Properties

Label 75.3.j.a.11.9
Level $75$
Weight $3$
Character 75.11
Analytic conductor $2.044$
Analytic rank $0$
Dimension $72$
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] = [75,3,Mod(11,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 11.9
Character \(\chi\) \(=\) 75.11
Dual form 75.3.j.a.41.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0749426 - 0.103150i) q^{2} +(1.19040 + 2.75372i) q^{3} +(1.23104 - 3.78877i) q^{4} +(-0.601131 + 4.96373i) q^{5} +(0.194834 - 0.329160i) q^{6} +8.18661 q^{7} +(-0.968106 + 0.314557i) q^{8} +(-6.16592 + 6.55603i) q^{9} +O(q^{10})\) \(q+(-0.0749426 - 0.103150i) q^{2} +(1.19040 + 2.75372i) q^{3} +(1.23104 - 3.78877i) q^{4} +(-0.601131 + 4.96373i) q^{5} +(0.194834 - 0.329160i) q^{6} +8.18661 q^{7} +(-0.968106 + 0.314557i) q^{8} +(-6.16592 + 6.55603i) q^{9} +(0.557058 - 0.309989i) q^{10} +(0.588883 + 0.810528i) q^{11} +(11.8986 - 1.12018i) q^{12} +(0.562554 + 0.408719i) q^{13} +(-0.613526 - 0.844446i) q^{14} +(-14.3843 + 4.25346i) q^{15} +(-12.7867 - 9.29006i) q^{16} +(11.4316 - 3.71436i) q^{17} +(1.13834 + 0.144686i) q^{18} +(-5.30271 - 16.3201i) q^{19} +(18.0664 + 8.38812i) q^{20} +(9.74530 + 22.5436i) q^{21} +(0.0394733 - 0.121486i) q^{22} +(-23.8282 - 32.7967i) q^{23} +(-2.01863 - 2.29144i) q^{24} +(-24.2773 - 5.96771i) q^{25} -0.0886577i q^{26} +(-25.3933 - 9.17492i) q^{27} +(10.0781 - 31.0171i) q^{28} +(-31.6359 - 10.2791i) q^{29} +(1.51674 + 1.16497i) q^{30} +(13.1968 + 40.6157i) q^{31} +6.08687i q^{32} +(-1.53096 + 2.58647i) q^{33} +(-1.23985 - 0.900805i) q^{34} +(-4.92122 + 40.6361i) q^{35} +(17.2487 + 31.4320i) q^{36} +(0.0259649 + 0.0188646i) q^{37} +(-1.28601 + 1.77004i) q^{38} +(-0.455836 + 2.03565i) q^{39} +(-0.979417 - 4.99451i) q^{40} +(25.8764 - 35.6159i) q^{41} +(1.59503 - 2.69470i) q^{42} +45.0376 q^{43} +(3.79584 - 1.23334i) q^{44} +(-28.8358 - 34.5470i) q^{45} +(-1.59722 + 4.91575i) q^{46} +(34.8458 + 11.3221i) q^{47} +(10.3610 - 46.2697i) q^{48} +18.0206 q^{49} +(1.20384 + 2.95143i) q^{50} +(23.8365 + 27.0579i) q^{51} +(2.24107 - 1.62823i) q^{52} +(39.7404 + 12.9124i) q^{53} +(0.956652 + 3.30690i) q^{54} +(-4.37724 + 2.43583i) q^{55} +(-7.92551 + 2.57515i) q^{56} +(38.6285 - 34.0295i) q^{57} +(1.31059 + 4.03357i) q^{58} +(-67.5093 + 92.9186i) q^{59} +(-1.59234 + 59.7349i) q^{60} +(24.5809 - 17.8591i) q^{61} +(3.20049 - 4.40509i) q^{62} +(-50.4779 + 53.6716i) q^{63} +(-50.5188 + 36.7041i) q^{64} +(-2.36694 + 2.54667i) q^{65} +(0.381528 - 0.0359185i) q^{66} +(22.6392 + 69.6762i) q^{67} -47.8843i q^{68} +(61.9479 - 104.657i) q^{69} +(4.56041 - 2.53776i) q^{70} +(-60.4809 - 19.6514i) q^{71} +(3.90702 - 8.28646i) q^{72} +(-86.8989 + 63.1357i) q^{73} -0.00409204i q^{74} +(-12.4662 - 73.9567i) q^{75} -68.3608 q^{76} +(4.82096 + 6.63548i) q^{77} +(0.244138 - 0.105538i) q^{78} +(7.80969 - 24.0358i) q^{79} +(53.7998 - 57.8851i) q^{80} +(-4.96298 - 80.8478i) q^{81} -5.61301 q^{82} +(98.8345 - 32.1133i) q^{83} +(97.4093 - 9.17050i) q^{84} +(11.5652 + 58.9764i) q^{85} +(-3.37523 - 4.64561i) q^{86} +(-9.35343 - 99.3525i) q^{87} +(-0.825059 - 0.599440i) q^{88} +(-44.0718 - 60.6596i) q^{89} +(-1.40248 + 5.56345i) q^{90} +(4.60541 + 3.34602i) q^{91} +(-153.593 + 49.9053i) q^{92} +(-96.1346 + 84.6891i) q^{93} +(-1.44357 - 4.44284i) q^{94} +(84.1961 - 16.5108i) q^{95} +(-16.7615 + 7.24579i) q^{96} +(25.4731 - 78.3983i) q^{97} +(-1.35051 - 1.85881i) q^{98} +(-8.94485 - 1.13691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9} - 20 q^{10} + 31 q^{12} - 42 q^{13} + 45 q^{15} - 130 q^{16} + 30 q^{18} - 36 q^{19} - 60 q^{21} - 70 q^{22} - 72 q^{24} + 100 q^{25} - 154 q^{27} - 62 q^{28} + 15 q^{30} + 114 q^{31} - 10 q^{33} + 178 q^{34} + 271 q^{36} - 98 q^{37} - 155 q^{39} - 120 q^{40} - 475 q^{42} - 52 q^{43} + 35 q^{45} + 198 q^{46} - 326 q^{48} + 112 q^{49} + 44 q^{51} + 412 q^{52} + 304 q^{54} + 10 q^{55} + 622 q^{57} + 190 q^{58} + 360 q^{60} - 306 q^{61} + 293 q^{63} + 474 q^{64} + 320 q^{66} + 472 q^{67} + 269 q^{69} - 840 q^{70} + 175 q^{72} + 318 q^{73} - 310 q^{75} + 112 q^{76} + 815 q^{78} - 346 q^{79} - 373 q^{81} - 1620 q^{82} - 730 q^{84} - 530 q^{85} - 370 q^{87} - 810 q^{88} - 230 q^{90} - 550 q^{91} - 272 q^{93} - 612 q^{94} - 698 q^{96} + 182 q^{97} - 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0749426 0.103150i −0.0374713 0.0515748i 0.789870 0.613274i \(-0.210148\pi\)
−0.827342 + 0.561699i \(0.810148\pi\)
\(3\) 1.19040 + 2.75372i 0.396799 + 0.917906i
\(4\) 1.23104 3.78877i 0.307761 0.947191i
\(5\) −0.601131 + 4.96373i −0.120226 + 0.992747i
\(6\) 0.194834 0.329160i 0.0324723 0.0548599i
\(7\) 8.18661 1.16952 0.584758 0.811208i \(-0.301190\pi\)
0.584758 + 0.811208i \(0.301190\pi\)
\(8\) −0.968106 + 0.314557i −0.121013 + 0.0393196i
\(9\) −6.16592 + 6.55603i −0.685102 + 0.728447i
\(10\) 0.557058 0.309989i 0.0557058 0.0309989i
\(11\) 0.588883 + 0.810528i 0.0535349 + 0.0736844i 0.834945 0.550333i \(-0.185499\pi\)
−0.781410 + 0.624018i \(0.785499\pi\)
\(12\) 11.8986 1.12018i 0.991552 0.0933485i
\(13\) 0.562554 + 0.408719i 0.0432734 + 0.0314399i 0.609212 0.793008i \(-0.291486\pi\)
−0.565938 + 0.824448i \(0.691486\pi\)
\(14\) −0.613526 0.844446i −0.0438233 0.0603176i
\(15\) −14.3843 + 4.25346i −0.958953 + 0.283564i
\(16\) −12.7867 9.29006i −0.799167 0.580629i
\(17\) 11.4316 3.71436i 0.672449 0.218492i 0.0471627 0.998887i \(-0.484982\pi\)
0.625287 + 0.780395i \(0.284982\pi\)
\(18\) 1.13834 + 0.144686i 0.0632412 + 0.00803812i
\(19\) −5.30271 16.3201i −0.279090 0.858952i −0.988108 0.153761i \(-0.950861\pi\)
0.709018 0.705191i \(-0.249139\pi\)
\(20\) 18.0664 + 8.38812i 0.903320 + 0.419406i
\(21\) 9.74530 + 22.5436i 0.464062 + 1.07350i
\(22\) 0.0394733 0.121486i 0.00179424 0.00552210i
\(23\) −23.8282 32.7967i −1.03601 1.42595i −0.900338 0.435191i \(-0.856681\pi\)
−0.135672 0.990754i \(-0.543319\pi\)
\(24\) −2.01863 2.29144i −0.0841096 0.0954768i
\(25\) −24.2773 5.96771i −0.971091 0.238708i
\(26\) 0.0886577i 0.00340991i
\(27\) −25.3933 9.17492i −0.940493 0.339812i
\(28\) 10.0781 31.0171i 0.359931 1.10775i
\(29\) −31.6359 10.2791i −1.09089 0.354452i −0.292301 0.956326i \(-0.594421\pi\)
−0.798591 + 0.601874i \(0.794421\pi\)
\(30\) 1.51674 + 1.16497i 0.0505580 + 0.0388323i
\(31\) 13.1968 + 40.6157i 0.425704 + 1.31018i 0.902318 + 0.431071i \(0.141864\pi\)
−0.476614 + 0.879113i \(0.658136\pi\)
\(32\) 6.08687i 0.190215i
\(33\) −1.53096 + 2.58647i −0.0463928 + 0.0783778i
\(34\) −1.23985 0.900805i −0.0364662 0.0264943i
\(35\) −4.92122 + 40.6361i −0.140606 + 1.16103i
\(36\) 17.2487 + 31.4320i 0.479131 + 0.873110i
\(37\) 0.0259649 + 0.0188646i 0.000701755 + 0.000509855i 0.588136 0.808762i \(-0.299862\pi\)
−0.587434 + 0.809272i \(0.699862\pi\)
\(38\) −1.28601 + 1.77004i −0.0338424 + 0.0465801i
\(39\) −0.455836 + 2.03565i −0.0116881 + 0.0521962i
\(40\) −0.979417 4.99451i −0.0244854 0.124863i
\(41\) 25.8764 35.6159i 0.631133 0.868680i −0.366971 0.930232i \(-0.619605\pi\)
0.998104 + 0.0615527i \(0.0196052\pi\)
\(42\) 1.59503 2.69470i 0.0379768 0.0641596i
\(43\) 45.0376 1.04739 0.523693 0.851907i \(-0.324554\pi\)
0.523693 + 0.851907i \(0.324554\pi\)
\(44\) 3.79584 1.23334i 0.0862692 0.0280306i
\(45\) −28.8358 34.5470i −0.640797 0.767711i
\(46\) −1.59722 + 4.91575i −0.0347222 + 0.106864i
\(47\) 34.8458 + 11.3221i 0.741401 + 0.240896i 0.655277 0.755389i \(-0.272552\pi\)
0.0861239 + 0.996284i \(0.472552\pi\)
\(48\) 10.3610 46.2697i 0.215854 0.963952i
\(49\) 18.0206 0.367766
\(50\) 1.20384 + 2.95143i 0.0240767 + 0.0590286i
\(51\) 23.8365 + 27.0579i 0.467382 + 0.530548i
\(52\) 2.24107 1.62823i 0.0430975 0.0313122i
\(53\) 39.7404 + 12.9124i 0.749819 + 0.243631i 0.658903 0.752228i \(-0.271021\pi\)
0.0909156 + 0.995859i \(0.471021\pi\)
\(54\) 0.956652 + 3.30690i 0.0177158 + 0.0612390i
\(55\) −4.37724 + 2.43583i −0.0795862 + 0.0442877i
\(56\) −7.92551 + 2.57515i −0.141527 + 0.0459849i
\(57\) 38.6285 34.0295i 0.677694 0.597009i
\(58\) 1.31059 + 4.03357i 0.0225963 + 0.0695444i
\(59\) −67.5093 + 92.9186i −1.14423 + 1.57489i −0.386538 + 0.922273i \(0.626329\pi\)
−0.757687 + 0.652618i \(0.773671\pi\)
\(60\) −1.59234 + 59.7349i −0.0265390 + 0.995582i
\(61\) 24.5809 17.8591i 0.402966 0.292772i −0.367782 0.929912i \(-0.619883\pi\)
0.770748 + 0.637140i \(0.219883\pi\)
\(62\) 3.20049 4.40509i 0.0516208 0.0710499i
\(63\) −50.4779 + 53.6716i −0.801237 + 0.851931i
\(64\) −50.5188 + 36.7041i −0.789356 + 0.573501i
\(65\) −2.36694 + 2.54667i −0.0364145 + 0.0391796i
\(66\) 0.381528 0.0359185i 0.00578072 0.000544220i
\(67\) 22.6392 + 69.6762i 0.337898 + 1.03994i 0.965277 + 0.261229i \(0.0841279\pi\)
−0.627378 + 0.778715i \(0.715872\pi\)
\(68\) 47.8843i 0.704181i
\(69\) 61.9479 104.657i 0.897796 1.51677i
\(70\) 4.56041 2.53776i 0.0651487 0.0362536i
\(71\) −60.4809 19.6514i −0.851844 0.276781i −0.149626 0.988743i \(-0.547807\pi\)
−0.702218 + 0.711962i \(0.747807\pi\)
\(72\) 3.90702 8.28646i 0.0542641 0.115090i
\(73\) −86.8989 + 63.1357i −1.19040 + 0.864873i −0.993306 0.115513i \(-0.963149\pi\)
−0.197089 + 0.980386i \(0.563149\pi\)
\(74\) 0.00409204i 5.52978e-5i
\(75\) −12.4662 73.9567i −0.166216 0.986089i
\(76\) −68.3608 −0.899485
\(77\) 4.82096 + 6.63548i 0.0626098 + 0.0861750i
\(78\) 0.244138 0.105538i 0.00312998 0.00135305i
\(79\) 7.80969 24.0358i 0.0988568 0.304250i −0.889383 0.457163i \(-0.848865\pi\)
0.988240 + 0.152913i \(0.0488655\pi\)
\(80\) 53.7998 57.8851i 0.672498 0.723563i
\(81\) −4.96298 80.8478i −0.0612713 0.998121i
\(82\) −5.61301 −0.0684514
\(83\) 98.8345 32.1133i 1.19078 0.386907i 0.354417 0.935087i \(-0.384679\pi\)
0.836360 + 0.548180i \(0.184679\pi\)
\(84\) 97.4093 9.17050i 1.15963 0.109173i
\(85\) 11.5652 + 58.9764i 0.136061 + 0.693840i
\(86\) −3.37523 4.64561i −0.0392469 0.0540187i
\(87\) −9.35343 99.3525i −0.107511 1.14198i
\(88\) −0.825059 0.599440i −0.00937567 0.00681182i
\(89\) −44.0718 60.6596i −0.495189 0.681569i 0.486146 0.873878i \(-0.338402\pi\)
−0.981334 + 0.192309i \(0.938402\pi\)
\(90\) −1.40248 + 5.56345i −0.0155831 + 0.0618161i
\(91\) 4.60541 + 3.34602i 0.0506089 + 0.0367695i
\(92\) −153.593 + 49.9053i −1.66949 + 0.542449i
\(93\) −96.1346 + 84.6891i −1.03371 + 0.910635i
\(94\) −1.44357 4.44284i −0.0153571 0.0472643i
\(95\) 84.1961 16.5108i 0.886275 0.173797i
\(96\) −16.7615 + 7.24579i −0.174599 + 0.0754769i
\(97\) 25.4731 78.3983i 0.262610 0.808230i −0.729625 0.683848i \(-0.760305\pi\)
0.992234 0.124382i \(-0.0396948\pi\)
\(98\) −1.35051 1.85881i −0.0137807 0.0189675i
\(99\) −8.94485 1.13691i −0.0903520 0.0114840i
\(100\) −52.4967 + 84.6344i −0.524967 + 0.846344i
\(101\) 86.4515i 0.855956i −0.903789 0.427978i \(-0.859226\pi\)
0.903789 0.427978i \(-0.140774\pi\)
\(102\) 1.00465 4.48652i 0.00984949 0.0439855i
\(103\) −15.3781 + 47.3289i −0.149302 + 0.459504i −0.997539 0.0701123i \(-0.977664\pi\)
0.848237 + 0.529617i \(0.177664\pi\)
\(104\) −0.673177 0.218729i −0.00647286 0.00210316i
\(105\) −117.759 + 34.8214i −1.12151 + 0.331633i
\(106\) −1.64634 5.06690i −0.0155315 0.0478009i
\(107\) 171.256i 1.60053i 0.599648 + 0.800264i \(0.295307\pi\)
−0.599648 + 0.800264i \(0.704693\pi\)
\(108\) −66.0219 + 84.9146i −0.611314 + 0.786246i
\(109\) 59.6708 + 43.3533i 0.547438 + 0.397737i 0.826840 0.562437i \(-0.190136\pi\)
−0.279402 + 0.960174i \(0.590136\pi\)
\(110\) 0.579297 + 0.268964i 0.00526633 + 0.00244513i
\(111\) −0.0210393 + 0.0939565i −0.000189543 + 0.000846455i
\(112\) −104.679 76.0541i −0.934638 0.679054i
\(113\) 13.0962 18.0253i 0.115895 0.159516i −0.747128 0.664680i \(-0.768568\pi\)
0.863024 + 0.505164i \(0.168568\pi\)
\(114\) −6.40506 1.43426i −0.0561847 0.0125812i
\(115\) 177.118 98.5618i 1.54016 0.857059i
\(116\) −77.8904 + 107.207i −0.671469 + 0.924197i
\(117\) −6.14823 + 1.16799i −0.0525490 + 0.00998282i
\(118\) 14.6438 0.124100
\(119\) 93.5863 30.4080i 0.786440 0.255530i
\(120\) 12.5876 8.64248i 0.104896 0.0720207i
\(121\) 37.0809 114.123i 0.306454 0.943167i
\(122\) −3.68431 1.19711i −0.0301993 0.00981234i
\(123\) 128.879 + 28.8594i 1.04780 + 0.234629i
\(124\) 170.129 1.37201
\(125\) 44.2159 116.919i 0.353727 0.935349i
\(126\) 9.31916 + 1.18449i 0.0739616 + 0.00940071i
\(127\) −67.1341 + 48.7758i −0.528615 + 0.384061i −0.819839 0.572594i \(-0.805937\pi\)
0.291225 + 0.956655i \(0.405937\pi\)
\(128\) 30.7279 + 9.98408i 0.240061 + 0.0780007i
\(129\) 53.6126 + 124.021i 0.415601 + 0.961401i
\(130\) 0.440073 + 0.0532949i 0.00338518 + 0.000409961i
\(131\) −33.8077 + 10.9848i −0.258074 + 0.0838534i −0.435197 0.900335i \(-0.643321\pi\)
0.177122 + 0.984189i \(0.443321\pi\)
\(132\) 7.91484 + 8.98451i 0.0599609 + 0.0680645i
\(133\) −43.4113 133.606i −0.326400 1.00456i
\(134\) 5.49044 7.55694i 0.0409734 0.0563951i
\(135\) 60.8066 120.530i 0.450419 0.892817i
\(136\) −9.89866 + 7.19180i −0.0727843 + 0.0528809i
\(137\) −44.9650 + 61.8890i −0.328211 + 0.451744i −0.940952 0.338540i \(-0.890067\pi\)
0.612741 + 0.790284i \(0.290067\pi\)
\(138\) −15.4379 + 1.45338i −0.111869 + 0.0105318i
\(139\) −201.713 + 146.553i −1.45117 + 1.05434i −0.465620 + 0.884985i \(0.654169\pi\)
−0.985555 + 0.169355i \(0.945831\pi\)
\(140\) 147.903 + 68.6703i 1.05645 + 0.490502i
\(141\) 10.3025 + 109.433i 0.0730673 + 0.776123i
\(142\) 2.50556 + 7.71132i 0.0176448 + 0.0543050i
\(143\) 0.696654i 0.00487171i
\(144\) 139.747 26.5480i 0.970468 0.184361i
\(145\) 70.0401 150.853i 0.483035 1.04037i
\(146\) 13.0249 + 4.23203i 0.0892113 + 0.0289865i
\(147\) 21.4516 + 49.6235i 0.145929 + 0.337575i
\(148\) 0.103438 0.0751519i 0.000698903 0.000507783i
\(149\) 189.493i 1.27176i 0.771786 + 0.635882i \(0.219364\pi\)
−0.771786 + 0.635882i \(0.780636\pi\)
\(150\) −6.69436 + 6.82839i −0.0446291 + 0.0455226i
\(151\) 179.251 1.18709 0.593545 0.804801i \(-0.297728\pi\)
0.593545 + 0.804801i \(0.297728\pi\)
\(152\) 10.2672 + 14.1316i 0.0675473 + 0.0929708i
\(153\) −46.1350 + 97.8486i −0.301536 + 0.639533i
\(154\) 0.323152 0.994560i 0.00209839 0.00645818i
\(155\) −209.538 + 41.0902i −1.35186 + 0.265098i
\(156\) 7.15145 + 4.23303i 0.0458427 + 0.0271348i
\(157\) −9.40173 −0.0598837 −0.0299418 0.999552i \(-0.509532\pi\)
−0.0299418 + 0.999552i \(0.509532\pi\)
\(158\) −3.06456 + 0.995735i −0.0193959 + 0.00630212i
\(159\) 11.7496 + 124.805i 0.0738969 + 0.784935i
\(160\) −30.2136 3.65901i −0.188835 0.0228688i
\(161\) −195.072 268.494i −1.21163 1.66766i
\(162\) −7.96749 + 6.57088i −0.0491820 + 0.0405610i
\(163\) 101.591 + 73.8101i 0.623257 + 0.452823i 0.854058 0.520178i \(-0.174135\pi\)
−0.230801 + 0.973001i \(0.574135\pi\)
\(164\) −103.085 141.884i −0.628568 0.865149i
\(165\) −11.9182 9.15409i −0.0722317 0.0554793i
\(166\) −10.7194 7.78809i −0.0645747 0.0469162i
\(167\) 82.5935 26.8363i 0.494572 0.160696i −0.0511026 0.998693i \(-0.516274\pi\)
0.545674 + 0.837997i \(0.316274\pi\)
\(168\) −16.5257 18.7592i −0.0983675 0.111662i
\(169\) −52.0745 160.269i −0.308133 0.948335i
\(170\) 5.21667 5.61279i 0.0306863 0.0330164i
\(171\) 139.691 + 65.8635i 0.816906 + 0.385167i
\(172\) 55.4433 170.637i 0.322345 0.992075i
\(173\) 118.104 + 162.556i 0.682680 + 0.939628i 0.999962 0.00870293i \(-0.00277026\pi\)
−0.317282 + 0.948331i \(0.602770\pi\)
\(174\) −9.54720 + 8.41054i −0.0548690 + 0.0483364i
\(175\) −198.749 48.8553i −1.13571 0.279173i
\(176\) 15.8347i 0.0899700i
\(177\) −336.234 75.2916i −1.89963 0.425376i
\(178\) −2.95416 + 9.09198i −0.0165964 + 0.0510785i
\(179\) 21.5339 + 6.99678i 0.120301 + 0.0390882i 0.368549 0.929608i \(-0.379855\pi\)
−0.248248 + 0.968697i \(0.579855\pi\)
\(180\) −166.389 + 66.7234i −0.924381 + 0.370685i
\(181\) −17.9218 55.1576i −0.0990155 0.304738i 0.889264 0.457395i \(-0.151217\pi\)
−0.988279 + 0.152656i \(0.951217\pi\)
\(182\) 0.725806i 0.00398795i
\(183\) 78.4398 + 46.4295i 0.428633 + 0.253713i
\(184\) 33.3847 + 24.2554i 0.181439 + 0.131823i
\(185\) −0.109247 + 0.117543i −0.000590526 + 0.000635367i
\(186\) 15.9402 + 3.56943i 0.0857002 + 0.0191905i
\(187\) 9.74250 + 7.07834i 0.0520989 + 0.0378521i
\(188\) 85.7936 118.085i 0.456349 0.628110i
\(189\) −207.885 75.1115i −1.09992 0.397415i
\(190\) −8.01296 7.44744i −0.0421735 0.0391971i
\(191\) 104.861 144.328i 0.549009 0.755646i −0.440869 0.897572i \(-0.645329\pi\)
0.989877 + 0.141926i \(0.0453295\pi\)
\(192\) −161.210 95.4221i −0.839635 0.496990i
\(193\) −149.794 −0.776135 −0.388068 0.921631i \(-0.626857\pi\)
−0.388068 + 0.921631i \(0.626857\pi\)
\(194\) −9.99578 + 3.24783i −0.0515246 + 0.0167414i
\(195\) −9.83042 3.48634i −0.0504124 0.0178787i
\(196\) 22.1841 68.2757i 0.113184 0.348345i
\(197\) 239.749 + 77.8991i 1.21700 + 0.395427i 0.845988 0.533202i \(-0.179011\pi\)
0.371011 + 0.928629i \(0.379011\pi\)
\(198\) 0.553078 + 1.00786i 0.00279332 + 0.00509021i
\(199\) 15.7757 0.0792750 0.0396375 0.999214i \(-0.487380\pi\)
0.0396375 + 0.999214i \(0.487380\pi\)
\(200\) 25.3802 1.85921i 0.126901 0.00929605i
\(201\) −164.919 + 145.284i −0.820493 + 0.722807i
\(202\) −8.91744 + 6.47890i −0.0441458 + 0.0320738i
\(203\) −258.991 84.1511i −1.27582 0.414538i
\(204\) 131.860 57.0013i 0.646372 0.279418i
\(205\) 161.232 + 149.854i 0.786500 + 0.730993i
\(206\) 6.03444 1.96071i 0.0292934 0.00951800i
\(207\) 361.939 + 46.0034i 1.74850 + 0.222239i
\(208\) −3.39616 10.4523i −0.0163277 0.0502515i
\(209\) 10.1052 13.9086i 0.0483503 0.0665484i
\(210\) 12.4170 + 9.53715i 0.0591284 + 0.0454150i
\(211\) −279.131 + 202.801i −1.32290 + 0.961140i −0.323004 + 0.946397i \(0.604693\pi\)
−0.999891 + 0.0147425i \(0.995307\pi\)
\(212\) 97.8444 134.671i 0.461530 0.635242i
\(213\) −17.8817 189.940i −0.0839518 0.891739i
\(214\) 17.6650 12.8344i 0.0825469 0.0599739i
\(215\) −27.0735 + 223.555i −0.125923 + 1.03979i
\(216\) 27.4695 + 0.894654i 0.127173 + 0.00414191i
\(217\) 108.037 + 332.505i 0.497868 + 1.53228i
\(218\) 9.40403i 0.0431378i
\(219\) −277.302 164.138i −1.26622 0.749490i
\(220\) 3.84019 + 19.5830i 0.0174554 + 0.0890134i
\(221\) 7.94904 + 2.58280i 0.0359685 + 0.0116869i
\(222\) 0.0112683 0.00487115i 5.07582e−5 2.19421e-5i
\(223\) 71.5176 51.9606i 0.320707 0.233007i −0.415770 0.909470i \(-0.636488\pi\)
0.736477 + 0.676463i \(0.236488\pi\)
\(224\) 49.8308i 0.222459i
\(225\) 188.816 122.366i 0.839183 0.543850i
\(226\) −2.84077 −0.0125698
\(227\) −138.027 189.977i −0.608047 0.836905i 0.388368 0.921504i \(-0.373039\pi\)
−0.996415 + 0.0845996i \(0.973039\pi\)
\(228\) −81.3764 188.246i −0.356914 0.825642i
\(229\) 57.0810 175.677i 0.249262 0.767150i −0.745644 0.666344i \(-0.767858\pi\)
0.994906 0.100805i \(-0.0321419\pi\)
\(230\) −23.4403 10.8832i −0.101914 0.0473182i
\(231\) −12.5334 + 21.1744i −0.0542571 + 0.0916641i
\(232\) 33.8603 0.145949
\(233\) −267.662 + 86.9687i −1.14876 + 0.373256i −0.820678 0.571391i \(-0.806404\pi\)
−0.328087 + 0.944647i \(0.606404\pi\)
\(234\) 0.581242 + 0.546656i 0.00248394 + 0.00233614i
\(235\) −77.1468 + 166.159i −0.328284 + 0.707061i
\(236\) 268.940 + 370.164i 1.13958 + 1.56849i
\(237\) 75.4843 7.10639i 0.318499 0.0299848i
\(238\) −10.1502 7.37454i −0.0426478 0.0309855i
\(239\) −113.345 156.006i −0.474247 0.652745i 0.503140 0.864205i \(-0.332178\pi\)
−0.977387 + 0.211460i \(0.932178\pi\)
\(240\) 223.442 + 79.2434i 0.931009 + 0.330181i
\(241\) −76.8811 55.8574i −0.319009 0.231774i 0.416744 0.909024i \(-0.363171\pi\)
−0.735752 + 0.677251i \(0.763171\pi\)
\(242\) −14.5507 + 4.72781i −0.0601269 + 0.0195364i
\(243\) 216.724 109.908i 0.891869 0.452294i
\(244\) −37.4036 115.117i −0.153294 0.471789i
\(245\) −10.8327 + 89.4492i −0.0442151 + 0.365099i
\(246\) −6.68171 15.4566i −0.0271614 0.0628319i
\(247\) 3.68727 11.3482i 0.0149282 0.0459443i
\(248\) −25.5519 35.1691i −0.103032 0.141811i
\(249\) 206.083 + 233.935i 0.827643 + 0.939497i
\(250\) −15.3738 + 4.20133i −0.0614951 + 0.0168053i
\(251\) 242.509i 0.966171i 0.875573 + 0.483085i \(0.160484\pi\)
−0.875573 + 0.483085i \(0.839516\pi\)
\(252\) 141.209 + 257.321i 0.560352 + 1.02112i
\(253\) 12.5506 38.6269i 0.0496073 0.152676i
\(254\) 10.0624 + 3.26947i 0.0396158 + 0.0128719i
\(255\) −148.637 + 102.053i −0.582891 + 0.400206i
\(256\) 75.9129 + 233.636i 0.296535 + 0.912640i
\(257\) 54.2631i 0.211140i 0.994412 + 0.105570i \(0.0336668\pi\)
−0.994412 + 0.105570i \(0.966333\pi\)
\(258\) 8.77484 14.8246i 0.0340110 0.0574595i
\(259\) 0.212565 + 0.154437i 0.000820714 + 0.000596283i
\(260\) 6.73494 + 12.1029i 0.0259036 + 0.0465494i
\(261\) 262.454 144.025i 1.00557 0.551822i
\(262\) 3.66671 + 2.66402i 0.0139951 + 0.0101680i
\(263\) −0.445193 + 0.612755i −0.00169275 + 0.00232987i −0.809863 0.586620i \(-0.800458\pi\)
0.808170 + 0.588950i \(0.200458\pi\)
\(264\) 0.668542 2.98555i 0.00253236 0.0113089i
\(265\) −87.9831 + 189.499i −0.332012 + 0.715089i
\(266\) −10.5281 + 14.4906i −0.0395792 + 0.0544761i
\(267\) 114.577 193.570i 0.429126 0.724982i
\(268\) 291.857 1.08902
\(269\) 138.978 45.1567i 0.516647 0.167869i −0.0390762 0.999236i \(-0.512442\pi\)
0.555723 + 0.831368i \(0.312442\pi\)
\(270\) −16.9897 + 2.76068i −0.0629247 + 0.0102248i
\(271\) −77.5376 + 238.636i −0.286116 + 0.880576i 0.699945 + 0.714196i \(0.253208\pi\)
−0.986062 + 0.166380i \(0.946792\pi\)
\(272\) −180.679 58.7062i −0.664262 0.215832i
\(273\) −3.73175 + 16.6651i −0.0136694 + 0.0610443i
\(274\) 9.75362 0.0355971
\(275\) −9.45949 23.1917i −0.0343982 0.0843335i
\(276\) −320.261 363.544i −1.16037 1.31719i
\(277\) 283.138 205.712i 1.02216 0.742642i 0.0554344 0.998462i \(-0.482346\pi\)
0.966724 + 0.255821i \(0.0823456\pi\)
\(278\) 30.2338 + 9.82357i 0.108755 + 0.0353366i
\(279\) −347.648 163.914i −1.24605 0.587506i
\(280\) −8.01811 40.8881i −0.0286361 0.146029i
\(281\) 265.260 86.1882i 0.943986 0.306720i 0.203717 0.979030i \(-0.434698\pi\)
0.740270 + 0.672310i \(0.234698\pi\)
\(282\) 10.5159 9.26392i 0.0372905 0.0328508i
\(283\) 21.3423 + 65.6850i 0.0754146 + 0.232102i 0.981657 0.190657i \(-0.0610617\pi\)
−0.906242 + 0.422759i \(0.861062\pi\)
\(284\) −148.909 + 204.956i −0.524329 + 0.721677i
\(285\) 145.693 + 212.198i 0.511202 + 0.744554i
\(286\) 0.0718596 0.0522091i 0.000251257 0.000182549i
\(287\) 211.840 291.573i 0.738119 1.01593i
\(288\) −39.9057 37.5311i −0.138561 0.130316i
\(289\) −116.920 + 84.9474i −0.404568 + 0.293936i
\(290\) −20.8094 + 4.08070i −0.0717566 + 0.0140714i
\(291\) 246.210 23.1792i 0.846082 0.0796535i
\(292\) 132.230 + 406.962i 0.452843 + 1.39371i
\(293\) 108.418i 0.370028i −0.982736 0.185014i \(-0.940767\pi\)
0.982736 0.185014i \(-0.0592330\pi\)
\(294\) 3.51101 5.93164i 0.0119422 0.0201756i
\(295\) −420.641 390.954i −1.42590 1.32527i
\(296\) −0.0310708 0.0100955i −0.000104969 3.41065e-5i
\(297\) −7.51717 25.9850i −0.0253103 0.0874915i
\(298\) 19.5461 14.2011i 0.0655910 0.0476547i
\(299\) 28.1890i 0.0942775i
\(300\) −295.551 43.8125i −0.985170 0.146042i
\(301\) 368.705 1.22493
\(302\) −13.4335 18.4896i −0.0444818 0.0612240i
\(303\) 238.063 102.912i 0.785687 0.339642i
\(304\) −83.8104 + 257.942i −0.275692 + 0.848493i
\(305\) 73.8713 + 132.749i 0.242201 + 0.435241i
\(306\) 13.5505 2.57421i 0.0442828 0.00841247i
\(307\) −408.372 −1.33020 −0.665101 0.746754i \(-0.731611\pi\)
−0.665101 + 0.746754i \(0.731611\pi\)
\(308\) 31.0751 10.0969i 0.100893 0.0327822i
\(309\) −148.637 + 13.9932i −0.481024 + 0.0452855i
\(310\) 19.9418 + 18.5344i 0.0643284 + 0.0597884i
\(311\) 151.641 + 208.715i 0.487590 + 0.671110i 0.979941 0.199286i \(-0.0638624\pi\)
−0.492351 + 0.870397i \(0.663862\pi\)
\(312\) −0.199031 2.11411i −0.000637920 0.00677601i
\(313\) 13.0347 + 9.47029i 0.0416445 + 0.0302565i 0.608413 0.793621i \(-0.291807\pi\)
−0.566768 + 0.823877i \(0.691807\pi\)
\(314\) 0.704590 + 0.969786i 0.00224392 + 0.00308849i
\(315\) −236.068 282.823i −0.749421 0.897850i
\(316\) −81.4518 59.1782i −0.257759 0.187273i
\(317\) −137.656 + 44.7271i −0.434246 + 0.141095i −0.517979 0.855393i \(-0.673316\pi\)
0.0837333 + 0.996488i \(0.473316\pi\)
\(318\) 11.9930 10.5652i 0.0377139 0.0332238i
\(319\) −10.2983 31.6950i −0.0322831 0.0993573i
\(320\) −151.821 272.826i −0.474440 0.852581i
\(321\) −471.592 + 203.863i −1.46913 + 0.635087i
\(322\) −13.0758 + 40.2433i −0.0406082 + 0.124979i
\(323\) −121.237 166.869i −0.375348 0.516622i
\(324\) −312.423 80.7237i −0.964269 0.249147i
\(325\) −11.2182 13.2798i −0.0345174 0.0408608i
\(326\) 16.0106i 0.0491122i
\(327\) −48.3510 + 215.924i −0.147862 + 0.660318i
\(328\) −13.8479 + 42.6195i −0.0422193 + 0.129938i
\(329\) 285.269 + 92.6896i 0.867080 + 0.281731i
\(330\) −0.0510582 + 1.91539i −0.000154722 + 0.00580422i
\(331\) −10.1144 31.1289i −0.0305571 0.0940451i 0.934615 0.355662i \(-0.115744\pi\)
−0.965172 + 0.261616i \(0.915744\pi\)
\(332\) 413.994i 1.24697i
\(333\) −0.283775 + 0.0539091i −0.000852176 + 0.000161889i
\(334\) −8.95792 6.50831i −0.0268201 0.0194860i
\(335\) −359.463 + 70.4903i −1.07302 + 0.210419i
\(336\) 84.8214 378.792i 0.252445 1.12736i
\(337\) −186.453 135.466i −0.553272 0.401976i 0.275718 0.961238i \(-0.411084\pi\)
−0.828990 + 0.559263i \(0.811084\pi\)
\(338\) −12.6291 + 17.3824i −0.0373641 + 0.0514273i
\(339\) 65.2263 + 14.6059i 0.192408 + 0.0430851i
\(340\) 237.685 + 28.7848i 0.699074 + 0.0846610i
\(341\) −25.1488 + 34.6143i −0.0737501 + 0.101508i
\(342\) −3.67501 19.3451i −0.0107456 0.0565645i
\(343\) −253.617 −0.739407
\(344\) −43.6012 + 14.1669i −0.126748 + 0.0411828i
\(345\) 482.252 + 370.406i 1.39783 + 1.07364i
\(346\) 7.91657 24.3647i 0.0228803 0.0704182i
\(347\) −59.9420 19.4763i −0.172744 0.0561278i 0.221368 0.975190i \(-0.428948\pi\)
−0.394112 + 0.919062i \(0.628948\pi\)
\(348\) −387.938 86.8694i −1.11476 0.249625i
\(349\) −54.2580 −0.155467 −0.0777335 0.996974i \(-0.524768\pi\)
−0.0777335 + 0.996974i \(0.524768\pi\)
\(350\) 9.85533 + 24.1622i 0.0281581 + 0.0690348i
\(351\) −10.5351 15.5401i −0.0300147 0.0442739i
\(352\) −4.93358 + 3.58446i −0.0140159 + 0.0101831i
\(353\) 95.0073 + 30.8697i 0.269142 + 0.0874497i 0.440479 0.897763i \(-0.354809\pi\)
−0.171337 + 0.985213i \(0.554809\pi\)
\(354\) 17.4320 + 40.3250i 0.0492429 + 0.113912i
\(355\) 133.901 288.398i 0.377187 0.812389i
\(356\) −284.079 + 92.3030i −0.797976 + 0.259278i
\(357\) 195.140 + 221.513i 0.546610 + 0.620484i
\(358\) −0.892090 2.74557i −0.00249187 0.00766919i
\(359\) 207.072 285.011i 0.576803 0.793901i −0.416537 0.909119i \(-0.636756\pi\)
0.993340 + 0.115217i \(0.0367564\pi\)
\(360\) 38.7831 + 24.3746i 0.107731 + 0.0677073i
\(361\) 53.8290 39.1090i 0.149111 0.108335i
\(362\) −4.34638 + 5.98228i −0.0120066 + 0.0165256i
\(363\) 358.404 33.7416i 0.987339 0.0929519i
\(364\) 18.3468 13.3297i 0.0504032 0.0366201i
\(365\) −261.151 469.296i −0.715483 1.28574i
\(366\) −1.08930 11.5706i −0.00297623 0.0316136i
\(367\) −27.9042 85.8802i −0.0760332 0.234006i 0.905815 0.423673i \(-0.139259\pi\)
−0.981849 + 0.189667i \(0.939259\pi\)
\(368\) 640.727i 1.74110i
\(369\) 73.9466 + 389.251i 0.200397 + 1.05488i
\(370\) 0.0203118 + 0.00245985i 5.48967e−5 + 6.64825e-6i
\(371\) 325.339 + 105.709i 0.876925 + 0.284930i
\(372\) 202.521 + 468.488i 0.544411 + 1.25938i
\(373\) 249.418 181.213i 0.668681 0.485825i −0.200903 0.979611i \(-0.564387\pi\)
0.869583 + 0.493786i \(0.164387\pi\)
\(374\) 1.53540i 0.00410536i
\(375\) 374.595 17.4213i 0.998920 0.0464567i
\(376\) −37.2959 −0.0991913
\(377\) −13.5956 18.7128i −0.0360626 0.0496360i
\(378\) 7.83174 + 27.0723i 0.0207189 + 0.0716199i
\(379\) 41.3784 127.350i 0.109178 0.336015i −0.881510 0.472165i \(-0.843473\pi\)
0.990688 + 0.136149i \(0.0434727\pi\)
\(380\) 41.0938 339.325i 0.108142 0.892960i
\(381\) −214.231 126.806i −0.562286 0.332824i
\(382\) −22.7460 −0.0595444
\(383\) 121.960 39.6273i 0.318434 0.103466i −0.145439 0.989367i \(-0.546459\pi\)
0.463873 + 0.885902i \(0.346459\pi\)
\(384\) 9.08497 + 96.5008i 0.0236588 + 0.251304i
\(385\) −35.8348 + 19.9412i −0.0930773 + 0.0517952i
\(386\) 11.2260 + 15.4512i 0.0290828 + 0.0400290i
\(387\) −277.698 + 295.268i −0.717566 + 0.762966i
\(388\) −265.674 193.024i −0.684727 0.497483i
\(389\) 300.719 + 413.904i 0.773055 + 1.06402i 0.996014 + 0.0891917i \(0.0284284\pi\)
−0.222959 + 0.974828i \(0.571572\pi\)
\(390\) 0.377102 + 1.27528i 0.000966929 + 0.00326995i
\(391\) −394.215 286.414i −1.00822 0.732516i
\(392\) −17.4458 + 5.66849i −0.0445046 + 0.0144604i
\(393\) −70.4936 80.0206i −0.179373 0.203615i
\(394\) −9.93213 30.5680i −0.0252085 0.0775837i
\(395\) 114.612 + 53.2138i 0.290158 + 0.134719i
\(396\) −15.3190 + 32.4904i −0.0386844 + 0.0820463i
\(397\) 192.511 592.487i 0.484914 1.49241i −0.347192 0.937794i \(-0.612865\pi\)
0.832106 0.554617i \(-0.187135\pi\)
\(398\) −1.18227 1.62726i −0.00297054 0.00408859i
\(399\) 316.237 278.586i 0.792573 0.698212i
\(400\) 254.985 + 301.844i 0.637463 + 0.754611i
\(401\) 157.706i 0.393282i 0.980476 + 0.196641i \(0.0630034\pi\)
−0.980476 + 0.196641i \(0.936997\pi\)
\(402\) 27.3455 + 6.12337i 0.0680236 + 0.0152323i
\(403\) −9.17648 + 28.2423i −0.0227704 + 0.0700802i
\(404\) −327.545 106.426i −0.810754 0.263430i
\(405\) 404.290 + 23.9652i 0.998248 + 0.0591734i
\(406\) 10.7293 + 33.0213i 0.0264268 + 0.0813332i
\(407\) 0.0321544i 7.90034e-5i
\(408\) −31.5875 18.6970i −0.0774204 0.0458260i
\(409\) 295.631 + 214.789i 0.722815 + 0.525156i 0.887282 0.461227i \(-0.152590\pi\)
−0.164467 + 0.986383i \(0.552590\pi\)
\(410\) 3.37415 27.8615i 0.00822965 0.0679549i
\(411\) −223.951 50.1484i −0.544893 0.122016i
\(412\) 160.387 + 116.528i 0.389289 + 0.282835i
\(413\) −552.672 + 760.688i −1.33819 + 1.84186i
\(414\) −22.3794 40.7815i −0.0540566 0.0985061i
\(415\) 99.9893 + 509.892i 0.240938 + 1.22866i
\(416\) −2.48782 + 3.42419i −0.00598034 + 0.00823123i
\(417\) −643.685 381.005i −1.54361 0.913681i
\(418\) −2.19198 −0.00524397
\(419\) 480.757 156.207i 1.14739 0.372810i 0.327231 0.944944i \(-0.393885\pi\)
0.820160 + 0.572135i \(0.193885\pi\)
\(420\) −13.0359 + 489.027i −0.0310378 + 1.16435i
\(421\) 137.305 422.580i 0.326139 1.00375i −0.644785 0.764364i \(-0.723053\pi\)
0.970924 0.239389i \(-0.0769471\pi\)
\(422\) 41.8376 + 13.5939i 0.0991413 + 0.0322129i
\(423\) −289.085 + 158.639i −0.683415 + 0.375033i
\(424\) −42.5346 −0.100318
\(425\) −299.695 + 21.9540i −0.705165 + 0.0516565i
\(426\) −18.2522 + 16.0791i −0.0428455 + 0.0377444i
\(427\) 201.234 146.205i 0.471274 0.342401i
\(428\) 648.851 + 210.824i 1.51601 + 0.492580i
\(429\) −1.91839 + 0.829294i −0.00447177 + 0.00193309i
\(430\) 25.0885 13.9611i 0.0583454 0.0324678i
\(431\) −140.064 + 45.5096i −0.324975 + 0.105591i −0.466961 0.884278i \(-0.654651\pi\)
0.141986 + 0.989869i \(0.454651\pi\)
\(432\) 239.460 + 353.222i 0.554307 + 0.817644i
\(433\) 97.5543 + 300.241i 0.225299 + 0.693398i 0.998261 + 0.0589462i \(0.0187740\pi\)
−0.772963 + 0.634452i \(0.781226\pi\)
\(434\) 26.2011 36.0628i 0.0603713 0.0830940i
\(435\) 498.782 + 13.2959i 1.14662 + 0.0305653i
\(436\) 237.713 172.709i 0.545213 0.396121i
\(437\) −408.891 + 562.790i −0.935677 + 1.28785i
\(438\) 3.85092 + 40.9046i 0.00879204 + 0.0933894i
\(439\) 630.308 457.946i 1.43578 1.04316i 0.446878 0.894595i \(-0.352536\pi\)
0.988903 0.148561i \(-0.0474642\pi\)
\(440\) 3.47143 3.73503i 0.00788961 0.00848870i
\(441\) −111.113 + 118.143i −0.251957 + 0.267899i
\(442\) −0.329307 1.01350i −0.000745039 0.00229299i
\(443\) 211.073i 0.476464i −0.971208 0.238232i \(-0.923432\pi\)
0.971208 0.238232i \(-0.0765678\pi\)
\(444\) 0.330079 + 0.195378i 0.000743421 + 0.000440040i
\(445\) 327.591 182.296i 0.736160 0.409654i
\(446\) −10.7194 3.48295i −0.0240346 0.00780931i
\(447\) −521.810 + 225.572i −1.16736 + 0.504634i
\(448\) −413.578 + 300.482i −0.923164 + 0.670718i
\(449\) 750.379i 1.67122i −0.549322 0.835611i \(-0.685114\pi\)
0.549322 0.835611i \(-0.314886\pi\)
\(450\) −26.7724 10.3059i −0.0594942 0.0229019i
\(451\) 44.1059 0.0977957
\(452\) −52.1718 71.8083i −0.115424 0.158868i
\(453\) 213.379 + 493.606i 0.471036 + 1.08964i
\(454\) −9.25202 + 28.4748i −0.0203789 + 0.0627198i
\(455\) −19.3772 + 20.8486i −0.0425873 + 0.0458211i
\(456\) −26.6923 + 45.0951i −0.0585358 + 0.0988927i
\(457\) −787.437 −1.72306 −0.861529 0.507709i \(-0.830492\pi\)
−0.861529 + 0.507709i \(0.830492\pi\)
\(458\) −22.3989 + 7.27783i −0.0489058 + 0.0158905i
\(459\) −324.366 10.5643i −0.706680 0.0230159i
\(460\) −155.387 792.393i −0.337798 1.72259i
\(461\) −229.796 316.286i −0.498472 0.686088i 0.483450 0.875372i \(-0.339383\pi\)
−0.981922 + 0.189284i \(0.939383\pi\)
\(462\) 3.12342 0.294051i 0.00676064 0.000636473i
\(463\) −46.4568 33.7528i −0.100339 0.0729003i 0.536485 0.843910i \(-0.319752\pi\)
−0.636823 + 0.771010i \(0.719752\pi\)
\(464\) 309.024 + 425.335i 0.666000 + 0.916670i
\(465\) −362.584 528.096i −0.779752 1.13569i
\(466\) 29.0301 + 21.0916i 0.0622963 + 0.0452609i
\(467\) 676.082 219.672i 1.44771 0.470390i 0.523420 0.852075i \(-0.324656\pi\)
0.924292 + 0.381685i \(0.124656\pi\)
\(468\) −3.14351 + 24.7321i −0.00671690 + 0.0528463i
\(469\) 185.338 + 570.412i 0.395177 + 1.21623i
\(470\) 22.9209 4.49475i 0.0487678 0.00956330i
\(471\) −11.1918 25.8897i −0.0237618 0.0549675i
\(472\) 36.1280 111.191i 0.0765424 0.235573i
\(473\) 26.5219 + 36.5042i 0.0560716 + 0.0771760i
\(474\) −6.39001 7.25361i −0.0134810 0.0153030i
\(475\) 31.3421 + 427.852i 0.0659833 + 0.900742i
\(476\) 392.010i 0.823551i
\(477\) −329.690 + 180.922i −0.691175 + 0.379292i
\(478\) −7.59760 + 23.3830i −0.0158946 + 0.0489184i
\(479\) 199.787 + 64.9147i 0.417092 + 0.135521i 0.510042 0.860149i \(-0.329630\pi\)
−0.0929503 + 0.995671i \(0.529630\pi\)
\(480\) −25.8903 87.5554i −0.0539381 0.182407i
\(481\) 0.00689634 + 0.0212247i 1.43375e−5 + 4.41263e-5i
\(482\) 12.1164i 0.0251377i
\(483\) 507.143 856.788i 1.04999 1.77389i
\(484\) −386.738 280.982i −0.799045 0.580540i
\(485\) 373.835 + 173.570i 0.770795 + 0.357875i
\(486\) −27.5788 14.1183i −0.0567465 0.0290499i
\(487\) 279.562 + 203.114i 0.574049 + 0.417071i 0.836574 0.547854i \(-0.184555\pi\)
−0.262525 + 0.964925i \(0.584555\pi\)
\(488\) −18.1792 + 25.0216i −0.0372525 + 0.0512737i
\(489\) −82.3188 + 367.616i −0.168341 + 0.751771i
\(490\) 10.0385 5.58617i 0.0204867 0.0114003i
\(491\) −94.8253 + 130.516i −0.193127 + 0.265816i −0.894588 0.446891i \(-0.852531\pi\)
0.701462 + 0.712707i \(0.252531\pi\)
\(492\) 267.998 452.766i 0.544711 0.920256i
\(493\) −399.830 −0.811015
\(494\) −1.44690 + 0.470127i −0.00292895 + 0.000951673i
\(495\) 11.0204 43.7164i 0.0222634 0.0883160i
\(496\) 208.578 641.939i 0.420521 1.29423i
\(497\) −495.134 160.879i −0.996245 0.323700i
\(498\) 8.68589 38.7891i 0.0174415 0.0778897i
\(499\) −669.740 −1.34216 −0.671082 0.741383i \(-0.734170\pi\)
−0.671082 + 0.741383i \(0.734170\pi\)
\(500\) −388.545 311.456i −0.777091 0.622911i
\(501\) 172.218 + 195.493i 0.343749 + 0.390206i
\(502\) 25.0147 18.1742i 0.0498301 0.0362037i
\(503\) −720.028 233.951i −1.43147 0.465112i −0.512240 0.858842i \(-0.671184\pi\)
−0.919226 + 0.393731i \(0.871184\pi\)
\(504\) 31.9852 67.8380i 0.0634628 0.134599i
\(505\) 429.122 + 51.9687i 0.849747 + 0.102908i
\(506\) −4.92493 + 1.60021i −0.00973306 + 0.00316246i
\(507\) 379.345 334.182i 0.748216 0.659135i
\(508\) 102.155 + 314.400i 0.201092 + 0.618898i
\(509\) 335.686 462.033i 0.659502 0.907726i −0.339963 0.940439i \(-0.610415\pi\)
0.999465 + 0.0327124i \(0.0104145\pi\)
\(510\) 21.6659 + 7.68379i 0.0424822 + 0.0150663i
\(511\) −711.407 + 516.867i −1.39219 + 1.01148i
\(512\) 94.3738 129.894i 0.184324 0.253700i
\(513\) −15.0818 + 463.073i −0.0293993 + 0.902676i
\(514\) 5.59722 4.06662i 0.0108895 0.00791170i
\(515\) −225.684 104.784i −0.438221 0.203464i
\(516\) 535.885 50.4503i 1.03854 0.0977719i
\(517\) 11.3433 + 34.9109i 0.0219405 + 0.0675260i
\(518\) 0.0334999i 6.46717e-5i
\(519\) −307.042 + 518.730i −0.591604 + 0.999479i
\(520\) 1.49038 3.20999i 0.00286611 0.00617305i
\(521\) −704.102 228.777i −1.35144 0.439111i −0.458267 0.888815i \(-0.651529\pi\)
−0.893178 + 0.449704i \(0.851529\pi\)
\(522\) −34.5252 16.2784i −0.0661402 0.0311847i
\(523\) 475.508 345.477i 0.909193 0.660567i −0.0316179 0.999500i \(-0.510066\pi\)
0.940811 + 0.338933i \(0.110066\pi\)
\(524\) 141.612i 0.270252i
\(525\) −102.056 605.455i −0.194392 1.15325i
\(526\) 0.0965694 0.000183592
\(527\) 301.723 + 415.286i 0.572529 + 0.788019i
\(528\) 43.6043 18.8496i 0.0825840 0.0357000i
\(529\) −344.372 + 1059.87i −0.650986 + 2.00353i
\(530\) 26.1404 5.12610i 0.0493215 0.00967189i
\(531\) −192.920 1015.52i −0.363315 1.91247i
\(532\) −559.643 −1.05196
\(533\) 29.1138 9.45964i 0.0546225 0.0177479i
\(534\) −28.5534 + 2.68813i −0.0534707 + 0.00503394i
\(535\) −850.071 102.948i −1.58892 0.192425i
\(536\) −43.8343 60.3327i −0.0817804 0.112561i
\(537\) 6.36669 + 67.6272i 0.0118560 + 0.125935i
\(538\) −15.0733 10.9514i −0.0280172 0.0203557i
\(539\) 10.6120 + 14.6062i 0.0196883 + 0.0270986i
\(540\) −381.806 378.760i −0.707047 0.701407i
\(541\) 281.394 + 204.445i 0.520138 + 0.377902i 0.816656 0.577125i \(-0.195826\pi\)
−0.296518 + 0.955027i \(0.595826\pi\)
\(542\) 30.4261 9.88604i 0.0561367 0.0182399i
\(543\) 130.554 115.011i 0.240432 0.211807i
\(544\) 22.6089 + 69.5829i 0.0415604 + 0.127910i
\(545\) −251.064 + 270.129i −0.460669 + 0.495649i
\(546\) 1.99866 0.863997i 0.00366056 0.00158241i
\(547\) −272.374 + 838.280i −0.497941 + 1.53250i 0.314383 + 0.949296i \(0.398202\pi\)
−0.812323 + 0.583207i \(0.801798\pi\)
\(548\) 179.129 + 246.550i 0.326878 + 0.449908i
\(549\) −34.4792 + 271.271i −0.0628036 + 0.494117i
\(550\) −1.68330 + 2.71379i −0.00306054 + 0.00493417i
\(551\) 570.807i 1.03595i
\(552\) −27.0515 + 120.806i −0.0490063 + 0.218851i
\(553\) 63.9349 196.771i 0.115615 0.355825i
\(554\) −42.4382 13.7890i −0.0766032 0.0248899i
\(555\) −0.453728 0.160914i −0.000817527 0.000289934i
\(556\) 306.938 + 944.658i 0.552047 + 1.69903i
\(557\) 116.530i 0.209210i −0.994514 0.104605i \(-0.966642\pi\)
0.994514 0.104605i \(-0.0333578\pi\)
\(558\) 9.14598 + 48.1439i 0.0163906 + 0.0862794i
\(559\) 25.3361 + 18.4077i 0.0453239 + 0.0329298i
\(560\) 440.438 473.882i 0.786497 0.846218i
\(561\) −7.89431 + 35.2541i −0.0140719 + 0.0628416i
\(562\) −28.7696 20.9023i −0.0511914 0.0371927i
\(563\) 141.849 195.238i 0.251951 0.346781i −0.664242 0.747517i \(-0.731246\pi\)
0.916193 + 0.400736i \(0.131246\pi\)
\(564\) 427.300 + 95.6836i 0.757624 + 0.169652i
\(565\) 81.6004 + 75.8414i 0.144425 + 0.134233i
\(566\) 5.17593 7.12406i 0.00914475 0.0125867i
\(567\) −40.6300 661.869i −0.0716578 1.16732i
\(568\) 64.7335 0.113967
\(569\) −542.163 + 176.159i −0.952835 + 0.309595i −0.743867 0.668328i \(-0.767010\pi\)
−0.208968 + 0.977923i \(0.567010\pi\)
\(570\) 10.9696 30.9308i 0.0192448 0.0542646i
\(571\) 38.7398 119.229i 0.0678455 0.208807i −0.911386 0.411553i \(-0.864987\pi\)
0.979231 + 0.202746i \(0.0649865\pi\)
\(572\) 2.63946 + 0.857612i 0.00461444 + 0.00149932i
\(573\) 522.265 + 116.949i 0.911457 + 0.204099i
\(574\) −45.9515 −0.0800549
\(575\) 382.763 + 938.416i 0.665675 + 1.63203i
\(576\) 70.8619 557.517i 0.123024 0.967911i
\(577\) 603.384 438.384i 1.04573 0.759765i 0.0743316 0.997234i \(-0.476318\pi\)
0.971395 + 0.237469i \(0.0763177\pi\)
\(578\) 17.5246 + 5.69409i 0.0303194 + 0.00985136i
\(579\) −178.314 412.491i −0.307969 0.712419i
\(580\) −485.324 451.072i −0.836765 0.777711i
\(581\) 809.120 262.899i 1.39263 0.452494i
\(582\) −20.8425 23.6594i −0.0358119 0.0406518i
\(583\) 12.9366 + 39.8146i 0.0221896 + 0.0682927i
\(584\) 64.2676 88.4567i 0.110047 0.151467i
\(585\) −2.10170 31.2203i −0.00359264 0.0533680i
\(586\) −11.1833 + 8.12514i −0.0190841 + 0.0138654i
\(587\) −10.4605 + 14.3977i −0.0178204 + 0.0245276i −0.817834 0.575454i \(-0.804825\pi\)
0.800014 + 0.599982i \(0.204825\pi\)
\(588\) 214.420 20.1863i 0.364659 0.0343305i
\(589\) 592.872 430.747i 1.00657 0.731319i
\(590\) −8.80287 + 72.6881i −0.0149201 + 0.123200i
\(591\) 70.8839 + 752.931i 0.119939 + 1.27400i
\(592\) −0.156752 0.482432i −0.000264783 0.000814918i
\(593\) 378.863i 0.638892i −0.947604 0.319446i \(-0.896503\pi\)
0.947604 0.319446i \(-0.103497\pi\)
\(594\) −2.11698 + 2.72278i −0.00356395 + 0.00458380i
\(595\) 94.6798 + 482.817i 0.159126 + 0.811457i
\(596\) 717.944 + 233.274i 1.20460 + 0.391400i
\(597\) 18.7794 + 43.4419i 0.0314562 + 0.0727670i
\(598\) −2.90768 + 2.11256i −0.00486235 + 0.00353270i
\(599\) 350.102i 0.584478i −0.956345 0.292239i \(-0.905600\pi\)
0.956345 0.292239i \(-0.0944002\pi\)
\(600\) 35.3322 + 67.6766i 0.0588870 + 0.112794i
\(601\) 238.239 0.396404 0.198202 0.980161i \(-0.436490\pi\)
0.198202 + 0.980161i \(0.436490\pi\)
\(602\) −27.6317 38.0318i −0.0458999 0.0631758i
\(603\) −596.391 281.195i −0.989039 0.466326i
\(604\) 220.666 679.139i 0.365340 1.12440i
\(605\) 544.187 + 252.663i 0.899482 + 0.417624i
\(606\) −28.4564 16.8437i −0.0469577 0.0277948i
\(607\) −2.48465 −0.00409333 −0.00204667 0.999998i \(-0.500651\pi\)
−0.00204667 + 0.999998i \(0.500651\pi\)
\(608\) 99.3382 32.2769i 0.163385 0.0530871i
\(609\) −76.5729 813.360i −0.125735 1.33557i
\(610\) 8.15687 17.5683i 0.0133719 0.0288005i
\(611\) 14.9751 + 20.6115i 0.0245092 + 0.0337340i
\(612\) 313.931 + 295.251i 0.512959 + 0.482436i
\(613\) 216.899 + 157.587i 0.353832 + 0.257074i 0.750475 0.660899i \(-0.229825\pi\)
−0.396643 + 0.917973i \(0.629825\pi\)
\(614\) 30.6044 + 42.1234i 0.0498444 + 0.0686049i
\(615\) −220.724 + 622.374i −0.358900 + 1.01199i
\(616\) −6.75443 4.90738i −0.0109650 0.00796653i
\(617\) −642.412 + 208.732i −1.04119 + 0.338302i −0.779204 0.626770i \(-0.784376\pi\)
−0.261983 + 0.965073i \(0.584376\pi\)
\(618\) 12.5826 + 14.2831i 0.0203602 + 0.0231118i
\(619\) 68.8977 + 212.045i 0.111305 + 0.342561i 0.991158 0.132684i \(-0.0423595\pi\)
−0.879854 + 0.475245i \(0.842359\pi\)
\(620\) −102.270 + 844.476i −0.164951 + 1.36206i
\(621\) 304.170 + 1051.44i 0.489807 + 1.69314i
\(622\) 10.1646 31.2833i 0.0163418 0.0502948i
\(623\) −360.799 496.597i −0.579131 0.797105i
\(624\) 24.7399 21.7945i 0.0396473 0.0349270i
\(625\) 553.773 + 289.759i 0.886037 + 0.463615i
\(626\) 2.05426i 0.00328156i
\(627\) 50.3296 + 11.2701i 0.0802705 + 0.0179747i
\(628\) −11.5740 + 35.6210i −0.0184299 + 0.0567213i
\(629\) 0.366892 + 0.119210i 0.000583294 + 0.000189524i
\(630\) −11.4815 + 45.5458i −0.0182246 + 0.0722949i
\(631\) 49.2832 + 151.678i 0.0781034 + 0.240377i 0.982483 0.186351i \(-0.0596661\pi\)
−0.904380 + 0.426728i \(0.859666\pi\)
\(632\) 25.7258i 0.0407053i
\(633\) −890.732 527.235i −1.40716 0.832914i
\(634\) 14.9299 + 10.8472i 0.0235487 + 0.0171091i
\(635\) −201.753 362.556i −0.317722 0.570955i
\(636\) 487.320 + 109.124i 0.766227 + 0.171578i
\(637\) 10.1375 + 7.36535i 0.0159145 + 0.0115626i
\(638\) −2.49754 + 3.43757i −0.00391464 + 0.00538805i
\(639\) 501.756 275.345i 0.785220 0.430901i
\(640\) −68.0298 + 146.523i −0.106297 + 0.228942i
\(641\) −44.0798 + 60.6706i −0.0687672 + 0.0946500i −0.842015 0.539454i \(-0.818631\pi\)
0.773248 + 0.634104i \(0.218631\pi\)
\(642\) 56.3707 + 33.3665i 0.0878049 + 0.0519728i
\(643\) 453.671 0.705554 0.352777 0.935707i \(-0.385237\pi\)
0.352777 + 0.935707i \(0.385237\pi\)
\(644\) −1257.40 + 408.555i −1.95249 + 0.634403i
\(645\) −647.834 + 191.566i −1.00439 + 0.297001i
\(646\) −8.12663 + 25.0112i −0.0125799 + 0.0387170i
\(647\) 358.234 + 116.397i 0.553685 + 0.179903i 0.572478 0.819920i \(-0.305982\pi\)
−0.0187928 + 0.999823i \(0.505982\pi\)
\(648\) 30.2359 + 76.7081i 0.0466604 + 0.118377i
\(649\) −115.068 −0.177301
\(650\) −0.529083 + 2.15237i −0.000813974 + 0.00331134i
\(651\) −787.017 + 693.316i −1.20893 + 1.06500i
\(652\) 404.712 294.041i 0.620724 0.450982i
\(653\) −42.5450 13.8237i −0.0651531 0.0211695i 0.276259 0.961083i \(-0.410905\pi\)
−0.341412 + 0.939914i \(0.610905\pi\)
\(654\) 25.8960 11.1945i 0.0395964 0.0171170i
\(655\) −34.2027 174.416i −0.0522179 0.266284i
\(656\) −661.747 + 215.015i −1.00876 + 0.327766i
\(657\) 121.892 959.001i 0.185527 1.45967i
\(658\) −11.8179 36.3718i −0.0179604 0.0552763i
\(659\) −542.582 + 746.801i −0.823342 + 1.13323i 0.165784 + 0.986162i \(0.446985\pi\)
−0.989126 + 0.147071i \(0.953015\pi\)
\(660\) −49.3546 + 33.8863i −0.0747796 + 0.0513428i
\(661\) −345.897 + 251.309i −0.523293 + 0.380195i −0.817843 0.575441i \(-0.804830\pi\)
0.294550 + 0.955636i \(0.404830\pi\)
\(662\) −2.45294 + 3.37618i −0.00370535 + 0.00509997i
\(663\) 2.35021 + 24.9640i 0.00354481 + 0.0376531i
\(664\) −85.5809 + 62.1781i −0.128887 + 0.0936418i
\(665\) 689.281 135.167i 1.03651 0.203259i
\(666\) 0.0268275 + 0.0252312i 4.02816e−5 + 3.78846e-5i
\(667\) 416.705 + 1282.49i 0.624745 + 1.92277i
\(668\) 345.964i 0.517910i
\(669\) 228.219 + 135.086i 0.341134 + 0.201922i
\(670\) 34.2102 + 31.7958i 0.0510600 + 0.0474564i
\(671\) 28.9506 + 9.40661i 0.0431454 + 0.0140188i
\(672\) −137.220 + 59.3184i −0.204196 + 0.0882714i
\(673\) 28.7515 20.8892i 0.0427214 0.0310389i −0.566220 0.824254i \(-0.691595\pi\)
0.608941 + 0.793215i \(0.291595\pi\)
\(674\) 29.3847i 0.0435975i
\(675\) 561.728 + 374.282i 0.832189 + 0.554492i
\(676\) −671.326 −0.993087
\(677\) 391.613 + 539.009i 0.578454 + 0.796173i 0.993525 0.113616i \(-0.0362433\pi\)
−0.415071 + 0.909789i \(0.636243\pi\)
\(678\) −3.38164 7.82267i −0.00498767 0.0115379i
\(679\) 208.539 641.816i 0.307126 0.945237i
\(680\) −29.7478 53.4575i −0.0437467 0.0786140i
\(681\) 358.838 606.235i 0.526927 0.890212i
\(682\) 5.45517 0.00799878
\(683\) −58.9497 + 19.1539i −0.0863100 + 0.0280438i −0.351854 0.936055i \(-0.614449\pi\)
0.265544 + 0.964099i \(0.414449\pi\)
\(684\) 421.507 448.175i 0.616238 0.655227i
\(685\) −280.170 260.397i −0.409008 0.380142i
\(686\) 19.0067 + 26.1605i 0.0277065 + 0.0381348i
\(687\) 551.715 51.9406i 0.803078 0.0756049i
\(688\) −575.881 418.402i −0.837036 0.608142i
\(689\) 17.0786 + 23.5066i 0.0247875 + 0.0341170i
\(690\) 2.06599 77.5033i 0.00299418 0.112324i
\(691\) −704.680 511.980i −1.01980 0.740926i −0.0535564 0.998565i \(-0.517056\pi\)
−0.966241 + 0.257638i \(0.917056\pi\)
\(692\) 761.276 247.354i 1.10011 0.357447i
\(693\) −73.2280 9.30747i −0.105668 0.0134307i
\(694\) 2.48323 + 7.64261i 0.00357815 + 0.0110124i
\(695\) −606.195 1089.35i −0.872223 1.56741i
\(696\) 40.3071 + 93.2416i 0.0579125 + 0.133968i
\(697\) 163.520 503.262i 0.234605 0.722040i
\(698\) 4.06624 + 5.59669i 0.00582555 + 0.00801818i
\(699\) −558.111 633.539i −0.798442 0.906350i
\(700\) −429.770 + 692.869i −0.613956 + 0.989813i
\(701\) 1025.22i 1.46251i −0.682104 0.731255i \(-0.738935\pi\)
0.682104 0.731255i \(-0.261065\pi\)
\(702\) −0.813427 + 2.25131i −0.00115873 + 0.00320700i
\(703\) 0.170188 0.523784i 0.000242088 0.000745069i
\(704\) −59.4994 19.3325i −0.0845162 0.0274610i
\(705\) −549.391 14.6450i −0.779278 0.0207730i
\(706\) −3.93589 12.1134i −0.00557491 0.0171578i
\(707\) 707.745i 1.00105i
\(708\) −699.182 + 1181.23i −0.987545 + 1.66840i
\(709\) −957.859 695.925i −1.35100 0.981559i −0.998961 0.0455733i \(-0.985489\pi\)
−0.352039 0.935985i \(-0.614511\pi\)
\(710\) −39.7831 + 7.80141i −0.0560325 + 0.0109879i
\(711\) 109.425 + 199.403i 0.153903 + 0.280454i
\(712\) 61.7471 + 44.8619i 0.0867234 + 0.0630083i
\(713\) 1017.60 1400.61i 1.42722 1.96439i
\(714\) 8.22466 36.7294i 0.0115191 0.0514417i
\(715\) −3.45800 0.418780i −0.00483637 0.000585707i
\(716\) 53.0183 72.9735i 0.0740479 0.101918i
\(717\) 294.671 497.829i 0.410978 0.694322i
\(718\) −44.9173 −0.0625589
\(719\) −927.942 + 301.507i −1.29060 + 0.419342i −0.872302 0.488968i \(-0.837374\pi\)
−0.418299 + 0.908309i \(0.637374\pi\)
\(720\) 47.7708 + 709.627i 0.0663484 + 0.985594i
\(721\) −125.895 + 387.464i −0.174611 + 0.537397i
\(722\) −8.06816 2.62151i −0.0111747 0.00363089i
\(723\) 62.2965 278.201i 0.0861639 0.384788i
\(724\) −231.042 −0.319119
\(725\) 706.690 + 438.343i 0.974745 + 0.604611i
\(726\) −30.3402 34.4406i −0.0417909 0.0474388i
\(727\) 667.894 485.253i 0.918699 0.667474i −0.0245011 0.999700i \(-0.507800\pi\)
0.943200 + 0.332226i \(0.107800\pi\)
\(728\) −5.51104 1.79065i −0.00757011 0.00245968i
\(729\) 560.642 + 465.963i 0.769056 + 0.639182i
\(730\) −28.8363 + 62.1079i −0.0395018 + 0.0850793i
\(731\) 514.853 167.286i 0.704314 0.228845i
\(732\) 272.473 240.033i 0.372231 0.327914i
\(733\) −176.209 542.314i −0.240394 0.739855i −0.996360 0.0852450i \(-0.972833\pi\)
0.755966 0.654610i \(-0.227167\pi\)
\(734\) −6.76730 + 9.31439i −0.00921976 + 0.0126899i
\(735\) −259.213 + 76.6498i −0.352671 + 0.104285i
\(736\) 199.629 145.039i 0.271236 0.197064i
\(737\) −43.1427 + 59.3809i −0.0585383 + 0.0805711i
\(738\) 34.6094 36.7991i 0.0468961 0.0498632i
\(739\) 373.051 271.037i 0.504805 0.366762i −0.306045 0.952017i \(-0.599006\pi\)
0.810849 + 0.585255i \(0.199006\pi\)
\(740\) 0.310854 + 0.558613i 0.000420073 + 0.000754883i
\(741\) 35.6392 3.35521i 0.0480960 0.00452795i
\(742\) −13.4779 41.4807i −0.0181643 0.0559039i
\(743\) 332.881i 0.448023i 0.974586 + 0.224012i \(0.0719153\pi\)
−0.974586 + 0.224012i \(0.928085\pi\)
\(744\) 66.4290 112.228i 0.0892863 0.150844i
\(745\) −940.592 113.910i −1.26254 0.152899i
\(746\) −37.3841 12.1468i −0.0501127 0.0162826i
\(747\) −398.870 + 845.970i −0.533962 + 1.13249i
\(748\) 38.8116 28.1983i 0.0518872 0.0376983i
\(749\) 1402.01i 1.87184i
\(750\) −29.8701 37.3338i −0.0398268 0.0497783i
\(751\) 962.325 1.28139 0.640695 0.767795i \(-0.278646\pi\)
0.640695 + 0.767795i \(0.278646\pi\)
\(752\) −340.379 468.492i −0.452632 0.622994i
\(753\) −667.801 + 288.681i −0.886853 + 0.383375i
\(754\) −0.911323 + 2.80477i −0.00120865 + 0.00371985i
\(755\) −107.753 + 889.752i −0.142719 + 1.17848i
\(756\) −540.496 + 695.163i −0.714941 + 0.919527i
\(757\) −935.169 −1.23536 −0.617681 0.786429i \(-0.711928\pi\)
−0.617681 + 0.786429i \(0.711928\pi\)
\(758\) −16.2371 + 5.27575i −0.0214210 + 0.00696009i
\(759\) 121.308 11.4204i 0.159826 0.0150466i
\(760\) −76.3172 + 42.4686i −0.100417 + 0.0558798i
\(761\) 5.34144 + 7.35186i 0.00701898 + 0.00966079i 0.812512 0.582944i \(-0.198099\pi\)
−0.805493 + 0.592605i \(0.798099\pi\)
\(762\) 2.97504 + 31.6010i 0.00390425 + 0.0414711i
\(763\) 488.501 + 354.917i 0.640237 + 0.465160i
\(764\) −417.738 574.967i −0.546778 0.752575i
\(765\) −457.961 287.822i −0.598642 0.376238i
\(766\) −13.2276 9.61039i −0.0172684 0.0125462i
\(767\) −75.9552 + 24.6794i −0.0990290 + 0.0321765i
\(768\) −553.001 + 487.162i −0.720053 + 0.634325i
\(769\) −47.8987 147.417i −0.0622870 0.191700i 0.915071 0.403293i \(-0.132135\pi\)
−0.977358 + 0.211594i \(0.932135\pi\)
\(770\) 4.74247 + 2.20190i 0.00615906 + 0.00285961i
\(771\) −149.425 + 64.5945i −0.193807 + 0.0837802i
\(772\) −184.403 + 567.535i −0.238864 + 0.735149i
\(773\) 710.654 + 978.131i 0.919345 + 1.26537i 0.963873 + 0.266361i \(0.0858215\pi\)
−0.0445284 + 0.999008i \(0.514179\pi\)
\(774\) 51.2682 + 6.51632i 0.0662379 + 0.00841902i
\(775\) −78.0009 1064.79i −0.100646 1.37393i
\(776\) 83.9106i 0.108132i
\(777\) −0.172241 + 0.769185i −0.000221674 + 0.000989942i
\(778\) 20.1574 62.0380i 0.0259092 0.0797404i
\(779\) −718.469 233.445i −0.922297 0.299672i
\(780\) −25.3106 + 32.9533i −0.0324495 + 0.0422478i
\(781\) −19.6882 60.5939i −0.0252089 0.0775850i
\(782\) 62.1277i 0.0794472i
\(783\) 709.030 + 551.278i 0.905530 + 0.704058i
\(784\) −230.423 167.412i −0.293907 0.213536i
\(785\) 5.65167 46.6677i 0.00719958 0.0594493i
\(786\) −2.97113 + 13.2683i −0.00378006 + 0.0168808i
\(787\) 386.532 + 280.832i 0.491147 + 0.356839i 0.805625 0.592426i \(-0.201830\pi\)
−0.314478 + 0.949265i \(0.601830\pi\)
\(788\) 590.283 812.455i 0.749090 1.03103i
\(789\) −2.21731 0.496513i −0.00281028 0.000629294i
\(790\) −3.10036 15.8102i −0.00392451 0.0200129i
\(791\) 107.213 147.566i 0.135541 0.186557i
\(792\) 9.01719 1.71301i 0.0113853 0.00216289i
\(793\) 21.1274 0.0266424
\(794\) −75.5421 + 24.5451i −0.0951412 + 0.0309132i
\(795\) −626.560 16.7021i −0.788126 0.0210089i
\(796\) 19.4206 59.7705i 0.0243978 0.0750886i
\(797\) −622.988 202.421i −0.781667 0.253979i −0.109115 0.994029i \(-0.534802\pi\)
−0.672552 + 0.740050i \(0.734802\pi\)
\(798\) −52.4357 11.7417i −0.0657089 0.0147139i
\(799\) 440.399 0.551188
\(800\) 36.3247 147.773i 0.0454058 0.184716i
\(801\) 669.429 + 85.0862i 0.835742 + 0.106225i
\(802\) 16.2673 11.8189i 0.0202835 0.0147368i
\(803\) −102.347 33.2544i −0.127455 0.0414127i
\(804\) 347.425 + 803.691i 0.432121 + 0.999616i
\(805\) 1450.00 806.887i 1.80124 1.00234i
\(806\) 3.60089 1.17000i 0.00446761 0.00145161i
\(807\) 289.788 + 328.952i 0.359092 + 0.407623i
\(808\) 27.1939 + 83.6943i 0.0336558 + 0.103582i
\(809\) 748.911 1030.79i 0.925725 1.27415i −0.0357792 0.999360i \(-0.511391\pi\)
0.961504 0.274791i \(-0.0886087\pi\)
\(810\) −27.8266 43.4984i −0.0343538 0.0537018i
\(811\) 471.255 342.387i 0.581079 0.422179i −0.258034 0.966136i \(-0.583075\pi\)
0.839113 + 0.543957i \(0.183075\pi\)
\(812\) −637.658 + 877.661i −0.785293 + 1.08086i
\(813\) −749.437 + 70.5549i −0.921816 + 0.0867834i
\(814\) 0.00331671 0.00240973i 4.07459e−6 2.96036e-6i
\(815\) −427.443 + 459.900i −0.524470 + 0.564295i
\(816\) −53.4194 567.423i −0.0654650 0.695371i
\(817\) −238.822 735.017i −0.292315 0.899654i
\(818\) 46.5911i 0.0569574i
\(819\) −50.3332 + 9.56187i −0.0614569 + 0.0116751i
\(820\) 766.244 426.396i 0.934444 0.519995i
\(821\) −890.226 289.252i −1.08432 0.352317i −0.288270 0.957549i \(-0.593080\pi\)
−0.796049 + 0.605232i \(0.793080\pi\)
\(822\) 11.6107 + 26.8587i 0.0141249 + 0.0326748i
\(823\) −191.282 + 138.975i −0.232420 + 0.168863i −0.697900 0.716195i \(-0.745882\pi\)
0.465479 + 0.885059i \(0.345882\pi\)
\(824\) 50.6567i 0.0614766i
\(825\) 52.6029 53.6561i 0.0637611 0.0650377i
\(826\) 119.883 0.145137
\(827\) 730.892 + 1005.99i 0.883787 + 1.21643i 0.975357 + 0.220630i \(0.0708115\pi\)
−0.0915700 + 0.995799i \(0.529189\pi\)
\(828\) 619.859 1314.67i 0.748622 1.58777i
\(829\) −97.7673 + 300.897i −0.117934 + 0.362963i −0.992548 0.121857i \(-0.961115\pi\)
0.874614 + 0.484820i \(0.161115\pi\)
\(830\) 45.1018 48.5265i 0.0543395 0.0584657i
\(831\) 903.518 + 534.803i 1.08727 + 0.643566i
\(832\) −43.4212 −0.0521890
\(833\) 206.004 66.9349i 0.247304 0.0803540i
\(834\) 8.93891 + 94.9494i 0.0107181 + 0.113848i
\(835\) 83.5585 + 426.104i 0.100070 + 0.510304i
\(836\) −40.2566 55.4084i −0.0481538 0.0662780i
\(837\) 37.5341 1152.45i 0.0448436 1.37688i
\(838\) −52.1419 37.8833i −0.0622218 0.0452068i
\(839\) 740.227 + 1018.83i 0.882273 + 1.21434i 0.975786 + 0.218726i \(0.0701902\pi\)
−0.0935133 + 0.995618i \(0.529810\pi\)
\(840\) 103.050 70.7526i 0.122678 0.0842293i
\(841\) 214.785 + 156.051i 0.255393 + 0.185554i
\(842\) −53.8790 + 17.5063i −0.0639893 + 0.0207914i
\(843\) 553.103 + 627.853i 0.656112 + 0.744784i
\(844\) 424.741 + 1307.22i 0.503248 + 1.54884i
\(845\) 826.835 162.141i 0.978502 0.191883i
\(846\) 38.0283 + 17.9301i 0.0449507 + 0.0211940i
\(847\) 303.567 934.282i 0.358402 1.10305i
\(848\) −388.190 534.298i −0.457771 0.630068i
\(849\) −155.472 + 136.962i −0.183124 + 0.161321i
\(850\) 24.7245 + 29.2682i 0.0290876 + 0.0344331i
\(851\) 1.30108i 0.00152888i
\(852\) −741.653 166.075i −0.870484 0.194924i
\(853\) 19.0181 58.5318i 0.0222956 0.0686187i −0.939290 0.343125i \(-0.888514\pi\)
0.961585 + 0.274507i \(0.0885145\pi\)
\(854\) −30.1620 9.80024i −0.0353185 0.0114757i
\(855\) −410.901 + 653.796i −0.480586 + 0.764674i
\(856\) −53.8699 165.794i −0.0629321 0.193685i
\(857\) 1119.52i 1.30632i 0.757219 + 0.653161i \(0.226558\pi\)
−0.757219 + 0.653161i \(0.773442\pi\)
\(858\) 0.229310 + 0.135732i 0.000267262 + 0.000158195i
\(859\) 549.156 + 398.985i 0.639297 + 0.464477i 0.859609 0.510953i \(-0.170707\pi\)
−0.220312 + 0.975430i \(0.570707\pi\)
\(860\) 813.667 + 377.781i 0.946125 + 0.439280i
\(861\) 1055.08 + 236.261i 1.22542 + 0.274403i
\(862\) 15.1911 + 11.0370i 0.0176231 + 0.0128039i
\(863\) −611.305 + 841.389i −0.708349 + 0.974958i 0.291483 + 0.956576i \(0.405851\pi\)
−0.999831 + 0.0183819i \(0.994149\pi\)
\(864\) 55.8465 154.566i 0.0646372 0.178896i
\(865\) −877.879 + 488.518i −1.01489 + 0.564760i
\(866\) 23.6588 32.5636i 0.0273196 0.0376023i
\(867\) −373.102 220.844i −0.430337 0.254722i
\(868\) 1392.78 1.60459
\(869\) 24.0807 7.82428i 0.0277108 0.00900378i
\(870\) −36.0085 52.4456i −0.0413891 0.0602823i
\(871\) −15.7423 + 48.4497i −0.0180738 + 0.0556254i
\(872\) −71.4047 23.2008i −0.0818862 0.0266064i
\(873\) 356.916 + 650.400i 0.408839 + 0.745017i
\(874\) 88.6950 0.101482
\(875\) 361.978 957.167i 0.413690 1.09390i
\(876\) −963.253 + 848.570i −1.09960 + 0.968688i
\(877\) −1145.78 + 832.455i −1.30647 + 0.949207i −0.999996 0.00267117i \(-0.999150\pi\)
−0.306475 + 0.951879i \(0.599150\pi\)
\(878\) −94.4738 30.6964i −0.107601 0.0349617i
\(879\) 298.553 129.061i 0.339651 0.146827i
\(880\) 78.5993 + 9.51874i 0.0893174 + 0.0108167i
\(881\) −1347.76 + 437.914i −1.52981 + 0.497065i −0.948543 0.316649i \(-0.897442\pi\)
−0.581265 + 0.813714i \(0.697442\pi\)
\(882\) 20.5135 + 2.60733i 0.0232580 + 0.00295615i
\(883\) −146.773 451.720i −0.166221 0.511575i 0.832903 0.553418i \(-0.186677\pi\)
−0.999124 + 0.0418436i \(0.986677\pi\)
\(884\) 19.5713 26.9375i 0.0221394 0.0304723i
\(885\) 575.848 1623.72i 0.650676 1.83471i
\(886\) −21.7722 + 15.8184i −0.0245735 + 0.0178537i
\(887\) −94.8558 + 130.558i −0.106940 + 0.147190i −0.859133 0.511753i \(-0.828996\pi\)
0.752193 + 0.658943i \(0.228996\pi\)
\(888\) −0.00918637 0.0975779i −1.03450e−5 0.000109885i
\(889\) −549.600 + 399.308i −0.618223 + 0.449165i
\(890\) −43.3543 20.1291i −0.0487127 0.0226170i
\(891\) 62.6068 51.6326i 0.0702658 0.0579490i
\(892\) −108.825 334.929i −0.122001 0.375481i
\(893\) 628.725i 0.704059i
\(894\) 62.3734 + 36.9196i 0.0697689 + 0.0412971i
\(895\) −47.6748 + 102.682i −0.0532680 + 0.114729i
\(896\) 251.557 + 81.7358i 0.280755 + 0.0912230i
\(897\) 77.6245 33.5561i 0.0865379 0.0374092i
\(898\) −77.4013 + 56.2353i −0.0861930 + 0.0626229i
\(899\) 1420.56i 1.58016i
\(900\) −231.176 866.018i −0.256862 0.962242i
\(901\) 502.259 0.557447
\(902\) −3.30541 4.54951i −0.00366453 0.00504380i
\(903\) 438.905 + 1015.31i 0.486052 + 1.12437i
\(904\) −7.00849 + 21.5699i −0.00775276 + 0.0238605i
\(905\) 284.561 55.8021i 0.314432 0.0616597i
\(906\) 34.9241 59.0021i 0.0385475 0.0651237i
\(907\) −186.575 −0.205705 −0.102853 0.994697i \(-0.532797\pi\)
−0.102853 + 0.994697i \(0.532797\pi\)
\(908\) −889.697 + 289.080i −0.979842 + 0.318370i
\(909\) 566.779 + 533.053i 0.623519 + 0.586417i
\(910\) 3.60271 + 0.436304i 0.00395902 + 0.000479455i
\(911\) −249.309 343.145i −0.273666 0.376668i 0.649957 0.759971i \(-0.274787\pi\)
−0.923623 + 0.383302i \(0.874787\pi\)
\(912\) −810.067 + 76.2628i −0.888231 + 0.0836215i
\(913\) 84.2307 + 61.1972i 0.0922571 + 0.0670287i
\(914\) 59.0126 + 81.2239i 0.0645652 + 0.0888664i
\(915\) −277.616 + 361.444i −0.303406 + 0.395021i
\(916\) −595.331 432.533i −0.649925 0.472198i
\(917\) −276.770 + 89.9282i −0.301822 + 0.0980678i
\(918\) 23.2191 + 34.2500i 0.0252932 + 0.0373093i
\(919\) 5.50213 + 16.9338i 0.00598709 + 0.0184264i 0.954005 0.299789i \(-0.0969164\pi\)
−0.948018 + 0.318216i \(0.896916\pi\)
\(920\) −140.466 + 151.132i −0.152680 + 0.164274i
\(921\) −486.124 1124.54i −0.527822 1.22100i
\(922\) −15.4034 + 47.4067i −0.0167065 + 0.0514172i
\(923\) −25.9919 35.7747i −0.0281602 0.0387592i
\(924\) 64.7957 + 73.5527i 0.0701252 + 0.0796025i
\(925\) −0.517780 0.612933i −0.000559762 0.000662631i
\(926\) 7.32153i 0.00790662i
\(927\) −215.470 392.646i −0.232438 0.423566i
\(928\) 62.5677 192.563i 0.0674221 0.207504i
\(929\) 71.9207 + 23.3685i 0.0774173 + 0.0251544i 0.347470 0.937691i \(-0.387041\pi\)
−0.270052 + 0.962846i \(0.587041\pi\)
\(930\) −27.2999 + 76.9773i −0.0293547 + 0.0827713i
\(931\) −95.5579 294.097i −0.102640 0.315894i
\(932\) 1121.17i 1.20297i
\(933\) −394.231 + 666.029i −0.422541 + 0.713857i
\(934\) −73.3264 53.2748i −0.0785079 0.0570394i
\(935\) −40.9915 + 44.1041i −0.0438412 + 0.0471702i
\(936\) 5.58475 3.06471i 0.00596661 0.00327426i
\(937\) −183.717 133.478i −0.196069 0.142453i 0.485419 0.874282i \(-0.338667\pi\)
−0.681488 + 0.731829i \(0.738667\pi\)
\(938\) 44.9481 61.8657i 0.0479191 0.0659549i
\(939\) −10.5620 + 47.1673i −0.0112481 + 0.0502315i
\(940\) 534.568 + 496.841i 0.568689 + 0.528554i
\(941\) 597.760 822.746i 0.635239 0.874331i −0.363112 0.931746i \(-0.618286\pi\)
0.998350 + 0.0574144i \(0.0182856\pi\)
\(942\) −1.83177 + 3.09467i −0.00194456 + 0.00328521i
\(943\) −1784.67 −1.89255
\(944\) 1726.44 560.954i 1.82885 0.594231i
\(945\) 497.799 986.735i 0.526772 1.04416i
\(946\) 1.77778 5.47145i 0.00187926 0.00578377i
\(947\) 557.864 + 181.261i 0.589086 + 0.191406i 0.588367 0.808594i \(-0.299771\pi\)
0.000718908 1.00000i \(0.499771\pi\)
\(948\) 66.0001 294.741i 0.0696204 0.310908i
\(949\) −74.6901 −0.0787040
\(950\) 41.7839 35.2973i 0.0439831 0.0371550i
\(951\) −287.031 325.823i −0.301820 0.342611i
\(952\) −81.0365 + 58.8764i −0.0851223 + 0.0618450i
\(953\) 671.032 + 218.032i 0.704126 + 0.228784i 0.639127 0.769101i \(-0.279296\pi\)
0.0649987 + 0.997885i \(0.479296\pi\)
\(954\) 43.3699 + 20.4487i 0.0454611 + 0.0214347i
\(955\) 653.372 + 607.261i 0.684159 + 0.635875i
\(956\) −730.603 + 237.387i −0.764229 + 0.248313i
\(957\) 75.0199 66.0882i 0.0783907 0.0690577i
\(958\) −8.27663 25.4728i −0.00863949 0.0265896i
\(959\) −368.111 + 506.661i −0.383848 + 0.528322i
\(960\) 570.558 742.842i 0.594332 0.773794i
\(961\) −698.012 + 507.135i −0.726339 + 0.527716i
\(962\) 0.00167250 0.00230199i 1.73856e−6 2.39292e-6i
\(963\) −1122.76 1055.95i −1.16590 1.09652i
\(964\) −306.275 + 222.522i −0.317712 + 0.230832i
\(965\) 90.0459 743.538i 0.0933118 0.770506i
\(966\) −126.384 + 11.8983i −0.130832 + 0.0123171i
\(967\) −72.7038 223.759i −0.0751849 0.231395i 0.906400 0.422419i \(-0.138819\pi\)
−0.981585 + 0.191024i \(0.938819\pi\)
\(968\) 122.147i 0.126185i
\(969\) 315.189 532.494i 0.325273 0.549529i
\(970\) −10.1126 51.5688i −0.0104253 0.0531637i
\(971\) −1108.13 360.055i −1.14123 0.370808i −0.323397 0.946263i \(-0.604825\pi\)
−0.817833 + 0.575455i \(0.804825\pi\)
\(972\) −149.617 956.418i −0.153927 0.983969i
\(973\) −1651.35 + 1199.77i −1.69717 + 1.23307i
\(974\) 44.0586i 0.0452347i
\(975\) 23.2146 46.6998i 0.0238099 0.0478972i
\(976\) −480.219 −0.492028
\(977\) −535.926 737.639i −0.548543 0.755004i 0.441271 0.897374i \(-0.354528\pi\)
−0.989814 + 0.142370i \(0.954528\pi\)
\(978\) 44.0886 19.0589i 0.0450804 0.0194877i
\(979\) 23.2132 71.4429i 0.0237111 0.0729754i
\(980\) 325.567 + 151.159i 0.332211 + 0.154243i
\(981\) −652.151 + 123.890i −0.664781 + 0.126290i
\(982\) 20.5691 0.0209461
\(983\) 1260.21 409.466i 1.28200 0.416547i 0.412715 0.910860i \(-0.364580\pi\)
0.869284 + 0.494313i \(0.164580\pi\)
\(984\) −133.847 + 12.6009i −0.136023 + 0.0128057i
\(985\) −530.791 + 1143.22i −0.538874 + 1.16063i
\(986\) 29.9643 + 41.2424i 0.0303898 + 0.0418279i
\(987\) 84.3424 + 895.888i 0.0854533 + 0.907688i
\(988\) −38.4566 27.9404i −0.0389237 0.0282797i
\(989\) −1073.17 1477.09i −1.08510 1.49351i
\(990\) −5.33523 + 2.13948i −0.00538912 + 0.00216109i
\(991\) 67.0319 + 48.7016i 0.0676407 + 0.0491438i 0.621092 0.783738i \(-0.286689\pi\)
−0.553451 + 0.832882i \(0.686689\pi\)
\(992\) −247.222 + 80.3274i −0.249216 + 0.0809752i
\(993\) 73.6801 64.9080i 0.0741995 0.0653655i
\(994\) 20.5120 + 63.1295i 0.0206358 + 0.0635106i
\(995\) −9.48327 + 78.3065i −0.00953093 + 0.0787000i
\(996\) 1140.02 492.816i 1.14460 0.494796i
\(997\) −239.774 + 737.949i −0.240496 + 0.740169i 0.755849 + 0.654746i \(0.227224\pi\)
−0.996345 + 0.0854235i \(0.972776\pi\)
\(998\) 50.1921 + 69.0834i 0.0502926 + 0.0692219i
\(999\) −0.486255 0.717262i −0.000486741 0.000717980i
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 75.3.j.a.11.9 72
3.2 odd 2 inner 75.3.j.a.11.10 yes 72
5.2 odd 4 375.3.h.b.74.20 144
5.3 odd 4 375.3.h.b.74.17 144
5.4 even 2 375.3.j.a.176.10 72
15.2 even 4 375.3.h.b.74.18 144
15.8 even 4 375.3.h.b.74.19 144
15.14 odd 2 375.3.j.a.176.9 72
25.9 even 10 375.3.j.a.326.9 72
25.12 odd 20 375.3.h.b.299.19 144
25.13 odd 20 375.3.h.b.299.18 144
25.16 even 5 inner 75.3.j.a.41.10 yes 72
75.38 even 20 375.3.h.b.299.20 144
75.41 odd 10 inner 75.3.j.a.41.9 yes 72
75.59 odd 10 375.3.j.a.326.10 72
75.62 even 20 375.3.h.b.299.17 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.3.j.a.11.9 72 1.1 even 1 trivial
75.3.j.a.11.10 yes 72 3.2 odd 2 inner
75.3.j.a.41.9 yes 72 75.41 odd 10 inner
75.3.j.a.41.10 yes 72 25.16 even 5 inner
375.3.h.b.74.17 144 5.3 odd 4
375.3.h.b.74.18 144 15.2 even 4
375.3.h.b.74.19 144 15.8 even 4
375.3.h.b.74.20 144 5.2 odd 4
375.3.h.b.299.17 144 75.62 even 20
375.3.h.b.299.18 144 25.13 odd 20
375.3.h.b.299.19 144 25.12 odd 20
375.3.h.b.299.20 144 75.38 even 20
375.3.j.a.176.9 72 15.14 odd 2
375.3.j.a.176.10 72 5.4 even 2
375.3.j.a.326.9 72 25.9 even 10
375.3.j.a.326.10 72 75.59 odd 10