Properties

Label 845.2.l.f.699.8
Level $845$
Weight $2$
Character 845.699
Analytic conductor $6.747$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(654,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.654");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.l (of order \(6\), degree \(2\), 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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 699.8
Character \(\chi\) \(=\) 845.699
Dual form 845.2.l.f.654.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.165418 + 0.286513i) q^{2} +(2.33117 - 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(-0.702335 - 2.12291i) q^{5} +(0.771236 + 0.445274i) q^{6} +(-1.67674 + 2.90420i) q^{7} +1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +O(q^{10})\) \(q+(0.165418 + 0.286513i) q^{2} +(2.33117 - 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(-0.702335 - 2.12291i) q^{5} +(0.771236 + 0.445274i) q^{6} +(-1.67674 + 2.90420i) q^{7} +1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +(0.492061 - 0.552395i) q^{10} +(2.81095 - 1.62291i) q^{11} -5.08898i q^{12} -1.10945 q^{14} +(-4.49448 - 4.00358i) q^{15} +(-1.67763 - 2.90574i) q^{16} +(-1.68772 - 0.974404i) q^{17} +1.40467 q^{18} +(-1.07890 - 0.622905i) q^{19} +(-4.13965 - 0.856821i) q^{20} +9.02690i q^{21} +(0.929966 + 0.536916i) q^{22} +(2.33117 - 1.34590i) q^{23} +(3.00053 - 1.73236i) q^{24} +(-4.01345 + 2.98198i) q^{25} -3.35348i q^{27} +(3.16995 + 5.49052i) q^{28} +(1.50000 + 2.59808i) q^{29} +(0.403608 - 1.94999i) q^{30} +3.78109i q^{31} +(1.84216 - 3.19071i) q^{32} +(4.36854 - 7.56654i) q^{33} -0.644737i q^{34} +(7.34297 + 1.51984i) q^{35} +(-4.01345 - 6.95150i) q^{36} +(-0.974404 - 1.68772i) q^{37} -0.412160i q^{38} +(-0.904000 - 2.73247i) q^{40} +(2.40850 - 1.39055i) q^{41} +(-2.58632 + 1.49321i) q^{42} +(7.56654 + 4.36854i) q^{43} -6.13636i q^{44} +(-9.29687 - 1.92426i) q^{45} +(0.771236 + 0.445274i) q^{46} -6.86960 q^{47} +(-7.82169 - 4.51586i) q^{48} +(-2.12291 - 3.67698i) q^{49} +(-1.51827 - 0.656632i) q^{50} -5.24581 q^{51} +12.8336i q^{53} +(0.960814 - 0.554726i) q^{54} +(-5.41950 - 4.82757i) q^{55} +(-2.15819 + 3.73809i) q^{56} -3.35348 q^{57} +(-0.496255 + 0.859539i) q^{58} +(2.19562 + 1.26764i) q^{59} +(-10.8034 + 3.57417i) q^{60} +(3.74581 - 6.48793i) q^{61} +(-1.08333 + 0.625462i) q^{62} +(7.11911 + 12.3307i) q^{63} -5.49162 q^{64} +2.89055 q^{66} +(-2.00758 - 3.47722i) q^{67} +(-3.19071 + 1.84216i) q^{68} +(3.62291 - 6.27506i) q^{69} +(0.779207 + 2.35526i) q^{70} +(-4.54300 - 2.62291i) q^{71} +(2.73247 - 4.73277i) q^{72} +5.46493 q^{73} +(0.322368 - 0.558359i) q^{74} +(-5.34259 + 12.3532i) q^{75} +(-2.03972 + 1.17763i) q^{76} +10.8848i q^{77} -13.7811 q^{79} +(-4.99036 + 5.60226i) q^{80} +(1.85526 + 3.21341i) q^{81} +(0.796819 + 0.460044i) q^{82} +8.61955 q^{83} +(14.7794 + 8.53289i) q^{84} +(-0.883225 + 4.26722i) q^{85} +2.89055i q^{86} +(6.99351 + 4.03771i) q^{87} +(3.61808 - 2.08890i) q^{88} +(8.93425 - 5.15819i) q^{89} +(-0.986548 - 2.98198i) q^{90} -5.08898i q^{92} +(5.08898 + 8.81438i) q^{93} +(-1.13636 - 1.96823i) q^{94} +(-0.564617 + 2.72790i) q^{95} -9.91745i q^{96} +(-2.63304 + 4.56055i) q^{97} +(0.702335 - 1.21648i) q^{98} -13.7811i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.165418 + 0.286513i 0.116968 + 0.202595i 0.918565 0.395270i \(-0.129349\pi\)
−0.801597 + 0.597865i \(0.796016\pi\)
\(3\) 2.33117 1.34590i 1.34590 0.777057i 0.358236 0.933631i \(-0.383378\pi\)
0.987666 + 0.156574i \(0.0500450\pi\)
\(4\) 0.945274 1.63726i 0.472637 0.818631i
\(5\) −0.702335 2.12291i −0.314094 0.949392i
\(6\) 0.771236 + 0.445274i 0.314856 + 0.181782i
\(7\) −1.67674 + 2.90420i −0.633748 + 1.09768i 0.353031 + 0.935611i \(0.385151\pi\)
−0.986779 + 0.162072i \(0.948182\pi\)
\(8\) 1.28714 0.455071
\(9\) 2.12291 3.67698i 0.707635 1.22566i
\(10\) 0.492061 0.552395i 0.155603 0.174683i
\(11\) 2.81095 1.62291i 0.847535 0.489324i −0.0122837 0.999925i \(-0.503910\pi\)
0.859818 + 0.510600i \(0.170577\pi\)
\(12\) 5.08898i 1.46906i
\(13\) 0 0
\(14\) −1.10945 −0.296514
\(15\) −4.49448 4.00358i −1.16047 1.03372i
\(16\) −1.67763 2.90574i −0.419408 0.726436i
\(17\) −1.68772 0.974404i −0.409332 0.236328i 0.281171 0.959658i \(-0.409277\pi\)
−0.690503 + 0.723330i \(0.742611\pi\)
\(18\) 1.40467 0.331084
\(19\) −1.07890 0.622905i −0.247517 0.142904i 0.371110 0.928589i \(-0.378977\pi\)
−0.618627 + 0.785685i \(0.712311\pi\)
\(20\) −4.13965 0.856821i −0.925654 0.191591i
\(21\) 9.02690i 1.96983i
\(22\) 0.929966 + 0.536916i 0.198269 + 0.114471i
\(23\) 2.33117 1.34590i 0.486083 0.280640i −0.236865 0.971543i \(-0.576120\pi\)
0.722948 + 0.690903i \(0.242787\pi\)
\(24\) 3.00053 1.73236i 0.612481 0.353616i
\(25\) −4.01345 + 2.98198i −0.802690 + 0.596396i
\(26\) 0 0
\(27\) 3.35348i 0.645377i
\(28\) 3.16995 + 5.49052i 0.599065 + 1.03761i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0.403608 1.94999i 0.0736883 0.356018i
\(31\) 3.78109i 0.679105i 0.940587 + 0.339552i \(0.110276\pi\)
−0.940587 + 0.339552i \(0.889724\pi\)
\(32\) 1.84216 3.19071i 0.325650 0.564043i
\(33\) 4.36854 7.56654i 0.760466 1.31717i
\(34\) 0.644737i 0.110571i
\(35\) 7.34297 + 1.51984i 1.24119 + 0.256900i
\(36\) −4.01345 6.95150i −0.668909 1.15858i
\(37\) −0.974404 1.68772i −0.160191 0.277459i 0.774746 0.632273i \(-0.217878\pi\)
−0.934937 + 0.354813i \(0.884544\pi\)
\(38\) 0.412160i 0.0668611i
\(39\) 0 0
\(40\) −0.904000 2.73247i −0.142935 0.432041i
\(41\) 2.40850 1.39055i 0.376144 0.217167i −0.299995 0.953941i \(-0.596985\pi\)
0.676139 + 0.736774i \(0.263652\pi\)
\(42\) −2.58632 + 1.49321i −0.399078 + 0.230408i
\(43\) 7.56654 + 4.36854i 1.15389 + 0.666197i 0.949831 0.312763i \(-0.101255\pi\)
0.204055 + 0.978959i \(0.434588\pi\)
\(44\) 6.13636i 0.925091i
\(45\) −9.29687 1.92426i −1.38590 0.286851i
\(46\) 0.771236 + 0.445274i 0.113713 + 0.0656520i
\(47\) −6.86960 −1.00203 −0.501017 0.865437i \(-0.667041\pi\)
−0.501017 + 0.865437i \(0.667041\pi\)
\(48\) −7.82169 4.51586i −1.12896 0.651808i
\(49\) −2.12291 3.67698i −0.303272 0.525283i
\(50\) −1.51827 0.656632i −0.214716 0.0928618i
\(51\) −5.24581 −0.734560
\(52\) 0 0
\(53\) 12.8336i 1.76282i 0.472347 + 0.881412i \(0.343407\pi\)
−0.472347 + 0.881412i \(0.656593\pi\)
\(54\) 0.960814 0.554726i 0.130750 0.0754887i
\(55\) −5.41950 4.82757i −0.730766 0.650949i
\(56\) −2.15819 + 3.73809i −0.288400 + 0.499524i
\(57\) −3.35348 −0.444179
\(58\) −0.496255 + 0.859539i −0.0651614 + 0.112863i
\(59\) 2.19562 + 1.26764i 0.285845 + 0.165033i 0.636067 0.771634i \(-0.280560\pi\)
−0.350221 + 0.936667i \(0.613894\pi\)
\(60\) −10.8034 + 3.57417i −1.39472 + 0.461423i
\(61\) 3.74581 6.48793i 0.479602 0.830695i −0.520124 0.854090i \(-0.674114\pi\)
0.999726 + 0.0233957i \(0.00744777\pi\)
\(62\) −1.08333 + 0.625462i −0.137583 + 0.0794338i
\(63\) 7.11911 + 12.3307i 0.896924 + 1.55352i
\(64\) −5.49162 −0.686453
\(65\) 0 0
\(66\) 2.89055 0.355802
\(67\) −2.00758 3.47722i −0.245264 0.424810i 0.716942 0.697133i \(-0.245541\pi\)
−0.962206 + 0.272323i \(0.912208\pi\)
\(68\) −3.19071 + 1.84216i −0.386930 + 0.223394i
\(69\) 3.62291 6.27506i 0.436147 0.755428i
\(70\) 0.779207 + 2.35526i 0.0931331 + 0.281508i
\(71\) −4.54300 2.62291i −0.539155 0.311282i 0.205581 0.978640i \(-0.434092\pi\)
−0.744737 + 0.667359i \(0.767425\pi\)
\(72\) 2.73247 4.73277i 0.322024 0.557762i
\(73\) 5.46493 0.639622 0.319811 0.947481i \(-0.396381\pi\)
0.319811 + 0.947481i \(0.396381\pi\)
\(74\) 0.322368 0.558359i 0.0374746 0.0649079i
\(75\) −5.34259 + 12.3532i −0.616909 + 1.42643i
\(76\) −2.03972 + 1.17763i −0.233972 + 0.135084i
\(77\) 10.8848i 1.24043i
\(78\) 0 0
\(79\) −13.7811 −1.55049 −0.775247 0.631658i \(-0.782375\pi\)
−0.775247 + 0.631658i \(0.782375\pi\)
\(80\) −4.99036 + 5.60226i −0.557939 + 0.626351i
\(81\) 1.85526 + 3.21341i 0.206140 + 0.357046i
\(82\) 0.796819 + 0.460044i 0.0879940 + 0.0508033i
\(83\) 8.61955 0.946119 0.473059 0.881031i \(-0.343150\pi\)
0.473059 + 0.881031i \(0.343150\pi\)
\(84\) 14.7794 + 8.53289i 1.61257 + 0.931015i
\(85\) −0.883225 + 4.26722i −0.0957992 + 0.462845i
\(86\) 2.89055i 0.311696i
\(87\) 6.99351 + 4.03771i 0.749783 + 0.432888i
\(88\) 3.61808 2.08890i 0.385688 0.222677i
\(89\) 8.93425 5.15819i 0.947028 0.546767i 0.0548717 0.998493i \(-0.482525\pi\)
0.892156 + 0.451726i \(0.149192\pi\)
\(90\) −0.986548 2.98198i −0.103991 0.314328i
\(91\) 0 0
\(92\) 5.08898i 0.530563i
\(93\) 5.08898 + 8.81438i 0.527703 + 0.914008i
\(94\) −1.13636 1.96823i −0.117206 0.203007i
\(95\) −0.564617 + 2.72790i −0.0579285 + 0.279876i
\(96\) 9.91745i 1.01220i
\(97\) −2.63304 + 4.56055i −0.267344 + 0.463054i −0.968175 0.250273i \(-0.919479\pi\)
0.700831 + 0.713328i \(0.252813\pi\)
\(98\) 0.702335 1.21648i 0.0709465 0.122883i
\(99\) 13.7811i 1.38505i
\(100\) 1.08847 + 9.38986i 0.108847 + 0.938986i
\(101\) 2.85526 + 4.94546i 0.284109 + 0.492092i 0.972393 0.233350i \(-0.0749688\pi\)
−0.688283 + 0.725442i \(0.741635\pi\)
\(102\) −0.867753 1.50299i −0.0859203 0.148818i
\(103\) 7.36863i 0.726052i −0.931779 0.363026i \(-0.881744\pi\)
0.931779 0.363026i \(-0.118256\pi\)
\(104\) 0 0
\(105\) 19.1633 6.33991i 1.87014 0.618712i
\(106\) −3.67698 + 2.12291i −0.357140 + 0.206195i
\(107\) 7.42568 4.28722i 0.717868 0.414461i −0.0960996 0.995372i \(-0.530637\pi\)
0.813967 + 0.580911i \(0.197303\pi\)
\(108\) −5.49052 3.16995i −0.528326 0.305029i
\(109\) 8.49162i 0.813350i 0.913573 + 0.406675i \(0.133312\pi\)
−0.913573 + 0.406675i \(0.866688\pi\)
\(110\) 0.486675 2.35133i 0.0464026 0.224190i
\(111\) −4.54300 2.62291i −0.431203 0.248955i
\(112\) 11.2518 1.06320
\(113\) −6.35006 3.66621i −0.597363 0.344888i 0.170640 0.985333i \(-0.445416\pi\)
−0.768004 + 0.640446i \(0.778750\pi\)
\(114\) −0.554726 0.960814i −0.0519549 0.0899885i
\(115\) −4.49448 4.00358i −0.419113 0.373336i
\(116\) 5.67164 0.526599
\(117\) 0 0
\(118\) 0.838765i 0.0772145i
\(119\) 5.65972 3.26764i 0.518826 0.299544i
\(120\) −5.78501 5.15315i −0.528097 0.470416i
\(121\) −0.232358 + 0.402456i −0.0211234 + 0.0365869i
\(122\) 2.47850 0.224393
\(123\) 3.74308 6.48321i 0.337502 0.584571i
\(124\) 6.19064 + 3.57417i 0.555936 + 0.320970i
\(125\) 9.14925 + 6.42583i 0.818333 + 0.574744i
\(126\) −2.35526 + 4.07944i −0.209824 + 0.363425i
\(127\) 7.93599 4.58185i 0.704205 0.406573i −0.104707 0.994503i \(-0.533390\pi\)
0.808912 + 0.587930i \(0.200057\pi\)
\(128\) −4.59273 7.95484i −0.405944 0.703115i
\(129\) 23.5185 2.07069
\(130\) 0 0
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) −8.25894 14.3049i −0.718848 1.24508i
\(133\) 3.61808 2.08890i 0.313727 0.181130i
\(134\) 0.664179 1.15039i 0.0573763 0.0993787i
\(135\) −7.11911 + 2.35526i −0.612716 + 0.202709i
\(136\) −2.17232 1.25419i −0.186275 0.107546i
\(137\) −8.42435 + 14.5914i −0.719741 + 1.24663i 0.241361 + 0.970435i \(0.422406\pi\)
−0.961102 + 0.276193i \(0.910927\pi\)
\(138\) 2.39718 0.204061
\(139\) −0.513452 + 0.889325i −0.0435505 + 0.0754316i −0.886979 0.461810i \(-0.847200\pi\)
0.843429 + 0.537241i \(0.180534\pi\)
\(140\) 9.42949 10.5857i 0.796937 0.894654i
\(141\) −16.0142 + 9.24581i −1.34864 + 0.778638i
\(142\) 1.73551i 0.145640i
\(143\) 0 0
\(144\) −14.2458 −1.18715
\(145\) 4.46197 5.00908i 0.370546 0.415981i
\(146\) 0.904000 + 1.56577i 0.0748155 + 0.129584i
\(147\) −9.89771 5.71445i −0.816349 0.471319i
\(148\) −3.68431 −0.302849
\(149\) 13.7279 + 7.92583i 1.12464 + 0.649309i 0.942581 0.333979i \(-0.108391\pi\)
0.182056 + 0.983288i \(0.441725\pi\)
\(150\) −4.42312 + 0.512727i −0.361146 + 0.0418640i
\(151\) 14.5454i 1.18369i −0.806052 0.591845i \(-0.798400\pi\)
0.806052 0.591845i \(-0.201600\pi\)
\(152\) −1.38869 0.801763i −0.112638 0.0650316i
\(153\) −7.16573 + 4.13713i −0.579315 + 0.334468i
\(154\) −3.11862 + 1.80054i −0.251306 + 0.145091i
\(155\) 8.02690 2.65559i 0.644736 0.213302i
\(156\) 0 0
\(157\) 10.9210i 0.871588i 0.900047 + 0.435794i \(0.143532\pi\)
−0.900047 + 0.435794i \(0.856468\pi\)
\(158\) −2.27964 3.94846i −0.181359 0.314123i
\(159\) 17.2727 + 29.9172i 1.36982 + 2.37259i
\(160\) −8.06738 1.66978i −0.637783 0.132008i
\(161\) 9.02690i 0.711420i
\(162\) −0.613789 + 1.06311i −0.0482238 + 0.0835261i
\(163\) −2.08890 + 3.61808i −0.163615 + 0.283390i −0.936163 0.351567i \(-0.885649\pi\)
0.772547 + 0.634957i \(0.218982\pi\)
\(164\) 5.25779i 0.410564i
\(165\) −19.1312 3.95976i −1.48936 0.308267i
\(166\) 1.42583 + 2.46961i 0.110666 + 0.191679i
\(167\) 1.67674 + 2.90420i 0.129750 + 0.224733i 0.923580 0.383407i \(-0.125249\pi\)
−0.793830 + 0.608140i \(0.791916\pi\)
\(168\) 11.6188i 0.896413i
\(169\) 0 0
\(170\) −1.36872 + 0.452821i −0.104976 + 0.0347298i
\(171\) −4.58082 + 2.64474i −0.350304 + 0.202248i
\(172\) 14.3049 8.25894i 1.09074 0.629738i
\(173\) −7.56654 4.36854i −0.575273 0.332134i 0.183979 0.982930i \(-0.441102\pi\)
−0.759253 + 0.650796i \(0.774435\pi\)
\(174\) 2.67164i 0.202537i
\(175\) −1.93074 16.6559i −0.145950 1.25906i
\(176\) −9.43149 5.44527i −0.710925 0.410453i
\(177\) 6.82449 0.512960
\(178\) 2.95577 + 1.70652i 0.221545 + 0.127909i
\(179\) 9.00507 + 15.5972i 0.673071 + 1.16579i 0.977029 + 0.213107i \(0.0683584\pi\)
−0.303958 + 0.952685i \(0.598308\pi\)
\(180\) −11.9386 + 13.4025i −0.889850 + 0.998960i
\(181\) −1.04366 −0.0775749 −0.0387875 0.999247i \(-0.512350\pi\)
−0.0387875 + 0.999247i \(0.512350\pi\)
\(182\) 0 0
\(183\) 20.1660i 1.49071i
\(184\) 3.00053 1.73236i 0.221202 0.127711i
\(185\) −2.89851 + 3.25391i −0.213102 + 0.239232i
\(186\) −1.68362 + 2.91612i −0.123449 + 0.213820i
\(187\) −6.32546 −0.462564
\(188\) −6.49365 + 11.2473i −0.473598 + 0.820296i
\(189\) 9.73916 + 5.62291i 0.708419 + 0.409006i
\(190\) −0.874976 + 0.289474i −0.0634774 + 0.0210006i
\(191\) −12.7593 + 22.0997i −0.923228 + 1.59908i −0.128841 + 0.991665i \(0.541126\pi\)
−0.794387 + 0.607412i \(0.792208\pi\)
\(192\) −12.8019 + 7.39118i −0.923898 + 0.533413i
\(193\) −9.91035 17.1652i −0.713362 1.23558i −0.963588 0.267392i \(-0.913838\pi\)
0.250225 0.968188i \(-0.419495\pi\)
\(194\) −1.74221 −0.125083
\(195\) 0 0
\(196\) −8.02690 −0.573350
\(197\) 10.8260 + 18.7512i 0.771319 + 1.33596i 0.936840 + 0.349758i \(0.113736\pi\)
−0.165521 + 0.986206i \(0.552930\pi\)
\(198\) 3.94846 2.27964i 0.280605 0.162007i
\(199\) −9.11453 + 15.7868i −0.646112 + 1.11910i 0.337932 + 0.941171i \(0.390273\pi\)
−0.984044 + 0.177928i \(0.943061\pi\)
\(200\) −5.16586 + 3.83821i −0.365281 + 0.271402i
\(201\) −9.36000 5.40400i −0.660204 0.381169i
\(202\) −0.944625 + 1.63614i −0.0664636 + 0.115118i
\(203\) −10.0604 −0.706104
\(204\) −4.95873 + 8.58877i −0.347180 + 0.601334i
\(205\) −4.64357 4.13638i −0.324321 0.288898i
\(206\) 2.11121 1.21891i 0.147095 0.0849252i
\(207\) 11.4289i 0.794363i
\(208\) 0 0
\(209\) −4.04366 −0.279706
\(210\) 4.98642 + 4.44178i 0.344096 + 0.306512i
\(211\) −9.64981 16.7140i −0.664320 1.15064i −0.979469 0.201594i \(-0.935388\pi\)
0.315149 0.949042i \(-0.397946\pi\)
\(212\) 21.0119 + 12.1312i 1.44310 + 0.833176i
\(213\) −14.1207 −0.967534
\(214\) 2.45669 + 1.41837i 0.167936 + 0.0969577i
\(215\) 3.95976 19.1312i 0.270053 1.30474i
\(216\) 4.31638i 0.293692i
\(217\) −10.9810 6.33991i −0.745442 0.430381i
\(218\) −2.43296 + 1.40467i −0.164781 + 0.0951362i
\(219\) 12.7397 7.35526i 0.860868 0.497023i
\(220\) −13.0269 + 4.30978i −0.878274 + 0.290565i
\(221\) 0 0
\(222\) 1.73551i 0.116480i
\(223\) −6.18537 10.7134i −0.414203 0.717421i 0.581141 0.813803i \(-0.302606\pi\)
−0.995344 + 0.0963818i \(0.969273\pi\)
\(224\) 6.17763 + 10.7000i 0.412760 + 0.714922i
\(225\) 2.44450 + 21.0878i 0.162967 + 1.40586i
\(226\) 2.42583i 0.161364i
\(227\) −3.08141 + 5.33715i −0.204520 + 0.354239i −0.949980 0.312311i \(-0.898897\pi\)
0.745460 + 0.666551i \(0.232230\pi\)
\(228\) −3.16995 + 5.49052i −0.209935 + 0.363619i
\(229\) 26.9832i 1.78310i −0.452920 0.891551i \(-0.649618\pi\)
0.452920 0.891551i \(-0.350382\pi\)
\(230\) 0.403608 1.94999i 0.0266131 0.128579i
\(231\) 14.6498 + 25.3742i 0.963887 + 1.66950i
\(232\) 1.93070 + 3.34408i 0.126757 + 0.219549i
\(233\) 0.824319i 0.0540029i 0.999635 + 0.0270015i \(0.00859588\pi\)
−0.999635 + 0.0270015i \(0.991404\pi\)
\(234\) 0 0
\(235\) 4.82476 + 14.5835i 0.314733 + 0.951323i
\(236\) 4.15092 2.39654i 0.270202 0.156001i
\(237\) −32.1261 + 18.5480i −2.08681 + 1.20482i
\(238\) 1.87244 + 1.08106i 0.121372 + 0.0700744i
\(239\) 4.00000i 0.258738i −0.991596 0.129369i \(-0.958705\pi\)
0.991596 0.129369i \(-0.0412952\pi\)
\(240\) −4.09329 + 19.7764i −0.264221 + 1.27656i
\(241\) 19.6534 + 11.3469i 1.26599 + 0.730917i 0.974226 0.225575i \(-0.0724260\pi\)
0.291760 + 0.956492i \(0.405759\pi\)
\(242\) −0.153745 −0.00988310
\(243\) 17.3625 + 10.0242i 1.11380 + 0.643054i
\(244\) −7.08163 12.2657i −0.453355 0.785234i
\(245\) −6.31489 + 7.08920i −0.403443 + 0.452912i
\(246\) 2.47670 0.157908
\(247\) 0 0
\(248\) 4.86678i 0.309041i
\(249\) 20.0936 11.6011i 1.27338 0.735188i
\(250\) −0.327631 + 3.68433i −0.0207212 + 0.233017i
\(251\) 9.51345 16.4778i 0.600484 1.04007i −0.392264 0.919853i \(-0.628308\pi\)
0.992748 0.120216i \(-0.0383586\pi\)
\(252\) 26.9180 1.69568
\(253\) 4.36854 7.56654i 0.274648 0.475704i
\(254\) 2.62552 + 1.51584i 0.164739 + 0.0951124i
\(255\) 3.68431 + 11.1364i 0.230721 + 0.697386i
\(256\) −3.97218 + 6.88001i −0.248261 + 0.430001i
\(257\) 1.82857 1.05573i 0.114063 0.0658544i −0.441883 0.897073i \(-0.645689\pi\)
0.555946 + 0.831218i \(0.312356\pi\)
\(258\) 3.89039 + 6.73836i 0.242205 + 0.419512i
\(259\) 6.53528 0.406083
\(260\) 0 0
\(261\) 12.7374 0.788427
\(262\) 1.65418 + 2.86513i 0.102196 + 0.177008i
\(263\) −25.9092 + 14.9587i −1.59763 + 0.922391i −0.605685 + 0.795704i \(0.707101\pi\)
−0.991943 + 0.126687i \(0.959566\pi\)
\(264\) 5.62291 9.73916i 0.346066 0.599404i
\(265\) 27.2444 9.01345i 1.67361 0.553692i
\(266\) 1.19699 + 0.691084i 0.0733923 + 0.0423731i
\(267\) 13.8848 24.0492i 0.849738 1.47179i
\(268\) −7.59083 −0.463684
\(269\) 9.29455 16.0986i 0.566699 0.981551i −0.430191 0.902738i \(-0.641554\pi\)
0.996889 0.0788127i \(-0.0251129\pi\)
\(270\) −1.85244 1.65011i −0.112736 0.100423i
\(271\) −5.04439 + 2.91238i −0.306425 + 0.176914i −0.645326 0.763908i \(-0.723278\pi\)
0.338901 + 0.940822i \(0.389945\pi\)
\(272\) 6.53876i 0.396471i
\(273\) 0 0
\(274\) −5.57417 −0.336748
\(275\) −6.44216 + 14.8957i −0.388477 + 0.898242i
\(276\) −6.84927 11.8633i −0.412278 0.714086i
\(277\) −11.7263 6.77017i −0.704564 0.406780i 0.104481 0.994527i \(-0.466682\pi\)
−0.809045 + 0.587747i \(0.800015\pi\)
\(278\) −0.339738 −0.0203761
\(279\) 13.9030 + 8.02690i 0.832351 + 0.480558i
\(280\) 9.45139 + 1.95624i 0.564829 + 0.116908i
\(281\) 0.464716i 0.0277226i 0.999904 + 0.0138613i \(0.00441233\pi\)
−0.999904 + 0.0138613i \(0.995588\pi\)
\(282\) −5.29809 3.05885i −0.315496 0.182152i
\(283\) −8.71259 + 5.03022i −0.517910 + 0.299015i −0.736079 0.676896i \(-0.763325\pi\)
0.218169 + 0.975911i \(0.429991\pi\)
\(284\) −8.58877 + 4.95873i −0.509649 + 0.294246i
\(285\) 2.35526 + 7.11911i 0.139514 + 0.421700i
\(286\) 0 0
\(287\) 9.32634i 0.550516i
\(288\) −7.82145 13.5471i −0.460883 0.798273i
\(289\) −6.60107 11.4334i −0.388298 0.672553i
\(290\) 2.17326 + 0.449818i 0.127618 + 0.0264142i
\(291\) 14.1752i 0.830967i
\(292\) 5.16586 8.94752i 0.302309 0.523614i
\(293\) −6.72506 + 11.6481i −0.392882 + 0.680492i −0.992828 0.119548i \(-0.961855\pi\)
0.599946 + 0.800040i \(0.295189\pi\)
\(294\) 3.78109i 0.220518i
\(295\) 1.14902 5.55140i 0.0668987 0.323215i
\(296\) −1.25419 2.17232i −0.0728983 0.126264i
\(297\) −5.44238 9.42647i −0.315799 0.546979i
\(298\) 5.24431i 0.303795i
\(299\) 0 0
\(300\) 15.1752 + 20.4244i 0.876143 + 1.17920i
\(301\) −25.3742 + 14.6498i −1.46255 + 0.844401i
\(302\) 4.16745 2.40608i 0.239810 0.138454i
\(303\) 13.3122 + 7.68581i 0.764767 + 0.441538i
\(304\) 4.18002i 0.239741i
\(305\) −16.4041 3.39530i −0.939295 0.194414i
\(306\) −2.37068 1.36872i −0.135523 0.0782442i
\(307\) −24.6077 −1.40444 −0.702219 0.711961i \(-0.747807\pi\)
−0.702219 + 0.711961i \(0.747807\pi\)
\(308\) 17.8212 + 10.2891i 1.01546 + 0.586274i
\(309\) −9.91745 17.1775i −0.564184 0.977196i
\(310\) 2.08866 + 1.86053i 0.118628 + 0.105671i
\(311\) −2.43781 −0.138236 −0.0691178 0.997609i \(-0.522018\pi\)
−0.0691178 + 0.997609i \(0.522018\pi\)
\(312\) 0 0
\(313\) 19.2965i 1.09071i −0.838207 0.545353i \(-0.816396\pi\)
0.838207 0.545353i \(-0.183604\pi\)
\(314\) −3.12900 + 1.80653i −0.176579 + 0.101948i
\(315\) 21.1768 23.7735i 1.19318 1.33948i
\(316\) −13.0269 + 22.5633i −0.732821 + 1.26928i
\(317\) −28.8217 −1.61879 −0.809395 0.587265i \(-0.800205\pi\)
−0.809395 + 0.587265i \(0.800205\pi\)
\(318\) −5.71445 + 9.89771i −0.320450 + 0.555036i
\(319\) 8.43286 + 4.86872i 0.472150 + 0.272596i
\(320\) 3.85695 + 11.6582i 0.215610 + 0.651713i
\(321\) 11.5404 19.9885i 0.644120 1.11565i
\(322\) −2.58632 + 1.49321i −0.144130 + 0.0832136i
\(323\) 1.21392 + 2.10258i 0.0675445 + 0.116990i
\(324\) 7.01492 0.389718
\(325\) 0 0
\(326\) −1.38217 −0.0765512
\(327\) 11.4289 + 19.7954i 0.632019 + 1.09469i
\(328\) 3.10006 1.78982i 0.171172 0.0988264i
\(329\) 11.5185 19.9507i 0.635037 1.09992i
\(330\) −2.03013 6.13636i −0.111755 0.337795i
\(331\) 2.57478 + 1.48655i 0.141522 + 0.0817081i 0.569089 0.822276i \(-0.307296\pi\)
−0.427567 + 0.903984i \(0.640629\pi\)
\(332\) 8.14783 14.1125i 0.447171 0.774522i
\(333\) −8.27427 −0.453427
\(334\) −0.554726 + 0.960814i −0.0303533 + 0.0525734i
\(335\) −5.97182 + 6.70407i −0.326276 + 0.366282i
\(336\) 26.2299 15.1438i 1.43096 0.826163i
\(337\) 1.90370i 0.103701i 0.998655 + 0.0518505i \(0.0165119\pi\)
−0.998655 + 0.0518505i \(0.983488\pi\)
\(338\) 0 0
\(339\) −19.7374 −1.07199
\(340\) 6.15167 + 5.47976i 0.333621 + 0.297182i
\(341\) 6.13636 + 10.6285i 0.332302 + 0.575565i
\(342\) −1.51550 0.874976i −0.0819490 0.0473133i
\(343\) −9.23611 −0.498703
\(344\) 9.73916 + 5.62291i 0.525100 + 0.303167i
\(345\) −15.8658 3.28390i −0.854188 0.176799i
\(346\) 2.89055i 0.155397i
\(347\) −10.9420 6.31735i −0.587396 0.339133i 0.176671 0.984270i \(-0.443467\pi\)
−0.764067 + 0.645137i \(0.776800\pi\)
\(348\) 13.2216 7.63347i 0.708750 0.409197i
\(349\) 7.77093 4.48655i 0.415968 0.240159i −0.277383 0.960760i \(-0.589467\pi\)
0.693351 + 0.720600i \(0.256134\pi\)
\(350\) 4.45274 3.30837i 0.238009 0.176840i
\(351\) 0 0
\(352\) 11.9586i 0.637395i
\(353\) −17.1252 29.6618i −0.911484 1.57874i −0.811969 0.583701i \(-0.801604\pi\)
−0.0995150 0.995036i \(-0.531729\pi\)
\(354\) 1.12890 + 1.95530i 0.0600001 + 0.103923i
\(355\) −2.37747 + 11.4865i −0.126183 + 0.609641i
\(356\) 19.5036i 1.03369i
\(357\) 8.79585 15.2349i 0.465526 0.806315i
\(358\) −2.97921 + 5.16014i −0.157456 + 0.272722i
\(359\) 22.4043i 1.18245i 0.806505 + 0.591227i \(0.201356\pi\)
−0.806505 + 0.591227i \(0.798644\pi\)
\(360\) −11.9663 2.47678i −0.630681 0.130538i
\(361\) −8.72398 15.1104i −0.459157 0.795283i
\(362\) −0.172641 0.299023i −0.00907381 0.0157163i
\(363\) 1.25092i 0.0656565i
\(364\) 0 0
\(365\) −3.83821 11.6015i −0.200901 0.607252i
\(366\) 5.77781 3.33582i 0.302011 0.174366i
\(367\) 11.4273 6.59753i 0.596498 0.344388i −0.171165 0.985242i \(-0.554753\pi\)
0.767663 + 0.640854i \(0.221420\pi\)
\(368\) −7.82169 4.51586i −0.407734 0.235405i
\(369\) 11.8080i 0.614700i
\(370\) −1.41175 0.292203i −0.0733935 0.0151909i
\(371\) −37.2712 21.5185i −1.93502 1.11719i
\(372\) 19.2419 0.997647
\(373\) 13.2168 + 7.63070i 0.684338 + 0.395103i 0.801488 0.598012i \(-0.204042\pi\)
−0.117149 + 0.993114i \(0.537376\pi\)
\(374\) −1.04635 1.81233i −0.0541053 0.0937131i
\(375\) 29.9770 + 2.66572i 1.54801 + 0.137657i
\(376\) −8.84210 −0.455997
\(377\) 0 0
\(378\) 3.72052i 0.191363i
\(379\) −15.7868 + 9.11453i −0.810915 + 0.468182i −0.847273 0.531157i \(-0.821757\pi\)
0.0363588 + 0.999339i \(0.488424\pi\)
\(380\) 3.93256 + 3.50304i 0.201736 + 0.179702i
\(381\) 12.3334 21.3621i 0.631861 1.09442i
\(382\) −8.44246 −0.431954
\(383\) 0.720440 1.24784i 0.0368128 0.0637616i −0.847032 0.531542i \(-0.821613\pi\)
0.883845 + 0.467780i \(0.154946\pi\)
\(384\) −21.4129 12.3627i −1.09272 0.630883i
\(385\) 23.1073 7.64474i 1.17766 0.389612i
\(386\) 3.27870 5.67888i 0.166882 0.289048i
\(387\) 32.1261 18.5480i 1.63306 0.942848i
\(388\) 4.97788 + 8.62194i 0.252714 + 0.437713i
\(389\) −18.7912 −0.952754 −0.476377 0.879241i \(-0.658050\pi\)
−0.476377 + 0.879241i \(0.658050\pi\)
\(390\) 0 0
\(391\) −5.24581 −0.265292
\(392\) −2.73247 4.73277i −0.138010 0.239041i
\(393\) 23.3117 13.4590i 1.17592 0.678918i
\(394\) −3.58163 + 6.20357i −0.180440 + 0.312531i
\(395\) 9.67894 + 29.2560i 0.487000 + 1.47203i
\(396\) −22.5633 13.0269i −1.13385 0.654627i
\(397\) −8.54634 + 14.8027i −0.428928 + 0.742926i −0.996778 0.0802063i \(-0.974442\pi\)
0.567850 + 0.823132i \(0.307775\pi\)
\(398\) −6.03084 −0.302298
\(399\) 5.62291 9.73916i 0.281497 0.487568i
\(400\) 15.3980 + 6.65940i 0.769898 + 0.332970i
\(401\) −19.2276 + 11.1011i −0.960182 + 0.554361i −0.896229 0.443592i \(-0.853704\pi\)
−0.0639527 + 0.997953i \(0.520371\pi\)
\(402\) 3.57568i 0.178339i
\(403\) 0 0
\(404\) 10.7960 0.537122
\(405\) 5.51875 6.19544i 0.274229 0.307854i
\(406\) −1.66418 2.88244i −0.0825918 0.143053i
\(407\) −5.47801 3.16273i −0.271535 0.156771i
\(408\) −6.75207 −0.334277
\(409\) −8.34221 4.81638i −0.412496 0.238155i 0.279366 0.960185i \(-0.409876\pi\)
−0.691862 + 0.722030i \(0.743209\pi\)
\(410\) 0.416996 2.01468i 0.0205939 0.0994978i
\(411\) 45.3534i 2.23712i
\(412\) −12.0644 6.96537i −0.594369 0.343159i
\(413\) −7.36296 + 4.25101i −0.362308 + 0.209178i
\(414\) 3.27452 1.89055i 0.160934 0.0929153i
\(415\) −6.05381 18.2985i −0.297170 0.898238i
\(416\) 0 0
\(417\) 2.76423i 0.135365i
\(418\) −0.668896 1.15856i −0.0327168 0.0566671i
\(419\) −0.978168 1.69424i −0.0477866 0.0827689i 0.841143 0.540813i \(-0.181883\pi\)
−0.888929 + 0.458044i \(0.848550\pi\)
\(420\) 7.73444 37.3682i 0.377402 1.82338i
\(421\) 12.0807i 0.588778i −0.955686 0.294389i \(-0.904884\pi\)
0.955686 0.294389i \(-0.0951161\pi\)
\(422\) 3.19251 5.52959i 0.155409 0.269176i
\(423\) −14.5835 + 25.2594i −0.709075 + 1.22815i
\(424\) 16.5185i 0.802210i
\(425\) 9.67923 1.12201i 0.469511 0.0544257i
\(426\) −2.33582 4.04576i −0.113171 0.196018i
\(427\) 12.5615 + 21.7571i 0.607893 + 1.05290i
\(428\) 16.2104i 0.783558i
\(429\) 0 0
\(430\) 6.13636 2.03013i 0.295921 0.0979016i
\(431\) 21.2948 12.2945i 1.02573 0.592207i 0.109974 0.993934i \(-0.464923\pi\)
0.915759 + 0.401727i \(0.131590\pi\)
\(432\) −9.74434 + 5.62590i −0.468825 + 0.270676i
\(433\) −31.2400 18.0364i −1.50130 0.866775i −0.999999 0.00150085i \(-0.999522\pi\)
−0.501299 0.865274i \(-0.667144\pi\)
\(434\) 4.19495i 0.201364i
\(435\) 3.65988 17.6824i 0.175478 0.847805i
\(436\) 13.9030 + 8.02690i 0.665833 + 0.384419i
\(437\) −3.35348 −0.160419
\(438\) 4.21475 + 2.43339i 0.201389 + 0.116272i
\(439\) −1.26764 2.19562i −0.0605013 0.104791i 0.834188 0.551480i \(-0.185937\pi\)
−0.894690 + 0.446688i \(0.852603\pi\)
\(440\) −6.97563 6.21373i −0.332550 0.296228i
\(441\) −18.0269 −0.858424
\(442\) 0 0
\(443\) 19.3579i 0.919721i −0.887991 0.459860i \(-0.847899\pi\)
0.887991 0.459860i \(-0.152101\pi\)
\(444\) −8.58877 + 4.95873i −0.407605 + 0.235331i
\(445\) −17.2252 15.3438i −0.816552 0.727365i
\(446\) 2.04635 3.54438i 0.0968973 0.167831i
\(447\) 42.6696 2.01820
\(448\) 9.20801 15.9487i 0.435038 0.753507i
\(449\) 21.4844 + 12.4040i 1.01391 + 0.585381i 0.912334 0.409447i \(-0.134278\pi\)
0.101576 + 0.994828i \(0.467612\pi\)
\(450\) −5.63757 + 4.18869i −0.265758 + 0.197457i
\(451\) 4.51345 7.81753i 0.212530 0.368113i
\(452\) −12.0051 + 6.93114i −0.564672 + 0.326013i
\(453\) −19.5767 33.9079i −0.919795 1.59313i
\(454\) −2.03888 −0.0956896
\(455\) 0 0
\(456\) −4.31638 −0.202133
\(457\) −3.78374 6.55363i −0.176996 0.306566i 0.763854 0.645389i \(-0.223305\pi\)
−0.940850 + 0.338823i \(0.889971\pi\)
\(458\) 7.73105 4.46352i 0.361248 0.208567i
\(459\) −3.26764 + 5.65972i −0.152520 + 0.264173i
\(460\) −10.8034 + 3.57417i −0.503712 + 0.166646i
\(461\) 10.6896 + 6.17164i 0.497864 + 0.287442i 0.727831 0.685756i \(-0.240528\pi\)
−0.229967 + 0.973198i \(0.573862\pi\)
\(462\) −4.84669 + 8.39472i −0.225489 + 0.390558i
\(463\) 22.8578 1.06229 0.531146 0.847281i \(-0.321762\pi\)
0.531146 + 0.847281i \(0.321762\pi\)
\(464\) 5.03289 8.71723i 0.233646 0.404687i
\(465\) 15.1379 16.9941i 0.702004 0.788081i
\(466\) −0.236178 + 0.136357i −0.0109407 + 0.00631664i
\(467\) 15.2976i 0.707889i −0.935266 0.353945i \(-0.884840\pi\)
0.935266 0.353945i \(-0.115160\pi\)
\(468\) 0 0
\(469\) 13.4647 0.621743
\(470\) −3.38026 + 3.79473i −0.155920 + 0.175038i
\(471\) 14.6985 + 25.4586i 0.677273 + 1.17307i
\(472\) 2.82606 + 1.63163i 0.130080 + 0.0751017i
\(473\) 28.3589 1.30394
\(474\) −10.6285 6.13636i −0.488182 0.281852i
\(475\) 6.18762 0.717267i 0.283907 0.0329105i
\(476\) 12.3553i 0.566303i
\(477\) 47.1887 + 27.2444i 2.16062 + 1.24744i
\(478\) 1.14605 0.661673i 0.0524192 0.0302642i
\(479\) 21.0296 12.1414i 0.960866 0.554756i 0.0644264 0.997922i \(-0.479478\pi\)
0.896439 + 0.443166i \(0.146145\pi\)
\(480\) −21.0538 + 6.96537i −0.960971 + 0.317924i
\(481\) 0 0
\(482\) 7.50793i 0.341977i
\(483\) 12.1493 + 21.0433i 0.552814 + 0.957501i
\(484\) 0.439284 + 0.760862i 0.0199674 + 0.0345846i
\(485\) 11.5309 + 2.38665i 0.523591 + 0.108372i
\(486\) 6.63276i 0.300868i
\(487\) −18.4441 + 31.9462i −0.835783 + 1.44762i 0.0576081 + 0.998339i \(0.481653\pi\)
−0.893391 + 0.449280i \(0.851681\pi\)
\(488\) 4.82136 8.35085i 0.218253 0.378025i
\(489\) 11.2458i 0.508553i
\(490\) −3.07574 0.636614i −0.138948 0.0287593i
\(491\) −17.6767 30.6170i −0.797739 1.38172i −0.921085 0.389361i \(-0.872696\pi\)
0.123346 0.992364i \(-0.460637\pi\)
\(492\) −7.07647 12.2568i −0.319032 0.552580i
\(493\) 5.84642i 0.263310i
\(494\) 0 0
\(495\) −29.2560 + 9.67894i −1.31496 + 0.435036i
\(496\) 10.9869 6.34328i 0.493326 0.284822i
\(497\) 15.2349 8.79585i 0.683377 0.394548i
\(498\) 6.64771 + 3.83806i 0.297891 + 0.171988i
\(499\) 16.2189i 0.726058i −0.931778 0.363029i \(-0.881743\pi\)
0.931778 0.363029i \(-0.118257\pi\)
\(500\) 19.1693 8.90554i 0.857278 0.398268i
\(501\) 7.81753 + 4.51345i 0.349261 + 0.201646i
\(502\) 6.29480 0.280950
\(503\) −17.5270 10.1192i −0.781489 0.451193i 0.0554688 0.998460i \(-0.482335\pi\)
−0.836958 + 0.547268i \(0.815668\pi\)
\(504\) 9.16326 + 15.8712i 0.408164 + 0.706961i
\(505\) 8.49339 9.53482i 0.377951 0.424294i
\(506\) 2.89055 0.128500
\(507\) 0 0
\(508\) 17.3244i 0.768646i
\(509\) 17.3526 10.0185i 0.769140 0.444063i −0.0634276 0.997986i \(-0.520203\pi\)
0.832568 + 0.553923i \(0.186870\pi\)
\(510\) −2.58126 + 2.89776i −0.114300 + 0.128315i
\(511\) −9.16326 + 15.8712i −0.405359 + 0.702102i
\(512\) −20.9992 −0.928042
\(513\) −2.08890 + 3.61808i −0.0922271 + 0.159742i
\(514\) 0.604959 + 0.349273i 0.0266836 + 0.0154058i
\(515\) −15.6429 + 5.17524i −0.689308 + 0.228048i
\(516\) 22.2314 38.5060i 0.978685 1.69513i
\(517\) −19.3101 + 11.1487i −0.849259 + 0.490320i
\(518\) 1.08106 + 1.87244i 0.0474988 + 0.0822704i
\(519\) −23.5185 −1.03235
\(520\) 0 0
\(521\) 16.0269 0.702151 0.351076 0.936347i \(-0.385816\pi\)
0.351076 + 0.936347i \(0.385816\pi\)
\(522\) 2.10700 + 3.64944i 0.0922210 + 0.159732i
\(523\) −10.1654 + 5.86898i −0.444501 + 0.256633i −0.705505 0.708705i \(-0.749280\pi\)
0.261004 + 0.965338i \(0.415946\pi\)
\(524\) 9.45274 16.3726i 0.412945 0.715241i
\(525\) −26.9180 36.2291i −1.17480 1.58117i
\(526\) −8.57170 4.94887i −0.373744 0.215781i
\(527\) 3.68431 6.38142i 0.160491 0.277979i
\(528\) −29.3152 −1.27578
\(529\) −7.87709 + 13.6435i −0.342482 + 0.593197i
\(530\) 7.08920 + 6.31489i 0.307935 + 0.274301i
\(531\) 9.32219 5.38217i 0.404548 0.233566i
\(532\) 7.89832i 0.342436i
\(533\) 0 0
\(534\) 9.18722 0.397570
\(535\) −14.3167 12.7530i −0.618964 0.551358i
\(536\) −2.58402 4.47565i −0.111613 0.193319i
\(537\) 41.9847 + 24.2399i 1.81177 + 1.04603i
\(538\) 6.14995 0.265143
\(539\) −11.9348 6.89055i −0.514067 0.296797i
\(540\) −2.87333 + 13.8822i −0.123648 + 0.597396i
\(541\) 21.8080i 0.937599i 0.883305 + 0.468800i \(0.155313\pi\)
−0.883305 + 0.468800i \(0.844687\pi\)
\(542\) −1.66887 0.963521i −0.0716840 0.0413868i
\(543\) −2.43296 + 1.40467i −0.104408 + 0.0602801i
\(544\) −6.21808 + 3.59001i −0.266598 + 0.153920i
\(545\) 18.0269 5.96396i 0.772188 0.255468i
\(546\) 0 0
\(547\) 6.30924i 0.269764i 0.990862 + 0.134882i \(0.0430655\pi\)
−0.990862 + 0.134882i \(0.956935\pi\)
\(548\) 15.9266 + 27.5858i 0.680352 + 1.17840i
\(549\) −15.9040 27.5465i −0.678766 1.17566i
\(550\) −5.33345 + 0.618252i −0.227419 + 0.0263624i
\(551\) 3.73743i 0.159220i
\(552\) 4.66317 8.07684i 0.198478 0.343773i
\(553\) 23.1073 40.0230i 0.982622 1.70195i
\(554\) 4.47964i 0.190322i
\(555\) −2.37747 + 11.4865i −0.100918 + 0.487576i
\(556\) 0.970706 + 1.68131i 0.0411671 + 0.0713035i
\(557\) 17.9189 + 31.0364i 0.759247 + 1.31506i 0.943235 + 0.332126i \(0.107766\pi\)
−0.183987 + 0.982929i \(0.558901\pi\)
\(558\) 5.31119i 0.224840i
\(559\) 0 0
\(560\) −7.90253 23.8865i −0.333943 1.00939i
\(561\) −14.7457 + 8.51345i −0.622565 + 0.359438i
\(562\) −0.133147 + 0.0768725i −0.00561647 + 0.00324267i
\(563\) 4.33196 + 2.50106i 0.182570 + 0.105407i 0.588500 0.808497i \(-0.299719\pi\)
−0.405929 + 0.913904i \(0.633052\pi\)
\(564\) 34.9593i 1.47205i
\(565\) −3.32315 + 16.0555i −0.139806 + 0.675459i
\(566\) −2.88244 1.66418i −0.121158 0.0699507i
\(567\) −12.4432 −0.522564
\(568\) −5.84746 3.37603i −0.245354 0.141655i
\(569\) 6.58402 + 11.4039i 0.276017 + 0.478075i 0.970391 0.241539i \(-0.0776522\pi\)
−0.694375 + 0.719614i \(0.744319\pi\)
\(570\) −1.65011 + 1.85244i −0.0691157 + 0.0775904i
\(571\) −19.8349 −0.830065 −0.415032 0.909807i \(-0.636230\pi\)
−0.415032 + 0.909807i \(0.636230\pi\)
\(572\) 0 0
\(573\) 68.6909i 2.86960i
\(574\) −2.67212 + 1.54275i −0.111532 + 0.0643930i
\(575\) −5.34259 + 12.3532i −0.222801 + 0.515165i
\(576\) −11.6582 + 20.1926i −0.485758 + 0.841357i
\(577\) 10.9210 0.454646 0.227323 0.973819i \(-0.427003\pi\)
0.227323 + 0.973819i \(0.427003\pi\)
\(578\) 2.18388 3.78258i 0.0908373 0.157335i
\(579\) −46.2054 26.6767i −1.92023 1.10865i
\(580\) −3.98339 12.0404i −0.165401 0.499949i
\(581\) −14.4527 + 25.0329i −0.599601 + 1.03854i
\(582\) −4.06139 + 2.34484i −0.168350 + 0.0971969i
\(583\) 20.8276 + 36.0745i 0.862593 + 1.49406i
\(584\) 7.03411 0.291073
\(585\) 0 0
\(586\) −4.44979 −0.183819
\(587\) −20.2247 35.0303i −0.834764 1.44585i −0.894222 0.447624i \(-0.852270\pi\)
0.0594576 0.998231i \(-0.481063\pi\)
\(588\) −18.7121 + 10.8034i −0.771673 + 0.445526i
\(589\) 2.35526 4.07944i 0.0970469 0.168090i
\(590\) 1.78062 0.589093i 0.0733069 0.0242526i
\(591\) 50.4744 + 29.1414i 2.07624 + 1.19872i
\(592\) −3.26938 + 5.66274i −0.134371 + 0.232737i
\(593\) 1.47709 0.0606569 0.0303284 0.999540i \(-0.490345\pi\)
0.0303284 + 0.999540i \(0.490345\pi\)
\(594\) 1.80054 3.11862i 0.0738769 0.127959i
\(595\) −10.9119 9.72008i −0.447345 0.398484i
\(596\) 25.9533 14.9842i 1.06309 0.613775i
\(597\) 49.0690i 2.00826i
\(598\) 0 0
\(599\) −2.27271 −0.0928606 −0.0464303 0.998922i \(-0.514785\pi\)
−0.0464303 + 0.998922i \(0.514785\pi\)
\(600\) −6.87664 + 15.9003i −0.280738 + 0.649125i
\(601\) −3.70215 6.41231i −0.151014 0.261563i 0.780587 0.625048i \(-0.214920\pi\)
−0.931600 + 0.363484i \(0.881587\pi\)
\(602\) −8.39472 4.84669i −0.342143 0.197536i
\(603\) −17.0476 −0.694231
\(604\) −23.8147 13.7494i −0.969005 0.559456i
\(605\) 1.01757 + 0.210615i 0.0413700 + 0.00856273i
\(606\) 5.08549i 0.206584i
\(607\) −9.26059 5.34661i −0.375876 0.217012i 0.300146 0.953893i \(-0.402964\pi\)
−0.676022 + 0.736881i \(0.736298\pi\)
\(608\) −3.97502 + 2.29498i −0.161208 + 0.0930736i
\(609\) −23.4526 + 13.5404i −0.950347 + 0.548683i
\(610\) −1.74074 5.26162i −0.0704804 0.213037i
\(611\) 0 0
\(612\) 15.6429i 0.632327i
\(613\) 3.04075 + 5.26673i 0.122815 + 0.212721i 0.920877 0.389854i \(-0.127475\pi\)
−0.798062 + 0.602575i \(0.794141\pi\)
\(614\) −4.07057 7.05043i −0.164275 0.284532i
\(615\) −16.3921 3.39283i −0.660994 0.136812i
\(616\) 14.0101i 0.564485i
\(617\) −15.9194 + 27.5732i −0.640892 + 1.11006i 0.344342 + 0.938844i \(0.388102\pi\)
−0.985234 + 0.171213i \(0.945231\pi\)
\(618\) 3.28106 5.68295i 0.131983 0.228602i
\(619\) 26.4043i 1.06128i −0.847598 0.530639i \(-0.821952\pi\)
0.847598 0.530639i \(-0.178048\pi\)
\(620\) 3.23972 15.6524i 0.130110 0.628616i
\(621\) −4.51345 7.81753i −0.181119 0.313707i
\(622\) −0.403259 0.698464i −0.0161692 0.0280059i
\(623\) 34.5957i 1.38605i
\(624\) 0 0
\(625\) 7.21560 23.9361i 0.288624 0.957443i
\(626\) 5.52871 3.19200i 0.220972 0.127578i
\(627\) −9.42647 + 5.44238i −0.376457 + 0.217348i
\(628\) 17.8805 + 10.3233i 0.713509 + 0.411944i
\(629\) 3.79785i 0.151430i
\(630\) 10.3144 + 2.13487i 0.410937 + 0.0850553i
\(631\) 30.4564 + 17.5840i 1.21245 + 0.700009i 0.963293 0.268454i \(-0.0865127\pi\)
0.249158 + 0.968463i \(0.419846\pi\)
\(632\) −17.7381 −0.705585
\(633\) −44.9907 25.9754i −1.78822 1.03243i
\(634\) −4.76764 8.25780i −0.189347 0.327959i
\(635\) −15.3005 13.6294i −0.607184 0.540865i
\(636\) 65.3098 2.58970
\(637\) 0 0
\(638\) 3.22150i 0.127540i
\(639\) −19.2887 + 11.1364i −0.763051 + 0.440547i
\(640\) −13.6617 + 15.3369i −0.540028 + 0.606244i
\(641\) 2.76257 4.78491i 0.109115 0.188993i −0.806297 0.591511i \(-0.798532\pi\)
0.915412 + 0.402518i \(0.131865\pi\)
\(642\) 7.63594 0.301367
\(643\) −16.0776 + 27.8472i −0.634039 + 1.09819i 0.352679 + 0.935744i \(0.385271\pi\)
−0.986718 + 0.162444i \(0.948062\pi\)
\(644\) 14.7794 + 8.53289i 0.582390 + 0.336243i
\(645\) −16.5179 49.9276i −0.650391 1.96590i
\(646\) −0.401610 + 0.695609i −0.0158011 + 0.0273684i
\(647\) −11.9376 + 6.89216i −0.469314 + 0.270959i −0.715953 0.698149i \(-0.754007\pi\)
0.246638 + 0.969108i \(0.420674\pi\)
\(648\) 2.38797 + 4.13609i 0.0938085 + 0.162481i
\(649\) 8.22905 0.323019
\(650\) 0 0
\(651\) −34.1316 −1.33772
\(652\) 3.94916 + 6.84015i 0.154661 + 0.267881i
\(653\) 7.36296 4.25101i 0.288135 0.166355i −0.348965 0.937136i \(-0.613467\pi\)
0.637100 + 0.770781i \(0.280134\pi\)
\(654\) −3.78109 + 6.54905i −0.147852 + 0.256088i
\(655\) −7.02335 21.2291i −0.274425 0.829488i
\(656\) −8.08115 4.66565i −0.315516 0.182163i
\(657\) 11.6015 20.0944i 0.452619 0.783959i
\(658\) 7.62150 0.297117
\(659\) 2.02183 3.50192i 0.0787594 0.136415i −0.823956 0.566654i \(-0.808237\pi\)
0.902715 + 0.430239i \(0.141571\pi\)
\(660\) −24.5674 + 27.5798i −0.956285 + 1.07354i
\(661\) −27.0830 + 15.6364i −1.05341 + 0.608184i −0.923601 0.383356i \(-0.874768\pi\)
−0.129805 + 0.991540i \(0.541435\pi\)
\(662\) 0.983609i 0.0382290i
\(663\) 0 0
\(664\) 11.0945 0.430551
\(665\) −6.97563 6.21373i −0.270503 0.240958i
\(666\) −1.36872 2.37068i −0.0530366 0.0918622i
\(667\) 6.99351 + 4.03771i 0.270790 + 0.156341i
\(668\) 6.33991 0.245298
\(669\) −28.8383 16.6498i −1.11495 0.643719i
\(670\) −2.90865 0.602029i −0.112371 0.0232584i
\(671\) 24.3164i 0.938723i
\(672\) 28.8022 + 16.6290i 1.11107 + 0.641477i
\(673\) 27.7768 16.0370i 1.07072 0.618179i 0.142340 0.989818i \(-0.454537\pi\)
0.928377 + 0.371639i \(0.121204\pi\)
\(674\) −0.545433 + 0.314906i −0.0210093 + 0.0121297i
\(675\) 10.0000 + 13.4590i 0.384900 + 0.518038i
\(676\) 0 0
\(677\) 14.2382i 0.547220i −0.961841 0.273610i \(-0.911782\pi\)
0.961841 0.273610i \(-0.0882177\pi\)
\(678\) −3.26493 5.65503i −0.125389 0.217180i
\(679\) −8.82983 15.2937i −0.338858 0.586919i
\(680\) −1.13683 + 5.49249i −0.0435954 + 0.210627i
\(681\) 16.5891i 0.635695i
\(682\) −2.03013 + 3.51629i −0.0777377 + 0.134646i
\(683\) 12.8923 22.3302i 0.493311 0.854440i −0.506659 0.862146i \(-0.669120\pi\)
0.999970 + 0.00770647i \(0.00245307\pi\)
\(684\) 10.0000i 0.382360i
\(685\) 36.8929 + 7.63605i 1.40961 + 0.291759i
\(686\) −1.52782 2.64626i −0.0583325 0.101035i
\(687\) −36.3168 62.9025i −1.38557 2.39988i
\(688\) 29.3152i 1.11763i
\(689\) 0 0
\(690\) −1.68362 5.08898i −0.0640944 0.193734i
\(691\) −0.0378138 + 0.0218318i −0.00143851 + 0.000830522i −0.500719 0.865610i \(-0.666931\pi\)
0.499281 + 0.866440i \(0.333598\pi\)
\(692\) −14.3049 + 8.25894i −0.543791 + 0.313958i
\(693\) 40.0230 + 23.1073i 1.52035 + 0.877774i
\(694\) 4.18002i 0.158671i
\(695\) 2.24857 + 0.465407i 0.0852931 + 0.0176539i
\(696\) 9.00160 + 5.19707i 0.341205 + 0.196995i
\(697\) −5.41982 −0.205290
\(698\) 2.57091 + 1.48431i 0.0973103 + 0.0561821i
\(699\) 1.10945 + 1.92163i 0.0419634 + 0.0726827i
\(700\) −29.0951 12.5832i −1.09969 0.475601i
\(701\) 14.5454 0.549373 0.274687 0.961534i \(-0.411426\pi\)
0.274687 + 0.961534i \(0.411426\pi\)
\(702\) 0 0
\(703\) 2.42785i 0.0915679i
\(704\) −15.4367 + 8.91238i −0.581792 + 0.335898i
\(705\) 30.8753 + 27.5030i 1.16283 + 1.03582i
\(706\) 5.66565 9.81320i 0.213230 0.369325i
\(707\) −19.1501 −0.720214
\(708\) 6.45101 11.1735i 0.242444 0.419925i
\(709\) −17.0025 9.81638i −0.638541 0.368662i 0.145511 0.989357i \(-0.453517\pi\)
−0.784052 + 0.620695i \(0.786851\pi\)
\(710\) −3.68431 + 1.21891i −0.138270 + 0.0457447i
\(711\) −29.2560 + 50.6728i −1.09718 + 1.90038i
\(712\) 11.4996 6.63929i 0.430965 0.248818i
\(713\) 5.08898 + 8.81438i 0.190584 + 0.330101i
\(714\) 5.81998 0.217807
\(715\) 0 0
\(716\) 34.0490 1.27247
\(717\) −5.38361 9.32468i −0.201055 0.348237i
\(718\) −6.41912 + 3.70608i −0.239559 + 0.138310i
\(719\) −23.7156 + 41.0766i −0.884443 + 1.53190i −0.0380914 + 0.999274i \(0.512128\pi\)
−0.846351 + 0.532625i \(0.821206\pi\)
\(720\) 10.0053 + 30.2425i 0.372876 + 1.12707i
\(721\) 21.3999 + 12.3553i 0.796976 + 0.460134i
\(722\) 2.88621 4.99906i 0.107414 0.186046i
\(723\) 61.0872 2.27186
\(724\) −0.986548 + 1.70875i −0.0366648 + 0.0635052i
\(725\) −13.7676 5.95429i −0.511315 0.221137i
\(726\) −0.358406 + 0.206926i −0.0133017 + 0.00767973i
\(727\) 34.0951i 1.26452i 0.774757 + 0.632259i \(0.217872\pi\)
−0.774757 + 0.632259i \(0.782128\pi\)
\(728\) 0 0
\(729\) 42.8349 1.58648
\(730\) 2.68908 3.01880i 0.0995272 0.111731i
\(731\) −8.51345 14.7457i −0.314881 0.545391i
\(732\) −33.0170 19.0624i −1.22034 0.704565i
\(733\) 14.3920 0.531580 0.265790 0.964031i \(-0.414367\pi\)
0.265790 + 0.964031i \(0.414367\pi\)
\(734\) 3.78055 + 2.18270i 0.139543 + 0.0805651i
\(735\) −5.17972 + 25.0253i −0.191057 + 0.923074i
\(736\) 9.91745i 0.365562i
\(737\) −11.2864 6.51621i −0.415740 0.240028i
\(738\) 3.38314 1.95326i 0.124535 0.0719004i
\(739\) −29.8328 + 17.2240i −1.09742 + 0.633594i −0.935541 0.353217i \(-0.885088\pi\)
−0.161876 + 0.986811i \(0.551754\pi\)
\(740\) 2.58762 + 7.82145i 0.0951228 + 0.287522i
\(741\) 0 0
\(742\) 14.2382i 0.522702i
\(743\) 20.3567 + 35.2589i 0.746816 + 1.29352i 0.949342 + 0.314246i \(0.101752\pi\)
−0.202526 + 0.979277i \(0.564915\pi\)
\(744\) 6.55021 + 11.3453i 0.240142 + 0.415939i
\(745\) 7.18418 34.7097i 0.263208 1.27167i
\(746\) 5.04903i 0.184858i
\(747\) 18.2985 31.6939i 0.669507 1.15962i
\(748\) −5.97929 + 10.3564i −0.218625 + 0.378669i
\(749\) 28.7542i 1.05066i
\(750\) 4.19498 + 9.02975i 0.153179 + 0.329720i
\(751\) 16.2509 + 28.1474i 0.593003 + 1.02711i 0.993825 + 0.110956i \(0.0353912\pi\)
−0.400822 + 0.916156i \(0.631275\pi\)
\(752\) 11.5247 + 19.9613i 0.420261 + 0.727914i
\(753\) 51.2167i 1.86644i
\(754\) 0 0
\(755\) −30.8786 + 10.2158i −1.12379 + 0.371790i
\(756\) 18.4123 10.6304i 0.669650 0.386623i
\(757\) 11.2864 6.51621i 0.410211 0.236836i −0.280669 0.959805i \(-0.590556\pi\)
0.690881 + 0.722969i \(0.257223\pi\)
\(758\) −5.22286 3.01542i −0.189703 0.109525i
\(759\) 23.5185i 0.853668i
\(760\) −0.726739 + 3.51117i −0.0263616 + 0.127364i
\(761\) −3.45532 1.99493i −0.125255 0.0723161i 0.436063 0.899916i \(-0.356372\pi\)
−0.561318 + 0.827600i \(0.689706\pi\)
\(762\) 8.16070 0.295631
\(763\) −24.6613 14.2382i −0.892800 0.515458i
\(764\) 24.1220 + 41.7805i 0.872703 + 1.51157i
\(765\) 13.8155 + 12.3065i 0.499500 + 0.444943i
\(766\) 0.476696 0.0172237
\(767\) 0 0
\(768\) 21.3847i 0.771652i
\(769\) −5.77367 + 3.33343i −0.208204 + 0.120207i −0.600476 0.799642i \(-0.705022\pi\)
0.392272 + 0.919849i \(0.371689\pi\)
\(770\) 6.01268 + 5.35596i 0.216682 + 0.193015i
\(771\) 2.84181 4.92216i 0.102345 0.177267i
\(772\) −37.4720 −1.34865
\(773\) 24.1675 41.8593i 0.869244 1.50557i 0.00647254 0.999979i \(-0.497940\pi\)
0.862771 0.505595i \(-0.168727\pi\)
\(774\) 10.6285 + 6.13636i 0.382033 + 0.220567i
\(775\) −11.2751 15.1752i −0.405015 0.545111i
\(776\) −3.38907 + 5.87005i −0.121661 + 0.210723i
\(777\) 15.2349 8.79585i 0.546548 0.315549i
\(778\) −3.10841 5.38393i −0.111442 0.193023i
\(779\) −3.46472 −0.124136
\(780\) 0 0
\(781\) −17.0269 −0.609271
\(782\) −0.867753 1.50299i −0.0310308 0.0537469i
\(783\) 8.71259 5.03022i 0.311363 0.179765i
\(784\) −7.12291 + 12.3372i −0.254389 + 0.440615i
\(785\) 23.1842 7.67017i 0.827478 0.273760i
\(786\) 7.71236 + 4.45274i 0.275091 + 0.158824i
\(787\) −13.9806 + 24.2151i −0.498355 + 0.863176i −0.999998 0.00189876i \(-0.999396\pi\)
0.501643 + 0.865074i \(0.332729\pi\)
\(788\) 40.9341 1.45822
\(789\) −40.2658 + 69.7424i −1.43350 + 2.48290i
\(790\) −6.78113 + 7.61261i −0.241262 + 0.270845i
\(791\) 21.2948 12.2945i 0.757155 0.437144i
\(792\) 17.7381i 0.630297i
\(793\) 0 0
\(794\) −5.65488 −0.200684
\(795\) 51.3802 57.6802i 1.82227 2.04571i
\(796\) 17.2314 + 29.8457i 0.610752 + 1.05785i
\(797\) −32.2529 18.6212i −1.14246 0.659597i −0.195418 0.980720i \(-0.562607\pi\)
−0.947038 + 0.321123i \(0.895940\pi\)
\(798\) 3.72052 0.131705
\(799\) 11.5939 + 6.69377i 0.410164 + 0.236808i
\(800\) 2.12122 + 18.2990i 0.0749965 + 0.646969i
\(801\) 43.8014i 1.54765i
\(802\) −6.36120 3.67264i −0.224622 0.129685i
\(803\) 15.3617 8.86907i 0.542102 0.312983i
\(804\) −17.6955 + 10.2165i −0.624073 + 0.360309i
\(805\) 19.1633 6.33991i 0.675416 0.223452i
\(806\) 0 0
\(807\) 50.0382i 1.76143i
\(808\) 3.67511 + 6.36548i 0.129290 + 0.223937i
\(809\) 7.26434 + 12.5822i 0.255400 + 0.442367i 0.965004 0.262234i \(-0.0844594\pi\)
−0.709604 + 0.704601i \(0.751126\pi\)
\(810\) 2.68797 + 0.556354i 0.0944458 + 0.0195483i
\(811\) 44.0538i 1.54694i 0.633834 + 0.773469i \(0.281480\pi\)
−0.633834 + 0.773469i \(0.718520\pi\)
\(812\) −9.50986 + 16.4716i −0.333731 + 0.578039i
\(813\) −7.83955 + 13.5785i −0.274945 + 0.476219i
\(814\) 2.09269i 0.0733489i
\(815\) 9.14794 + 1.89343i 0.320438 + 0.0663240i
\(816\) 8.80054 + 15.2430i 0.308080 + 0.533611i
\(817\) −5.44238 9.42647i −0.190405 0.329790i
\(818\) 3.18687i 0.111426i
\(819\) 0 0
\(820\) −11.1618 + 3.69273i −0.389787 + 0.128956i
\(821\) 23.4060 13.5135i 0.816875 0.471623i −0.0324629 0.999473i \(-0.510335\pi\)
0.849337 + 0.527850i \(0.177002\pi\)
\(822\) −12.9943 + 7.50229i −0.453230 + 0.261672i
\(823\) −34.2914 19.7981i −1.19532 0.690120i −0.235814 0.971798i \(-0.575775\pi\)
−0.959509 + 0.281679i \(0.909109\pi\)
\(824\) 9.48442i 0.330405i
\(825\) 5.03032 + 43.3948i 0.175133 + 1.51081i
\(826\) −2.43594 1.40639i −0.0847571 0.0489345i
\(827\) 26.5639 0.923716 0.461858 0.886954i \(-0.347183\pi\)
0.461858 + 0.886954i \(0.347183\pi\)
\(828\) −18.7121 10.8034i −0.650290 0.375445i
\(829\) −6.99162 12.1098i −0.242829 0.420592i 0.718690 0.695331i \(-0.244742\pi\)
−0.961519 + 0.274738i \(0.911409\pi\)
\(830\) 4.24134 4.76140i 0.147219 0.165271i
\(831\) −36.4480 −1.26437
\(832\) 0 0
\(833\) 8.27427i 0.286686i
\(834\) −0.791986 + 0.457254i −0.0274242 + 0.0158334i
\(835\) 4.98770 5.59927i 0.172607 0.193771i
\(836\) −3.82237 + 6.62054i −0.132199 + 0.228976i
\(837\) 12.6798 0.438278
\(838\) 0.323614 0.560515i 0.0111791 0.0193627i
\(839\) −12.4657 7.19707i −0.430364 0.248471i 0.269138 0.963102i \(-0.413261\pi\)
−0.699502 + 0.714631i \(0.746595\pi\)
\(840\) 24.6657 8.16032i 0.851048 0.281558i
\(841\) 10.0000 17.3205i 0.344828 0.597259i
\(842\) 3.46128 1.99837i 0.119284 0.0688684i
\(843\) 0.625462 + 1.08333i 0.0215421 + 0.0373119i
\(844\) −36.4868 −1.25593
\(845\) 0 0
\(846\) −9.64952 −0.331757
\(847\) −0.779207 1.34963i −0.0267739 0.0463737i
\(848\) 37.2910 21.5300i 1.28058 0.739343i
\(849\) −13.5404 + 23.4526i −0.464704 + 0.804891i
\(850\) 1.92259 + 2.58762i 0.0659444 + 0.0887547i
\(851\) −4.54300 2.62291i −0.155732 0.0899120i
\(852\) −13.3479 + 23.1193i −0.457292 + 0.792053i
\(853\) −27.2633 −0.933478 −0.466739 0.884395i \(-0.654571\pi\)
−0.466739 + 0.884395i \(0.654571\pi\)
\(854\) −4.15580 + 7.19806i −0.142209 + 0.246312i
\(855\) 8.83179 + 7.86715i 0.302041 + 0.269051i
\(856\) 9.55786 5.51823i 0.326681 0.188609i
\(857\) 50.6201i 1.72915i −0.502503 0.864575i \(-0.667587\pi\)
0.502503 0.864575i \(-0.332413\pi\)
\(858\) 0 0
\(859\) −1.27992 −0.0436702 −0.0218351 0.999762i \(-0.506951\pi\)
−0.0218351 + 0.999762i \(0.506951\pi\)
\(860\) −27.5798 24.5674i −0.940462 0.837742i
\(861\) 12.5523 + 21.7413i 0.427782 + 0.740941i
\(862\) 7.04509 + 4.06749i 0.239957 + 0.138539i
\(863\) −8.38448 −0.285411 −0.142706 0.989765i \(-0.545580\pi\)
−0.142706 + 0.989765i \(0.545580\pi\)
\(864\) −10.7000 6.17763i −0.364020 0.210167i
\(865\) −3.95976 + 19.1312i −0.134636 + 0.650481i
\(866\) 11.9342i 0.405541i
\(867\) −30.7765 17.7688i −1.04522 0.603460i
\(868\) −20.7602 + 11.9859i −0.704646 + 0.406828i
\(869\) −38.7380 + 22.3654i −1.31410 + 0.758695i
\(870\) 5.67164 1.87639i 0.192287 0.0636155i
\(871\) 0 0
\(872\) 10.9299i 0.370132i
\(873\) 11.1794 + 19.3632i 0.378365 + 0.655347i
\(874\) −0.554726 0.960814i −0.0187639 0.0325000i
\(875\) −34.0028 + 15.7968i −1.14950 + 0.534028i
\(876\) 27.8109i 0.939645i
\(877\) 27.9431 48.3989i 0.943572 1.63431i 0.184985 0.982741i \(-0.440776\pi\)
0.758586 0.651573i \(-0.225890\pi\)
\(878\) 0.419382 0.726391i 0.0141535 0.0245145i
\(879\) 36.2051i 1.22117i
\(880\) −4.93574 + 23.8466i −0.166384 + 0.803867i
\(881\) 12.5975 + 21.8195i 0.424420 + 0.735116i 0.996366 0.0851746i \(-0.0271448\pi\)
−0.571946 + 0.820291i \(0.693811\pi\)
\(882\) −2.98198 5.16494i −0.100408 0.173913i
\(883\) 30.7868i 1.03606i 0.855363 + 0.518029i \(0.173334\pi\)
−0.855363 + 0.518029i \(0.826666\pi\)
\(884\) 0 0
\(885\) −4.79307 14.4877i −0.161117 0.487000i
\(886\) 5.54628 3.20215i 0.186331 0.107578i
\(887\) 10.8011 6.23603i 0.362666 0.209385i −0.307584 0.951521i \(-0.599520\pi\)
0.670250 + 0.742136i \(0.266187\pi\)
\(888\) −5.84746 3.37603i −0.196228 0.113292i
\(889\) 30.7302i 1.03066i
\(890\) 1.54683 7.47338i 0.0518499 0.250508i
\(891\) 10.4301 + 6.02183i 0.349422 + 0.201739i
\(892\) −23.3875 −0.783071
\(893\) 7.41163 + 4.27911i 0.248021 + 0.143195i
\(894\) 7.05833 + 12.2254i 0.236066 + 0.408878i
\(895\) 26.7869 30.0714i 0.895387 1.00518i
\(896\) 30.8032 1.02906
\(897\) 0 0
\(898\) 8.20739i 0.273884i
\(899\) −9.82357 + 5.67164i −0.327634 + 0.189160i
\(900\) 36.8370 + 15.9315i 1.22790 + 0.531050i
\(901\) 12.5051 21.6594i 0.416604 0.721580i
\(902\) 2.98643 0.0994372
\(903\) −39.4344 + 68.3024i −1.31230 + 2.27296i
\(904\) −8.17338 4.71891i −0.271843 0.156948i
\(905\) 0.733001 + 2.21560i 0.0243658 + 0.0736490i
\(906\) 6.47670 11.2180i 0.215174 0.372692i
\(907\) −33.6807 + 19.4455i −1.11835 + 0.645678i −0.940979 0.338466i \(-0.890092\pi\)
−0.177369 + 0.984144i \(0.556759\pi\)
\(908\) 5.82555 + 10.0901i 0.193328 + 0.334853i
\(909\) 24.2458 0.804183
\(910\) 0 0
\(911\) 0.165096 0.00546989 0.00273494 0.999996i \(-0.499129\pi\)
0.00273494 + 0.999996i \(0.499129\pi\)
\(912\) 5.62590 + 9.74434i 0.186292 + 0.322667i
\(913\) 24.2292 13.9887i 0.801868 0.462959i
\(914\) 1.25180 2.16818i 0.0414059 0.0717171i
\(915\) −42.8105 + 14.1633i −1.41527 + 0.468223i
\(916\) −44.1786 25.5065i −1.45970 0.842760i
\(917\) −16.7674 + 29.0420i −0.553708 + 0.959050i
\(918\) −2.16211 −0.0713603
\(919\) 0.447663 0.775375i 0.0147670 0.0255773i −0.858547 0.512734i \(-0.828633\pi\)
0.873314 + 0.487157i \(0.161966\pi\)
\(920\) −5.78501 5.15315i −0.190726 0.169894i
\(921\) −57.3648 + 33.1196i −1.89024 + 1.09133i
\(922\) 4.08361i 0.134486i
\(923\) 0 0
\(924\) 55.3923 1.82227
\(925\) 8.94346 + 3.86792i 0.294059 + 0.127176i
\(926\) 3.78109 + 6.54905i 0.124254 + 0.215215i
\(927\) −27.0943 15.6429i −0.889893 0.513780i
\(928\) 11.0529 0.362831
\(929\) −10.6430 6.14474i −0.349185 0.201602i 0.315141 0.949045i \(-0.397948\pi\)
−0.664326 + 0.747443i \(0.731282\pi\)
\(930\) 7.37311 + 1.52608i 0.241774 + 0.0500421i
\(931\) 5.28947i 0.173356i
\(932\) 1.34963 + 0.779207i 0.0442085 + 0.0255238i
\(933\) −5.68295 + 3.28106i −0.186052 + 0.107417i
\(934\) 4.38296 2.53051i 0.143415 0.0828007i
\(935\) 4.44259 + 13.4284i 0.145288 + 0.439154i
\(936\) 0 0
\(937\) 5.77242i 0.188577i 0.995545 + 0.0942884i \(0.0300576\pi\)
−0.995545 + 0.0942884i \(0.969942\pi\)
\(938\) 2.22731 + 3.85781i 0.0727242 + 0.125962i
\(939\) −25.9713 44.9835i −0.847540 1.46798i
\(940\) 28.4377 + 5.88601i 0.927537 + 0.191981i
\(941\) 55.8887i 1.82192i −0.412495 0.910960i \(-0.635342\pi\)
0.412495 0.910960i \(-0.364658\pi\)
\(942\) −4.86282 + 8.42264i −0.158439 + 0.274425i
\(943\) 3.74308 6.48321i 0.121891 0.211122i
\(944\) 8.50655i 0.276864i
\(945\) 5.09675 24.6245i 0.165797 0.801034i
\(946\) 4.69108 + 8.12520i 0.152520 + 0.264173i
\(947\) −0.948188 1.64231i −0.0308120 0.0533679i 0.850208 0.526447i \(-0.176476\pi\)
−0.881020 + 0.473079i \(0.843143\pi\)
\(948\) 70.1318i 2.27777i
\(949\) 0 0
\(950\) 1.22905 + 1.65418i 0.0398757 + 0.0536688i
\(951\) −67.1884 + 38.7912i −2.17873 + 1.25789i
\(952\) 7.28483 4.20590i 0.236103 0.136314i
\(953\) 29.1438 + 16.8262i 0.944059 + 0.545053i 0.891230 0.453551i \(-0.149843\pi\)
0.0528285 + 0.998604i \(0.483176\pi\)
\(954\) 18.0269i 0.583643i
\(955\) 55.8768 + 11.5653i 1.80813 + 0.374245i
\(956\) −6.54905 3.78109i −0.211811 0.122289i
\(957\) 26.2113 0.847290
\(958\) 6.95735 + 4.01683i 0.224782 + 0.129778i
\(959\) −28.2509 48.9320i −0.912269 1.58010i
\(960\) 24.6820 + 21.9861i 0.796608 + 0.709600i
\(961\) 16.7033 0.538817
\(962\) 0 0
\(963\) 36.4054i 1.17315i
\(964\) 37.1556 21.4518i 1.19670 0.690917i
\(965\) −29.4798 + 33.0945i −0.948987 + 1.06535i
\(966\) −4.01944 + 6.96188i −0.129323 + 0.223995i
\(967\) −23.0493 −0.741216 −0.370608 0.928789i \(-0.620851\pi\)
−0.370608 + 0.928789i \(0.620851\pi\)
\(968\) −0.299076 + 0.518015i −0.00961267 + 0.0166496i
\(969\) 5.65972 + 3.26764i 0.181816 + 0.104972i
\(970\) 1.22361 + 3.69855i 0.0392879 + 0.118753i
\(971\) −7.45964 + 12.9205i −0.239391 + 0.414638i −0.960540 0.278143i \(-0.910281\pi\)
0.721148 + 0.692781i \(0.243615\pi\)
\(972\) 32.8246 18.9513i 1.05285 0.607862i
\(973\) −1.72185 2.98233i −0.0552000 0.0956092i
\(974\) −12.2040 −0.391041
\(975\) 0 0
\(976\) −25.1364 −0.804595
\(977\) 11.6821 + 20.2339i 0.373742 + 0.647341i 0.990138 0.140096i \(-0.0447411\pi\)
−0.616396 + 0.787437i \(0.711408\pi\)
\(978\) −3.22207 + 1.86026i −0.103030 + 0.0594846i
\(979\) 16.7425 28.9989i 0.535093 0.926808i
\(980\) 5.63757 + 17.0404i 0.180086 + 0.544334i
\(981\) 31.2235 + 18.0269i 0.996890 + 0.575555i
\(982\) 5.84810 10.1292i 0.186620 0.323236i
\(983\) 5.31119 0.169401 0.0847003 0.996406i \(-0.473007\pi\)
0.0847003 + 0.996406i \(0.473007\pi\)
\(984\) 4.81785 8.34476i 0.153587 0.266021i
\(985\) 32.2035 36.1521i 1.02609 1.15190i
\(986\) 1.67508 0.967105i 0.0533453 0.0307989i
\(987\) 62.0112i 1.97384i
\(988\) 0 0
\(989\) 23.5185 0.747846
\(990\) −7.61261 6.78113i −0.241945 0.215519i
\(991\) 12.0440 + 20.8607i 0.382589 + 0.662663i 0.991432 0.130628i \(-0.0416992\pi\)
−0.608843 + 0.793291i \(0.708366\pi\)
\(992\) 12.0644 + 6.96537i 0.383044 + 0.221151i
\(993\) 8.00299 0.253967
\(994\) 5.04025 + 2.90999i 0.159867 + 0.0922993i
\(995\) 39.9154 + 8.26164i 1.26540 + 0.261912i
\(996\) 43.8648i 1.38991i
\(997\) 17.6755 + 10.2050i 0.559790 + 0.323195i 0.753061 0.657951i \(-0.228576\pi\)
−0.193271 + 0.981145i \(0.561910\pi\)
\(998\) 4.64692 2.68290i 0.147096 0.0849258i
\(999\) −5.65972 + 3.26764i −0.179066 + 0.103384i
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 845.2.l.f.699.8 24
5.4 even 2 inner 845.2.l.f.699.5 24
13.2 odd 12 845.2.b.d.339.4 6
13.3 even 3 845.2.d.d.844.6 12
13.4 even 6 inner 845.2.l.f.654.5 24
13.5 odd 4 65.2.n.a.29.4 yes 12
13.6 odd 12 65.2.n.a.9.3 12
13.7 odd 12 845.2.n.e.529.4 12
13.8 odd 4 845.2.n.e.484.3 12
13.9 even 3 inner 845.2.l.f.654.7 24
13.10 even 6 845.2.d.d.844.8 12
13.11 odd 12 845.2.b.e.339.3 6
13.12 even 2 inner 845.2.l.f.699.6 24
39.5 even 4 585.2.bs.a.289.3 12
39.32 even 12 585.2.bs.a.334.4 12
52.19 even 12 1040.2.dh.a.529.6 12
52.31 even 4 1040.2.dh.a.289.1 12
65.2 even 12 4225.2.a.br.1.3 6
65.4 even 6 inner 845.2.l.f.654.8 24
65.9 even 6 inner 845.2.l.f.654.6 24
65.18 even 4 325.2.e.e.276.3 12
65.19 odd 12 65.2.n.a.9.4 yes 12
65.24 odd 12 845.2.b.e.339.4 6
65.28 even 12 4225.2.a.br.1.4 6
65.29 even 6 845.2.d.d.844.7 12
65.32 even 12 325.2.e.e.126.4 12
65.34 odd 4 845.2.n.e.484.4 12
65.37 even 12 4225.2.a.bq.1.4 6
65.44 odd 4 65.2.n.a.29.3 yes 12
65.49 even 6 845.2.d.d.844.5 12
65.54 odd 12 845.2.b.d.339.3 6
65.57 even 4 325.2.e.e.276.4 12
65.58 even 12 325.2.e.e.126.3 12
65.59 odd 12 845.2.n.e.529.3 12
65.63 even 12 4225.2.a.bq.1.3 6
65.64 even 2 inner 845.2.l.f.699.7 24
195.44 even 4 585.2.bs.a.289.4 12
195.149 even 12 585.2.bs.a.334.3 12
260.19 even 12 1040.2.dh.a.529.1 12
260.239 even 4 1040.2.dh.a.289.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.n.a.9.3 12 13.6 odd 12
65.2.n.a.9.4 yes 12 65.19 odd 12
65.2.n.a.29.3 yes 12 65.44 odd 4
65.2.n.a.29.4 yes 12 13.5 odd 4
325.2.e.e.126.3 12 65.58 even 12
325.2.e.e.126.4 12 65.32 even 12
325.2.e.e.276.3 12 65.18 even 4
325.2.e.e.276.4 12 65.57 even 4
585.2.bs.a.289.3 12 39.5 even 4
585.2.bs.a.289.4 12 195.44 even 4
585.2.bs.a.334.3 12 195.149 even 12
585.2.bs.a.334.4 12 39.32 even 12
845.2.b.d.339.3 6 65.54 odd 12
845.2.b.d.339.4 6 13.2 odd 12
845.2.b.e.339.3 6 13.11 odd 12
845.2.b.e.339.4 6 65.24 odd 12
845.2.d.d.844.5 12 65.49 even 6
845.2.d.d.844.6 12 13.3 even 3
845.2.d.d.844.7 12 65.29 even 6
845.2.d.d.844.8 12 13.10 even 6
845.2.l.f.654.5 24 13.4 even 6 inner
845.2.l.f.654.6 24 65.9 even 6 inner
845.2.l.f.654.7 24 13.9 even 3 inner
845.2.l.f.654.8 24 65.4 even 6 inner
845.2.l.f.699.5 24 5.4 even 2 inner
845.2.l.f.699.6 24 13.12 even 2 inner
845.2.l.f.699.7 24 65.64 even 2 inner
845.2.l.f.699.8 24 1.1 even 1 trivial
845.2.n.e.484.3 12 13.8 odd 4
845.2.n.e.484.4 12 65.34 odd 4
845.2.n.e.529.3 12 65.59 odd 12
845.2.n.e.529.4 12 13.7 odd 12
1040.2.dh.a.289.1 12 52.31 even 4
1040.2.dh.a.289.6 12 260.239 even 4
1040.2.dh.a.529.1 12 260.19 even 12
1040.2.dh.a.529.6 12 52.19 even 12
4225.2.a.bq.1.3 6 65.63 even 12
4225.2.a.bq.1.4 6 65.37 even 12
4225.2.a.br.1.3 6 65.2 even 12
4225.2.a.br.1.4 6 65.28 even 12