694\) 1.92499i 0.00277376i
\(695\) −91.8883 + 467.581i −0.132213 + 0.672778i
\(696\) −12.4449 29.9474i −0.0178806 0.0430279i
\(697\) −19.5411 72.9284i −0.0280360 0.104632i
\(698\) −19.9559 + 5.34718i −0.0285902 + 0.00766071i
\(699\) −66.0000 + 505.806i −0.0944206 + 0.723614i
\(700\) 885.943 + 112.486i 1.26563 + 0.160695i
\(701\) 147.235 0.210036 0.105018 0.994470i \(-0.466510\pi\)
0.105018 + 0.994470i \(0.466510\pi\)
\(702\) −63.4647 + 26.5444i −0.0904056 + 0.0378126i
\(703\) 163.194 + 163.194i 0.232140 + 0.232140i
\(704\) −738.513 + 426.381i −1.04902 + 0.605654i
\(705\) −604.041 + 533.430i −0.856796 + 0.756638i
\(706\) −45.9731 + 79.6277i −0.0651177 + 0.112787i
\(707\) −138.681 517.565i −0.196154 0.732058i
\(708\) −144.317 + 349.546i −0.203837 + 0.493710i
\(709\) −123.232 + 71.1480i −0.173811 + 0.100350i −0.584382 0.811479i \(-0.698663\pi\)
0.410571 + 0.911829i \(0.365330\pi\)
\(710\) −2.34219 34.5163i −0.00329886 0.0486145i
\(711\) 195.000 + 721.122i 0.274262 + 1.01424i
\(712\) 24.1362 24.1362i 0.0338992 0.0338992i
\(713\) 133.514 498.280i 0.187256 0.698849i
\(714\) −4.27545 3.27288i −0.00598803 0.00458386i
\(715\) −415.385 + 847.232i −0.580958 + 1.18494i
\(716\) 503.648 872.343i 0.703418 1.21836i
\(717\) 151.481 + 1140.49i 0.211270 + 1.59064i
\(718\) −13.7320 + 51.2486i −0.0191254 + 0.0713769i
\(719\) 1075.81i 1.49626i −0.663555 0.748128i \(-0.730953\pi\)
0.663555 0.748128i \(-0.269047\pi\)
\(720\) 391.874 + 580.681i 0.544270 + 0.806501i
\(721\) −709.245 −0.983696
\(722\) −57.0627 15.2899i −0.0790342 0.0211771i
\(723\) 373.097 903.670i 0.516041 1.24989i
\(724\) 813.567 + 469.713i 1.12371 + 0.648775i
\(725\) −67.5439 + 165.215i −0.0931640 + 0.227882i
\(726\) −43.7239 5.70530i −0.0602257 0.00785853i
\(727\) 696.238 + 186.556i 0.957687 + 0.256611i 0.703621 0.710576i \(-0.251565\pi\)
0.254066 + 0.967187i \(0.418232\pi\)
\(728\) 129.302 + 129.302i 0.177613 + 0.177613i
\(729\) 511.918 519.020i 0.702219 0.711961i
\(730\) −2.57259 + 2.94715i −0.00352410 + 0.00403718i
\(731\) 6.53293 + 11.3154i 0.00893698 + 0.0154793i
\(732\) −767.865 + 590.605i −1.04900 + 0.806838i
\(733\) 1179.49 316.043i 1.60913 0.431164i 0.661345 0.750082i \(-0.269986\pi\)
0.947782 + 0.318918i \(0.103319\pi\)
\(734\) 29.4125 + 16.9813i 0.0400715 + 0.0231353i
\(735\) −432.666 + 215.227i −0.588661 + 0.292826i
\(736\) −88.9088 153.995i −0.120800 0.209232i
\(737\) −661.216 + 661.216i −0.897173 + 0.897173i
\(738\) 61.9115 + 106.668i 0.0838910 + 0.144536i
\(739\) 683.603i 0.925038i −0.886609 0.462519i \(-0.846946\pi\)
0.886609 0.462519i \(-0.153054\pi\)
\(740\) −359.624 535.540i −0.485978 0.723703i
\(741\) −173.280 + 226.360i −0.233846 + 0.305479i
\(742\) −10.8438 40.4697i −0.0146143 0.0545413i
\(743\) −763.713 + 204.636i −1.02788 + 0.275419i −0.733081 0.680141i \(-0.761919\pi\)
−0.294797 + 0.955560i \(0.595252\pi\)
\(744\) −94.3431 72.2201i −0.126805 0.0970700i
\(745\) −250.873 + 1276.59i −0.336743 + 1.71354i
\(746\) −16.6900 −0.0223727
\(747\) −415.140 238.412i −0.555742 0.319159i
\(748\) −41.3454 41.3454i −0.0552746 0.0552746i
\(749\) −559.447 + 322.997i −0.746925 + 0.431238i
\(750\) −13.3452 + 70.0364i −0.0177937 + 0.0933818i
\(751\) 326.862 566.142i 0.435236 0.753851i −0.562079 0.827084i \(-0.689998\pi\)
0.997315 + 0.0732329i \(0.0233317\pi\)
\(752\) 216.464 + 807.855i 0.287851 + 1.07427i
\(753\) −784.541 1020.01i −1.04189 1.35459i
\(754\) −15.7535 + 9.09526i −0.0208932 + 0.0120627i
\(755\) −847.754 + 971.182i −1.12285 + 1.28633i
\(756\) −892.348 366.027i −1.18035 0.484163i
\(757\) 668.868 668.868i 0.883577 0.883577i −0.110319 0.993896i \(-0.535187\pi\)
0.993896 + 0.110319i \(0.0351874\pi\)
\(758\) −0.510741 + 1.90611i −0.000673800 + 0.00251466i
\(759\) −107.804 + 826.181i −0.142034 + 1.08851i
\(760\) −48.1997 23.6316i −0.0634206 0.0310942i
\(761\) 478.705 829.141i 0.629047 1.08954i −0.358696 0.933454i \(-0.616779\pi\)
0.987743 0.156087i \(-0.0498881\pi\)
\(762\) 12.1778 + 5.02782i 0.0159813 + 0.00659819i
\(763\) −111.577 + 416.413i −0.146235 + 0.545757i
\(764\) 216.396i 0.283241i
\(765\) −30.9165 + 35.5824i −0.0404138 + 0.0465130i
\(766\) −24.4926 −0.0319747
\(767\) 411.649 + 110.301i 0.536700 + 0.143808i
\(768\) 693.444 92.1038i 0.902922 0.119927i
\(769\) −435.970 251.708i −0.566932 0.327318i 0.188991 0.981979i \(-0.439478\pi\)
−0.755923 + 0.654661i \(0.772812\pi\)
\(770\) 114.150 39.0422i 0.148247 0.0507041i
\(771\) −671.823 + 877.621i −0.871365 + 1.13829i
\(772\) 766.640 + 205.421i 0.993057 + 0.266089i
\(773\) −362.267 362.267i −0.468651 0.468651i 0.432827 0.901477i \(-0.357516\pi\)
−0.901477 + 0.432827i \(0.857516\pi\)
\(774\) −15.1267 15.0574i −0.0195435 0.0194540i
\(775\) 88.3390 + 647.918i 0.113986 + 0.836024i
\(776\) 26.4279 + 45.7745i 0.0340566 + 0.0589878i
\(777\) 813.378 + 335.819i 1.04682 + 0.432199i
\(778\) 134.731 36.1011i 0.173176 0.0464024i
\(779\) 442.610 + 255.541i 0.568177 + 0.328037i
\(780\) 597.247 527.430i 0.765701 0.676192i
\(781\) 256.245 + 443.830i 0.328099 + 0.568284i
\(782\) 2.77732 2.77732i 0.00355155 0.00355155i
\(783\) 116.822 153.336i 0.149198 0.195831i
\(784\) 501.526i 0.639701i
\(785\) −192.939 + 129.562i −0.245782 + 0.165047i
\(786\) −31.2254 4.07443i −0.0397270 0.00518376i
\(787\) 134.565 + 502.205i 0.170985 + 0.638126i 0.997201 + 0.0747716i \(0.0238228\pi\)
−0.826215 + 0.563354i \(0.809511\pi\)
\(788\) −100.371 + 26.8943i −0.127374 + 0.0341299i
\(789\) −182.779 + 75.9557i −0.231659 + 0.0962683i
\(790\) 43.9876 + 65.5050i 0.0556806 + 0.0829177i
\(791\) 1570.39 1.98532
\(792\) 166.409 + 95.5677i 0.210113 + 0.120666i
\(793\) 771.945 + 771.945i 0.973449 + 0.973449i
\(794\) −35.2207 + 20.3347i −0.0443585 + 0.0256104i
\(795\) −359.494 + 72.7988i −0.452194 + 0.0915708i
\(796\) 408.438 707.435i 0.513113 0.888737i
\(797\) 72.1737 + 269.356i 0.0905567 + 0.337962i 0.996308 0.0858466i \(-0.0273595\pi\)
−0.905752 + 0.423809i \(0.860693\pi\)
\(798\) 36.1304 4.79887i 0.0452762 0.00601362i
\(799\) −48.7365 + 28.1380i −0.0609968 + 0.0352165i
\(800\) 179.457 + 136.393i 0.224321 + 0.170491i
\(801\) 196.099 + 52.0623i 0.244818 + 0.0649967i
\(802\) 0.879908 0.879908i 0.00109714 0.00109714i
\(803\) 14.9989 55.9768i 0.0186786 0.0697096i
\(804\) 729.181 303.018i 0.906941 0.376888i
\(805\) −287.592 840.848i −0.357257 1.04453i
\(806\) −33.3216 + 57.7147i −0.0413419 + 0.0716063i
\(807\) −349.387 + 268.732i −0.432945 + 0.333001i
\(808\) 23.3000 86.9569i 0.0288367 0.107620i
\(809\) 423.966i 0.524062i −0.965060 0.262031i \(-0.915608\pi\)
0.965060 0.262031i \(-0.0843922\pi\)
\(810\) 33.5793 69.2926i 0.0414559 0.0855464i
\(811\) −1163.79 −1.43501 −0.717506 0.696552i \(-0.754716\pi\)
−0.717506 + 0.696552i \(0.754716\pi\)
\(812\) −246.350 66.0092i −0.303386 0.0812921i
\(813\) 82.3340 + 107.045i 0.101272 + 0.131667i
\(814\) −75.4686 43.5718i −0.0927133 0.0535281i
\(815\) 239.169 487.816i 0.293459 0.598548i
\(816\) 18.7731 + 45.1756i 0.0230063 + 0.0553622i
\(817\) −85.4317 22.8914i −0.104568 0.0280188i
\(818\) −99.2357 99.2357i −0.121315 0.121315i
\(819\) −278.907 + 1050.54i −0.340546 + 1.28271i
\(820\) −1076.19 939.413i −1.31242 1.14563i
\(821\) −382.915 663.228i −0.466400 0.807829i 0.532863 0.846202i \(-0.321116\pi\)
−0.999264 + 0.0383722i \(0.987783\pi\)
\(822\) 14.7230 + 110.848i 0.0179112 + 0.134852i
\(823\) −955.510 + 256.028i −1.16101 + 0.311091i −0.787369 0.616482i \(-0.788557\pi\)
−0.373640 + 0.927574i \(0.621891\pi\)
\(824\) −103.197 59.5806i −0.125239 0.0723066i
\(825\) −279.223 1018.59i −0.338452 1.23465i
\(826\) −27.2441 47.1882i −0.0329832 0.0571286i
\(827\) −260.100 + 260.100i −0.314510 + 0.314510i −0.846654 0.532144i \(-0.821387\pi\)
0.532144 + 0.846654i \(0.321387\pi\)
\(828\) 350.387 610.119i 0.423172 0.736858i
\(829\) 325.275i 0.392370i 0.980567 + 0.196185i \(0.0628553\pi\)
−0.980567 + 0.196185i \(0.937145\pi\)
\(830\) −49.6164 9.75055i −0.0597788 0.0117476i
\(831\) −182.756 439.783i −0.219923 0.529221i
\(832\) −210.035 783.862i −0.252446 0.942142i
\(833\) −32.5965 + 8.73421i −0.0391315 + 0.0104852i
\(834\) 7.03342 53.9023i 0.00843336 0.0646310i
\(835\) 1294.61 869.349i 1.55043 1.04114i
\(836\) 395.803 0.473449
\(837\) 89.7687 700.497i 0.107251 0.836914i
\(838\) 36.5387 + 36.5387i 0.0436022 + 0.0436022i
\(839\) −81.4767 + 47.0406i −0.0971116 + 0.0560674i −0.547769 0.836629i \(-0.684523\pi\)
0.450658 + 0.892697i \(0.351190\pi\)
\(840\) −204.285 12.6815i −0.243197 0.0150971i
\(841\) −395.014 + 684.184i −0.469695 + 0.813536i
\(842\) −10.1364 37.8296i −0.0120385 0.0449283i
\(843\) −75.7757 + 183.535i −0.0898882 + 0.217716i
\(844\) −833.301 + 481.107i −0.987323 + 0.570031i
\(845\) −39.8834 34.8146i −0.0471993 0.0412007i
\(846\) 64.8536 65.1522i 0.0766591 0.0770120i
\(847\) −492.644 + 492.644i −0.581633 + 0.581633i
\(848\) −98.5244 + 367.698i −0.116184 + 0.433606i
\(849\) −958.837 733.994i −1.12937 0.864539i
\(850\) −1.88412 + 4.60861i −0.00221661 + 0.00542189i
\(851\) −320.958 + 555.915i −0.377154 + 0.653249i
\(852\) −56.9800 428.999i −0.0668779 0.503520i
\(853\) 263.924 984.979i 0.309407 1.15472i −0.619678 0.784856i \(-0.712737\pi\)
0.929085 0.369867i \(-0.120597\pi\)
\(854\) 139.579i 0.163442i
\(855\) −22.3335 318.300i −0.0261210 0.372281i
\(856\) −108.534 −0.126793
\(857\) 1522.95 + 408.073i 1.77707 + 0.476164i 0.990044 0.140756i \(-0.0449532\pi\)
0.787026 + 0.616920i \(0.211620\pi\)
\(858\) 41.0773 99.4922i 0.0478756 0.115958i
\(859\) −507.067 292.755i −0.590299 0.340809i 0.174917 0.984583i \(-0.444034\pi\)
−0.765216 + 0.643774i \(0.777368\pi\)
\(860\) 221.970 + 108.829i 0.258105 + 0.126545i
\(861\) 1932.30 + 252.136i 2.24426 + 0.292841i
\(862\) 43.7939 + 11.7345i 0.0508050 + 0.0136132i
\(863\) −550.423 550.423i −0.637802 0.637802i 0.312211 0.950013i \(-0.398930\pi\)
−0.950013 + 0.312211i \(0.898930\pi\)
\(864\) −148.860 192.621i −0.172292 0.222941i
\(865\) 994.853 67.5082i 1.15012 0.0780442i
\(866\) −10.7144 18.5579i −0.0123723 0.0214294i
\(867\) 684.622 526.579i 0.789644 0.607357i
\(868\) −902.531 + 241.833i −1.03978 + 0.278609i
\(869\) −1012.26 584.429i −1.16486 0.672530i
\(870\) 6.47821 19.3029i 0.00744622 0.0221872i
\(871\) −444.935 770.650i −0.510833 0.884788i
\(872\) −51.2158 + 51.2158i −0.0587337 + 0.0587337i
\(873\) −156.464 + 272.446i −0.179225 + 0.312080i
\(874\) 26.5875i 0.0304205i
\(875\) 748.589 + 841.794i 0.855530 + 0.962050i
\(876\) −29.7460 + 38.8581i −0.0339567 + 0.0443585i
\(877\) 236.500 + 882.630i 0.269669 + 1.00642i 0.959330 + 0.282287i \(0.0910930\pi\)
−0.689661 + 0.724133i \(0.742240\pi\)
\(878\) −59.4017 + 15.9166i −0.0676557 + 0.0181283i
\(879\) 517.247 + 395.955i 0.588450 + 0.450461i
\(880\) −1075.55 211.366i −1.22222 0.240189i
\(881\) −459.689 −0.521781 −0.260891 0.965368i \(-0.584016\pi\)
−0.260891 + 0.965368i \(0.584016\pi\)
\(882\) 47.6767 27.6723i 0.0540552 0.0313745i
\(883\) 107.163 + 107.163i 0.121362 + 0.121362i 0.765179 0.643817i \(-0.222650\pi\)
−0.643817 + 0.765179i \(0.722650\pi\)
\(884\) 48.1882 27.8215i 0.0545116 0.0314723i
\(885\) −427.095 + 212.456i −0.482593 + 0.240063i
\(886\) −71.8119 + 124.382i −0.0810519 + 0.140386i
\(887\) −172.159 642.507i −0.194092 0.724360i −0.992500 0.122244i \(-0.960991\pi\)
0.798408 0.602116i \(-0.205676\pi\)
\(888\) 90.1376 + 117.191i 0.101506 + 0.131972i
\(889\) 180.277 104.083i 0.202786 0.117078i
\(890\) 21.3813 1.45088i 0.0240239 0.00163020i
\(891\) 5.23854 + 1140.65i 0.00587940 + 1.28019i
\(892\) 576.746 576.746i 0.646576 0.646576i
\(893\) 98.5954 367.963i 0.110409 0.412053i
\(894\) 19.2026 147.164i 0.0214794 0.164613i
\(895\) 1202.23 411.192i 1.34327 0.459433i
\(896\) −214.387 + 371.329i −0.239271 + 0.414430i
\(897\) −732.877 302.582i −0.817031 0.337327i
\(898\) 25.3288 94.5284i 0.0282058 0.105266i
\(899\) 186.745i 0.207725i
\(900\) −110.305 + 885.019i −0.122561 + 0.983355i
\(901\) −25.6142 −0.0284287
\(902\) −186.402 49.9463i −0.206654 0.0553728i
\(903\) −334.295 + 44.4012i −0.370204 + 0.0491708i
\(904\) 228.495 + 131.922i 0.252760 + 0.145931i
\(905\) 383.487 + 1121.22i 0.423743 + 1.23892i
\(906\) 89.3891 116.772i 0.0986635 0.128887i
\(907\) −804.640 215.603i −0.887144 0.237710i −0.213657 0.976909i \(-0.568538\pi\)
−0.673487 + 0.739199i \(0.735204\pi\)
\(908\) 521.794 + 521.794i 0.574663 + 0.574663i
\(909\) 516.557 139.683i 0.568269 0.153667i
\(910\) 7.77262 + 114.543i 0.00854134 + 0.125872i
\(911\) −38.7954 67.1955i −0.0425855 0.0737602i 0.843947 0.536427i \(-0.180226\pi\)
−0.886533 + 0.462666i \(0.846893\pi\)
\(912\) −306.093 126.376i −0.335629 0.138571i
\(913\) 723.538 193.871i 0.792484 0.212345i
\(914\) 93.8309 + 54.1733i 0.102660 + 0.0592706i
\(915\) −1219.60 75.7099i −1.33290 0.0827430i
\(916\) −358.623 621.153i −0.391510 0.678115i
\(917\) −351.821 + 351.821i −0.383665 + 0.383665i
\(918\) 3.25871 4.27725i 0.00354979 0.00465932i
\(919\) 1478.95i 1.60930i 0.593750 + 0.804650i \(0.297647\pi\)
−0.593750 + 0.804650i \(0.702353\pi\)
\(920\) 28.7909 146.505i 0.0312944 0.159244i
\(921\) 921.730 + 120.272i 1.00079 + 0.130588i
\(922\) 11.7443 + 43.8305i 0.0127379 + 0.0475385i
\(923\) −471.083 + 126.226i −0.510383 + 0.136757i
\(924\) 1393.60 579.125i 1.50823 0.626758i
\(925\) 102.492 807.227i 0.110802 0.872678i
\(926\) 156.839 0.169373
\(927\) −1.62646 708.298i −0.00175454 0.764076i
\(928\) −45.5177 45.5177i −0.0490492 0.0490492i
\(929\) 1381.56 797.643i 1.48715 0.858604i 0.487253 0.873261i \(-0.337999\pi\)
0.999893 + 0.0146572i \(0.00466569\pi\)
\(930\) −14.8052 73.1107i −0.0159195 0.0786137i
\(931\) 114.218 197.831i 0.122683 0.212493i
\(932\) 174.439 + 651.014i 0.187166 + 0.698513i
\(933\) 409.491 54.3888i 0.438897 0.0582946i
\(934\) −113.927 + 65.7757i −0.121977 + 0.0704237i
\(935\) −4.99338 73.5863i −0.00534051 0.0787019i
\(936\) −128.833 + 129.426i −0.137642 + 0.138276i
\(937\) −921.265 + 921.265i −0.983207 + 0.983207i −0.999861 0.0166542i \(-0.994699\pi\)
0.0166542 + 0.999861i \(0.494699\pi\)
\(938\) −29.4471 + 109.898i −0.0313935 + 0.117162i
\(939\) −18.2824 + 7.59741i −0.0194700 + 0.00809096i
\(940\) −468.736 + 956.048i −0.498655 + 1.01707i
\(941\) −618.185 + 1070.73i −0.656945 + 1.13786i 0.324458 + 0.945900i \(0.394818\pi\)
−0.981402 + 0.191961i \(0.938515\pi\)
\(942\) 21.0144 16.1632i 0.0223082 0.0171584i
\(943\) −367.913 + 1373.07i −0.390152 + 1.45607i
\(944\) 495.068i 0.524436i
\(945\) −544.360 1088.04i −0.576043 1.15137i
\(946\) 33.3958 0.0353021
\(947\) −1561.01 418.272i −1.64838 0.441681i −0.689219 0.724553i \(-0.742046\pi\)
−0.959158 + 0.282872i \(0.908713\pi\)
\(948\) 601.764 + 782.372i 0.634772 + 0.825287i
\(949\) 47.7599 + 27.5742i 0.0503265 + 0.0290560i
\(950\) −13.0409 31.0777i −0.0137273 0.0327134i
\(951\) −509.250 1225.46i −0.535489 1.28860i
\(952\) −13.8064 3.69940i −0.0145025 0.00388593i
\(953\) 1074.57 + 1074.57i 1.12756 + 1.12756i 0.990573 + 0.136988i \(0.0437421\pi\)
0.136988 + 0.990573i \(0.456258\pi\)
\(954\) 40.3908 10.9222i 0.0423384 0.0114488i
\(955\) 179.503 205.638i 0.187961 0.215328i
\(956\) 760.073 + 1316.48i 0.795055 + 1.37708i
\(957\) 39.7127 + 298.995i 0.0414971 + 0.312429i
\(958\) −30.2804 + 8.11362i −0.0316080 + 0.00846933i
\(959\) 1530.10 + 883.405i 1.59552 + 0.921173i
\(960\) 756.994 + 502.036i 0.788536 + 0.522954i
\(961\) 138.418 + 239.748i 0.144036 + 0.249477i
\(962\) 58.6394 58.6394i 0.0609557 0.0609557i
\(963\) −323.849 557.960i −0.336292 0.579398i
\(964\) 1291.77i 1.34001i
\(965\) 558.127 + 831.144i 0.578370 + 0.861289i
\(966\) 38.9019 + 93.6132i 0.0402711 + 0.0969081i
\(967\) −46.6332 174.037i −0.0482246 0.179977i 0.937613 0.347682i \(-0.113031\pi\)
−0.985837 + 0.167705i \(0.946364\pi\)
\(968\) −113.066 + 30.2958i −0.116803 + 0.0312974i
\(969\) 2.88310 22.0953i 0.00297533 0.0228022i
\(970\) −6.39905 + 32.5621i −0.00659696 + 0.0335691i
\(971\) −40.8568 −0.0420770 −0.0210385 0.999779i \(-0.506697\pi\)
−0.0210385 + 0.999779i \(0.506697\pi\)
\(972\) 363.492 891.997i 0.373963 0.917693i
\(973\) −607.325 607.325i −0.624178 0.624178i
\(974\) −76.1338 + 43.9558i −0.0781661 + 0.0451292i
\(975\) 1005.06 5.78492i 1.03083 0.00593325i
\(976\) −634.092 + 1098.28i −0.649685 + 1.12529i
\(977\) −202.074 754.152i −0.206832 0.771906i −0.988883 0.148693i \(-0.952494\pi\)
0.782052 0.623213i \(-0.214173\pi\)
\(978\) −23.6513 + 57.2853i −0.0241834 + 0.0585739i
\(979\) −274.932 + 158.732i −0.280829 + 0.162137i
\(980\) −419.885 + 481.018i −0.428454 + 0.490835i
\(981\) −416.113 110.474i −0.424172 0.112613i
\(982\) 48.9385 48.9385i 0.0498355 0.0498355i
\(983\) 133.041 496.515i 0.135341 0.505101i −0.864655 0.502367i \(-0.832463\pi\)
0.999996 0.00273477i \(-0.000870506\pi\)
\(984\) 259.974 + 199.011i 0.264201 + 0.202247i
\(985\) −117.690 57.7016i −0.119482 0.0585803i
\(986\) 0.710935 1.23138i 0.000721030 0.00124886i
\(987\) −191.241 1439.84i −0.193760 1.45881i
\(988\) −97.4863 + 363.824i −0.0986704 + 0.368243i
\(989\) 245.999i 0.248735i
\(990\) 39.2519 + 113.908i 0.0396484 + 0.115059i
\(991\) 941.294 0.949843 0.474922 0.880028i \(-0.342476\pi\)
0.474922 + 0.880028i \(0.342476\pi\)
\(992\) −227.798 61.0382i −0.229635 0.0615304i
\(993\) −299.615 + 725.690i −0.301727 + 0.730805i
\(994\) 54.0013 + 31.1776i 0.0543272 + 0.0313658i
\(995\) 974.957 333.460i 0.979856 0.335136i
\(996\) −627.219 81.8425i −0.629738 0.0821712i
\(997\) −1287.52 344.990i −1.29140 0.346029i −0.453206 0.891406i \(-0.649720\pi\)
−0.838191 + 0.545377i \(0.816386\pi\)
\(998\) 54.8879 + 54.8879i 0.0549979 + 0.0549979i
\(999\) −333.505 + 813.063i −0.333839 + 0.813877i
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 45.3.k.a.13.6 yes 40
3.2 odd 2 135.3.l.a.118.5 40
5.2 odd 4 inner 45.3.k.a.22.5 yes 40
5.3 odd 4 225.3.o.b.157.6 40
5.4 even 2 225.3.o.b.193.5 40
9.2 odd 6 135.3.l.a.73.6 40
9.4 even 3 405.3.g.h.163.5 20
9.5 odd 6 405.3.g.g.163.6 20
9.7 even 3 inner 45.3.k.a.43.5 yes 40
15.2 even 4 135.3.l.a.37.6 40
45.2 even 12 135.3.l.a.127.5 40
45.7 odd 12 inner 45.3.k.a.7.6 40
45.22 odd 12 405.3.g.h.82.5 20
45.32 even 12 405.3.g.g.82.6 20
45.34 even 6 225.3.o.b.43.6 40
45.43 odd 12 225.3.o.b.7.5 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.k.a.7.6 40 45.7 odd 12 inner
45.3.k.a.13.6 yes 40 1.1 even 1 trivial
45.3.k.a.22.5 yes 40 5.2 odd 4 inner
45.3.k.a.43.5 yes 40 9.7 even 3 inner
135.3.l.a.37.6 40 15.2 even 4
135.3.l.a.73.6 40 9.2 odd 6
135.3.l.a.118.5 40 3.2 odd 2
135.3.l.a.127.5 40 45.2 even 12
225.3.o.b.7.5 40 45.43 odd 12
225.3.o.b.43.6 40 45.34 even 6
225.3.o.b.157.6 40 5.3 odd 4
225.3.o.b.193.5 40 5.4 even 2
405.3.g.g.82.6 20 45.32 even 12
405.3.g.g.163.6 20 9.5 odd 6
405.3.g.h.82.5 20 45.22 odd 12
405.3.g.h.163.5 20 9.4 even 3