Properties

Label 605.2.e.c.362.7
Level $605$
Weight $2$
Character 605.362
Analytic conductor $4.831$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(362,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.e (of order \(4\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 362.7
Character \(\chi\) \(=\) 605.362
Dual form 605.2.e.c.483.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.848475 + 0.848475i) q^{2} +(-0.258670 + 0.258670i) q^{3} +0.560180i q^{4} +(-0.152228 - 2.23088i) q^{5} -0.438950i q^{6} +(1.06376 - 1.06376i) q^{7} +(-2.17225 - 2.17225i) q^{8} +2.86618i q^{9} +O(q^{10})\) \(q+(-0.848475 + 0.848475i) q^{2} +(-0.258670 + 0.258670i) q^{3} +0.560180i q^{4} +(-0.152228 - 2.23088i) q^{5} -0.438950i q^{6} +(1.06376 - 1.06376i) q^{7} +(-2.17225 - 2.17225i) q^{8} +2.86618i q^{9} +(2.02201 + 1.76368i) q^{10} +(-0.144901 - 0.144901i) q^{12} +(-3.20135 - 3.20135i) q^{13} +1.80515i q^{14} +(0.616438 + 0.537684i) q^{15} +2.56584 q^{16} +(-2.50878 + 2.50878i) q^{17} +(-2.43188 - 2.43188i) q^{18} -7.43246 q^{19} +(1.24969 - 0.0852752i) q^{20} +0.550324i q^{21} +(1.84232 - 1.84232i) q^{23} +1.12379 q^{24} +(-4.95365 + 0.679206i) q^{25} +5.43253 q^{26} +(-1.51740 - 1.51740i) q^{27} +(0.595896 + 0.595896i) q^{28} -0.772905 q^{29} +(-0.979244 + 0.0668206i) q^{30} -6.48429 q^{31} +(2.16745 - 2.16745i) q^{32} -4.25728i q^{34} +(-2.53505 - 2.21118i) q^{35} -1.60558 q^{36} +(-2.92535 - 2.92535i) q^{37} +(6.30626 - 6.30626i) q^{38} +1.65618 q^{39} +(-4.51535 + 5.17670i) q^{40} -6.91063i q^{41} +(-0.466936 - 0.466936i) q^{42} +(-0.500677 - 0.500677i) q^{43} +(6.39410 - 0.436314i) q^{45} +3.12633i q^{46} +(5.46865 + 5.46865i) q^{47} +(-0.663705 + 0.663705i) q^{48} +4.73684i q^{49} +(3.62676 - 4.77934i) q^{50} -1.29789i q^{51} +(1.79333 - 1.79333i) q^{52} +(7.53208 - 7.53208i) q^{53} +2.57496 q^{54} -4.62150 q^{56} +(1.92255 - 1.92255i) q^{57} +(0.655791 - 0.655791i) q^{58} -12.2294i q^{59} +(-0.301200 + 0.345316i) q^{60} +3.31937i q^{61} +(5.50176 - 5.50176i) q^{62} +(3.04892 + 3.04892i) q^{63} +8.80973i q^{64} +(-6.65449 + 7.62916i) q^{65} +(-3.34899 - 3.34899i) q^{67} +(-1.40537 - 1.40537i) q^{68} +0.953105i q^{69} +(4.02706 - 0.274794i) q^{70} -11.9496 q^{71} +(6.22606 - 6.22606i) q^{72} +(-6.73109 - 6.73109i) q^{73} +4.96417 q^{74} +(1.10567 - 1.45705i) q^{75} -4.16351i q^{76} +(-1.40523 + 1.40523i) q^{78} +11.4583 q^{79} +(-0.390593 - 5.72408i) q^{80} -7.81353 q^{81} +(5.86350 + 5.86350i) q^{82} +(2.80014 + 2.80014i) q^{83} -0.308280 q^{84} +(5.97870 + 5.21488i) q^{85} +0.849623 q^{86} +(0.199927 - 0.199927i) q^{87} +9.96633i q^{89} +(-5.05504 + 5.79544i) q^{90} -6.81093 q^{91} +(1.03203 + 1.03203i) q^{92} +(1.67729 - 1.67729i) q^{93} -9.28003 q^{94} +(1.13143 + 16.5809i) q^{95} +1.12131i q^{96} +(-8.11524 - 8.11524i) q^{97} +(-4.01909 - 4.01909i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.848475 + 0.848475i −0.599963 + 0.599963i −0.940302 0.340340i \(-0.889458\pi\)
0.340340 + 0.940302i \(0.389458\pi\)
\(3\) −0.258670 + 0.258670i −0.149343 + 0.149343i −0.777825 0.628482i \(-0.783677\pi\)
0.628482 + 0.777825i \(0.283677\pi\)
\(4\) 0.560180i 0.280090i
\(5\) −0.152228 2.23088i −0.0680786 0.997680i
\(6\) 0.438950i 0.179200i
\(7\) 1.06376 1.06376i 0.402063 0.402063i −0.476897 0.878959i \(-0.658238\pi\)
0.878959 + 0.476897i \(0.158238\pi\)
\(8\) −2.17225 2.17225i −0.768006 0.768006i
\(9\) 2.86618i 0.955393i
\(10\) 2.02201 + 1.76368i 0.639415 + 0.557726i
\(11\) 0 0
\(12\) −0.144901 0.144901i −0.0418295 0.0418295i
\(13\) −3.20135 3.20135i −0.887895 0.887895i 0.106426 0.994321i \(-0.466059\pi\)
−0.994321 + 0.106426i \(0.966059\pi\)
\(14\) 1.80515i 0.482445i
\(15\) 0.616438 + 0.537684i 0.159164 + 0.138829i
\(16\) 2.56584 0.641460
\(17\) −2.50878 + 2.50878i −0.608469 + 0.608469i −0.942546 0.334077i \(-0.891575\pi\)
0.334077 + 0.942546i \(0.391575\pi\)
\(18\) −2.43188 2.43188i −0.573200 0.573200i
\(19\) −7.43246 −1.70512 −0.852562 0.522627i \(-0.824952\pi\)
−0.852562 + 0.522627i \(0.824952\pi\)
\(20\) 1.24969 0.0852752i 0.279440 0.0190681i
\(21\) 0.550324i 0.120091i
\(22\) 0 0
\(23\) 1.84232 1.84232i 0.384150 0.384150i −0.488445 0.872595i \(-0.662436\pi\)
0.872595 + 0.488445i \(0.162436\pi\)
\(24\) 1.12379 0.229393
\(25\) −4.95365 + 0.679206i −0.990731 + 0.135841i
\(26\) 5.43253 1.06541
\(27\) −1.51740 1.51740i −0.292024 0.292024i
\(28\) 0.595896 + 0.595896i 0.112614 + 0.112614i
\(29\) −0.772905 −0.143525 −0.0717624 0.997422i \(-0.522862\pi\)
−0.0717624 + 0.997422i \(0.522862\pi\)
\(30\) −0.979244 + 0.0668206i −0.178785 + 0.0121997i
\(31\) −6.48429 −1.16461 −0.582307 0.812969i \(-0.697850\pi\)
−0.582307 + 0.812969i \(0.697850\pi\)
\(32\) 2.16745 2.16745i 0.383154 0.383154i
\(33\) 0 0
\(34\) 4.25728i 0.730117i
\(35\) −2.53505 2.21118i −0.428502 0.373758i
\(36\) −1.60558 −0.267596
\(37\) −2.92535 2.92535i −0.480924 0.480924i 0.424503 0.905427i \(-0.360449\pi\)
−0.905427 + 0.424503i \(0.860449\pi\)
\(38\) 6.30626 6.30626i 1.02301 1.02301i
\(39\) 1.65618 0.265202
\(40\) −4.51535 + 5.17670i −0.713939 + 0.818509i
\(41\) 6.91063i 1.07926i −0.841902 0.539630i \(-0.818564\pi\)
0.841902 0.539630i \(-0.181436\pi\)
\(42\) −0.466936 0.466936i −0.0720499 0.0720499i
\(43\) −0.500677 0.500677i −0.0763525 0.0763525i 0.667899 0.744252i \(-0.267194\pi\)
−0.744252 + 0.667899i \(0.767194\pi\)
\(44\) 0 0
\(45\) 6.39410 0.436314i 0.953177 0.0650418i
\(46\) 3.12633i 0.460952i
\(47\) 5.46865 + 5.46865i 0.797684 + 0.797684i 0.982730 0.185046i \(-0.0592433\pi\)
−0.185046 + 0.982730i \(0.559243\pi\)
\(48\) −0.663705 + 0.663705i −0.0957976 + 0.0957976i
\(49\) 4.73684i 0.676691i
\(50\) 3.62676 4.77934i 0.512902 0.675901i
\(51\) 1.29789i 0.181741i
\(52\) 1.79333 1.79333i 0.248690 0.248690i
\(53\) 7.53208 7.53208i 1.03461 1.03461i 0.0352322 0.999379i \(-0.488783\pi\)
0.999379 0.0352322i \(-0.0112171\pi\)
\(54\) 2.57496 0.350407
\(55\) 0 0
\(56\) −4.62150 −0.617573
\(57\) 1.92255 1.92255i 0.254648 0.254648i
\(58\) 0.655791 0.655791i 0.0861095 0.0861095i
\(59\) 12.2294i 1.59214i −0.605206 0.796069i \(-0.706909\pi\)
0.605206 0.796069i \(-0.293091\pi\)
\(60\) −0.301200 + 0.345316i −0.0388847 + 0.0445801i
\(61\) 3.31937i 0.425001i 0.977161 + 0.212501i \(0.0681608\pi\)
−0.977161 + 0.212501i \(0.931839\pi\)
\(62\) 5.50176 5.50176i 0.698725 0.698725i
\(63\) 3.04892 + 3.04892i 0.384128 + 0.384128i
\(64\) 8.80973i 1.10122i
\(65\) −6.65449 + 7.62916i −0.825388 + 0.946281i
\(66\) 0 0
\(67\) −3.34899 3.34899i −0.409145 0.409145i 0.472296 0.881440i \(-0.343425\pi\)
−0.881440 + 0.472296i \(0.843425\pi\)
\(68\) −1.40537 1.40537i −0.170426 0.170426i
\(69\) 0.953105i 0.114740i
\(70\) 4.02706 0.274794i 0.481326 0.0328442i
\(71\) −11.9496 −1.41815 −0.709076 0.705132i \(-0.750888\pi\)
−0.709076 + 0.705132i \(0.750888\pi\)
\(72\) 6.22606 6.22606i 0.733748 0.733748i
\(73\) −6.73109 6.73109i −0.787815 0.787815i 0.193321 0.981136i \(-0.438074\pi\)
−0.981136 + 0.193321i \(0.938074\pi\)
\(74\) 4.96417 0.577073
\(75\) 1.10567 1.45705i 0.127672 0.168246i
\(76\) 4.16351i 0.477588i
\(77\) 0 0
\(78\) −1.40523 + 1.40523i −0.159111 + 0.159111i
\(79\) 11.4583 1.28915 0.644577 0.764539i \(-0.277033\pi\)
0.644577 + 0.764539i \(0.277033\pi\)
\(80\) −0.390593 5.72408i −0.0436697 0.639972i
\(81\) −7.81353 −0.868170
\(82\) 5.86350 + 5.86350i 0.647515 + 0.647515i
\(83\) 2.80014 + 2.80014i 0.307356 + 0.307356i 0.843883 0.536527i \(-0.180264\pi\)
−0.536527 + 0.843883i \(0.680264\pi\)
\(84\) −0.308280 −0.0336361
\(85\) 5.97870 + 5.21488i 0.648481 + 0.565634i
\(86\) 0.849623 0.0916172
\(87\) 0.199927 0.199927i 0.0214344 0.0214344i
\(88\) 0 0
\(89\) 9.96633i 1.05643i 0.849111 + 0.528214i \(0.177138\pi\)
−0.849111 + 0.528214i \(0.822862\pi\)
\(90\) −5.05504 + 5.79544i −0.532848 + 0.610893i
\(91\) −6.81093 −0.713979
\(92\) 1.03203 + 1.03203i 0.107597 + 0.107597i
\(93\) 1.67729 1.67729i 0.173927 0.173927i
\(94\) −9.28003 −0.957162
\(95\) 1.13143 + 16.5809i 0.116082 + 1.70117i
\(96\) 1.12131i 0.114443i
\(97\) −8.11524 8.11524i −0.823978 0.823978i 0.162698 0.986676i \(-0.447980\pi\)
−0.986676 + 0.162698i \(0.947980\pi\)
\(98\) −4.01909 4.01909i −0.405989 0.405989i
\(99\) 0 0
\(100\) −0.380477 2.77494i −0.0380477 0.277494i
\(101\) 3.77428i 0.375555i 0.982212 + 0.187778i \(0.0601284\pi\)
−0.982212 + 0.187778i \(0.939872\pi\)
\(102\) 1.10123 + 1.10123i 0.109038 + 0.109038i
\(103\) −9.28131 + 9.28131i −0.914515 + 0.914515i −0.996623 0.0821088i \(-0.973835\pi\)
0.0821088 + 0.996623i \(0.473835\pi\)
\(104\) 13.9083i 1.36382i
\(105\) 1.22771 0.0837749i 0.119812 0.00817559i
\(106\) 12.7816i 1.24146i
\(107\) −2.20766 + 2.20766i −0.213423 + 0.213423i −0.805720 0.592297i \(-0.798221\pi\)
0.592297 + 0.805720i \(0.298221\pi\)
\(108\) 0.850018 0.850018i 0.0817930 0.0817930i
\(109\) −2.26336 −0.216791 −0.108395 0.994108i \(-0.534571\pi\)
−0.108395 + 0.994108i \(0.534571\pi\)
\(110\) 0 0
\(111\) 1.51340 0.143645
\(112\) 2.72943 2.72943i 0.257907 0.257907i
\(113\) 13.9390 13.9390i 1.31127 1.31127i 0.390787 0.920481i \(-0.372203\pi\)
0.920481 0.390787i \(-0.127797\pi\)
\(114\) 3.26248i 0.305559i
\(115\) −4.39045 3.82954i −0.409412 0.357107i
\(116\) 0.432966i 0.0401998i
\(117\) 9.17565 9.17565i 0.848289 0.848289i
\(118\) 10.3764 + 10.3764i 0.955223 + 0.955223i
\(119\) 5.33748i 0.489286i
\(120\) −0.171073 2.50704i −0.0156167 0.228860i
\(121\) 0 0
\(122\) −2.81640 2.81640i −0.254985 0.254985i
\(123\) 1.78757 + 1.78757i 0.161180 + 0.161180i
\(124\) 3.63237i 0.326196i
\(125\) 2.26931 + 10.9476i 0.202974 + 0.979184i
\(126\) −5.17387 −0.460925
\(127\) −14.4700 + 14.4700i −1.28401 + 1.28401i −0.345637 + 0.938368i \(0.612337\pi\)
−0.938368 + 0.345637i \(0.887663\pi\)
\(128\) −3.13994 3.13994i −0.277534 0.277534i
\(129\) 0.259020 0.0228054
\(130\) −0.826985 12.1193i −0.0725314 1.06294i
\(131\) 8.57191i 0.748931i 0.927241 + 0.374465i \(0.122174\pi\)
−0.927241 + 0.374465i \(0.877826\pi\)
\(132\) 0 0
\(133\) −7.90634 + 7.90634i −0.685567 + 0.685567i
\(134\) 5.68307 0.490943
\(135\) −3.15415 + 3.61614i −0.271466 + 0.311227i
\(136\) 10.8994 0.934616
\(137\) −0.590371 0.590371i −0.0504388 0.0504388i 0.681438 0.731876i \(-0.261355\pi\)
−0.731876 + 0.681438i \(0.761355\pi\)
\(138\) −0.808686 0.808686i −0.0688399 0.0688399i
\(139\) 20.0766 1.70288 0.851438 0.524455i \(-0.175731\pi\)
0.851438 + 0.524455i \(0.175731\pi\)
\(140\) 1.23866 1.42008i 0.104686 0.120019i
\(141\) −2.82915 −0.238257
\(142\) 10.1389 10.1389i 0.850838 0.850838i
\(143\) 0 0
\(144\) 7.35416i 0.612847i
\(145\) 0.117658 + 1.72426i 0.00977096 + 0.143192i
\(146\) 11.4223 0.945319
\(147\) −1.22528 1.22528i −0.101059 0.101059i
\(148\) 1.63872 1.63872i 0.134702 0.134702i
\(149\) 2.37943 0.194930 0.0974651 0.995239i \(-0.468927\pi\)
0.0974651 + 0.995239i \(0.468927\pi\)
\(150\) 0.298137 + 2.17440i 0.0243428 + 0.177539i
\(151\) 17.9691i 1.46231i 0.682214 + 0.731153i \(0.261017\pi\)
−0.682214 + 0.731153i \(0.738983\pi\)
\(152\) 16.1452 + 16.1452i 1.30954 + 1.30954i
\(153\) −7.19062 7.19062i −0.581327 0.581327i
\(154\) 0 0
\(155\) 0.987093 + 14.4657i 0.0792852 + 1.16191i
\(156\) 0.927761i 0.0742803i
\(157\) −2.09908 2.09908i −0.167525 0.167525i 0.618365 0.785891i \(-0.287795\pi\)
−0.785891 + 0.618365i \(0.787795\pi\)
\(158\) −9.72205 + 9.72205i −0.773445 + 0.773445i
\(159\) 3.89664i 0.309024i
\(160\) −5.16526 4.50537i −0.408350 0.356180i
\(161\) 3.91957i 0.308905i
\(162\) 6.62958 6.62958i 0.520869 0.520869i
\(163\) 2.15084 2.15084i 0.168467 0.168467i −0.617838 0.786305i \(-0.711991\pi\)
0.786305 + 0.617838i \(0.211991\pi\)
\(164\) 3.87119 0.302290
\(165\) 0 0
\(166\) −4.75171 −0.368804
\(167\) −2.69793 + 2.69793i −0.208772 + 0.208772i −0.803746 0.594973i \(-0.797163\pi\)
0.594973 + 0.803746i \(0.297163\pi\)
\(168\) 1.19544 1.19544i 0.0922303 0.0922303i
\(169\) 7.49728i 0.576714i
\(170\) −9.49748 + 0.648078i −0.728423 + 0.0497053i
\(171\) 21.3028i 1.62906i
\(172\) 0.280469 0.280469i 0.0213855 0.0213855i
\(173\) 0.824604 + 0.824604i 0.0626935 + 0.0626935i 0.737758 0.675065i \(-0.235884\pi\)
−0.675065 + 0.737758i \(0.735884\pi\)
\(174\) 0.339266i 0.0257197i
\(175\) −4.54698 + 5.99200i −0.343719 + 0.452953i
\(176\) 0 0
\(177\) 3.16339 + 3.16339i 0.237775 + 0.237775i
\(178\) −8.45618 8.45618i −0.633818 0.633818i
\(179\) 6.06351i 0.453208i 0.973987 + 0.226604i \(0.0727623\pi\)
−0.973987 + 0.226604i \(0.927238\pi\)
\(180\) 0.244414 + 3.58185i 0.0182175 + 0.266975i
\(181\) 1.56433 0.116276 0.0581378 0.998309i \(-0.481484\pi\)
0.0581378 + 0.998309i \(0.481484\pi\)
\(182\) 5.77890 5.77890i 0.428361 0.428361i
\(183\) −0.858620 0.858620i −0.0634710 0.0634710i
\(184\) −8.00396 −0.590060
\(185\) −6.08078 + 6.97142i −0.447068 + 0.512549i
\(186\) 2.84628i 0.208699i
\(187\) 0 0
\(188\) −3.06342 + 3.06342i −0.223423 + 0.223423i
\(189\) −3.22830 −0.234824
\(190\) −15.0285 13.1085i −1.09028 0.950992i
\(191\) 1.33597 0.0966677 0.0483338 0.998831i \(-0.484609\pi\)
0.0483338 + 0.998831i \(0.484609\pi\)
\(192\) −2.27881 2.27881i −0.164459 0.164459i
\(193\) 1.17411 + 1.17411i 0.0845144 + 0.0845144i 0.748100 0.663586i \(-0.230966\pi\)
−0.663586 + 0.748100i \(0.730966\pi\)
\(194\) 13.7712 0.988712
\(195\) −0.252118 3.69475i −0.0180546 0.264587i
\(196\) −2.65348 −0.189534
\(197\) −3.99064 + 3.99064i −0.284321 + 0.284321i −0.834830 0.550508i \(-0.814434\pi\)
0.550508 + 0.834830i \(0.314434\pi\)
\(198\) 0 0
\(199\) 8.55260i 0.606278i −0.952946 0.303139i \(-0.901965\pi\)
0.952946 0.303139i \(-0.0980346\pi\)
\(200\) 12.2360 + 9.28516i 0.865214 + 0.656560i
\(201\) 1.73257 0.122206
\(202\) −3.20238 3.20238i −0.225319 0.225319i
\(203\) −0.822184 + 0.822184i −0.0577060 + 0.0577060i
\(204\) 0.727052 0.0509038
\(205\) −15.4168 + 1.05199i −1.07676 + 0.0734744i
\(206\) 15.7499i 1.09735i
\(207\) 5.28042 + 5.28042i 0.367015 + 0.367015i
\(208\) −8.21415 8.21415i −0.569549 0.569549i
\(209\) 0 0
\(210\) −0.970598 + 1.11276i −0.0669777 + 0.0767878i
\(211\) 12.1227i 0.834564i 0.908777 + 0.417282i \(0.137017\pi\)
−0.908777 + 0.417282i \(0.862983\pi\)
\(212\) 4.21932 + 4.21932i 0.289784 + 0.289784i
\(213\) 3.09099 3.09099i 0.211791 0.211791i
\(214\) 3.74629i 0.256091i
\(215\) −1.04073 + 1.19317i −0.0709774 + 0.0813733i
\(216\) 6.59235i 0.448553i
\(217\) −6.89772 + 6.89772i −0.468248 + 0.468248i
\(218\) 1.92040 1.92040i 0.130066 0.130066i
\(219\) 3.48226 0.235309
\(220\) 0 0
\(221\) 16.0630 1.08051
\(222\) −1.28408 + 1.28408i −0.0861818 + 0.0861818i
\(223\) 3.51789 3.51789i 0.235575 0.235575i −0.579440 0.815015i \(-0.696729\pi\)
0.815015 + 0.579440i \(0.196729\pi\)
\(224\) 4.61128i 0.308104i
\(225\) −1.94673 14.1981i −0.129782 0.946537i
\(226\) 23.6537i 1.57342i
\(227\) −4.85408 + 4.85408i −0.322177 + 0.322177i −0.849602 0.527425i \(-0.823158\pi\)
0.527425 + 0.849602i \(0.323158\pi\)
\(228\) 1.07697 + 1.07697i 0.0713244 + 0.0713244i
\(229\) 13.1801i 0.870964i −0.900197 0.435482i \(-0.856578\pi\)
0.900197 0.435482i \(-0.143422\pi\)
\(230\) 6.97446 0.475915i 0.459882 0.0313809i
\(231\) 0 0
\(232\) 1.67894 + 1.67894i 0.110228 + 0.110228i
\(233\) −10.6591 10.6591i −0.698301 0.698301i 0.265743 0.964044i \(-0.414383\pi\)
−0.964044 + 0.265743i \(0.914383\pi\)
\(234\) 15.5706i 1.01788i
\(235\) 11.3674 13.0324i 0.741528 0.850139i
\(236\) 6.85068 0.445942
\(237\) −2.96390 + 2.96390i −0.192526 + 0.192526i
\(238\) −4.52872 4.52872i −0.293553 0.293553i
\(239\) 13.3578 0.864047 0.432023 0.901862i \(-0.357800\pi\)
0.432023 + 0.901862i \(0.357800\pi\)
\(240\) 1.58168 + 1.37961i 0.102097 + 0.0890536i
\(241\) 6.28913i 0.405119i −0.979270 0.202559i \(-0.935074\pi\)
0.979270 0.202559i \(-0.0649259\pi\)
\(242\) 0 0
\(243\) 6.57333 6.57333i 0.421679 0.421679i
\(244\) −1.85944 −0.119039
\(245\) 10.5673 0.721080i 0.675121 0.0460681i
\(246\) −3.03342 −0.193404
\(247\) 23.7939 + 23.7939i 1.51397 + 1.51397i
\(248\) 14.0855 + 14.0855i 0.894430 + 0.894430i
\(249\) −1.44862 −0.0918029
\(250\) −11.2142 7.36332i −0.709250 0.465697i
\(251\) −4.11128 −0.259502 −0.129751 0.991547i \(-0.541418\pi\)
−0.129751 + 0.991547i \(0.541418\pi\)
\(252\) −1.70794 + 1.70794i −0.107590 + 0.107590i
\(253\) 0 0
\(254\) 24.5549i 1.54071i
\(255\) −2.89544 + 0.197576i −0.181320 + 0.0123727i
\(256\) −12.2911 −0.768195
\(257\) −5.68725 5.68725i −0.354761 0.354761i 0.507117 0.861877i \(-0.330711\pi\)
−0.861877 + 0.507117i \(0.830711\pi\)
\(258\) −0.219772 + 0.219772i −0.0136824 + 0.0136824i
\(259\) −6.22373 −0.386724
\(260\) −4.27370 3.72771i −0.265044 0.231183i
\(261\) 2.21528i 0.137123i
\(262\) −7.27305 7.27305i −0.449331 0.449331i
\(263\) 16.1103 + 16.1103i 0.993403 + 0.993403i 0.999978 0.00657518i \(-0.00209296\pi\)
−0.00657518 + 0.999978i \(0.502093\pi\)
\(264\) 0 0
\(265\) −17.9498 15.6566i −1.10265 0.961776i
\(266\) 13.4167i 0.822629i
\(267\) −2.57799 2.57799i −0.157770 0.157770i
\(268\) 1.87604 1.87604i 0.114597 0.114597i
\(269\) 14.0599i 0.857245i −0.903484 0.428622i \(-0.858999\pi\)
0.903484 0.428622i \(-0.141001\pi\)
\(270\) −0.391981 5.74442i −0.0238552 0.349594i
\(271\) 0.0709860i 0.00431209i −0.999998 0.00215605i \(-0.999314\pi\)
0.999998 0.00215605i \(-0.000686291\pi\)
\(272\) −6.43713 + 6.43713i −0.390308 + 0.390308i
\(273\) 1.76178 1.76178i 0.106628 0.106628i
\(274\) 1.00183 0.0605227
\(275\) 0 0
\(276\) −0.533910 −0.0321376
\(277\) 18.2120 18.2120i 1.09425 1.09425i 0.0991833 0.995069i \(-0.468377\pi\)
0.995069 0.0991833i \(-0.0316230\pi\)
\(278\) −17.0345 + 17.0345i −1.02166 + 1.02166i
\(279\) 18.5852i 1.11266i
\(280\) 0.703523 + 10.3100i 0.0420435 + 0.616141i
\(281\) 18.4946i 1.10330i −0.834077 0.551648i \(-0.813999\pi\)
0.834077 0.551648i \(-0.186001\pi\)
\(282\) 2.40046 2.40046i 0.142945 0.142945i
\(283\) −21.8500 21.8500i −1.29885 1.29885i −0.929155 0.369690i \(-0.879464\pi\)
−0.369690 0.929155i \(-0.620536\pi\)
\(284\) 6.69390i 0.397210i
\(285\) −4.58165 3.99632i −0.271394 0.236721i
\(286\) 0 0
\(287\) −7.35124 7.35124i −0.433930 0.433930i
\(288\) 6.21229 + 6.21229i 0.366063 + 0.366063i
\(289\) 4.41203i 0.259531i
\(290\) −1.56282 1.36316i −0.0917720 0.0800475i
\(291\) 4.19833 0.246111
\(292\) 3.77062 3.77062i 0.220659 0.220659i
\(293\) −21.0777 21.0777i −1.23137 1.23137i −0.963437 0.267936i \(-0.913659\pi\)
−0.267936 0.963437i \(-0.586341\pi\)
\(294\) 2.07923 0.121263
\(295\) −27.2824 + 1.86167i −1.58844 + 0.108390i
\(296\) 12.7092i 0.738705i
\(297\) 0 0
\(298\) −2.01888 + 2.01888i −0.116951 + 0.116951i
\(299\) −11.7958 −0.682170
\(300\) 0.816210 + 0.619374i 0.0471239 + 0.0357596i
\(301\) −1.06520 −0.0613970
\(302\) −15.2463 15.2463i −0.877329 0.877329i
\(303\) −0.976292 0.976292i −0.0560865 0.0560865i
\(304\) −19.0705 −1.09377
\(305\) 7.40511 0.505302i 0.424015 0.0289335i
\(306\) 12.2021 0.697549
\(307\) −0.837241 + 0.837241i −0.0477839 + 0.0477839i −0.730595 0.682811i \(-0.760757\pi\)
0.682811 + 0.730595i \(0.260757\pi\)
\(308\) 0 0
\(309\) 4.80159i 0.273153i
\(310\) −13.1113 11.4363i −0.744672 0.649535i
\(311\) −14.9492 −0.847689 −0.423844 0.905735i \(-0.639320\pi\)
−0.423844 + 0.905735i \(0.639320\pi\)
\(312\) −3.59765 3.59765i −0.203677 0.203677i
\(313\) 14.7481 14.7481i 0.833611 0.833611i −0.154398 0.988009i \(-0.549344\pi\)
0.988009 + 0.154398i \(0.0493437\pi\)
\(314\) 3.56204 0.201018
\(315\) 6.33765 7.26592i 0.357086 0.409388i
\(316\) 6.41868i 0.361079i
\(317\) 2.90042 + 2.90042i 0.162904 + 0.162904i 0.783852 0.620948i \(-0.213252\pi\)
−0.620948 + 0.783852i \(0.713252\pi\)
\(318\) −3.30621 3.30621i −0.185403 0.185403i
\(319\) 0 0
\(320\) 19.6534 1.34109i 1.09866 0.0749692i
\(321\) 1.14211i 0.0637463i
\(322\) 3.32566 + 3.32566i 0.185332 + 0.185332i
\(323\) 18.6464 18.6464i 1.03751 1.03751i
\(324\) 4.37698i 0.243165i
\(325\) 18.0328 + 13.6840i 1.00028 + 0.759052i
\(326\) 3.64988i 0.202148i
\(327\) 0.585463 0.585463i 0.0323762 0.0323762i
\(328\) −15.0116 + 15.0116i −0.828878 + 0.828878i
\(329\) 11.6346 0.641439
\(330\) 0 0
\(331\) 13.4680 0.740270 0.370135 0.928978i \(-0.379311\pi\)
0.370135 + 0.928978i \(0.379311\pi\)
\(332\) −1.56858 + 1.56858i −0.0860872 + 0.0860872i
\(333\) 8.38457 8.38457i 0.459472 0.459472i
\(334\) 4.57826i 0.250511i
\(335\) −6.96139 + 7.98101i −0.380341 + 0.436049i
\(336\) 1.41204i 0.0770333i
\(337\) −20.1440 + 20.1440i −1.09731 + 1.09731i −0.102589 + 0.994724i \(0.532713\pi\)
−0.994724 + 0.102589i \(0.967287\pi\)
\(338\) −6.36126 6.36126i −0.346007 0.346007i
\(339\) 7.21118i 0.391658i
\(340\) −2.92127 + 3.34914i −0.158428 + 0.181633i
\(341\) 0 0
\(342\) 18.0749 + 18.0749i 0.977377 + 0.977377i
\(343\) 12.4852 + 12.4852i 0.674135 + 0.674135i
\(344\) 2.17519i 0.117278i
\(345\) 2.12626 0.145090i 0.114474 0.00781136i
\(346\) −1.39931 −0.0752275
\(347\) 8.37190 8.37190i 0.449427 0.449427i −0.445737 0.895164i \(-0.647058\pi\)
0.895164 + 0.445737i \(0.147058\pi\)
\(348\) 0.111995 + 0.111995i 0.00600357 + 0.00600357i
\(349\) −8.20105 −0.438992 −0.219496 0.975613i \(-0.570441\pi\)
−0.219496 + 0.975613i \(0.570441\pi\)
\(350\) −1.22607 8.94207i −0.0655360 0.477973i
\(351\) 9.71548i 0.518574i
\(352\) 0 0
\(353\) 9.53600 9.53600i 0.507550 0.507550i −0.406224 0.913774i \(-0.633155\pi\)
0.913774 + 0.406224i \(0.133155\pi\)
\(354\) −5.36811 −0.285312
\(355\) 1.81906 + 26.6580i 0.0965457 + 1.41486i
\(356\) −5.58293 −0.295895
\(357\) −1.38064 1.38064i −0.0730714 0.0730714i
\(358\) −5.14474 5.14474i −0.271908 0.271908i
\(359\) 14.3410 0.756889 0.378444 0.925624i \(-0.376459\pi\)
0.378444 + 0.925624i \(0.376459\pi\)
\(360\) −14.8374 12.9418i −0.781998 0.682093i
\(361\) 36.2415 1.90745
\(362\) −1.32729 + 1.32729i −0.0697610 + 0.0697610i
\(363\) 0 0
\(364\) 3.81534i 0.199978i
\(365\) −13.9916 + 16.0409i −0.732354 + 0.839620i
\(366\) 1.45704 0.0761604
\(367\) 14.2153 + 14.2153i 0.742034 + 0.742034i 0.972969 0.230935i \(-0.0741784\pi\)
−0.230935 + 0.972969i \(0.574178\pi\)
\(368\) 4.72710 4.72710i 0.246417 0.246417i
\(369\) 19.8071 1.03112
\(370\) −0.755687 11.0745i −0.0392863 0.575734i
\(371\) 16.0246i 0.831958i
\(372\) 0.939584 + 0.939584i 0.0487151 + 0.0487151i
\(373\) 0.641626 + 0.641626i 0.0332221 + 0.0332221i 0.723523 0.690301i \(-0.242522\pi\)
−0.690301 + 0.723523i \(0.742522\pi\)
\(374\) 0 0
\(375\) −3.41882 2.24481i −0.176547 0.115922i
\(376\) 23.7585i 1.22525i
\(377\) 2.47434 + 2.47434i 0.127435 + 0.127435i
\(378\) 2.73913 2.73913i 0.140886 0.140886i
\(379\) 10.9413i 0.562018i −0.959705 0.281009i \(-0.909331\pi\)
0.959705 0.281009i \(-0.0906691\pi\)
\(380\) −9.28830 + 0.633804i −0.476480 + 0.0325135i
\(381\) 7.48590i 0.383514i
\(382\) −1.13354 + 1.13354i −0.0579970 + 0.0579970i
\(383\) −6.38190 + 6.38190i −0.326100 + 0.326100i −0.851101 0.525002i \(-0.824065\pi\)
0.525002 + 0.851101i \(0.324065\pi\)
\(384\) 1.62442 0.0828957
\(385\) 0 0
\(386\) −1.99241 −0.101411
\(387\) 1.43503 1.43503i 0.0729466 0.0729466i
\(388\) 4.54599 4.54599i 0.230788 0.230788i
\(389\) 16.7680i 0.850169i 0.905154 + 0.425085i \(0.139756\pi\)
−0.905154 + 0.425085i \(0.860244\pi\)
\(390\) 3.34882 + 2.92099i 0.169574 + 0.147910i
\(391\) 9.24396i 0.467487i
\(392\) 10.2896 10.2896i 0.519703 0.519703i
\(393\) −2.21729 2.21729i −0.111848 0.111848i
\(394\) 6.77191i 0.341164i
\(395\) −1.74427 25.5620i −0.0877638 1.28616i
\(396\) 0 0
\(397\) −11.6796 11.6796i −0.586184 0.586184i 0.350412 0.936596i \(-0.386042\pi\)
−0.936596 + 0.350412i \(0.886042\pi\)
\(398\) 7.25667 + 7.25667i 0.363744 + 0.363744i
\(399\) 4.09026i 0.204769i
\(400\) −12.7103 + 1.74273i −0.635514 + 0.0871367i
\(401\) 15.1557 0.756841 0.378421 0.925634i \(-0.376467\pi\)
0.378421 + 0.925634i \(0.376467\pi\)
\(402\) −1.47004 + 1.47004i −0.0733189 + 0.0733189i
\(403\) 20.7585 + 20.7585i 1.03405 + 1.03405i
\(404\) −2.11428 −0.105189
\(405\) 1.18944 + 17.4310i 0.0591037 + 0.866156i
\(406\) 1.39521i 0.0692429i
\(407\) 0 0
\(408\) −2.81934 + 2.81934i −0.139578 + 0.139578i
\(409\) −17.2482 −0.852868 −0.426434 0.904519i \(-0.640230\pi\)
−0.426434 + 0.904519i \(0.640230\pi\)
\(410\) 12.1882 13.9734i 0.601931 0.690095i
\(411\) 0.305422 0.0150654
\(412\) −5.19920 5.19920i −0.256146 0.256146i
\(413\) −13.0092 13.0092i −0.640140 0.640140i
\(414\) −8.96062 −0.440390
\(415\) 5.82052 6.67305i 0.285718 0.327567i
\(416\) −13.8775 −0.680401
\(417\) −5.19321 + 5.19321i −0.254313 + 0.254313i
\(418\) 0 0
\(419\) 19.0003i 0.928227i 0.885776 + 0.464113i \(0.153627\pi\)
−0.885776 + 0.464113i \(0.846373\pi\)
\(420\) 0.0469290 + 0.687737i 0.00228990 + 0.0335581i
\(421\) −2.15833 −0.105191 −0.0525953 0.998616i \(-0.516749\pi\)
−0.0525953 + 0.998616i \(0.516749\pi\)
\(422\) −10.2859 10.2859i −0.500707 0.500707i
\(423\) −15.6741 + 15.6741i −0.762102 + 0.762102i
\(424\) −32.7231 −1.58918
\(425\) 10.7237 14.1316i 0.520174 0.685484i
\(426\) 5.24525i 0.254133i
\(427\) 3.53100 + 3.53100i 0.170877 + 0.170877i
\(428\) −1.23669 1.23669i −0.0597775 0.0597775i
\(429\) 0 0
\(430\) −0.129337 1.89541i −0.00623717 0.0914047i
\(431\) 7.46697i 0.359671i −0.983697 0.179836i \(-0.942443\pi\)
0.983697 0.179836i \(-0.0575566\pi\)
\(432\) −3.89341 3.89341i −0.187322 0.187322i
\(433\) −14.8357 + 14.8357i −0.712961 + 0.712961i −0.967154 0.254193i \(-0.918190\pi\)
0.254193 + 0.967154i \(0.418190\pi\)
\(434\) 11.7051i 0.561863i
\(435\) −0.476448 0.415579i −0.0228439 0.0199255i
\(436\) 1.26789i 0.0607208i
\(437\) −13.6930 + 13.6930i −0.655024 + 0.655024i
\(438\) −2.95461 + 2.95461i −0.141177 + 0.141177i
\(439\) 28.9958 1.38389 0.691947 0.721948i \(-0.256753\pi\)
0.691947 + 0.721948i \(0.256753\pi\)
\(440\) 0 0
\(441\) −13.5766 −0.646506
\(442\) −13.6290 + 13.6290i −0.648267 + 0.648267i
\(443\) −19.8262 + 19.8262i −0.941972 + 0.941972i −0.998406 0.0564340i \(-0.982027\pi\)
0.0564340 + 0.998406i \(0.482027\pi\)
\(444\) 0.847774i 0.0402336i
\(445\) 22.2337 1.51716i 1.05398 0.0719201i
\(446\) 5.96969i 0.282673i
\(447\) −0.615486 + 0.615486i −0.0291115 + 0.0291115i
\(448\) 9.37142 + 9.37142i 0.442758 + 0.442758i
\(449\) 18.9599i 0.894773i −0.894341 0.447387i \(-0.852355\pi\)
0.894341 0.447387i \(-0.147645\pi\)
\(450\) 13.6985 + 10.3950i 0.645751 + 0.490023i
\(451\) 0 0
\(452\) 7.80833 + 7.80833i 0.367273 + 0.367273i
\(453\) −4.64806 4.64806i −0.218385 0.218385i
\(454\) 8.23714i 0.386588i
\(455\) 1.03682 + 15.1944i 0.0486067 + 0.712323i
\(456\) −8.35252 −0.391143
\(457\) −11.2549 + 11.2549i −0.526480 + 0.526480i −0.919521 0.393041i \(-0.871423\pi\)
0.393041 + 0.919521i \(0.371423\pi\)
\(458\) 11.1830 + 11.1830i 0.522546 + 0.522546i
\(459\) 7.61367 0.355376
\(460\) 2.14523 2.45944i 0.100022 0.114672i
\(461\) 33.0004i 1.53698i −0.639859 0.768492i \(-0.721007\pi\)
0.639859 0.768492i \(-0.278993\pi\)
\(462\) 0 0
\(463\) −8.68490 + 8.68490i −0.403622 + 0.403622i −0.879507 0.475886i \(-0.842128\pi\)
0.475886 + 0.879507i \(0.342128\pi\)
\(464\) −1.98315 −0.0920654
\(465\) −3.99717 3.48650i −0.185364 0.161683i
\(466\) 18.0880 0.837908
\(467\) 3.45801 + 3.45801i 0.160018 + 0.160018i 0.782575 0.622557i \(-0.213906\pi\)
−0.622557 + 0.782575i \(0.713906\pi\)
\(468\) 5.14001 + 5.14001i 0.237597 + 0.237597i
\(469\) −7.12504 −0.329004
\(470\) 1.41268 + 20.7026i 0.0651622 + 0.954941i
\(471\) 1.08594 0.0500374
\(472\) −26.5654 + 26.5654i −1.22277 + 1.22277i
\(473\) 0 0
\(474\) 5.02960i 0.231017i
\(475\) 36.8178 5.04817i 1.68932 0.231626i
\(476\) −2.98994 −0.137044
\(477\) 21.5883 + 21.5883i 0.988461 + 0.988461i
\(478\) −11.3338 + 11.3338i −0.518396 + 0.518396i
\(479\) −8.67558 −0.396397 −0.198199 0.980162i \(-0.563509\pi\)
−0.198199 + 0.980162i \(0.563509\pi\)
\(480\) 2.50150 0.170694i 0.114177 0.00779110i
\(481\) 18.7301i 0.854020i
\(482\) 5.33617 + 5.33617i 0.243056 + 0.243056i
\(483\) 1.01387 + 1.01387i 0.0461329 + 0.0461329i
\(484\) 0 0
\(485\) −16.8688 + 19.3395i −0.765971 + 0.878161i
\(486\) 11.1546i 0.505984i
\(487\) −27.0518 27.0518i −1.22584 1.22584i −0.965525 0.260311i \(-0.916175\pi\)
−0.260311 0.965525i \(-0.583825\pi\)
\(488\) 7.21049 7.21049i 0.326404 0.326404i
\(489\) 1.11272i 0.0503188i
\(490\) −8.35428 + 9.57792i −0.377408 + 0.432686i
\(491\) 3.54998i 0.160208i 0.996786 + 0.0801042i \(0.0255253\pi\)
−0.996786 + 0.0801042i \(0.974475\pi\)
\(492\) −1.00136 + 1.00136i −0.0451448 + 0.0451448i
\(493\) 1.93905 1.93905i 0.0873304 0.0873304i
\(494\) −40.3771 −1.81665
\(495\) 0 0
\(496\) −16.6377 −0.747053
\(497\) −12.7114 + 12.7114i −0.570186 + 0.570186i
\(498\) 1.22912 1.22912i 0.0550783 0.0550783i
\(499\) 25.7772i 1.15395i 0.816763 + 0.576973i \(0.195766\pi\)
−0.816763 + 0.576973i \(0.804234\pi\)
\(500\) −6.13263 + 1.27122i −0.274259 + 0.0568508i
\(501\) 1.39575i 0.0623574i
\(502\) 3.48832 3.48832i 0.155691 0.155691i
\(503\) −2.77955 2.77955i −0.123934 0.123934i 0.642419 0.766353i \(-0.277931\pi\)
−0.766353 + 0.642419i \(0.777931\pi\)
\(504\) 13.2460i 0.590026i
\(505\) 8.41997 0.574552i 0.374684 0.0255673i
\(506\) 0 0
\(507\) −1.93932 1.93932i −0.0861282 0.0861282i
\(508\) −8.10580 8.10580i −0.359637 0.359637i
\(509\) 18.6485i 0.826579i −0.910600 0.413289i \(-0.864380\pi\)
0.910600 0.413289i \(-0.135620\pi\)
\(510\) 2.28907 2.62435i 0.101362 0.116208i
\(511\) −14.3205 −0.633502
\(512\) 16.7086 16.7086i 0.738423 0.738423i
\(513\) 11.2780 + 11.2780i 0.497938 + 0.497938i
\(514\) 9.65098 0.425686
\(515\) 22.1184 + 19.2926i 0.974652 + 0.850134i
\(516\) 0.145098i 0.00638756i
\(517\) 0 0
\(518\) 5.28068 5.28068i 0.232020 0.232020i
\(519\) −0.426600 −0.0187257
\(520\) 31.0277 2.11723i 1.36065 0.0928467i
\(521\) −13.7453 −0.602194 −0.301097 0.953594i \(-0.597353\pi\)
−0.301097 + 0.953594i \(0.597353\pi\)
\(522\) 1.87961 + 1.87961i 0.0822685 + 0.0822685i
\(523\) −13.9488 13.9488i −0.609938 0.609938i 0.332992 0.942930i \(-0.391942\pi\)
−0.942930 + 0.332992i \(0.891942\pi\)
\(524\) −4.80181 −0.209768
\(525\) −0.373784 2.72612i −0.0163133 0.118977i
\(526\) −27.3384 −1.19201
\(527\) 16.2677 16.2677i 0.708631 0.708631i
\(528\) 0 0
\(529\) 16.2117i 0.704857i
\(530\) 28.5142 1.94572i 1.23858 0.0845166i
\(531\) 35.0518 1.52112
\(532\) −4.42897 4.42897i −0.192020 0.192020i
\(533\) −22.1234 + 22.1234i −0.958269 + 0.958269i
\(534\) 4.37472 0.189312
\(535\) 5.26109 + 4.58896i 0.227457 + 0.198398i
\(536\) 14.5497i 0.628451i
\(537\) −1.56845 1.56845i −0.0676835 0.0676835i
\(538\) 11.9294 + 11.9294i 0.514315 + 0.514315i
\(539\) 0 0
\(540\) −2.02569 1.76689i −0.0871716 0.0760349i
\(541\) 16.0662i 0.690738i 0.938467 + 0.345369i \(0.112246\pi\)
−0.938467 + 0.345369i \(0.887754\pi\)
\(542\) 0.0602299 + 0.0602299i 0.00258709 + 0.00258709i
\(543\) −0.404644 + 0.404644i −0.0173649 + 0.0173649i
\(544\) 10.8753i 0.466275i
\(545\) 0.344547 + 5.04928i 0.0147588 + 0.216288i
\(546\) 2.98965i 0.127945i
\(547\) 23.6289 23.6289i 1.01030 1.01030i 0.0103542 0.999946i \(-0.496704\pi\)
0.999946 0.0103542i \(-0.00329590\pi\)
\(548\) 0.330714 0.330714i 0.0141274 0.0141274i
\(549\) −9.51390 −0.406043
\(550\) 0 0
\(551\) 5.74459 0.244728
\(552\) 2.07038 2.07038i 0.0881213 0.0881213i
\(553\) 12.1888 12.1888i 0.518321 0.518321i
\(554\) 30.9048i 1.31302i
\(555\) −0.230382 3.37621i −0.00977917 0.143312i
\(556\) 11.2465i 0.476958i
\(557\) −25.6652 + 25.6652i −1.08747 + 1.08747i −0.0916796 + 0.995789i \(0.529224\pi\)
−0.995789 + 0.0916796i \(0.970776\pi\)
\(558\) 15.7690 + 15.7690i 0.667557 + 0.667557i
\(559\) 3.20568i 0.135586i
\(560\) −6.50454 5.67354i −0.274867 0.239751i
\(561\) 0 0
\(562\) 15.6922 + 15.6922i 0.661936 + 0.661936i
\(563\) 22.7913 + 22.7913i 0.960538 + 0.960538i 0.999250 0.0387120i \(-0.0123255\pi\)
−0.0387120 + 0.999250i \(0.512325\pi\)
\(564\) 1.58483i 0.0667334i
\(565\) −33.2181 28.9743i −1.39750 1.21896i
\(566\) 37.0783 1.55852
\(567\) −8.31171 + 8.31171i −0.349059 + 0.349059i
\(568\) 25.9574 + 25.9574i 1.08915 + 1.08915i
\(569\) 24.8116 1.04016 0.520078 0.854119i \(-0.325903\pi\)
0.520078 + 0.854119i \(0.325903\pi\)
\(570\) 7.27819 0.496641i 0.304850 0.0208020i
\(571\) 9.17242i 0.383854i −0.981409 0.191927i \(-0.938526\pi\)
0.981409 0.191927i \(-0.0614737\pi\)
\(572\) 0 0
\(573\) −0.345576 + 0.345576i −0.0144366 + 0.0144366i
\(574\) 12.4747 0.520684
\(575\) −7.87490 + 10.3775i −0.328406 + 0.432773i
\(576\) −25.2503 −1.05209
\(577\) −11.2891 11.2891i −0.469973 0.469973i 0.431933 0.901906i \(-0.357832\pi\)
−0.901906 + 0.431933i \(0.857832\pi\)
\(578\) −3.74350 3.74350i −0.155709 0.155709i
\(579\) −0.607414 −0.0252433
\(580\) −0.965894 + 0.0659096i −0.0401066 + 0.00273675i
\(581\) 5.95735 0.247153
\(582\) −3.56218 + 3.56218i −0.147657 + 0.147657i
\(583\) 0 0
\(584\) 29.2432i 1.21009i
\(585\) −21.8666 19.0730i −0.904071 0.788570i
\(586\) 35.7678 1.47755
\(587\) −11.2955 11.2955i −0.466215 0.466215i 0.434471 0.900686i \(-0.356935\pi\)
−0.900686 + 0.434471i \(0.856935\pi\)
\(588\) 0.686374 0.686374i 0.0283056 0.0283056i
\(589\) 48.1943 1.98581
\(590\) 21.5689 24.7280i 0.887977 1.01804i
\(591\) 2.06451i 0.0849228i
\(592\) −7.50597 7.50597i −0.308494 0.308494i
\(593\) −18.2153 18.2153i −0.748014 0.748014i 0.226092 0.974106i \(-0.427405\pi\)
−0.974106 + 0.226092i \(0.927405\pi\)
\(594\) 0 0
\(595\) 11.9073 0.812515i 0.488150 0.0333099i
\(596\) 1.33291i 0.0545980i
\(597\) 2.21230 + 2.21230i 0.0905434 + 0.0905434i
\(598\) 10.0085 10.0085i 0.409277 0.409277i
\(599\) 22.2495i 0.909090i 0.890724 + 0.454545i \(0.150198\pi\)
−0.890724 + 0.454545i \(0.849802\pi\)
\(600\) −5.56687 + 0.763285i −0.227266 + 0.0311610i
\(601\) 30.5129i 1.24465i −0.782760 0.622324i \(-0.786189\pi\)
0.782760 0.622324i \(-0.213811\pi\)
\(602\) 0.903794 0.903794i 0.0368359 0.0368359i
\(603\) 9.59882 9.59882i 0.390894 0.390894i
\(604\) −10.0659 −0.409577
\(605\) 0 0
\(606\) 1.65672 0.0672996
\(607\) 11.2506 11.2506i 0.456648 0.456648i −0.440905 0.897554i \(-0.645343\pi\)
0.897554 + 0.440905i \(0.145343\pi\)
\(608\) −16.1095 + 16.1095i −0.653325 + 0.653325i
\(609\) 0.425348i 0.0172360i
\(610\) −5.85432 + 6.71179i −0.237034 + 0.271752i
\(611\) 35.0141i 1.41652i
\(612\) 4.02804 4.02804i 0.162824 0.162824i
\(613\) 12.1960 + 12.1960i 0.492591 + 0.492591i 0.909122 0.416531i \(-0.136754\pi\)
−0.416531 + 0.909122i \(0.636754\pi\)
\(614\) 1.42076i 0.0573371i
\(615\) 3.71574 4.25998i 0.149833 0.171779i
\(616\) 0 0
\(617\) −8.28834 8.28834i −0.333676 0.333676i 0.520305 0.853981i \(-0.325818\pi\)
−0.853981 + 0.520305i \(0.825818\pi\)
\(618\) 4.07403 + 4.07403i 0.163881 + 0.163881i
\(619\) 8.34814i 0.335540i −0.985826 0.167770i \(-0.946343\pi\)
0.985826 0.167770i \(-0.0536566\pi\)
\(620\) −8.10338 + 0.552949i −0.325440 + 0.0222070i
\(621\) −5.59109 −0.224363
\(622\) 12.6840 12.6840i 0.508582 0.508582i
\(623\) 10.6018 + 10.6018i 0.424751 + 0.424751i
\(624\) 4.24950 0.170116
\(625\) 24.0774 6.72910i 0.963094 0.269164i
\(626\) 25.0268i 1.00027i
\(627\) 0 0
\(628\) 1.17586 1.17586i 0.0469221 0.0469221i
\(629\) 14.6781 0.585255
\(630\) 0.787610 + 11.5423i 0.0313791 + 0.459856i
\(631\) 20.1258 0.801194 0.400597 0.916254i \(-0.368803\pi\)
0.400597 + 0.916254i \(0.368803\pi\)
\(632\) −24.8902 24.8902i −0.990078 0.990078i
\(633\) −3.13579 3.13579i −0.124636 0.124636i
\(634\) −4.92186 −0.195472
\(635\) 34.4836 + 30.0781i 1.36844 + 1.19361i
\(636\) −2.18282 −0.0865545
\(637\) 15.1643 15.1643i 0.600830 0.600830i
\(638\) 0 0
\(639\) 34.2496i 1.35489i
\(640\) −6.52685 + 7.48283i −0.257996 + 0.295785i
\(641\) −15.7080 −0.620427 −0.310214 0.950667i \(-0.600401\pi\)
−0.310214 + 0.950667i \(0.600401\pi\)
\(642\) 0.969051 + 0.969051i 0.0382454 + 0.0382454i
\(643\) −35.1585 + 35.1585i −1.38652 + 1.38652i −0.553999 + 0.832517i \(0.686899\pi\)
−0.832517 + 0.553999i \(0.813101\pi\)
\(644\) 2.19566 0.0865212
\(645\) −0.0394301 0.577842i −0.00155256 0.0227525i
\(646\) 31.6421i 1.24494i
\(647\) −25.2859 25.2859i −0.994091 0.994091i 0.00589156 0.999983i \(-0.498125\pi\)
−0.999983 + 0.00589156i \(0.998125\pi\)
\(648\) 16.9729 + 16.9729i 0.666760 + 0.666760i
\(649\) 0 0
\(650\) −26.9109 + 3.68981i −1.05553 + 0.144726i
\(651\) 3.56846i 0.139859i
\(652\) 1.20486 + 1.20486i 0.0471859 + 0.0471859i
\(653\) 8.27696 8.27696i 0.323902 0.323902i −0.526360 0.850262i \(-0.676443\pi\)
0.850262 + 0.526360i \(0.176443\pi\)
\(654\) 0.993501i 0.0388490i
\(655\) 19.1229 1.30489i 0.747193 0.0509861i
\(656\) 17.7316i 0.692302i
\(657\) 19.2925 19.2925i 0.752673 0.752673i
\(658\) −9.87171 + 9.87171i −0.384839 + 0.384839i
\(659\) −44.7867 −1.74464 −0.872322 0.488933i \(-0.837386\pi\)
−0.872322 + 0.488933i \(0.837386\pi\)
\(660\) 0 0
\(661\) −20.9940 −0.816573 −0.408286 0.912854i \(-0.633873\pi\)
−0.408286 + 0.912854i \(0.633873\pi\)
\(662\) −11.4273 + 11.4273i −0.444134 + 0.444134i
\(663\) −4.15501 + 4.15501i −0.161367 + 0.161367i
\(664\) 12.1652i 0.472102i
\(665\) 18.8417 + 16.4345i 0.730649 + 0.637304i
\(666\) 14.2282i 0.551332i
\(667\) −1.42394 + 1.42394i −0.0551351 + 0.0551351i
\(668\) −1.51133 1.51133i −0.0584750 0.0584750i
\(669\) 1.81994i 0.0703631i
\(670\) −0.865125 12.6783i −0.0334227 0.489804i
\(671\) 0 0
\(672\) 1.19280 + 1.19280i 0.0460132 + 0.0460132i
\(673\) 12.8325 + 12.8325i 0.494655 + 0.494655i 0.909769 0.415114i \(-0.136258\pi\)
−0.415114 + 0.909769i \(0.636258\pi\)
\(674\) 34.1834i 1.31669i
\(675\) 8.54732 + 6.48606i 0.328986 + 0.249649i
\(676\) −4.19982 −0.161532
\(677\) −10.6666 + 10.6666i −0.409951 + 0.409951i −0.881721 0.471770i \(-0.843615\pi\)
0.471770 + 0.881721i \(0.343615\pi\)
\(678\) −6.11851 6.11851i −0.234980 0.234980i
\(679\) −17.2653 −0.662582
\(680\) −1.65920 24.3152i −0.0636273 0.932447i
\(681\) 2.51121i 0.0962297i
\(682\) 0 0
\(683\) 12.5210 12.5210i 0.479102 0.479102i −0.425743 0.904844i \(-0.639987\pi\)
0.904844 + 0.425743i \(0.139987\pi\)
\(684\) 11.9334 0.456284
\(685\) −1.22718 + 1.40692i −0.0468879 + 0.0537555i
\(686\) −21.1867 −0.808912
\(687\) 3.40929 + 3.40929i 0.130072 + 0.130072i
\(688\) −1.28466 1.28466i −0.0489771 0.0489771i
\(689\) −48.2257 −1.83725
\(690\) −1.68098 + 1.92719i −0.0639937 + 0.0733667i
\(691\) 27.4323 1.04358 0.521788 0.853075i \(-0.325265\pi\)
0.521788 + 0.853075i \(0.325265\pi\)
\(692\) −0.461926 + 0.461926i −0.0175598 + 0.0175598i
\(693\) 0 0
\(694\) 14.2067i 0.539279i
\(695\) −3.05623 44.7885i −0.115929 1.69893i
\(696\) −0.868583 −0.0329235
\(697\) 17.3373 + 17.3373i 0.656696 + 0.656696i
\(698\) 6.95838 6.95838i 0.263379 0.263379i
\(699\) 5.51437 0.208573
\(700\) −3.35660 2.54712i −0.126867 0.0962723i
\(701\) 33.8539i 1.27864i −0.768939 0.639322i \(-0.779215\pi\)
0.768939 0.639322i \(-0.220785\pi\)
\(702\) −8.24334 8.24334i −0.311125 0.311125i
\(703\) 21.7425 + 21.7425i 0.820035 + 0.820035i
\(704\) 0 0
\(705\) 0.430676 + 6.31149i 0.0162202 + 0.237704i
\(706\) 16.1821i 0.609022i
\(707\) 4.01492 + 4.01492i 0.150997 + 0.150997i
\(708\) −1.77206 + 1.77206i −0.0665983 + 0.0665983i
\(709\) 22.3780i 0.840424i −0.907426 0.420212i \(-0.861956\pi\)
0.907426 0.420212i \(-0.138044\pi\)
\(710\) −24.1621 21.0752i −0.906788 0.790940i
\(711\) 32.8414i 1.23165i
\(712\) 21.6493 21.6493i 0.811343 0.811343i
\(713\) −11.9461 + 11.9461i −0.447387 + 0.447387i
\(714\) 2.34288 0.0876802
\(715\) 0 0
\(716\) −3.39665 −0.126939
\(717\) −3.45527 + 3.45527i −0.129039 + 0.129039i
\(718\) −12.1680 + 12.1680i −0.454105 + 0.454105i
\(719\) 37.8017i 1.40976i −0.709325 0.704882i \(-0.751000\pi\)
0.709325 0.704882i \(-0.249000\pi\)
\(720\) 16.4062 1.11951i 0.611425 0.0417217i
\(721\) 19.7461i 0.735385i
\(722\) −30.7500 + 30.7500i −1.14440 + 1.14440i
\(723\) 1.62681 + 1.62681i 0.0605016 + 0.0605016i
\(724\) 0.876305i 0.0325676i
\(725\) 3.82870 0.524962i 0.142194 0.0194966i
\(726\) 0 0
\(727\) −13.9838 13.9838i −0.518630 0.518630i 0.398527 0.917157i \(-0.369522\pi\)
−0.917157 + 0.398527i \(0.869522\pi\)
\(728\) 14.7950 + 14.7950i 0.548340 + 0.548340i
\(729\) 20.0399i 0.742220i
\(730\) −1.73880 25.4818i −0.0643559 0.943126i
\(731\) 2.51218 0.0929162
\(732\) 0.480981 0.480981i 0.0177776 0.0177776i
\(733\) 19.6728 + 19.6728i 0.726630 + 0.726630i 0.969947 0.243317i \(-0.0782354\pi\)
−0.243317 + 0.969947i \(0.578235\pi\)
\(734\) −24.1227 −0.890386
\(735\) −2.54692 + 2.91997i −0.0939446 + 0.107705i
\(736\) 7.98626i 0.294378i
\(737\) 0 0
\(738\) −16.8058 + 16.8058i −0.618632 + 0.618632i
\(739\) −30.2242 −1.11182 −0.555908 0.831244i \(-0.687629\pi\)
−0.555908 + 0.831244i \(0.687629\pi\)
\(740\) −3.90525 3.40633i −0.143560 0.125219i
\(741\) −12.3095 −0.452202
\(742\) 13.5965 + 13.5965i 0.499144 + 0.499144i
\(743\) 5.51933 + 5.51933i 0.202485 + 0.202485i 0.801064 0.598579i \(-0.204268\pi\)
−0.598579 + 0.801064i \(0.704268\pi\)
\(744\) −7.28698 −0.267154
\(745\) −0.362216 5.30822i −0.0132706 0.194478i
\(746\) −1.08881 −0.0398640
\(747\) −8.02572 + 8.02572i −0.293646 + 0.293646i
\(748\) 0 0
\(749\) 4.69683i 0.171619i
\(750\) 4.80545 0.996115i 0.175470 0.0363730i
\(751\) 5.23553 0.191047 0.0955236 0.995427i \(-0.469547\pi\)
0.0955236 + 0.995427i \(0.469547\pi\)
\(752\) 14.0317 + 14.0317i 0.511683 + 0.511683i
\(753\) 1.06346 1.06346i 0.0387548 0.0387548i
\(754\) −4.19883 −0.152912
\(755\) 40.0869 2.73541i 1.45891 0.0995517i
\(756\) 1.80843i 0.0657719i
\(757\) −14.2275 14.2275i −0.517109 0.517109i 0.399587 0.916695i \(-0.369154\pi\)
−0.916695 + 0.399587i \(0.869154\pi\)
\(758\) 9.28344 + 9.28344i 0.337190 + 0.337190i
\(759\) 0 0
\(760\) 33.5602 38.4757i 1.21735 1.39566i
\(761\) 31.5754i 1.14461i −0.820041 0.572304i \(-0.806050\pi\)
0.820041 0.572304i \(-0.193950\pi\)
\(762\) 6.35160 + 6.35160i 0.230094 + 0.230094i
\(763\) −2.40767 + 2.40767i −0.0871634 + 0.0871634i
\(764\) 0.748385i 0.0270756i
\(765\) −14.9468 + 17.1360i −0.540403 + 0.619554i
\(766\) 10.8298i 0.391295i
\(767\) −39.1507 + 39.1507i −1.41365 + 1.41365i
\(768\) 3.17934 3.17934i 0.114725 0.114725i
\(769\) −22.1089 −0.797269 −0.398634 0.917110i \(-0.630516\pi\)
−0.398634 + 0.917110i \(0.630516\pi\)
\(770\) 0 0
\(771\) 2.94224 0.105962
\(772\) −0.657713 + 0.657713i −0.0236716 + 0.0236716i
\(773\) −2.46526 + 2.46526i −0.0886693 + 0.0886693i −0.750050 0.661381i \(-0.769971\pi\)
0.661381 + 0.750050i \(0.269971\pi\)
\(774\) 2.43517i 0.0875305i
\(775\) 32.1209 4.40417i 1.15382 0.158203i
\(776\) 35.2566i 1.26564i
\(777\) 1.60989 1.60989i 0.0577545 0.0577545i
\(778\) −14.2272 14.2272i −0.510070 0.510070i
\(779\) 51.3630i 1.84027i
\(780\) 2.06972 0.141231i 0.0741080 0.00505690i
\(781\) 0 0
\(782\) −7.84327 7.84327i −0.280475 0.280475i
\(783\) 1.17281 + 1.17281i 0.0419128 + 0.0419128i
\(784\) 12.1540i 0.434070i
\(785\) −4.36327 + 5.00235i −0.155732 + 0.178541i
\(786\) 3.76264 0.134209
\(787\) 18.5691 18.5691i 0.661917 0.661917i −0.293915 0.955832i \(-0.594958\pi\)
0.955832 + 0.293915i \(0.0949582\pi\)
\(788\) −2.23547 2.23547i −0.0796354 0.0796354i
\(789\) −8.33449 −0.296716
\(790\) 23.1687 + 20.2088i 0.824305 + 0.718995i
\(791\) 29.6554i 1.05442i
\(792\) 0 0
\(793\) 10.6265 10.6265i 0.377356 0.377356i
\(794\) 19.8198 0.703377
\(795\) 8.69295 0.593179i 0.308307 0.0210379i
\(796\) 4.79099 0.169812
\(797\) −2.48582 2.48582i −0.0880523 0.0880523i 0.661709 0.749761i \(-0.269832\pi\)
−0.749761 + 0.661709i \(0.769832\pi\)
\(798\) 3.47049 + 3.47049i 0.122854 + 0.122854i
\(799\) −27.4393 −0.970732
\(800\) −9.26463 + 12.2089i −0.327554 + 0.431651i
\(801\) −28.5653 −1.00930
\(802\) −12.8593 + 12.8593i −0.454076 + 0.454076i
\(803\) 0 0
\(804\) 0.970548i 0.0342286i
\(805\) −8.74409 + 0.596669i −0.308189 + 0.0210298i
\(806\) −35.2261 −1.24079
\(807\) 3.63686 + 3.63686i 0.128023 + 0.128023i
\(808\) 8.19868 8.19868i 0.288429 0.288429i
\(809\) −10.8292 −0.380735 −0.190367 0.981713i \(-0.560968\pi\)
−0.190367 + 0.981713i \(0.560968\pi\)
\(810\) −15.7990 13.7806i −0.555121 0.484201i
\(811\) 36.2429i 1.27266i −0.771416 0.636331i \(-0.780451\pi\)
0.771416 0.636331i \(-0.219549\pi\)
\(812\) −0.460571 0.460571i −0.0161629 0.0161629i
\(813\) 0.0183619 + 0.0183619i 0.000643981 + 0.000643981i
\(814\) 0 0
\(815\) −5.12569 4.47086i −0.179545 0.156607i
\(816\) 3.33018i 0.116580i
\(817\) 3.72126 + 3.72126i 0.130190 + 0.130190i
\(818\) 14.6347 14.6347i 0.511689 0.511689i
\(819\) 19.5213i 0.682131i
\(820\) −0.589305 8.63617i −0.0205794 0.301588i
\(821\) 43.9586i 1.53417i −0.641548 0.767083i \(-0.721708\pi\)
0.641548 0.767083i \(-0.278292\pi\)
\(822\) −0.259143 + 0.259143i −0.00903865 + 0.00903865i
\(823\) 16.9211 16.9211i 0.589832 0.589832i −0.347754 0.937586i \(-0.613056\pi\)
0.937586 + 0.347754i \(0.113056\pi\)
\(824\) 40.3226 1.40471
\(825\) 0 0
\(826\) 22.0759 0.768120
\(827\) −37.6563 + 37.6563i −1.30944 + 1.30944i −0.387618 + 0.921820i \(0.626702\pi\)
−0.921820 + 0.387618i \(0.873298\pi\)
\(828\) −2.95798 + 2.95798i −0.102797 + 0.102797i
\(829\) 28.4366i 0.987645i 0.869563 + 0.493822i \(0.164401\pi\)
−0.869563 + 0.493822i \(0.835599\pi\)
\(830\) 0.723344 + 10.6005i 0.0251076 + 0.367948i
\(831\) 9.42178i 0.326838i
\(832\) 28.2030 28.2030i 0.977764 0.977764i
\(833\) −11.8837 11.8837i −0.411745 0.411745i
\(834\) 8.81262i 0.305156i
\(835\) 6.42947 + 5.60806i 0.222501 + 0.194075i
\(836\) 0 0
\(837\) 9.83929 + 9.83929i 0.340096 + 0.340096i
\(838\) −16.1213 16.1213i −0.556901 0.556901i
\(839\) 5.92526i 0.204563i 0.994756 + 0.102281i \(0.0326142\pi\)
−0.994756 + 0.102281i \(0.967386\pi\)
\(840\) −2.84887 2.48491i −0.0982952 0.0857374i
\(841\) −28.4026 −0.979401
\(842\) 1.83129 1.83129i 0.0631104 0.0631104i
\(843\) 4.78399 + 4.78399i 0.164769 + 0.164769i
\(844\) −6.79092 −0.233753
\(845\) 16.7255 1.14130i 0.575376 0.0392619i
\(846\) 26.5982i 0.914466i
\(847\) 0 0
\(848\) 19.3261 19.3261i 0.663662 0.663662i
\(849\) 11.3038 0.387947
\(850\) 2.89157 + 21.0891i 0.0991800 + 0.723350i
\(851\) −10.7789 −0.369495
\(852\) 1.73151 + 1.73151i 0.0593205 + 0.0593205i
\(853\) −15.7577 15.7577i −0.539535 0.539535i 0.383858 0.923392i \(-0.374595\pi\)
−0.923392 + 0.383858i \(0.874595\pi\)
\(854\) −5.99194 −0.205040
\(855\) −47.5239 + 3.24288i −1.62528 + 0.110904i
\(856\) 9.59117 0.327820
\(857\) 25.6632 25.6632i 0.876637 0.876637i −0.116548 0.993185i \(-0.537183\pi\)
0.993185 + 0.116548i \(0.0371830\pi\)
\(858\) 0 0
\(859\) 30.6311i 1.04512i 0.852603 + 0.522559i \(0.175023\pi\)
−0.852603 + 0.522559i \(0.824977\pi\)
\(860\) −0.668388 0.582997i −0.0227918 0.0198800i
\(861\) 3.80309 0.129609
\(862\) 6.33554 + 6.33554i 0.215789 + 0.215789i
\(863\) 33.6775 33.6775i 1.14639 1.14639i 0.159138 0.987256i \(-0.449129\pi\)
0.987256 0.159138i \(-0.0508714\pi\)
\(864\) −6.57778 −0.223781
\(865\) 1.71406 1.96512i 0.0582799 0.0668161i
\(866\) 25.1755i 0.855499i
\(867\) −1.14126 1.14126i −0.0387592 0.0387592i
\(868\) −3.86396 3.86396i −0.131151 0.131151i
\(869\) 0 0
\(870\) 0.756863 0.0516459i 0.0256600 0.00175096i
\(871\) 21.4426i 0.726555i
\(872\) 4.91658 + 4.91658i 0.166496 + 0.166496i
\(873\) 23.2597 23.2597i 0.787223 0.787223i
\(874\) 23.2363i 0.785980i
\(875\) 14.0596 + 9.23161i 0.475302 + 0.312086i
\(876\) 1.95069i 0.0659077i
\(877\) 6.03697 6.03697i 0.203854 0.203854i −0.597795 0.801649i \(-0.703956\pi\)
0.801649 + 0.597795i \(0.203956\pi\)
\(878\) −24.6022 + 24.6022i −0.830285 + 0.830285i
\(879\) 10.9043 0.367794
\(880\) 0 0
\(881\) 18.6414 0.628046 0.314023 0.949415i \(-0.398323\pi\)
0.314023 + 0.949415i \(0.398323\pi\)
\(882\) 11.5194 11.5194i 0.387879 0.387879i
\(883\) −31.3527 + 31.3527i −1.05510 + 1.05510i −0.0567125 + 0.998391i \(0.518062\pi\)
−0.998391 + 0.0567125i \(0.981938\pi\)
\(884\) 8.99815i 0.302641i
\(885\) 6.57558 7.53869i 0.221036 0.253410i
\(886\) 33.6441i 1.13030i
\(887\) 2.34082 2.34082i 0.0785972 0.0785972i −0.666715 0.745312i \(-0.732300\pi\)
0.745312 + 0.666715i \(0.232300\pi\)
\(888\) −3.28748 3.28748i −0.110321 0.110321i
\(889\) 30.7852i 1.03250i
\(890\) −17.5775 + 20.1520i −0.589198 + 0.675497i
\(891\) 0 0
\(892\) 1.97065 + 1.97065i 0.0659823 + 0.0659823i
\(893\) −40.6455 40.6455i −1.36015 1.36015i
\(894\) 1.04445i 0.0349316i
\(895\) 13.5270 0.923038i 0.452157 0.0308538i
\(896\) −6.68029 −0.223173
\(897\) 3.05122 3.05122i 0.101877 0.101877i
\(898\) 16.0870 + 16.0870i 0.536830 + 0.536830i
\(899\) 5.01174 0.167151
\(900\) 7.95346 1.09052i 0.265115 0.0363506i
\(901\) 37.7927i 1.25906i
\(902\) 0 0
\(903\) 0.275534 0.275534i 0.00916921 0.00916921i
\(904\) −60.5578 −2.01412
\(905\) −0.238135 3.48983i −0.00791587 0.116006i
\(906\) 7.88754 0.262046
\(907\) −37.8445 37.8445i −1.25661 1.25661i −0.952703 0.303903i \(-0.901710\pi\)
−0.303903 0.952703i \(-0.598290\pi\)
\(908\) −2.71916 2.71916i −0.0902384 0.0902384i
\(909\) −10.8178 −0.358803
\(910\) −13.7718 12.0123i −0.456529 0.398205i
\(911\) −30.2935 −1.00367 −0.501834 0.864964i \(-0.667341\pi\)
−0.501834 + 0.864964i \(0.667341\pi\)
\(912\) 4.93296 4.93296i 0.163347 0.163347i
\(913\) 0 0
\(914\) 19.0990i 0.631737i
\(915\) −1.78477 + 2.04618i −0.0590027 + 0.0676447i
\(916\) 7.38321 0.243948
\(917\) 9.11844 + 9.11844i 0.301117 + 0.301117i
\(918\) −6.46001 + 6.46001i −0.213212 + 0.213212i
\(919\) −16.1318 −0.532140 −0.266070 0.963954i \(-0.585725\pi\)
−0.266070 + 0.963954i \(0.585725\pi\)
\(920\) 1.21843 + 17.8559i 0.0401704 + 0.588691i
\(921\) 0.433138i 0.0142724i
\(922\) 28.0001 + 28.0001i 0.922133 + 0.922133i
\(923\) 38.2547 + 38.2547i 1.25917 + 1.25917i
\(924\) 0 0
\(925\) 16.4781 + 12.5042i 0.541796 + 0.411137i
\(926\) 14.7378i 0.484316i
\(927\) −26.6019 26.6019i −0.873721 0.873721i
\(928\) −1.67523 + 1.67523i −0.0549921 + 0.0549921i
\(929\) 3.84293i 0.126082i −0.998011 0.0630411i \(-0.979920\pi\)
0.998011 0.0630411i \(-0.0200799\pi\)
\(930\) 6.34971 0.433284i 0.208215 0.0142079i
\(931\) 35.2063i 1.15384i
\(932\) 5.97101 5.97101i 0.195587 0.195587i
\(933\) 3.86689 3.86689i 0.126596 0.126596i
\(934\) −5.86807 −0.192009
\(935\) 0 0
\(936\) −39.8636 −1.30298
\(937\) 12.2864 12.2864i 0.401380 0.401380i −0.477339 0.878719i \(-0.658399\pi\)
0.878719 + 0.477339i \(0.158399\pi\)
\(938\) 6.04542 6.04542i 0.197390 0.197390i
\(939\) 7.62977i 0.248988i
\(940\) 7.30047 + 6.36779i 0.238115 + 0.207695i
\(941\) 4.12356i 0.134424i −0.997739 0.0672120i \(-0.978590\pi\)
0.997739 0.0672120i \(-0.0214104\pi\)
\(942\) −0.921393 + 0.921393i −0.0300206 + 0.0300206i
\(943\) −12.7316 12.7316i −0.414598 0.414598i
\(944\) 31.3788i 1.02129i
\(945\) 0.491439 + 7.20195i 0.0159865 + 0.234280i
\(946\) 0 0
\(947\) −9.37085 9.37085i −0.304512 0.304512i 0.538264 0.842776i \(-0.319080\pi\)
−0.842776 + 0.538264i \(0.819080\pi\)
\(948\) −1.66032 1.66032i −0.0539246 0.0539246i
\(949\) 43.0972i 1.39899i
\(950\) −26.9558 + 35.5223i −0.874561 + 1.15249i
\(951\) −1.50050 −0.0486570
\(952\) 11.5943 11.5943i 0.375774 0.375774i
\(953\) −9.73307 9.73307i −0.315285 0.315285i 0.531668 0.846953i \(-0.321565\pi\)
−0.846953 + 0.531668i \(0.821565\pi\)
\(954\) −36.6343 −1.18608
\(955\) −0.203373 2.98040i −0.00658100 0.0964434i
\(956\) 7.48279i 0.242011i
\(957\) 0 0
\(958\) 7.36101 7.36101i 0.237823 0.237823i
\(959\) −1.25602 −0.0405591
\(960\) −4.73685 + 5.43065i −0.152881 + 0.175274i
\(961\) 11.0461 0.356325
\(962\) −15.8920 15.8920i −0.512380 0.512380i
\(963\) −6.32755 6.32755i −0.203902 0.203902i
\(964\) 3.52304 0.113470
\(965\) 2.44057 2.79803i 0.0785647 0.0900719i
\(966\) −1.72049 −0.0553560
\(967\) −33.1678 + 33.1678i −1.06660 + 1.06660i −0.0689861 + 0.997618i \(0.521976\pi\)
−0.997618 + 0.0689861i \(0.978024\pi\)
\(968\) 0 0
\(969\) 9.64653i 0.309891i
\(970\) −2.09636 30.7218i −0.0673101 0.986418i
\(971\) 34.8809 1.11938 0.559691 0.828702i \(-0.310920\pi\)
0.559691 + 0.828702i \(0.310920\pi\)
\(972\) 3.68225 + 3.68225i 0.118108 + 0.118108i
\(973\) 21.3567 21.3567i 0.684663 0.684663i
\(974\) 45.9056 1.47091
\(975\) −8.20416 + 1.12489i −0.262744 + 0.0360253i
\(976\) 8.51696i 0.272621i
\(977\) −14.7673 14.7673i −0.472448 0.472448i 0.430258 0.902706i \(-0.358423\pi\)
−0.902706 + 0.430258i \(0.858423\pi\)
\(978\) −0.944112 0.944112i −0.0301894 0.0301894i
\(979\) 0 0
\(980\) 0.403934 + 5.91959i 0.0129032 + 0.189094i
\(981\) 6.48720i 0.207120i
\(982\) −3.01207 3.01207i −0.0961190 0.0961190i
\(983\) −5.93055 + 5.93055i −0.189155 + 0.189155i −0.795331 0.606176i \(-0.792703\pi\)
0.606176 + 0.795331i \(0.292703\pi\)
\(984\) 7.76610i 0.247574i
\(985\) 9.51012 + 8.29515i 0.303018 + 0.264305i
\(986\) 3.29047i 0.104790i
\(987\) −3.00953 + 3.00953i −0.0957944 + 0.0957944i
\(988\) −13.3289 + 13.3289i −0.424048 + 0.424048i
\(989\) −1.84481 −0.0586617
\(990\) 0 0
\(991\) 1.22056 0.0387723 0.0193861 0.999812i \(-0.493829\pi\)
0.0193861 + 0.999812i \(0.493829\pi\)
\(992\) −14.0544 + 14.0544i −0.446226 + 0.446226i
\(993\) −3.48377 + 3.48377i −0.110554 + 0.110554i
\(994\) 21.5707i 0.684181i
\(995\) −19.0798 + 1.30195i −0.604871 + 0.0412745i
\(996\) 0.811490i 0.0257130i
\(997\) 6.09123 6.09123i 0.192911 0.192911i −0.604042 0.796953i \(-0.706444\pi\)
0.796953 + 0.604042i \(0.206444\pi\)
\(998\) −21.8713 21.8713i −0.692325 0.692325i
\(999\) 8.87786i 0.280883i
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 605.2.e.c.362.7 40
5.3 odd 4 inner 605.2.e.c.483.14 yes 40
11.2 odd 10 605.2.m.g.282.7 160
11.3 even 5 605.2.m.g.112.14 160
11.4 even 5 605.2.m.g.457.7 160
11.5 even 5 605.2.m.g.602.14 160
11.6 odd 10 605.2.m.g.602.7 160
11.7 odd 10 605.2.m.g.457.14 160
11.8 odd 10 605.2.m.g.112.7 160
11.9 even 5 605.2.m.g.282.14 160
11.10 odd 2 inner 605.2.e.c.362.14 yes 40
55.3 odd 20 605.2.m.g.233.14 160
55.8 even 20 605.2.m.g.233.7 160
55.13 even 20 605.2.m.g.403.14 160
55.18 even 20 605.2.m.g.578.14 160
55.28 even 20 605.2.m.g.118.14 160
55.38 odd 20 605.2.m.g.118.7 160
55.43 even 4 inner 605.2.e.c.483.7 yes 40
55.48 odd 20 605.2.m.g.578.7 160
55.53 odd 20 605.2.m.g.403.7 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.e.c.362.7 40 1.1 even 1 trivial
605.2.e.c.362.14 yes 40 11.10 odd 2 inner
605.2.e.c.483.7 yes 40 55.43 even 4 inner
605.2.e.c.483.14 yes 40 5.3 odd 4 inner
605.2.m.g.112.7 160 11.8 odd 10
605.2.m.g.112.14 160 11.3 even 5
605.2.m.g.118.7 160 55.38 odd 20
605.2.m.g.118.14 160 55.28 even 20
605.2.m.g.233.7 160 55.8 even 20
605.2.m.g.233.14 160 55.3 odd 20
605.2.m.g.282.7 160 11.2 odd 10
605.2.m.g.282.14 160 11.9 even 5
605.2.m.g.403.7 160 55.53 odd 20
605.2.m.g.403.14 160 55.13 even 20
605.2.m.g.457.7 160 11.4 even 5
605.2.m.g.457.14 160 11.7 odd 10
605.2.m.g.578.7 160 55.48 odd 20
605.2.m.g.578.14 160 55.18 even 20
605.2.m.g.602.7 160 11.6 odd 10
605.2.m.g.602.14 160 11.5 even 5