Properties

Label 165.2.d.c.164.6
Level $165$
Weight $2$
Character 165.164
Analytic conductor $1.318$
Analytic rank $0$
Dimension $16$
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] = [165,2,Mod(164,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.164");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.d (of order \(2\), degree \(1\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 24x^{14} + 244x^{12} - 1224x^{10} + 2880x^{8} - 2208x^{6} + 3976x^{4} + 432x^{2} + 2116 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 164.6
Root \(2.60307 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 165.164
Dual form 165.2.d.c.164.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.50597i q^{2} +(-1.53819 + 0.796225i) q^{3} -0.267949 q^{4} +(1.12603 + 1.93185i) q^{5} +(1.19909 + 2.31647i) q^{6} +2.12976 q^{7} -2.60842i q^{8} +(1.73205 - 2.44949i) q^{9} +O(q^{10})\) \(q-1.50597i q^{2} +(-1.53819 + 0.796225i) q^{3} -0.267949 q^{4} +(1.12603 + 1.93185i) q^{5} +(1.19909 + 2.31647i) q^{6} +2.12976 q^{7} -2.60842i q^{8} +(1.73205 - 2.44949i) q^{9} +(2.90931 - 1.69577i) q^{10} +(3.27598 + 0.517638i) q^{11} +(0.412157 - 0.213348i) q^{12} -2.12976 q^{13} -3.20736i q^{14} +(-3.27024 - 2.07498i) q^{15} -4.46410 q^{16} +4.11439i q^{17} +(-3.68886 - 2.60842i) q^{18} -4.63294i q^{19} +(-0.301719 - 0.517638i) q^{20} +(-3.27598 + 1.69577i) q^{21} +(0.779548 - 4.93353i) q^{22} +5.32844 q^{23} +(2.07689 + 4.01224i) q^{24} +(-2.46410 + 4.35066i) q^{25} +3.20736i q^{26} +(-0.713876 + 5.14688i) q^{27} -0.570669 q^{28} -8.95015 q^{29} +(-3.12486 + 4.92489i) q^{30} +3.46410 q^{31} +1.50597i q^{32} +(-5.45123 + 1.81219i) q^{33} +6.19615 q^{34} +(2.39818 + 4.11439i) q^{35} +(-0.464102 + 0.656339i) q^{36} -1.16575i q^{37} -6.97707 q^{38} +(3.27598 - 1.69577i) q^{39} +(5.03908 - 2.93716i) q^{40} -2.39818 q^{41} +(2.55378 + 4.93353i) q^{42} -9.50749 q^{43} +(-0.877796 - 0.138701i) q^{44} +(6.68240 + 0.587860i) q^{45} -8.02448i q^{46} -3.07638 q^{47} +(6.86663 - 3.55443i) q^{48} -2.46410 q^{49} +(6.55196 + 3.71087i) q^{50} +(-3.27598 - 6.32871i) q^{51} +0.570669 q^{52} -4.50413 q^{53} +(7.75105 + 1.07508i) q^{54} +(2.68886 + 6.91159i) q^{55} -5.55532i q^{56} +(3.68886 + 7.12633i) q^{57} +13.4787i q^{58} +4.89898i q^{59} +(0.876258 + 0.555989i) q^{60} +3.39154i q^{61} -5.21684i q^{62} +(3.68886 - 5.21684i) q^{63} -6.66025 q^{64} +(-2.39818 - 4.11439i) q^{65} +(2.72911 + 8.20940i) q^{66} -12.3129i q^{67} -1.10245i q^{68} +(-8.19615 + 4.24264i) q^{69} +(6.19615 - 3.61160i) q^{70} -13.3843i q^{71} +(-6.38929 - 4.51791i) q^{72} +2.12976 q^{73} -1.75559 q^{74} +(0.326152 - 8.65411i) q^{75} +1.24139i q^{76} +(6.97707 + 1.10245i) q^{77} +(-2.55378 - 4.93353i) q^{78} +13.8988i q^{79} +(-5.02672 - 8.62398i) q^{80} +(-3.00000 - 8.48528i) q^{81} +3.61160i q^{82} -9.33123i q^{83} +(0.877796 - 0.454381i) q^{84} +(-7.94839 + 4.63294i) q^{85} +14.3180i q^{86} +(13.7670 - 7.12633i) q^{87} +(1.35022 - 8.54513i) q^{88} +4.62158i q^{89} +(0.885300 - 10.0635i) q^{90} -4.53590 q^{91} -1.42775 q^{92} +(-5.32844 + 2.75821i) q^{93} +4.63294i q^{94} +(8.95015 - 5.21684i) q^{95} +(-1.19909 - 2.31647i) q^{96} +1.16575i q^{97} +3.71087i q^{98} +(6.94211 - 7.12791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 32 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 32 q^{4} - 16 q^{16} + 16 q^{25} + 16 q^{34} + 48 q^{36} + 48 q^{45} + 16 q^{49} - 16 q^{55} - 48 q^{60} + 32 q^{64} - 48 q^{66} - 48 q^{69} + 16 q^{70} - 48 q^{81} - 128 q^{91} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50597i 1.06488i −0.846467 0.532441i \(-0.821275\pi\)
0.846467 0.532441i \(-0.178725\pi\)
\(3\) −1.53819 + 0.796225i −0.888074 + 0.459701i
\(4\) −0.267949 −0.133975
\(5\) 1.12603 + 1.93185i 0.503577 + 0.863950i
\(6\) 1.19909 + 2.31647i 0.489527 + 0.945694i
\(7\) 2.12976 0.804975 0.402488 0.915425i \(-0.368146\pi\)
0.402488 + 0.915425i \(0.368146\pi\)
\(8\) 2.60842i 0.922215i
\(9\) 1.73205 2.44949i 0.577350 0.816497i
\(10\) 2.90931 1.69577i 0.920006 0.536250i
\(11\) 3.27598 + 0.517638i 0.987745 + 0.156074i
\(12\) 0.412157 0.213348i 0.118979 0.0615882i
\(13\) −2.12976 −0.590690 −0.295345 0.955391i \(-0.595435\pi\)
−0.295345 + 0.955391i \(0.595435\pi\)
\(14\) 3.20736i 0.857204i
\(15\) −3.27024 2.07498i −0.844372 0.535757i
\(16\) −4.46410 −1.11603
\(17\) 4.11439i 0.997886i 0.866635 + 0.498943i \(0.166278\pi\)
−0.866635 + 0.498943i \(0.833722\pi\)
\(18\) −3.68886 2.60842i −0.869473 0.614810i
\(19\) 4.63294i 1.06287i −0.847100 0.531434i \(-0.821653\pi\)
0.847100 0.531434i \(-0.178347\pi\)
\(20\) −0.301719 0.517638i −0.0674665 0.115747i
\(21\) −3.27598 + 1.69577i −0.714878 + 0.370048i
\(22\) 0.779548 4.93353i 0.166200 1.05183i
\(23\) 5.32844 1.11106 0.555529 0.831497i \(-0.312516\pi\)
0.555529 + 0.831497i \(0.312516\pi\)
\(24\) 2.07689 + 4.01224i 0.423943 + 0.818995i
\(25\) −2.46410 + 4.35066i −0.492820 + 0.870131i
\(26\) 3.20736i 0.629016i
\(27\) −0.713876 + 5.14688i −0.137386 + 0.990518i
\(28\) −0.570669 −0.107846
\(29\) −8.95015 −1.66200 −0.831000 0.556272i \(-0.812231\pi\)
−0.831000 + 0.556272i \(0.812231\pi\)
\(30\) −3.12486 + 4.92489i −0.570518 + 0.899157i
\(31\) 3.46410 0.622171 0.311086 0.950382i \(-0.399307\pi\)
0.311086 + 0.950382i \(0.399307\pi\)
\(32\) 1.50597i 0.266221i
\(33\) −5.45123 + 1.81219i −0.948938 + 0.315462i
\(34\) 6.19615 1.06263
\(35\) 2.39818 + 4.11439i 0.405367 + 0.695459i
\(36\) −0.464102 + 0.656339i −0.0773503 + 0.109390i
\(37\) 1.16575i 0.191649i −0.995398 0.0958244i \(-0.969451\pi\)
0.995398 0.0958244i \(-0.0305487\pi\)
\(38\) −6.97707 −1.13183
\(39\) 3.27598 1.69577i 0.524577 0.271541i
\(40\) 5.03908 2.93716i 0.796748 0.464406i
\(41\) −2.39818 −0.374533 −0.187267 0.982309i \(-0.559963\pi\)
−0.187267 + 0.982309i \(0.559963\pi\)
\(42\) 2.55378 + 4.93353i 0.394058 + 0.761261i
\(43\) −9.50749 −1.44988 −0.724939 0.688813i \(-0.758132\pi\)
−0.724939 + 0.688813i \(0.758132\pi\)
\(44\) −0.877796 0.138701i −0.132333 0.0209099i
\(45\) 6.68240 + 0.587860i 0.996153 + 0.0876330i
\(46\) 8.02448i 1.18315i
\(47\) −3.07638 −0.448736 −0.224368 0.974505i \(-0.572032\pi\)
−0.224368 + 0.974505i \(0.572032\pi\)
\(48\) 6.86663 3.55443i 0.991113 0.513038i
\(49\) −2.46410 −0.352015
\(50\) 6.55196 + 3.71087i 0.926587 + 0.524796i
\(51\) −3.27598 6.32871i −0.458729 0.886197i
\(52\) 0.570669 0.0791375
\(53\) −4.50413 −0.618690 −0.309345 0.950950i \(-0.600110\pi\)
−0.309345 + 0.950950i \(0.600110\pi\)
\(54\) 7.75105 + 1.07508i 1.05478 + 0.146299i
\(55\) 2.68886 + 6.91159i 0.362566 + 0.931958i
\(56\) 5.55532i 0.742361i
\(57\) 3.68886 + 7.12633i 0.488602 + 0.943906i
\(58\) 13.4787i 1.76984i
\(59\) 4.89898i 0.637793i 0.947790 + 0.318896i \(0.103312\pi\)
−0.947790 + 0.318896i \(0.896688\pi\)
\(60\) 0.876258 + 0.555989i 0.113124 + 0.0717778i
\(61\) 3.39154i 0.434243i 0.976145 + 0.217121i \(0.0696668\pi\)
−0.976145 + 0.217121i \(0.930333\pi\)
\(62\) 5.21684i 0.662539i
\(63\) 3.68886 5.21684i 0.464753 0.657260i
\(64\) −6.66025 −0.832532
\(65\) −2.39818 4.11439i −0.297458 0.510327i
\(66\) 2.72911 + 8.20940i 0.335930 + 1.01051i
\(67\) 12.3129i 1.50426i −0.659014 0.752131i \(-0.729026\pi\)
0.659014 0.752131i \(-0.270974\pi\)
\(68\) 1.10245i 0.133691i
\(69\) −8.19615 + 4.24264i −0.986701 + 0.510754i
\(70\) 6.19615 3.61160i 0.740582 0.431668i
\(71\) 13.3843i 1.58842i −0.607644 0.794210i \(-0.707885\pi\)
0.607644 0.794210i \(-0.292115\pi\)
\(72\) −6.38929 4.51791i −0.752986 0.532441i
\(73\) 2.12976 0.249270 0.124635 0.992203i \(-0.460224\pi\)
0.124635 + 0.992203i \(0.460224\pi\)
\(74\) −1.75559 −0.204084
\(75\) 0.326152 8.65411i 0.0376608 0.999291i
\(76\) 1.24139i 0.142397i
\(77\) 6.97707 + 1.10245i 0.795111 + 0.125636i
\(78\) −2.55378 4.93353i −0.289159 0.558613i
\(79\) 13.8988i 1.56374i 0.623443 + 0.781869i \(0.285734\pi\)
−0.623443 + 0.781869i \(0.714266\pi\)
\(80\) −5.02672 8.62398i −0.562005 0.964191i
\(81\) −3.00000 8.48528i −0.333333 0.942809i
\(82\) 3.61160i 0.398834i
\(83\) 9.33123i 1.02424i −0.858915 0.512118i \(-0.828861\pi\)
0.858915 0.512118i \(-0.171139\pi\)
\(84\) 0.877796 0.454381i 0.0957754 0.0495770i
\(85\) −7.94839 + 4.63294i −0.862124 + 0.502513i
\(86\) 14.3180i 1.54395i
\(87\) 13.7670 7.12633i 1.47598 0.764023i
\(88\) 1.35022 8.54513i 0.143934 0.910914i
\(89\) 4.62158i 0.489886i 0.969537 + 0.244943i \(0.0787693\pi\)
−0.969537 + 0.244943i \(0.921231\pi\)
\(90\) 0.885300 10.0635i 0.0933189 1.06079i
\(91\) −4.53590 −0.475491
\(92\) −1.42775 −0.148853
\(93\) −5.32844 + 2.75821i −0.552534 + 0.286013i
\(94\) 4.63294i 0.477851i
\(95\) 8.95015 5.21684i 0.918266 0.535236i
\(96\) −1.19909 2.31647i −0.122382 0.236424i
\(97\) 1.16575i 0.118364i 0.998247 + 0.0591822i \(0.0188493\pi\)
−0.998247 + 0.0591822i \(0.981151\pi\)
\(98\) 3.71087i 0.374854i
\(99\) 6.94211 7.12791i 0.697709 0.716382i
\(100\) 0.660254 1.16575i 0.0660254 0.116575i
\(101\) 8.95015 0.890573 0.445286 0.895388i \(-0.353102\pi\)
0.445286 + 0.895388i \(0.353102\pi\)
\(102\) −9.53085 + 4.93353i −0.943695 + 0.488493i
\(103\) 5.94311i 0.585592i 0.956175 + 0.292796i \(0.0945856\pi\)
−0.956175 + 0.292796i \(0.905414\pi\)
\(104\) 5.55532i 0.544744i
\(105\) −6.96484 4.41921i −0.679699 0.431271i
\(106\) 6.78309i 0.658832i
\(107\) 1.10245i 0.106578i 0.998579 + 0.0532888i \(0.0169704\pi\)
−0.998579 + 0.0532888i \(0.983030\pi\)
\(108\) 0.191282 1.37910i 0.0184062 0.132704i
\(109\) 12.6574i 1.21236i −0.795327 0.606180i \(-0.792701\pi\)
0.795327 0.606180i \(-0.207299\pi\)
\(110\) 10.4086 4.04935i 0.992426 0.386090i
\(111\) 0.928203 + 1.79315i 0.0881012 + 0.170198i
\(112\) −9.50749 −0.898373
\(113\) 10.6569 1.00252 0.501258 0.865298i \(-0.332871\pi\)
0.501258 + 0.865298i \(0.332871\pi\)
\(114\) 10.7321 5.55532i 1.00515 0.520303i
\(115\) 6.00000 + 10.2938i 0.559503 + 0.959898i
\(116\) 2.39818 0.222666
\(117\) −3.68886 + 5.21684i −0.341035 + 0.482297i
\(118\) 7.37772 0.679174
\(119\) 8.76268i 0.803274i
\(120\) −5.41241 + 8.53015i −0.494083 + 0.778693i
\(121\) 10.4641 + 3.39154i 0.951282 + 0.308322i
\(122\) 5.10757 0.462418
\(123\) 3.68886 1.90949i 0.332613 0.172173i
\(124\) −0.928203 −0.0833551
\(125\) −11.1795 + 0.138701i −0.999923 + 0.0124058i
\(126\) −7.85641 5.55532i −0.699904 0.494907i
\(127\) 10.6488 0.944930 0.472465 0.881349i \(-0.343364\pi\)
0.472465 + 0.881349i \(0.343364\pi\)
\(128\) 13.0421i 1.15277i
\(129\) 14.6243 7.57010i 1.28760 0.666510i
\(130\) −6.19615 + 3.61160i −0.543439 + 0.316758i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 1.46065 0.485576i 0.127134 0.0422639i
\(133\) 9.86707i 0.855583i
\(134\) −18.5429 −1.60186
\(135\) −10.7469 + 4.41645i −0.924942 + 0.380108i
\(136\) 10.7321 0.920266
\(137\) 2.25207 0.192407 0.0962034 0.995362i \(-0.469330\pi\)
0.0962034 + 0.995362i \(0.469330\pi\)
\(138\) 6.38929 + 12.3432i 0.543893 + 1.05072i
\(139\) 17.2904i 1.46655i 0.679933 + 0.733274i \(0.262009\pi\)
−0.679933 + 0.733274i \(0.737991\pi\)
\(140\) −0.642592 1.10245i −0.0543089 0.0931738i
\(141\) 4.73205 2.44949i 0.398511 0.206284i
\(142\) −20.1563 −1.69148
\(143\) −6.97707 1.10245i −0.583452 0.0921913i
\(144\) −7.73205 + 10.9348i −0.644338 + 0.911231i
\(145\) −10.0782 17.2904i −0.836945 1.43589i
\(146\) 3.20736i 0.265443i
\(147\) 3.79025 1.96198i 0.312615 0.161821i
\(148\) 0.312363i 0.0256761i
\(149\) −15.5021 −1.26998 −0.634991 0.772519i \(-0.718996\pi\)
−0.634991 + 0.772519i \(0.718996\pi\)
\(150\) −13.0328 0.491176i −1.06413 0.0401044i
\(151\) 10.5073i 0.855069i 0.903999 + 0.427535i \(0.140618\pi\)
−0.903999 + 0.427535i \(0.859382\pi\)
\(152\) −12.0846 −0.980194
\(153\) 10.0782 + 7.12633i 0.814771 + 0.576130i
\(154\) 1.66025 10.5073i 0.133787 0.846700i
\(155\) 3.90069 + 6.69213i 0.313311 + 0.537525i
\(156\) −0.877796 + 0.454381i −0.0702800 + 0.0363796i
\(157\) 8.70131i 0.694440i 0.937784 + 0.347220i \(0.112874\pi\)
−0.937784 + 0.347220i \(0.887126\pi\)
\(158\) 20.9312 1.66520
\(159\) 6.92820 3.58630i 0.549442 0.284412i
\(160\) −2.90931 + 1.69577i −0.230001 + 0.134063i
\(161\) 11.3483 0.894374
\(162\) −12.7786 + 4.51791i −1.00398 + 0.354961i
\(163\) 5.94311i 0.465500i −0.972537 0.232750i \(-0.925228\pi\)
0.972537 0.232750i \(-0.0747724\pi\)
\(164\) 0.642592 0.0501780
\(165\) −9.63916 8.49039i −0.750407 0.660976i
\(166\) −14.0526 −1.09069
\(167\) 13.1502i 1.01759i −0.860886 0.508797i \(-0.830090\pi\)
0.860886 0.508797i \(-0.169910\pi\)
\(168\) 4.42328 + 8.54513i 0.341264 + 0.659271i
\(169\) −8.46410 −0.651085
\(170\) 6.97707 + 11.9700i 0.535117 + 0.918061i
\(171\) −11.3483 8.02448i −0.867829 0.613647i
\(172\) 2.54752 0.194247
\(173\) 14.5481i 1.10607i 0.833158 + 0.553034i \(0.186530\pi\)
−0.833158 + 0.553034i \(0.813470\pi\)
\(174\) −10.7321 20.7327i −0.813595 1.57174i
\(175\) −5.24796 + 9.26587i −0.396708 + 0.700434i
\(176\) −14.6243 2.31079i −1.10235 0.174182i
\(177\) −3.90069 7.53556i −0.293194 0.566407i
\(178\) 6.95996 0.521671
\(179\) 19.3185i 1.44393i −0.691928 0.721967i \(-0.743238\pi\)
0.691928 0.721967i \(-0.256762\pi\)
\(180\) −1.79054 0.157517i −0.133459 0.0117406i
\(181\) −9.46410 −0.703461 −0.351731 0.936101i \(-0.614407\pi\)
−0.351731 + 0.936101i \(0.614407\pi\)
\(182\) 6.83093i 0.506342i
\(183\) −2.70043 5.21684i −0.199622 0.385640i
\(184\) 13.8988i 1.02463i
\(185\) 2.25207 1.31268i 0.165575 0.0965100i
\(186\) 4.15378 + 8.02448i 0.304570 + 0.588384i
\(187\) −2.12976 + 13.4787i −0.155744 + 0.985657i
\(188\) 0.824313 0.0601192
\(189\) −1.52039 + 10.9616i −0.110592 + 0.797342i
\(190\) −7.85641 13.4787i −0.569964 0.977845i
\(191\) 9.52056i 0.688883i 0.938808 + 0.344442i \(0.111932\pi\)
−0.938808 + 0.344442i \(0.888068\pi\)
\(192\) 10.2447 5.30306i 0.739350 0.382716i
\(193\) 10.6488 0.766519 0.383260 0.923641i \(-0.374801\pi\)
0.383260 + 0.923641i \(0.374801\pi\)
\(194\) 1.75559 0.126044
\(195\) 6.96484 + 4.41921i 0.498763 + 0.316466i
\(196\) 0.660254 0.0471610
\(197\) 7.93338i 0.565230i 0.959233 + 0.282615i \(0.0912019\pi\)
−0.959233 + 0.282615i \(0.908798\pi\)
\(198\) −10.7344 10.4546i −0.762862 0.742978i
\(199\) 10.9282 0.774680 0.387340 0.921937i \(-0.373394\pi\)
0.387340 + 0.921937i \(0.373394\pi\)
\(200\) 11.3483 + 6.42741i 0.802448 + 0.454486i
\(201\) 9.80385 + 18.9396i 0.691510 + 1.33589i
\(202\) 13.4787i 0.948355i
\(203\) −19.0617 −1.33787
\(204\) 0.877796 + 1.69577i 0.0614580 + 0.118728i
\(205\) −2.70043 4.63294i −0.188606 0.323578i
\(206\) 8.95015 0.623586
\(207\) 9.22913 13.0520i 0.641469 0.907174i
\(208\) 9.50749 0.659226
\(209\) 2.39818 15.1774i 0.165886 1.04984i
\(210\) −6.65521 + 10.4889i −0.459253 + 0.723799i
\(211\) 1.24139i 0.0854609i −0.999087 0.0427305i \(-0.986394\pi\)
0.999087 0.0427305i \(-0.0136057\pi\)
\(212\) 1.20688 0.0828887
\(213\) 10.6569 + 20.5875i 0.730198 + 1.41063i
\(214\) 1.66025 0.113493
\(215\) −10.7057 18.3671i −0.730125 1.25262i
\(216\) 13.4252 + 1.86209i 0.913470 + 0.126699i
\(217\) 7.37772 0.500832
\(218\) −19.0617 −1.29102
\(219\) −3.27598 + 1.69577i −0.221370 + 0.114590i
\(220\) −0.720478 1.85195i −0.0485746 0.124859i
\(221\) 8.76268i 0.589442i
\(222\) 2.70043 1.39785i 0.181241 0.0938174i
\(223\) 12.6253i 0.845451i −0.906258 0.422725i \(-0.861074\pi\)
0.906258 0.422725i \(-0.138926\pi\)
\(224\) 3.20736i 0.214301i
\(225\) 6.38894 + 13.5713i 0.425929 + 0.904757i
\(226\) 16.0490i 1.06756i
\(227\) 9.33123i 0.619335i 0.950845 + 0.309668i \(0.100218\pi\)
−0.950845 + 0.309668i \(0.899782\pi\)
\(228\) −0.988427 1.90949i −0.0654602 0.126459i
\(229\) 21.3205 1.40890 0.704449 0.709754i \(-0.251194\pi\)
0.704449 + 0.709754i \(0.251194\pi\)
\(230\) 15.5021 9.03583i 1.02218 0.595805i
\(231\) −11.6098 + 3.85955i −0.763872 + 0.253939i
\(232\) 23.3457i 1.53272i
\(233\) 10.1383i 0.664180i 0.943248 + 0.332090i \(0.107754\pi\)
−0.943248 + 0.332090i \(0.892246\pi\)
\(234\) 7.85641 + 5.55532i 0.513589 + 0.363163i
\(235\) −3.46410 5.94311i −0.225973 0.387685i
\(236\) 1.31268i 0.0854480i
\(237\) −11.0666 21.3790i −0.718852 1.38872i
\(238\) 13.1963 0.855392
\(239\) 16.1447 1.04431 0.522157 0.852849i \(-0.325128\pi\)
0.522157 + 0.852849i \(0.325128\pi\)
\(240\) 14.5987 + 9.26291i 0.942341 + 0.597918i
\(241\) 12.6574i 0.815336i −0.913130 0.407668i \(-0.866342\pi\)
0.913130 0.407668i \(-0.133658\pi\)
\(242\) 5.10757 15.7586i 0.328327 1.01300i
\(243\) 11.3708 + 10.6633i 0.729435 + 0.684050i
\(244\) 0.908762i 0.0581775i
\(245\) −2.77466 4.76028i −0.177266 0.304123i
\(246\) −2.87564 5.55532i −0.183344 0.354194i
\(247\) 9.86707i 0.627826i
\(248\) 9.03583i 0.573776i
\(249\) 7.42976 + 14.3532i 0.470842 + 0.909597i
\(250\) 0.208879 + 16.8360i 0.0132107 + 1.06480i
\(251\) 16.9706i 1.07117i 0.844481 + 0.535586i \(0.179909\pi\)
−0.844481 + 0.535586i \(0.820091\pi\)
\(252\) −0.988427 + 1.39785i −0.0622651 + 0.0880561i
\(253\) 17.4559 + 2.75821i 1.09744 + 0.173407i
\(254\) 16.0368i 1.00624i
\(255\) 8.53727 13.4550i 0.534624 0.842587i
\(256\) 6.32051 0.395032
\(257\) −29.7186 −1.85379 −0.926897 0.375315i \(-0.877535\pi\)
−0.926897 + 0.375315i \(0.877535\pi\)
\(258\) −11.4004 22.0238i −0.709755 1.37114i
\(259\) 2.48278i 0.154273i
\(260\) 0.642592 + 1.10245i 0.0398518 + 0.0683709i
\(261\) −15.5021 + 21.9233i −0.959556 + 1.35702i
\(262\) 0 0
\(263\) 15.3551i 0.946837i −0.880838 0.473418i \(-0.843020\pi\)
0.880838 0.473418i \(-0.156980\pi\)
\(264\) 4.72696 + 14.2191i 0.290924 + 0.875125i
\(265\) −5.07180 8.70131i −0.311558 0.534517i
\(266\) −14.8595 −0.911095
\(267\) −3.67982 7.10886i −0.225201 0.435055i
\(268\) 3.29923i 0.201533i
\(269\) 8.48528i 0.517357i 0.965964 + 0.258678i \(0.0832870\pi\)
−0.965964 + 0.258678i \(0.916713\pi\)
\(270\) 6.65105 + 16.1845i 0.404770 + 0.984955i
\(271\) 24.0734i 1.46236i −0.682186 0.731179i \(-0.738971\pi\)
0.682186 0.731179i \(-0.261029\pi\)
\(272\) 18.3671i 1.11367i
\(273\) 6.97707 3.61160i 0.422271 0.218584i
\(274\) 3.39154i 0.204891i
\(275\) −10.3244 + 12.9772i −0.622586 + 0.782552i
\(276\) 2.19615 1.13681i 0.132193 0.0684280i
\(277\) 16.8852 1.01453 0.507267 0.861789i \(-0.330656\pi\)
0.507267 + 0.861789i \(0.330656\pi\)
\(278\) 26.0388 1.56170
\(279\) 6.00000 8.48528i 0.359211 0.508001i
\(280\) 10.7321 6.25547i 0.641363 0.373836i
\(281\) 5.90937 0.352523 0.176262 0.984343i \(-0.443599\pi\)
0.176262 + 0.984343i \(0.443599\pi\)
\(282\) −3.68886 7.12633i −0.219668 0.424367i
\(283\) −25.4043 −1.51013 −0.755063 0.655652i \(-0.772394\pi\)
−0.755063 + 0.655652i \(0.772394\pi\)
\(284\) 3.58630i 0.212808i
\(285\) −9.61324 + 15.1508i −0.569439 + 0.897457i
\(286\) −1.66025 + 10.5073i −0.0981729 + 0.621308i
\(287\) −5.10757 −0.301490
\(288\) 3.68886 + 2.60842i 0.217368 + 0.153703i
\(289\) 0.0717968 0.00422334
\(290\) −26.0388 + 15.1774i −1.52905 + 0.891248i
\(291\) −0.928203 1.79315i −0.0544122 0.105116i
\(292\) −0.570669 −0.0333959
\(293\) 4.11439i 0.240365i −0.992752 0.120183i \(-0.961652\pi\)
0.992752 0.120183i \(-0.0383480\pi\)
\(294\) −2.95469 5.70801i −0.172321 0.332898i
\(295\) −9.46410 + 5.51641i −0.551021 + 0.321178i
\(296\) −3.04078 −0.176742
\(297\) −5.00287 + 16.4916i −0.290296 + 0.956937i
\(298\) 23.3457i 1.35238i
\(299\) −11.3483 −0.656291
\(300\) −0.0873923 + 2.31886i −0.00504559 + 0.133880i
\(301\) −20.2487 −1.16712
\(302\) 15.8236 0.910548
\(303\) −13.7670 + 7.12633i −0.790894 + 0.409397i
\(304\) 20.6819i 1.18619i
\(305\) −6.55196 + 3.81899i −0.375164 + 0.218675i
\(306\) 10.7321 15.1774i 0.613511 0.867635i
\(307\) 9.50749 0.542621 0.271310 0.962492i \(-0.412543\pi\)
0.271310 + 0.962492i \(0.412543\pi\)
\(308\) −1.86950 0.295400i −0.106525 0.0168320i
\(309\) −4.73205 9.14162i −0.269197 0.520049i
\(310\) 10.0782 5.87433i 0.572401 0.333639i
\(311\) 14.6969i 0.833387i −0.909047 0.416693i \(-0.863189\pi\)
0.909047 0.416693i \(-0.136811\pi\)
\(312\) −4.42328 8.54513i −0.250419 0.483773i
\(313\) 30.4546i 1.72140i −0.509117 0.860698i \(-0.670028\pi\)
0.509117 0.860698i \(-0.329972\pi\)
\(314\) 13.1039 0.739497
\(315\) 14.2319 + 1.25200i 0.801879 + 0.0705424i
\(316\) 3.72417i 0.209501i
\(317\) 22.9624 1.28970 0.644848 0.764311i \(-0.276921\pi\)
0.644848 + 0.764311i \(0.276921\pi\)
\(318\) −5.40087 10.4337i −0.302866 0.585091i
\(319\) −29.3205 4.63294i −1.64163 0.259395i
\(320\) −7.49966 12.8666i −0.419244 0.719266i
\(321\) −0.877796 1.69577i −0.0489938 0.0946488i
\(322\) 17.0903i 0.952403i
\(323\) 19.0617 1.06062
\(324\) 0.803848 + 2.27362i 0.0446582 + 0.126312i
\(325\) 5.24796 9.26587i 0.291104 0.513978i
\(326\) −8.95015 −0.495703
\(327\) 10.0782 + 19.4695i 0.557323 + 1.07667i
\(328\) 6.25547i 0.345400i
\(329\) −6.55196 −0.361221
\(330\) −12.7863 + 14.5163i −0.703861 + 0.799096i
\(331\) 8.53590 0.469175 0.234588 0.972095i \(-0.424626\pi\)
0.234588 + 0.972095i \(0.424626\pi\)
\(332\) 2.50029i 0.137222i
\(333\) −2.85550 2.01915i −0.156481 0.110649i
\(334\) −19.8038 −1.08362
\(335\) 23.7867 13.8647i 1.29961 0.757511i
\(336\) 14.6243 7.57010i 0.797822 0.412983i
\(337\) −16.8852 −0.919796 −0.459898 0.887972i \(-0.652114\pi\)
−0.459898 + 0.887972i \(0.652114\pi\)
\(338\) 12.7467i 0.693329i
\(339\) −16.3923 + 8.48528i −0.890308 + 0.460857i
\(340\) 2.12976 1.24139i 0.115503 0.0673239i
\(341\) 11.3483 + 1.79315i 0.614547 + 0.0971046i
\(342\) −12.0846 + 17.0903i −0.653462 + 0.924135i
\(343\) −20.1563 −1.08834
\(344\) 24.7995i 1.33710i
\(345\) −17.4253 11.0564i −0.938146 0.595257i
\(346\) 21.9090 1.17783
\(347\) 27.4029i 1.47106i 0.677490 + 0.735532i \(0.263068\pi\)
−0.677490 + 0.735532i \(0.736932\pi\)
\(348\) −3.68886 + 1.90949i −0.197744 + 0.102360i
\(349\) 25.3148i 1.35507i −0.735490 0.677536i \(-0.763048\pi\)
0.735490 0.677536i \(-0.236952\pi\)
\(350\) 13.9541 + 7.90327i 0.745880 + 0.422448i
\(351\) 1.52039 10.9616i 0.0811523 0.585089i
\(352\) −0.779548 + 4.93353i −0.0415501 + 0.262958i
\(353\) 1.64863 0.0877475 0.0438738 0.999037i \(-0.486030\pi\)
0.0438738 + 0.999037i \(0.486030\pi\)
\(354\) −11.3483 + 5.87433i −0.603157 + 0.312217i
\(355\) 25.8564 15.0711i 1.37232 0.799892i
\(356\) 1.23835i 0.0656323i
\(357\) −6.97707 13.4787i −0.369266 0.713366i
\(358\) −29.0931 −1.53762
\(359\) 1.75559 0.0926566 0.0463283 0.998926i \(-0.485248\pi\)
0.0463283 + 0.998926i \(0.485248\pi\)
\(360\) 1.53339 17.4305i 0.0808165 0.918667i
\(361\) −2.46410 −0.129690
\(362\) 14.2527i 0.749103i
\(363\) −18.7962 + 3.11494i −0.986545 + 0.163492i
\(364\) 1.21539 0.0637038
\(365\) 2.39818 + 4.11439i 0.125527 + 0.215357i
\(366\) −7.85641 + 4.06678i −0.410661 + 0.212574i
\(367\) 14.9568i 0.780738i 0.920659 + 0.390369i \(0.127652\pi\)
−0.920659 + 0.390369i \(0.872348\pi\)
\(368\) −23.7867 −1.23997
\(369\) −4.15378 + 5.87433i −0.216237 + 0.305805i
\(370\) −1.97685 3.39154i −0.102772 0.176318i
\(371\) −9.59274 −0.498030
\(372\) 1.42775 0.739059i 0.0740255 0.0383184i
\(373\) 9.50749 0.492279 0.246140 0.969234i \(-0.420838\pi\)
0.246140 + 0.969234i \(0.420838\pi\)
\(374\) 20.2985 + 3.20736i 1.04961 + 0.165849i
\(375\) 17.0857 9.11473i 0.882303 0.470683i
\(376\) 8.02448i 0.413831i
\(377\) 19.0617 0.981728
\(378\) 16.5079 + 2.28966i 0.849076 + 0.117767i
\(379\) −2.92820 −0.150412 −0.0752058 0.997168i \(-0.523961\pi\)
−0.0752058 + 0.997168i \(0.523961\pi\)
\(380\) −2.39818 + 1.39785i −0.123024 + 0.0717081i
\(381\) −16.3799 + 8.47886i −0.839168 + 0.434385i
\(382\) 14.3377 0.733580
\(383\) −20.9312 −1.06953 −0.534767 0.844999i \(-0.679601\pi\)
−0.534767 + 0.844999i \(0.679601\pi\)
\(384\) −10.3844 20.0612i −0.529929 1.02374i
\(385\) 5.72664 + 14.7201i 0.291857 + 0.750203i
\(386\) 16.0368i 0.816253i
\(387\) −16.4675 + 23.2885i −0.837088 + 1.18382i
\(388\) 0.312363i 0.0158578i
\(389\) 20.9086i 1.06011i 0.847964 + 0.530054i \(0.177828\pi\)
−0.847964 + 0.530054i \(0.822172\pi\)
\(390\) 6.65521 10.4889i 0.337000 0.531124i
\(391\) 21.9233i 1.10871i
\(392\) 6.42741i 0.324633i
\(393\) 0 0
\(394\) 11.9474 0.601903
\(395\) −26.8504 + 15.6505i −1.35099 + 0.787463i
\(396\) −1.86013 + 1.90992i −0.0934752 + 0.0959769i
\(397\) 5.20405i 0.261184i 0.991436 + 0.130592i \(0.0416877\pi\)
−0.991436 + 0.130592i \(0.958312\pi\)
\(398\) 16.4576i 0.824943i
\(399\) 7.85641 + 15.1774i 0.393312 + 0.759821i
\(400\) 11.0000 19.4218i 0.550000 0.971088i
\(401\) 25.7332i 1.28506i 0.766262 + 0.642528i \(0.222115\pi\)
−0.766262 + 0.642528i \(0.777885\pi\)
\(402\) 28.5225 14.7643i 1.42257 0.736377i
\(403\) −7.37772 −0.367511
\(404\) −2.39818 −0.119314
\(405\) 13.0142 15.3503i 0.646681 0.762760i
\(406\) 28.7064i 1.42467i
\(407\) 0.603439 3.81899i 0.0299114 0.189300i
\(408\) −16.5079 + 8.54513i −0.817264 + 0.423047i
\(409\) 19.4405i 0.961271i 0.876920 + 0.480636i \(0.159594\pi\)
−0.876920 + 0.480636i \(0.840406\pi\)
\(410\) −6.97707 + 4.06678i −0.344573 + 0.200844i
\(411\) −3.46410 + 1.79315i −0.170872 + 0.0884496i
\(412\) 1.59245i 0.0784544i
\(413\) 10.4337i 0.513408i
\(414\) −19.6559 13.8988i −0.966034 0.683089i
\(415\) 18.0265 10.5073i 0.884888 0.515781i
\(416\) 3.20736i 0.157254i
\(417\) −13.7670 26.5958i −0.674174 1.30240i
\(418\) −22.8567 3.61160i −1.11796 0.176649i
\(419\) 1.23835i 0.0604973i 0.999542 + 0.0302486i \(0.00962991\pi\)
−0.999542 + 0.0302486i \(0.990370\pi\)
\(420\) 1.86622 + 1.18412i 0.0910624 + 0.0577794i
\(421\) 8.78461 0.428136 0.214068 0.976819i \(-0.431329\pi\)
0.214068 + 0.976819i \(0.431329\pi\)
\(422\) −1.86950 −0.0910058
\(423\) −5.32844 + 7.53556i −0.259078 + 0.366391i
\(424\) 11.7487i 0.570565i
\(425\) −17.9003 10.1383i −0.868292 0.491779i
\(426\) 31.0042 16.0490i 1.50216 0.777575i
\(427\) 7.22319i 0.349555i
\(428\) 0.295400i 0.0142787i
\(429\) 11.6098 3.85955i 0.560529 0.186341i
\(430\) −27.6603 + 16.1225i −1.33390 + 0.777498i
\(431\) 19.6559 0.946791 0.473395 0.880850i \(-0.343028\pi\)
0.473395 + 0.880850i \(0.343028\pi\)
\(432\) 3.18682 22.9762i 0.153326 1.10544i
\(433\) 37.6778i 1.81068i 0.424689 + 0.905339i \(0.360383\pi\)
−0.424689 + 0.905339i \(0.639617\pi\)
\(434\) 11.1106i 0.533328i
\(435\) 29.2691 + 18.5714i 1.40335 + 0.890428i
\(436\) 3.39154i 0.162426i
\(437\) 24.6863i 1.18091i
\(438\) 2.55378 + 4.93353i 0.122025 + 0.235733i
\(439\) 8.02448i 0.382988i 0.981494 + 0.191494i \(0.0613332\pi\)
−0.981494 + 0.191494i \(0.938667\pi\)
\(440\) 18.0283 7.01367i 0.859466 0.334364i
\(441\) −4.26795 + 6.03579i −0.203236 + 0.287419i
\(442\) −13.1963 −0.627686
\(443\) 34.4436 1.63646 0.818232 0.574888i \(-0.194954\pi\)
0.818232 + 0.574888i \(0.194954\pi\)
\(444\) −0.248711 0.480473i −0.0118033 0.0228023i
\(445\) −8.92820 + 5.20405i −0.423237 + 0.246695i
\(446\) −19.0133 −0.900306
\(447\) 23.8452 12.3432i 1.12784 0.583812i
\(448\) −14.1848 −0.670168
\(449\) 15.7322i 0.742449i 0.928543 + 0.371225i \(0.121062\pi\)
−0.928543 + 0.371225i \(0.878938\pi\)
\(450\) 20.4381 9.62155i 0.963459 0.453564i
\(451\) −7.85641 1.24139i −0.369944 0.0584548i
\(452\) −2.85550 −0.134312
\(453\) −8.36615 16.1622i −0.393076 0.759364i
\(454\) 14.0526 0.659519
\(455\) −5.10757 8.76268i −0.239447 0.410801i
\(456\) 18.5885 9.62209i 0.870484 0.450596i
\(457\) −3.27110 −0.153016 −0.0765079 0.997069i \(-0.524377\pi\)
−0.0765079 + 0.997069i \(0.524377\pi\)
\(458\) 32.1081i 1.50031i
\(459\) −21.1763 2.93716i −0.988424 0.137095i
\(460\) −1.60770 2.75821i −0.0749592 0.128602i
\(461\) 18.5429 0.863628 0.431814 0.901963i \(-0.357874\pi\)
0.431814 + 0.901963i \(0.357874\pi\)
\(462\) 5.81236 + 17.4841i 0.270416 + 0.813434i
\(463\) 7.10886i 0.330377i 0.986262 + 0.165188i \(0.0528232\pi\)
−0.986262 + 0.165188i \(0.947177\pi\)
\(464\) 39.9544 1.85483
\(465\) −11.3284 7.18793i −0.525344 0.333332i
\(466\) 15.2679 0.707274
\(467\) −4.12157 −0.190723 −0.0953616 0.995443i \(-0.530401\pi\)
−0.0953616 + 0.995443i \(0.530401\pi\)
\(468\) 0.988427 1.39785i 0.0456901 0.0646155i
\(469\) 26.2236i 1.21089i
\(470\) −8.95015 + 5.21684i −0.412839 + 0.240635i
\(471\) −6.92820 13.3843i −0.319235 0.616714i
\(472\) 12.7786 0.588182
\(473\) −31.1463 4.92144i −1.43211 0.226288i
\(474\) −32.1962 + 16.6660i −1.47882 + 0.765493i
\(475\) 20.1563 + 11.4160i 0.924835 + 0.523803i
\(476\) 2.34795i 0.107618i
\(477\) −7.80138 + 11.0328i −0.357201 + 0.505158i
\(478\) 24.3135i 1.11207i
\(479\) 24.4523 1.11725 0.558626 0.829420i \(-0.311329\pi\)
0.558626 + 0.829420i \(0.311329\pi\)
\(480\) 3.12486 4.92489i 0.142630 0.224789i
\(481\) 2.48278i 0.113205i
\(482\) −19.0617 −0.868237
\(483\) −17.4559 + 9.03583i −0.794270 + 0.411144i
\(484\) −2.80385 0.908762i −0.127448 0.0413074i
\(485\) −2.25207 + 1.31268i −0.102261 + 0.0596056i
\(486\) 16.0586 17.1240i 0.728433 0.776762i
\(487\) 32.0470i 1.45219i −0.687594 0.726095i \(-0.741333\pi\)
0.687594 0.726095i \(-0.258667\pi\)
\(488\) 8.84657 0.400465
\(489\) 4.73205 + 9.14162i 0.213991 + 0.413398i
\(490\) −7.16884 + 4.17856i −0.323855 + 0.188768i
\(491\) −19.6559 −0.887058 −0.443529 0.896260i \(-0.646274\pi\)
−0.443529 + 0.896260i \(0.646274\pi\)
\(492\) −0.988427 + 0.511648i −0.0445617 + 0.0230669i
\(493\) 36.8244i 1.65849i
\(494\) 14.8595 0.668561
\(495\) 21.5871 + 5.38488i 0.970268 + 0.242032i
\(496\) −15.4641 −0.694359
\(497\) 28.5053i 1.27864i
\(498\) 21.6155 11.1890i 0.968613 0.501391i
\(499\) 2.92820 0.131084 0.0655422 0.997850i \(-0.479122\pi\)
0.0655422 + 0.997850i \(0.479122\pi\)
\(500\) 2.99553 0.0371647i 0.133964 0.00166206i
\(501\) 10.4705 + 20.2275i 0.467789 + 0.903699i
\(502\) 25.5572 1.14067
\(503\) 25.7888i 1.14987i −0.818201 0.574933i \(-0.805028\pi\)
0.818201 0.574933i \(-0.194972\pi\)
\(504\) −13.6077 9.62209i −0.606135 0.428602i
\(505\) 10.0782 + 17.2904i 0.448472 + 0.769411i
\(506\) 4.15378 26.2880i 0.184658 1.16865i
\(507\) 13.0194 6.73933i 0.578211 0.299304i
\(508\) −2.85334 −0.126597
\(509\) 36.5665i 1.62078i −0.585890 0.810390i \(-0.699255\pi\)
0.585890 0.810390i \(-0.300745\pi\)
\(510\) −20.2629 12.8569i −0.897256 0.569312i
\(511\) 4.53590 0.200656
\(512\) 16.5657i 0.732107i
\(513\) 23.8452 + 3.30734i 1.05279 + 0.146023i
\(514\) 44.7553i 1.97407i
\(515\) −11.4812 + 6.69213i −0.505922 + 0.294891i
\(516\) −3.91857 + 2.02840i −0.172506 + 0.0892954i
\(517\) −10.0782 1.59245i −0.443237 0.0700359i
\(518\) −3.73900 −0.164282
\(519\) −11.5835 22.3777i −0.508461 0.982271i
\(520\) −10.7321 + 6.25547i −0.470632 + 0.274320i
\(521\) 21.5921i 0.945969i −0.881071 0.472984i \(-0.843177\pi\)
0.881071 0.472984i \(-0.156823\pi\)
\(522\) 33.0158 + 23.3457i 1.44506 + 1.02181i
\(523\) −3.27110 −0.143035 −0.0715177 0.997439i \(-0.522784\pi\)
−0.0715177 + 0.997439i \(0.522784\pi\)
\(524\) 0 0
\(525\) 0.694628 18.4312i 0.0303160 0.804404i
\(526\) −23.1244 −1.00827
\(527\) 14.2527i 0.620856i
\(528\) 24.3349 8.08982i 1.05904 0.352064i
\(529\) 5.39230 0.234448
\(530\) −13.1039 + 7.63798i −0.569198 + 0.331773i
\(531\) 12.0000 + 8.48528i 0.520756 + 0.368230i
\(532\) 2.64387i 0.114626i
\(533\) 5.10757 0.221233
\(534\) −10.7057 + 5.54170i −0.463283 + 0.239813i
\(535\) −2.12976 + 1.24139i −0.0920778 + 0.0536700i
\(536\) −32.1172 −1.38725
\(537\) 15.3819 + 29.7155i 0.663778 + 1.28232i
\(538\) 12.7786 0.550924
\(539\) −8.07235 1.27551i −0.347701 0.0549402i
\(540\) 2.87961 1.18338i 0.123919 0.0509248i
\(541\) 6.78309i 0.291628i −0.989312 0.145814i \(-0.953420\pi\)
0.989312 0.145814i \(-0.0465801\pi\)
\(542\) −36.2539 −1.55724
\(543\) 14.5576 7.53556i 0.624725 0.323382i
\(544\) −6.19615 −0.265658
\(545\) 24.4523 14.2527i 1.04742 0.610517i
\(546\) −5.43896 10.5073i −0.232766 0.449669i
\(547\) −25.4043 −1.08621 −0.543104 0.839665i \(-0.682751\pi\)
−0.543104 + 0.839665i \(0.682751\pi\)
\(548\) −0.603439 −0.0257776
\(549\) 8.30755 + 5.87433i 0.354558 + 0.250710i
\(550\) 19.5432 + 15.5483i 0.833326 + 0.662981i
\(551\) 41.4655i 1.76649i
\(552\) 11.0666 + 21.3790i 0.471025 + 0.909951i
\(553\) 29.6012i 1.25877i
\(554\) 25.4286i 1.08036i
\(555\) −2.41891 + 3.81230i −0.102677 + 0.161823i
\(556\) 4.63294i 0.196480i
\(557\) 4.11439i 0.174332i −0.996194 0.0871661i \(-0.972219\pi\)
0.996194 0.0871661i \(-0.0277811\pi\)
\(558\) −12.7786 9.03583i −0.540961 0.382517i
\(559\) 20.2487 0.856429
\(560\) −10.7057 18.3671i −0.452400 0.776150i
\(561\) −7.45607 22.4285i −0.314796 0.946932i
\(562\) 8.89934i 0.375396i
\(563\) 33.4268i 1.40877i 0.709818 + 0.704385i \(0.248777\pi\)
−0.709818 + 0.704385i \(0.751223\pi\)
\(564\) −1.26795 + 0.656339i −0.0533903 + 0.0276368i
\(565\) 12.0000 + 20.5875i 0.504844 + 0.866124i
\(566\) 38.2581i 1.60811i
\(567\) −6.38929 18.0717i −0.268325 0.758938i
\(568\) −34.9118 −1.46486
\(569\) −2.39818 −0.100537 −0.0502686 0.998736i \(-0.516008\pi\)
−0.0502686 + 0.998736i \(0.516008\pi\)
\(570\) 22.8167 + 14.4773i 0.955686 + 0.606386i
\(571\) 7.11572i 0.297784i −0.988853 0.148892i \(-0.952429\pi\)
0.988853 0.148892i \(-0.0475706\pi\)
\(572\) 1.86950 + 0.295400i 0.0781677 + 0.0123513i
\(573\) −7.58051 14.6444i −0.316680 0.611779i
\(574\) 7.69185i 0.321052i
\(575\) −13.1298 + 23.1822i −0.547552 + 0.966765i
\(576\) −11.5359 + 16.3142i −0.480662 + 0.679759i
\(577\) 35.6586i 1.48449i −0.670129 0.742244i \(-0.733761\pi\)
0.670129 0.742244i \(-0.266239\pi\)
\(578\) 0.108124i 0.00449736i
\(579\) −16.3799 + 8.47886i −0.680726 + 0.352369i
\(580\) 2.70043 + 4.63294i 0.112129 + 0.192372i
\(581\) 19.8733i 0.824484i
\(582\) −2.70043 + 1.39785i −0.111937 + 0.0579426i
\(583\) −14.7554 2.33151i −0.611108 0.0965612i
\(584\) 5.55532i 0.229881i
\(585\) −14.2319 1.25200i −0.588418 0.0517640i
\(586\) −6.19615 −0.255961
\(587\) −8.62570 −0.356021 −0.178010 0.984029i \(-0.556966\pi\)
−0.178010 + 0.984029i \(0.556966\pi\)
\(588\) −1.01560 + 0.525711i −0.0418825 + 0.0216800i
\(589\) 16.0490i 0.661286i
\(590\) 8.30755 + 14.2527i 0.342017 + 0.586773i
\(591\) −6.31676 12.2030i −0.259837 0.501966i
\(592\) 5.20405i 0.213885i
\(593\) 11.7524i 0.482612i −0.970449 0.241306i \(-0.922424\pi\)
0.970449 0.241306i \(-0.0775757\pi\)
\(594\) 24.8358 + 7.53417i 1.01903 + 0.309131i
\(595\) −16.9282 + 9.86707i −0.693989 + 0.404510i
\(596\) 4.15378 0.170145
\(597\) −16.8096 + 8.70131i −0.687973 + 0.356121i
\(598\) 17.0903i 0.698873i
\(599\) 18.0058i 0.735699i −0.929885 0.367849i \(-0.880094\pi\)
0.929885 0.367849i \(-0.119906\pi\)
\(600\) −22.5735 0.850742i −0.921561 0.0347314i
\(601\) 3.39154i 0.138344i −0.997605 0.0691720i \(-0.977964\pi\)
0.997605 0.0691720i \(-0.0220357\pi\)
\(602\) 30.4940i 1.24284i
\(603\) −30.1603 21.3266i −1.22822 0.868486i
\(604\) 2.81541i 0.114558i
\(605\) 5.23096 + 24.0341i 0.212669 + 0.977124i
\(606\) 10.7321 + 20.7327i 0.435960 + 0.842210i
\(607\) 30.8051 1.25034 0.625171 0.780488i \(-0.285029\pi\)
0.625171 + 0.780488i \(0.285029\pi\)
\(608\) 6.97707 0.282958
\(609\) 29.3205 15.1774i 1.18813 0.615020i
\(610\) 5.75129 + 9.86707i 0.232863 + 0.399506i
\(611\) 6.55196 0.265064
\(612\) −2.70043 1.90949i −0.109159 0.0771868i
\(613\) 45.5606 1.84017 0.920087 0.391714i \(-0.128118\pi\)
0.920087 + 0.391714i \(0.128118\pi\)
\(614\) 14.3180i 0.577827i
\(615\) 7.84264 + 4.97618i 0.316246 + 0.200659i
\(616\) 2.87564 18.1991i 0.115863 0.733263i
\(617\) −11.0986 −0.446814 −0.223407 0.974725i \(-0.571718\pi\)
−0.223407 + 0.974725i \(0.571718\pi\)
\(618\) −13.7670 + 7.12633i −0.553791 + 0.286663i
\(619\) 1.60770 0.0646187 0.0323094 0.999478i \(-0.489714\pi\)
0.0323094 + 0.999478i \(0.489714\pi\)
\(620\) −1.04519 1.79315i −0.0419757 0.0720147i
\(621\) −3.80385 + 27.4249i −0.152643 + 1.10052i
\(622\) −22.1332 −0.887459
\(623\) 9.84287i 0.394346i
\(624\) −14.6243 + 7.57010i −0.585441 + 0.303047i
\(625\) −12.8564 21.4409i −0.514256 0.857637i
\(626\) −45.8637 −1.83308
\(627\) 8.39578 + 25.2552i 0.335295 + 1.00860i
\(628\) 2.33151i 0.0930373i
\(629\) 4.79637 0.191244
\(630\) 1.88548 21.4329i 0.0751194 0.853906i
\(631\) 38.6410 1.53827 0.769137 0.639084i \(-0.220686\pi\)
0.769137 + 0.639084i \(0.220686\pi\)
\(632\) 36.2539 1.44210
\(633\) 0.988427 + 1.90949i 0.0392865 + 0.0758956i
\(634\) 34.5807i 1.37338i
\(635\) 11.9909 + 20.5719i 0.475845 + 0.816373i
\(636\) −1.85641 + 0.960947i −0.0736113 + 0.0381040i
\(637\) 5.24796 0.207932
\(638\) −6.97707 + 44.1558i −0.276225 + 1.74815i
\(639\) −32.7846 23.1822i −1.29694 0.917074i
\(640\) −25.1954 + 14.6858i −0.995935 + 0.580508i
\(641\) 3.30890i 0.130694i −0.997863 0.0653469i \(-0.979185\pi\)
0.997863 0.0653469i \(-0.0208154\pi\)
\(642\) −2.55378 + 1.32194i −0.100790 + 0.0521727i
\(643\) 29.7155i 1.17187i 0.810359 + 0.585933i \(0.199272\pi\)
−0.810359 + 0.585933i \(0.800728\pi\)
\(644\) −3.04078 −0.119823
\(645\) 31.0918 + 19.7278i 1.22424 + 0.776782i
\(646\) 28.7064i 1.12944i
\(647\) 11.9229 0.468739 0.234370 0.972148i \(-0.424697\pi\)
0.234370 + 0.972148i \(0.424697\pi\)
\(648\) −22.1332 + 7.82526i −0.869473 + 0.307405i
\(649\) −2.53590 + 16.0490i −0.0995427 + 0.629977i
\(650\) −13.9541 7.90327i −0.547326 0.309992i
\(651\) −11.3483 + 5.87433i −0.444776 + 0.230233i
\(652\) 1.59245i 0.0623652i
\(653\) 17.8548 0.698713 0.349357 0.936990i \(-0.386400\pi\)
0.349357 + 0.936990i \(0.386400\pi\)
\(654\) 29.3205 15.1774i 1.14652 0.593484i
\(655\) 0 0
\(656\) 10.7057 0.417989
\(657\) 3.68886 5.21684i 0.143916 0.203528i
\(658\) 9.86707i 0.384658i
\(659\) 21.4115 0.834073 0.417036 0.908890i \(-0.363069\pi\)
0.417036 + 0.908890i \(0.363069\pi\)
\(660\) 2.58280 + 2.27499i 0.100536 + 0.0885540i
\(661\) −4.53590 −0.176426 −0.0882130 0.996102i \(-0.528116\pi\)
−0.0882130 + 0.996102i \(0.528116\pi\)
\(662\) 12.8548i 0.499617i
\(663\) 6.97707 + 13.4787i 0.270967 + 0.523468i
\(664\) −24.3397 −0.944565
\(665\) 19.0617 11.1106i 0.739181 0.430852i
\(666\) −3.04078 + 4.30031i −0.117828 + 0.166634i
\(667\) −47.6903 −1.84658
\(668\) 3.52359i 0.136332i
\(669\) 10.0526 + 19.4201i 0.388654 + 0.750823i
\(670\) −20.8799 35.8221i −0.806661 1.38393i
\(671\) −1.75559 + 11.1106i −0.0677739 + 0.428921i
\(672\) −2.55378 4.93353i −0.0985144 0.190315i
\(673\) 49.8201 1.92042 0.960212 0.279272i \(-0.0900931\pi\)
0.960212 + 0.279272i \(0.0900931\pi\)
\(674\) 25.4286i 0.979475i
\(675\) −20.6332 15.7883i −0.794174 0.607691i
\(676\) 2.26795 0.0872288
\(677\) 13.9573i 0.536421i 0.963360 + 0.268211i \(0.0864323\pi\)
−0.963360 + 0.268211i \(0.913568\pi\)
\(678\) 12.7786 + 24.6863i 0.490759 + 0.948073i
\(679\) 2.48278i 0.0952805i
\(680\) 12.0846 + 20.7327i 0.463425 + 0.795064i
\(681\) −7.42976 14.3532i −0.284709 0.550015i
\(682\) 2.70043 17.0903i 0.103405 0.654420i
\(683\) 8.02226 0.306963 0.153482 0.988152i \(-0.450951\pi\)
0.153482 + 0.988152i \(0.450951\pi\)
\(684\) 3.04078 + 2.15015i 0.116267 + 0.0822132i
\(685\) 2.53590 + 4.35066i 0.0968917 + 0.166230i
\(686\) 30.3548i 1.15895i
\(687\) −32.7950 + 16.9759i −1.25121 + 0.647672i
\(688\) 42.4424 1.61810
\(689\) 9.59274 0.365454
\(690\) −16.6506 + 26.2420i −0.633878 + 0.999015i
\(691\) −29.8564 −1.13579 −0.567896 0.823101i \(-0.692242\pi\)
−0.567896 + 0.823101i \(0.692242\pi\)
\(692\) 3.89814i 0.148185i
\(693\) 14.7851 15.1808i 0.561638 0.576670i
\(694\) 41.2679 1.56651
\(695\) −33.4024 + 19.4695i −1.26703 + 0.738520i
\(696\) −18.5885 35.9101i −0.704594 1.36117i
\(697\) 9.86707i 0.373742i
\(698\) −38.1234 −1.44299
\(699\) −8.07235 15.5946i −0.305324 0.589841i
\(700\) 1.40619 2.48278i 0.0531488 0.0938404i
\(701\) 19.0133 0.718122 0.359061 0.933314i \(-0.383097\pi\)
0.359061 + 0.933314i \(0.383097\pi\)
\(702\) −16.5079 2.28966i −0.623051 0.0864177i
\(703\) −5.40087 −0.203698
\(704\) −21.8189 3.44760i −0.822329 0.129936i
\(705\) 10.0605 + 6.38342i 0.378900 + 0.240413i
\(706\) 2.48278i 0.0934408i
\(707\) 19.0617 0.716889
\(708\) 1.04519 + 2.01915i 0.0392805 + 0.0758842i
\(709\) −29.0718 −1.09181 −0.545907 0.837846i \(-0.683815\pi\)
−0.545907 + 0.837846i \(0.683815\pi\)
\(710\) −22.6967 38.9390i −0.851791 1.46135i
\(711\) 34.0450 + 24.0734i 1.27679 + 0.902825i
\(712\) 12.0550 0.451781
\(713\) 18.4583 0.691268
\(714\) −20.2985 + 10.5073i −0.759651 + 0.393225i
\(715\) −5.72664 14.7201i −0.214164 0.550499i
\(716\) 5.17638i 0.193450i
\(717\) −24.8336 + 12.8548i −0.927428 + 0.480072i
\(718\) 2.64387i 0.0986684i
\(719\) 6.48906i 0.242001i −0.992652 0.121001i \(-0.961390\pi\)
0.992652 0.121001i \(-0.0386103\pi\)
\(720\) −29.8309 2.62427i −1.11173 0.0978007i
\(721\) 12.6574i 0.471387i
\(722\) 3.71087i 0.138104i
\(723\) 10.0782 + 19.4695i 0.374811 + 0.724079i
\(724\) 2.53590 0.0942459
\(725\) 22.0541 38.9390i 0.819068 1.44616i
\(726\) 4.69102 + 28.3065i 0.174100 + 1.05055i
\(727\) 31.7347i 1.17697i −0.808507 0.588487i \(-0.799724\pi\)
0.808507 0.588487i \(-0.200276\pi\)
\(728\) 11.8315i 0.438505i
\(729\) −25.9808 7.34847i −0.962250 0.272166i
\(730\) 6.19615 3.61160i 0.229330 0.133671i
\(731\) 39.1175i 1.44681i
\(732\) 0.723579 + 1.39785i 0.0267442 + 0.0516659i
\(733\) 2.12976 0.0786647 0.0393323 0.999226i \(-0.487477\pi\)
0.0393323 + 0.999226i \(0.487477\pi\)
\(734\) 22.5245 0.831394
\(735\) 8.05820 + 5.11296i 0.297231 + 0.188594i
\(736\) 8.02448i 0.295786i
\(737\) 6.37363 40.3369i 0.234776 1.48583i
\(738\) 8.84657 + 6.25547i 0.325647 + 0.230267i
\(739\) 42.6052i 1.56726i −0.621230 0.783629i \(-0.713367\pi\)
0.621230 0.783629i \(-0.286633\pi\)
\(740\) −0.603439 + 0.351731i −0.0221829 + 0.0129299i
\(741\) −7.85641 15.1774i −0.288612 0.557556i
\(742\) 14.4464i 0.530344i
\(743\) 19.1741i 0.703430i −0.936107 0.351715i \(-0.885599\pi\)
0.936107 0.351715i \(-0.114401\pi\)
\(744\) 7.19455 + 13.8988i 0.263765 + 0.509555i
\(745\) −17.4559 29.9478i −0.639534 1.09720i
\(746\) 14.3180i 0.524219i
\(747\) −22.8567 16.1622i −0.836285 0.591342i
\(748\) 0.570669 3.61160i 0.0208657 0.132053i
\(749\) 2.34795i 0.0857924i
\(750\) −13.7265 25.7306i −0.501222 0.939548i
\(751\) −31.7128 −1.15722 −0.578608 0.815605i \(-0.696404\pi\)
−0.578608 + 0.815605i \(0.696404\pi\)
\(752\) 13.7333 0.500801
\(753\) −13.5124 26.1039i −0.492419 0.951280i
\(754\) 28.7064i 1.04542i
\(755\) −20.2985 + 11.8315i −0.738737 + 0.430593i
\(756\) 0.407387 2.93716i 0.0148165 0.106824i
\(757\) 7.84792i 0.285237i −0.989778 0.142619i \(-0.954448\pi\)
0.989778 0.142619i \(-0.0455523\pi\)
\(758\) 4.40979i 0.160171i
\(759\) −29.0466 + 9.65617i −1.05432 + 0.350497i
\(760\) −13.6077 23.3457i −0.493603 0.846839i
\(761\) −49.5471 −1.79608 −0.898040 0.439913i \(-0.855009\pi\)
−0.898040 + 0.439913i \(0.855009\pi\)
\(762\) 12.7689 + 24.6677i 0.462569 + 0.893615i
\(763\) 26.9573i 0.975921i
\(764\) 2.55103i 0.0922929i
\(765\) −2.41869 + 27.4940i −0.0874478 + 0.994047i
\(766\) 31.5218i 1.13893i
\(767\) 10.4337i 0.376738i
\(768\) −9.72214 + 5.03255i −0.350817 + 0.181596i
\(769\) 43.8466i 1.58115i 0.612366 + 0.790574i \(0.290218\pi\)
−0.612366 + 0.790574i \(0.709782\pi\)
\(770\) 22.1680 8.62416i 0.798878 0.310793i
\(771\) 45.7128 23.6627i 1.64631 0.852191i
\(772\) −2.85334 −0.102694
\(773\) −26.8631 −0.966198 −0.483099 0.875566i \(-0.660489\pi\)
−0.483099 + 0.875566i \(0.660489\pi\)
\(774\) 35.0718 + 24.7995i 1.26063 + 0.891400i
\(775\) −8.53590 + 15.0711i −0.306619 + 0.541370i
\(776\) 3.04078 0.109157
\(777\) 1.97685 + 3.81899i 0.0709193 + 0.137005i
\(778\) 31.4877 1.12889
\(779\) 11.1106i 0.398080i
\(780\) −1.86622 1.18412i −0.0668215 0.0423985i
\(781\) 6.92820 43.8466i 0.247911 1.56895i
\(782\) 33.0158 1.18064
\(783\) 6.38929 46.0653i 0.228335 1.64624i
\(784\) 11.0000 0.392857
\(785\) −16.8096 + 9.79796i −0.599962 + 0.349704i
\(786\) 0 0
\(787\) −22.2861 −0.794413 −0.397206 0.917729i \(-0.630020\pi\)
−0.397206 + 0.917729i \(0.630020\pi\)
\(788\) 2.12574i 0.0757264i
\(789\) 12.2261 + 23.6191i 0.435262 + 0.840861i
\(790\) 23.5692 + 40.4360i 0.838555 + 1.43865i
\(791\) 22.6967 0.807000
\(792\) −18.5926 18.1079i −0.660658 0.643438i
\(793\) 7.22319i 0.256503i
\(794\) 7.83714 0.278130
\(795\) 14.7296 + 9.34597i 0.522405 + 0.331467i
\(796\) −2.92820 −0.103787
\(797\) −35.2679 −1.24925 −0.624627 0.780923i \(-0.714749\pi\)
−0.624627 + 0.780923i \(0.714749\pi\)
\(798\) 22.8567 11.8315i 0.809120 0.418831i
\(799\) 12.6574i 0.447787i
\(800\) −6.55196 3.71087i −0.231647 0.131199i
\(801\) 11.3205 + 8.00481i 0.399990 + 0.282836i
\(802\) 38.7535 1.36843
\(803\) 6.97707 + 1.10245i 0.246215 + 0.0389045i
\(804\) −2.62693 5.07484i −0.0926448 0.178976i
\(805\) 12.7786 + 21.9233i 0.450386 + 0.772694i
\(806\) 11.1106i 0.391355i
\(807\) −6.75620 13.0520i −0.237829 0.459451i
\(808\) 23.3457i 0.821300i
\(809\) −7.66496 −0.269486 −0.134743 0.990881i \(-0.543021\pi\)
−0.134743 + 0.990881i \(0.543021\pi\)
\(810\) −23.1170 19.5990i −0.812250 0.688639i
\(811\) 36.7309i 1.28980i 0.764269 + 0.644898i \(0.223100\pi\)
−0.764269 + 0.644898i \(0.776900\pi\)
\(812\) 5.10757 0.179241
\(813\) 19.1679 + 37.0295i 0.672247 + 1.29868i
\(814\) −5.75129 0.908762i −0.201583 0.0318521i
\(815\) 11.4812 6.69213i 0.402169 0.234415i
\(816\) 14.6243 + 28.2520i 0.511953 + 0.989018i
\(817\) 44.0476i 1.54103i
\(818\) 29.2768 1.02364
\(819\) −7.85641 + 11.1106i −0.274525 + 0.388237i
\(820\) 0.723579 + 1.24139i 0.0252685 + 0.0433513i
\(821\) 41.7100 1.45569 0.727844 0.685743i \(-0.240523\pi\)
0.727844 + 0.685743i \(0.240523\pi\)
\(822\) 2.70043 + 5.21684i 0.0941884 + 0.181958i
\(823\) 22.4923i 0.784034i 0.919958 + 0.392017i \(0.128222\pi\)
−0.919958 + 0.392017i \(0.871778\pi\)
\(824\) 15.5021 0.540042
\(825\) 5.54817 28.1819i 0.193162 0.981167i
\(826\) 15.7128 0.546719
\(827\) 40.0415i 1.39238i −0.717859 0.696189i \(-0.754878\pi\)
0.717859 0.696189i \(-0.245122\pi\)
\(828\) −2.47294 + 3.49726i −0.0859406 + 0.121538i
\(829\) −44.1051 −1.53183 −0.765917 0.642939i \(-0.777715\pi\)
−0.765917 + 0.642939i \(0.777715\pi\)
\(830\) −15.8236 27.1475i −0.549246 0.942302i
\(831\) −25.9726 + 13.4444i −0.900981 + 0.466382i
\(832\) 14.1848 0.491769
\(833\) 10.1383i 0.351270i
\(834\) −40.0526 + 20.7327i −1.38691 + 0.717916i
\(835\) 25.4043 14.8076i 0.879151 0.512437i
\(836\) −0.642592 + 4.06678i −0.0222245 + 0.140652i
\(837\) −2.47294 + 17.8293i −0.0854773 + 0.616271i
\(838\) 1.86492 0.0644225
\(839\) 29.0421i 1.00265i 0.865260 + 0.501323i \(0.167153\pi\)
−0.865260 + 0.501323i \(0.832847\pi\)
\(840\) −11.5272 + 18.1672i −0.397725 + 0.626829i
\(841\) 51.1051 1.76225
\(842\) 13.2294i 0.455914i
\(843\) −9.08973 + 4.70519i −0.313067 + 0.162055i
\(844\) 0.332630i 0.0114496i
\(845\) −9.53085 16.3514i −0.327871 0.562505i
\(846\) 11.3483 + 8.02448i 0.390164 + 0.275887i
\(847\) 22.2861 + 7.22319i 0.765759 + 0.248192i
\(848\) 20.1069 0.690474
\(849\) 39.0766 20.2275i 1.34110 0.694207i
\(850\) −15.2679 + 26.9573i −0.523686 + 0.924629i
\(851\) 6.21166i 0.212933i
\(852\) −2.85550 5.51641i −0.0978280 0.188989i
\(853\) 29.6638 1.01567 0.507835 0.861455i \(-0.330446\pi\)
0.507835 + 0.861455i \(0.330446\pi\)
\(854\) 10.8779 0.372235
\(855\) 2.72352 30.9591i 0.0931424 1.05878i
\(856\) 2.87564 0.0982875
\(857\) 34.8246i 1.18959i 0.803879 + 0.594793i \(0.202766\pi\)
−0.803879 + 0.594793i \(0.797234\pi\)
\(858\) −5.81236 17.4841i −0.198431 0.596897i
\(859\) 39.4641 1.34650 0.673249 0.739416i \(-0.264898\pi\)
0.673249 + 0.739416i \(0.264898\pi\)
\(860\) 2.86859 + 4.92144i 0.0978182 + 0.167820i
\(861\) 7.85641 4.06678i 0.267746 0.138595i
\(862\) 29.6012i 1.00822i
\(863\) −4.12157 −0.140300 −0.0701499 0.997536i \(-0.522348\pi\)
−0.0701499 + 0.997536i \(0.522348\pi\)
\(864\) −7.75105 1.07508i −0.263696 0.0365749i
\(865\) −28.1047 + 16.3816i −0.955589 + 0.556991i
\(866\) 56.7417 1.92816
\(867\) −0.110437 + 0.0571664i −0.00375064 + 0.00194147i
\(868\) −1.97685 −0.0670988
\(869\) −7.19455 + 45.5322i −0.244059 + 1.54458i
\(870\) 27.9679 44.0785i 0.948201 1.49440i
\(871\) 26.2236i 0.888553i
\(872\) −33.0158 −1.11806
\(873\) 2.85550 + 2.01915i 0.0966442 + 0.0683377i
\(874\) −37.1769 −1.25753
\(875\) −23.8097 + 0.295400i −0.804914 + 0.00998634i
\(876\) 0.877796 0.454381i 0.0296580 0.0153521i
\(877\) −44.4192 −1.49993 −0.749966 0.661477i \(-0.769930\pi\)
−0.749966 + 0.661477i \(0.769930\pi\)
\(878\) 12.0846 0.407837
\(879\) 3.27598 + 6.32871i 0.110496 + 0.213462i
\(880\) −12.0033 30.8540i −0.404633 1.04009i
\(881\) 5.85993i 0.197426i 0.995116 + 0.0987130i \(0.0314726\pi\)
−0.995116 + 0.0987130i \(0.968527\pi\)
\(882\) 9.08973 + 6.42741i 0.306067 + 0.216422i
\(883\) 15.8102i 0.532055i 0.963965 + 0.266027i \(0.0857111\pi\)
−0.963965 + 0.266027i \(0.914289\pi\)
\(884\) 2.34795i 0.0789702i
\(885\) 10.1653 16.0208i 0.341702 0.538535i
\(886\) 51.8711i 1.74264i
\(887\) 9.33123i 0.313312i 0.987653 + 0.156656i \(0.0500714\pi\)
−0.987653 + 0.156656i \(0.949929\pi\)
\(888\) 4.67729 2.42114i 0.156960 0.0812482i
\(889\) 22.6795 0.760646
\(890\) 7.83714 + 13.4456i 0.262702 + 0.450698i
\(891\) −5.43564 29.3505i −0.182101 0.983280i
\(892\) 3.38293i 0.113269i
\(893\) 14.2527i 0.476947i
\(894\) −18.5885 35.9101i −0.621691 1.20101i
\(895\) 37.3205 21.7533i 1.24749 0.727132i
\(896\) 27.7766i 0.927951i
\(897\) 17.4559 9.03583i 0.582835 0.301697i
\(898\) 23.6923 0.790621
\(899\) −31.0042 −1.03405
\(900\) −1.71191 3.63643i −0.0570637 0.121214i
\(901\) 18.5317i 0.617382i
\(902\) −1.86950 + 11.8315i −0.0622475 + 0.393947i
\(903\) 31.1463 16.1225i 1.03649 0.536524i
\(904\) 27.7976i 0.924535i
\(905\) −10.6569 18.2832i −0.354247 0.607755i
\(906\) −24.3397 + 12.5992i −0.808634 + 0.418580i
\(907\) 38.7292i 1.28598i 0.765874 + 0.642991i \(0.222307\pi\)
−0.765874 + 0.642991i \(0.777693\pi\)
\(908\) 2.50029i 0.0829752i
\(909\) 15.5021 21.9233i 0.514172 0.727150i
\(910\) −13.1963 + 7.69185i −0.437455 + 0.254982i
\(911\) 53.2596i 1.76457i −0.470715 0.882285i \(-0.656004\pi\)
0.470715 0.882285i \(-0.343996\pi\)
\(912\) −16.4675 31.8127i −0.545292 1.05342i
\(913\) 4.83020 30.5689i 0.159856 1.01168i
\(914\) 4.92619i 0.162944i
\(915\) 7.03738 11.0912i 0.232649 0.366663i
\(916\) −5.71281 −0.188757
\(917\) 0 0
\(918\) −4.42328 + 31.8909i −0.145990 + 1.05256i
\(919\) 24.0734i 0.794110i 0.917795 + 0.397055i \(0.129968\pi\)
−0.917795 + 0.397055i \(0.870032\pi\)
\(920\) 26.8504 15.6505i 0.885233 0.515982i
\(921\) −14.6243 + 7.57010i −0.481887 + 0.249443i
\(922\) 27.9250i 0.919663i
\(923\) 28.5053i 0.938264i
\(924\) 3.11085 1.03416i 0.102339 0.0340214i
\(925\) 5.07180 + 2.87254i 0.166760 + 0.0944485i
\(926\) 10.7057 0.351812
\(927\) 14.5576 + 10.2938i 0.478134 + 0.338091i
\(928\) 13.4787i 0.442459i
\(929\) 7.52433i 0.246865i −0.992353 0.123433i \(-0.960610\pi\)
0.992353 0.123433i \(-0.0393903\pi\)
\(930\) −10.8248 + 17.0603i −0.354960 + 0.559430i
\(931\) 11.4160i 0.374145i
\(932\) 2.71654i 0.0889833i
\(933\) 11.7021 + 22.6067i 0.383109 + 0.740109i
\(934\) 6.20696i 0.203098i
\(935\) −28.4370 + 11.0630i −0.929988 + 0.361800i
\(936\) 13.6077 + 9.62209i 0.444781 + 0.314508i
\(937\) −59.1747 −1.93315 −0.966576 0.256379i \(-0.917471\pi\)
−0.966576 + 0.256379i \(0.917471\pi\)
\(938\) −39.4920 −1.28946
\(939\) 24.2487 + 46.8449i 0.791327 + 1.52873i
\(940\) 0.928203 + 1.59245i 0.0302747 + 0.0519400i
\(941\) −23.3393 −0.760838 −0.380419 0.924814i \(-0.624220\pi\)
−0.380419 + 0.924814i \(0.624220\pi\)
\(942\) −20.1563 + 10.4337i −0.656728 + 0.339947i
\(943\) −12.7786 −0.416128
\(944\) 21.8695i 0.711793i
\(945\) −22.8883 + 9.40601i −0.744556 + 0.305977i
\(946\) −7.41154 + 46.9055i −0.240970 + 1.52503i
\(947\) −39.5512 −1.28524 −0.642620 0.766185i \(-0.722153\pi\)
−0.642620 + 0.766185i \(0.722153\pi\)
\(948\) 2.96528 + 5.72848i 0.0963079 + 0.186053i
\(949\) −4.53590 −0.147241
\(950\) 17.1922 30.3548i 0.557789 0.984841i
\(951\) −35.3205 + 18.2832i −1.14535 + 0.592875i
\(952\) 22.8567 0.740791
\(953\) 32.6197i 1.05666i 0.849040 + 0.528328i \(0.177181\pi\)
−0.849040 + 0.528328i \(0.822819\pi\)
\(954\) 16.6151 + 11.7487i 0.537934 + 0.380377i
\(955\) −18.3923 + 10.7205i −0.595161 + 0.346906i
\(956\) −4.32596 −0.139912
\(957\) 48.7893 16.2194i 1.57714 0.524299i
\(958\) 36.8244i 1.18974i
\(959\) 4.79637 0.154883
\(960\) 21.7806 + 13.8199i 0.702967 + 0.446035i
\(961\) −19.0000 −0.612903
\(962\) 3.73900 0.120550
\(963\) 2.70043 + 1.90949i 0.0870203 + 0.0615326i
\(964\) 3.39154i 0.109234i
\(965\) 11.9909 + 20.5719i 0.386001 + 0.662234i
\(966\) 13.6077 + 26.2880i 0.437820 + 0.845804i
\(967\) −9.50749 −0.305740 −0.152870 0.988246i \(-0.548852\pi\)
−0.152870 + 0.988246i \(0.548852\pi\)
\(968\) 8.84657 27.2948i 0.284339 0.877287i
\(969\) −29.3205 + 15.1774i −0.941910 + 0.487569i
\(970\) 1.97685 + 3.39154i 0.0634730 + 0.108896i
\(971\) 13.4586i 0.431907i −0.976404 0.215953i \(-0.930714\pi\)
0.976404 0.215953i \(-0.0692859\pi\)
\(972\) −3.04679 2.85722i −0.0977257 0.0916454i
\(973\) 36.8244i 1.18054i
\(974\) −48.2619 −1.54641
\(975\) −0.694628 + 18.4312i −0.0222459 + 0.590271i
\(976\) 15.1402i 0.484626i
\(977\) 20.2686 0.648449 0.324225 0.945980i \(-0.394897\pi\)
0.324225 + 0.945980i \(0.394897\pi\)
\(978\) 13.7670 7.12633i 0.440221 0.227875i
\(979\) −2.39230 + 15.1402i −0.0764584 + 0.483883i
\(980\) 0.743468 + 1.27551i 0.0237492 + 0.0407448i
\(981\) −31.0042 21.9233i −0.989888 0.699957i
\(982\) 29.6012i 0.944612i
\(983\) −15.9853 −0.509853 −0.254926 0.966960i \(-0.582051\pi\)
−0.254926 + 0.966960i \(0.582051\pi\)
\(984\) −4.98076 9.62209i −0.158781 0.306741i
\(985\) −15.3261 + 8.93324i −0.488331 + 0.284637i
\(986\) −55.4565 −1.76609
\(987\) 10.0782 5.21684i 0.320791 0.166054i
\(988\) 2.64387i 0.0841128i
\(989\) −50.6601 −1.61090
\(990\) 8.10948 32.5096i 0.257736 1.03322i
\(991\) 0.248711 0.00790058 0.00395029 0.999992i \(-0.498743\pi\)
0.00395029 + 0.999992i \(0.498743\pi\)
\(992\) 5.21684i 0.165635i
\(993\) −13.1298 + 6.79650i −0.416662 + 0.215680i
\(994\) −42.9282 −1.36160
\(995\) 12.3055 + 21.1117i 0.390111 + 0.669285i
\(996\) −1.99080 3.84593i −0.0630808 0.121863i
\(997\) 40.1597 1.27187 0.635935 0.771742i \(-0.280614\pi\)
0.635935 + 0.771742i \(0.280614\pi\)
\(998\) 4.40979i 0.139589i
\(999\) 6.00000 + 0.832204i 0.189832 + 0.0263298i
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 165.2.d.c.164.6 yes 16
3.2 odd 2 inner 165.2.d.c.164.12 yes 16
5.2 odd 4 825.2.f.f.626.12 16
5.3 odd 4 825.2.f.f.626.5 16
5.4 even 2 inner 165.2.d.c.164.11 yes 16
11.10 odd 2 inner 165.2.d.c.164.10 yes 16
15.2 even 4 825.2.f.f.626.7 16
15.8 even 4 825.2.f.f.626.10 16
15.14 odd 2 inner 165.2.d.c.164.5 16
33.32 even 2 inner 165.2.d.c.164.8 yes 16
55.32 even 4 825.2.f.f.626.8 16
55.43 even 4 825.2.f.f.626.9 16
55.54 odd 2 inner 165.2.d.c.164.7 yes 16
165.32 odd 4 825.2.f.f.626.11 16
165.98 odd 4 825.2.f.f.626.6 16
165.164 even 2 inner 165.2.d.c.164.9 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.d.c.164.5 16 15.14 odd 2 inner
165.2.d.c.164.6 yes 16 1.1 even 1 trivial
165.2.d.c.164.7 yes 16 55.54 odd 2 inner
165.2.d.c.164.8 yes 16 33.32 even 2 inner
165.2.d.c.164.9 yes 16 165.164 even 2 inner
165.2.d.c.164.10 yes 16 11.10 odd 2 inner
165.2.d.c.164.11 yes 16 5.4 even 2 inner
165.2.d.c.164.12 yes 16 3.2 odd 2 inner
825.2.f.f.626.5 16 5.3 odd 4
825.2.f.f.626.6 16 165.98 odd 4
825.2.f.f.626.7 16 15.2 even 4
825.2.f.f.626.8 16 55.32 even 4
825.2.f.f.626.9 16 55.43 even 4
825.2.f.f.626.10 16 15.8 even 4
825.2.f.f.626.11 16 165.32 odd 4
825.2.f.f.626.12 16 5.2 odd 4