Properties

Label 100.4.l.b.3.17
Level $100$
Weight $4$
Character 100.3
Analytic conductor $5.900$
Analytic rank $0$
Dimension $336$
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] = [100,4,Mod(3,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.l (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: \(5.90019100057\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(42\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 3.17
Character \(\chi\) \(=\) 100.3
Dual form 100.4.l.b.67.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18699 + 2.56730i) q^{2} +(7.22567 - 1.14443i) q^{3} +(-5.18210 - 6.09474i) q^{4} +(-7.02886 - 8.69454i) q^{5} +(-5.63871 + 19.9089i) q^{6} +(11.6198 + 11.6198i) q^{7} +(21.7982 - 6.06960i) q^{8} +(25.2220 - 8.19513i) q^{9} +O(q^{10})\) \(q+(-1.18699 + 2.56730i) q^{2} +(7.22567 - 1.14443i) q^{3} +(-5.18210 - 6.09474i) q^{4} +(-7.02886 - 8.69454i) q^{5} +(-5.63871 + 19.9089i) q^{6} +(11.6198 + 11.6198i) q^{7} +(21.7982 - 6.06960i) q^{8} +(25.2220 - 8.19513i) q^{9} +(30.6647 - 7.72487i) q^{10} +(65.9267 + 21.4209i) q^{11} +(-44.4191 - 38.1080i) q^{12} +(18.1806 - 35.6814i) q^{13} +(-43.6243 + 16.0390i) q^{14} +(-60.7386 - 54.7798i) q^{15} +(-10.2918 + 63.1671i) q^{16} +(7.87771 - 49.7379i) q^{17} +(-8.89896 + 74.4801i) q^{18} +(46.2790 - 33.6237i) q^{19} +(-16.5667 + 87.8951i) q^{20} +(97.2592 + 70.6630i) q^{21} +(-133.248 + 143.827i) q^{22} +(6.85594 + 13.4555i) q^{23} +(150.560 - 68.8034i) q^{24} +(-26.1901 + 122.226i) q^{25} +(70.0248 + 89.0287i) q^{26} +(-3.12891 + 1.59426i) q^{27} +(10.6048 - 131.035i) q^{28} +(-134.554 + 185.198i) q^{29} +(212.733 - 90.9111i) q^{30} +(-131.944 - 181.605i) q^{31} +(-149.953 - 101.401i) q^{32} +(500.879 + 79.3315i) q^{33} +(118.342 + 79.2630i) q^{34} +(19.3549 - 182.703i) q^{35} +(-180.650 - 111.254i) q^{36} +(-215.758 - 109.934i) q^{37} +(31.3893 + 158.723i) q^{38} +(90.5319 - 278.628i) q^{39} +(-205.989 - 146.863i) q^{40} +(-32.8623 - 101.140i) q^{41} +(-296.859 + 165.817i) q^{42} +(-230.751 + 230.751i) q^{43} +(-211.084 - 512.811i) q^{44} +(-248.535 - 161.691i) q^{45} +(-42.6824 + 1.62965i) q^{46} +(54.4120 + 343.544i) q^{47} +(-2.07437 + 468.202i) q^{48} -72.9587i q^{49} +(-282.703 - 212.319i) q^{50} -368.405i q^{51} +(-311.683 + 74.0985i) q^{52} +(44.0201 + 277.932i) q^{53} +(-0.378954 - 9.92523i) q^{54} +(-277.145 - 723.767i) q^{55} +(323.819 + 182.763i) q^{56} +(295.917 - 295.917i) q^{57} +(-315.745 - 565.271i) q^{58} +(175.403 + 539.834i) q^{59} +(-19.1157 + 654.060i) q^{60} +(218.841 - 673.524i) q^{61} +(622.851 - 123.176i) q^{62} +(388.302 + 197.850i) q^{63} +(438.320 - 264.612i) q^{64} +(-438.022 + 92.7279i) q^{65} +(-798.208 + 1191.74i) q^{66} +(187.034 + 29.6233i) q^{67} +(-343.963 + 209.734i) q^{68} +(64.9377 + 89.3791i) q^{69} +(446.081 + 266.558i) q^{70} +(-40.8193 + 56.1830i) q^{71} +(500.052 - 331.726i) q^{72} +(93.5321 - 47.6570i) q^{73} +(538.338 - 423.425i) q^{74} +(-49.3621 + 913.134i) q^{75} +(-444.750 - 107.818i) q^{76} +(517.150 + 1014.96i) q^{77} +(607.863 + 563.153i) q^{78} +(-81.5616 - 59.2580i) q^{79} +(621.548 - 354.511i) q^{80} +(-600.072 + 435.978i) q^{81} +(298.663 + 35.6846i) q^{82} +(-44.4305 + 280.523i) q^{83} +(-73.3341 - 958.952i) q^{84} +(-487.820 + 281.108i) q^{85} +(-318.508 - 866.307i) q^{86} +(-760.299 + 1492.17i) q^{87} +(1567.10 + 66.7874i) q^{88} +(836.194 + 271.696i) q^{89} +(710.120 - 446.138i) q^{90} +(625.868 - 203.357i) q^{91} +(46.4799 - 111.513i) q^{92} +(-1161.22 - 1161.22i) q^{93} +(-946.568 - 268.092i) q^{94} +(-617.632 - 166.039i) q^{95} +(-1199.56 - 561.079i) q^{96} +(-1068.82 + 169.285i) q^{97} +(187.307 + 86.6015i) q^{98} +1838.35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 4 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} + 2 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 4 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} + 2 q^{8} - 20 q^{9} + 100 q^{10} + 70 q^{12} - 136 q^{13} - 10 q^{14} - 134 q^{16} + 312 q^{17} - 748 q^{18} - 1030 q^{20} - 12 q^{21} - 370 q^{22} - 360 q^{25} - 312 q^{26} + 870 q^{28} - 20 q^{29} + 1230 q^{30} + 1646 q^{32} - 100 q^{33} + 90 q^{34} + 170 q^{36} + 1452 q^{37} + 880 q^{38} + 620 q^{40} + 932 q^{41} - 470 q^{42} - 1340 q^{44} - 1200 q^{45} - 6 q^{46} - 3400 q^{48} - 2850 q^{50} - 2948 q^{52} + 3484 q^{53} - 3780 q^{54} - 6 q^{56} + 940 q^{57} + 24 q^{58} + 2810 q^{60} - 948 q^{61} + 2900 q^{62} + 4820 q^{64} - 2160 q^{65} - 870 q^{66} + 834 q^{68} - 20 q^{69} + 3030 q^{70} + 2756 q^{72} - 1456 q^{73} + 240 q^{76} - 3140 q^{77} - 3460 q^{78} - 1850 q^{80} + 2904 q^{81} - 6938 q^{82} - 11290 q^{84} + 900 q^{85} - 6 q^{86} - 1570 q^{88} - 6940 q^{89} + 2090 q^{90} + 6130 q^{92} - 1300 q^{93} + 11030 q^{94} - 1746 q^{96} - 13848 q^{97} + 11952 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18699 + 2.56730i −0.419665 + 0.907679i
\(3\) 7.22567 1.14443i 1.39058 0.220246i 0.584184 0.811621i \(-0.301415\pi\)
0.806397 + 0.591375i \(0.201415\pi\)
\(4\) −5.18210 6.09474i −0.647762 0.761843i
\(5\) −7.02886 8.69454i −0.628681 0.777663i
\(6\) −5.63871 + 19.9089i −0.383665 + 1.35463i
\(7\) 11.6198 + 11.6198i 0.627412 + 0.627412i 0.947416 0.320004i \(-0.103684\pi\)
−0.320004 + 0.947416i \(0.603684\pi\)
\(8\) 21.7982 6.06960i 0.963352 0.268241i
\(9\) 25.2220 8.19513i 0.934148 0.303523i
\(10\) 30.6647 7.72487i 0.969704 0.244282i
\(11\) 65.9267 + 21.4209i 1.80706 + 0.587149i 0.999995 0.00331463i \(-0.00105508\pi\)
0.807064 + 0.590464i \(0.201055\pi\)
\(12\) −44.4191 38.1080i −1.06856 0.916736i
\(13\) 18.1806 35.6814i 0.387876 0.761249i −0.611678 0.791107i \(-0.709505\pi\)
0.999554 + 0.0298572i \(0.00950526\pi\)
\(14\) −43.6243 + 16.0390i −0.832792 + 0.306186i
\(15\) −60.7386 54.7798i −1.04551 0.942939i
\(16\) −10.2918 + 63.1671i −0.160809 + 0.986986i
\(17\) 7.87771 49.7379i 0.112390 0.709601i −0.865567 0.500793i \(-0.833042\pi\)
0.977957 0.208808i \(-0.0669583\pi\)
\(18\) −8.89896 + 74.4801i −0.116528 + 0.975285i
\(19\) 46.2790 33.6237i 0.558797 0.405990i −0.272222 0.962235i \(-0.587758\pi\)
0.831018 + 0.556245i \(0.187758\pi\)
\(20\) −16.5667 + 87.8951i −0.185222 + 0.982697i
\(21\) 97.2592 + 70.6630i 1.01065 + 0.734282i
\(22\) −133.248 + 143.827i −1.29130 + 1.39382i
\(23\) 6.85594 + 13.4555i 0.0621549 + 0.121986i 0.919994 0.391933i \(-0.128193\pi\)
−0.857839 + 0.513919i \(0.828193\pi\)
\(24\) 150.560 68.8034i 1.28054 0.585185i
\(25\) −26.1901 + 122.226i −0.209521 + 0.977804i
\(26\) 70.0248 + 89.0287i 0.528192 + 0.671537i
\(27\) −3.12891 + 1.59426i −0.0223022 + 0.0113635i
\(28\) 10.6048 131.035i 0.0715757 0.884403i
\(29\) −134.554 + 185.198i −0.861591 + 1.18588i 0.119597 + 0.992823i \(0.461840\pi\)
−0.981188 + 0.193056i \(0.938160\pi\)
\(30\) 212.733 90.9111i 1.29465 0.553267i
\(31\) −131.944 181.605i −0.764445 1.05217i −0.996831 0.0795442i \(-0.974654\pi\)
0.232387 0.972623i \(-0.425346\pi\)
\(32\) −149.953 101.401i −0.828380 0.560166i
\(33\) 500.879 + 79.3315i 2.64218 + 0.418480i
\(34\) 118.342 + 79.2630i 0.596924 + 0.399809i
\(35\) 19.3549 182.703i 0.0934736 0.882358i
\(36\) −180.650 111.254i −0.836343 0.515063i
\(37\) −215.758 109.934i −0.958660 0.488462i −0.0966307 0.995320i \(-0.530807\pi\)
−0.862029 + 0.506859i \(0.830807\pi\)
\(38\) 31.3893 + 158.723i 0.134001 + 0.677588i
\(39\) 90.5319 278.628i 0.371710 1.14401i
\(40\) −205.989 146.863i −0.814242 0.580526i
\(41\) −32.8623 101.140i −0.125176 0.385253i 0.868757 0.495239i \(-0.164919\pi\)
−0.993933 + 0.109986i \(0.964919\pi\)
\(42\) −296.859 + 165.817i −1.09063 + 0.609195i
\(43\) −230.751 + 230.751i −0.818353 + 0.818353i −0.985869 0.167516i \(-0.946425\pi\)
0.167516 + 0.985869i \(0.446425\pi\)
\(44\) −211.084 512.811i −0.723229 1.75703i
\(45\) −248.535 161.691i −0.823320 0.535634i
\(46\) −42.6824 + 1.62965i −0.136808 + 0.00522345i
\(47\) 54.4120 + 343.544i 0.168868 + 1.06619i 0.915901 + 0.401405i \(0.131478\pi\)
−0.747033 + 0.664787i \(0.768522\pi\)
\(48\) −2.07437 + 468.202i −0.00623771 + 1.40790i
\(49\) 72.9587i 0.212708i
\(50\) −282.703 212.319i −0.799604 0.600528i
\(51\) 368.405i 1.01151i
\(52\) −311.683 + 74.0985i −0.831204 + 0.197608i
\(53\) 44.0201 + 277.932i 0.114087 + 0.720318i 0.976725 + 0.214496i \(0.0688109\pi\)
−0.862638 + 0.505822i \(0.831189\pi\)
\(54\) −0.378954 9.92523i −0.000954982 0.0250121i
\(55\) −277.145 723.767i −0.679459 1.77441i
\(56\) 323.819 + 182.763i 0.772716 + 0.436121i
\(57\) 295.917 295.917i 0.687634 0.687634i
\(58\) −315.745 565.271i −0.714817 1.27972i
\(59\) 175.403 + 539.834i 0.387042 + 1.19119i 0.934988 + 0.354680i \(0.115410\pi\)
−0.547945 + 0.836514i \(0.684590\pi\)
\(60\) −19.1157 + 654.060i −0.0411305 + 1.40731i
\(61\) 218.841 673.524i 0.459340 1.41370i −0.406623 0.913596i \(-0.633294\pi\)
0.865963 0.500108i \(-0.166706\pi\)
\(62\) 622.851 123.176i 1.27584 0.252312i
\(63\) 388.302 + 197.850i 0.776530 + 0.395662i
\(64\) 438.320 264.612i 0.856094 0.516821i
\(65\) −438.022 + 92.7279i −0.835846 + 0.176946i
\(66\) −798.208 + 1191.74i −1.48868 + 2.22263i
\(67\) 187.034 + 29.6233i 0.341043 + 0.0540158i 0.324607 0.945849i \(-0.394768\pi\)
0.0164359 + 0.999865i \(0.494768\pi\)
\(68\) −343.963 + 209.734i −0.613406 + 0.374029i
\(69\) 64.9377 + 89.3791i 0.113298 + 0.155942i
\(70\) 446.081 + 266.558i 0.761670 + 0.455139i
\(71\) −40.8193 + 56.1830i −0.0682304 + 0.0939112i −0.841768 0.539839i \(-0.818485\pi\)
0.773538 + 0.633750i \(0.218485\pi\)
\(72\) 500.052 331.726i 0.818496 0.542976i
\(73\) 93.5321 47.6570i 0.149960 0.0764086i −0.377400 0.926050i \(-0.623182\pi\)
0.527360 + 0.849642i \(0.323182\pi\)
\(74\) 538.338 423.425i 0.845683 0.665165i
\(75\) −49.3621 + 913.134i −0.0759979 + 1.40586i
\(76\) −444.750 107.818i −0.671267 0.162731i
\(77\) 517.150 + 1014.96i 0.765386 + 1.50216i
\(78\) 607.863 + 563.153i 0.882397 + 0.817494i
\(79\) −81.5616 59.2580i −0.116157 0.0843929i 0.528190 0.849126i \(-0.322871\pi\)
−0.644347 + 0.764733i \(0.722871\pi\)
\(80\) 621.548 354.511i 0.868640 0.495444i
\(81\) −600.072 + 435.978i −0.823144 + 0.598049i
\(82\) 298.663 + 35.6846i 0.402218 + 0.0480574i
\(83\) −44.4305 + 280.523i −0.0587575 + 0.370981i 0.940735 + 0.339141i \(0.110136\pi\)
−0.999493 + 0.0318393i \(0.989864\pi\)
\(84\) −73.3341 958.952i −0.0952548 1.24560i
\(85\) −487.820 + 281.108i −0.622488 + 0.358711i
\(86\) −318.508 866.307i −0.399367 1.08624i
\(87\) −760.299 + 1492.17i −0.936926 + 1.83882i
\(88\) 1567.10 + 66.7874i 1.89833 + 0.0809041i
\(89\) 836.194 + 271.696i 0.995914 + 0.323592i 0.761232 0.648480i \(-0.224595\pi\)
0.234682 + 0.972072i \(0.424595\pi\)
\(90\) 710.120 446.138i 0.831702 0.522523i
\(91\) 625.868 203.357i 0.720975 0.234259i
\(92\) 46.4799 111.513i 0.0526725 0.126370i
\(93\) −1161.22 1161.22i −1.29476 1.29476i
\(94\) −946.568 268.092i −1.03863 0.294166i
\(95\) −617.632 166.039i −0.667028 0.179318i
\(96\) −1199.56 561.079i −1.27530 0.596509i
\(97\) −1068.82 + 169.285i −1.11879 + 0.177198i −0.688319 0.725408i \(-0.741651\pi\)
−0.430467 + 0.902606i \(0.641651\pi\)
\(98\) 187.307 + 86.6015i 0.193070 + 0.0892660i
\(99\) 1838.35 1.86627
\(100\) 880.653 473.762i 0.880653 0.473762i
\(101\) −1152.79 −1.13571 −0.567857 0.823127i \(-0.692227\pi\)
−0.567857 + 0.823127i \(0.692227\pi\)
\(102\) 945.808 + 437.294i 0.918127 + 0.424496i
\(103\) −693.319 + 109.811i −0.663250 + 0.105049i −0.478978 0.877827i \(-0.658993\pi\)
−0.184272 + 0.982875i \(0.558993\pi\)
\(104\) 179.732 888.138i 0.169463 0.837395i
\(105\) −69.2399 1342.30i −0.0643535 1.24758i
\(106\) −765.787 216.890i −0.701696 0.198738i
\(107\) 700.541 + 700.541i 0.632933 + 0.632933i 0.948803 0.315870i \(-0.102296\pi\)
−0.315870 + 0.948803i \(0.602296\pi\)
\(108\) 25.9309 + 10.8083i 0.0231037 + 0.00962989i
\(109\) −846.440 + 275.025i −0.743801 + 0.241675i −0.656312 0.754490i \(-0.727884\pi\)
−0.0874891 + 0.996165i \(0.527884\pi\)
\(110\) 2187.10 + 147.591i 1.89574 + 0.127929i
\(111\) −1684.81 547.427i −1.44068 0.468104i
\(112\) −853.580 + 614.403i −0.720140 + 0.518353i
\(113\) 553.168 1085.65i 0.460510 0.903802i −0.537650 0.843168i \(-0.680688\pi\)
0.998160 0.0606339i \(-0.0193122\pi\)
\(114\) 408.457 + 1110.96i 0.335575 + 0.912727i
\(115\) 68.8003 154.187i 0.0557884 0.125026i
\(116\) 1826.01 139.641i 1.46156 0.111770i
\(117\) 166.137 1048.95i 0.131277 0.828849i
\(118\) −1594.12 190.467i −1.24365 0.148593i
\(119\) 669.484 486.409i 0.515727 0.374698i
\(120\) −1656.48 825.440i −1.26013 0.627934i
\(121\) 2810.67 + 2042.07i 2.11170 + 1.53424i
\(122\) 1469.38 + 1361.30i 1.09042 + 1.01022i
\(123\) −353.199 693.192i −0.258918 0.508155i
\(124\) −423.090 + 1745.26i −0.306408 + 1.26394i
\(125\) 1246.78 631.396i 0.892124 0.451790i
\(126\) −968.851 + 762.042i −0.685017 + 0.538795i
\(127\) −1610.38 + 820.528i −1.12518 + 0.573308i −0.914637 0.404277i \(-0.867523\pi\)
−0.210543 + 0.977585i \(0.567523\pi\)
\(128\) 159.057 + 1439.39i 0.109834 + 0.993950i
\(129\) −1403.25 + 1931.41i −0.957746 + 1.31822i
\(130\) 281.869 1234.60i 0.190166 0.832938i
\(131\) 125.531 + 172.779i 0.0837229 + 0.115235i 0.848824 0.528675i \(-0.177311\pi\)
−0.765101 + 0.643910i \(0.777311\pi\)
\(132\) −2112.10 3463.83i −1.39269 2.28400i
\(133\) 928.457 + 147.053i 0.605319 + 0.0958731i
\(134\) −298.060 + 445.011i −0.192153 + 0.286889i
\(135\) 35.8540 + 15.9986i 0.0228579 + 0.0101996i
\(136\) −130.169 1132.01i −0.0820731 0.713743i
\(137\) −1643.21 837.259i −1.02474 0.522130i −0.140950 0.990017i \(-0.545016\pi\)
−0.883789 + 0.467886i \(0.845016\pi\)
\(138\) −306.544 + 60.6225i −0.189092 + 0.0373951i
\(139\) 275.733 848.620i 0.168255 0.517835i −0.831007 0.556262i \(-0.812235\pi\)
0.999261 + 0.0384277i \(0.0122349\pi\)
\(140\) −1213.83 + 828.824i −0.732766 + 0.500346i
\(141\) 786.326 + 2420.06i 0.469650 + 1.44543i
\(142\) −95.7865 171.484i −0.0566072 0.101343i
\(143\) 1962.91 1962.91i 1.14788 1.14788i
\(144\) 258.083 + 1677.54i 0.149354 + 0.970800i
\(145\) 2555.98 131.845i 1.46388 0.0755110i
\(146\) 11.3280 + 296.694i 0.00642132 + 0.168182i
\(147\) −83.4964 527.175i −0.0468481 0.295787i
\(148\) 448.058 + 1884.68i 0.248852 + 1.04675i
\(149\) 1482.56i 0.815140i −0.913174 0.407570i \(-0.866376\pi\)
0.913174 0.407570i \(-0.133624\pi\)
\(150\) −2285.70 1210.61i −1.24418 0.658973i
\(151\) 1463.79i 0.788882i −0.918921 0.394441i \(-0.870938\pi\)
0.918921 0.394441i \(-0.129062\pi\)
\(152\) 804.716 1013.83i 0.429415 0.541003i
\(153\) −208.917 1319.05i −0.110392 0.696986i
\(154\) −3219.58 + 122.926i −1.68468 + 0.0643225i
\(155\) −651.557 + 2423.67i −0.337641 + 1.25596i
\(156\) −2167.31 + 892.111i −1.11233 + 0.457859i
\(157\) −1811.17 + 1811.17i −0.920681 + 0.920681i −0.997077 0.0763968i \(-0.975658\pi\)
0.0763968 + 0.997077i \(0.475658\pi\)
\(158\) 248.946 139.055i 0.125349 0.0700164i
\(159\) 636.149 + 1957.87i 0.317295 + 0.976533i
\(160\) 172.363 + 2016.50i 0.0851657 + 0.996367i
\(161\) −76.6863 + 236.016i −0.0375387 + 0.115532i
\(162\) −407.006 2058.07i −0.197392 0.998131i
\(163\) −3168.05 1614.20i −1.52233 0.775668i −0.525175 0.850994i \(-0.676000\pi\)
−0.997159 + 0.0753263i \(0.976000\pi\)
\(164\) −446.125 + 724.402i −0.212418 + 0.344916i
\(165\) −2830.86 4912.52i −1.33565 2.31782i
\(166\) −667.449 447.045i −0.312073 0.209021i
\(167\) 1538.44 + 243.665i 0.712862 + 0.112906i 0.502324 0.864680i \(-0.332479\pi\)
0.210538 + 0.977586i \(0.432479\pi\)
\(168\) 2548.97 + 949.998i 1.17058 + 0.436274i
\(169\) 348.735 + 479.992i 0.158732 + 0.218476i
\(170\) −142.651 1586.05i −0.0643578 0.715558i
\(171\) 891.700 1227.32i 0.398772 0.548862i
\(172\) 2602.14 + 210.594i 1.15355 + 0.0933584i
\(173\) −84.0458 + 42.8235i −0.0369357 + 0.0188197i −0.472361 0.881405i \(-0.656598\pi\)
0.435425 + 0.900225i \(0.356598\pi\)
\(174\) −2928.38 3723.11i −1.27586 1.62212i
\(175\) −1724.57 + 1115.92i −0.744942 + 0.482030i
\(176\) −2031.60 + 3943.94i −0.870099 + 1.68912i
\(177\) 1885.21 + 3699.93i 0.800569 + 1.57121i
\(178\) −1690.08 + 1824.26i −0.711668 + 0.768170i
\(179\) −35.9970 26.1533i −0.0150309 0.0109206i 0.580244 0.814442i \(-0.302957\pi\)
−0.595275 + 0.803522i \(0.702957\pi\)
\(180\) 302.465 + 2352.66i 0.125247 + 0.974204i
\(181\) 3717.61 2701.00i 1.52667 1.10919i 0.568619 0.822601i \(-0.307478\pi\)
0.958053 0.286591i \(-0.0925222\pi\)
\(182\) −220.822 + 1848.18i −0.0899364 + 0.752725i
\(183\) 810.471 5117.11i 0.327386 2.06704i
\(184\) 231.117 + 251.693i 0.0925987 + 0.100843i
\(185\) 560.707 + 2648.63i 0.222832 + 1.05260i
\(186\) 4359.55 1602.84i 1.71859 0.631859i
\(187\) 1584.78 3110.31i 0.619736 1.21630i
\(188\) 1811.84 2111.90i 0.702884 0.819290i
\(189\) −54.8824 17.8324i −0.0211223 0.00686304i
\(190\) 1159.40 1388.56i 0.442692 0.530194i
\(191\) 2544.88 826.883i 0.964091 0.313252i 0.215663 0.976468i \(-0.430809\pi\)
0.748428 + 0.663216i \(0.230809\pi\)
\(192\) 2864.32 2413.63i 1.07664 0.907232i
\(193\) 2360.35 + 2360.35i 0.880318 + 0.880318i 0.993567 0.113248i \(-0.0361256\pi\)
−0.113248 + 0.993567i \(0.536126\pi\)
\(194\) 834.078 2944.93i 0.308677 1.08986i
\(195\) −3058.88 + 1171.31i −1.12334 + 0.430149i
\(196\) −444.665 + 378.079i −0.162050 + 0.137784i
\(197\) −3616.92 + 572.863i −1.30809 + 0.207182i −0.771268 0.636511i \(-0.780377\pi\)
−0.536827 + 0.843693i \(0.680377\pi\)
\(198\) −2182.11 + 4719.60i −0.783211 + 1.69398i
\(199\) 1491.72 0.531381 0.265691 0.964058i \(-0.414400\pi\)
0.265691 + 0.964058i \(0.414400\pi\)
\(200\) 170.963 + 2823.26i 0.0604446 + 0.998172i
\(201\) 1385.35 0.486144
\(202\) 1368.36 2959.57i 0.476620 1.03086i
\(203\) −3715.48 + 588.474i −1.28461 + 0.203462i
\(204\) −2245.33 + 1909.11i −0.770612 + 0.655218i
\(205\) −648.378 + 996.619i −0.220901 + 0.339546i
\(206\) 541.047 1910.31i 0.182993 0.646103i
\(207\) 283.191 + 283.191i 0.0950875 + 0.0950875i
\(208\) 2066.78 + 1515.64i 0.688968 + 0.505244i
\(209\) 3771.27 1225.36i 1.24815 0.405550i
\(210\) 3528.29 + 1415.55i 1.15941 + 0.465152i
\(211\) 273.703 + 88.9314i 0.0893008 + 0.0290156i 0.353327 0.935500i \(-0.385050\pi\)
−0.264026 + 0.964516i \(0.585050\pi\)
\(212\) 1465.81 1708.56i 0.474868 0.553511i
\(213\) −230.649 + 452.674i −0.0741963 + 0.145618i
\(214\) −2630.04 + 966.964i −0.840120 + 0.308880i
\(215\) 3628.19 + 384.356i 1.15089 + 0.121920i
\(216\) −58.5280 + 53.7431i −0.0184367 + 0.0169294i
\(217\) 577.055 3643.38i 0.180521 1.13976i
\(218\) 298.646 2499.52i 0.0927836 0.776555i
\(219\) 621.291 451.395i 0.191703 0.139280i
\(220\) −2974.98 + 5439.76i −0.911696 + 1.66704i
\(221\) −1631.50 1185.35i −0.496590 0.360794i
\(222\) 3405.27 3675.62i 1.02949 1.11122i
\(223\) 935.724 + 1836.46i 0.280990 + 0.551474i 0.987762 0.155967i \(-0.0498495\pi\)
−0.706772 + 0.707441i \(0.749849\pi\)
\(224\) −564.165 2920.69i −0.168281 0.871191i
\(225\) 341.086 + 3297.40i 0.101063 + 0.977009i
\(226\) 2130.59 + 2708.81i 0.627102 + 0.797290i
\(227\) −2607.34 + 1328.51i −0.762358 + 0.388441i −0.791527 0.611134i \(-0.790714\pi\)
0.0291695 + 0.999574i \(0.490714\pi\)
\(228\) −3337.01 270.067i −0.969292 0.0784458i
\(229\) −921.927 + 1268.92i −0.266038 + 0.366170i −0.921047 0.389451i \(-0.872665\pi\)
0.655009 + 0.755621i \(0.272665\pi\)
\(230\) 314.178 + 359.650i 0.0900708 + 0.103107i
\(231\) 4898.32 + 6741.95i 1.39518 + 1.92029i
\(232\) −1808.96 + 4853.67i −0.511914 + 1.37353i
\(233\) −3533.93 559.719i −0.993628 0.157375i −0.361611 0.932329i \(-0.617773\pi\)
−0.632018 + 0.774954i \(0.717773\pi\)
\(234\) 2495.77 + 1671.62i 0.697237 + 0.466997i
\(235\) 2604.50 2887.81i 0.722974 0.801617i
\(236\) 2381.20 3866.51i 0.656791 1.06648i
\(237\) −657.154 334.837i −0.180113 0.0917720i
\(238\) 454.086 + 2296.13i 0.123672 + 0.625362i
\(239\) −1558.30 + 4795.94i −0.421748 + 1.29801i 0.484326 + 0.874888i \(0.339065\pi\)
−0.906074 + 0.423119i \(0.860935\pi\)
\(240\) 4085.39 3272.90i 1.09879 0.880269i
\(241\) −2052.86 6318.04i −0.548697 1.68872i −0.712033 0.702146i \(-0.752225\pi\)
0.163336 0.986571i \(-0.447775\pi\)
\(242\) −8578.87 + 4791.92i −2.27880 + 1.27288i
\(243\) −3769.93 + 3769.93i −0.995231 + 0.995231i
\(244\) −5239.01 + 2156.49i −1.37456 + 0.565799i
\(245\) −634.343 + 512.817i −0.165415 + 0.133725i
\(246\) 2198.88 83.9551i 0.569900 0.0217593i
\(247\) −358.361 2262.60i −0.0923155 0.582857i
\(248\) −3978.40 3157.81i −1.01866 0.808552i
\(249\) 2077.81i 0.528819i
\(250\) 141.063 + 3950.33i 0.0356865 + 0.999363i
\(251\) 4539.29i 1.14150i −0.821123 0.570751i \(-0.806652\pi\)
0.821123 0.570751i \(-0.193348\pi\)
\(252\) −806.374 3391.87i −0.201575 0.847889i
\(253\) 163.760 + 1033.94i 0.0406937 + 0.256930i
\(254\) −195.039 5108.29i −0.0481804 1.26190i
\(255\) −3203.11 + 2589.47i −0.786615 + 0.635917i
\(256\) −3884.16 1300.20i −0.948281 0.317432i
\(257\) 2306.85 2306.85i 0.559911 0.559911i −0.369371 0.929282i \(-0.620427\pi\)
0.929282 + 0.369371i \(0.120427\pi\)
\(258\) −3292.86 5895.14i −0.794592 1.42254i
\(259\) −1229.66 3784.49i −0.295008 0.907942i
\(260\) 2835.03 + 2189.11i 0.676234 + 0.522164i
\(261\) −1876.01 + 5773.76i −0.444912 + 1.36930i
\(262\) −592.580 + 117.189i −0.139732 + 0.0276335i
\(263\) 3583.60 + 1825.93i 0.840205 + 0.428106i 0.820463 0.571699i \(-0.193716\pi\)
0.0197418 + 0.999805i \(0.493716\pi\)
\(264\) 11399.8 1310.85i 2.65760 0.305597i
\(265\) 2107.08 2336.28i 0.488441 0.541572i
\(266\) −1479.60 + 2209.08i −0.341053 + 0.509200i
\(267\) 6352.99 + 1006.22i 1.45617 + 0.230634i
\(268\) −788.682 1293.44i −0.179763 0.294810i
\(269\) −1460.46 2010.16i −0.331026 0.455619i 0.610767 0.791810i \(-0.290861\pi\)
−0.941794 + 0.336191i \(0.890861\pi\)
\(270\) −83.6317 + 73.0579i −0.0188506 + 0.0164673i
\(271\) 1695.67 2333.89i 0.380091 0.523150i −0.575518 0.817789i \(-0.695199\pi\)
0.955609 + 0.294639i \(0.0951994\pi\)
\(272\) 3060.72 + 1009.50i 0.682293 + 0.225037i
\(273\) 4289.58 2185.65i 0.950979 0.484548i
\(274\) 4099.98 3224.81i 0.903974 0.711014i
\(275\) −4344.81 + 7496.91i −0.952733 + 1.64393i
\(276\) 208.229 858.950i 0.0454128 0.187329i
\(277\) −1716.12 3368.07i −0.372244 0.730570i 0.626565 0.779369i \(-0.284460\pi\)
−0.998809 + 0.0487995i \(0.984460\pi\)
\(278\) 1851.37 + 1715.20i 0.399417 + 0.370039i
\(279\) −4816.16 3499.14i −1.03346 0.750854i
\(280\) −687.035 4100.08i −0.146636 0.875094i
\(281\) 673.955 489.657i 0.143078 0.103952i −0.513944 0.857824i \(-0.671816\pi\)
0.657021 + 0.753872i \(0.271816\pi\)
\(282\) −7146.40 853.860i −1.50908 0.180307i
\(283\) 188.594 1190.73i 0.0396139 0.250112i −0.959932 0.280232i \(-0.909589\pi\)
0.999546 + 0.0301192i \(0.00958870\pi\)
\(284\) 553.950 42.3623i 0.115743 0.00885120i
\(285\) −4652.82 492.902i −0.967050 0.102446i
\(286\) 2709.43 + 7369.36i 0.560182 + 1.52363i
\(287\) 793.372 1557.08i 0.163175 0.320249i
\(288\) −4613.10 1328.65i −0.943853 0.271846i
\(289\) 2260.74 + 734.558i 0.460154 + 0.149513i
\(290\) −2695.44 + 6718.47i −0.545800 + 1.36042i
\(291\) −7529.21 + 2446.39i −1.51674 + 0.492817i
\(292\) −775.149 323.091i −0.155350 0.0647516i
\(293\) 1337.99 + 1337.99i 0.266779 + 0.266779i 0.827801 0.561022i \(-0.189592\pi\)
−0.561022 + 0.827801i \(0.689592\pi\)
\(294\) 1452.53 + 411.393i 0.288140 + 0.0816086i
\(295\) 3460.73 5319.47i 0.683022 1.04987i
\(296\) −5370.39 1086.80i −1.05455 0.213409i
\(297\) −240.429 + 38.0802i −0.0469734 + 0.00743986i
\(298\) 3806.18 + 1759.79i 0.739886 + 0.342086i
\(299\) 604.758 0.116970
\(300\) 5821.11 4431.10i 1.12027 0.852765i
\(301\) −5362.57 −1.02689
\(302\) 3757.98 + 1737.50i 0.716051 + 0.331066i
\(303\) −8329.70 + 1319.29i −1.57930 + 0.250137i
\(304\) 1647.62 + 3269.36i 0.310846 + 0.616811i
\(305\) −7394.19 + 2831.39i −1.38816 + 0.531556i
\(306\) 3634.38 + 1029.35i 0.678967 + 0.192301i
\(307\) 5635.94 + 5635.94i 1.04775 + 1.04775i 0.998801 + 0.0489522i \(0.0155882\pi\)
0.0489522 + 0.998801i \(0.484412\pi\)
\(308\) 3506.03 8411.54i 0.648618 1.55614i
\(309\) −4884.02 + 1586.91i −0.899166 + 0.292157i
\(310\) −5448.89 4549.62i −0.998311 0.833552i
\(311\) 5399.32 + 1754.35i 0.984461 + 0.319871i 0.756640 0.653832i \(-0.226840\pi\)
0.227821 + 0.973703i \(0.426840\pi\)
\(312\) 282.266 6623.08i 0.0512185 1.20179i
\(313\) 225.552 442.671i 0.0407315 0.0799402i −0.869744 0.493504i \(-0.835716\pi\)
0.910475 + 0.413563i \(0.135716\pi\)
\(314\) −2499.97 6799.66i −0.449305 1.22206i
\(315\) −1009.11 4766.76i −0.180498 0.852624i
\(316\) 61.4980 + 804.177i 0.0109479 + 0.143160i
\(317\) 53.7315 339.248i 0.00952008 0.0601074i −0.982471 0.186416i \(-0.940313\pi\)
0.991991 + 0.126308i \(0.0403129\pi\)
\(318\) −5781.54 690.784i −1.01954 0.121815i
\(319\) −12837.8 + 9327.24i −2.25323 + 1.63707i
\(320\) −5381.57 1951.07i −0.940122 0.340838i
\(321\) 5863.60 + 4260.15i 1.01955 + 0.740743i
\(322\) −514.899 477.027i −0.0891125 0.0825579i
\(323\) −1307.80 2566.70i −0.225288 0.442152i
\(324\) 5766.80 + 1398.01i 0.988821 + 0.239713i
\(325\) 3885.03 + 3156.63i 0.663085 + 0.538764i
\(326\) 7904.59 6217.29i 1.34293 1.05627i
\(327\) −5801.35 + 2955.93i −0.981086 + 0.499888i
\(328\) −1330.21 2005.20i −0.223929 0.337556i
\(329\) −3359.67 + 4624.18i −0.562992 + 0.774892i
\(330\) 15972.2 1436.55i 2.66436 0.239634i
\(331\) −975.069 1342.07i −0.161917 0.222860i 0.720348 0.693613i \(-0.243982\pi\)
−0.882265 + 0.470753i \(0.843982\pi\)
\(332\) 1939.96 1182.90i 0.320690 0.195543i
\(333\) −6342.78 1004.60i −1.04379 0.165320i
\(334\) −2451.68 + 3660.41i −0.401646 + 0.599667i
\(335\) −1057.08 1834.39i −0.172401 0.299175i
\(336\) −5464.54 + 5416.33i −0.887247 + 0.879420i
\(337\) 5691.27 + 2899.85i 0.919950 + 0.468738i 0.848792 0.528727i \(-0.177330\pi\)
0.0711582 + 0.997465i \(0.477330\pi\)
\(338\) −1646.23 + 325.561i −0.264921 + 0.0523910i
\(339\) 2754.55 8477.63i 0.441317 1.35824i
\(340\) 4241.21 + 1516.41i 0.676506 + 0.241879i
\(341\) −4808.47 14799.0i −0.763617 2.35017i
\(342\) 2092.46 + 3746.08i 0.330840 + 0.592295i
\(343\) 4833.37 4833.37i 0.760868 0.760868i
\(344\) −3629.38 + 6430.51i −0.568846 + 1.00788i
\(345\) 320.672 1192.84i 0.0500417 0.186146i
\(346\) −10.1791 266.602i −0.00158159 0.0414238i
\(347\) −558.494 3526.19i −0.0864021 0.545522i −0.992480 0.122410i \(-0.960938\pi\)
0.906077 0.423112i \(-0.139062\pi\)
\(348\) 13034.3 3098.74i 2.00780 0.477328i
\(349\) 3292.21i 0.504951i 0.967603 + 0.252476i \(0.0812447\pi\)
−0.967603 + 0.252476i \(0.918755\pi\)
\(350\) −817.848 5752.07i −0.124902 0.878460i
\(351\) 140.628i 0.0213852i
\(352\) −7713.80 9897.15i −1.16803 1.49864i
\(353\) 596.070 + 3763.44i 0.0898742 + 0.567443i 0.990998 + 0.133880i \(0.0427438\pi\)
−0.901123 + 0.433563i \(0.857256\pi\)
\(354\) −11736.6 + 448.112i −1.76212 + 0.0672793i
\(355\) 775.399 39.9972i 0.115926 0.00597981i
\(356\) −2677.32 6504.34i −0.398589 0.968340i
\(357\) 4280.81 4280.81i 0.634634 0.634634i
\(358\) 109.872 61.3713i 0.0162204 0.00906027i
\(359\) 2803.99 + 8629.79i 0.412225 + 1.26870i 0.914709 + 0.404113i \(0.132420\pi\)
−0.502484 + 0.864587i \(0.667580\pi\)
\(360\) −6399.01 2016.07i −0.936826 0.295156i
\(361\) −1108.35 + 3411.15i −0.161591 + 0.497325i
\(362\) 2521.51 + 12750.3i 0.366099 + 1.85122i
\(363\) 22646.0 + 11538.7i 3.27440 + 1.66839i
\(364\) −4482.71 2760.69i −0.645489 0.397526i
\(365\) −1071.78 478.244i −0.153697 0.0685820i
\(366\) 12175.2 + 8154.70i 1.73881 + 1.16463i
\(367\) −2003.50 317.324i −0.284965 0.0451339i 0.0123159 0.999924i \(-0.496080\pi\)
−0.297280 + 0.954790i \(0.596080\pi\)
\(368\) −920.507 + 294.589i −0.130393 + 0.0417296i
\(369\) −1657.70 2281.63i −0.233866 0.321889i
\(370\) −7465.39 1704.40i −1.04894 0.239480i
\(371\) −2718.02 + 3741.03i −0.380357 + 0.523516i
\(372\) −1059.78 + 13094.8i −0.147707 + 1.82510i
\(373\) 8136.48 4145.75i 1.12947 0.575492i 0.213579 0.976926i \(-0.431488\pi\)
0.915888 + 0.401434i \(0.131488\pi\)
\(374\) 6103.98 + 7760.53i 0.843929 + 1.07296i
\(375\) 8286.24 5989.11i 1.14107 0.824737i
\(376\) 3271.26 + 7158.37i 0.448676 + 0.981821i
\(377\) 4161.86 + 8168.11i 0.568559 + 1.11586i
\(378\) 110.926 119.733i 0.0150937 0.0162921i
\(379\) −1419.15 1031.07i −0.192340 0.139743i 0.487448 0.873152i \(-0.337928\pi\)
−0.679787 + 0.733409i \(0.737928\pi\)
\(380\) 2188.66 + 4624.73i 0.295463 + 0.624326i
\(381\) −10697.0 + 7771.83i −1.43838 + 1.04505i
\(382\) −897.900 + 7514.99i −0.120263 + 1.00655i
\(383\) 438.531 2768.77i 0.0585062 0.369394i −0.941013 0.338372i \(-0.890124\pi\)
0.999519 0.0310218i \(-0.00987614\pi\)
\(384\) 2796.58 + 10218.5i 0.371647 + 1.35798i
\(385\) 5189.67 11630.4i 0.686988 1.53959i
\(386\) −8861.44 + 3258.01i −1.16849 + 0.429607i
\(387\) −3928.97 + 7711.03i −0.516074 + 1.01285i
\(388\) 6570.48 + 5636.94i 0.859705 + 0.737557i
\(389\) 5907.56 + 1919.48i 0.769987 + 0.250184i 0.667559 0.744557i \(-0.267339\pi\)
0.102428 + 0.994740i \(0.467339\pi\)
\(390\) 623.768 9243.42i 0.0809890 1.20015i
\(391\) 723.260 235.001i 0.0935469 0.0303952i
\(392\) −442.830 1590.37i −0.0570569 0.204912i
\(393\) 1104.78 + 1104.78i 0.141803 + 0.141803i
\(394\) 2822.54 9965.71i 0.360907 1.27428i
\(395\) 58.0646 + 1125.66i 0.00739632 + 0.143387i
\(396\) −9526.51 11204.3i −1.20890 1.42181i
\(397\) 569.479 90.1967i 0.0719933 0.0114026i −0.120334 0.992733i \(-0.538397\pi\)
0.192327 + 0.981331i \(0.438397\pi\)
\(398\) −1770.66 + 3829.69i −0.223002 + 0.482324i
\(399\) 6877.01 0.862860
\(400\) −7451.09 2912.27i −0.931386 0.364034i
\(401\) 10408.7 1.29622 0.648110 0.761547i \(-0.275560\pi\)
0.648110 + 0.761547i \(0.275560\pi\)
\(402\) −1644.40 + 3556.61i −0.204018 + 0.441262i
\(403\) −8878.73 + 1406.25i −1.09747 + 0.173822i
\(404\) 5973.88 + 7025.98i 0.735673 + 0.865236i
\(405\) 8008.45 + 2152.92i 0.982576 + 0.264147i
\(406\) 2899.45 10237.3i 0.354427 1.25140i
\(407\) −11869.3 11869.3i −1.44555 1.44555i
\(408\) −2236.07 8030.56i −0.271328 0.974441i
\(409\) 1225.39 398.153i 0.148146 0.0481354i −0.234006 0.972235i \(-0.575183\pi\)
0.382151 + 0.924100i \(0.375183\pi\)
\(410\) −1789.00 2847.56i −0.215494 0.343003i
\(411\) −12831.5 4169.21i −1.53998 0.500369i
\(412\) 4262.12 + 3656.55i 0.509659 + 0.437246i
\(413\) −4234.64 + 8310.94i −0.504535 + 0.990205i
\(414\) −1063.18 + 390.891i −0.126214 + 0.0464040i
\(415\) 2751.31 1585.45i 0.325438 0.187535i
\(416\) −6344.36 + 3507.00i −0.747735 + 0.413329i
\(417\) 1021.17 6447.41i 0.119921 0.757148i
\(418\) −1330.60 + 11136.5i −0.155698 + 1.30312i
\(419\) 9973.17 7245.93i 1.16282 0.844838i 0.172688 0.984977i \(-0.444755\pi\)
0.990132 + 0.140139i \(0.0447549\pi\)
\(420\) −7822.19 + 7377.95i −0.908771 + 0.857160i
\(421\) −682.686 496.000i −0.0790311 0.0574194i 0.547568 0.836761i \(-0.315554\pi\)
−0.626599 + 0.779342i \(0.715554\pi\)
\(422\) −553.197 + 597.117i −0.0638133 + 0.0688796i
\(423\) 4187.77 + 8218.95i 0.481362 + 0.944726i
\(424\) 2646.49 + 5791.22i 0.303125 + 0.663317i
\(425\) 5872.93 + 2265.50i 0.670303 + 0.258571i
\(426\) −888.374 1129.47i −0.101037 0.128457i
\(427\) 10369.1 5283.34i 1.17517 0.598780i
\(428\) 639.346 7899.89i 0.0722055 0.892185i
\(429\) 11936.9 16429.8i 1.34340 1.84904i
\(430\) −5293.39 + 8858.44i −0.593651 + 0.993469i
\(431\) 1289.85 + 1775.33i 0.144153 + 0.198410i 0.874988 0.484144i \(-0.160869\pi\)
−0.730835 + 0.682554i \(0.760869\pi\)
\(432\) −68.5027 214.052i −0.00762925 0.0238393i
\(433\) −8409.89 1332.00i −0.933380 0.147833i −0.328820 0.944393i \(-0.606651\pi\)
−0.604560 + 0.796560i \(0.706651\pi\)
\(434\) 8668.71 + 5806.15i 0.958782 + 0.642175i
\(435\) 18317.8 3877.81i 2.01901 0.427418i
\(436\) 6062.54 + 3733.63i 0.665924 + 0.410111i
\(437\) 769.711 + 392.188i 0.0842570 + 0.0429311i
\(438\) 421.399 + 2130.85i 0.0459708 + 0.232456i
\(439\) 2885.41 8880.39i 0.313698 0.965462i −0.662590 0.748983i \(-0.730543\pi\)
0.976287 0.216479i \(-0.0694574\pi\)
\(440\) −10434.2 14094.6i −1.13053 1.52713i
\(441\) −597.906 1840.17i −0.0645617 0.198700i
\(442\) 4979.74 2781.55i 0.535887 0.299332i
\(443\) −2176.81 + 2176.81i −0.233462 + 0.233462i −0.814136 0.580674i \(-0.802789\pi\)
0.580674 + 0.814136i \(0.302789\pi\)
\(444\) 5394.41 + 13105.3i 0.576593 + 1.40079i
\(445\) −3515.22 9180.03i −0.374466 0.977922i
\(446\) −5825.45 + 222.421i −0.618483 + 0.0236142i
\(447\) −1696.69 10712.5i −0.179532 1.13352i
\(448\) 8167.96 + 2018.46i 0.861383 + 0.212864i
\(449\) 13177.4i 1.38504i −0.721400 0.692518i \(-0.756501\pi\)
0.721400 0.692518i \(-0.243499\pi\)
\(450\) −8870.30 3038.32i −0.929223 0.318284i
\(451\) 7371.74i 0.769671i
\(452\) −9483.34 + 2254.54i −0.986856 + 0.234612i
\(453\) −1675.20 10576.8i −0.173748 1.09700i
\(454\) −315.784 8270.76i −0.0326443 0.854991i
\(455\) −6167.23 4012.27i −0.635438 0.413402i
\(456\) 4654.35 8246.54i 0.477982 0.846885i
\(457\) 627.423 627.423i 0.0642223 0.0642223i −0.674266 0.738488i \(-0.735540\pi\)
0.738488 + 0.674266i \(0.235540\pi\)
\(458\) −2163.39 3873.07i −0.220718 0.395145i
\(459\) 54.6465 + 168.185i 0.00555703 + 0.0171028i
\(460\) −1296.26 + 379.689i −0.131388 + 0.0384850i
\(461\) −2842.14 + 8747.20i −0.287140 + 0.883726i 0.698609 + 0.715504i \(0.253803\pi\)
−0.985749 + 0.168222i \(0.946197\pi\)
\(462\) −23122.9 + 4572.81i −2.32852 + 0.460490i
\(463\) 9886.75 + 5037.55i 0.992389 + 0.505647i 0.873272 0.487233i \(-0.161994\pi\)
0.119117 + 0.992880i \(0.461994\pi\)
\(464\) −10313.6 10405.4i −1.03189 1.04108i
\(465\) −1934.21 + 18258.3i −0.192896 + 1.82087i
\(466\) 5631.72 8408.29i 0.559838 0.835851i
\(467\) −9899.03 1567.85i −0.980883 0.155357i −0.354656 0.934997i \(-0.615402\pi\)
−0.626228 + 0.779640i \(0.715402\pi\)
\(468\) −7254.01 + 4423.19i −0.716489 + 0.436885i
\(469\) 1829.09 + 2517.52i 0.180084 + 0.247864i
\(470\) 4322.36 + 10114.4i 0.424204 + 0.992640i
\(471\) −11014.1 + 15159.6i −1.07750 + 1.48306i
\(472\) 7100.04 + 10702.8i 0.692385 + 1.04372i
\(473\) −20155.5 + 10269.8i −1.95931 + 0.998317i
\(474\) 1639.66 1289.66i 0.158887 0.124971i
\(475\) 2897.62 + 6537.09i 0.279899 + 0.631457i
\(476\) −6433.87 1559.72i −0.619529 0.150188i
\(477\) 3387.96 + 6649.25i 0.325208 + 0.638256i
\(478\) −10463.0 9693.37i −1.00118 0.927540i
\(479\) −9738.03 7075.09i −0.928898 0.674884i 0.0168250 0.999858i \(-0.494644\pi\)
−0.945723 + 0.324975i \(0.894644\pi\)
\(480\) 3553.19 + 14373.3i 0.337876 + 1.36677i
\(481\) −7845.22 + 5699.88i −0.743682 + 0.540317i
\(482\) 18657.1 + 2229.16i 1.76308 + 0.210655i
\(483\) −284.005 + 1793.14i −0.0267550 + 0.168925i
\(484\) −2119.27 27712.6i −0.199029 2.60261i
\(485\) 8984.45 + 8103.03i 0.841160 + 0.758638i
\(486\) −5203.67 14153.4i −0.485686 1.32101i
\(487\) 2095.31 4112.27i 0.194964 0.382638i −0.772742 0.634720i \(-0.781115\pi\)
0.967706 + 0.252082i \(0.0811154\pi\)
\(488\) 682.317 16009.9i 0.0632932 1.48511i
\(489\) −24738.6 8038.05i −2.28777 0.743340i
\(490\) −563.597 2237.26i −0.0519606 0.206263i
\(491\) −18094.3 + 5879.20i −1.66311 + 0.540376i −0.981520 0.191361i \(-0.938710\pi\)
−0.681587 + 0.731737i \(0.738710\pi\)
\(492\) −2394.52 + 5744.85i −0.219417 + 0.526418i
\(493\) 8151.40 + 8151.40i 0.744666 + 0.744666i
\(494\) 6234.15 + 1765.67i 0.567789 + 0.160812i
\(495\) −12921.5 15983.6i −1.17329 1.45133i
\(496\) 12829.4 6465.46i 1.16140 0.585298i
\(497\) −1127.15 + 178.523i −0.101730 + 0.0161124i
\(498\) −5334.37 2466.35i −0.479998 0.221927i
\(499\) −13266.4 −1.19015 −0.595077 0.803669i \(-0.702879\pi\)
−0.595077 + 0.803669i \(0.702879\pi\)
\(500\) −10309.1 4326.86i −0.922077 0.387006i
\(501\) 11395.1 1.01616
\(502\) 11653.7 + 5388.10i 1.03612 + 0.479049i
\(503\) −7098.32 + 1124.26i −0.629221 + 0.0996589i −0.462897 0.886412i \(-0.653190\pi\)
−0.166325 + 0.986071i \(0.553190\pi\)
\(504\) 9665.13 + 1955.92i 0.854205 + 0.172865i
\(505\) 8102.83 + 10023.0i 0.714002 + 0.883204i
\(506\) −2848.82 806.858i −0.250288 0.0708878i
\(507\) 3069.16 + 3069.16i 0.268849 + 0.268849i
\(508\) 13346.0 + 5562.78i 1.16562 + 0.485843i
\(509\) 14507.5 4713.79i 1.26333 0.410481i 0.400651 0.916231i \(-0.368784\pi\)
0.862680 + 0.505750i \(0.168784\pi\)
\(510\) −2845.88 11297.0i −0.247094 0.980866i
\(511\) 1640.59 + 533.061i 0.142027 + 0.0461473i
\(512\) 7948.48 8428.49i 0.686087 0.727519i
\(513\) −91.1980 + 178.986i −0.00784891 + 0.0154044i
\(514\) 3184.16 + 8660.59i 0.273244 + 0.743195i
\(515\) 5828.00 + 5256.25i 0.498665 + 0.449743i
\(516\) 19043.2 1456.29i 1.62467 0.124244i
\(517\) −3771.81 + 23814.3i −0.320859 + 2.02582i
\(518\) 11175.5 + 1335.26i 0.947924 + 0.113259i
\(519\) −558.278 + 405.613i −0.0472171 + 0.0343053i
\(520\) −8985.26 + 4679.92i −0.757750 + 0.394669i
\(521\) −5924.30 4304.25i −0.498173 0.361944i 0.310146 0.950689i \(-0.399622\pi\)
−0.808319 + 0.588745i \(0.799622\pi\)
\(522\) −12596.2 11669.7i −1.05617 0.978485i
\(523\) 153.207 + 300.685i 0.0128093 + 0.0251396i 0.897322 0.441376i \(-0.145509\pi\)
−0.884513 + 0.466515i \(0.845509\pi\)
\(524\) 402.527 1660.43i 0.0335582 0.138428i
\(525\) −11184.0 + 10036.9i −0.929737 + 0.834373i
\(526\) −8941.43 + 7032.81i −0.741188 + 0.582975i
\(527\) −10072.1 + 5131.97i −0.832535 + 0.424198i
\(528\) −10166.1 + 30822.6i −0.837919 + 2.54050i
\(529\) 7017.54 9658.81i 0.576768 0.793853i
\(530\) 3496.85 + 8182.66i 0.286592 + 0.670626i
\(531\) 8848.02 + 12178.3i 0.723110 + 0.995276i
\(532\) −3915.10 6420.75i −0.319062 0.523261i
\(533\) −4206.26 666.206i −0.341826 0.0541399i
\(534\) −10124.2 + 15115.7i −0.820445 + 1.22494i
\(535\) 1166.87 11014.9i 0.0942961 0.890122i
\(536\) 4256.80 489.488i 0.343033 0.0394453i
\(537\) −290.033 147.779i −0.0233070 0.0118755i
\(538\) 6894.24 1363.41i 0.552476 0.109258i
\(539\) 1562.84 4809.93i 0.124891 0.384375i
\(540\) −88.2917 301.427i −0.00703605 0.0240210i
\(541\) −2286.41 7036.83i −0.181701 0.559218i 0.818175 0.574969i \(-0.194986\pi\)
−0.999876 + 0.0157511i \(0.994986\pi\)
\(542\) 3979.06 + 7123.61i 0.315341 + 0.564549i
\(543\) 23771.1 23771.1i 1.87866 1.87866i
\(544\) −6224.76 + 6659.53i −0.490596 + 0.524862i
\(545\) 8340.73 + 5426.30i 0.655555 + 0.426490i
\(546\) 519.527 + 13607.0i 0.0407211 + 1.06653i
\(547\) 1169.88 + 7386.32i 0.0914449 + 0.577361i 0.990282 + 0.139077i \(0.0444135\pi\)
−0.898837 + 0.438284i \(0.855587\pi\)
\(548\) 3412.41 + 14353.7i 0.266005 + 1.11891i
\(549\) 18781.1i 1.46003i
\(550\) −14089.6 20053.2i −1.09233 1.55468i
\(551\) 13095.0i 1.01246i
\(552\) 1958.02 + 1554.15i 0.150976 + 0.119836i
\(553\) −259.165 1636.30i −0.0199291 0.125827i
\(554\) 10683.9 407.920i 0.819341 0.0312831i
\(555\) 7082.66 + 18496.4i 0.541698 + 1.41465i
\(556\) −6601.00 + 2717.11i −0.503498 + 0.207250i
\(557\) −2228.66 + 2228.66i −0.169536 + 0.169536i −0.786775 0.617240i \(-0.788251\pi\)
0.617240 + 0.786775i \(0.288251\pi\)
\(558\) 14700.1 8211.08i 1.11524 0.622944i
\(559\) 4038.33 + 12428.7i 0.305551 + 0.940390i
\(560\) 11341.6 + 3102.93i 0.855843 + 0.234148i
\(561\) 7891.56 24287.7i 0.593907 1.82786i
\(562\) 457.118 + 2311.47i 0.0343103 + 0.173493i
\(563\) −4737.11 2413.68i −0.354610 0.180683i 0.267606 0.963528i \(-0.413767\pi\)
−0.622216 + 0.782846i \(0.713767\pi\)
\(564\) 10674.8 17333.5i 0.796972 1.29410i
\(565\) −13327.4 + 2821.37i −0.992368 + 0.210081i
\(566\) 2833.12 + 1897.57i 0.210397 + 0.140920i
\(567\) −12038.7 1906.75i −0.891674 0.141227i
\(568\) −548.778 + 1472.44i −0.0405391 + 0.108772i
\(569\) 7249.40 + 9977.94i 0.534114 + 0.735144i 0.987750 0.156042i \(-0.0498736\pi\)
−0.453637 + 0.891187i \(0.649874\pi\)
\(570\) 6788.29 11360.1i 0.498825 0.834778i
\(571\) 11959.9 16461.4i 0.876544 1.20646i −0.100822 0.994905i \(-0.532147\pi\)
0.977366 0.211555i \(-0.0678529\pi\)
\(572\) −22135.5 1791.45i −1.61806 0.130951i
\(573\) 17442.2 8887.23i 1.27165 0.647940i
\(574\) 3055.77 + 3885.07i 0.222205 + 0.282508i
\(575\) −1824.17 + 485.569i −0.132301 + 0.0352167i
\(576\) 8886.78 10266.1i 0.642851 0.742631i
\(577\) −10624.1 20850.9i −0.766528 1.50440i −0.860853 0.508854i \(-0.830069\pi\)
0.0943251 0.995541i \(-0.469931\pi\)
\(578\) −4569.31 + 4932.09i −0.328821 + 0.354927i
\(579\) 19756.3 + 14353.8i 1.41804 + 1.03027i
\(580\) −14048.9 14894.8i −1.00577 1.06633i
\(581\) −3775.90 + 2743.36i −0.269623 + 0.195893i
\(582\) 2656.50 22233.6i 0.189202 1.58353i
\(583\) −3051.45 + 19266.1i −0.216772 + 1.36864i
\(584\) 1749.57 1606.54i 0.123969 0.113834i
\(585\) −10287.9 + 5928.43i −0.727097 + 0.418992i
\(586\) −5023.21 + 1846.84i −0.354107 + 0.130192i
\(587\) 4569.50 8968.15i 0.321301 0.630588i −0.672706 0.739910i \(-0.734868\pi\)
0.994006 + 0.109322i \(0.0348680\pi\)
\(588\) −2780.31 + 3240.76i −0.194997 + 0.227290i
\(589\) −12212.4 3968.07i −0.854338 0.277591i
\(590\) 9548.83 + 15198.9i 0.666304 + 1.06056i
\(591\) −25479.0 + 8278.64i −1.77338 + 0.576206i
\(592\) 9164.76 12497.4i 0.636266 0.867634i
\(593\) −11178.9 11178.9i −0.774136 0.774136i 0.204691 0.978827i \(-0.434381\pi\)
−0.978827 + 0.204691i \(0.934381\pi\)
\(594\) 187.624 662.455i 0.0129601 0.0457590i
\(595\) −8934.82 2401.96i −0.615616 0.165497i
\(596\) −9035.81 + 7682.76i −0.621009 + 0.528017i
\(597\) 10778.6 1707.17i 0.738928 0.117035i
\(598\) −717.843 + 1552.60i −0.0490883 + 0.106171i
\(599\) 9107.29 0.621225 0.310613 0.950537i \(-0.399466\pi\)
0.310613 + 0.950537i \(0.399466\pi\)
\(600\) 4466.35 + 20204.2i 0.303897 + 1.37472i
\(601\) 6422.39 0.435898 0.217949 0.975960i \(-0.430063\pi\)
0.217949 + 0.975960i \(0.430063\pi\)
\(602\) 6365.34 13767.4i 0.430950 0.932086i
\(603\) 4960.14 785.609i 0.334979 0.0530555i
\(604\) −8921.39 + 7585.47i −0.601004 + 0.511008i
\(605\) −2000.95 38791.0i −0.134463 2.60674i
\(606\) 6500.26 22950.9i 0.435734 1.53847i
\(607\) 8349.48 + 8349.48i 0.558311 + 0.558311i 0.928826 0.370515i \(-0.120819\pi\)
−0.370515 + 0.928826i \(0.620819\pi\)
\(608\) −10349.1 + 349.228i −0.690318 + 0.0232945i
\(609\) −26173.3 + 8504.23i −1.74154 + 0.565860i
\(610\) 1507.82 22344.0i 0.100082 1.48308i
\(611\) 13247.4 + 4304.33i 0.877138 + 0.284999i
\(612\) −6956.64 + 8108.73i −0.459486 + 0.535582i
\(613\) −9010.32 + 17683.8i −0.593676 + 1.16515i 0.377325 + 0.926081i \(0.376844\pi\)
−0.971001 + 0.239074i \(0.923156\pi\)
\(614\) −21159.0 + 7779.35i −1.39073 + 0.511318i
\(615\) −3544.40 + 7943.26i −0.232397 + 0.520818i
\(616\) 17433.4 + 18985.5i 1.14028 + 1.24180i
\(617\) 3820.67 24122.8i 0.249294 1.57398i −0.472156 0.881515i \(-0.656524\pi\)
0.721450 0.692466i \(-0.243476\pi\)
\(618\) 1723.21 14422.4i 0.112164 0.938762i
\(619\) −24148.4 + 17544.8i −1.56802 + 1.13924i −0.639005 + 0.769202i \(0.720654\pi\)
−0.929018 + 0.370033i \(0.879346\pi\)
\(620\) 18148.0 8588.60i 1.17555 0.556333i
\(621\) −42.9032 31.1710i −0.00277238 0.00201425i
\(622\) −10912.9 + 11779.3i −0.703484 + 0.759336i
\(623\) 6559.37 + 12873.5i 0.421823 + 0.827874i
\(624\) 16668.4 + 8586.21i 1.06934 + 0.550839i
\(625\) −14253.2 6402.20i −0.912202 0.409741i
\(626\) 868.743 + 1104.51i 0.0554664 + 0.0705193i
\(627\) 25847.6 13170.0i 1.64634 0.838851i
\(628\) 20424.2 + 1652.96i 1.29780 + 0.105032i
\(629\) −7167.58 + 9865.33i −0.454356 + 0.625368i
\(630\) 13435.5 + 3067.43i 0.849658 + 0.193983i
\(631\) 15717.2 + 21632.8i 0.991585 + 1.36480i 0.930349 + 0.366676i \(0.119504\pi\)
0.0612360 + 0.998123i \(0.480496\pi\)
\(632\) −2137.56 796.669i −0.134538 0.0501421i
\(633\) 2079.46 + 329.354i 0.130571 + 0.0206803i
\(634\) 807.173 + 540.630i 0.0505630 + 0.0338662i
\(635\) 18453.2 + 8234.11i 1.15322 + 0.514584i
\(636\) 8636.10 14023.0i 0.538433 0.874290i
\(637\) −2603.27 1326.43i −0.161924 0.0825042i
\(638\) −8707.43 44030.0i −0.540330 2.73223i
\(639\) −569.118 + 1751.57i −0.0352331 + 0.108436i
\(640\) 11396.9 11500.2i 0.703908 0.710291i
\(641\) 8483.60 + 26109.8i 0.522749 + 1.60886i 0.768725 + 0.639580i \(0.220892\pi\)
−0.245976 + 0.969276i \(0.579108\pi\)
\(642\) −17897.2 + 9996.86i −1.10022 + 0.614556i
\(643\) −21758.4 + 21758.4i −1.33447 + 1.33447i −0.433152 + 0.901321i \(0.642599\pi\)
−0.901321 + 0.433152i \(0.857401\pi\)
\(644\) 1835.85 755.675i 0.112334 0.0462388i
\(645\) 26656.0 1374.99i 1.62725 0.0839382i
\(646\) 8141.85 310.862i 0.495877 0.0189330i
\(647\) 1629.80 + 10290.2i 0.0990326 + 0.625267i 0.986420 + 0.164243i \(0.0525180\pi\)
−0.887387 + 0.461025i \(0.847482\pi\)
\(648\) −10434.3 + 13145.7i −0.632556 + 0.796933i
\(649\) 39346.8i 2.37981i
\(650\) −12715.5 + 6227.15i −0.767299 + 0.375767i
\(651\) 26986.3i 1.62469i
\(652\) 6578.98 + 27673.4i 0.395173 + 1.66223i
\(653\) 2118.36 + 13374.8i 0.126949 + 0.801527i 0.966202 + 0.257785i \(0.0829928\pi\)
−0.839253 + 0.543741i \(0.817007\pi\)
\(654\) −702.622 18402.5i −0.0420103 1.10030i
\(655\) 619.890 2305.87i 0.0369788 0.137554i
\(656\) 6726.90 1034.91i 0.400368 0.0615950i
\(657\) 1968.51 1968.51i 0.116893 0.116893i
\(658\) −7883.78 14114.2i −0.467085 0.836211i
\(659\) −7564.17 23280.1i −0.447130 1.37612i −0.880131 0.474730i \(-0.842546\pi\)
0.433002 0.901393i \(-0.357454\pi\)
\(660\) −15270.8 + 42710.5i −0.900628 + 2.51895i
\(661\) 1216.76 3744.81i 0.0715985 0.220358i −0.908854 0.417115i \(-0.863041\pi\)
0.980452 + 0.196758i \(0.0630412\pi\)
\(662\) 4602.89 910.274i 0.270236 0.0534423i
\(663\) −13145.2 6697.82i −0.770012 0.392341i
\(664\) 734.158 + 6384.56i 0.0429079 + 0.373146i
\(665\) −5247.44 9106.12i −0.305995 0.531008i
\(666\) 10107.9 15091.4i 0.588100 0.878047i
\(667\) −3414.44 540.795i −0.198212 0.0313938i
\(668\) −6487.26 10639.1i −0.375748 0.616225i
\(669\) 8862.94 + 12198.8i 0.512199 + 0.704981i
\(670\) 5964.19 536.424i 0.343906 0.0309311i
\(671\) 28855.0 39715.5i 1.66011 2.28495i
\(672\) −7419.00 20458.3i −0.425884 1.17440i
\(673\) 20312.0 10349.5i 1.16340 0.592783i 0.237813 0.971311i \(-0.423570\pi\)
0.925590 + 0.378528i \(0.123570\pi\)
\(674\) −14200.3 + 11169.1i −0.811535 + 0.638306i
\(675\) −112.913 424.186i −0.00643853 0.0241881i
\(676\) 1118.25 4612.82i 0.0636238 0.262450i
\(677\) −4933.13 9681.82i −0.280053 0.549634i 0.707540 0.706674i \(-0.249805\pi\)
−0.987592 + 0.157039i \(0.949805\pi\)
\(678\) 18495.0 + 17134.7i 1.04764 + 0.970579i
\(679\) −14386.6 10452.5i −0.813117 0.590764i
\(680\) −8927.36 + 9088.51i −0.503454 + 0.512542i
\(681\) −17319.4 + 12583.3i −0.974567 + 0.708064i
\(682\) 43701.0 + 5221.45i 2.45366 + 0.293167i
\(683\) 1252.87 7910.33i 0.0701901 0.443163i −0.927417 0.374028i \(-0.877976\pi\)
0.997607 0.0691345i \(-0.0220237\pi\)
\(684\) −12101.1 + 925.406i −0.676456 + 0.0517307i
\(685\) 4270.34 + 20172.0i 0.238192 + 1.12516i
\(686\) 6671.56 + 18145.9i 0.371314 + 1.00993i
\(687\) −5209.34 + 10223.9i −0.289299 + 0.567782i
\(688\) −12201.0 16950.7i −0.676104 0.939301i
\(689\) 10717.3 + 3482.27i 0.592594 + 0.192545i
\(690\) 2681.74 + 2239.15i 0.147960 + 0.123541i
\(691\) −4142.51 + 1345.98i −0.228058 + 0.0741007i −0.420817 0.907146i \(-0.638257\pi\)
0.192759 + 0.981246i \(0.438257\pi\)
\(692\) 696.531 + 290.322i 0.0382632 + 0.0159485i
\(693\) 21361.3 + 21361.3i 1.17092 + 1.17092i
\(694\) 9715.74 + 2751.74i 0.531419 + 0.150511i
\(695\) −9316.46 + 3567.46i −0.508480 + 0.194707i
\(696\) −7516.24 + 37141.3i −0.409343 + 2.02275i
\(697\) −5289.35 + 837.751i −0.287444 + 0.0455267i
\(698\) −8452.10 3907.83i −0.458334 0.211911i
\(699\) −26175.6 −1.41638
\(700\) 15738.1 + 4728.00i 0.849777 + 0.255288i
\(701\) −19123.5 −1.03036 −0.515181 0.857081i \(-0.672275\pi\)
−0.515181 + 0.857081i \(0.672275\pi\)
\(702\) −361.036 166.925i −0.0194109 0.00897461i
\(703\) −13681.5 + 2166.93i −0.734006 + 0.116255i
\(704\) 34565.2 8055.81i 1.85046 0.431271i
\(705\) 15514.4 23847.0i 0.828801 1.27395i
\(706\) −10369.4 2936.88i −0.552773 0.156559i
\(707\) −13395.3 13395.3i −0.712561 0.712561i
\(708\) 12780.8 30663.2i 0.678434 1.62768i
\(709\) 23488.0 7631.70i 1.24416 0.404252i 0.388335 0.921518i \(-0.373050\pi\)
0.855824 + 0.517266i \(0.173050\pi\)
\(710\) −817.708 + 2038.16i −0.0432226 + 0.107734i
\(711\) −2542.77 826.197i −0.134123 0.0435792i
\(712\) 19876.6 + 847.110i 1.04622 + 0.0445882i
\(713\) 1538.99 3020.45i 0.0808356 0.158649i
\(714\) 5908.85 + 16071.4i 0.309710 + 0.842378i
\(715\) −30863.7 3269.58i −1.61432 0.171014i
\(716\) 27.1419 + 354.921i 0.00141668 + 0.0185252i
\(717\) −5771.09 + 36437.2i −0.300593 + 1.89787i
\(718\) −25483.6 3044.81i −1.32457 0.158261i
\(719\) 967.403 702.859i 0.0501781 0.0364565i −0.562414 0.826856i \(-0.690127\pi\)
0.612592 + 0.790400i \(0.290127\pi\)
\(720\) 12771.4 14035.1i 0.661060 0.726470i
\(721\) −9332.24 6780.27i −0.482040 0.350223i
\(722\) −7441.86 6894.49i −0.383598 0.355383i
\(723\) −22063.8 43302.7i −1.13494 2.22745i
\(724\) −35726.9 8661.02i −1.83395 0.444592i
\(725\) −19112.0 21296.4i −0.979035 1.09093i
\(726\) −56504.0 + 44442.8i −2.88851 + 2.27194i
\(727\) 32438.5 16528.2i 1.65485 0.843189i 0.659006 0.752138i \(-0.270977\pi\)
0.995846 0.0910518i \(-0.0290229\pi\)
\(728\) 12408.5 8231.57i 0.631715 0.419069i
\(729\) −11154.4 + 15352.7i −0.566703 + 0.780000i
\(730\) 2499.99 2183.91i 0.126752 0.110726i
\(731\) 9659.28 + 13294.9i 0.488730 + 0.672679i
\(732\) −35387.4 + 21577.8i −1.78683 + 1.08953i
\(733\) 5735.36 + 908.392i 0.289005 + 0.0457739i 0.299254 0.954174i \(-0.403262\pi\)
−0.0102488 + 0.999947i \(0.503262\pi\)
\(734\) 3192.81 4766.94i 0.160557 0.239715i
\(735\) −3996.66 + 4431.41i −0.200570 + 0.222388i
\(736\) 336.337 2712.90i 0.0168445 0.135868i
\(737\) 11696.0 + 5959.40i 0.584569 + 0.297853i
\(738\) 7825.33 1547.55i 0.390318 0.0771897i
\(739\) −4050.25 + 12465.4i −0.201611 + 0.620496i 0.798224 + 0.602360i \(0.205773\pi\)
−0.999836 + 0.0181355i \(0.994227\pi\)
\(740\) 13237.1 17142.8i 0.657574 0.851598i
\(741\) −5178.79 15938.7i −0.256744 0.790178i
\(742\) −6378.09 11418.6i −0.315562 0.564944i
\(743\) 17314.9 17314.9i 0.854944 0.854944i −0.135793 0.990737i \(-0.543358\pi\)
0.990737 + 0.135793i \(0.0433583\pi\)
\(744\) −32360.5 18264.3i −1.59461 0.900000i
\(745\) −12890.2 + 10420.7i −0.633905 + 0.512463i
\(746\) 985.439 + 25809.8i 0.0483639 + 1.26671i
\(747\) 1178.29 + 7439.46i 0.0577129 + 0.364385i
\(748\) −27169.0 + 6459.08i −1.32807 + 0.315732i
\(749\) 16280.3i 0.794220i
\(750\) 5540.16 + 28382.3i 0.269731 + 1.38183i
\(751\) 2900.20i 0.140918i 0.997515 + 0.0704592i \(0.0224465\pi\)
−0.997515 + 0.0704592i \(0.977554\pi\)
\(752\) −22260.7 98.6260i −1.07947 0.00478261i
\(753\) −5194.91 32799.4i −0.251412 1.58735i
\(754\) −25910.1 + 989.269i −1.25145 + 0.0477812i
\(755\) −12726.9 + 10288.7i −0.613485 + 0.495955i
\(756\) 175.722 + 426.903i 0.00845365 + 0.0205375i
\(757\) 8951.58 8951.58i 0.429790 0.429790i −0.458767 0.888557i \(-0.651709\pi\)
0.888557 + 0.458767i \(0.151709\pi\)
\(758\) 4331.59 2419.51i 0.207560 0.115937i
\(759\) 2366.55 + 7283.49i 0.113176 + 0.348319i
\(760\) −14471.0 + 129.438i −0.690683 + 0.00617789i
\(761\) 6848.37 21077.1i 0.326220 1.00400i −0.644667 0.764463i \(-0.723004\pi\)
0.970887 0.239538i \(-0.0769959\pi\)
\(762\) −7255.38 36687.6i −0.344927 1.74416i
\(763\) −13031.2 6639.75i −0.618300 0.315040i
\(764\) −18227.5 11225.4i −0.863150 0.531573i
\(765\) −10000.1 + 11087.9i −0.472619 + 0.524029i
\(766\) 6587.75 + 4412.36i 0.310738 + 0.208127i
\(767\) 22451.0 + 3555.89i 1.05692 + 0.167400i
\(768\) −29553.6 4949.66i −1.38857 0.232559i
\(769\) −6487.63 8929.46i −0.304226 0.418731i 0.629344 0.777127i \(-0.283324\pi\)
−0.933570 + 0.358396i \(0.883324\pi\)
\(770\) 23698.8 + 27128.7i 1.10915 + 1.26968i
\(771\) 14028.5 19308.5i 0.655283 0.901919i
\(772\) 2154.16 26617.2i 0.100427 1.24090i
\(773\) −4476.25 + 2280.76i −0.208279 + 0.106123i −0.555018 0.831838i \(-0.687289\pi\)
0.346740 + 0.937961i \(0.387289\pi\)
\(774\) −15132.9 19239.8i −0.702766 0.893488i
\(775\) 25652.4 11370.6i 1.18898 0.527026i
\(776\) −22270.8 + 10177.4i −1.03025 + 0.470809i
\(777\) −13216.2 25938.2i −0.610203 1.19759i
\(778\) −11940.1 + 12888.1i −0.550224 + 0.593907i
\(779\) −4921.52 3575.69i −0.226357 0.164458i
\(780\) 22990.2 + 12573.3i 1.05536 + 0.577173i
\(781\) −3894.57 + 2829.57i −0.178436 + 0.129642i
\(782\) −255.184 + 2135.77i −0.0116693 + 0.0976664i
\(783\) 125.755 793.983i 0.00573959 0.0362384i
\(784\) 4608.59 + 750.874i 0.209939 + 0.0342053i
\(785\) 28477.7 + 3016.82i 1.29479 + 0.137165i
\(786\) −4147.67 + 1524.94i −0.188222 + 0.0692020i
\(787\) −2535.21 + 4975.64i −0.114829 + 0.225365i −0.941267 0.337663i \(-0.890364\pi\)
0.826438 + 0.563028i \(0.190364\pi\)
\(788\) 22234.7 + 19075.5i 1.00517 + 0.862358i
\(789\) 27983.5 + 9092.40i 1.26266 + 0.410264i
\(790\) −2958.83 1187.08i −0.133254 0.0534612i
\(791\) 19042.8 6187.39i 0.855986 0.278127i
\(792\) 40072.7 11158.0i 1.79788 0.500611i
\(793\) −20053.6 20053.6i −0.898014 0.898014i
\(794\) −444.406 + 1569.09i −0.0198632 + 0.0701321i
\(795\) 12551.3 19292.6i 0.559937 0.860676i
\(796\) −7730.21 9091.62i −0.344209 0.404829i
\(797\) 26980.3 4273.26i 1.19911 0.189920i 0.475239 0.879856i \(-0.342361\pi\)
0.723870 + 0.689936i \(0.242361\pi\)
\(798\) −8162.96 + 17655.4i −0.362112 + 0.783200i
\(799\) 17515.8 0.775550
\(800\) 16321.1 15672.4i 0.721296 0.692627i
\(801\) 23317.1 1.02855
\(802\) −12355.0 + 26722.2i −0.543979 + 1.17655i
\(803\) 7187.12 1138.33i 0.315850 0.0500258i
\(804\) −7179.01 8443.34i −0.314905 0.370365i
\(805\) 2591.07 992.174i 0.113445 0.0434404i
\(806\) 6928.71 24463.6i 0.302796 1.06910i
\(807\) −12853.3 12853.3i −0.560667 0.560667i
\(808\) −25128.8 + 6996.99i −1.09409 + 0.304645i
\(809\) 15808.8 5136.59i 0.687030 0.223230i 0.0553594 0.998466i \(-0.482370\pi\)
0.631671 + 0.775237i \(0.282370\pi\)
\(810\) −15033.2 + 18004.6i −0.652114 + 0.781010i
\(811\) 17209.7 + 5591.79i 0.745149 + 0.242114i 0.656893 0.753984i \(-0.271870\pi\)
0.0882565 + 0.996098i \(0.471870\pi\)
\(812\) 22840.5 + 19595.3i 0.987126 + 0.846874i
\(813\) 9581.37 18804.5i 0.413325 0.811196i
\(814\) 44561.0 16383.4i 1.91875 0.705450i
\(815\) 8233.03 + 38890.7i 0.353854 + 1.67151i
\(816\) 23271.1 + 3791.54i 0.998346 + 0.162660i
\(817\) −2920.23 + 18437.6i −0.125050 + 0.789536i
\(818\) −432.348 + 3618.55i −0.0184801 + 0.154669i
\(819\) 14119.1 10258.1i 0.602395 0.437666i
\(820\) 9434.09 1212.88i 0.401772 0.0516530i
\(821\) 34052.0 + 24740.2i 1.44753 + 1.05169i 0.986400 + 0.164362i \(0.0525566\pi\)
0.461132 + 0.887332i \(0.347443\pi\)
\(822\) 25934.5 27993.5i 1.10045 1.18782i
\(823\) −9370.08 18389.8i −0.396866 0.778892i 0.602956 0.797774i \(-0.293989\pi\)
−0.999822 + 0.0188818i \(0.993989\pi\)
\(824\) −14446.6 + 6601.85i −0.610765 + 0.279109i
\(825\) −22814.4 + 59142.5i −0.962783 + 2.49585i
\(826\) −16310.2 20736.6i −0.687052 0.873510i
\(827\) −30518.4 + 15549.9i −1.28323 + 0.653836i −0.956624 0.291326i \(-0.905904\pi\)
−0.326602 + 0.945162i \(0.605904\pi\)
\(828\) 258.453 3193.49i 0.0108477 0.134036i
\(829\) 3094.43 4259.12i 0.129643 0.178438i −0.739261 0.673419i \(-0.764825\pi\)
0.868904 + 0.494981i \(0.164825\pi\)
\(830\) 804.554 + 8945.38i 0.0336464 + 0.374095i
\(831\) −16254.6 22372.6i −0.678540 0.933931i
\(832\) −1472.82 20450.7i −0.0613713 0.852163i
\(833\) −3628.81 574.748i −0.150938 0.0239062i
\(834\) 15340.3 + 10274.7i 0.636921 + 0.426598i
\(835\) −8694.92 15088.7i −0.360359 0.625348i
\(836\) −27011.4 16635.0i −1.11747 0.688198i
\(837\) 702.365 + 357.873i 0.0290051 + 0.0147788i
\(838\) 6764.43 + 34205.0i 0.278846 + 1.41002i
\(839\) −1439.44 + 4430.14i −0.0592312 + 0.182295i −0.976294 0.216447i \(-0.930553\pi\)
0.917063 + 0.398742i \(0.130553\pi\)
\(840\) −9656.55 28839.5i −0.396646 1.18459i
\(841\) −8656.90 26643.2i −0.354951 1.09243i
\(842\) 2083.73 1163.91i 0.0852850 0.0476379i
\(843\) 4309.39 4309.39i 0.176066 0.176066i
\(844\) −876.340 2129.00i −0.0357403 0.0868284i
\(845\) 1722.10 6405.89i 0.0701091 0.260792i
\(846\) −26071.4 + 995.427i −1.05952 + 0.0404533i
\(847\) 8931.00 + 56388.1i 0.362306 + 2.28751i
\(848\) −18009.2 79.7898i −0.729290 0.00323112i
\(849\) 8819.68i 0.356526i
\(850\) −12787.3 + 12388.5i −0.516003 + 0.499906i
\(851\) 3656.85i 0.147303i
\(852\) 3954.18 940.055i 0.159000 0.0378002i
\(853\) 614.798 + 3881.68i 0.0246779 + 0.155810i 0.996950 0.0780419i \(-0.0248668\pi\)
−0.972272 + 0.233852i \(0.924867\pi\)
\(854\) 1255.84 + 32892.0i 0.0503210 + 1.31797i
\(855\) −16938.6 + 873.741i −0.677530 + 0.0349489i
\(856\) 19522.5 + 11018.5i 0.779516 + 0.439959i
\(857\) −13421.5 + 13421.5i −0.534969 + 0.534969i −0.922047 0.387078i \(-0.873484\pi\)
0.387078 + 0.922047i \(0.373484\pi\)
\(858\) 28011.2 + 50147.8i 1.11455 + 1.99536i
\(859\) 2941.95 + 9054.40i 0.116855 + 0.359641i 0.992329 0.123622i \(-0.0394512\pi\)
−0.875475 + 0.483264i \(0.839451\pi\)
\(860\) −16459.1 24104.6i −0.652616 0.955769i
\(861\) 3950.67 12158.9i 0.156374 0.481271i
\(862\) −6088.87 + 1204.14i −0.240589 + 0.0475791i
\(863\) 17931.3 + 9136.46i 0.707287 + 0.360381i 0.770343 0.637629i \(-0.220085\pi\)
−0.0630563 + 0.998010i \(0.520085\pi\)
\(864\) 630.848 + 78.2108i 0.0248401 + 0.00307961i
\(865\) 963.077 + 429.739i 0.0378562 + 0.0168920i
\(866\) 13402.1 20009.7i 0.525892 0.785169i
\(867\) 17176.0 + 2720.41i 0.672811 + 0.106563i
\(868\) −25195.8 + 15363.4i −0.985256 + 0.600768i
\(869\) −4107.73 5653.80i −0.160351 0.220704i
\(870\) −11787.5 + 51630.2i −0.459351 + 2.01199i
\(871\) 4457.39 6135.07i 0.173402 0.238667i
\(872\) −16781.6 + 11132.6i −0.651715 + 0.432336i
\(873\) −25570.5 + 13028.8i −0.991329 + 0.505107i
\(874\) −1920.51 + 1510.56i −0.0743273 + 0.0584616i
\(875\) 21824.1 + 7150.69i 0.843188 + 0.276271i
\(876\) −5970.73 1447.44i −0.230288 0.0558270i
\(877\) −5694.21 11175.5i −0.219247 0.430297i 0.755017 0.655705i \(-0.227628\pi\)
−0.974264 + 0.225408i \(0.927628\pi\)
\(878\) 19373.7 + 17948.7i 0.744682 + 0.689908i
\(879\) 11199.1 + 8136.63i 0.429734 + 0.312220i
\(880\) 48570.6 10057.6i 1.86058 0.385275i
\(881\) −10169.4 + 7388.49i −0.388893 + 0.282548i −0.765002 0.644028i \(-0.777262\pi\)
0.376108 + 0.926576i \(0.377262\pi\)
\(882\) 5433.97 + 649.257i 0.207451 + 0.0247864i
\(883\) −924.104 + 5834.57i −0.0352192 + 0.222366i −0.999020 0.0442574i \(-0.985908\pi\)
0.963801 + 0.266623i \(0.0859078\pi\)
\(884\) 1230.16 + 16086.2i 0.0468040 + 0.612032i
\(885\) 18918.3 42397.3i 0.718567 1.61036i
\(886\) −3004.68 8172.41i −0.113933 0.309884i
\(887\) 10567.4 20739.7i 0.400022 0.785087i −0.599866 0.800101i \(-0.704779\pi\)
0.999887 + 0.0150140i \(0.00477928\pi\)
\(888\) −40048.4 1706.80i −1.51344 0.0645007i
\(889\) −28246.7 9177.92i −1.06565 0.346251i
\(890\) 27740.5 + 1871.99i 1.04479 + 0.0705049i
\(891\) −48899.8 + 15888.5i −1.83861 + 0.597402i
\(892\) 6343.75 15219.7i 0.238122 0.571294i
\(893\) 14069.3 + 14069.3i 0.527226 + 0.527226i
\(894\) 29516.1 + 8359.71i 1.10421 + 0.312741i
\(895\) 25.6266 + 496.805i 0.000957099 + 0.0185546i
\(896\) −14877.3 + 18573.7i −0.554705 + 0.692528i
\(897\) 4369.78 692.105i 0.162656 0.0257622i
\(898\) 33830.5 + 15641.5i 1.25717 + 0.581252i
\(899\) 51386.5 1.90638
\(900\) 18329.3 19166.3i 0.678862 0.709863i
\(901\) 14170.5 0.523961
\(902\) 18925.5 + 8750.20i 0.698614 + 0.323004i
\(903\) −38748.2 + 6137.11i −1.42797 + 0.226169i
\(904\) 5468.57 27022.7i 0.201197 0.994207i
\(905\) −49614.5 13337.9i −1.82237 0.489909i
\(906\) 29142.4 + 8253.86i 1.06864 + 0.302667i
\(907\) 15075.8 + 15075.8i 0.551912 + 0.551912i 0.926992 0.375080i \(-0.122385\pi\)
−0.375080 + 0.926992i \(0.622385\pi\)
\(908\) 21608.4 + 9006.62i 0.789757 + 0.329180i
\(909\) −29075.7 + 9447.28i −1.06093 + 0.344716i
\(910\) 17621.2 11070.6i 0.641908 0.403283i
\(911\) −4767.83 1549.16i −0.173398 0.0563403i 0.221032 0.975267i \(-0.429058\pi\)
−0.394429 + 0.918926i \(0.629058\pi\)
\(912\) 15646.7 + 21737.7i 0.568107 + 0.789262i
\(913\) −8938.20 + 17542.2i −0.323999 + 0.635884i
\(914\) 866.038 + 2355.53i 0.0313414 + 0.0852451i
\(915\) −50187.6 + 28920.8i −1.81328 + 1.04491i
\(916\) 12511.3 956.776i 0.451293 0.0345118i
\(917\) −549.009 + 3466.31i −0.0197709 + 0.124828i
\(918\) −496.646 59.3398i −0.0178559 0.00213345i
\(919\) 14773.0 10733.2i 0.530269 0.385263i −0.290189 0.956969i \(-0.593718\pi\)
0.820459 + 0.571706i \(0.193718\pi\)
\(920\) 563.870 3778.57i 0.0202068 0.135409i
\(921\) 47173.4 + 34273.5i 1.68775 + 1.22622i
\(922\) −19083.1 17679.5i −0.681637 0.631500i
\(923\) 1262.57 + 2477.93i 0.0450249 + 0.0883663i
\(924\) 15706.9 64791.4i 0.559221 2.30680i
\(925\) 19087.5 23492.0i 0.678479 0.835039i
\(926\) −24668.4 + 19402.7i −0.875437 + 0.688568i
\(927\) −16587.0 + 8451.49i −0.587689 + 0.299443i
\(928\) 38956.1 14127.1i 1.37801 0.499723i
\(929\) −9507.97 + 13086.6i −0.335787 + 0.462172i −0.943205 0.332211i \(-0.892205\pi\)
0.607418 + 0.794383i \(0.292205\pi\)
\(930\) −44578.6 26638.1i −1.57182 0.939246i
\(931\) −2453.14 3376.46i −0.0863571 0.118860i
\(932\) 14901.8 + 24438.9i 0.523739 + 0.858930i
\(933\) 41021.4 + 6497.16i 1.43942 + 0.227982i
\(934\) 15775.2 23552.8i 0.552657 0.825129i
\(935\) −38181.9 + 8082.99i −1.33549 + 0.282719i
\(936\) −2745.21 23873.5i −0.0958655 0.833687i
\(937\) −20637.7 10515.4i −0.719534 0.366621i 0.0555699 0.998455i \(-0.482302\pi\)
−0.775104 + 0.631834i \(0.782302\pi\)
\(938\) −8634.36 + 1707.54i −0.300556 + 0.0594384i
\(939\) 1123.16 3456.73i 0.0390340 0.120134i
\(940\) −31097.2 908.855i −1.07902 0.0315357i
\(941\) 11795.7 + 36303.5i 0.408639 + 1.25766i 0.917818 + 0.397001i \(0.129949\pi\)
−0.509180 + 0.860660i \(0.670051\pi\)
\(942\) −25845.7 46271.0i −0.893948 1.60042i
\(943\) 1135.59 1135.59i 0.0392151 0.0392151i
\(944\) −35905.0 + 5523.83i −1.23793 + 0.190451i
\(945\) 230.717 + 602.519i 0.00794203 + 0.0207407i
\(946\) −2441.11 63935.5i −0.0838978 2.19738i
\(947\) −6734.36 42519.1i −0.231085 1.45901i −0.781387 0.624047i \(-0.785487\pi\)
0.550302 0.834966i \(-0.314513\pi\)
\(948\) 1364.69 + 5740.34i 0.0467543 + 0.196664i
\(949\) 4203.79i 0.143794i
\(950\) −20222.1 320.407i −0.690624 0.0109425i
\(951\) 2512.78i 0.0856809i
\(952\) 11641.2 14666.3i 0.396317 0.499305i
\(953\) −3264.45 20610.9i −0.110961 0.700580i −0.978966 0.204024i \(-0.934598\pi\)
0.868005 0.496556i \(-0.165402\pi\)
\(954\) −21092.1 + 805.315i −0.715810 + 0.0273302i
\(955\) −25077.0 16314.6i −0.849710 0.552803i
\(956\) 37305.3 15355.6i 1.26207 0.519494i
\(957\) −82087.6 + 82087.6i −2.77274 + 2.77274i
\(958\) 29722.9 16602.4i 1.00240 0.559916i
\(959\) −9365.06 28822.7i −0.315343 0.970525i
\(960\) −41118.3 7938.92i −1.38238 0.266904i
\(961\) −6365.27 + 19590.3i −0.213664 + 0.657591i
\(962\) −5321.12 26906.8i −0.178336 0.901777i
\(963\) 23410.1 + 11928.0i 0.783363 + 0.399143i
\(964\) −27868.7 + 45252.3i −0.931111 + 1.51191i
\(965\) 3931.57 37112.7i 0.131152 1.23803i
\(966\) −4266.42 2857.57i −0.142101 0.0951767i
\(967\) −25909.2 4103.61i −0.861617 0.136467i −0.290039 0.957015i \(-0.593668\pi\)
−0.571578 + 0.820548i \(0.693668\pi\)
\(968\) 73662.1 + 27453.8i 2.44586 + 0.911569i
\(969\) −12387.1 17049.4i −0.410663 0.565229i
\(970\) −31467.4 + 13447.6i −1.04161 + 0.445129i
\(971\) −18145.6 + 24975.3i −0.599711 + 0.825432i −0.995682 0.0928313i \(-0.970408\pi\)
0.395970 + 0.918263i \(0.370408\pi\)
\(972\) 42512.9 + 3440.61i 1.40288 + 0.113537i
\(973\) 13064.8 6656.85i 0.430461 0.219331i
\(974\) 8070.33 + 10260.5i 0.265493 + 0.337544i
\(975\) 31684.5 + 18362.6i 1.04073 + 0.603153i
\(976\) 40292.3 + 20755.3i 1.32144 + 0.680698i
\(977\) −13162.6 25833.1i −0.431022 0.845929i −0.999726 0.0233870i \(-0.992555\pi\)
0.568704 0.822542i \(-0.307445\pi\)
\(978\) 50000.6 53970.3i 1.63481 1.76460i
\(979\) 49307.5 + 35824.0i 1.60968 + 1.16950i
\(980\) 6412.71 + 1208.69i 0.209027 + 0.0393981i
\(981\) −19095.1 + 13873.4i −0.621466 + 0.451522i
\(982\) 6384.14 53432.2i 0.207460 1.73634i
\(983\) −9191.31 + 58031.7i −0.298227 + 1.88293i 0.149499 + 0.988762i \(0.452234\pi\)
−0.447726 + 0.894171i \(0.647766\pi\)
\(984\) −11906.5 12966.5i −0.385737 0.420080i
\(985\) 30403.6 + 27420.9i 0.983492 + 0.887006i
\(986\) −30602.8 + 11251.5i −0.988429 + 0.363407i
\(987\) −18983.8 + 37257.7i −0.612219 + 1.20155i
\(988\) −11932.9 + 13909.1i −0.384247 + 0.447883i
\(989\) −4686.89 1522.86i −0.150692 0.0489628i
\(990\) 56372.5 14201.0i 1.80973 0.455897i
\(991\) −8302.54 + 2697.66i −0.266134 + 0.0864723i −0.439044 0.898465i \(-0.644683\pi\)
0.172910 + 0.984938i \(0.444683\pi\)
\(992\) 1370.42 + 40611.4i 0.0438616 + 1.29981i
\(993\) −8581.43 8581.43i −0.274243 0.274243i
\(994\) 879.597 3105.64i 0.0280675 0.0990997i
\(995\) −10485.1 12969.8i −0.334069 0.413236i
\(996\) 12663.7 10767.4i 0.402877 0.342549i
\(997\) −8382.23 + 1327.62i −0.266267 + 0.0421725i −0.288140 0.957588i \(-0.593037\pi\)
0.0218734 + 0.999761i \(0.493037\pi\)
\(998\) 15747.2 34059.0i 0.499467 1.08028i
\(999\) 850.351 0.0269308
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 100.4.l.b.3.17 336
4.3 odd 2 inner 100.4.l.b.3.39 yes 336
25.17 odd 20 inner 100.4.l.b.67.39 yes 336
100.67 even 20 inner 100.4.l.b.67.17 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
100.4.l.b.3.17 336 1.1 even 1 trivial
100.4.l.b.3.39 yes 336 4.3 odd 2 inner
100.4.l.b.67.17 yes 336 100.67 even 20 inner
100.4.l.b.67.39 yes 336 25.17 odd 20 inner