Properties

Label 847.2.f.r.372.1
Level $847$
Weight $2$
Character 847.372
Analytic conductor $6.763$
Analytic rank $0$
Dimension $8$
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] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.446265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 4x^{6} - 7x^{5} + 19x^{4} + 21x^{3} + 36x^{2} + 27x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 372.1
Root \(1.86298 + 1.35354i\) of defining polynomial
Character \(\chi\) \(=\) 847.372
Dual form 847.2.f.r.148.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.711597 + 2.19007i) q^{2} +(1.86298 - 1.35354i) q^{3} +(-2.67200 - 1.94132i) q^{4} +(1.11418 + 3.42908i) q^{5} +(1.63865 + 5.04324i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(2.42705 - 1.76336i) q^{8} +(0.711597 - 2.19007i) q^{9} +O(q^{10})\) \(q+(-0.711597 + 2.19007i) q^{2} +(1.86298 - 1.35354i) q^{3} +(-2.67200 - 1.94132i) q^{4} +(1.11418 + 3.42908i) q^{5} +(1.63865 + 5.04324i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(2.42705 - 1.76336i) q^{8} +(0.711597 - 2.19007i) q^{9} -8.30278 q^{10} -7.60555 q^{12} +(-2.04123 + 6.28225i) q^{13} +(1.86298 - 1.35354i) q^{14} +(6.71709 + 4.88025i) q^{15} +(0.0935628 + 0.287957i) q^{16} +(-0.833488 - 2.56521i) q^{17} +(4.29004 + 3.11689i) q^{18} +(-2.42705 + 1.76336i) q^{19} +(3.67988 - 11.3255i) q^{20} -2.30278 q^{21} -2.69722 q^{23} +(2.13479 - 6.57021i) q^{24} +(-6.47214 + 4.70228i) q^{25} +(-12.3060 - 8.94086i) q^{26} +(0.496143 + 1.52697i) q^{27} +(1.02061 + 3.14113i) q^{28} +(3.80013 + 2.76096i) q^{29} +(-15.4679 + 11.2381i) q^{30} +(0.309017 - 0.951057i) q^{31} +5.30278 q^{32} +6.21110 q^{34} +(1.11418 - 3.42908i) q^{35} +(-6.15302 + 4.47043i) q^{36} +(4.21587 + 3.06301i) q^{37} +(-2.13479 - 6.57021i) q^{38} +(4.70049 + 14.4666i) q^{39} +(8.75086 + 6.35787i) q^{40} +(5.66312 - 4.11450i) q^{41} +(1.63865 - 5.04324i) q^{42} -1.69722 q^{43} +8.30278 q^{45} +(1.91934 - 5.90711i) q^{46} +(1.54387 - 1.12169i) q^{47} +(0.564066 + 0.409818i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-5.69277 - 17.5206i) q^{50} +(-5.02489 - 3.65079i) q^{51} +(17.6500 - 12.8235i) q^{52} +(-3.98889 + 12.2765i) q^{53} -3.69722 q^{54} -3.00000 q^{56} +(-2.13479 + 6.57021i) q^{57} +(-8.75086 + 6.35787i) q^{58} +(-5.41817 - 3.93653i) q^{59} +(-8.47393 - 26.0801i) q^{60} +(1.32963 + 4.09218i) q^{61} +(1.86298 + 1.35354i) q^{62} +(-1.86298 + 1.35354i) q^{63} +(-3.96056 + 12.1894i) q^{64} -23.8167 q^{65} +8.51388 q^{67} +(-2.75282 + 8.47232i) q^{68} +(-5.02489 + 3.65079i) q^{69} +(6.71709 + 4.88025i) q^{70} +(-1.32963 - 4.09218i) q^{71} +(-2.13479 - 6.57021i) q^{72} +(-4.04508 - 2.93893i) q^{73} +(-9.70820 + 7.05342i) q^{74} +(-5.69277 + 17.5206i) q^{75} +9.90833 q^{76} -35.0278 q^{78} +(2.56570 - 7.89641i) q^{79} +(-0.883182 + 0.641669i) q^{80} +(8.58007 + 6.23379i) q^{81} +(4.98118 + 15.3305i) q^{82} +(-0.927051 - 2.85317i) q^{83} +(6.15302 + 4.47043i) q^{84} +(7.86767 - 5.71620i) q^{85} +(1.20774 - 3.71704i) q^{86} +10.8167 q^{87} -14.7250 q^{89} +(-5.90823 + 18.1837i) q^{90} +(5.34400 - 3.88265i) q^{91} +(7.20699 + 5.23618i) q^{92} +(-0.711597 - 2.19007i) q^{93} +(1.35796 + 4.17937i) q^{94} +(-8.75086 - 6.35787i) q^{95} +(9.87899 - 7.17751i) q^{96} +(-1.11418 + 3.42908i) q^{97} -2.30278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + q^{3} - 3 q^{4} - 7 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + q^{3} - 3 q^{4} - 7 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 52 q^{10} - 32 q^{12} + 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} + 9 q^{17} + 7 q^{18} - 6 q^{19} - 13 q^{20} - 4 q^{21} - 36 q^{23} - 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} - 3 q^{28} + 13 q^{29} - 13 q^{30} - 2 q^{31} + 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} - 16 q^{39} + 14 q^{41} - 7 q^{42} - 28 q^{43} + 52 q^{45} + 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} + 8 q^{50} + 2 q^{51} + 22 q^{52} + 15 q^{53} - 44 q^{54} - 24 q^{56} + 3 q^{57} - 17 q^{59} + 26 q^{60} - 5 q^{61} + q^{62} - q^{63} + 4 q^{64} - 104 q^{65} - 4 q^{67} + 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} + 3 q^{72} - 10 q^{73} - 24 q^{74} + 8 q^{75} + 36 q^{76} - 136 q^{78} - 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} + 6 q^{83} + 8 q^{84} - 13 q^{85} + 3 q^{86} + 12 q^{89} + 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} - 16 q^{94} + 10 q^{96} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.711597 + 2.19007i −0.503175 + 1.54861i 0.300642 + 0.953737i \(0.402799\pi\)
−0.803817 + 0.594876i \(0.797201\pi\)
\(3\) 1.86298 1.35354i 1.07559 0.781465i 0.0986852 0.995119i \(-0.468536\pi\)
0.976910 + 0.213653i \(0.0685363\pi\)
\(4\) −2.67200 1.94132i −1.33600 0.970661i
\(5\) 1.11418 + 3.42908i 0.498275 + 1.53353i 0.811790 + 0.583949i \(0.198493\pi\)
−0.313515 + 0.949583i \(0.601507\pi\)
\(6\) 1.63865 + 5.04324i 0.668975 + 2.05889i
\(7\) −0.809017 0.587785i −0.305780 0.222162i
\(8\) 2.42705 1.76336i 0.858092 0.623440i
\(9\) 0.711597 2.19007i 0.237199 0.730023i
\(10\) −8.30278 −2.62557
\(11\) 0 0
\(12\) −7.60555 −2.19553
\(13\) −2.04123 + 6.28225i −0.566135 + 1.74238i 0.0984213 + 0.995145i \(0.468621\pi\)
−0.664556 + 0.747239i \(0.731379\pi\)
\(14\) 1.86298 1.35354i 0.497904 0.361748i
\(15\) 6.71709 + 4.88025i 1.73434 + 1.26007i
\(16\) 0.0935628 + 0.287957i 0.0233907 + 0.0719892i
\(17\) −0.833488 2.56521i −0.202151 0.622155i −0.999818 0.0190584i \(-0.993933\pi\)
0.797668 0.603097i \(-0.206067\pi\)
\(18\) 4.29004 + 3.11689i 1.01117 + 0.734659i
\(19\) −2.42705 + 1.76336i −0.556804 + 0.404542i −0.830288 0.557335i \(-0.811824\pi\)
0.273484 + 0.961877i \(0.411824\pi\)
\(20\) 3.67988 11.3255i 0.822845 2.53246i
\(21\) −2.30278 −0.502507
\(22\) 0 0
\(23\) −2.69722 −0.562410 −0.281205 0.959648i \(-0.590734\pi\)
−0.281205 + 0.959648i \(0.590734\pi\)
\(24\) 2.13479 6.57021i 0.435762 1.34114i
\(25\) −6.47214 + 4.70228i −1.29443 + 0.940456i
\(26\) −12.3060 8.94086i −2.41341 1.75345i
\(27\) 0.496143 + 1.52697i 0.0954827 + 0.293866i
\(28\) 1.02061 + 3.14113i 0.192878 + 0.593617i
\(29\) 3.80013 + 2.76096i 0.705667 + 0.512697i 0.881773 0.471674i \(-0.156350\pi\)
−0.176106 + 0.984371i \(0.556350\pi\)
\(30\) −15.4679 + 11.2381i −2.82405 + 2.05179i
\(31\) 0.309017 0.951057i 0.0555011 0.170815i −0.919463 0.393176i \(-0.871376\pi\)
0.974964 + 0.222361i \(0.0713764\pi\)
\(32\) 5.30278 0.937407
\(33\) 0 0
\(34\) 6.21110 1.06520
\(35\) 1.11418 3.42908i 0.188330 0.579621i
\(36\) −6.15302 + 4.47043i −1.02550 + 0.745072i
\(37\) 4.21587 + 3.06301i 0.693085 + 0.503556i 0.877673 0.479260i \(-0.159095\pi\)
−0.184588 + 0.982816i \(0.559095\pi\)
\(38\) −2.13479 6.57021i −0.346309 1.06583i
\(39\) 4.70049 + 14.4666i 0.752681 + 2.31651i
\(40\) 8.75086 + 6.35787i 1.38363 + 1.00527i
\(41\) 5.66312 4.11450i 0.884431 0.642576i −0.0499893 0.998750i \(-0.515919\pi\)
0.934420 + 0.356173i \(0.115919\pi\)
\(42\) 1.63865 5.04324i 0.252849 0.778189i
\(43\) −1.69722 −0.258824 −0.129412 0.991591i \(-0.541309\pi\)
−0.129412 + 0.991591i \(0.541309\pi\)
\(44\) 0 0
\(45\) 8.30278 1.23770
\(46\) 1.91934 5.90711i 0.282991 0.870956i
\(47\) 1.54387 1.12169i 0.225196 0.163615i −0.469466 0.882950i \(-0.655554\pi\)
0.694663 + 0.719336i \(0.255554\pi\)
\(48\) 0.564066 + 0.409818i 0.0814160 + 0.0591522i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) −5.69277 17.5206i −0.805080 2.47778i
\(51\) −5.02489 3.65079i −0.703625 0.511213i
\(52\) 17.6500 12.8235i 2.44762 1.77830i
\(53\) −3.98889 + 12.2765i −0.547917 + 1.68631i 0.166036 + 0.986120i \(0.446903\pi\)
−0.713953 + 0.700194i \(0.753097\pi\)
\(54\) −3.69722 −0.503129
\(55\) 0 0
\(56\) −3.00000 −0.400892
\(57\) −2.13479 + 6.57021i −0.282760 + 0.870245i
\(58\) −8.75086 + 6.35787i −1.14904 + 0.834829i
\(59\) −5.41817 3.93653i −0.705385 0.512493i 0.176296 0.984337i \(-0.443588\pi\)
−0.881682 + 0.471845i \(0.843588\pi\)
\(60\) −8.47393 26.0801i −1.09398 3.36692i
\(61\) 1.32963 + 4.09218i 0.170242 + 0.523950i 0.999384 0.0350870i \(-0.0111708\pi\)
−0.829142 + 0.559037i \(0.811171\pi\)
\(62\) 1.86298 + 1.35354i 0.236599 + 0.171899i
\(63\) −1.86298 + 1.35354i −0.234714 + 0.170530i
\(64\) −3.96056 + 12.1894i −0.495070 + 1.52367i
\(65\) −23.8167 −2.95409
\(66\) 0 0
\(67\) 8.51388 1.04014 0.520068 0.854125i \(-0.325907\pi\)
0.520068 + 0.854125i \(0.325907\pi\)
\(68\) −2.75282 + 8.47232i −0.333829 + 1.02742i
\(69\) −5.02489 + 3.65079i −0.604925 + 0.439504i
\(70\) 6.71709 + 4.88025i 0.802845 + 0.583301i
\(71\) −1.32963 4.09218i −0.157798 0.485653i 0.840636 0.541601i \(-0.182182\pi\)
−0.998434 + 0.0559485i \(0.982182\pi\)
\(72\) −2.13479 6.57021i −0.251587 0.774307i
\(73\) −4.04508 2.93893i −0.473441 0.343975i 0.325340 0.945597i \(-0.394521\pi\)
−0.798781 + 0.601622i \(0.794521\pi\)
\(74\) −9.70820 + 7.05342i −1.12856 + 0.819944i
\(75\) −5.69277 + 17.5206i −0.657345 + 2.02310i
\(76\) 9.90833 1.13656
\(77\) 0 0
\(78\) −35.0278 −3.96611
\(79\) 2.56570 7.89641i 0.288664 0.888415i −0.696613 0.717447i \(-0.745310\pi\)
0.985277 0.170968i \(-0.0546895\pi\)
\(80\) −0.883182 + 0.641669i −0.0987428 + 0.0717408i
\(81\) 8.58007 + 6.23379i 0.953341 + 0.692643i
\(82\) 4.98118 + 15.3305i 0.550079 + 1.69297i
\(83\) −0.927051 2.85317i −0.101757 0.313176i 0.887199 0.461388i \(-0.152648\pi\)
−0.988956 + 0.148212i \(0.952648\pi\)
\(84\) 6.15302 + 4.47043i 0.671350 + 0.487764i
\(85\) 7.86767 5.71620i 0.853369 0.620009i
\(86\) 1.20774 3.71704i 0.130234 0.400819i
\(87\) 10.8167 1.15967
\(88\) 0 0
\(89\) −14.7250 −1.56084 −0.780422 0.625253i \(-0.784996\pi\)
−0.780422 + 0.625253i \(0.784996\pi\)
\(90\) −5.90823 + 18.1837i −0.622782 + 1.91673i
\(91\) 5.34400 3.88265i 0.560204 0.407012i
\(92\) 7.20699 + 5.23618i 0.751380 + 0.545910i
\(93\) −0.711597 2.19007i −0.0737892 0.227100i
\(94\) 1.35796 + 4.17937i 0.140063 + 0.431069i
\(95\) −8.75086 6.35787i −0.897819 0.652304i
\(96\) 9.87899 7.17751i 1.00827 0.732551i
\(97\) −1.11418 + 3.42908i −0.113127 + 0.348171i −0.991552 0.129711i \(-0.958595\pi\)
0.878424 + 0.477881i \(0.158595\pi\)
\(98\) −2.30278 −0.232615
\(99\) 0 0
\(100\) 26.4222 2.64222
\(101\) 1.63865 5.04324i 0.163052 0.501821i −0.835836 0.548979i \(-0.815017\pi\)
0.998887 + 0.0471583i \(0.0150165\pi\)
\(102\) 11.5712 8.40696i 1.14572 0.832413i
\(103\) 11.5712 + 8.40696i 1.14014 + 0.828362i 0.987139 0.159863i \(-0.0511053\pi\)
0.153004 + 0.988226i \(0.451105\pi\)
\(104\) 6.12368 + 18.8468i 0.600477 + 1.84808i
\(105\) −2.56570 7.89641i −0.250387 0.770611i
\(106\) −24.0480 17.4719i −2.33575 1.69702i
\(107\) 10.0273 7.28527i 0.969378 0.704294i 0.0140679 0.999901i \(-0.495522\pi\)
0.955310 + 0.295607i \(0.0955219\pi\)
\(108\) 1.63865 5.04324i 0.157679 0.485286i
\(109\) 8.00000 0.766261 0.383131 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) 12.0000 1.13899
\(112\) 0.0935628 0.287957i 0.00884086 0.0272094i
\(113\) 8.65424 6.28767i 0.814122 0.591494i −0.100901 0.994897i \(-0.532172\pi\)
0.915023 + 0.403402i \(0.132172\pi\)
\(114\) −12.8701 9.35068i −1.20540 0.875771i
\(115\) −3.00518 9.24901i −0.280235 0.862474i
\(116\) −4.79405 14.7546i −0.445117 1.36993i
\(117\) 12.3060 + 8.94086i 1.13769 + 0.826583i
\(118\) 12.4768 9.06494i 1.14858 0.834496i
\(119\) −0.833488 + 2.56521i −0.0764057 + 0.235153i
\(120\) 24.9083 2.27381
\(121\) 0 0
\(122\) −9.90833 −0.897058
\(123\) 4.98118 15.3305i 0.449138 1.38230i
\(124\) −2.67200 + 1.94132i −0.239953 + 0.174336i
\(125\) −8.75086 6.35787i −0.782700 0.568665i
\(126\) −1.63865 5.04324i −0.145982 0.449287i
\(127\) −0.618034 1.90211i −0.0548416 0.168785i 0.919884 0.392191i \(-0.128283\pi\)
−0.974726 + 0.223405i \(0.928283\pi\)
\(128\) −15.2972 11.1140i −1.35209 0.982351i
\(129\) −3.16190 + 2.29726i −0.278390 + 0.202262i
\(130\) 16.9479 52.1601i 1.48643 4.57475i
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 3.00000 0.260133
\(134\) −6.05845 + 18.6460i −0.523370 + 1.61077i
\(135\) −4.68332 + 3.40263i −0.403076 + 0.292852i
\(136\) −6.54630 4.75617i −0.561341 0.407838i
\(137\) −3.12708 9.62415i −0.267164 0.822247i −0.991187 0.132471i \(-0.957709\pi\)
0.724023 0.689776i \(-0.242291\pi\)
\(138\) −4.41980 13.6027i −0.376238 1.15794i
\(139\) 17.4793 + 12.6994i 1.48257 + 1.07715i 0.976717 + 0.214532i \(0.0688227\pi\)
0.505854 + 0.862619i \(0.331177\pi\)
\(140\) −9.63404 + 6.99954i −0.814225 + 0.591569i
\(141\) 1.35796 4.17937i 0.114361 0.351966i
\(142\) 9.90833 0.831488
\(143\) 0 0
\(144\) 0.697224 0.0581020
\(145\) −5.23354 + 16.1072i −0.434622 + 1.33763i
\(146\) 9.31492 6.76769i 0.770909 0.560098i
\(147\) 1.86298 + 1.35354i 0.153656 + 0.111638i
\(148\) −5.31852 16.3687i −0.437180 1.34550i
\(149\) 1.51676 + 4.66810i 0.124258 + 0.382425i 0.993765 0.111494i \(-0.0355637\pi\)
−0.869508 + 0.493920i \(0.835564\pi\)
\(150\) −34.3203 24.9351i −2.80224 2.03595i
\(151\) −0.170786 + 0.124083i −0.0138983 + 0.0100977i −0.594713 0.803938i \(-0.702734\pi\)
0.580814 + 0.814036i \(0.302734\pi\)
\(152\) −2.78115 + 8.55951i −0.225581 + 0.694268i
\(153\) −6.21110 −0.502138
\(154\) 0 0
\(155\) 3.60555 0.289605
\(156\) 15.5247 47.7800i 1.24297 3.82546i
\(157\) −5.83390 + 4.23858i −0.465596 + 0.338275i −0.795723 0.605661i \(-0.792909\pi\)
0.330126 + 0.943937i \(0.392909\pi\)
\(158\) 15.4679 + 11.2381i 1.23056 + 0.894057i
\(159\) 9.18552 + 28.2701i 0.728459 + 2.24197i
\(160\) 5.90823 + 18.1837i 0.467086 + 1.43754i
\(161\) 2.18210 + 1.58539i 0.171974 + 0.124946i
\(162\) −19.7580 + 14.3550i −1.55233 + 1.12784i
\(163\) 0.870394 2.67880i 0.0681745 0.209820i −0.911165 0.412041i \(-0.864816\pi\)
0.979340 + 0.202221i \(0.0648161\pi\)
\(164\) −23.1194 −1.80532
\(165\) 0 0
\(166\) 6.90833 0.536190
\(167\) 1.61032 4.95605i 0.124610 0.383511i −0.869220 0.494426i \(-0.835378\pi\)
0.993830 + 0.110915i \(0.0353782\pi\)
\(168\) −5.58895 + 4.06061i −0.431197 + 0.313283i
\(169\) −24.7829 18.0058i −1.90637 1.38506i
\(170\) 6.92027 + 21.2984i 0.530760 + 1.63351i
\(171\) 2.13479 + 6.57021i 0.163252 + 0.502436i
\(172\) 4.53499 + 3.29486i 0.345789 + 0.251231i
\(173\) −1.05397 + 0.765752i −0.0801317 + 0.0582191i −0.627130 0.778915i \(-0.715770\pi\)
0.546998 + 0.837134i \(0.315770\pi\)
\(174\) −7.69710 + 23.6892i −0.583515 + 1.79588i
\(175\) 8.00000 0.604743
\(176\) 0 0
\(177\) −15.4222 −1.15920
\(178\) 10.4782 32.2487i 0.785378 2.41714i
\(179\) 5.17322 3.75856i 0.386664 0.280928i −0.377423 0.926041i \(-0.623190\pi\)
0.764087 + 0.645113i \(0.223190\pi\)
\(180\) −22.1850 16.1184i −1.65357 1.20139i
\(181\) −7.79066 23.9772i −0.579075 1.78221i −0.621863 0.783126i \(-0.713624\pi\)
0.0427881 0.999084i \(-0.486376\pi\)
\(182\) 4.70049 + 14.4666i 0.348423 + 1.07234i
\(183\) 8.01600 + 5.82397i 0.592560 + 0.430520i
\(184\) −6.54630 + 4.75617i −0.482600 + 0.350629i
\(185\) −5.80609 + 17.8693i −0.426872 + 1.31378i
\(186\) 5.30278 0.388818
\(187\) 0 0
\(188\) −6.30278 −0.459677
\(189\) 0.496143 1.52697i 0.0360891 0.111071i
\(190\) 20.1513 14.6407i 1.46193 1.06215i
\(191\) 21.6951 + 15.7624i 1.56980 + 1.14053i 0.927343 + 0.374211i \(0.122086\pi\)
0.642461 + 0.766318i \(0.277914\pi\)
\(192\) 9.12029 + 28.0694i 0.658200 + 2.02573i
\(193\) 0.654940 + 2.01570i 0.0471436 + 0.145093i 0.971857 0.235570i \(-0.0756957\pi\)
−0.924714 + 0.380663i \(0.875696\pi\)
\(194\) −6.71709 4.88025i −0.482259 0.350381i
\(195\) −44.3701 + 32.2367i −3.17741 + 2.30852i
\(196\) 1.02061 3.14113i 0.0729010 0.224366i
\(197\) 10.6056 0.755614 0.377807 0.925884i \(-0.376678\pi\)
0.377807 + 0.925884i \(0.376678\pi\)
\(198\) 0 0
\(199\) 19.4222 1.37680 0.688402 0.725330i \(-0.258313\pi\)
0.688402 + 0.725330i \(0.258313\pi\)
\(200\) −7.41641 + 22.8254i −0.524419 + 1.61400i
\(201\) 15.8612 11.5239i 1.11876 0.812830i
\(202\) 9.87899 + 7.17751i 0.695083 + 0.505008i
\(203\) −1.45152 4.46733i −0.101877 0.313545i
\(204\) 6.33914 + 19.5099i 0.443828 + 1.36596i
\(205\) 20.4187 + 14.8350i 1.42610 + 1.03612i
\(206\) −26.6459 + 19.3593i −1.85650 + 1.34883i
\(207\) −1.91934 + 5.90711i −0.133403 + 0.410572i
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 19.1194 1.31937
\(211\) −4.79405 + 14.7546i −0.330036 + 1.01575i 0.639080 + 0.769141i \(0.279315\pi\)
−0.969116 + 0.246606i \(0.920685\pi\)
\(212\) 34.4911 25.0592i 2.36886 1.72107i
\(213\) −8.01600 5.82397i −0.549248 0.399052i
\(214\) 8.81985 + 27.1447i 0.602913 + 1.85557i
\(215\) −1.89101 5.81992i −0.128966 0.396915i
\(216\) 3.89675 + 2.83116i 0.265141 + 0.192636i
\(217\) −0.809017 + 0.587785i −0.0549197 + 0.0399015i
\(218\) −5.69277 + 17.5206i −0.385563 + 1.18664i
\(219\) −11.5139 −0.778036
\(220\) 0 0
\(221\) 17.8167 1.19848
\(222\) −8.53916 + 26.2808i −0.573111 + 1.76385i
\(223\) −11.2521 + 8.17511i −0.753495 + 0.547446i −0.896908 0.442217i \(-0.854192\pi\)
0.143414 + 0.989663i \(0.454192\pi\)
\(224\) −4.29004 3.11689i −0.286640 0.208256i
\(225\) 5.69277 + 17.5206i 0.379518 + 1.16804i
\(226\) 7.61211 + 23.4277i 0.506350 + 1.55839i
\(227\) 5.26984 + 3.82876i 0.349771 + 0.254124i 0.748773 0.662826i \(-0.230643\pi\)
−0.399002 + 0.916950i \(0.630643\pi\)
\(228\) 18.4591 13.4113i 1.22248 0.888185i
\(229\) −0.805160 + 2.47803i −0.0532064 + 0.163753i −0.974129 0.225993i \(-0.927437\pi\)
0.920922 + 0.389746i \(0.127437\pi\)
\(230\) 22.3944 1.47665
\(231\) 0 0
\(232\) 14.0917 0.925164
\(233\) −5.56231 + 17.1190i −0.364399 + 1.12150i 0.585958 + 0.810341i \(0.300718\pi\)
−0.950357 + 0.311163i \(0.899282\pi\)
\(234\) −28.3381 + 20.5888i −1.85252 + 1.34593i
\(235\) 5.56650 + 4.04430i 0.363118 + 0.263821i
\(236\) 6.83528 + 21.0368i 0.444939 + 1.36938i
\(237\) −5.90823 18.1837i −0.383781 1.18116i
\(238\) −5.02489 3.65079i −0.325715 0.236646i
\(239\) 21.3018 15.4767i 1.37790 1.00110i 0.380829 0.924645i \(-0.375639\pi\)
0.997073 0.0764590i \(-0.0243614\pi\)
\(240\) −0.776831 + 2.39084i −0.0501442 + 0.154328i
\(241\) −0.486122 −0.0313139 −0.0156569 0.999877i \(-0.504984\pi\)
−0.0156569 + 0.999877i \(0.504984\pi\)
\(242\) 0 0
\(243\) 19.6056 1.25770
\(244\) 4.39147 13.5156i 0.281135 0.865245i
\(245\) −2.91695 + 2.11929i −0.186357 + 0.135396i
\(246\) 30.0302 + 21.8183i 1.91466 + 1.39108i
\(247\) −6.12368 18.8468i −0.389641 1.19919i
\(248\) −0.927051 2.85317i −0.0588678 0.181176i
\(249\) −5.58895 4.06061i −0.354186 0.257331i
\(250\) 20.1513 14.6407i 1.27448 0.925962i
\(251\) 1.35796 4.17937i 0.0857136 0.263799i −0.899009 0.437930i \(-0.855712\pi\)
0.984722 + 0.174131i \(0.0557116\pi\)
\(252\) 7.60555 0.479105
\(253\) 0 0
\(254\) 4.60555 0.288978
\(255\) 6.92027 21.2984i 0.433364 1.33376i
\(256\) 14.4881 10.5263i 0.905509 0.657891i
\(257\) −5.24738 3.81245i −0.327323 0.237814i 0.411971 0.911197i \(-0.364840\pi\)
−0.739294 + 0.673383i \(0.764840\pi\)
\(258\) −2.78115 8.55951i −0.173147 0.532892i
\(259\) −1.61032 4.95605i −0.100060 0.307954i
\(260\) 63.6381 + 46.2358i 3.94667 + 2.86742i
\(261\) 8.75086 6.35787i 0.541664 0.393542i
\(262\) −4.26958 + 13.1404i −0.263776 + 0.811818i
\(263\) −20.2389 −1.24798 −0.623991 0.781432i \(-0.714490\pi\)
−0.623991 + 0.781432i \(0.714490\pi\)
\(264\) 0 0
\(265\) −46.5416 −2.85903
\(266\) −2.13479 + 6.57021i −0.130892 + 0.402845i
\(267\) −27.4324 + 19.9308i −1.67884 + 1.21975i
\(268\) −22.7491 16.5282i −1.38962 1.00962i
\(269\) 4.98118 + 15.3305i 0.303708 + 0.934716i 0.980156 + 0.198226i \(0.0635181\pi\)
−0.676448 + 0.736490i \(0.736482\pi\)
\(270\) −4.11936 12.6781i −0.250696 0.771564i
\(271\) −23.0682 16.7600i −1.40129 1.01810i −0.994517 0.104572i \(-0.966653\pi\)
−0.406777 0.913528i \(-0.633347\pi\)
\(272\) 0.660687 0.480017i 0.0400600 0.0291053i
\(273\) 4.70049 14.4666i 0.284487 0.875560i
\(274\) 23.3028 1.40777
\(275\) 0 0
\(276\) 20.5139 1.23479
\(277\) −9.25076 + 28.4709i −0.555824 + 1.71065i 0.137933 + 0.990442i \(0.455954\pi\)
−0.693757 + 0.720209i \(0.744046\pi\)
\(278\) −40.2508 + 29.2439i −2.41408 + 1.75393i
\(279\) −1.86298 1.35354i −0.111534 0.0810342i
\(280\) −3.34253 10.2872i −0.199754 0.614781i
\(281\) −1.97599 6.08148i −0.117878 0.362791i 0.874659 0.484740i \(-0.161086\pi\)
−0.992536 + 0.121949i \(0.961086\pi\)
\(282\) 8.18679 + 5.94805i 0.487516 + 0.354201i
\(283\) 3.55518 2.58299i 0.211334 0.153543i −0.477083 0.878858i \(-0.658306\pi\)
0.688417 + 0.725315i \(0.258306\pi\)
\(284\) −4.39147 + 13.5156i −0.260586 + 0.802001i
\(285\) −24.9083 −1.47544
\(286\) 0 0
\(287\) −7.00000 −0.413197
\(288\) 3.77344 11.6134i 0.222352 0.684329i
\(289\) 7.86767 5.71620i 0.462804 0.336247i
\(290\) −31.5517 22.9236i −1.85278 1.34612i
\(291\) 2.56570 + 7.89641i 0.150404 + 0.462896i
\(292\) 5.10307 + 15.7056i 0.298635 + 0.919103i
\(293\) 3.89675 + 2.83116i 0.227651 + 0.165398i 0.695764 0.718271i \(-0.255066\pi\)
−0.468113 + 0.883669i \(0.655066\pi\)
\(294\) −4.29004 + 3.11689i −0.250200 + 0.181781i
\(295\) 7.46189 22.9653i 0.434448 1.33709i
\(296\) 15.6333 0.908668
\(297\) 0 0
\(298\) −11.3028 −0.654752
\(299\) 5.50565 16.9446i 0.318400 0.979934i
\(300\) 49.2242 35.7634i 2.84196 2.06480i
\(301\) 1.37308 + 0.997603i 0.0791432 + 0.0575009i
\(302\) −0.150220 0.462329i −0.00864418 0.0266041i
\(303\) −3.77344 11.6134i −0.216778 0.667175i
\(304\) −0.734852 0.533901i −0.0421466 0.0306213i
\(305\) −12.5510 + 9.11883i −0.718668 + 0.522143i
\(306\) 4.41980 13.6027i 0.252663 0.777617i
\(307\) 16.6333 0.949313 0.474657 0.880171i \(-0.342572\pi\)
0.474657 + 0.880171i \(0.342572\pi\)
\(308\) 0 0
\(309\) 32.9361 1.87367
\(310\) −2.56570 + 7.89641i −0.145722 + 0.448486i
\(311\) −5.17322 + 3.75856i −0.293346 + 0.213129i −0.724718 0.689046i \(-0.758030\pi\)
0.431371 + 0.902174i \(0.358030\pi\)
\(312\) 36.9181 + 26.8226i 2.09008 + 1.51853i
\(313\) 4.72882 + 14.5538i 0.267289 + 0.822630i 0.991157 + 0.132692i \(0.0423621\pi\)
−0.723869 + 0.689938i \(0.757638\pi\)
\(314\) −5.13140 15.7928i −0.289582 0.891240i
\(315\) −6.71709 4.88025i −0.378465 0.274971i
\(316\) −22.1850 + 16.1184i −1.24801 + 0.906729i
\(317\) 5.34685 16.4559i 0.300309 0.924256i −0.681077 0.732212i \(-0.738488\pi\)
0.981386 0.192045i \(-0.0615119\pi\)
\(318\) −68.4500 −3.83848
\(319\) 0 0
\(320\) −46.2111 −2.58328
\(321\) 8.81985 27.1447i 0.492276 1.51507i
\(322\) −5.02489 + 3.65079i −0.280026 + 0.203451i
\(323\) 6.54630 + 4.75617i 0.364246 + 0.264640i
\(324\) −10.8242 33.3134i −0.601343 1.85074i
\(325\) −16.3298 50.2580i −0.905815 2.78781i
\(326\) 5.24738 + 3.81245i 0.290626 + 0.211152i
\(327\) 14.9039 10.8283i 0.824186 0.598806i
\(328\) 6.48936 19.9722i 0.358315 1.10278i
\(329\) −1.90833 −0.105209
\(330\) 0 0
\(331\) 23.8167 1.30908 0.654541 0.756027i \(-0.272862\pi\)
0.654541 + 0.756027i \(0.272862\pi\)
\(332\) −3.06184 + 9.42338i −0.168040 + 0.517175i
\(333\) 9.70820 7.05342i 0.532006 0.386525i
\(334\) 9.70820 + 7.05342i 0.531209 + 0.385946i
\(335\) 9.48596 + 29.1948i 0.518274 + 1.59508i
\(336\) −0.215454 0.663100i −0.0117540 0.0361751i
\(337\) 9.53742 + 6.92934i 0.519536 + 0.377465i 0.816429 0.577446i \(-0.195950\pi\)
−0.296893 + 0.954911i \(0.595950\pi\)
\(338\) 57.0694 41.4633i 3.10417 2.25531i
\(339\) 7.61211 23.4277i 0.413433 1.27242i
\(340\) −32.1194 −1.74192
\(341\) 0 0
\(342\) −15.9083 −0.860224
\(343\) 0.309017 0.951057i 0.0166853 0.0513522i
\(344\) −4.11925 + 2.99281i −0.222095 + 0.161362i
\(345\) −18.1175 13.1631i −0.975413 0.708679i
\(346\) −0.927051 2.85317i −0.0498386 0.153387i
\(347\) −2.96828 9.13542i −0.159346 0.490415i 0.839230 0.543777i \(-0.183006\pi\)
−0.998575 + 0.0533619i \(0.983006\pi\)
\(348\) −28.9021 20.9986i −1.54932 1.12564i
\(349\) −3.80013 + 2.76096i −0.203417 + 0.147791i −0.684830 0.728703i \(-0.740124\pi\)
0.481413 + 0.876494i \(0.340124\pi\)
\(350\) −5.69277 + 17.5206i −0.304292 + 0.936513i
\(351\) −10.6056 −0.566082
\(352\) 0 0
\(353\) 5.09167 0.271002 0.135501 0.990777i \(-0.456736\pi\)
0.135501 + 0.990777i \(0.456736\pi\)
\(354\) 10.9744 33.7757i 0.583282 1.79516i
\(355\) 12.5510 9.11883i 0.666137 0.483977i
\(356\) 39.3452 + 28.5859i 2.08529 + 1.51505i
\(357\) 1.91934 + 5.90711i 0.101582 + 0.312637i
\(358\) 4.55027 + 14.0043i 0.240489 + 0.740150i
\(359\) −27.4549 19.9471i −1.44901 1.05277i −0.986061 0.166386i \(-0.946790\pi\)
−0.462952 0.886383i \(-0.653210\pi\)
\(360\) 20.1513 14.6407i 1.06206 0.771635i
\(361\) −3.09017 + 9.51057i −0.162641 + 0.500556i
\(362\) 58.0555 3.05133
\(363\) 0 0
\(364\) −21.8167 −1.14350
\(365\) 5.57088 17.1454i 0.291593 0.897432i
\(366\) −18.4591 + 13.4113i −0.964871 + 0.701019i
\(367\) 14.2656 + 10.3646i 0.744661 + 0.541028i 0.894167 0.447733i \(-0.147769\pi\)
−0.149507 + 0.988761i \(0.547769\pi\)
\(368\) −0.252360 0.776684i −0.0131552 0.0404874i
\(369\) −4.98118 15.3305i −0.259310 0.798073i
\(370\) −35.0034 25.4315i −1.81974 1.32212i
\(371\) 10.4431 7.58732i 0.542176 0.393914i
\(372\) −2.35024 + 7.23331i −0.121855 + 0.375030i
\(373\) 20.1194 1.04174 0.520872 0.853635i \(-0.325607\pi\)
0.520872 + 0.853635i \(0.325607\pi\)
\(374\) 0 0
\(375\) −24.9083 −1.28626
\(376\) 1.76912 5.44478i 0.0912352 0.280793i
\(377\) −25.1020 + 18.2377i −1.29282 + 0.939287i
\(378\) 2.99112 + 2.17317i 0.153846 + 0.111776i
\(379\) −4.88761 15.0425i −0.251060 0.772683i −0.994580 0.103970i \(-0.966845\pi\)
0.743521 0.668713i \(-0.233155\pi\)
\(380\) 11.0396 + 33.9765i 0.566321 + 1.74296i
\(381\) −3.72597 2.70708i −0.190887 0.138688i
\(382\) −49.9590 + 36.2973i −2.55613 + 1.85713i
\(383\) 11.9383 36.7425i 0.610021 1.87745i 0.152361 0.988325i \(-0.451313\pi\)
0.457661 0.889127i \(-0.348687\pi\)
\(384\) −43.5416 −2.22197
\(385\) 0 0
\(386\) −4.88057 −0.248414
\(387\) −1.20774 + 3.71704i −0.0613928 + 0.188948i
\(388\) 9.63404 6.99954i 0.489094 0.355348i
\(389\) 6.32381 + 4.59451i 0.320630 + 0.232951i 0.736444 0.676498i \(-0.236503\pi\)
−0.415814 + 0.909449i \(0.636503\pi\)
\(390\) −39.0271 120.113i −1.97621 6.08216i
\(391\) 2.24810 + 6.91895i 0.113692 + 0.349907i
\(392\) 2.42705 + 1.76336i 0.122585 + 0.0890629i
\(393\) 11.1779 8.12123i 0.563851 0.409662i
\(394\) −7.54688 + 23.2269i −0.380206 + 1.17015i
\(395\) 29.9361 1.50625
\(396\) 0 0
\(397\) 30.2111 1.51625 0.758126 0.652108i \(-0.226115\pi\)
0.758126 + 0.652108i \(0.226115\pi\)
\(398\) −13.8208 + 42.5360i −0.692773 + 2.13214i
\(399\) 5.58895 4.06061i 0.279798 0.203285i
\(400\) −1.95961 1.42374i −0.0979803 0.0711868i
\(401\) −6.55459 20.1730i −0.327321 1.00739i −0.970382 0.241575i \(-0.922336\pi\)
0.643062 0.765815i \(-0.277664\pi\)
\(402\) 13.9512 + 42.9375i 0.695825 + 2.14153i
\(403\) 5.34400 + 3.88265i 0.266204 + 0.193408i
\(404\) −14.1690 + 10.2944i −0.704935 + 0.512166i
\(405\) −11.8165 + 36.3673i −0.587164 + 1.80711i
\(406\) 10.8167 0.536822
\(407\) 0 0
\(408\) −18.6333 −0.922486
\(409\) −6.36747 + 19.5970i −0.314851 + 0.969011i 0.660965 + 0.750417i \(0.270147\pi\)
−0.975816 + 0.218595i \(0.929853\pi\)
\(410\) −47.0196 + 34.1617i −2.32213 + 1.68713i
\(411\) −18.8523 13.6970i −0.929917 0.675625i
\(412\) −14.5976 44.9268i −0.719173 2.21339i
\(413\) 2.06956 + 6.36944i 0.101836 + 0.313420i
\(414\) −11.5712 8.40696i −0.568693 0.413180i
\(415\) 8.75086 6.35787i 0.429563 0.312096i
\(416\) −10.8242 + 33.3134i −0.530699 + 1.63332i
\(417\) 49.7527 2.43640
\(418\) 0 0
\(419\) −38.4222 −1.87705 −0.938524 0.345215i \(-0.887806\pi\)
−0.938524 + 0.345215i \(0.887806\pi\)
\(420\) −8.47393 + 26.0801i −0.413485 + 1.27258i
\(421\) 17.6500 12.8235i 0.860210 0.624980i −0.0677317 0.997704i \(-0.521576\pi\)
0.927942 + 0.372724i \(0.121576\pi\)
\(422\) −28.9021 20.9986i −1.40693 1.02220i
\(423\) −1.35796 4.17937i −0.0660262 0.203208i
\(424\) 11.9667 + 36.8296i 0.581153 + 1.78861i
\(425\) 17.4568 + 12.6831i 0.846779 + 0.615221i
\(426\) 18.4591 13.4113i 0.894344 0.649779i
\(427\) 1.32963 4.09218i 0.0643453 0.198035i
\(428\) −40.9361 −1.97872
\(429\) 0 0
\(430\) 14.0917 0.679561
\(431\) 0.963957 2.96675i 0.0464322 0.142903i −0.925153 0.379595i \(-0.876063\pi\)
0.971585 + 0.236692i \(0.0760632\pi\)
\(432\) −0.393281 + 0.285735i −0.0189217 + 0.0137474i
\(433\) −23.5806 17.1323i −1.13321 0.823325i −0.147051 0.989129i \(-0.546978\pi\)
−0.986159 + 0.165804i \(0.946978\pi\)
\(434\) −0.711597 2.19007i −0.0341577 0.105127i
\(435\) 12.0517 + 37.0912i 0.577833 + 1.77839i
\(436\) −21.3760 15.5306i −1.02373 0.743780i
\(437\) 6.54630 4.75617i 0.313152 0.227518i
\(438\) 8.19324 25.2162i 0.391488 1.20488i
\(439\) −27.7250 −1.32324 −0.661621 0.749839i \(-0.730131\pi\)
−0.661621 + 0.749839i \(0.730131\pi\)
\(440\) 0 0
\(441\) 2.30278 0.109656
\(442\) −12.6783 + 39.0197i −0.603044 + 1.85598i
\(443\) −21.7917 + 15.8326i −1.03536 + 0.752231i −0.969374 0.245590i \(-0.921018\pi\)
−0.0659834 + 0.997821i \(0.521018\pi\)
\(444\) −32.0640 23.2959i −1.52169 1.10557i
\(445\) −16.4062 50.4932i −0.777730 2.39361i
\(446\) −9.89712 30.4602i −0.468642 1.44233i
\(447\) 9.14414 + 6.64360i 0.432503 + 0.314232i
\(448\) 10.3689 7.53344i 0.489884 0.355922i
\(449\) 12.4628 38.3566i 0.588157 1.81016i 0.00195147 0.999998i \(-0.499379\pi\)
0.586205 0.810162i \(-0.300621\pi\)
\(450\) −42.4222 −1.99980
\(451\) 0 0
\(452\) −35.3305 −1.66181
\(453\) −0.150220 + 0.462329i −0.00705795 + 0.0217221i
\(454\) −12.1353 + 8.81678i −0.569536 + 0.413792i
\(455\) 19.2681 + 13.9991i 0.903301 + 0.656287i
\(456\) 6.40437 + 19.7106i 0.299912 + 0.923035i
\(457\) −6.52626 20.0858i −0.305286 0.939573i −0.979570 0.201101i \(-0.935548\pi\)
0.674285 0.738471i \(-0.264452\pi\)
\(458\) −4.85410 3.52671i −0.226817 0.164792i
\(459\) 3.50347 2.54542i 0.163528 0.118810i
\(460\) −9.92545 + 30.5474i −0.462776 + 1.42428i
\(461\) −8.09167 −0.376867 −0.188433 0.982086i \(-0.560341\pi\)
−0.188433 + 0.982086i \(0.560341\pi\)
\(462\) 0 0
\(463\) −30.8167 −1.43217 −0.716086 0.698012i \(-0.754068\pi\)
−0.716086 + 0.698012i \(0.754068\pi\)
\(464\) −0.439486 + 1.35260i −0.0204026 + 0.0627928i
\(465\) 6.71709 4.88025i 0.311497 0.226316i
\(466\) −33.5337 24.3637i −1.55342 1.12863i
\(467\) −4.18460 12.8789i −0.193640 0.595963i −0.999990 0.00452363i \(-0.998560\pi\)
0.806350 0.591439i \(-0.201440\pi\)
\(468\) −15.5247 47.7800i −0.717628 2.20863i
\(469\) −6.88787 5.00433i −0.318052 0.231079i
\(470\) −12.8184 + 9.31311i −0.591269 + 0.429582i
\(471\) −5.13140 + 15.7928i −0.236442 + 0.727695i
\(472\) −20.0917 −0.924794
\(473\) 0 0
\(474\) 44.0278 2.02226
\(475\) 7.41641 22.8254i 0.340288 1.04730i
\(476\) 7.20699 5.23618i 0.330332 0.240000i
\(477\) 24.0480 + 17.4719i 1.10108 + 0.799984i
\(478\) 18.7367 + 57.6657i 0.856998 + 2.63757i
\(479\) 8.84818 + 27.2319i 0.404284 + 1.24426i 0.921492 + 0.388397i \(0.126971\pi\)
−0.517208 + 0.855860i \(0.673029\pi\)
\(480\) 35.6192 + 25.8789i 1.62579 + 1.18120i
\(481\) −27.8481 + 20.2329i −1.26977 + 0.922539i
\(482\) 0.345923 1.06464i 0.0157563 0.0484931i
\(483\) 6.21110 0.282615
\(484\) 0 0
\(485\) −13.0000 −0.590300
\(486\) −13.9512 + 42.9375i −0.632841 + 1.94769i
\(487\) 2.27872 1.65559i 0.103259 0.0750218i −0.534958 0.844879i \(-0.679672\pi\)
0.638216 + 0.769857i \(0.279672\pi\)
\(488\) 10.4431 + 7.58732i 0.472735 + 0.343462i
\(489\) −2.00432 6.16867i −0.0906386 0.278957i
\(490\) −2.56570 7.89641i −0.115906 0.356723i
\(491\) −10.2723 7.46324i −0.463581 0.336811i 0.331353 0.943507i \(-0.392495\pi\)
−0.794934 + 0.606695i \(0.792495\pi\)
\(492\) −43.0711 + 31.2930i −1.94180 + 1.41080i
\(493\) 3.91508 12.0494i 0.176326 0.542677i
\(494\) 45.6333 2.05314
\(495\) 0 0
\(496\) 0.302776 0.0135950
\(497\) −1.32963 + 4.09218i −0.0596421 + 0.183559i
\(498\) 12.8701 9.35068i 0.576723 0.419014i
\(499\) −2.35289 1.70947i −0.105330 0.0765265i 0.533874 0.845564i \(-0.320736\pi\)
−0.639203 + 0.769038i \(0.720736\pi\)
\(500\) 11.0396 + 33.9765i 0.493707 + 1.51947i
\(501\) −3.70820 11.4127i −0.165670 0.509881i
\(502\) 8.18679 + 5.94805i 0.365394 + 0.265475i
\(503\) 4.51253 3.27855i 0.201204 0.146183i −0.482621 0.875829i \(-0.660315\pi\)
0.683825 + 0.729646i \(0.260315\pi\)
\(504\) −2.13479 + 6.57021i −0.0950911 + 0.292660i
\(505\) 19.1194 0.850803
\(506\) 0 0
\(507\) −70.5416 −3.13286
\(508\) −2.04123 + 6.28225i −0.0905648 + 0.278730i
\(509\) −18.0433 + 13.1092i −0.799756 + 0.581057i −0.910843 0.412754i \(-0.864567\pi\)
0.111086 + 0.993811i \(0.464567\pi\)
\(510\) 41.7205 + 30.3117i 1.84742 + 1.34223i
\(511\) 1.54508 + 4.75528i 0.0683505 + 0.210361i
\(512\) 1.05752 + 3.25471i 0.0467362 + 0.143839i
\(513\) −3.89675 2.83116i −0.172046 0.124999i
\(514\) 12.0835 8.77921i 0.532982 0.387234i
\(515\) −15.9358 + 49.0454i −0.702216 + 2.16120i
\(516\) 12.9083 0.568257
\(517\) 0 0
\(518\) 12.0000 0.527250
\(519\) −0.927051 + 2.85317i −0.0406930 + 0.125240i
\(520\) −57.8042 + 41.9972i −2.53488 + 1.84170i
\(521\) −6.00469 4.36266i −0.263070 0.191132i 0.448429 0.893818i \(-0.351984\pi\)
−0.711499 + 0.702687i \(0.751984\pi\)
\(522\) 7.69710 + 23.6892i 0.336893 + 1.03685i
\(523\) 13.7641 + 42.3616i 0.601863 + 1.85234i 0.517066 + 0.855946i \(0.327024\pi\)
0.0847974 + 0.996398i \(0.472976\pi\)
\(524\) −16.0320 11.6479i −0.700362 0.508842i
\(525\) 14.9039 10.8283i 0.650459 0.472586i
\(526\) 14.4019 44.3245i 0.627953 1.93264i
\(527\) −2.69722 −0.117493
\(528\) 0 0
\(529\) −15.7250 −0.683695
\(530\) 33.1189 101.929i 1.43859 4.42753i
\(531\) −12.4768 + 9.06494i −0.541448 + 0.393385i
\(532\) −8.01600 5.82397i −0.347538 0.252501i
\(533\) 14.2886 + 43.9758i 0.618908 + 1.90480i
\(534\) −24.1291 74.2616i −1.04417 3.21361i
\(535\) 36.1540 + 26.2674i 1.56307 + 1.13564i
\(536\) 20.6636 15.0130i 0.892532 0.648463i
\(537\) 4.55027 14.0043i 0.196359 0.604330i
\(538\) −37.1194 −1.60033
\(539\) 0 0
\(540\) 19.1194 0.822769
\(541\) 10.0104 30.8090i 0.430382 1.32458i −0.467363 0.884065i \(-0.654796\pi\)
0.897745 0.440515i \(-0.145204\pi\)
\(542\) 53.1209 38.5946i 2.28174 1.65778i
\(543\) −46.9679 34.1242i −2.01559 1.46441i
\(544\) −4.41980 13.6027i −0.189497 0.583213i
\(545\) 8.91341 + 27.4327i 0.381809 + 1.17509i
\(546\) 28.3381 + 20.5888i 1.21276 + 0.881119i
\(547\) −24.2188 + 17.5960i −1.03552 + 0.752350i −0.969406 0.245462i \(-0.921060\pi\)
−0.0661149 + 0.997812i \(0.521060\pi\)
\(548\) −10.3280 + 31.7864i −0.441192 + 1.35785i
\(549\) 9.90833 0.422877
\(550\) 0 0
\(551\) −14.0917 −0.600325
\(552\) −5.75801 + 17.7213i −0.245077 + 0.754270i
\(553\) −6.71709 + 4.88025i −0.285640 + 0.207529i
\(554\) −55.7705 40.5196i −2.36946 1.72151i
\(555\) 13.3701 + 41.1490i 0.567530 + 1.74668i
\(556\) −22.0509 67.8658i −0.935167 2.87815i
\(557\) 5.85636 + 4.25489i 0.248142 + 0.180286i 0.704903 0.709304i \(-0.250991\pi\)
−0.456761 + 0.889589i \(0.650991\pi\)
\(558\) 4.29004 3.11689i 0.181612 0.131949i
\(559\) 3.46442 10.6624i 0.146529 0.450971i
\(560\) 1.09167 0.0461316
\(561\) 0 0
\(562\) 14.7250 0.621136
\(563\) 0.0935628 0.287957i 0.00394320 0.0121359i −0.949066 0.315079i \(-0.897969\pi\)
0.953009 + 0.302943i \(0.0979691\pi\)
\(564\) −11.7420 + 8.53104i −0.494426 + 0.359222i
\(565\) 31.2033 + 22.6705i 1.31273 + 0.953756i
\(566\) 3.12708 + 9.62415i 0.131441 + 0.404533i
\(567\) −3.27730 10.0865i −0.137633 0.423592i
\(568\) −10.4431 7.58732i −0.438181 0.318357i
\(569\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(570\) 17.7247 54.5510i 0.742405 2.28489i
\(571\) −25.8444 −1.08155 −0.540777 0.841166i \(-0.681870\pi\)
−0.540777 + 0.841166i \(0.681870\pi\)
\(572\) 0 0
\(573\) 61.7527 2.57976
\(574\) 4.98118 15.3305i 0.207910 0.639882i
\(575\) 17.4568 12.6831i 0.727999 0.528922i
\(576\) 23.8772 + 17.3478i 0.994885 + 0.722826i
\(577\) 0.683268 + 2.10288i 0.0284448 + 0.0875442i 0.964271 0.264917i \(-0.0853447\pi\)
−0.935826 + 0.352462i \(0.885345\pi\)
\(578\) 6.92027 + 21.2984i 0.287845 + 0.885896i
\(579\) 3.94846 + 2.86873i 0.164093 + 0.119220i
\(580\) 45.2532 32.8784i 1.87904 1.36520i
\(581\) −0.927051 + 2.85317i −0.0384606 + 0.118369i
\(582\) −19.1194 −0.792526
\(583\) 0 0
\(584\) −15.0000 −0.620704
\(585\) −16.9479 + 52.1601i −0.700708 + 2.15656i
\(586\) −8.97335 + 6.51952i −0.370686 + 0.269319i
\(587\) 11.0071 + 7.99714i 0.454313 + 0.330077i 0.791296 0.611433i \(-0.209407\pi\)
−0.336984 + 0.941511i \(0.609407\pi\)
\(588\) −2.35024 7.23331i −0.0969225 0.298297i
\(589\) 0.927051 + 2.85317i 0.0381985 + 0.117563i
\(590\) 44.9858 + 32.6841i 1.85204 + 1.34558i
\(591\) 19.7580 14.3550i 0.812735 0.590486i
\(592\) −0.487565 + 1.50057i −0.0200388 + 0.0616731i
\(593\) −22.6056 −0.928299 −0.464149 0.885757i \(-0.653640\pi\)
−0.464149 + 0.885757i \(0.653640\pi\)
\(594\) 0 0
\(595\) −9.72498 −0.398685
\(596\) 5.00951 15.4177i 0.205197 0.631533i
\(597\) 36.1833 26.2887i 1.48088 1.07592i
\(598\) 33.1922 + 24.1155i 1.35733 + 0.986157i
\(599\) −4.57002 14.0651i −0.186726 0.574683i 0.813248 0.581917i \(-0.197697\pi\)
−0.999974 + 0.00723398i \(0.997697\pi\)
\(600\) 17.0783 + 52.5617i 0.697220 + 2.14582i
\(601\) −4.70577 3.41894i −0.191952 0.139462i 0.487658 0.873035i \(-0.337851\pi\)
−0.679611 + 0.733573i \(0.737851\pi\)
\(602\) −3.16190 + 2.29726i −0.128870 + 0.0936292i
\(603\) 6.05845 18.6460i 0.246719 0.759323i
\(604\) 0.697224 0.0283697
\(605\) 0 0
\(606\) 28.1194 1.14227
\(607\) 6.34771 19.5363i 0.257646 0.792952i −0.735651 0.677361i \(-0.763124\pi\)
0.993297 0.115591i \(-0.0368763\pi\)
\(608\) −12.8701 + 9.35068i −0.521952 + 0.379220i
\(609\) −8.75086 6.35787i −0.354603 0.257634i
\(610\) −11.0396 33.9765i −0.446981 1.37567i
\(611\) 3.89533 + 11.9886i 0.157588 + 0.485007i
\(612\) 16.5961 + 12.0578i 0.670857 + 0.487406i
\(613\) −26.7425 + 19.4295i −1.08012 + 0.784752i −0.977704 0.209990i \(-0.932657\pi\)
−0.102415 + 0.994742i \(0.532657\pi\)
\(614\) −11.8362 + 36.4281i −0.477671 + 1.47012i
\(615\) 58.1194 2.34360
\(616\) 0 0
\(617\) 21.6333 0.870924 0.435462 0.900207i \(-0.356585\pi\)
0.435462 + 0.900207i \(0.356585\pi\)
\(618\) −23.4372 + 72.1323i −0.942783 + 2.90159i
\(619\) −32.2123 + 23.4036i −1.29472 + 0.940672i −0.999889 0.0148766i \(-0.995264\pi\)
−0.294834 + 0.955548i \(0.595264\pi\)
\(620\) −9.63404 6.99954i −0.386912 0.281108i
\(621\) −1.33821 4.11858i −0.0537004 0.165273i
\(622\) −4.55027 14.0043i −0.182449 0.561521i
\(623\) 11.9128 + 8.65513i 0.477275 + 0.346760i
\(624\) −3.72597 + 2.70708i −0.149158 + 0.108370i
\(625\) −0.309017 + 0.951057i −0.0123607 + 0.0380423i
\(626\) −35.2389 −1.40843
\(627\) 0 0
\(628\) 23.8167 0.950388
\(629\) 4.34339 13.3676i 0.173182 0.533001i
\(630\) 15.4679 11.2381i 0.616258 0.447737i
\(631\) 25.1244 + 18.2540i 1.00019 + 0.726679i 0.962129 0.272596i \(-0.0878823\pi\)
0.0380596 + 0.999275i \(0.487882\pi\)
\(632\) −7.69710 23.6892i −0.306174 0.942307i
\(633\) 11.0396 + 33.9765i 0.438786 + 1.35044i
\(634\) 32.2348 + 23.4200i 1.28021 + 0.930125i
\(635\) 5.83390 4.23858i 0.231511 0.168203i
\(636\) 30.3377 93.3699i 1.20297 3.70236i
\(637\) −6.60555 −0.261721
\(638\) 0 0
\(639\) −9.90833 −0.391967
\(640\) 21.0672 64.8382i 0.832755 2.56296i
\(641\) 23.3132 16.9380i 0.920815 0.669011i −0.0229121 0.999737i \(-0.507294\pi\)
0.943727 + 0.330727i \(0.107294\pi\)
\(642\) 53.1726 + 38.6322i 2.09856 + 1.52469i
\(643\) −0.382828 1.17822i −0.0150973 0.0464647i 0.943224 0.332157i \(-0.107776\pi\)
−0.958321 + 0.285692i \(0.907776\pi\)
\(644\) −2.75282 8.47232i −0.108476 0.333856i
\(645\) −11.4004 8.28288i −0.448890 0.326138i
\(646\) −15.0747 + 10.9524i −0.593105 + 0.430916i
\(647\) 3.27730 10.0865i 0.128844 0.396540i −0.865738 0.500497i \(-0.833150\pi\)
0.994582 + 0.103957i \(0.0331505\pi\)
\(648\) 31.8167 1.24988
\(649\) 0 0
\(650\) 121.689 4.77303
\(651\) −0.711597 + 2.19007i −0.0278897 + 0.0858356i
\(652\) −7.52610 + 5.46803i −0.294745 + 0.214145i
\(653\) 5.51479 + 4.00673i 0.215810 + 0.156795i 0.690439 0.723391i \(-0.257418\pi\)
−0.474628 + 0.880186i \(0.657418\pi\)
\(654\) 13.1092 + 40.3459i 0.512610 + 1.57765i
\(655\) 6.68506 + 20.5745i 0.261207 + 0.803912i
\(656\) 1.71465 + 1.24577i 0.0669460 + 0.0486391i
\(657\) −9.31492 + 6.76769i −0.363410 + 0.264033i
\(658\) 1.35796 4.17937i 0.0529388 0.162929i
\(659\) −4.63331 −0.180488 −0.0902440 0.995920i \(-0.528765\pi\)
−0.0902440 + 0.995920i \(0.528765\pi\)
\(660\) 0 0
\(661\) −18.3028 −0.711895 −0.355948 0.934506i \(-0.615842\pi\)
−0.355948 + 0.934506i \(0.615842\pi\)
\(662\) −16.9479 + 52.1601i −0.658697 + 2.02726i
\(663\) 33.1922 24.1155i 1.28908 0.936569i
\(664\) −7.28115 5.29007i −0.282564 0.205294i
\(665\) 3.34253 + 10.2872i 0.129618 + 0.398922i
\(666\) 8.53916 + 26.2808i 0.330886 + 1.01836i
\(667\) −10.2498 7.44693i −0.396874 0.288346i
\(668\) −13.9241 + 10.1164i −0.538739 + 0.391417i
\(669\) −9.89712 + 30.4602i −0.382645 + 1.17766i
\(670\) −70.6888 −2.73095
\(671\) 0 0
\(672\) −12.2111 −0.471054
\(673\) 2.60260 8.00999i 0.100323 0.308763i −0.888281 0.459300i \(-0.848100\pi\)
0.988604 + 0.150537i \(0.0481004\pi\)
\(674\) −21.9625 + 15.9567i −0.845965 + 0.614630i
\(675\) −10.3913 7.54975i −0.399963 0.290590i
\(676\) 31.2648 + 96.2231i 1.20249 + 3.70089i
\(677\) −3.18373 9.79852i −0.122361 0.376588i 0.871050 0.491194i \(-0.163439\pi\)
−0.993411 + 0.114606i \(0.963439\pi\)
\(678\) 45.8915 + 33.3421i 1.76245 + 1.28050i
\(679\) 2.91695 2.11929i 0.111942 0.0813309i
\(680\) 9.01555 27.7470i 0.345731 1.06405i
\(681\) 15.0000 0.574801
\(682\) 0 0
\(683\) 15.6972 0.600638 0.300319 0.953839i \(-0.402907\pi\)
0.300319 + 0.953839i \(0.402907\pi\)
\(684\) 7.05073 21.6999i 0.269592 0.829717i
\(685\) 29.5179 21.4460i 1.12782 0.819410i
\(686\) 1.86298 + 1.35354i 0.0711291 + 0.0516783i
\(687\) 1.85410 + 5.70634i 0.0707384 + 0.217710i
\(688\) −0.158797 0.488727i −0.00605408 0.0186325i
\(689\) −68.9821 50.1185i −2.62801 1.90936i
\(690\) 41.7205 30.3117i 1.58827 1.15395i
\(691\) −5.26187 + 16.1944i −0.200171 + 0.616062i 0.799706 + 0.600391i \(0.204988\pi\)
−0.999877 + 0.0156711i \(0.995012\pi\)
\(692\) 4.30278 0.163567
\(693\) 0 0
\(694\) 22.1194 0.839642
\(695\) −24.0724 + 74.0872i −0.913118 + 2.81029i
\(696\) 26.2526 19.0736i 0.995101 0.722983i
\(697\) −15.2747 11.0977i −0.578571 0.420356i
\(698\) −3.34253 10.2872i −0.126517 0.389378i
\(699\) 12.8087 + 39.4213i 0.484471 + 1.49105i
\(700\) −21.3760 15.5306i −0.807937 0.587001i
\(701\) −25.1761 + 18.2915i −0.950890 + 0.690862i −0.951017 0.309138i \(-0.899960\pi\)
0.000127232 1.00000i \(0.499960\pi\)
\(702\) 7.54688 23.2269i 0.284838 0.876643i
\(703\) −15.6333 −0.589621
\(704\) 0 0
\(705\) 15.8444 0.596735
\(706\) −3.62322 + 11.1511i −0.136362 + 0.419678i
\(707\) −4.29004 + 3.11689i −0.161343 + 0.117223i
\(708\) 41.2082 + 29.9395i 1.54870 + 1.12519i
\(709\) 7.82756 + 24.0908i 0.293970 + 0.904748i 0.983565 + 0.180553i \(0.0577886\pi\)
−0.689595 + 0.724195i \(0.742211\pi\)
\(710\) 11.0396 + 33.9765i 0.414310 + 1.27511i
\(711\) −15.4679 11.2381i −0.580093 0.421462i
\(712\) −35.7383 + 25.9654i −1.33935 + 0.973094i
\(713\) −0.833488 + 2.56521i −0.0312144 + 0.0960680i
\(714\) −14.3028 −0.535268
\(715\) 0 0
\(716\) −21.1194 −0.789270
\(717\) 18.7367 57.6657i 0.699736 2.15357i
\(718\) 63.2224 45.9338i 2.35944 1.71423i
\(719\) −17.1826 12.4839i −0.640803 0.465570i 0.219323 0.975652i \(-0.429615\pi\)
−0.860126 + 0.510082i \(0.829615\pi\)
\(720\) 0.776831 + 2.39084i 0.0289508 + 0.0891014i
\(721\) −4.41980 13.6027i −0.164602 0.506593i
\(722\) −18.6298 13.5354i −0.693331 0.503735i
\(723\) −0.905637 + 0.657984i −0.0336810 + 0.0244707i
\(724\) −25.7308 + 79.1913i −0.956278 + 2.94312i
\(725\) −37.5778 −1.39560
\(726\) 0 0
\(727\) 24.1194 0.894540 0.447270 0.894399i \(-0.352396\pi\)
0.447270 + 0.894399i \(0.352396\pi\)
\(728\) 6.12368 18.8468i 0.226959 0.698507i
\(729\) 10.7846 7.83549i 0.399431 0.290203i
\(730\) 33.5854 + 24.4012i 1.24305 + 0.903131i
\(731\) 1.41462 + 4.35374i 0.0523215 + 0.161029i
\(732\) −10.1126 31.1233i −0.373772 1.15035i
\(733\) −5.49233 3.99041i −0.202864 0.147389i 0.481715 0.876328i \(-0.340014\pi\)
−0.684579 + 0.728939i \(0.740014\pi\)
\(734\) −32.8506 + 23.8673i −1.21254 + 0.880960i
\(735\) −2.56570 + 7.89641i −0.0946372 + 0.291263i
\(736\) −14.3028 −0.527207
\(737\) 0 0
\(738\) 37.1194 1.36639
\(739\) 13.3246 41.0090i 0.490155 1.50854i −0.334219 0.942495i \(-0.608473\pi\)
0.824374 0.566046i \(-0.191527\pi\)
\(740\) 50.2040 36.4753i 1.84553 1.34086i
\(741\) −36.9181 26.8226i −1.35622 0.985352i
\(742\) 9.18552 + 28.2701i 0.337211 + 1.03783i
\(743\) −13.8860 42.7368i −0.509428 1.56786i −0.793196 0.608966i \(-0.791584\pi\)
0.283768 0.958893i \(-0.408416\pi\)
\(744\) −5.58895 4.06061i −0.204901 0.148869i
\(745\) −14.3174 + 10.4022i −0.524547 + 0.381106i
\(746\) −14.3169 + 44.0630i −0.524180 + 1.61326i
\(747\) −6.90833 −0.252762
\(748\) 0 0
\(749\) −12.3944 −0.452883
\(750\) 17.7247 54.5510i 0.647214 1.99192i
\(751\) −6.17548 + 4.48675i −0.225346 + 0.163724i −0.694730 0.719271i \(-0.744476\pi\)
0.469384 + 0.882994i \(0.344476\pi\)
\(752\) 0.467446 + 0.339619i 0.0170460 + 0.0123846i
\(753\) −3.12708 9.62415i −0.113957 0.350723i
\(754\) −22.0793 67.9530i −0.804079 2.47470i
\(755\) −0.615776 0.447387i −0.0224104 0.0162821i
\(756\) −4.29004 + 3.11689i −0.156027 + 0.113360i
\(757\) −7.35975 + 22.6510i −0.267495 + 0.823264i 0.723613 + 0.690205i \(0.242480\pi\)
−0.991108 + 0.133059i \(0.957520\pi\)
\(758\) 36.4222 1.32291
\(759\) 0 0
\(760\) −32.4500 −1.17708
\(761\) −12.9787 + 39.9444i −0.470478 + 1.44798i 0.381482 + 0.924376i \(0.375414\pi\)
−0.851960 + 0.523606i \(0.824586\pi\)
\(762\) 8.58007 6.23379i 0.310823 0.225826i
\(763\) −6.47214 4.70228i −0.234307 0.170234i
\(764\) −27.3694 84.2345i −0.990192 3.04750i
\(765\) −6.92027 21.2984i −0.250203 0.770045i
\(766\) 71.9733 + 52.2916i 2.60050 + 1.88937i
\(767\) 35.7900 26.0029i 1.29230 0.938912i
\(768\) 12.7435 39.2205i 0.459842 1.41525i
\(769\) 39.3305 1.41830 0.709148 0.705060i \(-0.249080\pi\)
0.709148 + 0.705060i \(0.249080\pi\)
\(770\) 0 0
\(771\) −14.9361 −0.537910
\(772\) 2.16312 6.65740i 0.0778524 0.239605i
\(773\) −24.7829 + 18.0058i −0.891378 + 0.647624i −0.936237 0.351369i \(-0.885716\pi\)
0.0448591 + 0.998993i \(0.485716\pi\)
\(774\) −7.28115 5.29007i −0.261716 0.190148i
\(775\) 2.47214 + 7.60845i 0.0888017 + 0.273304i
\(776\) 3.34253 + 10.2872i 0.119990 + 0.369291i
\(777\) −9.70820 7.05342i −0.348280 0.253040i
\(778\) −14.5623 + 10.5801i −0.522084 + 0.379316i
\(779\) −6.48936 + 19.9722i −0.232505 + 0.715578i
\(780\) 181.139 6.48581
\(781\) 0 0
\(782\) −16.7527 −0.599077
\(783\) −2.33049 + 7.17252i −0.0832850 + 0.256325i
\(784\) −0.244951 + 0.177967i −0.00874824 + 0.00635597i
\(785\) −21.0344 15.2824i −0.750751 0.545453i
\(786\) 9.83189 + 30.2594i 0.350692 + 1.07932i
\(787\) 6.94859 + 21.3856i 0.247691 + 0.762313i 0.995182 + 0.0980421i \(0.0312580\pi\)
−0.747492 + 0.664271i \(0.768742\pi\)
\(788\) −28.3381 20.5888i −1.00950 0.733446i
\(789\) −37.7047 + 27.3941i −1.34232 + 0.975254i
\(790\) −21.3024 + 65.5621i −0.757906 + 2.33260i
\(791\) −10.6972 −0.380350
\(792\) 0 0
\(793\) −28.4222 −1.00930
\(794\) −21.4981 + 66.1644i −0.762940 + 2.34809i
\(795\) −86.7063 + 62.9959i −3.07516 + 2.23423i
\(796\) −51.8962 37.7048i −1.83941 1.33641i
\(797\) −8.84818 27.2319i −0.313419 0.964603i −0.976400 0.215968i \(-0.930709\pi\)
0.662982 0.748635i \(-0.269291\pi\)
\(798\) 4.91594 + 15.1297i 0.174023 + 0.535586i
\(799\) −4.16416 3.02544i −0.147317 0.107032i
\(800\) −34.3203 + 24.9351i −1.21341 + 0.881591i
\(801\) −10.4782 + 32.2487i −0.370231 + 1.13945i
\(802\) 48.8444 1.72476
\(803\) 0 0
\(804\) −64.7527 −2.28365
\(805\) −3.00518 + 9.24901i −0.105919 + 0.325985i
\(806\) −12.3060 + 8.94086i −0.433462 + 0.314928i
\(807\) 30.0302 + 21.8183i 1.05711 + 0.768039i
\(808\) −4.91594 15.1297i −0.172942 0.532262i
\(809\) −2.50046 7.69564i −0.0879117 0.270564i 0.897430 0.441157i \(-0.145432\pi\)
−0.985342 + 0.170593i \(0.945432\pi\)
\(810\) −71.2384 51.7577i −2.50306 1.81858i
\(811\) −33.0438 + 24.0077i −1.16033 + 0.843026i −0.989819 0.142331i \(-0.954540\pi\)
−0.170506 + 0.985357i \(0.554540\pi\)
\(812\) −4.79405 + 14.7546i −0.168238 + 0.517784i
\(813\) −65.6611 −2.30283
\(814\) 0 0
\(815\) 10.1556 0.355735
\(816\) 0.581128 1.78853i 0.0203436 0.0626110i
\(817\) 4.11925 2.99281i 0.144114 0.104705i
\(818\) −38.3878 27.8904i −1.34220 0.975165i
\(819\) −4.70049 14.4666i −0.164248 0.505505i
\(820\) −25.7591 79.2784i −0.899548 2.76852i
\(821\) −22.1850 16.1184i −0.774263 0.562535i 0.128989 0.991646i \(-0.458827\pi\)
−0.903252 + 0.429111i \(0.858827\pi\)
\(822\) 43.4127 31.5412i 1.51419 1.10013i
\(823\) 10.8808 33.4877i 0.379282 1.16731i −0.561262 0.827638i \(-0.689684\pi\)
0.940544 0.339672i \(-0.110316\pi\)
\(824\) 42.9083 1.49478
\(825\) 0 0
\(826\) −15.4222 −0.536607
\(827\) 4.38290 13.4892i 0.152408 0.469064i −0.845481 0.534006i \(-0.820686\pi\)
0.997889 + 0.0649415i \(0.0206861\pi\)
\(828\) 16.5961 12.0578i 0.576754 0.419036i
\(829\) −10.7397 7.80286i −0.373006 0.271005i 0.385450 0.922729i \(-0.374046\pi\)
−0.758456 + 0.651724i \(0.774046\pi\)
\(830\) 7.69710 + 23.6892i 0.267170 + 0.822265i
\(831\) 21.3024 + 65.5621i 0.738973 + 2.27432i
\(832\) −68.4922 49.7625i −2.37454 1.72521i
\(833\) 2.18210 1.58539i 0.0756053 0.0549305i
\(834\) −35.4039 + 108.962i −1.22594 + 3.77304i
\(835\) 18.7889 0.650217
\(836\) 0 0
\(837\) 1.60555 0.0554960
\(838\) 27.3411 84.1473i 0.944483 2.90682i
\(839\) −34.1495 + 24.8111i −1.17897 + 0.856573i −0.992055 0.125803i \(-0.959849\pi\)
−0.186916 + 0.982376i \(0.559849\pi\)
\(840\) −20.1513 14.6407i −0.695285 0.505154i
\(841\) −2.14337 6.59661i −0.0739092 0.227469i
\(842\) 15.5247 + 47.7800i 0.535015 + 1.64661i
\(843\) −11.9128 8.65513i −0.410297 0.298098i
\(844\) 41.4531 30.1174i 1.42687 1.03669i
\(845\) 34.1309 105.044i 1.17414 3.61363i
\(846\) 10.1194 0.347913
\(847\) 0 0
\(848\) −3.90833 −0.134212
\(849\) 3.12708 9.62415i 0.107321 0.330300i
\(850\) −40.1991 + 29.2064i −1.37882 + 1.00177i
\(851\) −11.3711 8.26162i −0.389798 0.283205i
\(852\) 10.1126 + 31.1233i 0.346451 + 1.06627i
\(853\) 14.1298 + 43.4870i 0.483795 + 1.48897i 0.833719 + 0.552190i \(0.186208\pi\)
−0.349924 + 0.936778i \(0.613792\pi\)
\(854\) 8.01600 + 5.82397i 0.274302 + 0.199292i
\(855\) −20.1513 + 14.6407i −0.689159 + 0.500703i
\(856\) 11.4903 35.3635i 0.392730 1.20870i
\(857\) −35.3583 −1.20782 −0.603908 0.797054i \(-0.706391\pi\)
−0.603908 + 0.797054i \(0.706391\pi\)
\(858\) 0 0
\(859\) −25.3028 −0.863320 −0.431660 0.902036i \(-0.642072\pi\)
−0.431660 + 0.902036i \(0.642072\pi\)
\(860\) −6.24557 + 19.2219i −0.212972 + 0.655461i
\(861\) −13.0409 + 9.47476i −0.444432 + 0.322899i
\(862\) 5.81145 + 4.22226i 0.197939 + 0.143811i
\(863\) 9.71000 + 29.8843i 0.330532 + 1.01727i 0.968881 + 0.247526i \(0.0796176\pi\)
−0.638349 + 0.769747i \(0.720382\pi\)
\(864\) 2.63093 + 8.09718i 0.0895062 + 0.275472i
\(865\) −3.80013 2.76096i −0.129208 0.0938754i
\(866\) 54.3008 39.4518i 1.84521 1.34063i
\(867\) 6.92027 21.2984i 0.235025 0.723331i
\(868\) 3.30278 0.112104
\(869\) 0 0
\(870\) −89.8082 −3.04478
\(871\) −17.3788 + 53.4863i −0.588857 + 1.81232i
\(872\) 19.4164 14.1068i 0.657523 0.477718i
\(873\) 6.71709 + 4.88025i 0.227339 + 0.165171i
\(874\) 5.75801 + 17.7213i 0.194768 + 0.599433i
\(875\) 3.34253 + 10.2872i 0.112998 + 0.347772i
\(876\) 30.7651 + 22.3522i 1.03946 + 0.755209i
\(877\) 38.0687 27.6585i 1.28549 0.933962i 0.285785 0.958294i \(-0.407746\pi\)
0.999704 + 0.0243313i \(0.00774567\pi\)
\(878\) 19.7290 60.7196i 0.665822 2.04919i
\(879\) 11.0917 0.374113
\(880\) 0 0
\(881\) 34.3305 1.15663 0.578313 0.815815i \(-0.303711\pi\)
0.578313 + 0.815815i \(0.303711\pi\)
\(882\) −1.63865 + 5.04324i −0.0551761 + 0.169815i
\(883\) 6.24964 4.54063i 0.210317 0.152804i −0.477640 0.878556i \(-0.658508\pi\)
0.687957 + 0.725751i \(0.258508\pi\)
\(884\) −47.6061 34.5879i −1.60117 1.16332i
\(885\) −17.1831 52.8840i −0.577602 1.77768i
\(886\) −19.1676 58.9919i −0.643949 1.98187i
\(887\) 35.6934 + 25.9327i 1.19847 + 0.870737i 0.994133 0.108165i \(-0.0344974\pi\)
0.204333 + 0.978901i \(0.434497\pi\)
\(888\) 29.1246 21.1603i 0.977358 0.710092i
\(889\) −0.618034 + 1.90211i −0.0207282 + 0.0637948i
\(890\) 122.258 4.09810
\(891\) 0 0
\(892\) 45.9361 1.53805
\(893\) −1.76912 + 5.44478i −0.0592012 + 0.182203i
\(894\) −21.0569 + 15.2987i −0.704248 + 0.511666i
\(895\) 18.6523 + 13.5517i 0.623478 + 0.452983i
\(896\) 5.84299 + 17.9829i 0.195201 + 0.600766i
\(897\) −12.6783 39.0197i −0.423315 1.30283i
\(898\) 75.1352 + 54.5889i 2.50729 + 1.82165i
\(899\) 3.80013 2.76096i 0.126742 0.0920831i
\(900\) 18.8020 57.8665i 0.626732 1.92888i
\(901\) 34.8167 1.15991
\(902\) 0 0
\(903\) 3.90833 0.130061
\(904\) 9.91687 30.5210i 0.329830 1.01511i
\(905\) 73.5396 53.4296i 2.44454 1.77606i
\(906\) −0.905637 0.657984i −0.0300878 0.0218601i
\(907\) 0.121891 + 0.375143i 0.00404734 + 0.0124564i 0.953060 0.302782i \(-0.0979155\pi\)
−0.949012 + 0.315239i \(0.897915\pi\)
\(908\) −6.64815 20.4609i −0.220627 0.679019i
\(909\) −9.87899 7.17751i −0.327665 0.238063i
\(910\) −44.3701 + 32.2367i −1.47085 + 1.06864i
\(911\) −15.5899 + 47.9808i −0.516516 + 1.58967i 0.263990 + 0.964525i \(0.414961\pi\)
−0.780506 + 0.625148i \(0.785039\pi\)
\(912\) −2.09167 −0.0692622
\(913\) 0 0
\(914\) 48.6333 1.60865
\(915\) −11.0396 + 33.9765i −0.364959 + 1.12323i
\(916\) 6.96204 5.05822i 0.230032 0.167128i
\(917\) −4.85410 3.52671i −0.160297 0.116462i
\(918\) 3.08159 + 9.48417i 0.101708 + 0.313024i
\(919\) −17.1436 52.7624i −0.565514 1.74047i −0.666420 0.745577i \(-0.732174\pi\)
0.100906 0.994896i \(-0.467826\pi\)
\(920\) −23.6030 17.1486i −0.778169 0.565373i
\(921\) 30.9876 22.5138i 1.02108 0.741855i
\(922\) 5.75801 17.7213i 0.189630 0.583621i
\(923\) 28.4222 0.935528
\(924\) 0 0
\(925\) −41.6888 −1.37072
\(926\) 21.9290 67.4906i 0.720633 2.21788i
\(927\) 26.6459 19.3593i 0.875165 0.635844i
\(928\) 20.1513 + 14.6407i 0.661498 + 0.480606i
\(929\) −8.53916 26.2808i −0.280161 0.862246i −0.987808 0.155680i \(-0.950243\pi\)
0.707647 0.706566i \(-0.249757\pi\)
\(930\) 5.90823 + 18.1837i 0.193738 + 0.596266i
\(931\) −2.42705 1.76336i −0.0795434 0.0577917i
\(932\) 48.0960 34.9438i 1.57544 1.14462i
\(933\) −4.55027 + 14.0043i −0.148969 + 0.458480i
\(934\) 31.1833 1.02035
\(935\) 0 0
\(936\) 45.6333 1.49157
\(937\) −9.76665 + 30.0587i −0.319063 + 0.981974i 0.654987 + 0.755640i \(0.272674\pi\)
−0.974050 + 0.226334i \(0.927326\pi\)
\(938\) 15.8612 11.5239i 0.517887 0.376267i
\(939\) 28.5088 + 20.7129i 0.930351 + 0.675939i
\(940\) −7.02241 21.6127i −0.229046 0.704930i
\(941\) −11.5641 35.5906i −0.376979 1.16022i −0.942134 0.335237i \(-0.891184\pi\)
0.565155 0.824985i \(-0.308816\pi\)
\(942\) −30.9359 22.4762i −1.00795 0.732315i
\(943\) −15.2747 + 11.0977i −0.497413 + 0.361392i
\(944\) 0.626611 1.92851i 0.0203945 0.0627677i
\(945\) 5.78890 0.188313
\(946\) 0 0
\(947\) 46.6611 1.51628 0.758140 0.652091i \(-0.226108\pi\)
0.758140 + 0.652091i \(0.226108\pi\)
\(948\) −19.5136 + 60.0565i −0.633771 + 1.95055i
\(949\) 26.7200 19.4132i 0.867368 0.630180i
\(950\) 44.7116 + 32.4849i 1.45064 + 1.05395i
\(951\) −12.3126 37.8943i −0.399263 1.22881i
\(952\) 2.50046 + 7.69564i 0.0810405 + 0.249417i
\(953\) −4.87656 3.54303i −0.157967 0.114770i 0.505994 0.862537i \(-0.331126\pi\)
−0.663961 + 0.747767i \(0.731126\pi\)
\(954\) −55.3772 + 40.2339i −1.79290 + 1.30262i
\(955\) −29.8785 + 91.9565i −0.966845 + 2.97564i
\(956\) −86.9638 −2.81261
\(957\) 0 0
\(958\) −65.9361 −2.13030
\(959\) −3.12708 + 9.62415i −0.100979 + 0.310780i
\(960\) −86.0906 + 62.5485i −2.77856 + 2.01874i
\(961\) 24.2705 + 17.6336i 0.782920 + 0.568824i
\(962\) −24.4947 75.3870i −0.789742 2.43058i
\(963\) −8.81985 27.1447i −0.284216 0.874726i
\(964\) 1.29892 + 0.943719i 0.0418353 + 0.0303952i
\(965\) −6.18227 + 4.49169i −0.199014 + 0.144592i
\(966\) −4.41980 + 13.6027i −0.142205 + 0.437661i
\(967\) −40.5139 −1.30284 −0.651419 0.758718i \(-0.725826\pi\)
−0.651419 + 0.758718i \(0.725826\pi\)
\(968\) 0 0
\(969\) 18.6333 0.598588
\(970\) 9.25076 28.4709i 0.297024 0.914146i
\(971\) 5.15076 3.74225i 0.165296 0.120094i −0.502062 0.864832i \(-0.667425\pi\)
0.667358 + 0.744737i \(0.267425\pi\)
\(972\) −52.3861 38.0607i −1.68028 1.22080i
\(973\) −6.67648 20.5481i −0.214038 0.658742i
\(974\) 2.00432 + 6.16867i 0.0642226 + 0.197657i
\(975\) −98.4483 71.5269i −3.15287 2.29069i
\(976\) −1.05397 + 0.765752i −0.0337367 + 0.0245111i
\(977\) 12.3693 38.0687i 0.395728 1.21792i −0.532666 0.846326i \(-0.678810\pi\)
0.928393 0.371599i \(-0.121190\pi\)
\(978\) 14.9361 0.477603
\(979\) 0 0
\(980\) 11.9083 0.380398
\(981\) 5.69277 17.5206i 0.181756 0.559388i
\(982\) 23.6547 17.1862i 0.754853 0.548433i
\(983\) 7.50365 + 5.45172i 0.239329 + 0.173883i 0.700984 0.713177i \(-0.252744\pi\)
−0.461655 + 0.887059i \(0.652744\pi\)
\(984\) −14.9435 45.9915i −0.476382 1.46615i
\(985\) 11.8165 + 36.3673i 0.376504 + 1.15876i
\(986\) 23.6030 + 17.1486i 0.751673 + 0.546123i
\(987\) −3.55518 + 2.58299i −0.113163 + 0.0822175i
\(988\) −20.2252 + 62.2466i −0.643448 + 1.98033i
\(989\) 4.57779 0.145565
\(990\) 0 0
\(991\) −43.7250 −1.38897 −0.694485 0.719507i \(-0.744368\pi\)
−0.694485 + 0.719507i \(0.744368\pi\)
\(992\) 1.63865 5.04324i 0.0520271 0.160123i
\(993\) 44.3701 32.2367i 1.40804 1.02300i
\(994\) −8.01600 5.82397i −0.254252 0.184725i
\(995\) 21.6398 + 66.6004i 0.686027 + 2.11137i
\(996\) 7.05073 + 21.6999i 0.223411 + 0.687589i
\(997\) 36.9698 + 26.8602i 1.17085 + 0.850670i 0.991110 0.133045i \(-0.0424755\pi\)
0.179736 + 0.983715i \(0.442476\pi\)
\(998\) 5.41817 3.93653i 0.171509 0.124609i
\(999\) −2.58545 + 7.95720i −0.0818000 + 0.251755i
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 847.2.f.r.372.1 8
11.2 odd 10 847.2.f.o.729.1 8
11.3 even 5 inner 847.2.f.r.323.2 8
11.4 even 5 847.2.a.e.1.1 2
11.5 even 5 inner 847.2.f.r.148.1 8
11.6 odd 10 847.2.f.o.148.2 8
11.7 odd 10 847.2.a.g.1.2 yes 2
11.8 odd 10 847.2.f.o.323.1 8
11.9 even 5 inner 847.2.f.r.729.2 8
11.10 odd 2 847.2.f.o.372.2 8
33.26 odd 10 7623.2.a.bs.1.2 2
33.29 even 10 7623.2.a.bc.1.1 2
77.48 odd 10 5929.2.a.k.1.1 2
77.62 even 10 5929.2.a.p.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.e.1.1 2 11.4 even 5
847.2.a.g.1.2 yes 2 11.7 odd 10
847.2.f.o.148.2 8 11.6 odd 10
847.2.f.o.323.1 8 11.8 odd 10
847.2.f.o.372.2 8 11.10 odd 2
847.2.f.o.729.1 8 11.2 odd 10
847.2.f.r.148.1 8 11.5 even 5 inner
847.2.f.r.323.2 8 11.3 even 5 inner
847.2.f.r.372.1 8 1.1 even 1 trivial
847.2.f.r.729.2 8 11.9 even 5 inner
5929.2.a.k.1.1 2 77.48 odd 10
5929.2.a.p.1.2 2 77.62 even 10
7623.2.a.bc.1.1 2 33.29 even 10
7623.2.a.bs.1.2 2 33.26 odd 10