Properties

Label 25.3.f.a.12.3
Level $25$
Weight $3$
Character 25.12
Analytic conductor $0.681$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,3,Mod(2,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.f (of order \(20\), degree \(8\), 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: \(0.681200660901\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 12.3
Character \(\chi\) \(=\) 25.12
Dual form 25.3.f.a.23.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0933465 + 0.589367i) q^{2} +(0.210730 + 0.107372i) q^{3} +(3.46559 - 1.12604i) q^{4} +(-3.31432 + 3.74370i) q^{5} +(-0.0436108 + 0.134220i) q^{6} +(-7.64532 - 7.64532i) q^{7} +(2.07076 + 4.06409i) q^{8} +(-5.25719 - 7.23590i) q^{9} +O(q^{10})\) \(q+(0.0933465 + 0.589367i) q^{2} +(0.210730 + 0.107372i) q^{3} +(3.46559 - 1.12604i) q^{4} +(-3.31432 + 3.74370i) q^{5} +(-0.0436108 + 0.134220i) q^{6} +(-7.64532 - 7.64532i) q^{7} +(2.07076 + 4.06409i) q^{8} +(-5.25719 - 7.23590i) q^{9} +(-2.51579 - 1.60389i) q^{10} +(7.33868 + 5.33186i) q^{11} +(0.851210 + 0.134818i) q^{12} +(-2.12306 + 13.4044i) q^{13} +(3.79223 - 5.21956i) q^{14} +(-1.10040 + 0.433046i) q^{15} +(9.59007 - 6.96760i) q^{16} +(0.704962 - 0.359196i) q^{17} +(3.77386 - 3.77386i) q^{18} +(13.5696 + 4.40902i) q^{19} +(-7.27050 + 16.7062i) q^{20} +(-0.790204 - 2.43200i) q^{21} +(-2.45738 + 4.82288i) q^{22} +(13.5597 - 2.14764i) q^{23} +1.07877i q^{24} +(-3.03063 - 24.8156i) q^{25} -8.09832 q^{26} +(-0.663895 - 4.19167i) q^{27} +(-35.1044 - 17.8866i) q^{28} +(-36.6306 + 11.9020i) q^{29} +(-0.357941 - 0.608115i) q^{30} +(-2.87530 + 8.84925i) q^{31} +(17.9028 + 17.9028i) q^{32} +(0.973987 + 1.91156i) q^{33} +(0.277504 + 0.381951i) q^{34} +(53.9608 - 3.28280i) q^{35} +(-26.3671 - 19.1568i) q^{36} +(9.13820 + 1.44735i) q^{37} +(-1.33186 + 8.40902i) q^{38} +(-1.88666 + 2.59677i) q^{39} +(-22.0779 - 5.71738i) q^{40} +(-33.7351 + 24.5100i) q^{41} +(1.35958 - 0.692738i) q^{42} +(49.4021 - 49.4021i) q^{43} +(31.4367 + 10.2144i) q^{44} +(44.5130 + 4.30070i) q^{45} +(2.53150 + 7.79114i) q^{46} +(9.65116 - 18.9415i) q^{47} +(2.76905 - 0.438574i) q^{48} +67.9017i q^{49} +(14.3426 - 4.10260i) q^{50} +0.187125 q^{51} +(7.73627 + 48.8449i) q^{52} +(-56.8742 - 28.9788i) q^{53} +(2.40846 - 0.782556i) q^{54} +(-44.2836 + 9.80236i) q^{55} +(15.2397 - 46.9029i) q^{56} +(2.38611 + 2.38611i) q^{57} +(-10.4340 - 20.4778i) q^{58} +(-45.6440 - 62.8235i) q^{59} +(-3.32590 + 2.73985i) q^{60} +(11.4153 + 8.29369i) q^{61} +(-5.48385 - 0.868557i) q^{62} +(-15.1279 + 95.5136i) q^{63} +(18.9902 - 26.1378i) q^{64} +(-43.1458 - 52.3747i) q^{65} +(-1.03569 + 0.752473i) q^{66} +(-46.8978 + 23.8956i) q^{67} +(2.03864 - 2.03864i) q^{68} +(3.08803 + 1.00336i) q^{69} +(6.97183 + 31.4963i) q^{70} +(-0.846117 - 2.60408i) q^{71} +(18.5210 - 36.3495i) q^{72} +(60.7976 - 9.62940i) q^{73} +5.52086i q^{74} +(2.02587 - 5.55481i) q^{75} +51.9912 q^{76} +(-15.3427 - 96.8703i) q^{77} +(-1.70656 - 0.869536i) q^{78} +(-6.18905 + 2.01094i) q^{79} +(-5.69992 + 58.9952i) q^{80} +(-24.5646 + 75.6022i) q^{81} +(-17.5944 - 17.5944i) q^{82} +(50.9593 + 100.013i) q^{83} +(-5.47704 - 7.53850i) q^{84} +(-0.991742 + 3.82966i) q^{85} +(33.7274 + 24.5044i) q^{86} +(-8.99712 - 1.42500i) q^{87} +(-6.47255 + 40.8661i) q^{88} +(65.5853 - 90.2704i) q^{89} +(1.62045 + 26.6360i) q^{90} +(118.713 - 86.2498i) q^{91} +(44.5739 - 22.7115i) q^{92} +(-1.55608 + 1.55608i) q^{93} +(12.0644 + 3.91995i) q^{94} +(-61.4799 + 36.1875i) q^{95} +(1.85040 + 5.69493i) q^{96} +(-58.6053 + 115.019i) q^{97} +(-40.0190 + 6.33839i) q^{98} -81.1325i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{9}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0933465 + 0.589367i 0.0466733 + 0.294683i 0.999973 0.00734232i \(-0.00233715\pi\)
−0.953300 + 0.302026i \(0.902337\pi\)
\(3\) 0.210730 + 0.107372i 0.0702435 + 0.0357908i 0.488759 0.872419i \(-0.337450\pi\)
−0.418516 + 0.908209i \(0.637450\pi\)
\(4\) 3.46559 1.12604i 0.866397 0.281509i
\(5\) −3.31432 + 3.74370i −0.662863 + 0.748741i
\(6\) −0.0436108 + 0.134220i −0.00726847 + 0.0223701i
\(7\) −7.64532 7.64532i −1.09219 1.09219i −0.995295 0.0968934i \(-0.969109\pi\)
−0.0968934 0.995295i \(-0.530891\pi\)
\(8\) 2.07076 + 4.06409i 0.258845 + 0.508011i
\(9\) −5.25719 7.23590i −0.584132 0.803989i
\(10\) −2.51579 1.60389i −0.251579 0.160389i
\(11\) 7.33868 + 5.33186i 0.667152 + 0.484715i 0.869071 0.494688i \(-0.164718\pi\)
−0.201918 + 0.979402i \(0.564718\pi\)
\(12\) 0.851210 + 0.134818i 0.0709342 + 0.0112349i
\(13\) −2.12306 + 13.4044i −0.163312 + 1.03111i 0.760799 + 0.648987i \(0.224807\pi\)
−0.924111 + 0.382124i \(0.875193\pi\)
\(14\) 3.79223 5.21956i 0.270874 0.372826i
\(15\) −1.10040 + 0.433046i −0.0733598 + 0.0288697i
\(16\) 9.59007 6.96760i 0.599380 0.435475i
\(17\) 0.704962 0.359196i 0.0414683 0.0211292i −0.433133 0.901330i \(-0.642592\pi\)
0.474602 + 0.880201i \(0.342592\pi\)
\(18\) 3.77386 3.77386i 0.209659 0.209659i
\(19\) 13.5696 + 4.40902i 0.714187 + 0.232054i 0.643501 0.765445i \(-0.277481\pi\)
0.0706862 + 0.997499i \(0.477481\pi\)
\(20\) −7.27050 + 16.7062i −0.363525 + 0.835308i
\(21\) −0.790204 2.43200i −0.0376288 0.115809i
\(22\) −2.45738 + 4.82288i −0.111699 + 0.219222i
\(23\) 13.5597 2.14764i 0.589551 0.0933757i 0.145470 0.989363i \(-0.453530\pi\)
0.444080 + 0.895987i \(0.353530\pi\)
\(24\) 1.07877i 0.0449488i
\(25\) −3.03063 24.8156i −0.121225 0.992625i
\(26\) −8.09832 −0.311474
\(27\) −0.663895 4.19167i −0.0245887 0.155247i
\(28\) −35.1044 17.8866i −1.25373 0.638807i
\(29\) −36.6306 + 11.9020i −1.26312 + 0.410413i −0.862606 0.505876i \(-0.831169\pi\)
−0.400517 + 0.916289i \(0.631169\pi\)
\(30\) −0.357941 0.608115i −0.0119314 0.0202705i
\(31\) −2.87530 + 8.84925i −0.0927515 + 0.285460i −0.986661 0.162787i \(-0.947952\pi\)
0.893910 + 0.448247i \(0.147952\pi\)
\(32\) 17.9028 + 17.9028i 0.559462 + 0.559462i
\(33\) 0.973987 + 1.91156i 0.0295148 + 0.0579260i
\(34\) 0.277504 + 0.381951i 0.00816188 + 0.0112339i
\(35\) 53.9608 3.28280i 1.54174 0.0937944i
\(36\) −26.3671 19.1568i −0.732420 0.532135i
\(37\) 9.13820 + 1.44735i 0.246978 + 0.0391175i 0.278696 0.960379i \(-0.410098\pi\)
−0.0317178 + 0.999497i \(0.510098\pi\)
\(38\) −1.33186 + 8.40902i −0.0350489 + 0.221290i
\(39\) −1.88666 + 2.59677i −0.0483759 + 0.0665838i
\(40\) −22.0779 5.71738i −0.551947 0.142934i
\(41\) −33.7351 + 24.5100i −0.822807 + 0.597805i −0.917515 0.397701i \(-0.869808\pi\)
0.0947079 + 0.995505i \(0.469808\pi\)
\(42\) 1.35958 0.692738i 0.0323708 0.0164938i
\(43\) 49.4021 49.4021i 1.14889 1.14889i 0.162113 0.986772i \(-0.448169\pi\)
0.986772 0.162113i \(-0.0518308\pi\)
\(44\) 31.4367 + 10.2144i 0.714470 + 0.232145i
\(45\) 44.5130 + 4.30070i 0.989179 + 0.0955711i
\(46\) 2.53150 + 7.79114i 0.0550325 + 0.169373i
\(47\) 9.65116 18.9415i 0.205344 0.403010i −0.765250 0.643733i \(-0.777385\pi\)
0.970594 + 0.240723i \(0.0773847\pi\)
\(48\) 2.76905 0.438574i 0.0576885 0.00913696i
\(49\) 67.9017i 1.38575i
\(50\) 14.3426 4.10260i 0.286852 0.0820521i
\(51\) 0.187125 0.00366911
\(52\) 7.73627 + 48.8449i 0.148775 + 0.939325i
\(53\) −56.8742 28.9788i −1.07310 0.546771i −0.174102 0.984728i \(-0.555702\pi\)
−0.898996 + 0.437957i \(0.855702\pi\)
\(54\) 2.40846 0.782556i 0.0446011 0.0144918i
\(55\) −44.2836 + 9.80236i −0.805156 + 0.178225i
\(56\) 15.2397 46.9029i 0.272137 0.837551i
\(57\) 2.38611 + 2.38611i 0.0418616 + 0.0418616i
\(58\) −10.4340 20.4778i −0.179896 0.353066i
\(59\) −45.6440 62.8235i −0.773627 1.06481i −0.995957 0.0898343i \(-0.971366\pi\)
0.222330 0.974971i \(-0.428634\pi\)
\(60\) −3.32590 + 2.73985i −0.0554316 + 0.0456641i
\(61\) 11.4153 + 8.29369i 0.187136 + 0.135962i 0.677409 0.735607i \(-0.263103\pi\)
−0.490273 + 0.871569i \(0.663103\pi\)
\(62\) −5.48385 0.868557i −0.0884492 0.0140090i
\(63\) −15.1279 + 95.5136i −0.240125 + 1.51609i
\(64\) 18.9902 26.1378i 0.296722 0.408403i
\(65\) −43.1458 52.3747i −0.663781 0.805764i
\(66\) −1.03569 + 0.752473i −0.0156923 + 0.0114011i
\(67\) −46.8978 + 23.8956i −0.699968 + 0.356651i −0.767485 0.641067i \(-0.778492\pi\)
0.0675175 + 0.997718i \(0.478492\pi\)
\(68\) 2.03864 2.03864i 0.0299800 0.0299800i
\(69\) 3.08803 + 1.00336i 0.0447541 + 0.0145415i
\(70\) 6.97183 + 31.4963i 0.0995975 + 0.449947i
\(71\) −0.846117 2.60408i −0.0119171 0.0366772i 0.944921 0.327298i \(-0.106138\pi\)
−0.956838 + 0.290621i \(0.906138\pi\)
\(72\) 18.5210 36.3495i 0.257236 0.504854i
\(73\) 60.7976 9.62940i 0.832844 0.131910i 0.274571 0.961567i \(-0.411464\pi\)
0.558273 + 0.829657i \(0.311464\pi\)
\(74\) 5.52086i 0.0746062i
\(75\) 2.02587 5.55481i 0.0270116 0.0740642i
\(76\) 51.9912 0.684095
\(77\) −15.3427 96.8703i −0.199256 1.25806i
\(78\) −1.70656 0.869536i −0.0218790 0.0111479i
\(79\) −6.18905 + 2.01094i −0.0783423 + 0.0254550i −0.347926 0.937522i \(-0.613114\pi\)
0.269584 + 0.962977i \(0.413114\pi\)
\(80\) −5.69992 + 58.9952i −0.0712490 + 0.737440i
\(81\) −24.5646 + 75.6022i −0.303267 + 0.933360i
\(82\) −17.5944 17.5944i −0.214566 0.214566i
\(83\) 50.9593 + 100.013i 0.613967 + 1.20498i 0.963413 + 0.268021i \(0.0863698\pi\)
−0.349446 + 0.936957i \(0.613630\pi\)
\(84\) −5.47704 7.53850i −0.0652029 0.0897440i
\(85\) −0.991742 + 3.82966i −0.0116676 + 0.0450548i
\(86\) 33.7274 + 24.5044i 0.392180 + 0.284935i
\(87\) −8.99712 1.42500i −0.103415 0.0163794i
\(88\) −6.47255 + 40.8661i −0.0735517 + 0.464387i
\(89\) 65.5853 90.2704i 0.736914 1.01427i −0.261877 0.965101i \(-0.584341\pi\)
0.998790 0.0491732i \(-0.0156586\pi\)
\(90\) 1.62045 + 26.6360i 0.0180050 + 0.295955i
\(91\) 118.713 86.2498i 1.30454 0.947800i
\(92\) 44.5739 22.7115i 0.484499 0.246864i
\(93\) −1.55608 + 1.55608i −0.0167320 + 0.0167320i
\(94\) 12.0644 + 3.91995i 0.128344 + 0.0417016i
\(95\) −61.4799 + 36.1875i −0.647156 + 0.380921i
\(96\) 1.85040 + 5.69493i 0.0192749 + 0.0593222i
\(97\) −58.6053 + 115.019i −0.604178 + 1.18577i 0.363029 + 0.931778i \(0.381743\pi\)
−0.967207 + 0.253989i \(0.918257\pi\)
\(98\) −40.0190 + 6.33839i −0.408357 + 0.0646775i
\(99\) 81.1325i 0.819521i
\(100\) −38.4462 82.5881i −0.384462 0.825881i
\(101\) −32.5145 −0.321926 −0.160963 0.986960i \(-0.551460\pi\)
−0.160963 + 0.986960i \(0.551460\pi\)
\(102\) 0.0174674 + 0.110285i 0.000171249 + 0.00108123i
\(103\) −46.2893 23.5856i −0.449411 0.228986i 0.214611 0.976700i \(-0.431152\pi\)
−0.664022 + 0.747713i \(0.731152\pi\)
\(104\) −58.8732 + 19.1291i −0.566089 + 0.183933i
\(105\) 11.7237 + 5.10212i 0.111654 + 0.0485916i
\(106\) 11.7702 36.2248i 0.111039 0.341744i
\(107\) −34.7993 34.7993i −0.325227 0.325227i 0.525541 0.850768i \(-0.323863\pi\)
−0.850768 + 0.525541i \(0.823863\pi\)
\(108\) −7.02076 13.7790i −0.0650071 0.127584i
\(109\) 76.0086 + 104.617i 0.697326 + 0.959787i 0.999978 + 0.00668585i \(0.00212819\pi\)
−0.302651 + 0.953101i \(0.597872\pi\)
\(110\) −9.91090 25.1843i −0.0900991 0.228948i
\(111\) 1.77029 + 1.28619i 0.0159486 + 0.0115873i
\(112\) −126.589 20.0497i −1.13026 0.179015i
\(113\) 11.9724 75.5905i 0.105950 0.668942i −0.876357 0.481663i \(-0.840033\pi\)
0.982307 0.187279i \(-0.0599670\pi\)
\(114\) −1.18356 + 1.62903i −0.0103821 + 0.0142897i
\(115\) −36.9009 + 57.8813i −0.320877 + 0.503316i
\(116\) −113.544 + 82.4948i −0.978830 + 0.711162i
\(117\) 108.155 55.1075i 0.924398 0.471004i
\(118\) 32.7654 32.7654i 0.277673 0.277673i
\(119\) −8.13582 2.64349i −0.0683682 0.0222142i
\(120\) −4.03859 3.57538i −0.0336550 0.0297949i
\(121\) −11.9636 36.8202i −0.0988729 0.304299i
\(122\) −3.82245 + 7.50197i −0.0313315 + 0.0614916i
\(123\) −9.74071 + 1.54278i −0.0791928 + 0.0125429i
\(124\) 33.9055i 0.273432i
\(125\) 102.947 + 70.9011i 0.823574 + 0.567208i
\(126\) −57.7047 −0.457974
\(127\) 9.58264 + 60.5024i 0.0754539 + 0.476397i 0.996262 + 0.0863815i \(0.0275304\pi\)
−0.920808 + 0.390016i \(0.872470\pi\)
\(128\) 107.413 + 54.7295i 0.839162 + 0.427575i
\(129\) 15.7149 5.10609i 0.121821 0.0395821i
\(130\) 26.8404 30.3177i 0.206464 0.233213i
\(131\) −1.09573 + 3.37230i −0.00836432 + 0.0257427i −0.955152 0.296117i \(-0.904308\pi\)
0.946787 + 0.321860i \(0.104308\pi\)
\(132\) 5.52792 + 5.52792i 0.0418782 + 0.0418782i
\(133\) −70.0353 137.452i −0.526581 1.03347i
\(134\) −18.4610 25.4094i −0.137769 0.189623i
\(135\) 17.8927 + 11.4071i 0.132539 + 0.0844969i
\(136\) 2.91961 + 2.12122i 0.0214677 + 0.0155972i
\(137\) 246.624 + 39.0615i 1.80018 + 0.285120i 0.964497 0.264094i \(-0.0850728\pi\)
0.835682 + 0.549214i \(0.185073\pi\)
\(138\) −0.303091 + 1.91364i −0.00219631 + 0.0138670i
\(139\) −81.3839 + 112.015i −0.585496 + 0.805866i −0.994284 0.106763i \(-0.965951\pi\)
0.408789 + 0.912629i \(0.365951\pi\)
\(140\) 183.309 72.1387i 1.30935 0.515276i
\(141\) 4.06758 2.95527i 0.0288481 0.0209594i
\(142\) 1.45578 0.741755i 0.0102519 0.00522363i
\(143\) −87.0511 + 87.0511i −0.608749 + 0.608749i
\(144\) −100.834 32.7628i −0.700234 0.227520i
\(145\) 76.8477 176.581i 0.529984 1.21780i
\(146\) 11.3505 + 34.9332i 0.0777431 + 0.239269i
\(147\) −7.29078 + 14.3090i −0.0495971 + 0.0973399i
\(148\) 33.2990 5.27404i 0.224993 0.0356354i
\(149\) 103.072i 0.691761i 0.938279 + 0.345880i \(0.112420\pi\)
−0.938279 + 0.345880i \(0.887580\pi\)
\(150\) 3.46293 + 0.675459i 0.0230862 + 0.00450306i
\(151\) −47.0940 −0.311880 −0.155940 0.987766i \(-0.549841\pi\)
−0.155940 + 0.987766i \(0.549841\pi\)
\(152\) 10.1806 + 64.2780i 0.0669778 + 0.422881i
\(153\) −6.30522 3.21267i −0.0412106 0.0209978i
\(154\) 55.6599 18.0850i 0.361428 0.117435i
\(155\) −23.5993 40.0935i −0.152254 0.258667i
\(156\) −3.61433 + 11.1238i −0.0231688 + 0.0713062i
\(157\) 94.7590 + 94.7590i 0.603561 + 0.603561i 0.941256 0.337695i \(-0.109647\pi\)
−0.337695 + 0.941256i \(0.609647\pi\)
\(158\) −1.76291 3.45990i −0.0111577 0.0218981i
\(159\) −8.87359 12.2134i −0.0558087 0.0768141i
\(160\) −126.358 + 7.68724i −0.789739 + 0.0480452i
\(161\) −120.087 87.2486i −0.745884 0.541917i
\(162\) −46.8504 7.42038i −0.289200 0.0458048i
\(163\) 41.3763 261.240i 0.253842 1.60270i −0.450459 0.892797i \(-0.648740\pi\)
0.704302 0.709901i \(-0.251260\pi\)
\(164\) −89.3128 + 122.928i −0.544590 + 0.749564i
\(165\) −10.3844 2.68919i −0.0629358 0.0162981i
\(166\) −54.1876 + 39.3696i −0.326431 + 0.237166i
\(167\) −239.969 + 122.270i −1.43694 + 0.732158i −0.986973 0.160886i \(-0.948565\pi\)
−0.449969 + 0.893044i \(0.648565\pi\)
\(168\) 8.24754 8.24754i 0.0490925 0.0490925i
\(169\) −14.4433 4.69292i −0.0854634 0.0277687i
\(170\) −2.34965 0.227015i −0.0138215 0.00133538i
\(171\) −39.4345 121.367i −0.230611 0.709749i
\(172\) 115.579 226.836i 0.671968 1.31881i
\(173\) −184.026 + 29.1468i −1.06373 + 0.168479i −0.663682 0.748014i \(-0.731007\pi\)
−0.400050 + 0.916493i \(0.631007\pi\)
\(174\) 5.43562i 0.0312392i
\(175\) −166.553 + 212.893i −0.951733 + 1.21653i
\(176\) 107.529 0.610959
\(177\) −2.87305 18.1397i −0.0162319 0.102484i
\(178\) 59.3246 + 30.2274i 0.333284 + 0.169817i
\(179\) 194.558 63.2157i 1.08692 0.353161i 0.289862 0.957068i \(-0.406391\pi\)
0.797054 + 0.603908i \(0.206391\pi\)
\(180\) 159.107 35.2189i 0.883925 0.195661i
\(181\) 8.53397 26.2649i 0.0471490 0.145110i −0.924710 0.380671i \(-0.875693\pi\)
0.971859 + 0.235562i \(0.0756929\pi\)
\(182\) 61.9142 + 61.9142i 0.340188 + 0.340188i
\(183\) 1.51503 + 2.97342i 0.00827887 + 0.0162482i
\(184\) 36.8070 + 50.6605i 0.200038 + 0.275329i
\(185\) −35.7053 + 29.4137i −0.193002 + 0.158993i
\(186\) −1.06236 0.771846i −0.00571159 0.00414971i
\(187\) 7.08867 + 1.12273i 0.0379073 + 0.00600393i
\(188\) 12.1181 76.5108i 0.0644581 0.406973i
\(189\) −26.9710 + 37.1223i −0.142703 + 0.196414i
\(190\) −27.0667 32.8562i −0.142456 0.172927i
\(191\) 75.2465 54.6697i 0.393960 0.286229i −0.373116 0.927785i \(-0.621711\pi\)
0.767076 + 0.641556i \(0.221711\pi\)
\(192\) 6.80830 3.46900i 0.0354599 0.0180677i
\(193\) −172.622 + 172.622i −0.894415 + 0.894415i −0.994935 0.100520i \(-0.967949\pi\)
0.100520 + 0.994935i \(0.467949\pi\)
\(194\) −73.2592 23.8034i −0.377625 0.122698i
\(195\) −3.46853 15.6696i −0.0177873 0.0803569i
\(196\) 76.4599 + 235.319i 0.390101 + 1.20061i
\(197\) −19.6944 + 38.6524i −0.0999715 + 0.196205i −0.935575 0.353128i \(-0.885118\pi\)
0.835604 + 0.549333i \(0.185118\pi\)
\(198\) 47.8168 7.57344i 0.241499 0.0382497i
\(199\) 331.210i 1.66437i −0.554496 0.832186i \(-0.687089\pi\)
0.554496 0.832186i \(-0.312911\pi\)
\(200\) 94.5773 63.7039i 0.472886 0.318519i
\(201\) −12.4485 −0.0619330
\(202\) −3.03512 19.1630i −0.0150253 0.0948663i
\(203\) 371.047 + 189.058i 1.82782 + 0.931319i
\(204\) 0.648496 0.210709i 0.00317890 0.00103289i
\(205\) 20.0507 207.528i 0.0978081 1.01233i
\(206\) 9.57961 29.4830i 0.0465030 0.143121i
\(207\) −86.8259 86.8259i −0.419449 0.419449i
\(208\) 73.0365 + 143.342i 0.351137 + 0.689145i
\(209\) 76.0744 + 104.707i 0.363992 + 0.500992i
\(210\) −1.91266 + 7.38580i −0.00910789 + 0.0351705i
\(211\) 203.359 + 147.749i 0.963785 + 0.700231i 0.954027 0.299722i \(-0.0968939\pi\)
0.00975810 + 0.999952i \(0.496894\pi\)
\(212\) −229.734 36.3862i −1.08365 0.171633i
\(213\) 0.101304 0.639609i 0.000475606 0.00300286i
\(214\) 17.2612 23.7580i 0.0806597 0.111019i
\(215\) 21.2126 + 348.681i 0.0986634 + 1.62177i
\(216\) 15.6606 11.3781i 0.0725026 0.0526762i
\(217\) 89.6379 45.6728i 0.413078 0.210474i
\(218\) −54.5625 + 54.5625i −0.250287 + 0.250287i
\(219\) 13.8458 + 4.49879i 0.0632230 + 0.0205424i
\(220\) −142.431 + 83.8359i −0.647413 + 0.381072i
\(221\) 3.31815 + 10.2122i 0.0150143 + 0.0462091i
\(222\) −0.592788 + 1.16341i −0.00267022 + 0.00524060i
\(223\) −74.7975 + 11.8468i −0.335415 + 0.0531245i −0.321870 0.946784i \(-0.604312\pi\)
−0.0135446 + 0.999908i \(0.504312\pi\)
\(224\) 273.745i 1.22208i
\(225\) −163.631 + 152.390i −0.727248 + 0.677288i
\(226\) 45.6681 0.202071
\(227\) −53.6868 338.965i −0.236506 1.49324i −0.764850 0.644208i \(-0.777187\pi\)
0.528345 0.849030i \(-0.322813\pi\)
\(228\) 10.9561 + 5.58243i 0.0480532 + 0.0244843i
\(229\) 22.2341 7.22430i 0.0970921 0.0315471i −0.260068 0.965590i \(-0.583745\pi\)
0.357160 + 0.934043i \(0.383745\pi\)
\(230\) −37.5579 16.3451i −0.163295 0.0710658i
\(231\) 7.16802 22.0609i 0.0310304 0.0955017i
\(232\) −124.224 124.224i −0.535447 0.535447i
\(233\) −86.9078 170.566i −0.372995 0.732044i 0.625858 0.779937i \(-0.284749\pi\)
−0.998852 + 0.0478936i \(0.984749\pi\)
\(234\) 42.5744 + 58.5986i 0.181942 + 0.250421i
\(235\) 38.9242 + 98.9090i 0.165635 + 0.420890i
\(236\) −228.925 166.324i −0.970020 0.704761i
\(237\) −1.52014 0.240767i −0.00641409 0.00101589i
\(238\) 0.798534 5.04174i 0.00335518 0.0211838i
\(239\) 32.3070 44.4668i 0.135176 0.186054i −0.736063 0.676913i \(-0.763317\pi\)
0.871239 + 0.490860i \(0.163317\pi\)
\(240\) −7.53561 + 11.8201i −0.0313984 + 0.0492503i
\(241\) −27.3775 + 19.8909i −0.113600 + 0.0825349i −0.643135 0.765753i \(-0.722366\pi\)
0.529535 + 0.848288i \(0.322366\pi\)
\(242\) 20.5839 10.4880i 0.0850573 0.0433388i
\(243\) −40.3022 + 40.3022i −0.165853 + 0.165853i
\(244\) 48.8996 + 15.8885i 0.200408 + 0.0651166i
\(245\) −254.204 225.048i −1.03757 0.918562i
\(246\) −1.81852 5.59684i −0.00739237 0.0227514i
\(247\) −87.9094 + 172.532i −0.355908 + 0.698510i
\(248\) −41.9182 + 6.63919i −0.169025 + 0.0267709i
\(249\) 26.5474i 0.106616i
\(250\) −32.1770 + 67.2918i −0.128708 + 0.269167i
\(251\) 221.852 0.883872 0.441936 0.897046i \(-0.354292\pi\)
0.441936 + 0.897046i \(0.354292\pi\)
\(252\) 55.1250 + 348.045i 0.218750 + 1.38113i
\(253\) 110.961 + 56.5374i 0.438581 + 0.223468i
\(254\) −34.7636 + 11.2954i −0.136865 + 0.0444700i
\(255\) −0.620190 + 0.700539i −0.00243212 + 0.00274721i
\(256\) 17.7059 54.4930i 0.0691635 0.212863i
\(257\) −20.3380 20.3380i −0.0791363 0.0791363i 0.666431 0.745567i \(-0.267821\pi\)
−0.745567 + 0.666431i \(0.767821\pi\)
\(258\) 4.47630 + 8.78523i 0.0173500 + 0.0340513i
\(259\) −58.7990 80.9299i −0.227023 0.312471i
\(260\) −208.501 132.925i −0.801928 0.511251i
\(261\) 278.695 + 202.484i 1.06780 + 0.775801i
\(262\) −2.08980 0.330992i −0.00797634 0.00126333i
\(263\) −0.847808 + 5.35285i −0.00322361 + 0.0203530i −0.989248 0.146250i \(-0.953280\pi\)
0.986024 + 0.166603i \(0.0532797\pi\)
\(264\) −5.75185 + 7.91675i −0.0217873 + 0.0299877i
\(265\) 296.987 116.875i 1.12071 0.441038i
\(266\) 74.4721 54.1071i 0.279970 0.203410i
\(267\) 23.5134 11.9807i 0.0880651 0.0448714i
\(268\) −135.621 + 135.621i −0.506049 + 0.506049i
\(269\) −59.0391 19.1830i −0.219476 0.0713122i 0.197215 0.980360i \(-0.436810\pi\)
−0.416691 + 0.909048i \(0.636810\pi\)
\(270\) −5.05274 + 11.6102i −0.0187138 + 0.0430007i
\(271\) −99.9539 307.626i −0.368833 1.13515i −0.947546 0.319621i \(-0.896444\pi\)
0.578712 0.815532i \(-0.303556\pi\)
\(272\) 4.25790 8.35660i 0.0156540 0.0307228i
\(273\) 34.2772 5.42898i 0.125558 0.0198864i
\(274\) 148.999i 0.543790i
\(275\) 110.073 198.273i 0.400264 0.720992i
\(276\) 11.8317 0.0428684
\(277\) 11.4134 + 72.0614i 0.0412036 + 0.260150i 0.999688 0.0249971i \(-0.00795767\pi\)
−0.958484 + 0.285147i \(0.907958\pi\)
\(278\) −73.6150 37.5087i −0.264802 0.134924i
\(279\) 79.1483 25.7168i 0.283686 0.0921750i
\(280\) 125.081 + 212.504i 0.446719 + 0.758942i
\(281\) −84.2374 + 259.256i −0.299777 + 0.922619i 0.681798 + 0.731541i \(0.261199\pi\)
−0.981575 + 0.191079i \(0.938801\pi\)
\(282\) 2.12143 + 2.12143i 0.00752282 + 0.00752282i
\(283\) 89.6096 + 175.869i 0.316642 + 0.621445i 0.993392 0.114768i \(-0.0366124\pi\)
−0.676750 + 0.736212i \(0.736612\pi\)
\(284\) −5.86459 8.07191i −0.0206499 0.0284222i
\(285\) −16.8412 + 1.02457i −0.0590920 + 0.00359497i
\(286\) −59.4309 43.1791i −0.207800 0.150976i
\(287\) 445.302 + 70.5289i 1.55158 + 0.245745i
\(288\) 35.4245 223.661i 0.123002 0.776601i
\(289\) −169.502 + 233.299i −0.586512 + 0.807265i
\(290\) 111.244 + 28.8083i 0.383601 + 0.0993389i
\(291\) −24.6998 + 17.9455i −0.0848792 + 0.0616683i
\(292\) 199.856 101.832i 0.684440 0.348739i
\(293\) 237.228 237.228i 0.809652 0.809652i −0.174929 0.984581i \(-0.555970\pi\)
0.984581 + 0.174929i \(0.0559695\pi\)
\(294\) −9.11379 2.96125i −0.0309993 0.0100723i
\(295\) 386.471 + 37.3396i 1.31007 + 0.126575i
\(296\) 13.0408 + 40.1356i 0.0440569 + 0.135593i
\(297\) 17.4773 34.3011i 0.0588461 0.115492i
\(298\) −60.7474 + 9.62145i −0.203850 + 0.0322867i
\(299\) 186.319i 0.623142i
\(300\) 0.765905 21.5319i 0.00255302 0.0717730i
\(301\) −755.389 −2.50960
\(302\) −4.39606 27.7556i −0.0145565 0.0919060i
\(303\) −6.85180 3.49117i −0.0226132 0.0115220i
\(304\) 160.853 52.2644i 0.529123 0.171922i
\(305\) −68.8829 + 15.2475i −0.225846 + 0.0499919i
\(306\) 1.30487 4.01598i 0.00426428 0.0131241i
\(307\) −79.0993 79.0993i −0.257653 0.257653i 0.566446 0.824099i \(-0.308318\pi\)
−0.824099 + 0.566446i \(0.808318\pi\)
\(308\) −162.251 318.436i −0.526789 1.03388i
\(309\) −7.22212 9.94040i −0.0233726 0.0321696i
\(310\) 21.4268 17.6512i 0.0691188 0.0569395i
\(311\) −91.8901 66.7620i −0.295466 0.214669i 0.430169 0.902748i \(-0.358454\pi\)
−0.725635 + 0.688080i \(0.758454\pi\)
\(312\) −14.4603 2.29029i −0.0463472 0.00734067i
\(313\) −16.0776 + 101.510i −0.0513662 + 0.324314i 0.948603 + 0.316469i \(0.102497\pi\)
−0.999969 + 0.00784510i \(0.997503\pi\)
\(314\) −47.0024 + 64.6933i −0.149689 + 0.206029i
\(315\) −307.436 373.197i −0.975988 1.18475i
\(316\) −19.1843 + 13.9382i −0.0607097 + 0.0441082i
\(317\) −363.850 + 185.391i −1.14779 + 0.584829i −0.921172 0.389155i \(-0.872767\pi\)
−0.226618 + 0.973984i \(0.572767\pi\)
\(318\) 6.36988 6.36988i 0.0200311 0.0200311i
\(319\) −332.280 107.964i −1.04163 0.338446i
\(320\) 34.9126 + 157.723i 0.109102 + 0.492884i
\(321\) −3.59678 11.0698i −0.0112049 0.0344852i
\(322\) 40.2117 78.9199i 0.124881 0.245093i
\(323\) 11.1497 1.76594i 0.0345193 0.00546731i
\(324\) 289.667i 0.894033i
\(325\) 339.074 + 12.0611i 1.04330 + 0.0371111i
\(326\) 157.828 0.484136
\(327\) 4.78435 + 30.2072i 0.0146310 + 0.0923767i
\(328\) −169.468 86.3483i −0.516671 0.263257i
\(329\) −218.600 + 71.0273i −0.664437 + 0.215889i
\(330\) 0.615569 6.37125i 0.00186536 0.0193068i
\(331\) −37.2677 + 114.698i −0.112591 + 0.346520i −0.991437 0.130586i \(-0.958314\pi\)
0.878846 + 0.477106i \(0.158314\pi\)
\(332\) 289.222 + 289.222i 0.871151 + 0.871151i
\(333\) −37.5684 73.7321i −0.112818 0.221418i
\(334\) −94.4624 130.016i −0.282822 0.389271i
\(335\) 65.9760 254.769i 0.196943 0.760505i
\(336\) −24.5233 17.8172i −0.0729860 0.0530274i
\(337\) −38.2752 6.06219i −0.113576 0.0179887i 0.0993876 0.995049i \(-0.468312\pi\)
−0.212964 + 0.977060i \(0.568312\pi\)
\(338\) 1.41762 8.95048i 0.00419413 0.0264807i
\(339\) 10.6393 14.6437i 0.0313843 0.0431968i
\(340\) 0.875365 + 14.3887i 0.00257460 + 0.0423198i
\(341\) −68.2838 + 49.6111i −0.200246 + 0.145487i
\(342\) 67.8486 34.5706i 0.198388 0.101084i
\(343\) 144.510 144.510i 0.421311 0.421311i
\(344\) 303.074 + 98.4748i 0.881030 + 0.286264i
\(345\) −13.9910 + 8.23522i −0.0405536 + 0.0238702i
\(346\) −34.3563 105.738i −0.0992958 0.305601i
\(347\) −106.794 + 209.594i −0.307762 + 0.604018i −0.992143 0.125107i \(-0.960073\pi\)
0.684381 + 0.729125i \(0.260073\pi\)
\(348\) −32.7849 + 5.19262i −0.0942095 + 0.0149213i
\(349\) 16.9114i 0.0484568i −0.999706 0.0242284i \(-0.992287\pi\)
0.999706 0.0242284i \(-0.00771289\pi\)
\(350\) −141.019 78.2881i −0.402913 0.223680i
\(351\) 57.5965 0.164093
\(352\) 35.9276 + 226.838i 0.102067 + 0.644426i
\(353\) −449.055 228.805i −1.27211 0.648173i −0.318132 0.948046i \(-0.603056\pi\)
−0.953979 + 0.299873i \(0.903056\pi\)
\(354\) 10.4228 3.38656i 0.0294429 0.00956656i
\(355\) 12.5532 + 5.46313i 0.0353611 + 0.0153891i
\(356\) 125.644 386.692i 0.352932 1.08621i
\(357\) −1.43063 1.43063i −0.00400736 0.00400736i
\(358\) 55.4186 + 108.765i 0.154800 + 0.303813i
\(359\) 198.037 + 272.575i 0.551636 + 0.759262i 0.990233 0.139422i \(-0.0445245\pi\)
−0.438597 + 0.898684i \(0.644525\pi\)
\(360\) 74.6973 + 189.811i 0.207493 + 0.527252i
\(361\) −127.362 92.5336i −0.352802 0.256326i
\(362\) 16.2763 + 2.57791i 0.0449620 + 0.00712129i
\(363\) 1.43238 9.04370i 0.00394596 0.0249138i
\(364\) 314.289 432.581i 0.863430 1.18841i
\(365\) −165.453 + 259.523i −0.453296 + 0.711022i
\(366\) −1.61101 + 1.17047i −0.00440167 + 0.00319800i
\(367\) 416.928 212.435i 1.13604 0.578843i 0.218247 0.975894i \(-0.429966\pi\)
0.917797 + 0.397050i \(0.129966\pi\)
\(368\) 115.074 115.074i 0.312702 0.312702i
\(369\) 354.704 + 115.250i 0.961256 + 0.312331i
\(370\) −20.6684 18.2979i −0.0558607 0.0494537i
\(371\) 213.269 + 656.374i 0.574848 + 1.76920i
\(372\) −3.64052 + 7.14493i −0.00978635 + 0.0192068i
\(373\) 474.868 75.2117i 1.27310 0.201640i 0.516940 0.856022i \(-0.327071\pi\)
0.756164 + 0.654382i \(0.227071\pi\)
\(374\) 4.28263i 0.0114509i
\(375\) 14.0812 + 25.9947i 0.0375498 + 0.0693191i
\(376\) 96.9651 0.257886
\(377\) −81.7709 516.281i −0.216899 1.36945i
\(378\) −24.3963 12.4305i −0.0645405 0.0328850i
\(379\) −597.265 + 194.063i −1.57590 + 0.512040i −0.960995 0.276564i \(-0.910804\pi\)
−0.614901 + 0.788604i \(0.710804\pi\)
\(380\) −172.315 + 194.640i −0.453461 + 0.512210i
\(381\) −4.47694 + 13.7786i −0.0117505 + 0.0361643i
\(382\) 39.2445 + 39.2445i 0.102734 + 0.102734i
\(383\) 175.227 + 343.902i 0.457511 + 0.897916i 0.998385 + 0.0568121i \(0.0180936\pi\)
−0.540874 + 0.841104i \(0.681906\pi\)
\(384\) 16.7587 + 23.0664i 0.0436424 + 0.0600686i
\(385\) 413.504 + 263.620i 1.07404 + 0.684727i
\(386\) −117.851 85.6241i −0.305315 0.221824i
\(387\) −617.184 97.7524i −1.59479 0.252590i
\(388\) −73.5856 + 464.601i −0.189654 + 1.19743i
\(389\) 230.009 316.581i 0.591284 0.813833i −0.403592 0.914939i \(-0.632238\pi\)
0.994876 + 0.101107i \(0.0322383\pi\)
\(390\) 8.91137 3.50694i 0.0228497 0.00899216i
\(391\) 8.78762 6.38458i 0.0224747 0.0163289i
\(392\) −275.959 + 140.608i −0.703977 + 0.358694i
\(393\) −0.592995 + 0.592995i −0.00150889 + 0.00150889i
\(394\) −24.6188 7.99915i −0.0624844 0.0203024i
\(395\) 12.9841 29.8348i 0.0328711 0.0755313i
\(396\) −91.3583 281.172i −0.230703 0.710030i
\(397\) 155.364 304.919i 0.391345 0.768058i −0.608326 0.793687i \(-0.708159\pi\)
0.999672 + 0.0256288i \(0.00815880\pi\)
\(398\) 195.204 30.9173i 0.490463 0.0776817i
\(399\) 36.4852i 0.0914415i
\(400\) −201.969 216.867i −0.504923 0.542169i
\(401\) 665.647 1.65997 0.829983 0.557788i \(-0.188350\pi\)
0.829983 + 0.557788i \(0.188350\pi\)
\(402\) −1.16203 7.33675i −0.00289062 0.0182506i
\(403\) −112.515 57.3292i −0.279193 0.142256i
\(404\) −112.682 + 36.6126i −0.278916 + 0.0906252i
\(405\) −201.617 342.532i −0.497820 0.845759i
\(406\) −76.7884 + 236.331i −0.189134 + 0.582095i
\(407\) 59.3452 + 59.3452i 0.145811 + 0.145811i
\(408\) 0.387490 + 0.760491i 0.000949730 + 0.00186395i
\(409\) −369.812 509.003i −0.904187 1.24451i −0.969113 0.246616i \(-0.920681\pi\)
0.0649265 0.997890i \(-0.479319\pi\)
\(410\) 124.182 7.55483i 0.302882 0.0184264i
\(411\) 47.7771 + 34.7121i 0.116246 + 0.0844577i
\(412\) −186.978 29.6144i −0.453830 0.0718796i
\(413\) −131.343 + 829.269i −0.318022 + 2.00791i
\(414\) 43.0674 59.2772i 0.104028 0.143182i
\(415\) −543.315 140.699i −1.30919 0.339033i
\(416\) −277.986 + 201.968i −0.668235 + 0.485501i
\(417\) −29.1774 + 14.8666i −0.0699699 + 0.0356514i
\(418\) −54.6098 + 54.6098i −0.130645 + 0.130645i
\(419\) −111.166 36.1200i −0.265312 0.0862052i 0.173340 0.984862i \(-0.444544\pi\)
−0.438652 + 0.898657i \(0.644544\pi\)
\(420\) 46.3745 + 4.48055i 0.110416 + 0.0106680i
\(421\) 1.06048 + 3.26382i 0.00251896 + 0.00775255i 0.952308 0.305138i \(-0.0987026\pi\)
−0.949789 + 0.312891i \(0.898703\pi\)
\(422\) −68.0953 + 133.645i −0.161363 + 0.316693i
\(423\) −187.796 + 29.7440i −0.443963 + 0.0703169i
\(424\) 291.150i 0.686675i
\(425\) −11.0501 16.4055i −0.0260003 0.0386011i
\(426\) 0.386421 0.000907090
\(427\) −23.8656 150.681i −0.0558913 0.352884i
\(428\) −159.785 81.4147i −0.373330 0.190221i
\(429\) −27.6912 + 8.99742i −0.0645482 + 0.0209730i
\(430\) −203.521 + 45.0501i −0.473304 + 0.104768i
\(431\) 144.037 443.300i 0.334193 1.02854i −0.632926 0.774212i \(-0.718146\pi\)
0.967118 0.254327i \(-0.0818538\pi\)
\(432\) −35.5727 35.5727i −0.0823441 0.0823441i
\(433\) 90.0802 + 176.792i 0.208037 + 0.408296i 0.971323 0.237765i \(-0.0764149\pi\)
−0.763285 + 0.646062i \(0.776415\pi\)
\(434\) 35.2854 + 48.5662i 0.0813028 + 0.111904i
\(435\) 35.1541 28.9596i 0.0808140 0.0665739i
\(436\) 381.217 + 276.970i 0.874350 + 0.635253i
\(437\) 193.468 + 30.6423i 0.442718 + 0.0701196i
\(438\) −1.35897 + 8.58022i −0.00310268 + 0.0195896i
\(439\) 288.145 396.598i 0.656367 0.903412i −0.342987 0.939340i \(-0.611439\pi\)
0.999354 + 0.0359283i \(0.0114388\pi\)
\(440\) −131.538 159.674i −0.298951 0.362896i
\(441\) 491.330 356.972i 1.11413 0.809461i
\(442\) −5.70900 + 2.90888i −0.0129163 + 0.00658118i
\(443\) 241.629 241.629i 0.545437 0.545437i −0.379681 0.925118i \(-0.623966\pi\)
0.925118 + 0.379681i \(0.123966\pi\)
\(444\) 7.58340 + 2.46399i 0.0170797 + 0.00554954i
\(445\) 120.575 + 544.717i 0.270956 + 1.22408i
\(446\) −13.9642 42.9773i −0.0313098 0.0963617i
\(447\) −11.0671 + 21.7205i −0.0247587 + 0.0485917i
\(448\) −345.018 + 54.6455i −0.770130 + 0.121977i
\(449\) 344.192i 0.766575i 0.923629 + 0.383288i \(0.125208\pi\)
−0.923629 + 0.383288i \(0.874792\pi\)
\(450\) −105.088 82.2135i −0.233528 0.182697i
\(451\) −378.255 −0.838703
\(452\) −43.6265 275.447i −0.0965187 0.609395i
\(453\) −9.92413 5.05660i −0.0219076 0.0111625i
\(454\) 194.763 63.2824i 0.428994 0.139389i
\(455\) −70.5576 + 730.284i −0.155072 + 1.60502i
\(456\) −4.75632 + 14.6384i −0.0104305 + 0.0321018i
\(457\) −145.902 145.902i −0.319260 0.319260i 0.529223 0.848483i \(-0.322484\pi\)
−0.848483 + 0.529223i \(0.822484\pi\)
\(458\) 6.33324 + 12.4297i 0.0138280 + 0.0271390i
\(459\) −1.97365 2.71650i −0.00429989 0.00591829i
\(460\) −62.7067 + 242.145i −0.136319 + 0.526401i
\(461\) 270.507 + 196.534i 0.586782 + 0.426322i 0.841163 0.540782i \(-0.181872\pi\)
−0.254381 + 0.967104i \(0.581872\pi\)
\(462\) 13.6711 + 2.16529i 0.0295911 + 0.00468676i
\(463\) −4.34214 + 27.4152i −0.00937827 + 0.0592120i −0.991934 0.126758i \(-0.959543\pi\)
0.982555 + 0.185970i \(0.0595428\pi\)
\(464\) −268.362 + 369.368i −0.578365 + 0.796052i
\(465\) −0.668161 10.9828i −0.00143690 0.0236190i
\(466\) 92.4135 67.1423i 0.198312 0.144082i
\(467\) −365.168 + 186.062i −0.781943 + 0.398420i −0.798921 0.601436i \(-0.794596\pi\)
0.0169777 + 0.999856i \(0.494596\pi\)
\(468\) 312.766 312.766i 0.668303 0.668303i
\(469\) 541.238 + 175.859i 1.15403 + 0.374966i
\(470\) −54.6603 + 32.1735i −0.116298 + 0.0684542i
\(471\) 9.79409 + 30.1431i 0.0207943 + 0.0639981i
\(472\) 160.803 315.594i 0.340684 0.668631i
\(473\) 625.951 99.1408i 1.32336 0.209600i
\(474\) 0.918395i 0.00193754i
\(475\) 68.2883 350.099i 0.143765 0.737051i
\(476\) −31.1721 −0.0654875
\(477\) 89.3103 + 563.883i 0.187233 + 1.18215i
\(478\) 29.2230 + 14.8899i 0.0611360 + 0.0311504i
\(479\) 579.516 188.296i 1.20985 0.393103i 0.366472 0.930429i \(-0.380566\pi\)
0.843374 + 0.537326i \(0.180566\pi\)
\(480\) −27.4529 11.9475i −0.0571936 0.0248906i
\(481\) −38.8018 + 119.420i −0.0806691 + 0.248274i
\(482\) −14.2786 14.2786i −0.0296237 0.0296237i
\(483\) −15.9380 31.2800i −0.0329978 0.0647619i
\(484\) −82.9219 114.132i −0.171326 0.235810i
\(485\) −236.362 600.611i −0.487344 1.23837i
\(486\) −27.5149 19.9907i −0.0566150 0.0411332i
\(487\) 229.164 + 36.2960i 0.470563 + 0.0745298i 0.387213 0.921990i \(-0.373438\pi\)
0.0833503 + 0.996520i \(0.473438\pi\)
\(488\) −10.0680 + 63.5670i −0.0206312 + 0.130260i
\(489\) 36.7692 50.6085i 0.0751927 0.103494i
\(490\) 108.907 170.827i 0.222258 0.348626i
\(491\) −288.845 + 209.858i −0.588279 + 0.427409i −0.841699 0.539947i \(-0.818444\pi\)
0.253421 + 0.967356i \(0.418444\pi\)
\(492\) −32.0200 + 16.3150i −0.0650814 + 0.0331606i
\(493\) −21.5480 + 21.5480i −0.0437079 + 0.0437079i
\(494\) −109.891 35.7056i −0.222451 0.0722786i
\(495\) 303.736 + 268.899i 0.613608 + 0.543230i
\(496\) 34.0837 + 104.899i 0.0687171 + 0.211490i
\(497\) −13.4402 + 26.3779i −0.0270426 + 0.0530742i
\(498\) −15.6462 + 2.47811i −0.0314180 + 0.00497613i
\(499\) 752.086i 1.50719i 0.657341 + 0.753593i \(0.271681\pi\)
−0.657341 + 0.753593i \(0.728319\pi\)
\(500\) 436.608 + 129.792i 0.873216 + 0.259584i
\(501\) −63.6973 −0.127140
\(502\) 20.7091 + 130.752i 0.0412532 + 0.260463i
\(503\) −728.768 371.326i −1.44884 0.738222i −0.460102 0.887866i \(-0.652187\pi\)
−0.988740 + 0.149644i \(0.952187\pi\)
\(504\) −419.502 + 136.305i −0.832346 + 0.270446i
\(505\) 107.763 121.725i 0.213393 0.241039i
\(506\) −22.9635 + 70.6743i −0.0453823 + 0.139672i
\(507\) −2.53975 2.53975i −0.00500938 0.00500938i
\(508\) 101.337 + 198.886i 0.199483 + 0.391508i
\(509\) −529.260 728.463i −1.03980 1.43117i −0.897327 0.441367i \(-0.854494\pi\)
−0.142476 0.989798i \(-0.545506\pi\)
\(510\) −0.470767 0.300126i −0.000923072 0.000588483i
\(511\) −538.437 391.197i −1.05369 0.765552i
\(512\) 510.041 + 80.7826i 0.996174 + 0.157778i
\(513\) 9.47238 59.8062i 0.0184647 0.116581i
\(514\) 10.0881 13.8850i 0.0196266 0.0270137i
\(515\) 241.715 95.1234i 0.469349 0.184706i
\(516\) 48.7118 35.3912i 0.0944028 0.0685876i
\(517\) 171.820 87.5466i 0.332340 0.169336i
\(518\) 42.2087 42.2087i 0.0814840 0.0814840i
\(519\) −41.9094 13.6172i −0.0807503 0.0262374i
\(520\) 123.511 283.804i 0.237521 0.545776i
\(521\) −145.536 447.915i −0.279340 0.859721i −0.988038 0.154209i \(-0.950717\pi\)
0.708698 0.705512i \(-0.249283\pi\)
\(522\) −93.3221 + 183.155i −0.178778 + 0.350872i
\(523\) −582.366 + 92.2377i −1.11351 + 0.176363i −0.685967 0.727632i \(-0.740621\pi\)
−0.427543 + 0.903995i \(0.640621\pi\)
\(524\) 12.9208i 0.0246580i
\(525\) −57.9567 + 26.9799i −0.110394 + 0.0513902i
\(526\) −3.23393 −0.00614816
\(527\) 1.15164 + 7.27118i 0.00218528 + 0.0137973i
\(528\) 22.6596 + 11.5456i 0.0429158 + 0.0218667i
\(529\) −323.857 + 105.227i −0.612205 + 0.198918i
\(530\) 96.6050 + 164.125i 0.182274 + 0.309669i
\(531\) −214.626 + 660.550i −0.404192 + 1.24397i
\(532\) −397.489 397.489i −0.747160 0.747160i
\(533\) −256.921 504.236i −0.482029 0.946035i
\(534\) 9.25590 + 12.7397i 0.0173331 + 0.0238570i
\(535\) 245.614 14.9424i 0.459092 0.0279297i
\(536\) −194.228 141.115i −0.362366 0.263274i
\(537\) 47.7869 + 7.56870i 0.0889887 + 0.0140944i
\(538\) 5.79471 36.5864i 0.0107708 0.0680044i
\(539\) −362.043 + 498.309i −0.671693 + 0.924506i
\(540\) 74.8536 + 19.3844i 0.138618 + 0.0358970i
\(541\) 4.98311 3.62044i 0.00921092 0.00669212i −0.583170 0.812350i \(-0.698188\pi\)
0.592381 + 0.805658i \(0.298188\pi\)
\(542\) 171.974 87.6253i 0.317296 0.161670i
\(543\) 4.61849 4.61849i 0.00850551 0.00850551i
\(544\) 19.0514 + 6.19017i 0.0350209 + 0.0113790i
\(545\) −643.571 62.1796i −1.18086 0.114091i
\(546\) 6.39932 + 19.6951i 0.0117204 + 0.0360716i
\(547\) −137.666 + 270.185i −0.251675 + 0.493940i −0.981932 0.189232i \(-0.939400\pi\)
0.730257 + 0.683172i \(0.239400\pi\)
\(548\) 898.683 142.337i 1.63993 0.259740i
\(549\) 126.201i 0.229875i
\(550\) 127.130 + 46.3651i 0.231146 + 0.0843002i
\(551\) −549.537 −0.997344
\(552\) 2.31681 + 14.6278i 0.00419712 + 0.0264996i
\(553\) 62.6915 + 31.9429i 0.113366 + 0.0577630i
\(554\) −41.4052 + 13.4534i −0.0747387 + 0.0242841i
\(555\) −10.6824 + 2.36460i −0.0192476 + 0.00426054i
\(556\) −155.910 + 479.840i −0.280413 + 0.863022i
\(557\) 39.2190 + 39.2190i 0.0704112 + 0.0704112i 0.741435 0.671024i \(-0.234145\pi\)
−0.671024 + 0.741435i \(0.734145\pi\)
\(558\) 22.5449 + 44.2468i 0.0404030 + 0.0792953i
\(559\) 557.324 + 767.091i 0.997002 + 1.37226i
\(560\) 494.615 407.459i 0.883240 0.727606i
\(561\) 1.37325 + 0.997722i 0.00244786 + 0.00177847i
\(562\) −160.660 25.4461i −0.285872 0.0452777i
\(563\) 93.1829 588.334i 0.165511 1.04500i −0.755411 0.655251i \(-0.772563\pi\)
0.920922 0.389746i \(-0.127437\pi\)
\(564\) 10.7688 14.8220i 0.0190936 0.0262802i
\(565\) 243.308 + 295.352i 0.430634 + 0.522746i
\(566\) −95.2865 + 69.2297i −0.168351 + 0.122314i
\(567\) 765.807 390.198i 1.35063 0.688180i
\(568\) 8.83112 8.83112i 0.0155477 0.0155477i
\(569\) 258.923 + 84.1291i 0.455049 + 0.147854i 0.527568 0.849513i \(-0.323104\pi\)
−0.0725195 + 0.997367i \(0.523104\pi\)
\(570\) −2.17592 9.83002i −0.00381739 0.0172456i
\(571\) −69.9094 215.159i −0.122433 0.376811i 0.870991 0.491298i \(-0.163477\pi\)
−0.993425 + 0.114487i \(0.963477\pi\)
\(572\) −203.660 + 399.706i −0.356049 + 0.698786i
\(573\) 21.7267 3.44118i 0.0379175 0.00600555i
\(574\) 269.030i 0.468693i
\(575\) −94.3893 329.983i −0.164155 0.573884i
\(576\) −288.966 −0.501677
\(577\) 140.082 + 884.446i 0.242777 + 1.53284i 0.744391 + 0.667744i \(0.232740\pi\)
−0.501614 + 0.865092i \(0.667260\pi\)
\(578\) −153.321 78.1211i −0.265262 0.135158i
\(579\) −54.9116 + 17.8419i −0.0948387 + 0.0308150i
\(580\) 67.4857 698.490i 0.116355 1.20429i
\(581\) 375.033 1154.23i 0.645495 1.98663i
\(582\) −12.8821 12.8821i −0.0221342 0.0221342i
\(583\) −262.870 515.912i −0.450892 0.884926i
\(584\) 165.032 + 227.147i 0.282589 + 0.388950i
\(585\) −152.152 + 587.542i −0.260089 + 1.00435i
\(586\) 161.959 + 117.670i 0.276380 + 0.200802i
\(587\) 346.752 + 54.9201i 0.590718 + 0.0935606i 0.444635 0.895712i \(-0.353333\pi\)
0.146083 + 0.989272i \(0.453333\pi\)
\(588\) −9.15440 + 57.7986i −0.0155687 + 0.0982970i
\(589\) −78.0330 + 107.403i −0.132484 + 0.182348i
\(590\) 14.0691 + 231.259i 0.0238459 + 0.391964i
\(591\) −8.30041 + 6.03060i −0.0140447 + 0.0102041i
\(592\) 97.7205 49.7911i 0.165068 0.0841066i
\(593\) −355.629 + 355.629i −0.599711 + 0.599711i −0.940236 0.340525i \(-0.889395\pi\)
0.340525 + 0.940236i \(0.389395\pi\)
\(594\) 21.8474 + 7.09864i 0.0367801 + 0.0119506i
\(595\) 36.8611 21.6967i 0.0619514 0.0364651i
\(596\) 116.063 + 357.206i 0.194737 + 0.599339i
\(597\) 35.5629 69.7960i 0.0595693 0.116911i
\(598\) −109.811 + 17.3923i −0.183630 + 0.0290841i
\(599\) 1001.80i 1.67245i −0.548390 0.836223i \(-0.684759\pi\)
0.548390 0.836223i \(-0.315241\pi\)
\(600\) 26.7704 3.26935i 0.0446173 0.00544891i
\(601\) 796.655 1.32555 0.662775 0.748819i \(-0.269379\pi\)
0.662775 + 0.748819i \(0.269379\pi\)
\(602\) −70.5129 445.201i −0.117131 0.739537i
\(603\) 419.457 + 213.724i 0.695617 + 0.354435i
\(604\) −163.208 + 53.0295i −0.270212 + 0.0877973i
\(605\) 177.495 + 77.2456i 0.293380 + 0.127679i
\(606\) 1.41799 4.36411i 0.00233991 0.00720151i
\(607\) 728.906 + 728.906i 1.20083 + 1.20083i 0.973913 + 0.226920i \(0.0728657\pi\)
0.226920 + 0.973913i \(0.427134\pi\)
\(608\) 163.999 + 321.867i 0.269736 + 0.529386i
\(609\) 57.8912 + 79.6804i 0.0950595 + 0.130838i
\(610\) −15.4164 39.1740i −0.0252727 0.0642197i
\(611\) 233.410 + 169.582i 0.382013 + 0.277549i
\(612\) −25.4689 4.03387i −0.0416158 0.00659130i
\(613\) −19.5383 + 123.360i −0.0318732 + 0.201240i −0.998486 0.0550007i \(-0.982484\pi\)
0.966613 + 0.256240i \(0.0824839\pi\)
\(614\) 39.2349 54.0022i 0.0639004 0.0879514i
\(615\) 26.5081 41.5796i 0.0431026 0.0676091i
\(616\) 361.919 262.949i 0.587530 0.426866i
\(617\) −639.236 + 325.707i −1.03604 + 0.527888i −0.887399 0.461003i \(-0.847490\pi\)
−0.148640 + 0.988891i \(0.547490\pi\)
\(618\) 5.18438 5.18438i 0.00838897 0.00838897i
\(619\) −196.553 63.8639i −0.317533 0.103173i 0.145914 0.989297i \(-0.453388\pi\)
−0.463447 + 0.886125i \(0.653388\pi\)
\(620\) −126.932 112.374i −0.204729 0.181248i
\(621\) −18.0044 55.4118i −0.0289926 0.0892300i
\(622\) 30.7697 60.3889i 0.0494690 0.0970883i
\(623\) −1191.57 + 188.726i −1.91263 + 0.302930i
\(624\) 38.0487i 0.0609754i
\(625\) −606.631 + 150.414i −0.970609 + 0.240662i
\(626\) −61.3275 −0.0979673
\(627\) 4.78849 + 30.2333i 0.00763714 + 0.0482190i
\(628\) 435.098 + 221.693i 0.692831 + 0.353015i
\(629\) 6.96196 2.26208i 0.0110683 0.00359631i
\(630\) 191.252 216.029i 0.303574 0.342904i
\(631\) 68.8404 211.869i 0.109097 0.335767i −0.881573 0.472048i \(-0.843515\pi\)
0.990670 + 0.136281i \(0.0435149\pi\)
\(632\) −20.9887 20.9887i −0.0332099 0.0332099i
\(633\) 26.9897 + 52.9703i 0.0426377 + 0.0836813i
\(634\) −143.227 197.135i −0.225910 0.310939i
\(635\) −258.263 164.650i −0.406713 0.259291i
\(636\) −44.5050 32.3348i −0.0699764 0.0508408i
\(637\) −910.185 144.159i −1.42886 0.226310i
\(638\) 32.6134 205.913i 0.0511181 0.322747i
\(639\) −14.3947 + 19.8126i −0.0225269 + 0.0310056i
\(640\) −560.891 + 220.731i −0.876392 + 0.344892i
\(641\) −709.800 + 515.700i −1.10733 + 0.804524i −0.982241 0.187622i \(-0.939922\pi\)
−0.125090 + 0.992145i \(0.539922\pi\)
\(642\) 6.18840 3.15315i 0.00963926 0.00491145i
\(643\) 430.122 430.122i 0.668929 0.668929i −0.288539 0.957468i \(-0.593169\pi\)
0.957468 + 0.288539i \(0.0931694\pi\)
\(644\) −514.418 167.145i −0.798786 0.259541i
\(645\) −32.9686 + 75.7553i −0.0511141 + 0.117450i
\(646\) 2.08158 + 6.40643i 0.00322225 + 0.00991707i
\(647\) 400.518 786.060i 0.619038 1.21493i −0.342308 0.939588i \(-0.611209\pi\)
0.961346 0.275343i \(-0.0887914\pi\)
\(648\) −358.122 + 56.7209i −0.552657 + 0.0875323i
\(649\) 704.409i 1.08538i
\(650\) 24.5430 + 200.965i 0.0377584 + 0.309177i
\(651\) 23.7934 0.0365490
\(652\) −150.773 951.940i −0.231246 1.46003i
\(653\) 868.933 + 442.744i 1.33068 + 0.678015i 0.967302 0.253627i \(-0.0816237\pi\)
0.363377 + 0.931642i \(0.381624\pi\)
\(654\) −17.3565 + 5.63947i −0.0265390 + 0.00862304i
\(655\) −8.99330 15.2789i −0.0137302 0.0233266i
\(656\) −152.746 + 470.105i −0.232845 + 0.716624i
\(657\) −389.302 389.302i −0.592545 0.592545i
\(658\) −62.2667 122.205i −0.0946302 0.185722i
\(659\) 337.348 + 464.320i 0.511909 + 0.704582i 0.984240 0.176839i \(-0.0565872\pi\)
−0.472331 + 0.881421i \(0.656587\pi\)
\(660\) −39.0162 + 2.37362i −0.0591154 + 0.00359639i
\(661\) 83.1335 + 60.4000i 0.125769 + 0.0913767i 0.648892 0.760881i \(-0.275233\pi\)
−0.523122 + 0.852258i \(0.675233\pi\)
\(662\) −71.0781 11.2577i −0.107369 0.0170055i
\(663\) −0.397276 + 2.50830i −0.000599210 + 0.00378326i
\(664\) −300.938 + 414.206i −0.453220 + 0.623804i
\(665\) 746.698 + 193.368i 1.12285 + 0.290779i
\(666\) 39.9484 29.0242i 0.0599825 0.0435799i
\(667\) −471.137 + 240.056i −0.706353 + 0.359905i
\(668\) −693.953 + 693.953i −1.03885 + 1.03885i
\(669\) −17.0341 5.53472i −0.0254621 0.00827313i
\(670\) 156.311 + 15.1023i 0.233300 + 0.0225407i
\(671\) 39.5523 + 121.729i 0.0589453 + 0.181415i
\(672\) 29.3927 57.6864i 0.0437391 0.0858429i
\(673\) 742.996 117.679i 1.10401 0.174857i 0.422280 0.906465i \(-0.361230\pi\)
0.681726 + 0.731608i \(0.261230\pi\)
\(674\) 23.1240i 0.0343086i
\(675\) −102.007 + 29.1784i −0.151121 + 0.0432272i
\(676\) −55.3389 −0.0818624
\(677\) −104.837 661.912i −0.154855 0.977714i −0.935651 0.352928i \(-0.885186\pi\)
0.780796 0.624786i \(-0.214814\pi\)
\(678\) 9.62365 + 4.90350i 0.0141942 + 0.00723230i
\(679\) 1327.42 431.304i 1.95496 0.635204i
\(680\) −17.6177 + 3.89976i −0.0259084 + 0.00573494i
\(681\) 25.0821 77.1947i 0.0368313 0.113355i
\(682\) −35.6132 35.6132i −0.0522188 0.0522188i
\(683\) 477.148 + 936.456i 0.698607 + 1.37109i 0.918442 + 0.395556i \(0.129448\pi\)
−0.219835 + 0.975537i \(0.570552\pi\)
\(684\) −273.328 376.203i −0.399602 0.550005i
\(685\) −963.626 + 793.827i −1.40675 + 1.15887i
\(686\) 98.6588 + 71.6798i 0.143817 + 0.104489i
\(687\) 5.46109 + 0.864952i 0.00794919 + 0.00125903i
\(688\) 129.556 817.983i 0.188308 1.18893i
\(689\) 509.193 700.843i 0.739031 1.01719i
\(690\) −6.15957 7.47710i −0.00892692 0.0108364i
\(691\) 281.760 204.711i 0.407757 0.296253i −0.364936 0.931033i \(-0.618909\pi\)
0.772693 + 0.634780i \(0.218909\pi\)
\(692\) −604.937 + 308.231i −0.874186 + 0.445420i
\(693\) −620.284 + 620.284i −0.895071 + 0.895071i
\(694\) −133.497 43.3757i −0.192358 0.0625010i
\(695\) −149.620 675.931i −0.215281 0.972563i
\(696\) −12.8395 39.5160i −0.0184476 0.0567758i
\(697\) −14.9781 + 29.3961i −0.0214893 + 0.0421752i
\(698\) 9.96703 1.57862i 0.0142794 0.00226164i
\(699\) 45.2750i 0.0647711i
\(700\) −337.479 + 925.346i −0.482112 + 1.32192i
\(701\) 685.412 0.977764 0.488882 0.872350i \(-0.337405\pi\)
0.488882 + 0.872350i \(0.337405\pi\)
\(702\) 5.37643 + 33.9455i 0.00765874 + 0.0483554i
\(703\) 117.620 + 59.9304i 0.167312 + 0.0852495i
\(704\) 278.726 90.5637i 0.395918 0.128642i
\(705\) −2.41759 + 25.0225i −0.00342921 + 0.0354930i
\(706\) 92.9324 286.016i 0.131632 0.405122i
\(707\) 248.584 + 248.584i 0.351604 + 0.351604i
\(708\) −30.3828 59.6297i −0.0429136 0.0842227i
\(709\) −142.144 195.644i −0.200485 0.275944i 0.696922 0.717146i \(-0.254552\pi\)
−0.897408 + 0.441202i \(0.854552\pi\)
\(710\) −2.04799 + 7.90841i −0.00288450 + 0.0111386i
\(711\) 47.0880 + 34.2114i 0.0662278 + 0.0481173i
\(712\) 502.679 + 79.6165i 0.706009 + 0.111821i
\(713\) −19.9831 + 126.168i −0.0280267 + 0.176954i
\(714\) 0.709620 0.976708i 0.000993865 0.00136794i
\(715\) −37.3787 614.408i −0.0522778 0.859312i
\(716\) 603.074 438.159i 0.842283 0.611954i
\(717\) 11.5826 5.90162i 0.0161542 0.00823099i
\(718\) −142.161 + 142.161i −0.197995 + 0.197995i
\(719\) −126.747 41.1825i −0.176282 0.0572774i 0.219546 0.975602i \(-0.429542\pi\)
−0.395828 + 0.918325i \(0.629542\pi\)
\(720\) 456.849 268.905i 0.634512 0.373479i
\(721\) 173.577 + 534.216i 0.240745 + 0.740937i
\(722\) 42.6475 83.7004i 0.0590685 0.115928i
\(723\) −7.90500 + 1.25203i −0.0109336 + 0.00173171i
\(724\) 100.633i 0.138996i
\(725\) 406.369 + 872.940i 0.560509 + 1.20405i
\(726\) 5.46377 0.00752585
\(727\) 202.138 + 1276.25i 0.278044 + 1.75550i 0.591881 + 0.806025i \(0.298385\pi\)
−0.313837 + 0.949477i \(0.601615\pi\)
\(728\) 596.352 + 303.857i 0.819165 + 0.417386i
\(729\) 667.599 216.916i 0.915774 0.297553i
\(730\) −168.399 73.2869i −0.230683 0.100393i
\(731\) 17.0815 52.5716i 0.0233674 0.0719173i
\(732\) 8.59866 + 8.59866i 0.0117468 + 0.0117468i
\(733\) −379.282 744.383i −0.517438 1.01553i −0.990885 0.134707i \(-0.956991\pi\)
0.473448 0.880822i \(-0.343009\pi\)
\(734\) 164.121 + 225.893i 0.223598 + 0.307757i
\(735\) −29.4046 74.7189i −0.0400062 0.101658i
\(736\) 281.205 + 204.307i 0.382072 + 0.277591i
\(737\) −471.576 74.6903i −0.639859 0.101344i
\(738\) −34.8143 + 219.809i −0.0471738 + 0.297844i
\(739\) −651.261 + 896.383i −0.881273 + 1.21297i 0.0947939 + 0.995497i \(0.469781\pi\)
−0.976067 + 0.217471i \(0.930219\pi\)
\(740\) −90.6189 + 142.141i −0.122458 + 0.192083i
\(741\) −37.0504 + 26.9187i −0.0500005 + 0.0363275i
\(742\) −366.937 + 186.964i −0.494524 + 0.251973i
\(743\) −333.821 + 333.821i −0.449289 + 0.449289i −0.895118 0.445829i \(-0.852909\pi\)
0.445829 + 0.895118i \(0.352909\pi\)
\(744\) −9.54631 3.10178i −0.0128311 0.00416906i
\(745\) −385.872 341.614i −0.517950 0.458543i
\(746\) 88.6545 + 272.851i 0.118840 + 0.365751i
\(747\) 455.783 894.524i 0.610151 1.19749i
\(748\) 25.8306 4.09117i 0.0345329 0.00546948i
\(749\) 532.104i 0.710419i
\(750\) −14.0060 + 10.7255i −0.0186746 + 0.0143007i
\(751\) 698.285 0.929807 0.464904 0.885361i \(-0.346089\pi\)
0.464904 + 0.885361i \(0.346089\pi\)
\(752\) −39.4212 248.895i −0.0524217 0.330978i
\(753\) 46.7510 + 23.8208i 0.0620863 + 0.0316345i
\(754\) 296.646 96.3861i 0.393430 0.127833i
\(755\) 156.084 176.306i 0.206734 0.233518i
\(756\) −51.6690 + 159.021i −0.0683453 + 0.210345i
\(757\) −465.289 465.289i −0.614648 0.614648i 0.329505 0.944154i \(-0.393118\pi\)
−0.944154 + 0.329505i \(0.893118\pi\)
\(758\) −170.127 333.893i −0.224442 0.440492i
\(759\) 17.3123 + 23.8283i 0.0228093 + 0.0313944i
\(760\) −274.379 174.924i −0.361026 0.230163i
\(761\) −1146.83 833.219i −1.50700 1.09490i −0.967486 0.252924i \(-0.918608\pi\)
−0.539515 0.841976i \(-0.681392\pi\)
\(762\) −8.53856 1.35238i −0.0112055 0.00177477i
\(763\) 218.719 1380.94i 0.286657 1.80988i
\(764\) 199.213 274.193i 0.260750 0.358891i
\(765\) 32.9248 12.9571i 0.0430389 0.0169373i
\(766\) −186.327 + 135.375i −0.243247 + 0.176730i
\(767\) 939.020 478.454i 1.22428 0.623800i
\(768\) 9.58222 9.58222i 0.0124768 0.0124768i
\(769\) −805.374 261.682i −1.04730 0.340288i −0.265692 0.964058i \(-0.585600\pi\)
−0.781608 + 0.623770i \(0.785600\pi\)
\(770\) −116.770 + 268.314i −0.151649 + 0.348459i
\(771\) −2.10210 6.46959i −0.00272645 0.00839116i
\(772\) −403.858 + 792.616i −0.523132 + 1.02670i
\(773\) −319.914 + 50.6693i −0.413860 + 0.0655489i −0.359893 0.932994i \(-0.617187\pi\)
−0.0539672 + 0.998543i \(0.517187\pi\)
\(774\) 372.873i 0.481748i
\(775\) 228.314 + 44.5335i 0.294598 + 0.0574626i
\(776\) −588.807 −0.758772
\(777\) −3.70109 23.3678i −0.00476331 0.0300744i
\(778\) 208.053 + 106.008i 0.267420 + 0.136257i
\(779\) −565.836 + 183.851i −0.726361 + 0.236009i
\(780\) −29.6651 50.3987i −0.0380321 0.0646137i
\(781\) 7.67522 23.6219i 0.00982742 0.0302457i
\(782\) 4.58315 + 4.58315i 0.00586081 + 0.00586081i
\(783\) 74.2081 + 145.642i 0.0947740 + 0.186005i
\(784\) 473.112 + 651.183i 0.603459 + 0.830590i
\(785\) −668.811 + 40.6884i −0.851989 + 0.0518323i
\(786\) −0.404845 0.294137i −0.000515070 0.000374221i
\(787\) −813.494 128.845i −1.03366 0.163716i −0.383524 0.923531i \(-0.625290\pi\)
−0.650140 + 0.759815i \(0.725290\pi\)
\(788\) −24.7285 + 156.130i −0.0313814 + 0.198134i
\(789\) −0.753408 + 1.03698i −0.000954890 + 0.00131429i
\(790\) 18.7957 + 4.86740i 0.0237920 + 0.00616127i
\(791\) −669.446 + 486.381i −0.846328 + 0.614893i
\(792\) 329.730 168.006i 0.416326 0.212129i
\(793\) −135.408 + 135.408i −0.170754 + 0.170754i
\(794\) 194.212 + 63.1033i 0.244599 + 0.0794751i
\(795\) 75.1334 + 7.25914i 0.0945074 + 0.00913099i
\(796\) −372.955 1147.84i −0.468536 1.44201i
\(797\) −393.451 + 772.191i −0.493665 + 0.968872i 0.500974 + 0.865462i \(0.332975\pi\)
−0.994639 + 0.103410i \(0.967025\pi\)
\(798\) 21.5031 3.40576i 0.0269463 0.00426787i
\(799\) 16.8197i 0.0210509i
\(800\) 390.012 498.526i 0.487516 0.623157i
\(801\) −997.982 −1.24592
\(802\) 62.1358 + 392.310i 0.0774761 + 0.489165i
\(803\) 497.517 + 253.497i 0.619573 + 0.315688i
\(804\) −43.1415 + 14.0175i −0.0536585 + 0.0174347i
\(805\) 724.640 160.402i 0.900174 0.199257i
\(806\) 23.2851 71.6640i 0.0288896 0.0889132i
\(807\) −10.3816 10.3816i −0.0128645 0.0128645i
\(808\) −67.3298 132.142i −0.0833289 0.163542i
\(809\) 72.5617 + 99.8726i 0.0896931 + 0.123452i 0.851505 0.524346i \(-0.175690\pi\)
−0.761812 + 0.647798i \(0.775690\pi\)
\(810\) 183.057 150.801i 0.225996 0.186174i
\(811\) 378.763 + 275.188i 0.467033 + 0.339319i 0.796284 0.604923i \(-0.206796\pi\)
−0.329251 + 0.944242i \(0.606796\pi\)
\(812\) 1498.78 + 237.384i 1.84579 + 0.292344i
\(813\) 11.9673 75.5585i 0.0147199 0.0929379i
\(814\) −29.4364 + 40.5158i −0.0361627 + 0.0497737i
\(815\) 840.870 + 1020.73i 1.03174 + 1.25243i
\(816\) 1.79454 1.30381i 0.00219919 0.00159780i
\(817\) 888.179 452.550i 1.08712 0.553916i
\(818\) 265.469 265.469i 0.324534 0.324534i
\(819\) −1248.19 405.562i −1.52404 0.495191i
\(820\) −164.197 741.784i −0.200240 0.904615i
\(821\) 285.639 + 879.107i 0.347916 + 1.07078i 0.960004 + 0.279986i \(0.0903298\pi\)
−0.612088 + 0.790790i \(0.709670\pi\)
\(822\) −15.9983 + 31.3985i −0.0194627 + 0.0381977i
\(823\) −757.643 + 119.999i −0.920587 + 0.145807i −0.598702 0.800972i \(-0.704316\pi\)
−0.321885 + 0.946779i \(0.604316\pi\)
\(824\) 236.964i 0.287578i
\(825\) 44.4847 29.9633i 0.0539208 0.0363192i
\(826\) −501.004 −0.606542
\(827\) −36.5445 230.733i −0.0441892 0.279000i 0.955693 0.294366i \(-0.0951085\pi\)
−0.999882 + 0.0153664i \(0.995109\pi\)
\(828\) −398.672 203.133i −0.481488 0.245330i
\(829\) −1244.32 + 404.304i −1.50099 + 0.487701i −0.940306 0.340330i \(-0.889461\pi\)
−0.560682 + 0.828031i \(0.689461\pi\)
\(830\) 32.2067 333.345i 0.0388033 0.401621i
\(831\) −5.33226 + 16.4110i −0.00641668 + 0.0197485i
\(832\) 310.046 + 310.046i 0.372651 + 0.372651i
\(833\) 24.3900 + 47.8681i 0.0292797 + 0.0574647i
\(834\) −11.4855 15.8085i −0.0137716 0.0189550i
\(835\) 337.590 1303.62i 0.404299 1.56122i
\(836\) 381.547 + 277.210i 0.456396 + 0.331591i
\(837\) 39.0020 + 6.17731i 0.0465974 + 0.00738030i
\(838\) 10.9110 68.8892i 0.0130203 0.0822067i
\(839\) −614.547 + 845.852i −0.732476 + 1.00817i 0.266541 + 0.963824i \(0.414119\pi\)
−0.999016 + 0.0443428i \(0.985881\pi\)
\(840\) 3.54139 + 58.2113i 0.00421594 + 0.0692991i
\(841\) 519.757 377.626i 0.618023 0.449020i
\(842\) −1.82460 + 0.929679i −0.00216698 + 0.00110413i
\(843\) −45.5884 + 45.5884i −0.0540787 + 0.0540787i
\(844\) 871.127 + 283.046i 1.03214 + 0.335363i
\(845\) 65.4386 38.5177i 0.0774421 0.0455830i
\(846\) −35.0603 107.905i −0.0414424 0.127547i
\(847\) −190.037 + 372.968i −0.224364 + 0.440340i
\(848\) −747.341 + 118.367i −0.881298 + 0.139584i
\(849\) 46.6825i 0.0549853i
\(850\) 8.63735 8.04398i 0.0101616 0.00946351i
\(851\) 127.019 0.149259
\(852\) −0.369145 2.33069i −0.000433269 0.00273555i
\(853\) 32.3156 + 16.4656i 0.0378846 + 0.0193032i 0.472830 0.881154i \(-0.343232\pi\)
−0.434946 + 0.900457i \(0.643232\pi\)
\(854\) 86.5788 28.1311i 0.101380 0.0329405i
\(855\) 585.061 + 254.617i 0.684281 + 0.297798i
\(856\) 69.3667 213.489i 0.0810358 0.249403i
\(857\) 687.485 + 687.485i 0.802199 + 0.802199i 0.983439 0.181240i \(-0.0580110\pi\)
−0.181240 + 0.983439i \(0.558011\pi\)
\(858\) −7.88766 15.4804i −0.00919307 0.0180424i
\(859\) 884.589 + 1217.53i 1.02979 + 1.41738i 0.905106 + 0.425187i \(0.139792\pi\)
0.124684 + 0.992197i \(0.460208\pi\)
\(860\) 466.142 + 1184.50i 0.542025 + 1.37732i
\(861\) 86.2658 + 62.6758i 0.100193 + 0.0727942i
\(862\) 274.712 + 43.5101i 0.318691 + 0.0504757i
\(863\) 205.361 1296.60i 0.237962 1.50243i −0.522269 0.852781i \(-0.674914\pi\)
0.760231 0.649653i \(-0.225086\pi\)
\(864\) 63.1570 86.9282i 0.0730984 0.100611i
\(865\) 500.802 785.540i 0.578962 0.908138i
\(866\) −95.7869 + 69.5932i −0.110608 + 0.0803617i
\(867\) −60.7692 + 30.9634i −0.0700913 + 0.0357133i
\(868\) 259.219 259.219i 0.298639 0.298639i
\(869\) −56.1415 18.2415i −0.0646047 0.0209913i
\(870\) 20.3494 + 18.0154i 0.0233901 + 0.0207073i
\(871\) −220.741 679.371i −0.253434 0.779990i
\(872\) −267.777 + 525.542i −0.307084 + 0.602686i
\(873\) 1140.37 180.617i 1.30626 0.206892i
\(874\) 116.884i 0.133734i
\(875\) −245.000 1329.12i −0.280000 1.51900i
\(876\) 53.0498 0.0605591
\(877\) −58.9645 372.287i −0.0672343 0.424501i −0.998230 0.0594706i \(-0.981059\pi\)
0.930996 0.365030i \(-0.118941\pi\)
\(878\) 260.639 + 132.802i 0.296855 + 0.151255i
\(879\) 75.4629 24.5194i 0.0858509 0.0278947i
\(880\) −356.384 + 402.556i −0.404982 + 0.457449i
\(881\) −297.148 + 914.528i −0.337285 + 1.03806i 0.628300 + 0.777971i \(0.283751\pi\)
−0.965585 + 0.260086i \(0.916249\pi\)
\(882\) 256.252 + 256.252i 0.290535 + 0.290535i
\(883\) 16.1759 + 31.7470i 0.0183192 + 0.0359535i 0.899985 0.435921i \(-0.143577\pi\)
−0.881666 + 0.471875i \(0.843577\pi\)
\(884\) 22.9987 + 31.6549i 0.0260166 + 0.0358088i
\(885\) 77.4320 + 49.3650i 0.0874938 + 0.0557796i
\(886\) 164.963 + 119.853i 0.186189 + 0.135274i
\(887\) −296.686 46.9904i −0.334482 0.0529768i −0.0130655 0.999915i \(-0.504159\pi\)
−0.321417 + 0.946938i \(0.604159\pi\)
\(888\) −1.56136 + 9.85802i −0.00175828 + 0.0111014i
\(889\) 389.298 535.823i 0.437905 0.602725i
\(890\) −309.783 + 121.910i −0.348070 + 0.136978i
\(891\) −583.372 + 423.845i −0.654739 + 0.475696i
\(892\) −245.877 + 125.281i −0.275647 + 0.140449i
\(893\) 214.475 214.475i 0.240174 0.240174i
\(894\) −13.8344 4.49507i −0.0154747 0.00502805i
\(895\) −408.166 + 937.884i −0.456051 + 1.04792i
\(896\) −402.780 1239.63i −0.449531 1.38352i
\(897\) −20.0056 + 39.2632i −0.0223028 + 0.0437717i
\(898\) −202.855 + 32.1291i −0.225897 + 0.0357786i
\(899\) 358.375i 0.398637i
\(900\) −395.480 + 712.374i −0.439422 + 0.791527i
\(901\) −50.5032 −0.0560524
\(902\) −35.3088 222.931i −0.0391450 0.247152i
\(903\) −159.183 81.1080i −0.176283 0.0898206i
\(904\) 331.998 107.873i 0.367255 0.119328i
\(905\) 70.0436 + 118.999i 0.0773962 + 0.131490i
\(906\) 2.05381 6.32097i 0.00226689 0.00697678i
\(907\) −505.478 505.478i −0.557307 0.557307i 0.371233 0.928540i \(-0.378935\pi\)
−0.928540 + 0.371233i \(0.878935\pi\)
\(908\) −567.744 1114.26i −0.625268 1.22716i
\(909\) 170.935 + 235.272i 0.188047 + 0.258825i
\(910\) −436.992 + 26.5852i −0.480210 + 0.0292145i
\(911\) −1112.30 808.135i −1.22097 0.887086i −0.224788 0.974408i \(-0.572169\pi\)
−0.996180 + 0.0873220i \(0.972169\pi\)
\(912\) 39.5084 + 6.25752i 0.0433207 + 0.00686132i
\(913\) −159.283 + 1005.67i −0.174461 + 1.10150i
\(914\) 72.3704 99.6093i 0.0791798 0.108982i
\(915\) −16.1529 4.18302i −0.0176534 0.00457160i
\(916\) 68.9194 50.0728i 0.0752395 0.0546647i
\(917\) 34.1594 17.4051i 0.0372513 0.0189805i
\(918\) 1.41678 1.41678i 0.00154333 0.00154333i
\(919\) 1241.96 + 403.536i 1.35142 + 0.439104i 0.893170 0.449718i \(-0.148476\pi\)
0.458252 + 0.888822i \(0.348476\pi\)
\(920\) −311.648 30.1104i −0.338748 0.0327287i
\(921\) −8.17554 25.1617i −0.00887681 0.0273200i
\(922\) −90.5801 + 177.773i −0.0982430 + 0.192813i
\(923\) 36.7026 5.81312i 0.0397645 0.00629808i
\(924\) 84.5254i 0.0914777i
\(925\) 8.22240 231.157i 0.00888909 0.249899i
\(926\) −16.5629 −0.0178865
\(927\) 72.6888 + 458.939i 0.0784129 + 0.495080i
\(928\) −868.868 442.711i −0.936281 0.477059i
\(929\) −430.474 + 139.870i −0.463374 + 0.150559i −0.531394 0.847125i \(-0.678332\pi\)
0.0680204 + 0.997684i \(0.478332\pi\)
\(930\) 6.41054 1.41900i 0.00689306 0.00152581i
\(931\) −299.380 + 921.397i −0.321568 + 0.989685i
\(932\) −493.250 493.250i −0.529239 0.529239i
\(933\) −12.1956 23.9353i −0.0130714 0.0256541i
\(934\) −143.746 197.849i −0.153904 0.211830i
\(935\) −27.6973 + 22.8168i −0.0296227 + 0.0244030i
\(936\) 447.924 + 325.436i 0.478551 + 0.347688i
\(937\) −517.916 82.0298i −0.552738 0.0875451i −0.126184 0.992007i \(-0.540273\pi\)
−0.426555 + 0.904462i \(0.640273\pi\)
\(938\) −53.1227 + 335.404i −0.0566341 + 0.357573i
\(939\) −14.2874 + 19.6650i −0.0152156 + 0.0209425i
\(940\) 246.271 + 298.948i 0.261990 + 0.318029i
\(941\) 983.490 714.547i 1.04515 0.759349i 0.0738692 0.997268i \(-0.476465\pi\)
0.971285 + 0.237919i \(0.0764653\pi\)
\(942\) −16.8511 + 8.58607i −0.0178887 + 0.00911472i
\(943\) −404.798 + 404.798i −0.429266 + 0.429266i
\(944\) −875.458 284.454i −0.927392 0.301328i
\(945\) −49.5847 224.006i −0.0524706 0.237044i
\(946\) 116.861 + 359.660i 0.123531 + 0.380190i
\(947\) 561.219 1101.45i 0.592628 1.16310i −0.378736 0.925505i \(-0.623641\pi\)
0.971365 0.237594i \(-0.0763588\pi\)
\(948\) −5.53929 + 0.877337i −0.00584313 + 0.000925461i
\(949\) 835.402i 0.880297i
\(950\) 212.711 + 7.56630i 0.223907 + 0.00796452i
\(951\) −96.5800 −0.101556
\(952\) −6.10394 38.5387i −0.00641170 0.0404819i
\(953\) 90.7422 + 46.2355i 0.0952174 + 0.0485157i 0.500951 0.865476i \(-0.332984\pi\)
−0.405733 + 0.913992i \(0.632984\pi\)
\(954\) −323.997 + 105.273i −0.339620 + 0.110349i
\(955\) −44.7232 + 462.893i −0.0468306 + 0.484705i
\(956\) 61.8915 190.483i 0.0647401 0.199250i
\(957\) −58.4290 58.4290i −0.0610544 0.0610544i
\(958\) 165.071 + 323.971i 0.172308 + 0.338174i
\(959\) −1586.89 2184.16i −1.65473 2.27754i
\(960\) −9.57794 + 36.9856i −0.00997702 + 0.0385267i
\(961\) 707.423 + 513.973i 0.736133 + 0.534832i
\(962\) −74.0040 11.7211i −0.0769273 0.0121841i
\(963\) −68.8578 + 434.751i −0.0715034 + 0.451455i
\(964\) −72.4811 + 99.7617i −0.0751879 + 0.103487i
\(965\) −74.1218 1218.37i −0.0768102 1.26256i
\(966\) 16.9476 12.3132i 0.0175441 0.0127466i
\(967\) −421.887 + 214.962i −0.436284 + 0.222298i −0.658316 0.752741i \(-0.728731\pi\)
0.222032 + 0.975039i \(0.428731\pi\)
\(968\) 124.867 124.867i 0.128995 0.128995i
\(969\) 2.53920 + 0.825036i 0.00262043 + 0.000851430i
\(970\) 331.917 195.369i 0.342182 0.201411i
\(971\) 520.392 + 1601.60i 0.535934 + 1.64943i 0.741623 + 0.670817i \(0.234056\pi\)
−0.205690 + 0.978617i \(0.565944\pi\)
\(972\) −94.2891 + 185.053i −0.0970052 + 0.190383i
\(973\) 1478.60 234.187i 1.51963 0.240686i
\(974\) 138.450i 0.142146i
\(975\) 70.1582 + 38.9489i 0.0719571 + 0.0399475i
\(976\) 167.260 0.171373
\(977\) 17.9443 + 113.296i 0.0183667 + 0.115963i 0.995168 0.0981833i \(-0.0313032\pi\)
−0.976802 + 0.214146i \(0.931303\pi\)
\(978\) 33.2592 + 16.9464i 0.0340074 + 0.0173276i
\(979\) 962.619 312.774i 0.983267 0.319483i
\(980\) −1134.38 493.679i −1.15753 0.503755i
\(981\) 357.405 1099.98i 0.364328 1.12128i
\(982\) −150.646 150.646i −0.153407 0.153407i
\(983\) 583.651 + 1145.48i 0.593744 + 1.16529i 0.970978 + 0.239170i \(0.0768755\pi\)
−0.377233 + 0.926118i \(0.623125\pi\)
\(984\) −26.4406 36.3924i −0.0268706 0.0369842i
\(985\) −79.4297 201.836i −0.0806393 0.204910i
\(986\) −14.7111 10.6882i −0.0149200 0.0108400i
\(987\) −53.6920 8.50397i −0.0543992 0.00861598i
\(988\) −110.380 + 696.913i −0.111721 + 0.705378i
\(989\) 563.778 775.973i 0.570048 0.784604i
\(990\) −130.127 + 204.113i −0.131442 + 0.206174i
\(991\) −392.287 + 285.013i −0.395850 + 0.287602i −0.767848 0.640631i \(-0.778673\pi\)
0.371999 + 0.928233i \(0.378673\pi\)
\(992\) −209.902 + 106.950i −0.211595 + 0.107813i
\(993\) −20.1689 + 20.1689i −0.0203110 + 0.0203110i
\(994\) −16.8008 5.45892i −0.0169022 0.00549187i
\(995\) 1239.95 + 1097.73i 1.24618 + 1.10325i
\(996\) 29.8934 + 92.0024i 0.0300135 + 0.0923719i
\(997\) 589.304 1156.57i 0.591077 1.16005i −0.380820 0.924649i \(-0.624358\pi\)
0.971897 0.235405i \(-0.0756417\pi\)
\(998\) −443.254 + 70.2046i −0.444143 + 0.0703453i
\(999\) 39.2652i 0.0393045i
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 25.3.f.a.12.3 32
3.2 odd 2 225.3.r.a.37.2 32
4.3 odd 2 400.3.bg.c.337.2 32
5.2 odd 4 125.3.f.b.43.2 32
5.3 odd 4 125.3.f.a.43.3 32
5.4 even 2 125.3.f.c.82.2 32
25.2 odd 20 125.3.f.c.93.2 32
25.11 even 5 125.3.f.a.32.3 32
25.14 even 10 125.3.f.b.32.2 32
25.23 odd 20 inner 25.3.f.a.23.3 yes 32
75.23 even 20 225.3.r.a.73.2 32
100.23 even 20 400.3.bg.c.273.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.f.a.12.3 32 1.1 even 1 trivial
25.3.f.a.23.3 yes 32 25.23 odd 20 inner
125.3.f.a.32.3 32 25.11 even 5
125.3.f.a.43.3 32 5.3 odd 4
125.3.f.b.32.2 32 25.14 even 10
125.3.f.b.43.2 32 5.2 odd 4
125.3.f.c.82.2 32 5.4 even 2
125.3.f.c.93.2 32 25.2 odd 20
225.3.r.a.37.2 32 3.2 odd 2
225.3.r.a.73.2 32 75.23 even 20
400.3.bg.c.273.2 32 100.23 even 20
400.3.bg.c.337.2 32 4.3 odd 2