Properties

Label 731.2.f.c.259.6
Level $731$
Weight $2$
Character 731.259
Analytic conductor $5.837$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [731,2,Mod(259,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.259");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.f (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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 259.6
Character \(\chi\) \(=\) 731.259
Dual form 731.2.f.c.302.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.09057i q^{2} +(2.10973 - 2.10973i) q^{3} -2.37046 q^{4} +(0.614601 - 0.614601i) q^{5} +(-4.41052 - 4.41052i) q^{6} +(0.361953 + 0.361953i) q^{7} +0.774475i q^{8} -5.90190i q^{9} +O(q^{10})\) \(q-2.09057i q^{2} +(2.10973 - 2.10973i) q^{3} -2.37046 q^{4} +(0.614601 - 0.614601i) q^{5} +(-4.41052 - 4.41052i) q^{6} +(0.361953 + 0.361953i) q^{7} +0.774475i q^{8} -5.90190i q^{9} +(-1.28486 - 1.28486i) q^{10} +(2.58266 + 2.58266i) q^{11} +(-5.00103 + 5.00103i) q^{12} +3.15824 q^{13} +(0.756686 - 0.756686i) q^{14} -2.59328i q^{15} -3.12183 q^{16} +(-2.89763 - 2.93321i) q^{17} -12.3383 q^{18} -3.80968i q^{19} +(-1.45689 + 1.45689i) q^{20} +1.52724 q^{21} +(5.39923 - 5.39923i) q^{22} +(5.66072 + 5.66072i) q^{23} +(1.63393 + 1.63393i) q^{24} +4.24453i q^{25} -6.60251i q^{26} +(-6.12222 - 6.12222i) q^{27} +(-0.857995 - 0.857995i) q^{28} +(-7.39798 + 7.39798i) q^{29} -5.42142 q^{30} +(-5.78436 + 5.78436i) q^{31} +8.07535i q^{32} +10.8974 q^{33} +(-6.13207 + 6.05769i) q^{34} +0.444913 q^{35} +13.9902i q^{36} +(-0.561554 + 0.561554i) q^{37} -7.96438 q^{38} +(6.66303 - 6.66303i) q^{39} +(0.475993 + 0.475993i) q^{40} +(4.80148 + 4.80148i) q^{41} -3.19280i q^{42} +1.00000i q^{43} +(-6.12211 - 6.12211i) q^{44} +(-3.62731 - 3.62731i) q^{45} +(11.8341 - 11.8341i) q^{46} +0.314930 q^{47} +(-6.58622 + 6.58622i) q^{48} -6.73798i q^{49} +8.87347 q^{50} +(-12.3015 - 0.0750672i) q^{51} -7.48649 q^{52} -13.7069i q^{53} +(-12.7989 + 12.7989i) q^{54} +3.17462 q^{55} +(-0.280323 + 0.280323i) q^{56} +(-8.03738 - 8.03738i) q^{57} +(15.4659 + 15.4659i) q^{58} -0.208025i q^{59} +6.14728i q^{60} +(7.40409 + 7.40409i) q^{61} +(12.0926 + 12.0926i) q^{62} +(2.13621 - 2.13621i) q^{63} +10.6384 q^{64} +(1.94106 - 1.94106i) q^{65} -22.7818i q^{66} +7.38083 q^{67} +(6.86872 + 6.95307i) q^{68} +23.8851 q^{69} -0.930120i q^{70} +(-10.8478 + 10.8478i) q^{71} +4.57088 q^{72} +(5.70503 - 5.70503i) q^{73} +(1.17397 + 1.17397i) q^{74} +(8.95480 + 8.95480i) q^{75} +9.03070i q^{76} +1.86960i q^{77} +(-13.9295 - 13.9295i) q^{78} +(-9.50340 - 9.50340i) q^{79} +(-1.91868 + 1.91868i) q^{80} -8.12672 q^{81} +(10.0378 - 10.0378i) q^{82} +1.37119i q^{83} -3.62027 q^{84} +(-3.58364 - 0.0218684i) q^{85} +2.09057 q^{86} +31.2154i q^{87} +(-2.00021 + 2.00021i) q^{88} -14.0931 q^{89} +(-7.58313 + 7.58313i) q^{90} +(1.14313 + 1.14313i) q^{91} +(-13.4185 - 13.4185i) q^{92} +24.4069i q^{93} -0.658382i q^{94} +(-2.34143 - 2.34143i) q^{95} +(17.0368 + 17.0368i) q^{96} +(4.97145 - 4.97145i) q^{97} -14.0862 q^{98} +(15.2426 - 15.2426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.09057i 1.47825i −0.673567 0.739126i \(-0.735239\pi\)
0.673567 0.739126i \(-0.264761\pi\)
\(3\) 2.10973 2.10973i 1.21805 1.21805i 0.249738 0.968313i \(-0.419655\pi\)
0.968313 0.249738i \(-0.0803446\pi\)
\(4\) −2.37046 −1.18523
\(5\) 0.614601 0.614601i 0.274858 0.274858i −0.556194 0.831052i \(-0.687739\pi\)
0.831052 + 0.556194i \(0.187739\pi\)
\(6\) −4.41052 4.41052i −1.80059 1.80059i
\(7\) 0.361953 + 0.361953i 0.136805 + 0.136805i 0.772193 0.635388i \(-0.219160\pi\)
−0.635388 + 0.772193i \(0.719160\pi\)
\(8\) 0.774475i 0.273818i
\(9\) 5.90190i 1.96730i
\(10\) −1.28486 1.28486i −0.406309 0.406309i
\(11\) 2.58266 + 2.58266i 0.778703 + 0.778703i 0.979610 0.200908i \(-0.0643891\pi\)
−0.200908 + 0.979610i \(0.564389\pi\)
\(12\) −5.00103 + 5.00103i −1.44367 + 1.44367i
\(13\) 3.15824 0.875939 0.437969 0.898990i \(-0.355698\pi\)
0.437969 + 0.898990i \(0.355698\pi\)
\(14\) 0.756686 0.756686i 0.202233 0.202233i
\(15\) 2.59328i 0.669582i
\(16\) −3.12183 −0.780458
\(17\) −2.89763 2.93321i −0.702779 0.711409i
\(18\) −12.3383 −2.90817
\(19\) 3.80968i 0.874000i −0.899461 0.437000i \(-0.856041\pi\)
0.899461 0.437000i \(-0.143959\pi\)
\(20\) −1.45689 + 1.45689i −0.325770 + 0.325770i
\(21\) 1.52724 0.333272
\(22\) 5.39923 5.39923i 1.15112 1.15112i
\(23\) 5.66072 + 5.66072i 1.18034 + 1.18034i 0.979656 + 0.200685i \(0.0643168\pi\)
0.200685 + 0.979656i \(0.435683\pi\)
\(24\) 1.63393 + 1.63393i 0.333525 + 0.333525i
\(25\) 4.24453i 0.848906i
\(26\) 6.60251i 1.29486i
\(27\) −6.12222 6.12222i −1.17822 1.17822i
\(28\) −0.857995 0.857995i −0.162146 0.162146i
\(29\) −7.39798 + 7.39798i −1.37377 + 1.37377i −0.518988 + 0.854781i \(0.673691\pi\)
−0.854781 + 0.518988i \(0.826309\pi\)
\(30\) −5.42142 −0.989812
\(31\) −5.78436 + 5.78436i −1.03890 + 1.03890i −0.0396901 + 0.999212i \(0.512637\pi\)
−0.999212 + 0.0396901i \(0.987363\pi\)
\(32\) 8.07535i 1.42753i
\(33\) 10.8974 1.89700
\(34\) −6.13207 + 6.05769i −1.05164 + 1.03888i
\(35\) 0.444913 0.0752040
\(36\) 13.9902i 2.33170i
\(37\) −0.561554 + 0.561554i −0.0923189 + 0.0923189i −0.751758 0.659439i \(-0.770794\pi\)
0.659439 + 0.751758i \(0.270794\pi\)
\(38\) −7.96438 −1.29199
\(39\) 6.66303 6.66303i 1.06694 1.06694i
\(40\) 0.475993 + 0.475993i 0.0752611 + 0.0752611i
\(41\) 4.80148 + 4.80148i 0.749864 + 0.749864i 0.974454 0.224589i \(-0.0721040\pi\)
−0.224589 + 0.974454i \(0.572104\pi\)
\(42\) 3.19280i 0.492660i
\(43\) 1.00000i 0.152499i
\(44\) −6.12211 6.12211i −0.922943 0.922943i
\(45\) −3.62731 3.62731i −0.540728 0.540728i
\(46\) 11.8341 11.8341i 1.74484 1.74484i
\(47\) 0.314930 0.0459373 0.0229686 0.999736i \(-0.492688\pi\)
0.0229686 + 0.999736i \(0.492688\pi\)
\(48\) −6.58622 + 6.58622i −0.950639 + 0.950639i
\(49\) 6.73798i 0.962569i
\(50\) 8.87347 1.25490
\(51\) −12.3015 0.0750672i −1.72255 0.0105115i
\(52\) −7.48649 −1.03819
\(53\) 13.7069i 1.88279i −0.337309 0.941394i \(-0.609517\pi\)
0.337309 0.941394i \(-0.390483\pi\)
\(54\) −12.7989 + 12.7989i −1.74171 + 1.74171i
\(55\) 3.17462 0.428065
\(56\) −0.280323 + 0.280323i −0.0374598 + 0.0374598i
\(57\) −8.03738 8.03738i −1.06458 1.06458i
\(58\) 15.4659 + 15.4659i 2.03078 + 2.03078i
\(59\) 0.208025i 0.0270826i −0.999908 0.0135413i \(-0.995690\pi\)
0.999908 0.0135413i \(-0.00431046\pi\)
\(60\) 6.14728i 0.793610i
\(61\) 7.40409 + 7.40409i 0.947996 + 0.947996i 0.998713 0.0507170i \(-0.0161507\pi\)
−0.0507170 + 0.998713i \(0.516151\pi\)
\(62\) 12.0926 + 12.0926i 1.53576 + 1.53576i
\(63\) 2.13621 2.13621i 0.269137 0.269137i
\(64\) 10.6384 1.32980
\(65\) 1.94106 1.94106i 0.240759 0.240759i
\(66\) 22.7818i 2.80425i
\(67\) 7.38083 0.901711 0.450856 0.892597i \(-0.351119\pi\)
0.450856 + 0.892597i \(0.351119\pi\)
\(68\) 6.86872 + 6.95307i 0.832955 + 0.843183i
\(69\) 23.8851 2.87543
\(70\) 0.930120i 0.111171i
\(71\) −10.8478 + 10.8478i −1.28739 + 1.28739i −0.351030 + 0.936364i \(0.614168\pi\)
−0.936364 + 0.351030i \(0.885832\pi\)
\(72\) 4.57088 0.538683
\(73\) 5.70503 5.70503i 0.667724 0.667724i −0.289465 0.957189i \(-0.593477\pi\)
0.957189 + 0.289465i \(0.0934774\pi\)
\(74\) 1.17397 + 1.17397i 0.136471 + 0.136471i
\(75\) 8.95480 + 8.95480i 1.03401 + 1.03401i
\(76\) 9.03070i 1.03589i
\(77\) 1.86960i 0.213061i
\(78\) −13.9295 13.9295i −1.57720 1.57720i
\(79\) −9.50340 9.50340i −1.06922 1.06922i −0.997419 0.0717973i \(-0.977127\pi\)
−0.0717973 0.997419i \(-0.522873\pi\)
\(80\) −1.91868 + 1.91868i −0.214515 + 0.214515i
\(81\) −8.12672 −0.902969
\(82\) 10.0378 10.0378i 1.10849 1.10849i
\(83\) 1.37119i 0.150508i 0.997164 + 0.0752539i \(0.0239767\pi\)
−0.997164 + 0.0752539i \(0.976023\pi\)
\(84\) −3.62027 −0.395004
\(85\) −3.58364 0.0218684i −0.388701 0.00237196i
\(86\) 2.09057 0.225431
\(87\) 31.2154i 3.34664i
\(88\) −2.00021 + 2.00021i −0.213223 + 0.213223i
\(89\) −14.0931 −1.49386 −0.746930 0.664902i \(-0.768473\pi\)
−0.746930 + 0.664902i \(0.768473\pi\)
\(90\) −7.58313 + 7.58313i −0.799333 + 0.799333i
\(91\) 1.14313 + 1.14313i 0.119833 + 0.119833i
\(92\) −13.4185 13.4185i −1.39898 1.39898i
\(93\) 24.4069i 2.53087i
\(94\) 0.658382i 0.0679069i
\(95\) −2.34143 2.34143i −0.240226 0.240226i
\(96\) 17.0368 + 17.0368i 1.73881 + 1.73881i
\(97\) 4.97145 4.97145i 0.504774 0.504774i −0.408143 0.912918i \(-0.633824\pi\)
0.912918 + 0.408143i \(0.133824\pi\)
\(98\) −14.0862 −1.42292
\(99\) 15.2426 15.2426i 1.53194 1.53194i
\(100\) 10.0615i 1.00615i
\(101\) −3.15654 −0.314088 −0.157044 0.987592i \(-0.550196\pi\)
−0.157044 + 0.987592i \(0.550196\pi\)
\(102\) −0.156933 + 25.7171i −0.0155387 + 2.54637i
\(103\) 10.2693 1.01187 0.505935 0.862572i \(-0.331148\pi\)
0.505935 + 0.862572i \(0.331148\pi\)
\(104\) 2.44598i 0.239848i
\(105\) 0.938645 0.938645i 0.0916024 0.0916024i
\(106\) −28.6552 −2.78324
\(107\) 0.853338 0.853338i 0.0824953 0.0824953i −0.664655 0.747150i \(-0.731421\pi\)
0.747150 + 0.664655i \(0.231421\pi\)
\(108\) 14.5125 + 14.5125i 1.39646 + 1.39646i
\(109\) −1.45735 1.45735i −0.139589 0.139589i 0.633859 0.773448i \(-0.281470\pi\)
−0.773448 + 0.633859i \(0.781470\pi\)
\(110\) 6.63674i 0.632789i
\(111\) 2.36945i 0.224898i
\(112\) −1.12996 1.12996i −0.106771 0.106771i
\(113\) −7.70604 7.70604i −0.724923 0.724923i 0.244680 0.969604i \(-0.421317\pi\)
−0.969604 + 0.244680i \(0.921317\pi\)
\(114\) −16.8027 + 16.8027i −1.57371 + 1.57371i
\(115\) 6.95816 0.648852
\(116\) 17.5366 17.5366i 1.62823 1.62823i
\(117\) 18.6396i 1.72323i
\(118\) −0.434890 −0.0400349
\(119\) 0.0128788 2.11049i 0.00118060 0.193468i
\(120\) 2.00843 0.183344
\(121\) 2.34031i 0.212756i
\(122\) 15.4787 15.4787i 1.40138 1.40138i
\(123\) 20.2596 1.82675
\(124\) 13.7116 13.7116i 1.23134 1.23134i
\(125\) 5.68170 + 5.68170i 0.508187 + 0.508187i
\(126\) −4.46588 4.46588i −0.397853 0.397853i
\(127\) 2.25447i 0.200052i −0.994985 0.100026i \(-0.968107\pi\)
0.994985 0.100026i \(-0.0318926\pi\)
\(128\) 6.08951i 0.538242i
\(129\) 2.10973 + 2.10973i 0.185751 + 0.185751i
\(130\) −4.05791 4.05791i −0.355902 0.355902i
\(131\) −6.64848 + 6.64848i −0.580880 + 0.580880i −0.935145 0.354265i \(-0.884731\pi\)
0.354265 + 0.935145i \(0.384731\pi\)
\(132\) −25.8320 −2.24838
\(133\) 1.37892 1.37892i 0.119568 0.119568i
\(134\) 15.4301i 1.33296i
\(135\) −7.52544 −0.647687
\(136\) 2.27170 2.24414i 0.194797 0.192434i
\(137\) 11.7398 1.00300 0.501500 0.865157i \(-0.332782\pi\)
0.501500 + 0.865157i \(0.332782\pi\)
\(138\) 49.9334i 4.25062i
\(139\) −6.04278 + 6.04278i −0.512542 + 0.512542i −0.915305 0.402762i \(-0.868050\pi\)
0.402762 + 0.915305i \(0.368050\pi\)
\(140\) −1.05465 −0.0891342
\(141\) 0.664416 0.664416i 0.0559540 0.0559540i
\(142\) 22.6780 + 22.6780i 1.90309 + 1.90309i
\(143\) 8.15668 + 8.15668i 0.682096 + 0.682096i
\(144\) 18.4247i 1.53540i
\(145\) 9.09361i 0.755183i
\(146\) −11.9267 11.9267i −0.987064 0.987064i
\(147\) −14.2153 14.2153i −1.17246 1.17246i
\(148\) 1.33114 1.33114i 0.109419 0.109419i
\(149\) −10.5675 −0.865720 −0.432860 0.901461i \(-0.642496\pi\)
−0.432860 + 0.901461i \(0.642496\pi\)
\(150\) 18.7206 18.7206i 1.52853 1.52853i
\(151\) 17.1640i 1.39679i −0.715715 0.698393i \(-0.753899\pi\)
0.715715 0.698393i \(-0.246101\pi\)
\(152\) 2.95050 0.239317
\(153\) −17.3115 + 17.1015i −1.39955 + 1.38258i
\(154\) 3.90853 0.314958
\(155\) 7.11015i 0.571101i
\(156\) −15.7945 + 15.7945i −1.26457 + 1.26457i
\(157\) 5.84563 0.466532 0.233266 0.972413i \(-0.425059\pi\)
0.233266 + 0.972413i \(0.425059\pi\)
\(158\) −19.8675 + 19.8675i −1.58057 + 1.58057i
\(159\) −28.9178 28.9178i −2.29333 2.29333i
\(160\) 4.96312 + 4.96312i 0.392369 + 0.392369i
\(161\) 4.09782i 0.322954i
\(162\) 16.9894i 1.33482i
\(163\) −10.8126 10.8126i −0.846910 0.846910i 0.142836 0.989746i \(-0.454378\pi\)
−0.989746 + 0.142836i \(0.954378\pi\)
\(164\) −11.3817 11.3817i −0.888763 0.888763i
\(165\) 6.69758 6.69758i 0.521406 0.521406i
\(166\) 2.86657 0.222489
\(167\) −8.98998 + 8.98998i −0.695666 + 0.695666i −0.963473 0.267807i \(-0.913701\pi\)
0.267807 + 0.963473i \(0.413701\pi\)
\(168\) 1.18281i 0.0912559i
\(169\) −3.02551 −0.232731
\(170\) −0.0457173 + 7.49184i −0.00350636 + 0.574598i
\(171\) −22.4843 −1.71942
\(172\) 2.37046i 0.180746i
\(173\) 0.538292 0.538292i 0.0409256 0.0409256i −0.686348 0.727273i \(-0.740787\pi\)
0.727273 + 0.686348i \(0.240787\pi\)
\(174\) 65.2579 4.94719
\(175\) −1.53632 + 1.53632i −0.116135 + 0.116135i
\(176\) −8.06265 8.06265i −0.607745 0.607745i
\(177\) −0.438877 0.438877i −0.0329880 0.0329880i
\(178\) 29.4624i 2.20830i
\(179\) 9.13551i 0.682820i −0.939914 0.341410i \(-0.889096\pi\)
0.939914 0.341410i \(-0.110904\pi\)
\(180\) 8.59841 + 8.59841i 0.640888 + 0.640888i
\(181\) −0.316782 0.316782i −0.0235462 0.0235462i 0.695236 0.718782i \(-0.255300\pi\)
−0.718782 + 0.695236i \(0.755300\pi\)
\(182\) 2.38980 2.38980i 0.177144 0.177144i
\(183\) 31.2412 2.30942
\(184\) −4.38408 + 4.38408i −0.323199 + 0.323199i
\(185\) 0.690263i 0.0507492i
\(186\) 51.0241 3.74127
\(187\) 0.0918950 15.0591i 0.00672003 1.10123i
\(188\) −0.746530 −0.0544463
\(189\) 4.43191i 0.322374i
\(190\) −4.89492 + 4.89492i −0.355115 + 0.355115i
\(191\) 11.5950 0.838987 0.419493 0.907758i \(-0.362208\pi\)
0.419493 + 0.907758i \(0.362208\pi\)
\(192\) 22.4441 22.4441i 1.61976 1.61976i
\(193\) 9.01307 + 9.01307i 0.648775 + 0.648775i 0.952697 0.303922i \(-0.0982961\pi\)
−0.303922 + 0.952697i \(0.598296\pi\)
\(194\) −10.3931 10.3931i −0.746184 0.746184i
\(195\) 8.19021i 0.586513i
\(196\) 15.9721i 1.14087i
\(197\) −9.64370 9.64370i −0.687085 0.687085i 0.274502 0.961587i \(-0.411487\pi\)
−0.961587 + 0.274502i \(0.911487\pi\)
\(198\) −31.8657 31.8657i −2.26460 2.26460i
\(199\) 8.19448 8.19448i 0.580891 0.580891i −0.354257 0.935148i \(-0.615266\pi\)
0.935148 + 0.354257i \(0.115266\pi\)
\(200\) −3.28728 −0.232446
\(201\) 15.5715 15.5715i 1.09833 1.09833i
\(202\) 6.59895i 0.464301i
\(203\) −5.35543 −0.375878
\(204\) 29.1602 + 0.177944i 2.04162 + 0.0124586i
\(205\) 5.90198 0.412212
\(206\) 21.4687i 1.49580i
\(207\) 33.4090 33.4090i 2.32208 2.32208i
\(208\) −9.85951 −0.683634
\(209\) 9.83912 9.83912i 0.680586 0.680586i
\(210\) −1.96230 1.96230i −0.135411 0.135411i
\(211\) 4.08646 + 4.08646i 0.281324 + 0.281324i 0.833637 0.552313i \(-0.186255\pi\)
−0.552313 + 0.833637i \(0.686255\pi\)
\(212\) 32.4917i 2.23154i
\(213\) 45.7717i 3.13623i
\(214\) −1.78396 1.78396i −0.121949 0.121949i
\(215\) 0.614601 + 0.614601i 0.0419154 + 0.0419154i
\(216\) 4.74151 4.74151i 0.322619 0.322619i
\(217\) −4.18733 −0.284255
\(218\) −3.04669 + 3.04669i −0.206348 + 0.206348i
\(219\) 24.0721i 1.62664i
\(220\) −7.52531 −0.507356
\(221\) −9.15142 9.26379i −0.615591 0.623150i
\(222\) 4.95349 0.332457
\(223\) 12.8406i 0.859872i 0.902859 + 0.429936i \(0.141464\pi\)
−0.902859 + 0.429936i \(0.858536\pi\)
\(224\) −2.92289 + 2.92289i −0.195294 + 0.195294i
\(225\) 25.0508 1.67005
\(226\) −16.1100 + 16.1100i −1.07162 + 1.07162i
\(227\) −13.0830 13.0830i −0.868346 0.868346i 0.123943 0.992289i \(-0.460446\pi\)
−0.992289 + 0.123943i \(0.960446\pi\)
\(228\) 19.0523 + 19.0523i 1.26177 + 1.26177i
\(229\) 17.2477i 1.13976i 0.821729 + 0.569878i \(0.193010\pi\)
−0.821729 + 0.569878i \(0.806990\pi\)
\(230\) 14.5465i 0.959167i
\(231\) 3.94436 + 3.94436i 0.259520 + 0.259520i
\(232\) −5.72955 5.72955i −0.376163 0.376163i
\(233\) −14.3015 + 14.3015i −0.936925 + 0.936925i −0.998125 0.0612005i \(-0.980507\pi\)
0.0612005 + 0.998125i \(0.480507\pi\)
\(234\) −38.9674 −2.54738
\(235\) 0.193556 0.193556i 0.0126262 0.0126262i
\(236\) 0.493116i 0.0320991i
\(237\) −40.0992 −2.60472
\(238\) −4.41212 0.0269240i −0.285995 0.00174522i
\(239\) 20.2213 1.30801 0.654004 0.756491i \(-0.273088\pi\)
0.654004 + 0.756491i \(0.273088\pi\)
\(240\) 8.09579i 0.522581i
\(241\) 4.06077 4.06077i 0.261577 0.261577i −0.564117 0.825695i \(-0.690783\pi\)
0.825695 + 0.564117i \(0.190783\pi\)
\(242\) 4.89257 0.314506
\(243\) 1.22149 1.22149i 0.0783584 0.0783584i
\(244\) −17.5511 17.5511i −1.12359 1.12359i
\(245\) −4.14117 4.14117i −0.264570 0.264570i
\(246\) 42.3540i 2.70039i
\(247\) 12.0319i 0.765571i
\(248\) −4.47985 4.47985i −0.284470 0.284470i
\(249\) 2.89284 + 2.89284i 0.183326 + 0.183326i
\(250\) 11.8780 11.8780i 0.751228 0.751228i
\(251\) 12.7565 0.805181 0.402591 0.915380i \(-0.368110\pi\)
0.402591 + 0.915380i \(0.368110\pi\)
\(252\) −5.06380 + 5.06380i −0.318990 + 0.318990i
\(253\) 29.2395i 1.83827i
\(254\) −4.71312 −0.295727
\(255\) −7.60664 + 7.51437i −0.476347 + 0.470568i
\(256\) 8.54622 0.534139
\(257\) 21.4390i 1.33733i −0.743563 0.668665i \(-0.766866\pi\)
0.743563 0.668665i \(-0.233134\pi\)
\(258\) 4.41052 4.41052i 0.274587 0.274587i
\(259\) −0.406512 −0.0252594
\(260\) −4.60121 + 4.60121i −0.285355 + 0.285355i
\(261\) 43.6621 + 43.6621i 2.70262 + 2.70262i
\(262\) 13.8991 + 13.8991i 0.858688 + 0.858688i
\(263\) 12.1712i 0.750507i −0.926922 0.375253i \(-0.877556\pi\)
0.926922 0.375253i \(-0.122444\pi\)
\(264\) 8.43979i 0.519433i
\(265\) −8.42428 8.42428i −0.517499 0.517499i
\(266\) −2.88273 2.88273i −0.176751 0.176751i
\(267\) −29.7325 + 29.7325i −1.81960 + 1.81960i
\(268\) −17.4960 −1.06874
\(269\) −21.0402 + 21.0402i −1.28285 + 1.28285i −0.343804 + 0.939041i \(0.611716\pi\)
−0.939041 + 0.343804i \(0.888284\pi\)
\(270\) 15.7324i 0.957445i
\(271\) 20.6716 1.25571 0.627856 0.778330i \(-0.283933\pi\)
0.627856 + 0.778330i \(0.283933\pi\)
\(272\) 9.04592 + 9.15700i 0.548490 + 0.555225i
\(273\) 4.82340 0.291926
\(274\) 24.5429i 1.48269i
\(275\) −10.9622 + 10.9622i −0.661046 + 0.661046i
\(276\) −56.6188 −3.40805
\(277\) 0.606036 0.606036i 0.0364132 0.0364132i −0.688666 0.725079i \(-0.741803\pi\)
0.725079 + 0.688666i \(0.241803\pi\)
\(278\) 12.6328 + 12.6328i 0.757667 + 0.757667i
\(279\) 34.1387 + 34.1387i 2.04383 + 2.04383i
\(280\) 0.344574i 0.0205922i
\(281\) 4.56543i 0.272350i −0.990685 0.136175i \(-0.956519\pi\)
0.990685 0.136175i \(-0.0434810\pi\)
\(282\) −1.38901 1.38901i −0.0827141 0.0827141i
\(283\) −8.97699 8.97699i −0.533627 0.533627i 0.388023 0.921650i \(-0.373158\pi\)
−0.921650 + 0.388023i \(0.873158\pi\)
\(284\) 25.7142 25.7142i 1.52586 1.52586i
\(285\) −9.87957 −0.585215
\(286\) 17.0521 17.0521i 1.00831 1.00831i
\(287\) 3.47581i 0.205171i
\(288\) 47.6599 2.80839
\(289\) −0.207470 + 16.9987i −0.0122041 + 0.999926i
\(290\) 19.0108 1.11635
\(291\) 20.9768i 1.22968i
\(292\) −13.5236 + 13.5236i −0.791407 + 0.791407i
\(293\) −11.6884 −0.682845 −0.341422 0.939910i \(-0.610909\pi\)
−0.341422 + 0.939910i \(0.610909\pi\)
\(294\) −29.7180 + 29.7180i −1.73319 + 1.73319i
\(295\) −0.127853 0.127853i −0.00744386 0.00744386i
\(296\) −0.434910 0.434910i −0.0252786 0.0252786i
\(297\) 31.6233i 1.83497i
\(298\) 22.0920i 1.27975i
\(299\) 17.8779 + 17.8779i 1.03391 + 1.03391i
\(300\) −21.2270 21.2270i −1.22554 1.22554i
\(301\) −0.361953 + 0.361953i −0.0208626 + 0.0208626i
\(302\) −35.8824 −2.06480
\(303\) −6.65944 + 6.65944i −0.382575 + 0.382575i
\(304\) 11.8932i 0.682121i
\(305\) 9.10112 0.521128
\(306\) 35.7519 + 36.1909i 2.04380 + 2.06889i
\(307\) 0.406775 0.0232159 0.0116079 0.999933i \(-0.496305\pi\)
0.0116079 + 0.999933i \(0.496305\pi\)
\(308\) 4.43183i 0.252527i
\(309\) 21.6655 21.6655i 1.23251 1.23251i
\(310\) 14.8642 0.844232
\(311\) 10.0196 10.0196i 0.568162 0.568162i −0.363451 0.931613i \(-0.618402\pi\)
0.931613 + 0.363451i \(0.118402\pi\)
\(312\) 5.16035 + 5.16035i 0.292147 + 0.292147i
\(313\) 10.9733 + 10.9733i 0.620246 + 0.620246i 0.945594 0.325348i \(-0.105482\pi\)
−0.325348 + 0.945594i \(0.605482\pi\)
\(314\) 12.2207i 0.689653i
\(315\) 2.62583i 0.147949i
\(316\) 22.5275 + 22.5275i 1.26727 + 1.26727i
\(317\) 13.5264 + 13.5264i 0.759718 + 0.759718i 0.976271 0.216553i \(-0.0694813\pi\)
−0.216553 + 0.976271i \(0.569481\pi\)
\(318\) −60.4546 + 60.4546i −3.39013 + 3.39013i
\(319\) −38.2130 −2.13952
\(320\) 6.53835 6.53835i 0.365505 0.365505i
\(321\) 3.60062i 0.200967i
\(322\) 8.56677 0.477407
\(323\) −11.1746 + 11.0390i −0.621771 + 0.614229i
\(324\) 19.2641 1.07023
\(325\) 13.4053i 0.743590i
\(326\) −22.6045 + 22.6045i −1.25195 + 1.25195i
\(327\) −6.14924 −0.340054
\(328\) −3.71862 + 3.71862i −0.205327 + 0.205327i
\(329\) 0.113990 + 0.113990i 0.00628446 + 0.00628446i
\(330\) −14.0017 14.0017i −0.770769 0.770769i
\(331\) 19.6996i 1.08279i −0.840769 0.541393i \(-0.817897\pi\)
0.840769 0.541393i \(-0.182103\pi\)
\(332\) 3.25036i 0.178387i
\(333\) 3.31424 + 3.31424i 0.181619 + 0.181619i
\(334\) 18.7941 + 18.7941i 1.02837 + 1.02837i
\(335\) 4.53626 4.53626i 0.247843 0.247843i
\(336\) −4.76780 −0.260105
\(337\) −8.48804 + 8.48804i −0.462373 + 0.462373i −0.899433 0.437060i \(-0.856020\pi\)
0.437060 + 0.899433i \(0.356020\pi\)
\(338\) 6.32502i 0.344036i
\(339\) −32.5153 −1.76599
\(340\) 8.49489 + 0.0518382i 0.460700 + 0.00281132i
\(341\) −29.8781 −1.61799
\(342\) 47.0050i 2.54174i
\(343\) 4.97250 4.97250i 0.268490 0.268490i
\(344\) −0.774475 −0.0417569
\(345\) 14.6798 14.6798i 0.790335 0.790335i
\(346\) −1.12533 1.12533i −0.0604984 0.0604984i
\(347\) −16.4140 16.4140i −0.881149 0.881149i 0.112502 0.993651i \(-0.464113\pi\)
−0.993651 + 0.112502i \(0.964113\pi\)
\(348\) 73.9950i 3.96655i
\(349\) 8.86653i 0.474615i −0.971435 0.237307i \(-0.923735\pi\)
0.971435 0.237307i \(-0.0762648\pi\)
\(350\) 3.21178 + 3.21178i 0.171677 + 0.171677i
\(351\) −19.3354 19.3354i −1.03205 1.03205i
\(352\) −20.8559 + 20.8559i −1.11162 + 1.11162i
\(353\) −21.3545 −1.13658 −0.568292 0.822827i \(-0.692396\pi\)
−0.568292 + 0.822827i \(0.692396\pi\)
\(354\) −0.917500 + 0.917500i −0.0487646 + 0.0487646i
\(355\) 13.3341i 0.707701i
\(356\) 33.4070 1.77057
\(357\) −4.42539 4.47973i −0.234216 0.237092i
\(358\) −19.0984 −1.00938
\(359\) 19.9916i 1.05512i −0.849519 0.527558i \(-0.823108\pi\)
0.849519 0.527558i \(-0.176892\pi\)
\(360\) 2.80926 2.80926i 0.148061 0.148061i
\(361\) 4.48635 0.236124
\(362\) −0.662254 + 0.662254i −0.0348073 + 0.0348073i
\(363\) 4.93742 + 4.93742i 0.259147 + 0.259147i
\(364\) −2.70976 2.70976i −0.142030 0.142030i
\(365\) 7.01264i 0.367058i
\(366\) 65.3118i 3.41390i
\(367\) 16.3299 + 16.3299i 0.852412 + 0.852412i 0.990430 0.138018i \(-0.0440731\pi\)
−0.138018 + 0.990430i \(0.544073\pi\)
\(368\) −17.6718 17.6718i −0.921207 0.921207i
\(369\) 28.3378 28.3378i 1.47521 1.47521i
\(370\) 1.44304 0.0750201
\(371\) 4.96125 4.96125i 0.257575 0.257575i
\(372\) 57.8555i 2.99967i
\(373\) −33.7506 −1.74754 −0.873769 0.486341i \(-0.838331\pi\)
−0.873769 + 0.486341i \(0.838331\pi\)
\(374\) −31.4821 0.192112i −1.62790 0.00993390i
\(375\) 23.9737 1.23799
\(376\) 0.243905i 0.0125785i
\(377\) −23.3646 + 23.3646i −1.20334 + 1.20334i
\(378\) −9.26519 −0.476550
\(379\) −2.28196 + 2.28196i −0.117216 + 0.117216i −0.763282 0.646066i \(-0.776413\pi\)
0.646066 + 0.763282i \(0.276413\pi\)
\(380\) 5.55028 + 5.55028i 0.284723 + 0.284723i
\(381\) −4.75632 4.75632i −0.243674 0.243674i
\(382\) 24.2402i 1.24023i
\(383\) 27.3194i 1.39595i 0.716120 + 0.697977i \(0.245916\pi\)
−0.716120 + 0.697977i \(0.754084\pi\)
\(384\) −12.8472 12.8472i −0.655606 0.655606i
\(385\) 1.14906 + 1.14906i 0.0585616 + 0.0585616i
\(386\) 18.8424 18.8424i 0.959054 0.959054i
\(387\) 5.90190 0.300010
\(388\) −11.7846 + 11.7846i −0.598274 + 0.598274i
\(389\) 19.6679i 0.997204i 0.866831 + 0.498602i \(0.166153\pi\)
−0.866831 + 0.498602i \(0.833847\pi\)
\(390\) −17.1222 −0.867015
\(391\) 0.201417 33.0068i 0.0101861 1.66922i
\(392\) 5.21840 0.263569
\(393\) 28.0529i 1.41508i
\(394\) −20.1608 + 20.1608i −1.01569 + 1.01569i
\(395\) −11.6816 −0.587765
\(396\) −36.1321 + 36.1321i −1.81570 + 1.81570i
\(397\) 9.29444 + 9.29444i 0.466474 + 0.466474i 0.900770 0.434296i \(-0.143003\pi\)
−0.434296 + 0.900770i \(0.643003\pi\)
\(398\) −17.1311 17.1311i −0.858704 0.858704i
\(399\) 5.81831i 0.291280i
\(400\) 13.2507i 0.662536i
\(401\) 13.0237 + 13.0237i 0.650374 + 0.650374i 0.953083 0.302709i \(-0.0978911\pi\)
−0.302709 + 0.953083i \(0.597891\pi\)
\(402\) −32.5533 32.5533i −1.62361 1.62361i
\(403\) −18.2684 + 18.2684i −0.910015 + 0.910015i
\(404\) 7.48246 0.372266
\(405\) −4.99469 + 4.99469i −0.248188 + 0.248188i
\(406\) 11.1959i 0.555642i
\(407\) −2.90061 −0.143778
\(408\) 0.0581377 9.52720i 0.00287824 0.471667i
\(409\) 7.76215 0.383814 0.191907 0.981413i \(-0.438533\pi\)
0.191907 + 0.981413i \(0.438533\pi\)
\(410\) 12.3385i 0.609354i
\(411\) 24.7678 24.7678i 1.22171 1.22171i
\(412\) −24.3431 −1.19930
\(413\) 0.0752953 0.0752953i 0.00370504 0.00370504i
\(414\) −69.8436 69.8436i −3.43263 3.43263i
\(415\) 0.842736 + 0.842736i 0.0413683 + 0.0413683i
\(416\) 25.5039i 1.25043i
\(417\) 25.4973i 1.24861i
\(418\) −20.5693 20.5693i −1.00608 1.00608i
\(419\) 22.5720 + 22.5720i 1.10271 + 1.10271i 0.994082 + 0.108631i \(0.0346468\pi\)
0.108631 + 0.994082i \(0.465353\pi\)
\(420\) −2.22502 + 2.22502i −0.108570 + 0.108570i
\(421\) −11.2929 −0.550383 −0.275191 0.961389i \(-0.588741\pi\)
−0.275191 + 0.961389i \(0.588741\pi\)
\(422\) 8.54302 8.54302i 0.415868 0.415868i
\(423\) 1.85869i 0.0903724i
\(424\) 10.6157 0.515542
\(425\) 12.4501 12.2991i 0.603919 0.596593i
\(426\) 95.6887 4.63613
\(427\) 5.35986i 0.259382i
\(428\) −2.02281 + 2.02281i −0.0977760 + 0.0977760i
\(429\) 34.4167 1.66166
\(430\) 1.28486 1.28486i 0.0619616 0.0619616i
\(431\) 11.9687 + 11.9687i 0.576512 + 0.576512i 0.933940 0.357429i \(-0.116346\pi\)
−0.357429 + 0.933940i \(0.616346\pi\)
\(432\) 19.1125 + 19.1125i 0.919553 + 0.919553i
\(433\) 36.3357i 1.74618i 0.487559 + 0.873090i \(0.337887\pi\)
−0.487559 + 0.873090i \(0.662113\pi\)
\(434\) 8.75389i 0.420200i
\(435\) 19.1850 + 19.1850i 0.919852 + 0.919852i
\(436\) 3.45460 + 3.45460i 0.165445 + 0.165445i
\(437\) 21.5655 21.5655i 1.03162 1.03162i
\(438\) −50.3244 −2.40459
\(439\) −22.4307 + 22.4307i −1.07056 + 1.07056i −0.0732456 + 0.997314i \(0.523336\pi\)
−0.997314 + 0.0732456i \(0.976664\pi\)
\(440\) 2.45866i 0.117212i
\(441\) −39.7669 −1.89366
\(442\) −19.3666 + 19.1316i −0.921174 + 0.909999i
\(443\) −20.6673 −0.981935 −0.490968 0.871178i \(-0.663357\pi\)
−0.490968 + 0.871178i \(0.663357\pi\)
\(444\) 5.61670i 0.266557i
\(445\) −8.66160 + 8.66160i −0.410599 + 0.410599i
\(446\) 26.8442 1.27111
\(447\) −22.2945 + 22.2945i −1.05449 + 1.05449i
\(448\) 3.85059 + 3.85059i 0.181923 + 0.181923i
\(449\) −7.15280 7.15280i −0.337562 0.337562i 0.517887 0.855449i \(-0.326719\pi\)
−0.855449 + 0.517887i \(0.826719\pi\)
\(450\) 52.3703i 2.46876i
\(451\) 24.8012i 1.16784i
\(452\) 18.2669 + 18.2669i 0.859202 + 0.859202i
\(453\) −36.2113 36.2113i −1.70136 1.70136i
\(454\) −27.3508 + 27.3508i −1.28364 + 1.28364i
\(455\) 1.40514 0.0658741
\(456\) 6.22475 6.22475i 0.291501 0.291501i
\(457\) 7.77735i 0.363809i −0.983316 0.181905i \(-0.941774\pi\)
0.983316 0.181905i \(-0.0582262\pi\)
\(458\) 36.0573 1.68485
\(459\) −0.217837 + 35.6977i −0.0101678 + 1.66623i
\(460\) −16.4941 −0.769040
\(461\) 14.0654i 0.655093i −0.944835 0.327547i \(-0.893778\pi\)
0.944835 0.327547i \(-0.106222\pi\)
\(462\) 8.24593 8.24593i 0.383636 0.383636i
\(463\) 22.6758 1.05383 0.526916 0.849917i \(-0.323348\pi\)
0.526916 + 0.849917i \(0.323348\pi\)
\(464\) 23.0952 23.0952i 1.07217 1.07217i
\(465\) 15.0005 + 15.0005i 0.695630 + 0.695630i
\(466\) 29.8983 + 29.8983i 1.38501 + 1.38501i
\(467\) 5.71487i 0.264453i −0.991220 0.132226i \(-0.957787\pi\)
0.991220 0.132226i \(-0.0422126\pi\)
\(468\) 44.1845i 2.04243i
\(469\) 2.67151 + 2.67151i 0.123359 + 0.123359i
\(470\) −0.404642 0.404642i −0.0186647 0.0186647i
\(471\) 12.3327 12.3327i 0.568261 0.568261i
\(472\) 0.161110 0.00741571
\(473\) −2.58266 + 2.58266i −0.118751 + 0.118751i
\(474\) 83.8300i 3.85044i
\(475\) 16.1703 0.741944
\(476\) −0.0305287 + 5.00284i −0.00139928 + 0.229305i
\(477\) −80.8968 −3.70401
\(478\) 42.2740i 1.93357i
\(479\) 6.53308 6.53308i 0.298504 0.298504i −0.541924 0.840428i \(-0.682304\pi\)
0.840428 + 0.541924i \(0.182304\pi\)
\(480\) 20.9416 0.955851
\(481\) −1.77352 + 1.77352i −0.0808657 + 0.0808657i
\(482\) −8.48931 8.48931i −0.386677 0.386677i
\(483\) 8.64529 + 8.64529i 0.393374 + 0.393374i
\(484\) 5.54762i 0.252164i
\(485\) 6.11092i 0.277482i
\(486\) −2.55360 2.55360i −0.115833 0.115833i
\(487\) 17.3700 + 17.3700i 0.787112 + 0.787112i 0.981020 0.193908i \(-0.0621163\pi\)
−0.193908 + 0.981020i \(0.562116\pi\)
\(488\) −5.73428 + 5.73428i −0.259579 + 0.259579i
\(489\) −45.6234 −2.06316
\(490\) −8.65738 + 8.65738i −0.391101 + 0.391101i
\(491\) 27.3151i 1.23272i 0.787466 + 0.616358i \(0.211392\pi\)
−0.787466 + 0.616358i \(0.788608\pi\)
\(492\) −48.0246 −2.16512
\(493\) 43.1364 + 0.263231i 1.94277 + 0.0118553i
\(494\) −25.1534 −1.13171
\(495\) 18.7363i 0.842133i
\(496\) 18.0578 18.0578i 0.810820 0.810820i
\(497\) −7.85276 −0.352245
\(498\) 6.04767 6.04767i 0.271003 0.271003i
\(499\) −12.6629 12.6629i −0.566867 0.566867i 0.364382 0.931249i \(-0.381280\pi\)
−0.931249 + 0.364382i \(0.881280\pi\)
\(500\) −13.4683 13.4683i −0.602318 0.602318i
\(501\) 37.9328i 1.69471i
\(502\) 26.6682i 1.19026i
\(503\) −19.5149 19.5149i −0.870125 0.870125i 0.122360 0.992486i \(-0.460954\pi\)
−0.992486 + 0.122360i \(0.960954\pi\)
\(504\) 1.65444 + 1.65444i 0.0736947 + 0.0736947i
\(505\) −1.94001 + 1.94001i −0.0863294 + 0.0863294i
\(506\) 61.1270 2.71743
\(507\) −6.38300 + 6.38300i −0.283479 + 0.283479i
\(508\) 5.34414i 0.237108i
\(509\) −24.5577 −1.08850 −0.544250 0.838923i \(-0.683186\pi\)
−0.544250 + 0.838923i \(0.683186\pi\)
\(510\) 15.7093 + 15.9022i 0.695619 + 0.704161i
\(511\) 4.12991 0.182696
\(512\) 30.0455i 1.32783i
\(513\) −23.3237 + 23.3237i −1.02977 + 1.02977i
\(514\) −44.8197 −1.97691
\(515\) 6.31155 6.31155i 0.278120 0.278120i
\(516\) −5.00103 5.00103i −0.220158 0.220158i
\(517\) 0.813358 + 0.813358i 0.0357715 + 0.0357715i
\(518\) 0.849840i 0.0373398i
\(519\) 2.27130i 0.0996989i
\(520\) 1.50330 + 1.50330i 0.0659242 + 0.0659242i
\(521\) 2.34848 + 2.34848i 0.102889 + 0.102889i 0.756677 0.653789i \(-0.226821\pi\)
−0.653789 + 0.756677i \(0.726821\pi\)
\(522\) 91.2785 91.2785i 3.99515 3.99515i
\(523\) 9.63657 0.421378 0.210689 0.977553i \(-0.432429\pi\)
0.210689 + 0.977553i \(0.432429\pi\)
\(524\) 15.7600 15.7600i 0.688477 0.688477i
\(525\) 6.48243i 0.282917i
\(526\) −25.4446 −1.10944
\(527\) 33.7277 + 0.205816i 1.46920 + 0.00896549i
\(528\) −34.0200 −1.48053
\(529\) 41.0874i 1.78641i
\(530\) −17.6115 + 17.6115i −0.764995 + 0.764995i
\(531\) −1.22774 −0.0532796
\(532\) −3.26869 + 3.26869i −0.141716 + 0.141716i
\(533\) 15.1642 + 15.1642i 0.656835 + 0.656835i
\(534\) 62.1577 + 62.1577i 2.68983 + 2.68983i
\(535\) 1.04892i 0.0453490i
\(536\) 5.71627i 0.246905i
\(537\) −19.2734 19.2734i −0.831710 0.831710i
\(538\) 43.9860 + 43.9860i 1.89637 + 1.89637i
\(539\) 17.4019 17.4019i 0.749555 0.749555i
\(540\) 17.8388 0.767659
\(541\) 6.96161 6.96161i 0.299303 0.299303i −0.541438 0.840741i \(-0.682120\pi\)
0.840741 + 0.541438i \(0.182120\pi\)
\(542\) 43.2154i 1.85626i
\(543\) −1.33665 −0.0573611
\(544\) 23.6867 23.3994i 1.01556 1.00324i
\(545\) −1.79138 −0.0767344
\(546\) 10.0836i 0.431540i
\(547\) −4.62998 + 4.62998i −0.197964 + 0.197964i −0.799127 0.601163i \(-0.794704\pi\)
0.601163 + 0.799127i \(0.294704\pi\)
\(548\) −27.8288 −1.18879
\(549\) 43.6982 43.6982i 1.86499 1.86499i
\(550\) 22.9172 + 22.9172i 0.977192 + 0.977192i
\(551\) 28.1839 + 28.1839i 1.20067 + 1.20067i
\(552\) 18.4984i 0.787346i
\(553\) 6.87957i 0.292549i
\(554\) −1.26696 1.26696i −0.0538279 0.0538279i
\(555\) 1.45627 + 1.45627i 0.0618151 + 0.0618151i
\(556\) 14.3242 14.3242i 0.607481 0.607481i
\(557\) −0.179965 −0.00762538 −0.00381269 0.999993i \(-0.501214\pi\)
−0.00381269 + 0.999993i \(0.501214\pi\)
\(558\) 71.3692 71.3692i 3.02130 3.02130i
\(559\) 3.15824i 0.133579i
\(560\) −1.38894 −0.0586936
\(561\) −31.5767 31.9645i −1.33317 1.34954i
\(562\) −9.54432 −0.402603
\(563\) 4.44720i 0.187427i 0.995599 + 0.0937136i \(0.0298738\pi\)
−0.995599 + 0.0937136i \(0.970126\pi\)
\(564\) −1.57497 + 1.57497i −0.0663184 + 0.0663184i
\(565\) −9.47228 −0.398502
\(566\) −18.7670 + 18.7670i −0.788835 + 0.788835i
\(567\) −2.94149 2.94149i −0.123531 0.123531i
\(568\) −8.40133 8.40133i −0.352512 0.352512i
\(569\) 27.8668i 1.16824i 0.811668 + 0.584119i \(0.198560\pi\)
−0.811668 + 0.584119i \(0.801440\pi\)
\(570\) 20.6539i 0.865096i
\(571\) −5.48524 5.48524i −0.229550 0.229550i 0.582955 0.812505i \(-0.301897\pi\)
−0.812505 + 0.582955i \(0.801897\pi\)
\(572\) −19.3351 19.3351i −0.808441 0.808441i
\(573\) 24.4623 24.4623i 1.02193 1.02193i
\(574\) 7.26642 0.303294
\(575\) −24.0271 + 24.0271i −1.00200 + 1.00200i
\(576\) 62.7866i 2.61611i
\(577\) 13.6386 0.567781 0.283890 0.958857i \(-0.408375\pi\)
0.283890 + 0.958857i \(0.408375\pi\)
\(578\) 35.5370 + 0.433729i 1.47814 + 0.0180408i
\(579\) 38.0303 1.58048
\(580\) 21.5561i 0.895066i
\(581\) −0.496307 + 0.496307i −0.0205903 + 0.0205903i
\(582\) −43.8534 −1.81778
\(583\) 35.4003 35.4003i 1.46613 1.46613i
\(584\) 4.41841 + 4.41841i 0.182835 + 0.182835i
\(585\) −11.4559 11.4559i −0.473645 0.473645i
\(586\) 24.4354i 1.00942i
\(587\) 15.2874i 0.630977i −0.948929 0.315489i \(-0.897832\pi\)
0.948929 0.315489i \(-0.102168\pi\)
\(588\) 33.6968 + 33.6968i 1.38963 + 1.38963i
\(589\) 22.0366 + 22.0366i 0.908001 + 0.908001i
\(590\) −0.267284 + 0.267284i −0.0110039 + 0.0110039i
\(591\) −40.6911 −1.67381
\(592\) 1.75308 1.75308i 0.0720511 0.0720511i
\(593\) 19.3137i 0.793118i −0.918009 0.396559i \(-0.870204\pi\)
0.918009 0.396559i \(-0.129796\pi\)
\(594\) −66.1105 −2.71255
\(595\) −1.28919 1.30502i −0.0528518 0.0535008i
\(596\) 25.0498 1.02608
\(597\) 34.5762i 1.41511i
\(598\) 37.3749 37.3749i 1.52837 1.52837i
\(599\) 4.21393 0.172176 0.0860882 0.996288i \(-0.472563\pi\)
0.0860882 + 0.996288i \(0.472563\pi\)
\(600\) −6.93527 + 6.93527i −0.283131 + 0.283131i
\(601\) −30.9038 30.9038i −1.26059 1.26059i −0.950807 0.309784i \(-0.899743\pi\)
−0.309784 0.950807i \(-0.600257\pi\)
\(602\) 0.756686 + 0.756686i 0.0308402 + 0.0308402i
\(603\) 43.5609i 1.77394i
\(604\) 40.6866i 1.65551i
\(605\) 1.43836 + 1.43836i 0.0584775 + 0.0584775i
\(606\) 13.9220 + 13.9220i 0.565542 + 0.565542i
\(607\) 13.7380 13.7380i 0.557608 0.557608i −0.371018 0.928626i \(-0.620991\pi\)
0.928626 + 0.371018i \(0.120991\pi\)
\(608\) 30.7645 1.24766
\(609\) −11.2985 + 11.2985i −0.457839 + 0.457839i
\(610\) 19.0265i 0.770360i
\(611\) 0.994625 0.0402382
\(612\) 41.0363 40.5385i 1.65879 1.63867i
\(613\) 18.5457 0.749053 0.374526 0.927216i \(-0.377805\pi\)
0.374526 + 0.927216i \(0.377805\pi\)
\(614\) 0.850389i 0.0343189i
\(615\) 12.4516 12.4516i 0.502096 0.502096i
\(616\) −1.44796 −0.0583401
\(617\) −24.0671 + 24.0671i −0.968905 + 0.968905i −0.999531 0.0306260i \(-0.990250\pi\)
0.0306260 + 0.999531i \(0.490250\pi\)
\(618\) −45.2932 45.2932i −1.82196 1.82196i
\(619\) 11.4724 + 11.4724i 0.461116 + 0.461116i 0.899021 0.437905i \(-0.144280\pi\)
−0.437905 + 0.899021i \(0.644280\pi\)
\(620\) 16.8543i 0.676887i
\(621\) 69.3123i 2.78141i
\(622\) −20.9467 20.9467i −0.839887 0.839887i
\(623\) −5.10102 5.10102i −0.204368 0.204368i
\(624\) −20.8009 + 20.8009i −0.832701 + 0.832701i
\(625\) −14.2387 −0.569548
\(626\) 22.9403 22.9403i 0.916880 0.916880i
\(627\) 41.5157i 1.65798i
\(628\) −13.8569 −0.552949
\(629\) 3.27433 + 0.0199809i 0.130556 + 0.000796691i
\(630\) −5.48947 −0.218706
\(631\) 10.1732i 0.404989i −0.979283 0.202495i \(-0.935095\pi\)
0.979283 0.202495i \(-0.0649048\pi\)
\(632\) 7.36015 7.36015i 0.292771 0.292771i
\(633\) 17.2426 0.685334
\(634\) 28.2778 28.2778i 1.12306 1.12306i
\(635\) −1.38560 1.38560i −0.0549859 0.0549859i
\(636\) 68.5486 + 68.5486i 2.71813 + 2.71813i
\(637\) 21.2802i 0.843151i
\(638\) 79.8867i 3.16275i
\(639\) 64.0225 + 64.0225i 2.53269 + 2.53269i
\(640\) −3.74262 3.74262i −0.147940 0.147940i
\(641\) −31.1467 + 31.1467i −1.23022 + 1.23022i −0.266344 + 0.963878i \(0.585816\pi\)
−0.963878 + 0.266344i \(0.914184\pi\)
\(642\) −7.52733 −0.297080
\(643\) −0.268561 + 0.268561i −0.0105910 + 0.0105910i −0.712382 0.701791i \(-0.752384\pi\)
0.701791 + 0.712382i \(0.252384\pi\)
\(644\) 9.71374i 0.382775i
\(645\) 2.59328 0.102110
\(646\) 23.0778 + 23.3612i 0.907985 + 0.919135i
\(647\) −39.7977 −1.56461 −0.782305 0.622895i \(-0.785956\pi\)
−0.782305 + 0.622895i \(0.785956\pi\)
\(648\) 6.29394i 0.247249i
\(649\) 0.537260 0.537260i 0.0210893 0.0210893i
\(650\) 28.0246 1.09921
\(651\) −8.83413 + 8.83413i −0.346237 + 0.346237i
\(652\) 25.6309 + 25.6309i 1.00378 + 1.00378i
\(653\) 32.2637 + 32.2637i 1.26257 + 1.26257i 0.949841 + 0.312734i \(0.101245\pi\)
0.312734 + 0.949841i \(0.398755\pi\)
\(654\) 12.8554i 0.502685i
\(655\) 8.17232i 0.319319i
\(656\) −14.9894 14.9894i −0.585238 0.585238i
\(657\) −33.6705 33.6705i −1.31361 1.31361i
\(658\) 0.238303 0.238303i 0.00929002 0.00929002i
\(659\) 30.5606 1.19047 0.595236 0.803551i \(-0.297058\pi\)
0.595236 + 0.803551i \(0.297058\pi\)
\(660\) −15.8763 + 15.8763i −0.617986 + 0.617986i
\(661\) 27.4724i 1.06855i −0.845310 0.534275i \(-0.820585\pi\)
0.845310 0.534275i \(-0.179415\pi\)
\(662\) −41.1832 −1.60063
\(663\) −38.8511 0.237080i −1.50885 0.00920744i
\(664\) −1.06195 −0.0412118
\(665\) 1.69498i 0.0657283i
\(666\) 6.92863 6.92863i 0.268479 0.268479i
\(667\) −83.7557 −3.24303
\(668\) 21.3104 21.3104i 0.824525 0.824525i
\(669\) 27.0902 + 27.0902i 1.04737 + 1.04737i
\(670\) −9.48335 9.48335i −0.366374 0.366374i
\(671\) 38.2445i 1.47641i
\(672\) 12.3330i 0.475757i
\(673\) −29.1269 29.1269i −1.12276 1.12276i −0.991325 0.131434i \(-0.958042\pi\)
−0.131434 0.991325i \(-0.541958\pi\)
\(674\) 17.7448 + 17.7448i 0.683504 + 0.683504i
\(675\) 25.9859 25.9859i 1.00020 1.00020i
\(676\) 7.17185 0.275840
\(677\) 24.9876 24.9876i 0.960352 0.960352i −0.0388918 0.999243i \(-0.512383\pi\)
0.999243 + 0.0388918i \(0.0123828\pi\)
\(678\) 67.9753i 2.61058i
\(679\) 3.59886 0.138112
\(680\) 0.0169365 2.77544i 0.000649487 0.106433i
\(681\) −55.2029 −2.11538
\(682\) 62.4622i 2.39180i
\(683\) 0.459703 0.459703i 0.0175901 0.0175901i −0.698257 0.715847i \(-0.746041\pi\)
0.715847 + 0.698257i \(0.246041\pi\)
\(684\) 53.2983 2.03791
\(685\) 7.21531 7.21531i 0.275683 0.275683i
\(686\) −10.3953 10.3953i −0.396896 0.396896i
\(687\) 36.3878 + 36.3878i 1.38828 + 1.38828i
\(688\) 3.12183i 0.119019i
\(689\) 43.2897i 1.64921i
\(690\) −30.6891 30.6891i −1.16832 1.16832i
\(691\) 4.21161 + 4.21161i 0.160217 + 0.160217i 0.782663 0.622446i \(-0.213861\pi\)
−0.622446 + 0.782663i \(0.713861\pi\)
\(692\) −1.27600 + 1.27600i −0.0485063 + 0.0485063i
\(693\) 11.0342 0.419155
\(694\) −34.3145 + 34.3145i −1.30256 + 1.30256i
\(695\) 7.42780i 0.281753i
\(696\) −24.1756 −0.916373
\(697\) 0.170844 27.9966i 0.00647116 1.06045i
\(698\) −18.5361 −0.701600
\(699\) 60.3447i 2.28245i
\(700\) 3.64179 3.64179i 0.137647 0.137647i
\(701\) −19.1236 −0.722289 −0.361144 0.932510i \(-0.617614\pi\)
−0.361144 + 0.932510i \(0.617614\pi\)
\(702\) −40.4220 + 40.4220i −1.52563 + 1.52563i
\(703\) 2.13934 + 2.13934i 0.0806868 + 0.0806868i
\(704\) 27.4753 + 27.4753i 1.03552 + 1.03552i
\(705\) 0.816702i 0.0307588i
\(706\) 44.6429i 1.68016i
\(707\) −1.14252 1.14252i −0.0429688 0.0429688i
\(708\) 1.04034 + 1.04034i 0.0390984 + 0.0390984i
\(709\) 8.89433 8.89433i 0.334034 0.334034i −0.520082 0.854116i \(-0.674099\pi\)
0.854116 + 0.520082i \(0.174099\pi\)
\(710\) 27.8758 1.04616
\(711\) −56.0881 + 56.0881i −2.10347 + 2.10347i
\(712\) 10.9147i 0.409046i
\(713\) −65.4873 −2.45252
\(714\) −9.36516 + 9.25156i −0.350482 + 0.346231i
\(715\) 10.0262 0.374959
\(716\) 21.6554i 0.809300i
\(717\) 42.6614 42.6614i 1.59322 1.59322i
\(718\) −41.7937 −1.55973
\(719\) 27.5168 27.5168i 1.02620 1.02620i 0.0265562 0.999647i \(-0.491546\pi\)
0.999647 0.0265562i \(-0.00845409\pi\)
\(720\) 11.3239 + 11.3239i 0.422016 + 0.422016i
\(721\) 3.71702 + 3.71702i 0.138429 + 0.138429i
\(722\) 9.37901i 0.349051i
\(723\) 17.1342i 0.637229i
\(724\) 0.750920 + 0.750920i 0.0279077 + 0.0279077i
\(725\) −31.4009 31.4009i −1.16620 1.16620i
\(726\) 10.3220 10.3220i 0.383085 0.383085i
\(727\) −29.6948 −1.10132 −0.550660 0.834730i \(-0.685624\pi\)
−0.550660 + 0.834730i \(0.685624\pi\)
\(728\) −0.885329 + 0.885329i −0.0328125 + 0.0328125i
\(729\) 29.5342i 1.09386i
\(730\) −14.6604 −0.542605
\(731\) 2.93321 2.89763i 0.108489 0.107173i
\(732\) −74.0561 −2.73719
\(733\) 4.47182i 0.165171i 0.996584 + 0.0825853i \(0.0263177\pi\)
−0.996584 + 0.0825853i \(0.973682\pi\)
\(734\) 34.1386 34.1386i 1.26008 1.26008i
\(735\) −17.4735 −0.644519
\(736\) −45.7122 + 45.7122i −1.68498 + 1.68498i
\(737\) 19.0622 + 19.0622i 0.702165 + 0.702165i
\(738\) −59.2421 59.2421i −2.18073 2.18073i
\(739\) 35.9843i 1.32370i −0.749635 0.661852i \(-0.769771\pi\)
0.749635 0.661852i \(-0.230229\pi\)
\(740\) 1.63624i 0.0601495i
\(741\) −25.3840 25.3840i −0.932505 0.932505i
\(742\) −10.3718 10.3718i −0.380761 0.380761i
\(743\) −6.21792 + 6.21792i −0.228113 + 0.228113i −0.811904 0.583791i \(-0.801569\pi\)
0.583791 + 0.811904i \(0.301569\pi\)
\(744\) −18.9025 −0.692999
\(745\) −6.49477 + 6.49477i −0.237950 + 0.237950i
\(746\) 70.5578i 2.58330i
\(747\) 8.09264 0.296094
\(748\) −0.217834 + 35.6971i −0.00796479 + 1.30521i
\(749\) 0.617736 0.0225716
\(750\) 50.1185i 1.83007i
\(751\) 27.4042 27.4042i 0.999993 0.999993i −6.52405e−6 1.00000i \(-0.500002\pi\)
1.00000 6.52405e-6i \(2.07667e-6\pi\)
\(752\) −0.983159 −0.0358521
\(753\) 26.9127 26.9127i 0.980752 0.980752i
\(754\) 48.8452 + 48.8452i 1.77884 + 1.77884i
\(755\) −10.5490 10.5490i −0.383917 0.383917i
\(756\) 10.5057i 0.382087i
\(757\) 18.6277i 0.677034i −0.940960 0.338517i \(-0.890075\pi\)
0.940960 0.338517i \(-0.109925\pi\)
\(758\) 4.77058 + 4.77058i 0.173275 + 0.173275i
\(759\) 61.6873 + 61.6873i 2.23911 + 2.23911i
\(760\) 1.81338 1.81338i 0.0657783 0.0657783i
\(761\) 17.8310 0.646373 0.323187 0.946335i \(-0.395246\pi\)
0.323187 + 0.946335i \(0.395246\pi\)
\(762\) −9.94340 + 9.94340i −0.360211 + 0.360211i
\(763\) 1.05499i 0.0381931i
\(764\) −27.4856 −0.994393
\(765\) −0.129065 + 21.1503i −0.00466636 + 0.764691i
\(766\) 57.1129 2.06357
\(767\) 0.656994i 0.0237227i
\(768\) 18.0302 18.0302i 0.650609 0.650609i
\(769\) −50.7843 −1.83133 −0.915664 0.401944i \(-0.868335\pi\)
−0.915664 + 0.401944i \(0.868335\pi\)
\(770\) 2.40219 2.40219i 0.0865688 0.0865688i
\(771\) −45.2305 45.2305i −1.62894 1.62894i
\(772\) −21.3652 21.3652i −0.768949 0.768949i
\(773\) 25.2039i 0.906522i 0.891378 + 0.453261i \(0.149739\pi\)
−0.891378 + 0.453261i \(0.850261\pi\)
\(774\) 12.3383i 0.443491i
\(775\) −24.5519 24.5519i −0.881930 0.881930i
\(776\) 3.85027 + 3.85027i 0.138216 + 0.138216i
\(777\) −0.857630 + 0.857630i −0.0307673 + 0.0307673i
\(778\) 41.1171 1.47412
\(779\) 18.2921 18.2921i 0.655382 0.655382i
\(780\) 19.4146i 0.695154i
\(781\) −56.0323 −2.00499
\(782\) −69.0028 0.421075i −2.46753 0.0150576i
\(783\) 90.5840 3.23721
\(784\) 21.0349i 0.751245i
\(785\) 3.59273 3.59273i 0.128230 0.128230i
\(786\) 58.6465 2.09185
\(787\) −11.3665 + 11.3665i −0.405171 + 0.405171i −0.880051 0.474880i \(-0.842492\pi\)
0.474880 + 0.880051i \(0.342492\pi\)
\(788\) 22.8600 + 22.8600i 0.814354 + 0.814354i
\(789\) −25.6779 25.6779i −0.914156 0.914156i
\(790\) 24.4212i 0.868866i
\(791\) 5.57844i 0.198347i
\(792\) 11.8050 + 11.8050i 0.419474 + 0.419474i
\(793\) 23.3839 + 23.3839i 0.830386 + 0.830386i
\(794\) 19.4306 19.4306i 0.689567 0.689567i
\(795\) −35.5459 −1.26068
\(796\) −19.4247 + 19.4247i −0.688491 + 0.688491i
\(797\) 18.8984i 0.669417i 0.942322 + 0.334708i \(0.108638\pi\)
−0.942322 + 0.334708i \(0.891362\pi\)
\(798\) −12.1635 −0.430585
\(799\) −0.912551 0.923757i −0.0322837 0.0326802i
\(800\) −34.2761 −1.21184
\(801\) 83.1758i 2.93887i
\(802\) 27.2269 27.2269i 0.961417 0.961417i
\(803\) 29.4684 1.03992
\(804\) −36.9117 + 36.9117i −1.30178 + 1.30178i
\(805\) 2.51853 + 2.51853i 0.0887664 + 0.0887664i
\(806\) 38.1913 + 38.1913i 1.34523 + 1.34523i
\(807\) 88.7783i 3.12514i
\(808\) 2.44466i 0.0860029i
\(809\) −9.87247 9.87247i −0.347098 0.347098i 0.511930 0.859027i \(-0.328931\pi\)
−0.859027 + 0.511930i \(0.828931\pi\)
\(810\) 10.4417 + 10.4417i 0.366885 + 0.366885i
\(811\) 22.5590 22.5590i 0.792155 0.792155i −0.189689 0.981844i \(-0.560748\pi\)
0.981844 + 0.189689i \(0.0607479\pi\)
\(812\) 12.6949 0.445502
\(813\) 43.6115 43.6115i 1.52952 1.52952i
\(814\) 6.06392i 0.212540i
\(815\) −13.2909 −0.465560
\(816\) 38.4032 + 0.234347i 1.34438 + 0.00820380i
\(817\) 3.80968 0.133284
\(818\) 16.2273i 0.567374i
\(819\) 6.74666 6.74666i 0.235748 0.235748i
\(820\) −13.9904 −0.488567
\(821\) −7.39357 + 7.39357i −0.258037 + 0.258037i −0.824255 0.566218i \(-0.808406\pi\)
0.566218 + 0.824255i \(0.308406\pi\)
\(822\) −51.7787 51.7787i −1.80599 1.80599i
\(823\) 20.0101 + 20.0101i 0.697510 + 0.697510i 0.963873 0.266363i \(-0.0858220\pi\)
−0.266363 + 0.963873i \(0.585822\pi\)
\(824\) 7.95336i 0.277068i
\(825\) 46.2545i 1.61038i
\(826\) −0.157410 0.157410i −0.00547699 0.00547699i
\(827\) −15.1447 15.1447i −0.526633 0.526633i 0.392934 0.919567i \(-0.371460\pi\)
−0.919567 + 0.392934i \(0.871460\pi\)
\(828\) −79.1947 + 79.1947i −2.75221 + 2.75221i
\(829\) 2.07180 0.0719566 0.0359783 0.999353i \(-0.488545\pi\)
0.0359783 + 0.999353i \(0.488545\pi\)
\(830\) 1.76179 1.76179i 0.0611528 0.0611528i
\(831\) 2.55714i 0.0887063i
\(832\) 33.5985 1.16482
\(833\) −19.7639 + 19.5242i −0.684780 + 0.676473i
\(834\) 53.3037 1.84576
\(835\) 11.0505i 0.382418i
\(836\) −23.3233 + 23.3233i −0.806652 + 0.806652i
\(837\) 70.8262 2.44811
\(838\) 47.1882 47.1882i 1.63009 1.63009i
\(839\) −28.8183 28.8183i −0.994919 0.994919i 0.00506777 0.999987i \(-0.498387\pi\)
−0.999987 + 0.00506777i \(0.998387\pi\)
\(840\) 0.726958 + 0.726958i 0.0250824 + 0.0250824i
\(841\) 80.4601i 2.77449i
\(842\) 23.6086i 0.813605i
\(843\) −9.63180 9.63180i −0.331737 0.331737i
\(844\) −9.68681 9.68681i −0.333434 0.333434i
\(845\) −1.85948 + 1.85948i −0.0639681 + 0.0639681i
\(846\) −3.88570 −0.133593
\(847\) −0.847082 + 0.847082i −0.0291061 + 0.0291061i
\(848\) 42.7907i 1.46944i
\(849\) −37.8780 −1.29997
\(850\) −25.7120 26.0278i −0.881916 0.892745i
\(851\) −6.35760 −0.217936
\(852\) 108.500i 3.71715i
\(853\) 0.740344 0.740344i 0.0253489 0.0253489i −0.694319 0.719668i \(-0.744294\pi\)
0.719668 + 0.694319i \(0.244294\pi\)
\(854\) 11.2051 0.383432
\(855\) −13.8189 + 13.8189i −0.472596 + 0.472596i
\(856\) 0.660889 + 0.660889i 0.0225887 + 0.0225887i
\(857\) 4.22965 + 4.22965i 0.144482 + 0.144482i 0.775648 0.631166i \(-0.217423\pi\)
−0.631166 + 0.775648i \(0.717423\pi\)
\(858\) 71.9504i 2.45635i
\(859\) 23.9653i 0.817684i −0.912605 0.408842i \(-0.865933\pi\)
0.912605 0.408842i \(-0.134067\pi\)
\(860\) −1.45689 1.45689i −0.0496795 0.0496795i
\(861\) 7.33302 + 7.33302i 0.249909 + 0.249909i
\(862\) 25.0213 25.0213i 0.852230 0.852230i
\(863\) 36.6324 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(864\) 49.4390 49.4390i 1.68195 1.68195i
\(865\) 0.661670i 0.0224974i
\(866\) 75.9620 2.58130
\(867\) 35.4250 + 36.3004i 1.20310 + 1.23283i
\(868\) 9.92591 0.336907
\(869\) 49.0882i 1.66520i
\(870\) 40.1076 40.1076i 1.35977 1.35977i
\(871\) 23.3104 0.789844
\(872\) 1.12868 1.12868i 0.0382221 0.0382221i
\(873\) −29.3410 29.3410i −0.993043 0.993043i
\(874\) −45.0841 45.0841i −1.52499 1.52499i
\(875\) 4.11301i 0.139045i
\(876\) 57.0621i 1.92795i
\(877\) 15.3288 + 15.3288i 0.517615 + 0.517615i 0.916849 0.399234i \(-0.130724\pi\)
−0.399234 + 0.916849i \(0.630724\pi\)
\(878\) 46.8929 + 46.8929i 1.58256 + 1.58256i
\(879\) −24.6594 + 24.6594i −0.831740 + 0.831740i
\(880\) −9.91062 −0.334087
\(881\) 2.57557 2.57557i 0.0867731 0.0867731i −0.662388 0.749161i \(-0.730457\pi\)
0.749161 + 0.662388i \(0.230457\pi\)
\(882\) 83.1353i 2.79931i
\(883\) −29.1580 −0.981245 −0.490622 0.871372i \(-0.663231\pi\)
−0.490622 + 0.871372i \(0.663231\pi\)
\(884\) 21.6931 + 21.9595i 0.729618 + 0.738577i
\(885\) −0.539468 −0.0181340
\(886\) 43.2064i 1.45155i
\(887\) 3.46375 3.46375i 0.116301 0.116301i −0.646561 0.762862i \(-0.723793\pi\)
0.762862 + 0.646561i \(0.223793\pi\)
\(888\) −1.83508 −0.0615813
\(889\) 0.816012 0.816012i 0.0273682 0.0273682i
\(890\) 18.1076 + 18.1076i 0.606970 + 0.606970i
\(891\) −20.9886 20.9886i −0.703144 0.703144i
\(892\) 30.4382i 1.01915i
\(893\) 1.19978i 0.0401492i
\(894\) 46.6080 + 46.6080i 1.55880 + 1.55880i
\(895\) −5.61469 5.61469i −0.187679 0.187679i
\(896\) 2.20412 2.20412i 0.0736343 0.0736343i
\(897\) 75.4350 2.51870
\(898\) −14.9534 + 14.9534i −0.499001 + 0.499001i
\(899\) 85.5851i 2.85442i
\(900\) −59.3820 −1.97940
\(901\) −40.2053 + 39.7176i −1.33943 + 1.32318i
\(902\) 51.8485 1.72637
\(903\) 1.52724i 0.0508235i
\(904\) 5.96814 5.96814i 0.198497 0.198497i
\(905\) −0.389389 −0.0129437
\(906\) −75.7021 + 75.7021i −2.51503 + 2.51503i
\(907\) 21.9163 + 21.9163i 0.727717 + 0.727717i 0.970165 0.242447i \(-0.0779502\pi\)
−0.242447 + 0.970165i \(0.577950\pi\)
\(908\) 31.0127 + 31.0127i 1.02919 + 1.02919i
\(909\) 18.6296i 0.617904i
\(910\) 2.93754i 0.0973786i
\(911\) 22.0011 + 22.0011i 0.728930 + 0.728930i 0.970407 0.241476i \(-0.0776317\pi\)
−0.241476 + 0.970407i \(0.577632\pi\)
\(912\) 25.0914 + 25.0914i 0.830858 + 0.830858i
\(913\) −3.54133 + 3.54133i −0.117201 + 0.117201i
\(914\) −16.2591 −0.537802
\(915\) 19.2009 19.2009i 0.634761 0.634761i
\(916\) 40.8849i 1.35088i
\(917\) −4.81287 −0.158935
\(918\) 74.6283 + 0.455403i 2.46310 + 0.0150306i
\(919\) −4.67940 −0.154359 −0.0771796 0.997017i \(-0.524591\pi\)
−0.0771796 + 0.997017i \(0.524591\pi\)
\(920\) 5.38893i 0.177668i
\(921\) 0.858184 0.858184i 0.0282781 0.0282781i
\(922\) −29.4047 −0.968393
\(923\) −34.2599 + 34.2599i −1.12768 + 1.12768i
\(924\) −9.34995 9.34995i −0.307591 0.307591i
\(925\) −2.38353 2.38353i −0.0783701 0.0783701i
\(926\) 47.4052i 1.55783i
\(927\) 60.6087i 1.99065i
\(928\) −59.7412 59.7412i −1.96110 1.96110i
\(929\) 15.7587 + 15.7587i 0.517028 + 0.517028i 0.916671 0.399643i \(-0.130866\pi\)
−0.399643 + 0.916671i \(0.630866\pi\)
\(930\) 31.3595 31.3595i 1.02832 1.02832i
\(931\) −25.6695 −0.841285
\(932\) 33.9013 33.9013i 1.11047 1.11047i
\(933\) 42.2775i 1.38410i
\(934\) −11.9473 −0.390928
\(935\) −9.19887 9.31182i −0.300835 0.304529i
\(936\) 14.4359 0.471853
\(937\) 35.1355i 1.14783i −0.818917 0.573913i \(-0.805425\pi\)
0.818917 0.573913i \(-0.194575\pi\)
\(938\) 5.58497 5.58497i 0.182356 0.182356i
\(939\) 46.3012 1.51098
\(940\) −0.458818 + 0.458818i −0.0149650 + 0.0149650i
\(941\) 16.4475 + 16.4475i 0.536172 + 0.536172i 0.922402 0.386230i \(-0.126223\pi\)
−0.386230 + 0.922402i \(0.626223\pi\)
\(942\) −25.7823 25.7823i −0.840033 0.840033i
\(943\) 54.3596i 1.77019i
\(944\) 0.649420i 0.0211368i
\(945\) −2.72385 2.72385i −0.0886070 0.0886070i
\(946\) 5.39923 + 5.39923i 0.175544 + 0.175544i
\(947\) −6.83298 + 6.83298i −0.222042 + 0.222042i −0.809358 0.587316i \(-0.800185\pi\)
0.587316 + 0.809358i \(0.300185\pi\)
\(948\) 95.0536 3.08720
\(949\) 18.0179 18.0179i 0.584885 0.584885i
\(950\) 33.8051i 1.09678i
\(951\) 57.0740 1.85075
\(952\) 1.63452 + 0.00997432i 0.0529752 + 0.000323270i
\(953\) −32.7614 −1.06125 −0.530623 0.847608i \(-0.678042\pi\)
−0.530623 + 0.847608i \(0.678042\pi\)
\(954\) 169.120i 5.47546i
\(955\) 7.12631 7.12631i 0.230602 0.230602i
\(956\) −47.9338 −1.55029
\(957\) −80.6190 + 80.6190i −2.60604 + 2.60604i
\(958\) −13.6578 13.6578i −0.441264 0.441264i
\(959\) 4.24926 + 4.24926i 0.137216 + 0.137216i
\(960\) 27.5883i 0.890408i
\(961\) 35.9177i 1.15864i
\(962\) 3.70767 + 3.70767i 0.119540 + 0.119540i
\(963\) −5.03632 5.03632i −0.162293 0.162293i
\(964\) −9.62590 + 9.62590i −0.310030 + 0.310030i
\(965\) 11.0789 0.356642
\(966\) 18.0735 18.0735i 0.581507 0.581507i
\(967\) 50.6195i 1.62781i −0.580995 0.813907i \(-0.697336\pi\)
0.580995 0.813907i \(-0.302664\pi\)
\(968\) −1.81251 −0.0582564
\(969\) −0.285982 + 46.8647i −0.00918706 + 1.50551i
\(970\) −12.7753 −0.410189
\(971\) 42.5150i 1.36437i 0.731180 + 0.682185i \(0.238970\pi\)
−0.731180 + 0.682185i \(0.761030\pi\)
\(972\) −2.89549 + 2.89549i −0.0928728 + 0.0928728i
\(973\) −4.37440 −0.140237
\(974\) 36.3132 36.3132i 1.16355 1.16355i
\(975\) 28.2814 + 28.2814i 0.905731 + 0.905731i
\(976\) −23.1143 23.1143i −0.739871 0.739871i
\(977\) 26.4066i 0.844823i 0.906404 + 0.422411i \(0.138816\pi\)
−0.906404 + 0.422411i \(0.861184\pi\)
\(978\) 95.3786i 3.04987i
\(979\) −36.3976 36.3976i −1.16327 1.16327i
\(980\) 9.81649 + 9.81649i 0.313576 + 0.313576i
\(981\) −8.60116 + 8.60116i −0.274614 + 0.274614i
\(982\) 57.1041 1.82226
\(983\) 6.82777 6.82777i 0.217772 0.217772i −0.589787 0.807559i \(-0.700788\pi\)
0.807559 + 0.589787i \(0.200788\pi\)
\(984\) 15.6906i 0.500197i
\(985\) −11.8540 −0.377701
\(986\) 0.550301 90.1795i 0.0175252 2.87190i
\(987\) 0.480975 0.0153096
\(988\) 28.5211i 0.907378i
\(989\) −5.66072 + 5.66072i −0.180000 + 0.180000i
\(990\) −39.1694 −1.24488
\(991\) 12.1164 12.1164i 0.384889 0.384889i −0.487971 0.872860i \(-0.662263\pi\)
0.872860 + 0.487971i \(0.162263\pi\)
\(992\) −46.7107 46.7107i −1.48307 1.48307i
\(993\) −41.5607 41.5607i −1.31889 1.31889i
\(994\) 16.4167i 0.520707i
\(995\) 10.0727i 0.319325i
\(996\) −6.85737 6.85737i −0.217284 0.217284i
\(997\) −32.4500 32.4500i −1.02770 1.02770i −0.999605 0.0280966i \(-0.991055\pi\)
−0.0280966 0.999605i \(-0.508945\pi\)
\(998\) −26.4725 + 26.4725i −0.837973 + 0.837973i
\(999\) 6.87591 0.217544
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 731.2.f.c.259.6 56
17.13 even 4 inner 731.2.f.c.302.23 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.f.c.259.6 56 1.1 even 1 trivial
731.2.f.c.302.23 yes 56 17.13 even 4 inner