Properties

Label 76.3.g.c.11.10
Level $76$
Weight $3$
Character 76.11
Analytic conductor $2.071$
Analytic rank $0$
Dimension $28$
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] = [76,3,Mod(7,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.10
Character \(\chi\) \(=\) 76.11
Dual form 76.3.g.c.7.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.789173 - 1.83772i) q^{2} +(-3.65809 - 2.11200i) q^{3} +(-2.75441 - 2.90055i) q^{4} +(-1.06722 + 1.84849i) q^{5} +(-6.76812 + 5.05580i) q^{6} +1.82388i q^{7} +(-7.50411 + 2.77279i) q^{8} +(4.42107 + 7.65753i) q^{9} +O(q^{10})\) \(q+(0.789173 - 1.83772i) q^{2} +(-3.65809 - 2.11200i) q^{3} +(-2.75441 - 2.90055i) q^{4} +(-1.06722 + 1.84849i) q^{5} +(-6.76812 + 5.05580i) q^{6} +1.82388i q^{7} +(-7.50411 + 2.77279i) q^{8} +(4.42107 + 7.65753i) q^{9} +(2.55477 + 3.42003i) q^{10} -13.8522i q^{11} +(3.94991 + 16.4278i) q^{12} +(-9.95291 - 17.2389i) q^{13} +(3.35178 + 1.43936i) q^{14} +(7.80801 - 4.50795i) q^{15} +(-0.826437 + 15.9786i) q^{16} +(3.83013 - 6.63399i) q^{17} +(17.5614 - 2.08157i) q^{18} +(16.7080 - 9.04663i) q^{19} +(8.30122 - 1.99595i) q^{20} +(3.85204 - 6.67193i) q^{21} +(-25.4565 - 10.9318i) q^{22} +(-9.14824 + 5.28174i) q^{23} +(33.3068 + 5.70555i) q^{24} +(10.2221 + 17.7051i) q^{25} +(-39.5349 + 4.68612i) q^{26} +0.666761i q^{27} +(5.29027 - 5.02372i) q^{28} +(-0.0147659 - 0.0255754i) q^{29} +(-2.12248 - 17.9065i) q^{30} -42.2313i q^{31} +(28.7120 + 14.1287i) q^{32} +(-29.2559 + 50.6727i) q^{33} +(-9.16876 - 12.2741i) q^{34} +(-3.37143 - 1.94649i) q^{35} +(10.0336 - 33.9155i) q^{36} +19.5805 q^{37} +(-3.43961 - 37.8440i) q^{38} +84.0821i q^{39} +(2.88310 - 16.8304i) q^{40} +(15.7368 - 27.2570i) q^{41} +(-9.22119 - 12.3443i) q^{42} +(51.3500 + 29.6469i) q^{43} +(-40.1791 + 38.1547i) q^{44} -18.8731 q^{45} +(2.48680 + 20.9801i) q^{46} +(-77.5317 + 44.7629i) q^{47} +(36.7700 - 56.7059i) q^{48} +45.6735 q^{49} +(40.6040 - 4.81285i) q^{50} +(-28.0219 + 16.1785i) q^{51} +(-22.5881 + 76.3521i) q^{52} +(-29.8268 - 51.6616i) q^{53} +(1.22532 + 0.526190i) q^{54} +(25.6057 + 14.7834i) q^{55} +(-5.05724 - 13.6866i) q^{56} +(-80.2259 - 2.19398i) q^{57} +(-0.0586532 + 0.00695224i) q^{58} +(-63.9584 - 36.9264i) q^{59} +(-34.5820 - 10.2308i) q^{60} +(-23.6620 - 40.9837i) q^{61} +(-77.6093 - 33.3278i) q^{62} +(-13.9664 + 8.06352i) q^{63} +(48.6233 - 41.6146i) q^{64} +42.4880 q^{65} +(70.0341 + 93.7536i) q^{66} +(-5.77732 + 3.33554i) q^{67} +(-29.7920 + 7.16321i) q^{68} +44.6201 q^{69} +(-6.23774 + 4.65961i) q^{70} +(24.1399 + 13.9372i) q^{71} +(-54.4089 - 45.2042i) q^{72} +(-46.2611 + 80.1266i) q^{73} +(15.4524 - 35.9834i) q^{74} -86.3559i q^{75} +(-72.2610 - 23.5444i) q^{76} +25.2648 q^{77} +(154.519 + 66.3553i) q^{78} +(110.683 + 63.9027i) q^{79} +(-28.6543 - 18.5805i) q^{80} +(41.1979 - 71.3568i) q^{81} +(-37.6716 - 50.4304i) q^{82} -88.9093i q^{83} +(-29.9624 + 7.20418i) q^{84} +(8.17523 + 14.1599i) q^{85} +(95.0066 - 70.9702i) q^{86} +0.124743i q^{87} +(38.4093 + 103.949i) q^{88} +(31.2173 + 54.0700i) q^{89} +(-14.8942 + 34.6835i) q^{90} +(31.4418 - 18.1529i) q^{91} +(40.5180 + 11.9869i) q^{92} +(-89.1925 + 154.486i) q^{93} +(21.0757 + 177.807i) q^{94} +(-1.10865 + 40.5394i) q^{95} +(-75.1914 - 112.324i) q^{96} +(64.8024 - 112.241i) q^{97} +(36.0443 - 83.9349i) q^{98} +(106.074 - 61.2417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 5 q^{2} - 11 q^{4} + 6 q^{5} - 3 q^{6} - 62 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 5 q^{2} - 11 q^{4} + 6 q^{5} - 3 q^{6} - 62 q^{8} + 20 q^{9} + 26 q^{12} + 30 q^{13} - 30 q^{14} - 19 q^{16} + 38 q^{17} - 60 q^{18} - 44 q^{20} + 80 q^{21} + 45 q^{22} + 17 q^{24} - 16 q^{25} - 56 q^{26} + 54 q^{28} + 6 q^{29} + 96 q^{30} - 45 q^{32} - 176 q^{33} - 20 q^{34} + 30 q^{36} + 104 q^{37} - 258 q^{38} + 94 q^{40} - 2 q^{41} - 2 q^{42} + 201 q^{44} - 360 q^{45} + 164 q^{46} - 17 q^{48} - 20 q^{49} + 490 q^{50} - 102 q^{52} - 242 q^{53} - 13 q^{54} + 276 q^{56} - 254 q^{57} + 96 q^{58} + 10 q^{60} - 58 q^{61} - 36 q^{62} - 74 q^{64} - 260 q^{65} + 167 q^{66} + 396 q^{68} + 340 q^{69} + 60 q^{70} - 422 q^{72} - 82 q^{73} - 136 q^{74} + 123 q^{76} - 144 q^{77} + 224 q^{78} - 174 q^{80} + 410 q^{81} - 305 q^{82} + 252 q^{84} + 714 q^{85} + 166 q^{86} - 718 q^{88} + 150 q^{89} - 272 q^{90} - 588 q^{92} + 344 q^{93} - 488 q^{94} - 122 q^{96} + 94 q^{97} + 307 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.789173 1.83772i 0.394587 0.918859i
\(3\) −3.65809 2.11200i −1.21936 0.703999i −0.254581 0.967051i \(-0.581938\pi\)
−0.964782 + 0.263052i \(0.915271\pi\)
\(4\) −2.75441 2.90055i −0.688603 0.725139i
\(5\) −1.06722 + 1.84849i −0.213445 + 0.369698i −0.952790 0.303629i \(-0.901802\pi\)
0.739345 + 0.673326i \(0.235135\pi\)
\(6\) −6.76812 + 5.05580i −1.12802 + 0.842633i
\(7\) 1.82388i 0.260555i 0.991478 + 0.130277i \(0.0415868\pi\)
−0.991478 + 0.130277i \(0.958413\pi\)
\(8\) −7.50411 + 2.77279i −0.938014 + 0.346599i
\(9\) 4.42107 + 7.65753i 0.491231 + 0.850836i
\(10\) 2.55477 + 3.42003i 0.255477 + 0.342003i
\(11\) 13.8522i 1.25929i −0.776882 0.629647i \(-0.783200\pi\)
0.776882 0.629647i \(-0.216800\pi\)
\(12\) 3.94991 + 16.4278i 0.329159 + 1.36898i
\(13\) −9.95291 17.2389i −0.765608 1.32607i −0.939924 0.341383i \(-0.889105\pi\)
0.174316 0.984690i \(-0.444229\pi\)
\(14\) 3.35178 + 1.43936i 0.239413 + 0.102811i
\(15\) 7.80801 4.50795i 0.520534 0.300530i
\(16\) −0.826437 + 15.9786i −0.0516523 + 0.998665i
\(17\) 3.83013 6.63399i 0.225302 0.390235i −0.731108 0.682262i \(-0.760996\pi\)
0.956410 + 0.292027i \(0.0943298\pi\)
\(18\) 17.5614 2.08157i 0.975631 0.115643i
\(19\) 16.7080 9.04663i 0.879370 0.476138i
\(20\) 8.30122 1.99595i 0.415061 0.0997975i
\(21\) 3.85204 6.67193i 0.183430 0.317711i
\(22\) −25.4565 10.9318i −1.15711 0.496900i
\(23\) −9.14824 + 5.28174i −0.397749 + 0.229641i −0.685512 0.728061i \(-0.740422\pi\)
0.287763 + 0.957702i \(0.407088\pi\)
\(24\) 33.3068 + 5.70555i 1.38778 + 0.237731i
\(25\) 10.2221 + 17.7051i 0.408882 + 0.708205i
\(26\) −39.5349 + 4.68612i −1.52057 + 0.180235i
\(27\) 0.666761i 0.0246949i
\(28\) 5.29027 5.02372i 0.188938 0.179419i
\(29\) −0.0147659 0.0255754i −0.000509170 0.000881909i 0.865771 0.500441i \(-0.166829\pi\)
−0.866280 + 0.499559i \(0.833495\pi\)
\(30\) −2.12248 17.9065i −0.0707492 0.596882i
\(31\) 42.2313i 1.36230i −0.732143 0.681150i \(-0.761480\pi\)
0.732143 0.681150i \(-0.238520\pi\)
\(32\) 28.7120 + 14.1287i 0.897251 + 0.441521i
\(33\) −29.2559 + 50.6727i −0.886542 + 1.53554i
\(34\) −9.16876 12.2741i −0.269669 0.361002i
\(35\) −3.37143 1.94649i −0.0963264 0.0556141i
\(36\) 10.0336 33.9155i 0.278712 0.942098i
\(37\) 19.5805 0.529202 0.264601 0.964358i \(-0.414760\pi\)
0.264601 + 0.964358i \(0.414760\pi\)
\(38\) −3.43961 37.8440i −0.0905161 0.995895i
\(39\) 84.0821i 2.15595i
\(40\) 2.88310 16.8304i 0.0720776 0.420761i
\(41\) 15.7368 27.2570i 0.383825 0.664805i −0.607780 0.794105i \(-0.707940\pi\)
0.991605 + 0.129300i \(0.0412732\pi\)
\(42\) −9.22119 12.3443i −0.219552 0.293911i
\(43\) 51.3500 + 29.6469i 1.19418 + 0.689463i 0.959253 0.282549i \(-0.0911799\pi\)
0.234932 + 0.972012i \(0.424513\pi\)
\(44\) −40.1791 + 38.1547i −0.913162 + 0.867153i
\(45\) −18.8731 −0.419403
\(46\) 2.48680 + 20.9801i 0.0540608 + 0.456089i
\(47\) −77.5317 + 44.7629i −1.64961 + 0.952403i −0.672384 + 0.740202i \(0.734730\pi\)
−0.977226 + 0.212201i \(0.931937\pi\)
\(48\) 36.7700 56.7059i 0.766043 1.18137i
\(49\) 45.6735 0.932111
\(50\) 40.6040 4.81285i 0.812080 0.0962569i
\(51\) −28.0219 + 16.1785i −0.549450 + 0.317225i
\(52\) −22.5881 + 76.3521i −0.434387 + 1.46831i
\(53\) −29.8268 51.6616i −0.562770 0.974747i −0.997253 0.0740668i \(-0.976402\pi\)
0.434483 0.900680i \(-0.356931\pi\)
\(54\) 1.22532 + 0.526190i 0.0226911 + 0.00974426i
\(55\) 25.6057 + 14.7834i 0.465558 + 0.268790i
\(56\) −5.05724 13.6866i −0.0903079 0.244404i
\(57\) −80.2259 2.19398i −1.40747 0.0384909i
\(58\) −0.0586532 + 0.00695224i −0.00101126 + 0.000119866i
\(59\) −63.9584 36.9264i −1.08404 0.625871i −0.152057 0.988372i \(-0.548590\pi\)
−0.931984 + 0.362500i \(0.881923\pi\)
\(60\) −34.5820 10.2308i −0.576367 0.170513i
\(61\) −23.6620 40.9837i −0.387901 0.671864i 0.604266 0.796783i \(-0.293466\pi\)
−0.992167 + 0.124919i \(0.960133\pi\)
\(62\) −77.6093 33.3278i −1.25176 0.537546i
\(63\) −13.9664 + 8.06352i −0.221689 + 0.127992i
\(64\) 48.6233 41.6146i 0.759739 0.650229i
\(65\) 42.4880 0.653661
\(66\) 70.0341 + 93.7536i 1.06112 + 1.42051i
\(67\) −5.77732 + 3.33554i −0.0862287 + 0.0497842i −0.542494 0.840059i \(-0.682520\pi\)
0.456266 + 0.889844i \(0.349187\pi\)
\(68\) −29.7920 + 7.16321i −0.438118 + 0.105341i
\(69\) 44.6201 0.646668
\(70\) −6.23774 + 4.65961i −0.0891106 + 0.0665658i
\(71\) 24.1399 + 13.9372i 0.339999 + 0.196298i 0.660272 0.751027i \(-0.270441\pi\)
−0.320273 + 0.947325i \(0.603775\pi\)
\(72\) −54.4089 45.2042i −0.755680 0.627836i
\(73\) −46.2611 + 80.1266i −0.633714 + 1.09762i 0.353072 + 0.935596i \(0.385137\pi\)
−0.986786 + 0.162028i \(0.948196\pi\)
\(74\) 15.4524 35.9834i 0.208816 0.486262i
\(75\) 86.3559i 1.15141i
\(76\) −72.2610 23.5444i −0.950803 0.309795i
\(77\) 25.2648 0.328115
\(78\) 154.519 + 66.3553i 1.98101 + 0.850710i
\(79\) 110.683 + 63.9027i 1.40105 + 0.808895i 0.994500 0.104735i \(-0.0333994\pi\)
0.406547 + 0.913630i \(0.366733\pi\)
\(80\) −28.6543 18.5805i −0.358179 0.232256i
\(81\) 41.1979 71.3568i 0.508616 0.880948i
\(82\) −37.6716 50.4304i −0.459409 0.615004i
\(83\) 88.9093i 1.07120i −0.844473 0.535598i \(-0.820086\pi\)
0.844473 0.535598i \(-0.179914\pi\)
\(84\) −29.9624 + 7.20418i −0.356695 + 0.0857640i
\(85\) 8.17523 + 14.1599i 0.0961792 + 0.166587i
\(86\) 95.0066 70.9702i 1.10473 0.825234i
\(87\) 0.124743i 0.00143382i
\(88\) 38.4093 + 103.949i 0.436469 + 1.18123i
\(89\) 31.2173 + 54.0700i 0.350756 + 0.607528i 0.986382 0.164469i \(-0.0525912\pi\)
−0.635626 + 0.771997i \(0.719258\pi\)
\(90\) −14.8942 + 34.6835i −0.165491 + 0.385372i
\(91\) 31.4418 18.1529i 0.345514 0.199483i
\(92\) 40.5180 + 11.9869i 0.440413 + 0.130292i
\(93\) −89.1925 + 154.486i −0.959059 + 1.66114i
\(94\) 21.0757 + 177.807i 0.224210 + 1.89156i
\(95\) −1.10865 + 40.5394i −0.0116700 + 0.426730i
\(96\) −75.1914 112.324i −0.783244 1.17004i
\(97\) 64.8024 112.241i 0.668066 1.15712i −0.310378 0.950613i \(-0.600456\pi\)
0.978444 0.206511i \(-0.0662109\pi\)
\(98\) 36.0443 83.9349i 0.367799 0.856479i
\(99\) 106.074 61.2417i 1.07145 0.618603i
\(100\) 23.1989 78.4169i 0.231989 0.784169i
\(101\) 45.6483 + 79.0651i 0.451963 + 0.782823i 0.998508 0.0546069i \(-0.0173906\pi\)
−0.546545 + 0.837430i \(0.684057\pi\)
\(102\) 7.61730 + 64.2640i 0.0746794 + 0.630040i
\(103\) 67.8160i 0.658408i −0.944259 0.329204i \(-0.893220\pi\)
0.944259 0.329204i \(-0.106780\pi\)
\(104\) 122.488 + 101.766i 1.17777 + 0.978515i
\(105\) 8.22198 + 14.2409i 0.0783046 + 0.135628i
\(106\) −118.478 + 14.0433i −1.11772 + 0.132484i
\(107\) 95.8811i 0.896085i −0.894012 0.448043i \(-0.852121\pi\)
0.894012 0.448043i \(-0.147879\pi\)
\(108\) 1.93398 1.83653i 0.0179072 0.0170049i
\(109\) −30.9046 + 53.5283i −0.283528 + 0.491085i −0.972251 0.233939i \(-0.924838\pi\)
0.688723 + 0.725025i \(0.258172\pi\)
\(110\) 47.3751 35.3893i 0.430683 0.321721i
\(111\) −71.6271 41.3539i −0.645289 0.372558i
\(112\) −29.1432 1.50733i −0.260207 0.0134583i
\(113\) −33.7438 −0.298618 −0.149309 0.988791i \(-0.547705\pi\)
−0.149309 + 0.988791i \(0.547705\pi\)
\(114\) −67.3441 + 145.701i −0.590738 + 1.27808i
\(115\) 22.5472i 0.196063i
\(116\) −0.0335113 + 0.113274i −0.000288890 + 0.000976504i
\(117\) 88.0051 152.429i 0.752180 1.30281i
\(118\) −118.335 + 88.3962i −1.00284 + 0.749120i
\(119\) 12.0996 + 6.98572i 0.101677 + 0.0587035i
\(120\) −46.0925 + 55.4781i −0.384104 + 0.462318i
\(121\) −70.8842 −0.585820
\(122\) −93.9898 + 11.1407i −0.770409 + 0.0913176i
\(123\) −115.133 + 66.4724i −0.936045 + 0.540426i
\(124\) −122.494 + 116.322i −0.987857 + 0.938084i
\(125\) −96.9982 −0.775986
\(126\) 3.79654 + 32.0299i 0.0301313 + 0.254205i
\(127\) −28.8460 + 16.6543i −0.227134 + 0.131136i −0.609249 0.792979i \(-0.708529\pi\)
0.382115 + 0.924115i \(0.375196\pi\)
\(128\) −38.1037 122.197i −0.297685 0.954664i
\(129\) −125.228 216.902i −0.970763 1.68141i
\(130\) 33.5304 78.0809i 0.257926 0.600622i
\(131\) −11.8573 6.84581i −0.0905136 0.0522581i 0.454060 0.890971i \(-0.349975\pi\)
−0.544574 + 0.838713i \(0.683309\pi\)
\(132\) 227.562 54.7151i 1.72395 0.414508i
\(133\) 16.5000 + 30.4735i 0.124060 + 0.229124i
\(134\) 1.57047 + 13.2494i 0.0117199 + 0.0988762i
\(135\) −1.23250 0.711584i −0.00912963 0.00527099i
\(136\) −10.3471 + 60.4023i −0.0760816 + 0.444135i
\(137\) −66.7629 115.637i −0.487320 0.844063i 0.512574 0.858643i \(-0.328692\pi\)
−0.999894 + 0.0145800i \(0.995359\pi\)
\(138\) 35.2130 81.9991i 0.255166 0.594196i
\(139\) 192.509 111.145i 1.38496 0.799606i 0.392216 0.919873i \(-0.371709\pi\)
0.992741 + 0.120268i \(0.0383753\pi\)
\(140\) 3.64038 + 15.1404i 0.0260027 + 0.108146i
\(141\) 378.157 2.68196
\(142\) 44.6632 33.3635i 0.314530 0.234954i
\(143\) −238.798 + 137.870i −1.66991 + 0.964125i
\(144\) −126.011 + 64.3143i −0.875074 + 0.446627i
\(145\) 0.0630343 0.000434719
\(146\) 110.742 + 148.249i 0.758507 + 1.01540i
\(147\) −167.078 96.4623i −1.13658 0.656206i
\(148\) −53.9327 56.7942i −0.364410 0.383745i
\(149\) −11.8549 + 20.5333i −0.0795632 + 0.137808i −0.903062 0.429511i \(-0.858686\pi\)
0.823498 + 0.567319i \(0.192019\pi\)
\(150\) −158.698 68.1498i −1.05799 0.454332i
\(151\) 77.7402i 0.514836i 0.966300 + 0.257418i \(0.0828717\pi\)
−0.966300 + 0.257418i \(0.917128\pi\)
\(152\) −100.295 + 114.215i −0.659832 + 0.751413i
\(153\) 67.7332 0.442701
\(154\) 19.9383 46.4296i 0.129470 0.301491i
\(155\) 78.0641 + 45.0703i 0.503639 + 0.290776i
\(156\) 243.885 231.597i 1.56336 1.48459i
\(157\) −126.399 + 218.929i −0.805087 + 1.39445i 0.111146 + 0.993804i \(0.464548\pi\)
−0.916233 + 0.400647i \(0.868785\pi\)
\(158\) 204.783 152.973i 1.29609 0.968185i
\(159\) 251.977i 1.58476i
\(160\) −56.7589 + 37.9954i −0.354743 + 0.237471i
\(161\) −9.63327 16.6853i −0.0598340 0.103636i
\(162\) −98.6214 132.023i −0.608774 0.814956i
\(163\) 58.1739i 0.356895i 0.983949 + 0.178448i \(0.0571075\pi\)
−0.983949 + 0.178448i \(0.942893\pi\)
\(164\) −122.406 + 29.4314i −0.746379 + 0.179460i
\(165\) −62.4452 108.158i −0.378456 0.655505i
\(166\) −163.390 70.1649i −0.984278 0.422680i
\(167\) 139.337 80.4465i 0.834356 0.481716i −0.0209856 0.999780i \(-0.506680\pi\)
0.855342 + 0.518064i \(0.173347\pi\)
\(168\) −10.4063 + 60.7477i −0.0619421 + 0.361594i
\(169\) −113.621 + 196.797i −0.672312 + 1.16448i
\(170\) 32.4736 3.84914i 0.191021 0.0226420i
\(171\) 143.142 + 87.9464i 0.837089 + 0.514306i
\(172\) −55.4464 230.603i −0.322363 1.34072i
\(173\) −123.372 + 213.686i −0.713132 + 1.23518i 0.250544 + 0.968105i \(0.419391\pi\)
−0.963676 + 0.267075i \(0.913943\pi\)
\(174\) 0.229242 + 0.0984435i 0.00131748 + 0.000565767i
\(175\) −32.2921 + 18.6438i −0.184526 + 0.106536i
\(176\) 221.340 + 11.4480i 1.25761 + 0.0650454i
\(177\) 155.977 + 270.160i 0.881226 + 1.52633i
\(178\) 124.001 14.6980i 0.696636 0.0825732i
\(179\) 129.378i 0.722780i 0.932415 + 0.361390i \(0.117698\pi\)
−0.932415 + 0.361390i \(0.882302\pi\)
\(180\) 51.9843 + 54.7425i 0.288802 + 0.304125i
\(181\) −96.1456 166.529i −0.531191 0.920051i −0.999337 0.0363994i \(-0.988411\pi\)
0.468146 0.883651i \(-0.344922\pi\)
\(182\) −8.54694 72.1070i −0.0469612 0.396192i
\(183\) 199.896i 1.09233i
\(184\) 54.0042 65.0009i 0.293501 0.353266i
\(185\) −20.8968 + 36.1943i −0.112955 + 0.195645i
\(186\) 213.513 + 285.827i 1.14792 + 1.53670i
\(187\) −91.8955 53.0559i −0.491420 0.283721i
\(188\) 343.392 + 101.589i 1.82655 + 0.540369i
\(189\) −1.21609 −0.00643436
\(190\) 73.6250 + 34.0300i 0.387500 + 0.179105i
\(191\) 1.29081i 0.00675816i 0.999994 + 0.00337908i \(0.00107560\pi\)
−0.999994 + 0.00337908i \(0.998924\pi\)
\(192\) −265.758 + 49.5377i −1.38416 + 0.258009i
\(193\) 186.582 323.169i 0.966744 1.67445i 0.261889 0.965098i \(-0.415655\pi\)
0.704855 0.709351i \(-0.251012\pi\)
\(194\) −155.127 207.666i −0.799624 1.07044i
\(195\) −155.425 89.7345i −0.797050 0.460177i
\(196\) −125.803 132.478i −0.641854 0.675910i
\(197\) 191.769 0.973448 0.486724 0.873556i \(-0.338192\pi\)
0.486724 + 0.873556i \(0.338192\pi\)
\(198\) −28.8344 243.264i −0.145628 1.22861i
\(199\) 285.397 164.774i 1.43415 0.828009i 0.436720 0.899598i \(-0.356140\pi\)
0.997434 + 0.0715885i \(0.0228068\pi\)
\(200\) −125.800 104.518i −0.629000 0.522588i
\(201\) 28.1786 0.140192
\(202\) 181.324 21.4925i 0.897642 0.106399i
\(203\) 0.0466465 0.0269314i 0.000229786 0.000132667i
\(204\) 124.111 + 36.7170i 0.608385 + 0.179985i
\(205\) 33.5895 + 58.1787i 0.163851 + 0.283799i
\(206\) −124.627 53.5186i −0.604984 0.259799i
\(207\) −80.8901 46.7019i −0.390773 0.225613i
\(208\) 283.680 144.787i 1.36385 0.696092i
\(209\) −125.316 231.444i −0.599598 1.10739i
\(210\) 32.6593 3.87115i 0.155520 0.0184341i
\(211\) 48.2556 + 27.8604i 0.228700 + 0.132040i 0.609972 0.792423i \(-0.291181\pi\)
−0.381272 + 0.924463i \(0.624514\pi\)
\(212\) −67.6919 + 228.812i −0.319301 + 1.07930i
\(213\) −58.8706 101.967i −0.276388 0.478718i
\(214\) −176.202 75.6668i −0.823376 0.353583i
\(215\) −109.604 + 63.2798i −0.509785 + 0.294325i
\(216\) −1.84879 5.00345i −0.00855920 0.0231641i
\(217\) 77.0250 0.354954
\(218\) 73.9808 + 99.0370i 0.339362 + 0.454298i
\(219\) 338.454 195.407i 1.54545 0.892268i
\(220\) −27.6484 114.990i −0.125674 0.522683i
\(221\) −152.484 −0.689973
\(222\) −132.523 + 98.9950i −0.596951 + 0.445923i
\(223\) 35.7192 + 20.6225i 0.160176 + 0.0924774i 0.577945 0.816076i \(-0.303855\pi\)
−0.417770 + 0.908553i \(0.637188\pi\)
\(224\) −25.7691 + 52.3674i −0.115040 + 0.233783i
\(225\) −90.3850 + 156.551i −0.401711 + 0.695784i
\(226\) −26.6297 + 62.0116i −0.117831 + 0.274388i
\(227\) 277.068i 1.22057i 0.792184 + 0.610283i \(0.208944\pi\)
−0.792184 + 0.610283i \(0.791056\pi\)
\(228\) 214.611 + 238.743i 0.941278 + 1.04712i
\(229\) 141.178 0.616496 0.308248 0.951306i \(-0.400257\pi\)
0.308248 + 0.951306i \(0.400257\pi\)
\(230\) −41.4354 17.7937i −0.180154 0.0773637i
\(231\) −92.4210 53.3593i −0.400091 0.230993i
\(232\) 0.181720 + 0.150977i 0.000783277 + 0.000650765i
\(233\) 44.5846 77.2228i 0.191350 0.331428i −0.754348 0.656475i \(-0.772047\pi\)
0.945698 + 0.325047i \(0.105380\pi\)
\(234\) −210.671 282.022i −0.900302 1.20522i
\(235\) 191.088i 0.813143i
\(236\) 69.0607 + 287.225i 0.292630 + 1.21706i
\(237\) −269.925 467.523i −1.13892 1.97267i
\(238\) 22.3865 16.7227i 0.0940608 0.0702636i
\(239\) 82.2938i 0.344325i −0.985069 0.172163i \(-0.944925\pi\)
0.985069 0.172163i \(-0.0550755\pi\)
\(240\) 65.5782 + 128.487i 0.273242 + 0.535362i
\(241\) −22.2946 38.6154i −0.0925088 0.160230i 0.816057 0.577971i \(-0.196155\pi\)
−0.908566 + 0.417741i \(0.862822\pi\)
\(242\) −55.9399 + 130.265i −0.231157 + 0.538286i
\(243\) −296.214 + 171.019i −1.21899 + 0.703783i
\(244\) −53.7007 + 181.519i −0.220085 + 0.743929i
\(245\) −48.7438 + 84.4268i −0.198954 + 0.344599i
\(246\) 31.2971 + 264.041i 0.127224 + 1.07334i
\(247\) −322.248 197.989i −1.30465 0.801573i
\(248\) 117.099 + 316.908i 0.472172 + 1.27786i
\(249\) −187.776 + 325.238i −0.754122 + 1.30618i
\(250\) −76.5484 + 178.255i −0.306194 + 0.713021i
\(251\) −94.8716 + 54.7741i −0.377974 + 0.218224i −0.676937 0.736041i \(-0.736693\pi\)
0.298962 + 0.954265i \(0.403360\pi\)
\(252\) 61.8580 + 18.3001i 0.245468 + 0.0726196i
\(253\) 73.1638 + 126.723i 0.289185 + 0.500883i
\(254\) 7.84132 + 66.1540i 0.0308713 + 0.260449i
\(255\) 69.0643i 0.270840i
\(256\) −254.634 26.4107i −0.994664 0.103167i
\(257\) 224.002 + 387.982i 0.871602 + 1.50966i 0.860339 + 0.509722i \(0.170252\pi\)
0.0112627 + 0.999937i \(0.496415\pi\)
\(258\) −497.432 + 58.9612i −1.92803 + 0.228532i
\(259\) 35.7125i 0.137886i
\(260\) −117.029 123.239i −0.450113 0.473995i
\(261\) 0.130563 0.226141i 0.000500240 0.000866441i
\(262\) −21.9381 + 16.3878i −0.0837332 + 0.0625489i
\(263\) 272.533 + 157.347i 1.03625 + 0.598277i 0.918768 0.394798i \(-0.129186\pi\)
0.117478 + 0.993075i \(0.462519\pi\)
\(264\) 79.0346 461.374i 0.299374 1.74763i
\(265\) 127.328 0.480482
\(266\) 69.0231 6.27345i 0.259485 0.0235844i
\(267\) 263.724i 0.987730i
\(268\) 25.5880 + 7.57000i 0.0954778 + 0.0282463i
\(269\) 145.563 252.123i 0.541128 0.937261i −0.457712 0.889101i \(-0.651331\pi\)
0.998840 0.0481601i \(-0.0153358\pi\)
\(270\) −2.28035 + 1.70342i −0.00844573 + 0.00630897i
\(271\) −111.647 64.4596i −0.411983 0.237858i 0.279659 0.960100i \(-0.409779\pi\)
−0.691641 + 0.722241i \(0.743112\pi\)
\(272\) 102.837 + 66.6829i 0.378076 + 0.245158i
\(273\) −153.356 −0.561743
\(274\) −265.195 + 31.4339i −0.967865 + 0.114722i
\(275\) 245.255 141.598i 0.891838 0.514903i
\(276\) −122.902 129.423i −0.445297 0.468924i
\(277\) 23.1010 0.0833971 0.0416986 0.999130i \(-0.486723\pi\)
0.0416986 + 0.999130i \(0.486723\pi\)
\(278\) −52.3304 441.490i −0.188239 1.58809i
\(279\) 323.387 186.708i 1.15909 0.669204i
\(280\) 30.6968 + 5.25844i 0.109631 + 0.0187802i
\(281\) 33.2086 + 57.5190i 0.118180 + 0.204694i 0.919046 0.394149i \(-0.128961\pi\)
−0.800866 + 0.598843i \(0.795627\pi\)
\(282\) 298.431 694.946i 1.05827 2.46435i
\(283\) −84.3920 48.7237i −0.298205 0.172169i 0.343431 0.939178i \(-0.388411\pi\)
−0.641636 + 0.767009i \(0.721744\pi\)
\(284\) −26.0657 108.408i −0.0917806 0.381718i
\(285\) 89.6747 145.955i 0.314648 0.512123i
\(286\) 64.9132 + 547.646i 0.226969 + 1.91485i
\(287\) 49.7136 + 28.7022i 0.173218 + 0.100007i
\(288\) 18.7473 + 282.327i 0.0650949 + 0.980302i
\(289\) 115.160 + 199.463i 0.398478 + 0.690184i
\(290\) 0.0497450 0.115839i 0.000171534 0.000399446i
\(291\) −474.106 + 273.725i −1.62923 + 0.940636i
\(292\) 359.834 86.5187i 1.23231 0.296297i
\(293\) 263.379 0.898903 0.449451 0.893305i \(-0.351619\pi\)
0.449451 + 0.893305i \(0.351619\pi\)
\(294\) −309.123 + 230.916i −1.05144 + 0.785428i
\(295\) 136.516 78.8176i 0.462766 0.267178i
\(296\) −146.934 + 54.2925i −0.496399 + 0.183421i
\(297\) 9.23612 0.0310981
\(298\) 28.3789 + 37.9903i 0.0952311 + 0.127484i
\(299\) 182.103 + 105.137i 0.609041 + 0.351630i
\(300\) −250.480 + 237.860i −0.834934 + 0.792866i
\(301\) −54.0725 + 93.6563i −0.179643 + 0.311151i
\(302\) 142.865 + 61.3505i 0.473062 + 0.203147i
\(303\) 385.636i 1.27273i
\(304\) 130.745 + 274.448i 0.430081 + 0.902790i
\(305\) 101.010 0.331182
\(306\) 53.4533 124.475i 0.174684 0.406780i
\(307\) −245.559 141.774i −0.799866 0.461803i 0.0435580 0.999051i \(-0.486131\pi\)
−0.843424 + 0.537248i \(0.819464\pi\)
\(308\) −69.5898 73.2821i −0.225941 0.237929i
\(309\) −143.227 + 248.077i −0.463519 + 0.802838i
\(310\) 144.433 107.891i 0.465912 0.348037i
\(311\) 254.508i 0.818352i −0.912455 0.409176i \(-0.865816\pi\)
0.912455 0.409176i \(-0.134184\pi\)
\(312\) −233.142 630.961i −0.747250 2.02231i
\(313\) −167.705 290.473i −0.535798 0.928029i −0.999124 0.0418410i \(-0.986678\pi\)
0.463327 0.886188i \(-0.346656\pi\)
\(314\) 302.579 + 405.058i 0.963627 + 1.28999i
\(315\) 34.4224i 0.109277i
\(316\) −119.512 497.056i −0.378204 1.57296i
\(317\) −132.064 228.741i −0.416605 0.721580i 0.578991 0.815334i \(-0.303447\pi\)
−0.995595 + 0.0937538i \(0.970113\pi\)
\(318\) 463.062 + 198.853i 1.45617 + 0.625325i
\(319\) −0.354276 + 0.204541i −0.00111058 + 0.000641195i
\(320\) 25.0321 + 134.292i 0.0782255 + 0.419662i
\(321\) −202.501 + 350.742i −0.630844 + 1.09265i
\(322\) −38.2652 + 4.53563i −0.118836 + 0.0140858i
\(323\) 3.97881 145.491i 0.0123183 0.450436i
\(324\) −320.450 + 77.0493i −0.989044 + 0.237806i
\(325\) 203.479 352.435i 0.626088 1.08442i
\(326\) 106.907 + 45.9093i 0.327936 + 0.140826i
\(327\) 226.103 130.541i 0.691448 0.399208i
\(328\) −42.5130 + 248.174i −0.129613 + 0.756629i
\(329\) −81.6424 141.409i −0.248153 0.429814i
\(330\) −248.044 + 29.4010i −0.751650 + 0.0890940i
\(331\) 611.200i 1.84653i 0.384170 + 0.923263i \(0.374488\pi\)
−0.384170 + 0.923263i \(0.625512\pi\)
\(332\) −257.886 + 244.893i −0.776766 + 0.737629i
\(333\) 86.5667 + 149.938i 0.259960 + 0.450264i
\(334\) −37.8766 319.549i −0.113403 0.956734i
\(335\) 14.2391i 0.0425047i
\(336\) 103.425 + 67.0643i 0.307812 + 0.199596i
\(337\) 34.4295 59.6337i 0.102165 0.176955i −0.810412 0.585861i \(-0.800756\pi\)
0.912576 + 0.408906i \(0.134090\pi\)
\(338\) 271.991 + 364.110i 0.804706 + 1.07725i
\(339\) 123.438 + 71.2669i 0.364124 + 0.210227i
\(340\) 18.5537 62.7149i 0.0545696 0.184456i
\(341\) −584.998 −1.71554
\(342\) 274.585 193.650i 0.802879 0.566228i
\(343\) 172.673i 0.503421i
\(344\) −467.540 80.0910i −1.35913 0.232823i
\(345\) −47.6197 + 82.4797i −0.138028 + 0.239072i
\(346\) 295.333 + 395.358i 0.853564 + 1.14265i
\(347\) 426.970 + 246.511i 1.23046 + 0.710407i 0.967126 0.254297i \(-0.0818440\pi\)
0.263336 + 0.964704i \(0.415177\pi\)
\(348\) 0.361823 0.343592i 0.00103972 0.000987335i
\(349\) −180.545 −0.517320 −0.258660 0.965968i \(-0.583281\pi\)
−0.258660 + 0.965968i \(0.583281\pi\)
\(350\) 8.77807 + 74.0570i 0.0250802 + 0.211591i
\(351\) 11.4943 6.63621i 0.0327472 0.0189066i
\(352\) 195.714 397.726i 0.556005 1.12990i
\(353\) 441.313 1.25018 0.625089 0.780553i \(-0.285063\pi\)
0.625089 + 0.780553i \(0.285063\pi\)
\(354\) 619.571 73.4386i 1.75020 0.207454i
\(355\) −51.5254 + 29.7482i −0.145142 + 0.0837978i
\(356\) 70.8476 239.479i 0.199010 0.672693i
\(357\) −29.5077 51.1088i −0.0826545 0.143162i
\(358\) 237.760 + 102.101i 0.664133 + 0.285199i
\(359\) −119.997 69.2800i −0.334252 0.192981i 0.323475 0.946237i \(-0.395149\pi\)
−0.657727 + 0.753256i \(0.728482\pi\)
\(360\) 141.626 52.3312i 0.393405 0.145364i
\(361\) 197.317 302.303i 0.546585 0.837404i
\(362\) −381.909 + 45.2682i −1.05500 + 0.125050i
\(363\) 259.301 + 149.707i 0.714327 + 0.412417i
\(364\) −139.257 41.1981i −0.382575 0.113181i
\(365\) −98.7420 171.026i −0.270526 0.468565i
\(366\) 367.352 + 157.753i 1.00370 + 0.431018i
\(367\) −304.552 + 175.833i −0.829841 + 0.479109i −0.853798 0.520604i \(-0.825707\pi\)
0.0239571 + 0.999713i \(0.492373\pi\)
\(368\) −76.8345 150.541i −0.208790 0.409080i
\(369\) 278.295 0.754187
\(370\) 50.0237 + 66.9659i 0.135199 + 0.180989i
\(371\) 94.2247 54.4006i 0.253975 0.146632i
\(372\) 693.768 166.810i 1.86497 0.448414i
\(373\) −196.793 −0.527594 −0.263797 0.964578i \(-0.584975\pi\)
−0.263797 + 0.964578i \(0.584975\pi\)
\(374\) −170.023 + 127.008i −0.454608 + 0.339593i
\(375\) 354.828 + 204.860i 0.946208 + 0.546293i
\(376\) 457.688 550.885i 1.21726 1.46512i
\(377\) −0.293928 + 0.509099i −0.000779650 + 0.00135039i
\(378\) −0.959709 + 2.23484i −0.00253891 + 0.00591227i
\(379\) 169.249i 0.446566i 0.974754 + 0.223283i \(0.0716774\pi\)
−0.974754 + 0.223283i \(0.928323\pi\)
\(380\) 120.640 108.446i 0.317475 0.285385i
\(381\) 140.695 0.369279
\(382\) 2.37214 + 1.01867i 0.00620980 + 0.00266668i
\(383\) −343.442 198.286i −0.896715 0.517718i −0.0205817 0.999788i \(-0.506552\pi\)
−0.876133 + 0.482070i \(0.839885\pi\)
\(384\) −118.693 + 527.482i −0.309096 + 1.37365i
\(385\) −26.9633 + 46.7017i −0.0700345 + 0.121303i
\(386\) −446.648 597.920i −1.15712 1.54902i
\(387\) 524.285i 1.35474i
\(388\) −504.054 + 121.195i −1.29911 + 0.312358i
\(389\) 192.573 + 333.547i 0.495047 + 0.857447i 0.999984 0.00570929i \(-0.00181733\pi\)
−0.504936 + 0.863157i \(0.668484\pi\)
\(390\) −287.564 + 214.811i −0.737343 + 0.550797i
\(391\) 80.9191i 0.206954i
\(392\) −342.739 + 126.643i −0.874333 + 0.323069i
\(393\) 28.9167 + 50.0851i 0.0735793 + 0.127443i
\(394\) 151.339 352.418i 0.384110 0.894462i
\(395\) −236.247 + 136.397i −0.598093 + 0.345309i
\(396\) −469.806 138.988i −1.18638 0.350980i
\(397\) −141.267 + 244.682i −0.355837 + 0.616328i −0.987261 0.159110i \(-0.949138\pi\)
0.631424 + 0.775438i \(0.282471\pi\)
\(398\) −77.5804 654.513i −0.194926 1.64451i
\(399\) 4.00157 146.323i 0.0100290 0.366724i
\(400\) −291.352 + 148.702i −0.728380 + 0.371756i
\(401\) −4.00500 + 6.93686i −0.00998753 + 0.0172989i −0.870976 0.491326i \(-0.836513\pi\)
0.860988 + 0.508625i \(0.169846\pi\)
\(402\) 22.2378 51.7843i 0.0553179 0.128817i
\(403\) −728.023 + 420.325i −1.80651 + 1.04299i
\(404\) 103.599 350.183i 0.256432 0.866790i
\(405\) 87.9348 + 152.308i 0.217123 + 0.376068i
\(406\) −0.0126801 0.106977i −3.12317e−5 0.000263489i
\(407\) 271.233i 0.666421i
\(408\) 165.420 199.104i 0.405442 0.488000i
\(409\) −77.6731 134.534i −0.189910 0.328933i 0.755310 0.655367i \(-0.227486\pi\)
−0.945220 + 0.326434i \(0.894153\pi\)
\(410\) 133.424 15.8149i 0.325424 0.0385730i
\(411\) 564.012i 1.37229i
\(412\) −196.704 + 186.793i −0.477437 + 0.453382i
\(413\) 67.3495 116.653i 0.163074 0.282452i
\(414\) −149.661 + 111.797i −0.361501 + 0.270042i
\(415\) 164.348 + 94.8862i 0.396019 + 0.228642i
\(416\) −42.2048 635.586i −0.101454 1.52785i
\(417\) −938.954 −2.25169
\(418\) −524.224 + 47.6463i −1.25412 + 0.113986i
\(419\) 402.751i 0.961220i −0.876934 0.480610i \(-0.840415\pi\)
0.876934 0.480610i \(-0.159585\pi\)
\(420\) 18.6598 63.0736i 0.0444280 0.150175i
\(421\) −227.604 + 394.222i −0.540628 + 0.936395i 0.458240 + 0.888828i \(0.348480\pi\)
−0.998868 + 0.0475667i \(0.984853\pi\)
\(422\) 89.2816 66.6935i 0.211568 0.158041i
\(423\) −685.547 395.801i −1.62068 0.935699i
\(424\) 367.070 + 304.971i 0.865732 + 0.719270i
\(425\) 156.608 0.368488
\(426\) −233.846 + 27.7180i −0.548933 + 0.0650658i
\(427\) 74.7495 43.1566i 0.175057 0.101069i
\(428\) −278.108 + 264.096i −0.649786 + 0.617047i
\(429\) 1164.72 2.71498
\(430\) 29.7940 + 251.360i 0.0692884 + 0.584557i
\(431\) −427.854 + 247.021i −0.992700 + 0.573135i −0.906080 0.423106i \(-0.860940\pi\)
−0.0866195 + 0.996241i \(0.527606\pi\)
\(432\) −10.6539 0.551036i −0.0246619 0.00127555i
\(433\) −127.503 220.842i −0.294465 0.510029i 0.680395 0.732845i \(-0.261808\pi\)
−0.974860 + 0.222817i \(0.928475\pi\)
\(434\) 60.7861 141.550i 0.140060 0.326153i
\(435\) −0.230585 0.133128i −0.000530081 0.000306042i
\(436\) 240.386 57.7985i 0.551343 0.132565i
\(437\) −105.067 + 171.008i −0.240428 + 0.391323i
\(438\) −92.0032 776.193i −0.210053 1.77213i
\(439\) 80.1980 + 46.3023i 0.182683 + 0.105472i 0.588553 0.808459i \(-0.299698\pi\)
−0.405869 + 0.913931i \(0.633031\pi\)
\(440\) −233.139 39.9374i −0.529862 0.0907668i
\(441\) 201.926 + 349.746i 0.457881 + 0.793074i
\(442\) −120.336 + 280.222i −0.272254 + 0.633987i
\(443\) 319.754 184.610i 0.721792 0.416727i −0.0936200 0.995608i \(-0.529844\pi\)
0.815412 + 0.578881i \(0.196511\pi\)
\(444\) 77.3412 + 321.664i 0.174192 + 0.724469i
\(445\) −133.264 −0.299469
\(446\) 66.0869 49.3670i 0.148177 0.110688i
\(447\) 86.7327 50.0751i 0.194033 0.112025i
\(448\) 75.9002 + 88.6832i 0.169420 + 0.197954i
\(449\) −457.229 −1.01833 −0.509163 0.860670i \(-0.670045\pi\)
−0.509163 + 0.860670i \(0.670045\pi\)
\(450\) 216.368 + 289.648i 0.480817 + 0.643663i
\(451\) −377.570 217.990i −0.837184 0.483349i
\(452\) 92.9444 + 97.8759i 0.205629 + 0.216540i
\(453\) 164.187 284.381i 0.362444 0.627772i
\(454\) 509.174 + 218.655i 1.12153 + 0.481619i
\(455\) 77.4931i 0.170314i
\(456\) 608.108 205.986i 1.33357 0.451723i
\(457\) 83.5243 0.182767 0.0913833 0.995816i \(-0.470871\pi\)
0.0913833 + 0.995816i \(0.470871\pi\)
\(458\) 111.414 259.445i 0.243261 0.566473i
\(459\) 4.42328 + 2.55378i 0.00963679 + 0.00556380i
\(460\) −65.3994 + 62.1043i −0.142173 + 0.135009i
\(461\) −120.895 + 209.396i −0.262245 + 0.454221i −0.966838 0.255390i \(-0.917796\pi\)
0.704593 + 0.709611i \(0.251129\pi\)
\(462\) −170.996 + 127.734i −0.370120 + 0.276481i
\(463\) 159.241i 0.343934i 0.985103 + 0.171967i \(0.0550123\pi\)
−0.985103 + 0.171967i \(0.944988\pi\)
\(464\) 0.420863 0.214803i 0.000907032 0.000462938i
\(465\) −190.377 329.742i −0.409413 0.709124i
\(466\) −106.729 142.876i −0.229032 0.306601i
\(467\) 17.6334i 0.0377588i 0.999822 + 0.0188794i \(0.00600986\pi\)
−0.999822 + 0.0188794i \(0.993990\pi\)
\(468\) −684.532 + 164.589i −1.46267 + 0.351687i
\(469\) −6.08363 10.5372i −0.0129715 0.0224673i
\(470\) −351.167 150.802i −0.747163 0.320855i
\(471\) 924.755 533.907i 1.96339 1.13356i
\(472\) 582.340 + 99.7565i 1.23377 + 0.211349i
\(473\) 410.676 711.311i 0.868236 1.50383i
\(474\) −1072.19 + 127.089i −2.26201 + 0.268119i
\(475\) 330.962 + 203.343i 0.696763 + 0.428090i
\(476\) −13.0649 54.3371i −0.0274472 0.114154i
\(477\) 263.733 456.799i 0.552900 0.957651i
\(478\) −151.233 64.9440i −0.316386 0.135866i
\(479\) 164.704 95.0917i 0.343849 0.198521i −0.318124 0.948049i \(-0.603053\pi\)
0.661973 + 0.749528i \(0.269719\pi\)
\(480\) 287.875 19.1157i 0.599740 0.0398244i
\(481\) −194.883 337.547i −0.405161 0.701760i
\(482\) −88.5585 + 10.4970i −0.183731 + 0.0217779i
\(483\) 81.3818i 0.168492i
\(484\) 195.244 + 205.603i 0.403397 + 0.424801i
\(485\) 138.317 + 239.573i 0.285191 + 0.493965i
\(486\) 80.5209 + 679.322i 0.165681 + 1.39778i
\(487\) 421.853i 0.866228i −0.901339 0.433114i \(-0.857415\pi\)
0.901339 0.433114i \(-0.142585\pi\)
\(488\) 291.201 + 241.937i 0.596723 + 0.495772i
\(489\) 122.863 212.805i 0.251254 0.435185i
\(490\) 116.685 + 156.205i 0.238133 + 0.318785i
\(491\) −707.298 408.359i −1.44053 0.831688i −0.442641 0.896699i \(-0.645958\pi\)
−0.997885 + 0.0650112i \(0.979292\pi\)
\(492\) 509.932 + 150.859i 1.03645 + 0.306624i
\(493\) −0.226222 −0.000458869
\(494\) −618.157 + 435.953i −1.25133 + 0.882496i
\(495\) 261.435i 0.528151i
\(496\) 674.799 + 34.9015i 1.36048 + 0.0703660i
\(497\) −25.4198 + 44.0284i −0.0511465 + 0.0885883i
\(498\) 449.508 + 601.749i 0.902626 + 1.20833i
\(499\) 446.851 + 257.989i 0.895492 + 0.517013i 0.875735 0.482792i \(-0.160377\pi\)
0.0197574 + 0.999805i \(0.493711\pi\)
\(500\) 267.173 + 281.349i 0.534346 + 0.562697i
\(501\) −679.612 −1.35651
\(502\) 25.7893 + 217.573i 0.0513730 + 0.433413i
\(503\) 328.542 189.684i 0.653165 0.377105i −0.136503 0.990640i \(-0.543586\pi\)
0.789668 + 0.613535i \(0.210253\pi\)
\(504\) 82.4472 99.2355i 0.163586 0.196896i
\(505\) −194.868 −0.385877
\(506\) 290.621 34.4477i 0.574350 0.0680784i
\(507\) 831.270 479.934i 1.63959 0.946615i
\(508\) 127.760 + 37.7968i 0.251497 + 0.0744032i
\(509\) 56.0386 + 97.0617i 0.110096 + 0.190691i 0.915809 0.401615i \(-0.131551\pi\)
−0.805713 + 0.592306i \(0.798218\pi\)
\(510\) −126.921 54.5037i −0.248864 0.106870i
\(511\) −146.141 84.3748i −0.285991 0.165117i
\(512\) −249.486 + 447.103i −0.487277 + 0.873248i
\(513\) 6.03194 + 11.1403i 0.0117582 + 0.0217159i
\(514\) 889.778 105.467i 1.73109 0.205188i
\(515\) 125.357 + 72.3749i 0.243412 + 0.140534i
\(516\) −284.206 + 960.669i −0.550786 + 1.86176i
\(517\) 620.066 + 1073.99i 1.19935 + 2.07734i
\(518\) 65.6295 + 28.1833i 0.126698 + 0.0544080i
\(519\) 902.610 521.122i 1.73913 1.00409i
\(520\) −318.834 + 117.810i −0.613143 + 0.226558i
\(521\) −269.639 −0.517542 −0.258771 0.965939i \(-0.583317\pi\)
−0.258771 + 0.965939i \(0.583317\pi\)
\(522\) −0.312547 0.418402i −0.000598749 0.000801536i
\(523\) −416.867 + 240.678i −0.797068 + 0.460188i −0.842445 0.538782i \(-0.818885\pi\)
0.0453767 + 0.998970i \(0.485551\pi\)
\(524\) 12.8032 + 53.2489i 0.0244336 + 0.101620i
\(525\) 157.503 0.300006
\(526\) 504.235 376.664i 0.958621 0.716092i
\(527\) −280.162 161.752i −0.531617 0.306929i
\(528\) −785.502 509.347i −1.48769 0.964672i
\(529\) −208.706 + 361.490i −0.394530 + 0.683346i
\(530\) 100.484 233.992i 0.189592 0.441495i
\(531\) 653.018i 1.22979i
\(532\) 42.9423 131.796i 0.0807186 0.247736i
\(533\) −626.509 −1.17544
\(534\) −484.650 208.124i −0.907584 0.389745i
\(535\) 177.235 + 102.327i 0.331281 + 0.191265i
\(536\) 34.1049 41.0496i 0.0636286 0.0765850i
\(537\) 273.245 473.275i 0.508837 0.881331i
\(538\) −348.456 466.473i −0.647688 0.867050i
\(539\) 632.679i 1.17380i
\(540\) 1.33082 + 5.53493i 0.00246449 + 0.0102499i
\(541\) 52.7461 + 91.3589i 0.0974974 + 0.168870i 0.910648 0.413183i \(-0.135583\pi\)
−0.813151 + 0.582053i \(0.802250\pi\)
\(542\) −206.568 + 154.306i −0.381121 + 0.284698i
\(543\) 812.238i 1.49583i
\(544\) 203.700 136.361i 0.374449 0.250663i
\(545\) −65.9643 114.253i −0.121035 0.209639i
\(546\) −121.024 + 281.825i −0.221656 + 0.516163i
\(547\) −547.959 + 316.364i −1.00175 + 0.578363i −0.908767 0.417304i \(-0.862975\pi\)
−0.0929871 + 0.995667i \(0.529642\pi\)
\(548\) −151.518 + 512.160i −0.276493 + 0.934599i
\(549\) 209.223 362.384i 0.381097 0.660080i
\(550\) −66.6687 562.456i −0.121216 1.02265i
\(551\) −0.478081 0.293732i −0.000867660 0.000533089i
\(552\) −334.834 + 123.722i −0.606583 + 0.224134i
\(553\) −116.551 + 201.872i −0.210761 + 0.365049i
\(554\) 18.2307 42.4531i 0.0329074 0.0766302i
\(555\) 152.884 88.2679i 0.275467 0.159041i
\(556\) −852.632 252.244i −1.53351 0.453676i
\(557\) 526.047 + 911.140i 0.944429 + 1.63580i 0.756891 + 0.653541i \(0.226717\pi\)
0.187538 + 0.982257i \(0.439949\pi\)
\(558\) −87.9075 741.640i −0.157540 1.32910i
\(559\) 1180.29i 2.11143i
\(560\) 33.8886 52.2621i 0.0605153 0.0933253i
\(561\) 224.108 + 388.166i 0.399479 + 0.691919i
\(562\) 131.911 15.6356i 0.234717 0.0278213i
\(563\) 619.106i 1.09966i −0.835278 0.549828i \(-0.814693\pi\)
0.835278 0.549828i \(-0.185307\pi\)
\(564\) −1041.60 1096.87i −1.84681 1.94480i
\(565\) 36.0123 62.3751i 0.0637385 0.110398i
\(566\) −156.140 + 116.637i −0.275866 + 0.206073i
\(567\) 130.146 + 75.1401i 0.229535 + 0.132522i
\(568\) −219.793 37.6513i −0.386960 0.0662874i
\(569\) 246.403 0.433046 0.216523 0.976277i \(-0.430528\pi\)
0.216523 + 0.976277i \(0.430528\pi\)
\(570\) −197.456 279.981i −0.346413 0.491194i
\(571\) 88.9193i 0.155726i −0.996964 0.0778628i \(-0.975190\pi\)
0.996964 0.0778628i \(-0.0248096\pi\)
\(572\) 1057.65 + 312.895i 1.84903 + 0.547020i
\(573\) 2.72619 4.72189i 0.00475774 0.00824065i
\(574\) 91.9791 68.7086i 0.160242 0.119701i
\(575\) −187.028 107.981i −0.325266 0.187792i
\(576\) 533.632 + 188.353i 0.926445 + 0.327001i
\(577\) 659.532 1.14304 0.571518 0.820589i \(-0.306355\pi\)
0.571518 + 0.820589i \(0.306355\pi\)
\(578\) 457.438 54.2208i 0.791416 0.0938076i
\(579\) −1365.06 + 788.120i −2.35762 + 1.36117i
\(580\) −0.173622 0.182835i −0.000299349 0.000315232i
\(581\) 162.160 0.279105
\(582\) 128.878 + 1087.29i 0.221440 + 1.86819i
\(583\) −715.628 + 413.168i −1.22749 + 0.708693i
\(584\) 124.974 729.551i 0.213997 1.24923i
\(585\) 187.842 + 325.353i 0.321098 + 0.556158i
\(586\) 207.851 484.015i 0.354695 0.825965i
\(587\) 847.759 + 489.454i 1.44422 + 0.833822i 0.998128 0.0611631i \(-0.0194810\pi\)
0.446095 + 0.894986i \(0.352814\pi\)
\(588\) 180.406 + 750.314i 0.306813 + 1.27604i
\(589\) −382.051 705.603i −0.648644 1.19797i
\(590\) −37.1096 313.079i −0.0628977 0.530642i
\(591\) −701.509 405.017i −1.18699 0.685307i
\(592\) −16.1820 + 312.869i −0.0273345 + 0.528496i
\(593\) −102.396 177.355i −0.172675 0.299081i 0.766679 0.642030i \(-0.221908\pi\)
−0.939354 + 0.342949i \(0.888574\pi\)
\(594\) 7.28890 16.9734i 0.0122709 0.0285747i
\(595\) −25.8260 + 14.9107i −0.0434051 + 0.0250599i
\(596\) 92.2114 22.1714i 0.154717 0.0372003i
\(597\) −1392.01 −2.33167
\(598\) 336.924 251.683i 0.563417 0.420874i
\(599\) −844.006 + 487.287i −1.40903 + 0.813501i −0.995294 0.0968983i \(-0.969108\pi\)
−0.413731 + 0.910399i \(0.635775\pi\)
\(600\) 239.447 + 648.024i 0.399078 + 1.08004i
\(601\) 371.313 0.617825 0.308913 0.951090i \(-0.400035\pi\)
0.308913 + 0.951090i \(0.400035\pi\)
\(602\) 129.441 + 173.281i 0.215019 + 0.287842i
\(603\) −51.0840 29.4933i −0.0847164 0.0489110i
\(604\) 225.490 214.129i 0.373328 0.354518i
\(605\) 75.6494 131.029i 0.125040 0.216576i
\(606\) −708.690 304.334i −1.16946 0.502201i
\(607\) 692.679i 1.14115i 0.821245 + 0.570576i \(0.193280\pi\)
−0.821245 + 0.570576i \(0.806720\pi\)
\(608\) 607.539 23.6846i 0.999241 0.0389550i
\(609\) −0.227516 −0.000373589
\(610\) 79.7148 185.629i 0.130680 0.304309i
\(611\) 1543.33 + 891.043i 2.52591 + 1.45834i
\(612\) −186.565 196.464i −0.304845 0.321020i
\(613\) 257.281 445.624i 0.419708 0.726955i −0.576202 0.817307i \(-0.695466\pi\)
0.995910 + 0.0903521i \(0.0287992\pi\)
\(614\) −454.328 + 339.384i −0.739948 + 0.552743i
\(615\) 283.764i 0.461404i
\(616\) −189.590 + 70.0541i −0.307776 + 0.113724i
\(617\) 10.0069 + 17.3324i 0.0162186 + 0.0280915i 0.874021 0.485888i \(-0.161504\pi\)
−0.857802 + 0.513980i \(0.828171\pi\)
\(618\) 342.864 + 458.987i 0.554797 + 0.742698i
\(619\) 266.861i 0.431117i −0.976491 0.215558i \(-0.930843\pi\)
0.976491 0.215558i \(-0.0691572\pi\)
\(620\) −84.2917 350.571i −0.135954 0.565438i
\(621\) −3.52166 6.09969i −0.00567094 0.00982236i
\(622\) −467.713 200.851i −0.751950 0.322911i
\(623\) −98.6174 + 56.9368i −0.158294 + 0.0913913i
\(624\) −1343.52 69.4886i −2.15307 0.111360i
\(625\) −152.033 + 263.328i −0.243252 + 0.421325i
\(626\) −666.155 + 78.9603i −1.06415 + 0.126135i
\(627\) −30.3915 + 1111.31i −0.0484713 + 1.77242i
\(628\) 983.169 236.394i 1.56556 0.376423i
\(629\) 74.9959 129.897i 0.119230 0.206513i
\(630\) −63.2586 27.1652i −0.100410 0.0431194i
\(631\) 707.959 408.740i 1.12196 0.647766i 0.180062 0.983655i \(-0.442370\pi\)
0.941901 + 0.335890i \(0.109037\pi\)
\(632\) −1007.76 172.633i −1.59456 0.273153i
\(633\) −117.682 203.832i −0.185912 0.322009i
\(634\) −524.582 + 62.1794i −0.827417 + 0.0980748i
\(635\) 71.0954i 0.111961i
\(636\) 730.873 694.048i 1.14917 1.09127i
\(637\) −454.584 787.362i −0.713632 1.23605i
\(638\) 0.0963040 + 0.812477i 0.000150947 + 0.00127348i
\(639\) 246.469i 0.385711i
\(640\) 266.545 + 59.9774i 0.416476 + 0.0937147i
\(641\) 118.269 204.847i 0.184506 0.319574i −0.758904 0.651203i \(-0.774265\pi\)
0.943410 + 0.331628i \(0.107598\pi\)
\(642\) 484.756 + 648.935i 0.755071 + 1.01080i
\(643\) −364.648 210.529i −0.567103 0.327417i 0.188888 0.981999i \(-0.439512\pi\)
−0.755992 + 0.654581i \(0.772845\pi\)
\(644\) −21.8627 + 73.9001i −0.0339483 + 0.114752i
\(645\) 534.588 0.828818
\(646\) −264.231 122.129i −0.409026 0.189055i
\(647\) 633.110i 0.978532i 0.872135 + 0.489266i \(0.162735\pi\)
−0.872135 + 0.489266i \(0.837265\pi\)
\(648\) −111.296 + 649.702i −0.171753 + 1.00263i
\(649\) −511.513 + 885.967i −0.788156 + 1.36513i
\(650\) −487.096 652.068i −0.749379 1.00318i
\(651\) −281.764 162.677i −0.432818 0.249887i
\(652\) 168.737 160.235i 0.258798 0.245759i
\(653\) −763.077 −1.16857 −0.584286 0.811548i \(-0.698625\pi\)
−0.584286 + 0.811548i \(0.698625\pi\)
\(654\) −61.4625 518.534i −0.0939793 0.792865i
\(655\) 25.3088 14.6120i 0.0386393 0.0223084i
\(656\) 422.524 + 273.979i 0.644092 + 0.417652i
\(657\) −818.095 −1.24520
\(658\) −324.299 + 38.4396i −0.492856 + 0.0584189i
\(659\) −308.832 + 178.304i −0.468637 + 0.270568i −0.715669 0.698440i \(-0.753878\pi\)
0.247032 + 0.969007i \(0.420545\pi\)
\(660\) −141.719 + 479.038i −0.214726 + 0.725815i
\(661\) 131.256 + 227.342i 0.198572 + 0.343937i 0.948066 0.318075i \(-0.103036\pi\)
−0.749494 + 0.662011i \(0.769703\pi\)
\(662\) 1123.21 + 482.343i 1.69670 + 0.728614i
\(663\) 557.800 + 322.046i 0.841327 + 0.485740i
\(664\) 246.527 + 667.185i 0.371275 + 1.00480i
\(665\) −73.9391 2.02205i −0.111187 0.00304068i
\(666\) 343.860 40.7582i 0.516306 0.0611984i
\(667\) 0.270165 + 0.155980i 0.000405045 + 0.000233853i
\(668\) −617.132 182.573i −0.923851 0.273313i
\(669\) −87.1092 150.878i −0.130208 0.225527i
\(670\) −26.1674 11.2371i −0.0390558 0.0167718i
\(671\) −567.716 + 327.771i −0.846074 + 0.488481i
\(672\) 204.865 137.140i 0.304859 0.204078i
\(673\) 776.136 1.15325 0.576624 0.817010i \(-0.304370\pi\)
0.576624 + 0.817010i \(0.304370\pi\)
\(674\) −82.4190 110.333i −0.122283 0.163699i
\(675\) −11.8051 + 6.81567i −0.0174890 + 0.0100973i
\(676\) 883.779 212.496i 1.30737 0.314344i
\(677\) 114.432 0.169029 0.0845144 0.996422i \(-0.473066\pi\)
0.0845144 + 0.996422i \(0.473066\pi\)
\(678\) 228.382 170.602i 0.336847 0.251626i
\(679\) 204.715 + 118.192i 0.301494 + 0.174068i
\(680\) −100.610 83.5893i −0.147956 0.122925i
\(681\) 585.168 1013.54i 0.859278 1.48831i
\(682\) −461.665 + 1075.06i −0.676928 + 1.57634i
\(683\) 614.331i 0.899460i −0.893164 0.449730i \(-0.851520\pi\)
0.893164 0.449730i \(-0.148480\pi\)
\(684\) −139.179 657.433i −0.203478 0.961159i
\(685\) 285.004 0.416064
\(686\) 317.325 + 136.269i 0.462573 + 0.198643i
\(687\) −516.440 298.167i −0.751733 0.434013i
\(688\) −516.155 + 796.001i −0.750225 + 1.15698i
\(689\) −593.727 + 1028.37i −0.861723 + 1.49255i
\(690\) 113.994 + 152.602i 0.165209 + 0.221163i
\(691\) 388.024i 0.561540i −0.959775 0.280770i \(-0.909410\pi\)
0.959775 0.280770i \(-0.0905898\pi\)
\(692\) 959.625 230.733i 1.38674 0.333429i
\(693\) 111.698 + 193.466i 0.161180 + 0.279172i
\(694\) 789.972 590.111i 1.13829 0.850303i
\(695\) 474.468i 0.682687i
\(696\) −0.345885 0.936082i −0.000496961 0.00134495i
\(697\) −120.548 208.796i −0.172953 0.299564i
\(698\) −142.481 + 331.790i −0.204128 + 0.475344i
\(699\) −326.189 + 188.325i −0.466651 + 0.269421i
\(700\) 143.023 + 42.3122i 0.204319 + 0.0604459i
\(701\) 630.359 1091.81i 0.899229 1.55751i 0.0707461 0.997494i \(-0.477462\pi\)
0.828482 0.560015i \(-0.189205\pi\)
\(702\) −3.12452 26.3603i −0.00445089 0.0375503i
\(703\) 327.151 177.137i 0.465365 0.251973i
\(704\) −576.455 673.541i −0.818828 0.956734i
\(705\) −403.579 + 699.019i −0.572452 + 0.991516i
\(706\) 348.272 811.009i 0.493304 1.14874i
\(707\) −144.206 + 83.2571i −0.203968 + 0.117761i
\(708\) 353.989 1196.55i 0.499985 1.69005i
\(709\) −644.880 1116.97i −0.909563 1.57541i −0.814672 0.579921i \(-0.803083\pi\)
−0.0948904 0.995488i \(-0.530250\pi\)
\(710\) 14.0063 + 118.166i 0.0197272 + 0.166431i
\(711\) 1130.07i 1.58942i
\(712\) −384.183 319.188i −0.539583 0.448298i
\(713\) 223.055 + 386.342i 0.312840 + 0.541854i
\(714\) −117.210 + 13.8931i −0.164160 + 0.0194581i
\(715\) 588.553i 0.823151i
\(716\) 375.267 356.359i 0.524116 0.497708i
\(717\) −173.804 + 301.038i −0.242405 + 0.419858i
\(718\) −222.015 + 165.846i −0.309213 + 0.230983i
\(719\) 826.687 + 477.288i 1.14977 + 0.663822i 0.948832 0.315781i \(-0.102266\pi\)
0.200942 + 0.979603i \(0.435600\pi\)
\(720\) 15.5975 301.567i 0.0216631 0.418843i
\(721\) 123.689 0.171551
\(722\) −399.830 601.182i −0.553781 0.832662i
\(723\) 188.345i 0.260504i
\(724\) −218.202 + 737.565i −0.301384 + 1.01874i
\(725\) 0.301877 0.522866i 0.000416382 0.000721194i
\(726\) 479.753 358.376i 0.660816 0.493631i
\(727\) 882.411 + 509.460i 1.21377 + 0.700771i 0.963578 0.267426i \(-0.0861730\pi\)
0.250192 + 0.968196i \(0.419506\pi\)
\(728\) −185.609 + 223.403i −0.254957 + 0.306873i
\(729\) 703.208 0.964620
\(730\) −392.222 + 46.4906i −0.537291 + 0.0636858i
\(731\) 393.354 227.103i 0.538105 0.310675i
\(732\) 579.809 550.596i 0.792089 0.752180i
\(733\) −442.473 −0.603647 −0.301823 0.953364i \(-0.597595\pi\)
−0.301823 + 0.953364i \(0.597595\pi\)
\(734\) 82.7874 + 698.443i 0.112789 + 0.951557i
\(735\) 356.619 205.894i 0.485195 0.280128i
\(736\) −337.288 + 22.3969i −0.458272 + 0.0304306i
\(737\) 46.2046 + 80.0288i 0.0626929 + 0.108587i
\(738\) 219.623 511.427i 0.297592 0.692991i
\(739\) −396.012 228.638i −0.535876 0.309388i 0.207530 0.978229i \(-0.433458\pi\)
−0.743406 + 0.668841i \(0.766791\pi\)
\(740\) 162.542 39.0817i 0.219651 0.0528131i
\(741\) 760.660 + 1404.85i 1.02653 + 1.89588i
\(742\) −25.6134 216.090i −0.0345194 0.291226i
\(743\) −1040.55 600.759i −1.40046 0.808559i −0.406025 0.913862i \(-0.633085\pi\)
−0.994440 + 0.105303i \(0.966419\pi\)
\(744\) 240.953 1406.59i 0.323862 1.89058i
\(745\) −25.3037 43.8273i −0.0339647 0.0588287i
\(746\) −155.304 + 361.649i −0.208182 + 0.484785i
\(747\) 680.825 393.075i 0.911413 0.526204i
\(748\) 99.2265 + 412.686i 0.132656 + 0.551719i
\(749\) 174.876 0.233479
\(750\) 656.496 490.404i 0.875327 0.653871i
\(751\) −257.509 + 148.673i −0.342888 + 0.197967i −0.661548 0.749902i \(-0.730100\pi\)
0.318660 + 0.947869i \(0.396767\pi\)
\(752\) −651.176 1275.84i −0.865925 1.69660i
\(753\) 462.731 0.614517
\(754\) 0.703619 + 0.941924i 0.000933182 + 0.00124924i
\(755\) −143.702 82.9663i −0.190334 0.109889i
\(756\) 3.34962 + 3.52735i 0.00443072 + 0.00466580i
\(757\) −153.556 + 265.967i −0.202848 + 0.351344i −0.949445 0.313933i \(-0.898353\pi\)
0.746597 + 0.665277i \(0.231687\pi\)
\(758\) 311.031 + 133.566i 0.410331 + 0.176209i
\(759\) 618.088i 0.814345i
\(760\) −104.088 307.286i −0.136958 0.404324i
\(761\) −198.836 −0.261283 −0.130641 0.991430i \(-0.541704\pi\)
−0.130641 + 0.991430i \(0.541704\pi\)
\(762\) 111.033 258.558i 0.145712 0.339315i
\(763\) −97.6294 56.3664i −0.127955 0.0738746i
\(764\) 3.74406 3.55542i 0.00490060 0.00465369i
\(765\) −72.2866 + 125.204i −0.0944923 + 0.163665i
\(766\) −635.429 + 474.667i −0.829542 + 0.619669i
\(767\) 1470.10i 1.91669i
\(768\) 875.694 + 634.399i 1.14023 + 0.826041i
\(769\) 360.826 + 624.969i 0.469214 + 0.812703i 0.999381 0.0351906i \(-0.0112038\pi\)
−0.530166 + 0.847894i \(0.677870\pi\)
\(770\) 64.5459 + 86.4066i 0.0838259 + 0.112216i
\(771\) 1892.36i 2.45443i
\(772\) −1451.29 + 348.950i −1.87991 + 0.452007i
\(773\) 593.625 + 1028.19i 0.767950 + 1.33013i 0.938673 + 0.344810i \(0.112056\pi\)
−0.170723 + 0.985319i \(0.554610\pi\)
\(774\) 963.487 + 413.751i 1.24482 + 0.534563i
\(775\) 747.711 431.691i 0.964789 0.557021i
\(776\) −175.063 + 1021.95i −0.225597 + 1.31695i
\(777\) 75.4247 130.639i 0.0970717 0.168133i
\(778\) 764.939 90.6692i 0.983212 0.116541i
\(779\) 16.3477 597.776i 0.0209855 0.767364i
\(780\) 167.824 + 697.984i 0.215159 + 0.894851i
\(781\) 193.061 334.392i 0.247197 0.428158i
\(782\) 148.706 + 63.8592i 0.190162 + 0.0816613i
\(783\) 0.0170527 0.00984536i 2.17786e−5 1.25739e-5i
\(784\) −37.7462 + 729.800i −0.0481457 + 0.930867i
\(785\) −269.791 467.292i −0.343683 0.595277i
\(786\) 114.863 13.6148i 0.146136 0.0173216i
\(787\) 701.705i 0.891620i −0.895128 0.445810i \(-0.852916\pi\)
0.895128 0.445810i \(-0.147084\pi\)
\(788\) −528.212 556.237i −0.670319 0.705885i
\(789\) −664.633 1151.18i −0.842373 1.45903i
\(790\) 64.2198 + 541.796i 0.0812908 + 0.685817i
\(791\) 61.5448i 0.0778064i
\(792\) −626.179 + 753.685i −0.790630 + 0.951622i
\(793\) −471.010 + 815.814i −0.593960 + 1.02877i
\(794\) 338.172 + 452.706i 0.425910 + 0.570159i
\(795\) −465.776 268.916i −0.585882 0.338259i
\(796\) −1264.04 373.954i −1.58798 0.469791i
\(797\) 262.955 0.329930 0.164965 0.986299i \(-0.447249\pi\)
0.164965 + 0.986299i \(0.447249\pi\)
\(798\) −265.742 122.828i −0.333010 0.153919i
\(799\) 685.792i 0.858313i
\(800\) 43.3461 + 652.774i 0.0541826 + 0.815968i
\(801\) −276.028 + 478.095i −0.344605 + 0.596873i
\(802\) 9.58735 + 12.8344i 0.0119543 + 0.0160030i
\(803\) 1109.93 + 640.819i 1.38223 + 0.798031i
\(804\) −77.6155 81.7336i −0.0965367 0.101659i
\(805\) 41.1235 0.0510851
\(806\) 197.901 + 1669.61i 0.245535 + 2.07148i
\(807\) −1064.97 + 614.859i −1.31966 + 0.761907i
\(808\) −561.780 466.740i −0.695273 0.577649i
\(809\) −1368.29 −1.69134 −0.845669 0.533708i \(-0.820798\pi\)
−0.845669 + 0.533708i \(0.820798\pi\)
\(810\) 349.294 41.4023i 0.431227 0.0511139i
\(811\) −219.521 + 126.740i −0.270679 + 0.156277i −0.629196 0.777246i \(-0.716616\pi\)
0.358517 + 0.933523i \(0.383283\pi\)
\(812\) −0.206599 0.0611206i −0.000254433 7.52717e-5i
\(813\) 272.277 + 471.598i 0.334904 + 0.580071i
\(814\) −498.450 214.050i −0.612346 0.262961i
\(815\) −107.534 62.0846i −0.131943 0.0761774i
\(816\) −235.352 461.123i −0.288421 0.565102i
\(817\) 1126.16 + 30.7977i 1.37841 + 0.0376961i
\(818\) −308.532 + 36.5708i −0.377179 + 0.0447075i
\(819\) 278.013 + 160.511i 0.339455 + 0.195984i
\(820\) 76.2312 257.676i 0.0929649 0.314239i
\(821\) −772.109 1337.33i −0.940450 1.62891i −0.764615 0.644487i \(-0.777071\pi\)
−0.175835 0.984420i \(-0.556263\pi\)
\(822\) 1036.50 + 445.103i 1.26094 + 0.541488i
\(823\) 394.293 227.645i 0.479093 0.276604i −0.240946 0.970539i \(-0.577458\pi\)
0.720038 + 0.693934i \(0.244124\pi\)
\(824\) 188.040 + 508.899i 0.228203 + 0.617596i
\(825\) −1196.22 −1.44997
\(826\) −161.224 215.828i −0.195187 0.261294i
\(827\) 961.939 555.376i 1.16317 0.671555i 0.211106 0.977463i \(-0.432294\pi\)
0.952061 + 0.305909i \(0.0989602\pi\)
\(828\) 87.3431 + 363.262i 0.105487 + 0.438723i
\(829\) 200.976 0.242432 0.121216 0.992626i \(-0.461321\pi\)
0.121216 + 0.992626i \(0.461321\pi\)
\(830\) 304.073 227.143i 0.366353 0.273666i
\(831\) −84.5055 48.7893i −0.101691 0.0587115i
\(832\) −1201.34 424.027i −1.44391 0.509648i
\(833\) 174.935 302.997i 0.210007 0.363742i
\(834\) −740.997 + 1725.53i −0.888486 + 2.06898i
\(835\) 343.418i 0.411279i
\(836\) −326.143 + 1000.98i −0.390123 + 1.19734i
\(837\) 28.1582 0.0336418
\(838\) −740.143 317.840i −0.883225 0.379284i
\(839\) −671.461 387.668i −0.800311 0.462060i 0.0432688 0.999063i \(-0.486223\pi\)
−0.843580 + 0.537004i \(0.819556\pi\)
\(840\) −101.186 84.0674i −0.120459 0.100080i
\(841\) 420.500 728.327i 0.499999 0.866025i
\(842\) 544.850 + 729.382i 0.647090 + 0.866250i
\(843\) 280.546i 0.332795i
\(844\) −52.1052 216.707i −0.0617360 0.256762i
\(845\) −242.518 420.053i −0.287003 0.497104i
\(846\) −1268.38 + 947.486i −1.49927 + 1.11996i
\(847\) 129.284i 0.152638i
\(848\) 850.132 433.897i 1.00251 0.511671i
\(849\) 205.809 + 356.471i 0.242413 + 0.419872i
\(850\) 123.590 287.800i 0.145401 0.338589i
\(851\) −179.127 + 103.419i −0.210490 + 0.121526i
\(852\) −133.607 + 451.616i −0.156815 + 0.530066i
\(853\) −328.774 + 569.453i −0.385432 + 0.667588i −0.991829 0.127574i \(-0.959281\pi\)
0.606397 + 0.795162i \(0.292614\pi\)
\(854\) −20.3194 171.426i −0.0237932 0.200734i
\(855\) −315.333 + 170.738i −0.368810 + 0.199694i
\(856\) 265.858 + 719.502i 0.310582 + 0.840540i
\(857\) 325.821 564.338i 0.380187 0.658504i −0.610901 0.791707i \(-0.709193\pi\)
0.991089 + 0.133203i \(0.0425262\pi\)
\(858\) 919.169 2140.43i 1.07129 2.49468i
\(859\) −746.478 + 430.979i −0.869008 + 0.501722i −0.867019 0.498276i \(-0.833967\pi\)
−0.00198969 + 0.999998i \(0.500633\pi\)
\(860\) 485.441 + 143.613i 0.564466 + 0.166992i
\(861\) −121.238 209.990i −0.140810 0.243891i
\(862\) 116.305 + 981.217i 0.134925 + 1.13830i
\(863\) 658.610i 0.763163i −0.924335 0.381582i \(-0.875380\pi\)
0.924335 0.381582i \(-0.124620\pi\)
\(864\) −9.42045 + 19.1441i −0.0109033 + 0.0221575i
\(865\) −263.331 456.103i −0.304429 0.527286i
\(866\) −506.468 + 60.0323i −0.584836 + 0.0693214i
\(867\) 972.872i 1.12211i
\(868\) −212.159 223.415i −0.244422 0.257391i
\(869\) 885.195 1533.20i 1.01864 1.76433i
\(870\) −0.426624 + 0.318689i −0.000490372 + 0.000366309i
\(871\) 115.002 + 66.3966i 0.132035 + 0.0762304i
\(872\) 83.4886 487.374i 0.0957438 0.558915i
\(873\) 1145.98 1.31270
\(874\) 231.349 + 328.039i 0.264701 + 0.375331i
\(875\) 176.913i 0.202187i
\(876\) −1499.03 443.475i −1.71122 0.506250i
\(877\) 571.800 990.387i 0.651996 1.12929i −0.330642 0.943756i \(-0.607265\pi\)
0.982638 0.185534i \(-0.0594014\pi\)
\(878\) 148.381 110.841i 0.168999 0.126242i
\(879\) −963.462 556.255i −1.09609 0.632827i
\(880\) −257.381 + 396.926i −0.292478 + 0.451053i
\(881\) 1399.10 1.58808 0.794041 0.607864i \(-0.207973\pi\)
0.794041 + 0.607864i \(0.207973\pi\)
\(882\) 802.088 95.0726i 0.909397 0.107792i
\(883\) 347.651 200.716i 0.393716 0.227312i −0.290053 0.957011i \(-0.593673\pi\)
0.683769 + 0.729699i \(0.260340\pi\)
\(884\) 420.003 + 442.288i 0.475117 + 0.500326i
\(885\) −665.850 −0.752373
\(886\) −86.9198 733.306i −0.0981036 0.827660i
\(887\) −782.180 + 451.592i −0.881826 + 0.509123i −0.871260 0.490821i \(-0.836697\pi\)
−0.0105662 + 0.999944i \(0.503363\pi\)
\(888\) 652.163 + 111.717i 0.734418 + 0.125808i
\(889\) −30.3754 52.6118i −0.0341681 0.0591809i
\(890\) −105.168 + 244.901i −0.118166 + 0.275170i
\(891\) −988.451 570.682i −1.10937 0.640496i
\(892\) −38.5687 160.408i −0.0432384 0.179830i
\(893\) −890.449 + 1449.30i −0.997143 + 1.62296i
\(894\) −23.5769 198.908i −0.0263723 0.222492i
\(895\) −239.153 138.075i −0.267210 0.154274i
\(896\) 222.873 69.4968i 0.248742 0.0775634i
\(897\) −444.100 769.203i −0.495094 0.857529i
\(898\) −360.832 + 840.257i −0.401818 + 0.935698i
\(899\) −1.08008 + 0.623585i −0.00120143 + 0.000693643i
\(900\) 703.043 169.040i 0.781159 0.187823i
\(901\) −456.963 −0.507173
\(902\) −698.573 + 521.835i −0.774471 + 0.578531i
\(903\) 395.604 228.402i 0.438100 0.252937i
\(904\) 253.217 93.5646i 0.280108 0.103501i
\(905\) 410.436 0.453521
\(906\) −393.039 526.155i −0.433818 0.580745i
\(907\) 1216.26 + 702.209i 1.34097 + 0.774211i 0.986950 0.161026i \(-0.0514802\pi\)
0.354023 + 0.935237i \(0.384814\pi\)
\(908\) 803.652 763.160i 0.885080 0.840485i
\(909\) −403.629 + 699.105i −0.444036 + 0.769093i
\(910\) 142.410 + 61.1555i 0.156495 + 0.0672038i
\(911\) 584.988i 0.642138i 0.947056 + 0.321069i \(0.104042\pi\)
−0.947056 + 0.321069i \(0.895958\pi\)
\(912\) 101.359 1280.09i 0.111139 1.40361i
\(913\) −1231.59 −1.34895
\(914\) 65.9151 153.494i 0.0721172 0.167937i
\(915\) −369.505 213.334i −0.403831 0.233152i
\(916\) −388.861 409.494i −0.424521 0.447045i
\(917\) 12.4859 21.6263i 0.0136161 0.0235837i
\(918\) 8.18387 6.11337i 0.00891489 0.00665944i
\(919\) 299.511i 0.325909i −0.986634 0.162955i \(-0.947898\pi\)
0.986634 0.162955i \(-0.0521025\pi\)
\(920\) 62.5187 + 169.197i 0.0679551 + 0.183909i
\(921\) 598.851 + 1037.24i 0.650218 + 1.12621i
\(922\) 289.404 + 387.420i 0.313887 + 0.420196i
\(923\) 554.862i 0.601151i
\(924\) 99.7939 + 415.046i 0.108002 + 0.449184i
\(925\) 200.153 + 346.675i 0.216381 + 0.374784i
\(926\) 292.641 + 125.669i 0.316027 + 0.135712i
\(927\) 519.303 299.820i 0.560197 0.323430i
\(928\) −0.0626142 0.942944i −6.74722e−5 0.00101610i
\(929\) −119.560 + 207.084i −0.128697 + 0.222910i −0.923172 0.384387i \(-0.874413\pi\)
0.794475 + 0.607297i \(0.207746\pi\)
\(930\) −756.214 + 89.6350i −0.813133 + 0.0963818i
\(931\) 763.114 413.191i 0.819671 0.443814i
\(932\) −346.793 + 83.3833i −0.372096 + 0.0894670i
\(933\) −537.520 + 931.011i −0.576120 + 0.997869i
\(934\) 32.4052 + 13.9158i 0.0346950 + 0.0148991i
\(935\) 196.146 113.245i 0.209782 0.121118i
\(936\) −237.745 + 1387.87i −0.254002 + 1.48276i
\(937\) −472.094 817.691i −0.503836 0.872669i −0.999990 0.00443477i \(-0.998588\pi\)
0.496154 0.868234i \(-0.334745\pi\)
\(938\) −24.1654 + 2.86435i −0.0257627 + 0.00305368i
\(939\) 1416.77i 1.50880i
\(940\) −554.263 + 526.336i −0.589641 + 0.559932i
\(941\) 490.567 + 849.688i 0.521326 + 0.902963i 0.999692 + 0.0248024i \(0.00789565\pi\)
−0.478367 + 0.878160i \(0.658771\pi\)
\(942\) −251.379 2120.78i −0.266857 2.25136i
\(943\) 332.471i 0.352568i
\(944\) 642.892 991.451i 0.681029 1.05027i
\(945\) 1.29785 2.24794i 0.00137338 0.00237877i
\(946\) −983.095 1316.05i −1.03921 1.39118i
\(947\) −780.522 450.635i −0.824205 0.475855i 0.0276593 0.999617i \(-0.491195\pi\)
−0.851864 + 0.523762i \(0.824528\pi\)
\(948\) −612.594 + 2070.68i −0.646196 + 2.18427i
\(949\) 1841.73 1.94071
\(950\) 634.873 447.743i 0.668288 0.471308i
\(951\) 1115.67i 1.17316i
\(952\) −110.167 18.8719i −0.115721 0.0198234i
\(953\) −596.943 + 1033.94i −0.626383 + 1.08493i 0.361889 + 0.932221i \(0.382132\pi\)
−0.988272 + 0.152706i \(0.951201\pi\)
\(954\) −631.337 845.161i −0.661779 0.885913i
\(955\) −2.38604 1.37758i −0.00249848 0.00144250i
\(956\) −238.698 + 226.671i −0.249684 + 0.237103i
\(957\) 1.72796 0.00180560
\(958\) −44.7720 377.723i −0.0467348 0.394282i
\(959\) 210.908 121.768i 0.219925 0.126974i
\(960\) 192.054 544.119i 0.200056 0.566790i
\(961\) −822.485 −0.855864
\(962\) −774.112 + 91.7565i −0.804690 + 0.0953810i
\(963\) 734.212 423.898i 0.762422 0.440184i
\(964\) −50.5976 + 171.029i −0.0524871 + 0.177416i
\(965\) 398.249 + 689.787i 0.412693 + 0.714806i
\(966\) 149.557 + 64.2244i 0.154821 + 0.0664848i
\(967\) −18.5798 10.7271i −0.0192139 0.0110931i 0.490362 0.871519i \(-0.336864\pi\)
−0.509576 + 0.860426i \(0.670198\pi\)
\(968\) 531.923 196.547i 0.549507 0.203044i
\(969\) −321.831 + 523.815i −0.332127 + 0.540572i
\(970\) 549.424 65.1239i 0.566416 0.0671381i
\(971\) 1084.55 + 626.166i 1.11694 + 0.644867i 0.940619 0.339465i \(-0.110246\pi\)
0.176324 + 0.984332i \(0.443580\pi\)
\(972\) 1311.95 + 388.128i 1.34974 + 0.399308i
\(973\) 202.716 + 351.114i 0.208341 + 0.360857i
\(974\) −775.247 332.915i −0.795942 0.341802i
\(975\) −1488.68 + 859.493i −1.52686 + 0.881531i
\(976\) 674.419 344.215i 0.691003 0.352680i
\(977\) 692.289 0.708586 0.354293 0.935134i \(-0.384722\pi\)
0.354293 + 0.935134i \(0.384722\pi\)
\(978\) −294.116 393.728i −0.300732 0.402585i
\(979\) 748.990 432.430i 0.765056 0.441705i
\(980\) 379.145 91.1620i 0.386883 0.0930224i
\(981\) −546.526 −0.557111
\(982\) −1308.63 + 977.548i −1.33262 + 0.995467i
\(983\) 980.241 + 565.942i 0.997193 + 0.575730i 0.907417 0.420232i \(-0.138051\pi\)
0.0897765 + 0.995962i \(0.471385\pi\)
\(984\) 679.660 818.057i 0.690712 0.831358i
\(985\) −204.661 + 354.483i −0.207778 + 0.359881i
\(986\) −0.178529 + 0.415733i −0.000181063 + 0.000421635i
\(987\) 689.714i 0.698799i
\(988\) 313.326 + 1480.04i 0.317132 + 1.49802i
\(989\) −626.349 −0.633315
\(990\) 480.443 + 206.317i 0.485296 + 0.208401i
\(991\) 1188.45 + 686.153i 1.19924 + 0.692384i 0.960387 0.278671i \(-0.0898938\pi\)
0.238857 + 0.971055i \(0.423227\pi\)
\(992\) 596.673 1212.55i 0.601485 1.22233i
\(993\) 1290.85 2235.82i 1.29995 2.25158i
\(994\) 60.8511 + 81.4604i 0.0612184 + 0.0819522i
\(995\) 703.403i 0.706938i
\(996\) 1460.58 351.184i 1.46645 0.352594i
\(997\) 658.351 + 1140.30i 0.660332 + 1.14373i 0.980528 + 0.196377i \(0.0629176\pi\)
−0.320197 + 0.947351i \(0.603749\pi\)
\(998\) 826.754 617.587i 0.828411 0.618825i
\(999\) 13.0555i 0.0130686i
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 76.3.g.c.11.10 yes 28
4.3 odd 2 inner 76.3.g.c.11.12 yes 28
19.7 even 3 inner 76.3.g.c.7.12 yes 28
76.7 odd 6 inner 76.3.g.c.7.10 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.3.g.c.7.10 28 76.7 odd 6 inner
76.3.g.c.7.12 yes 28 19.7 even 3 inner
76.3.g.c.11.10 yes 28 1.1 even 1 trivial
76.3.g.c.11.12 yes 28 4.3 odd 2 inner