Properties

Label 930.2.h.c.371.10
Level $930$
Weight $2$
Character 930.371
Analytic conductor $7.426$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(371,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.371");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.h (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: \(7.42608738798\)
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: \( x^{16} - 2x^{14} + 10x^{12} - 42x^{10} + 82x^{8} - 378x^{6} + 810x^{4} - 1458x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 371.10
Root \(-1.06195 - 1.36831i\) of defining polynomial
Character \(\chi\) \(=\) 930.371
Dual form 930.2.h.c.371.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.36831 + 1.06195i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.06195 - 1.36831i) q^{6} +1.28192 q^{7} -1.00000i q^{8} +(0.744540 - 2.90614i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.36831 + 1.06195i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.06195 - 1.36831i) q^{6} +1.28192 q^{7} -1.00000i q^{8} +(0.744540 - 2.90614i) q^{9} -1.00000 q^{10} -0.392733 q^{11} +(1.36831 - 1.06195i) q^{12} +4.84655i q^{13} +1.28192i q^{14} +(-1.06195 - 1.36831i) q^{15} +1.00000 q^{16} -6.52820 q^{17} +(2.90614 + 0.744540i) q^{18} -4.77100 q^{19} -1.00000i q^{20} +(-1.75406 + 1.36133i) q^{21} -0.392733i q^{22} -2.51663 q^{23} +(1.06195 + 1.36831i) q^{24} -1.00000 q^{25} -4.84655 q^{26} +(2.06741 + 4.76716i) q^{27} -1.28192 q^{28} -4.57705 q^{29} +(1.36831 - 1.06195i) q^{30} +(4.60512 - 3.12935i) q^{31} +1.00000i q^{32} +(0.537380 - 0.417061i) q^{33} -6.52820i q^{34} +1.28192i q^{35} +(-0.744540 + 2.90614i) q^{36} -2.12389i q^{37} -4.77100i q^{38} +(-5.14678 - 6.63158i) q^{39} +1.00000 q^{40} -5.07476i q^{41} +(-1.36133 - 1.75406i) q^{42} -3.28588i q^{43} +0.392733 q^{44} +(2.90614 + 0.744540i) q^{45} -2.51663i q^{46} +0.834122i q^{47} +(-1.36831 + 1.06195i) q^{48} -5.35668 q^{49} -1.00000i q^{50} +(8.93260 - 6.93260i) q^{51} -4.84655i q^{52} -0.123231 q^{53} +(-4.76716 + 2.06741i) q^{54} -0.392733i q^{55} -1.28192i q^{56} +(6.52820 - 5.06655i) q^{57} -4.57705i q^{58} +5.86520i q^{59} +(1.06195 + 1.36831i) q^{60} -9.87755i q^{61} +(3.12935 + 4.60512i) q^{62} +(0.954441 - 3.72544i) q^{63} -1.00000 q^{64} -4.84655 q^{65} +(0.417061 + 0.537380i) q^{66} +10.9782 q^{67} +6.52820 q^{68} +(3.44352 - 2.67252i) q^{69} -1.28192 q^{70} -9.33484i q^{71} +(-2.90614 - 0.744540i) q^{72} +9.18740i q^{73} +2.12389 q^{74} +(1.36831 - 1.06195i) q^{75} +4.77100 q^{76} -0.503452 q^{77} +(6.63158 - 5.14678i) q^{78} +6.12151i q^{79} +1.00000i q^{80} +(-7.89132 - 4.32748i) q^{81} +5.07476 q^{82} -2.73662 q^{83} +(1.75406 - 1.36133i) q^{84} -6.52820i q^{85} +3.28588 q^{86} +(6.26282 - 4.86058i) q^{87} +0.392733i q^{88} -11.0557 q^{89} +(-0.744540 + 2.90614i) q^{90} +6.21290i q^{91} +2.51663 q^{92} +(-2.97803 + 9.17231i) q^{93} -0.834122 q^{94} -4.77100i q^{95} +(-1.06195 - 1.36831i) q^{96} -17.9181 q^{97} -5.35668i q^{98} +(-0.292405 + 1.14134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9} - 16 q^{10} + 16 q^{16} + 12 q^{18} - 4 q^{19} - 16 q^{25} + 20 q^{28} - 4 q^{31} - 16 q^{33} + 4 q^{36} - 4 q^{39} + 16 q^{40} + 12 q^{45} + 4 q^{49} + 52 q^{51} - 12 q^{63} - 16 q^{64} + 4 q^{66} + 112 q^{67} - 4 q^{69} + 20 q^{70} - 12 q^{72} + 4 q^{76} - 28 q^{78} - 32 q^{81} + 32 q^{82} - 24 q^{87} + 4 q^{90} + 16 q^{93} - 8 q^{94} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.36831 + 1.06195i −0.789994 + 0.613115i
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i
\(6\) −1.06195 1.36831i −0.433538 0.558610i
\(7\) 1.28192 0.484520 0.242260 0.970211i \(-0.422111\pi\)
0.242260 + 0.970211i \(0.422111\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.744540 2.90614i 0.248180 0.968714i
\(10\) −1.00000 −0.316228
\(11\) −0.392733 −0.118413 −0.0592067 0.998246i \(-0.518857\pi\)
−0.0592067 + 0.998246i \(0.518857\pi\)
\(12\) 1.36831 1.06195i 0.394997 0.306557i
\(13\) 4.84655i 1.34419i 0.740464 + 0.672096i \(0.234606\pi\)
−0.740464 + 0.672096i \(0.765394\pi\)
\(14\) 1.28192i 0.342608i
\(15\) −1.06195 1.36831i −0.274193 0.353296i
\(16\) 1.00000 0.250000
\(17\) −6.52820 −1.58332 −0.791661 0.610961i \(-0.790783\pi\)
−0.791661 + 0.610961i \(0.790783\pi\)
\(18\) 2.90614 + 0.744540i 0.684984 + 0.175490i
\(19\) −4.77100 −1.09454 −0.547271 0.836955i \(-0.684333\pi\)
−0.547271 + 0.836955i \(0.684333\pi\)
\(20\) 1.00000i 0.223607i
\(21\) −1.75406 + 1.36133i −0.382768 + 0.297067i
\(22\) 0.392733i 0.0837309i
\(23\) −2.51663 −0.524753 −0.262376 0.964966i \(-0.584506\pi\)
−0.262376 + 0.964966i \(0.584506\pi\)
\(24\) 1.06195 + 1.36831i 0.216769 + 0.279305i
\(25\) −1.00000 −0.200000
\(26\) −4.84655 −0.950487
\(27\) 2.06741 + 4.76716i 0.397872 + 0.917441i
\(28\) −1.28192 −0.242260
\(29\) −4.57705 −0.849937 −0.424969 0.905208i \(-0.639715\pi\)
−0.424969 + 0.905208i \(0.639715\pi\)
\(30\) 1.36831 1.06195i 0.249818 0.193884i
\(31\) 4.60512 3.12935i 0.827105 0.562048i
\(32\) 1.00000i 0.176777i
\(33\) 0.537380 0.417061i 0.0935459 0.0726010i
\(34\) 6.52820i 1.11958i
\(35\) 1.28192i 0.216684i
\(36\) −0.744540 + 2.90614i −0.124090 + 0.484357i
\(37\) 2.12389i 0.349166i −0.984642 0.174583i \(-0.944142\pi\)
0.984642 0.174583i \(-0.0558577\pi\)
\(38\) 4.77100i 0.773959i
\(39\) −5.14678 6.63158i −0.824144 1.06190i
\(40\) 1.00000 0.158114
\(41\) 5.07476i 0.792544i −0.918133 0.396272i \(-0.870304\pi\)
0.918133 0.396272i \(-0.129696\pi\)
\(42\) −1.36133 1.75406i −0.210058 0.270658i
\(43\) 3.28588i 0.501092i −0.968105 0.250546i \(-0.919390\pi\)
0.968105 0.250546i \(-0.0806101\pi\)
\(44\) 0.392733 0.0592067
\(45\) 2.90614 + 0.744540i 0.433222 + 0.110990i
\(46\) 2.51663i 0.371056i
\(47\) 0.834122i 0.121669i 0.998148 + 0.0608346i \(0.0193762\pi\)
−0.998148 + 0.0608346i \(0.980624\pi\)
\(48\) −1.36831 + 1.06195i −0.197498 + 0.153279i
\(49\) −5.35668 −0.765240
\(50\) 1.00000i 0.141421i
\(51\) 8.93260 6.93260i 1.25081 0.970758i
\(52\) 4.84655i 0.672096i
\(53\) −0.123231 −0.0169271 −0.00846355 0.999964i \(-0.502694\pi\)
−0.00846355 + 0.999964i \(0.502694\pi\)
\(54\) −4.76716 + 2.06741i −0.648729 + 0.281338i
\(55\) 0.392733i 0.0529561i
\(56\) 1.28192i 0.171304i
\(57\) 6.52820 5.06655i 0.864682 0.671080i
\(58\) 4.57705i 0.600996i
\(59\) 5.86520i 0.763585i 0.924248 + 0.381792i \(0.124693\pi\)
−0.924248 + 0.381792i \(0.875307\pi\)
\(60\) 1.06195 + 1.36831i 0.137097 + 0.176648i
\(61\) 9.87755i 1.26469i −0.774687 0.632345i \(-0.782092\pi\)
0.774687 0.632345i \(-0.217908\pi\)
\(62\) 3.12935 + 4.60512i 0.397428 + 0.584851i
\(63\) 0.954441 3.72544i 0.120248 0.469362i
\(64\) −1.00000 −0.125000
\(65\) −4.84655 −0.601141
\(66\) 0.417061 + 0.537380i 0.0513367 + 0.0661469i
\(67\) 10.9782 1.34120 0.670598 0.741821i \(-0.266038\pi\)
0.670598 + 0.741821i \(0.266038\pi\)
\(68\) 6.52820 0.791661
\(69\) 3.44352 2.67252i 0.414551 0.321734i
\(70\) −1.28192 −0.153219
\(71\) 9.33484i 1.10784i −0.832569 0.553921i \(-0.813131\pi\)
0.832569 0.553921i \(-0.186869\pi\)
\(72\) −2.90614 0.744540i −0.342492 0.0877449i
\(73\) 9.18740i 1.07530i 0.843167 + 0.537652i \(0.180689\pi\)
−0.843167 + 0.537652i \(0.819311\pi\)
\(74\) 2.12389 0.246897
\(75\) 1.36831 1.06195i 0.157999 0.122623i
\(76\) 4.77100 0.547271
\(77\) −0.503452 −0.0573737
\(78\) 6.63158 5.14678i 0.750879 0.582758i
\(79\) 6.12151i 0.688724i 0.938837 + 0.344362i \(0.111905\pi\)
−0.938837 + 0.344362i \(0.888095\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −7.89132 4.32748i −0.876813 0.480831i
\(82\) 5.07476 0.560413
\(83\) −2.73662 −0.300383 −0.150191 0.988657i \(-0.547989\pi\)
−0.150191 + 0.988657i \(0.547989\pi\)
\(84\) 1.75406 1.36133i 0.191384 0.148533i
\(85\) 6.52820i 0.708083i
\(86\) 3.28588 0.354325
\(87\) 6.26282 4.86058i 0.671445 0.521109i
\(88\) 0.392733i 0.0418655i
\(89\) −11.0557 −1.17191 −0.585953 0.810345i \(-0.699280\pi\)
−0.585953 + 0.810345i \(0.699280\pi\)
\(90\) −0.744540 + 2.90614i −0.0784814 + 0.306334i
\(91\) 6.21290i 0.651288i
\(92\) 2.51663 0.262376
\(93\) −2.97803 + 9.17231i −0.308807 + 0.951125i
\(94\) −0.834122 −0.0860332
\(95\) 4.77100i 0.489494i
\(96\) −1.06195 1.36831i −0.108384 0.139652i
\(97\) −17.9181 −1.81931 −0.909655 0.415365i \(-0.863654\pi\)
−0.909655 + 0.415365i \(0.863654\pi\)
\(98\) 5.35668i 0.541106i
\(99\) −0.292405 + 1.14134i −0.0293879 + 0.114709i
\(100\) 1.00000 0.100000
\(101\) 5.01164i 0.498677i 0.968416 + 0.249338i \(0.0802131\pi\)
−0.968416 + 0.249338i \(0.919787\pi\)
\(102\) 6.93260 + 8.93260i 0.686430 + 0.884459i
\(103\) −6.96961 −0.686736 −0.343368 0.939201i \(-0.611568\pi\)
−0.343368 + 0.939201i \(0.611568\pi\)
\(104\) 4.84655 0.475244
\(105\) −1.36133 1.75406i −0.132852 0.171179i
\(106\) 0.123231i 0.0119693i
\(107\) 13.7406i 1.32835i 0.747575 + 0.664177i \(0.231218\pi\)
−0.747575 + 0.664177i \(0.768782\pi\)
\(108\) −2.06741 4.76716i −0.198936 0.458720i
\(109\) −8.88704 −0.851224 −0.425612 0.904906i \(-0.639941\pi\)
−0.425612 + 0.904906i \(0.639941\pi\)
\(110\) 0.392733 0.0374456
\(111\) 2.25546 + 2.90614i 0.214079 + 0.275839i
\(112\) 1.28192 0.121130
\(113\) 4.34265i 0.408522i −0.978916 0.204261i \(-0.934521\pi\)
0.978916 0.204261i \(-0.0654791\pi\)
\(114\) 5.06655 + 6.52820i 0.474526 + 0.611422i
\(115\) 2.51663i 0.234677i
\(116\) 4.57705 0.424969
\(117\) 14.0848 + 3.60845i 1.30214 + 0.333602i
\(118\) −5.86520 −0.539936
\(119\) −8.36864 −0.767152
\(120\) −1.36831 + 1.06195i −0.124909 + 0.0969420i
\(121\) −10.8458 −0.985978
\(122\) 9.87755 0.894271
\(123\) 5.38912 + 6.94384i 0.485921 + 0.626105i
\(124\) −4.60512 + 3.12935i −0.413552 + 0.281024i
\(125\) 1.00000i 0.0894427i
\(126\) 3.72544 + 0.954441i 0.331889 + 0.0850284i
\(127\) 10.7481i 0.953737i −0.878975 0.476869i \(-0.841772\pi\)
0.878975 0.476869i \(-0.158228\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 3.48943 + 4.49610i 0.307227 + 0.395859i
\(130\) 4.84655i 0.425071i
\(131\) 14.9782i 1.30865i 0.756214 + 0.654324i \(0.227047\pi\)
−0.756214 + 0.654324i \(0.772953\pi\)
\(132\) −0.537380 + 0.417061i −0.0467729 + 0.0363005i
\(133\) −6.11604 −0.530328
\(134\) 10.9782i 0.948369i
\(135\) −4.76716 + 2.06741i −0.410292 + 0.177934i
\(136\) 6.52820i 0.559789i
\(137\) 18.3592 1.56853 0.784265 0.620427i \(-0.213041\pi\)
0.784265 + 0.620427i \(0.213041\pi\)
\(138\) 2.67252 + 3.44352i 0.227500 + 0.293132i
\(139\) 5.31671i 0.450957i −0.974248 0.225479i \(-0.927605\pi\)
0.974248 0.225479i \(-0.0723946\pi\)
\(140\) 1.28192i 0.108342i
\(141\) −0.885793 1.14134i −0.0745972 0.0961180i
\(142\) 9.33484 0.783362
\(143\) 1.90340i 0.159170i
\(144\) 0.744540 2.90614i 0.0620450 0.242178i
\(145\) 4.57705i 0.380103i
\(146\) −9.18740 −0.760355
\(147\) 7.32960 5.68851i 0.604535 0.469180i
\(148\) 2.12389i 0.174583i
\(149\) 5.26789i 0.431562i −0.976442 0.215781i \(-0.930770\pi\)
0.976442 0.215781i \(-0.0692297\pi\)
\(150\) 1.06195 + 1.36831i 0.0867075 + 0.111722i
\(151\) 4.12085i 0.335350i 0.985842 + 0.167675i \(0.0536260\pi\)
−0.985842 + 0.167675i \(0.946374\pi\)
\(152\) 4.77100i 0.386979i
\(153\) −4.86051 + 18.9719i −0.392949 + 1.53379i
\(154\) 0.503452i 0.0405693i
\(155\) 3.12935 + 4.60512i 0.251356 + 0.369892i
\(156\) 5.14678 + 6.63158i 0.412072 + 0.530952i
\(157\) −2.19861 −0.175468 −0.0877340 0.996144i \(-0.527963\pi\)
−0.0877340 + 0.996144i \(0.527963\pi\)
\(158\) −6.12151 −0.487002
\(159\) 0.168618 0.130865i 0.0133723 0.0103783i
\(160\) −1.00000 −0.0790569
\(161\) −3.22611 −0.254253
\(162\) 4.32748 7.89132i 0.339999 0.620001i
\(163\) 12.1058 0.948203 0.474101 0.880470i \(-0.342773\pi\)
0.474101 + 0.880470i \(0.342773\pi\)
\(164\) 5.07476i 0.396272i
\(165\) 0.417061 + 0.537380i 0.0324682 + 0.0418350i
\(166\) 2.73662i 0.212403i
\(167\) 16.9254 1.30973 0.654864 0.755747i \(-0.272726\pi\)
0.654864 + 0.755747i \(0.272726\pi\)
\(168\) 1.36133 + 1.75406i 0.105029 + 0.135329i
\(169\) −10.4891 −0.806852
\(170\) 6.52820 0.500690
\(171\) −3.55220 + 13.8652i −0.271644 + 1.06030i
\(172\) 3.28588i 0.250546i
\(173\) 18.7522i 1.42571i 0.701313 + 0.712854i \(0.252598\pi\)
−0.701313 + 0.712854i \(0.747402\pi\)
\(174\) 4.86058 + 6.26282i 0.368480 + 0.474783i
\(175\) −1.28192 −0.0969041
\(176\) −0.392733 −0.0296034
\(177\) −6.22853 8.02541i −0.468165 0.603227i
\(178\) 11.0557i 0.828663i
\(179\) −2.59405 −0.193888 −0.0969442 0.995290i \(-0.530907\pi\)
−0.0969442 + 0.995290i \(0.530907\pi\)
\(180\) −2.90614 0.744540i −0.216611 0.0554948i
\(181\) 4.02779i 0.299383i 0.988733 + 0.149692i \(0.0478281\pi\)
−0.988733 + 0.149692i \(0.952172\pi\)
\(182\) −6.21290 −0.460530
\(183\) 10.4894 + 13.5155i 0.775401 + 0.999098i
\(184\) 2.51663i 0.185528i
\(185\) 2.12389 0.156152
\(186\) −9.17231 2.97803i −0.672547 0.218360i
\(187\) 2.56384 0.187487
\(188\) 0.834122i 0.0608346i
\(189\) 2.65025 + 6.11112i 0.192777 + 0.444519i
\(190\) 4.77100 0.346125
\(191\) 7.48908i 0.541891i −0.962595 0.270945i \(-0.912664\pi\)
0.962595 0.270945i \(-0.0873363\pi\)
\(192\) 1.36831 1.06195i 0.0987492 0.0766394i
\(193\) −19.5334 −1.40605 −0.703024 0.711166i \(-0.748167\pi\)
−0.703024 + 0.711166i \(0.748167\pi\)
\(194\) 17.9181i 1.28645i
\(195\) 6.63158 5.14678i 0.474898 0.368569i
\(196\) 5.35668 0.382620
\(197\) 0.598768 0.0426605 0.0213302 0.999772i \(-0.493210\pi\)
0.0213302 + 0.999772i \(0.493210\pi\)
\(198\) −1.14134 0.292405i −0.0811113 0.0207804i
\(199\) 12.0672i 0.855419i 0.903916 + 0.427709i \(0.140679\pi\)
−0.903916 + 0.427709i \(0.859321\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −15.0215 + 11.6582i −1.05954 + 0.822307i
\(202\) −5.01164 −0.352618
\(203\) −5.86742 −0.411812
\(204\) −8.93260 + 6.93260i −0.625407 + 0.485379i
\(205\) 5.07476 0.354437
\(206\) 6.96961i 0.485596i
\(207\) −1.87373 + 7.31367i −0.130233 + 0.508335i
\(208\) 4.84655i 0.336048i
\(209\) 1.87373 0.129609
\(210\) 1.75406 1.36133i 0.121042 0.0939407i
\(211\) −15.3737 −1.05837 −0.529186 0.848506i \(-0.677502\pi\)
−0.529186 + 0.848506i \(0.677502\pi\)
\(212\) 0.123231 0.00846355
\(213\) 9.91310 + 12.7729i 0.679234 + 0.875188i
\(214\) −13.7406 −0.939289
\(215\) 3.28588 0.224095
\(216\) 4.76716 2.06741i 0.324364 0.140669i
\(217\) 5.90340 4.01158i 0.400749 0.272324i
\(218\) 8.88704i 0.601907i
\(219\) −9.75652 12.5712i −0.659285 0.849483i
\(220\) 0.392733i 0.0264780i
\(221\) 31.6393i 2.12829i
\(222\) −2.90614 + 2.25546i −0.195047 + 0.151377i
\(223\) 18.0137i 1.20629i −0.797633 0.603143i \(-0.793915\pi\)
0.797633 0.603143i \(-0.206085\pi\)
\(224\) 1.28192i 0.0856519i
\(225\) −0.744540 + 2.90614i −0.0496360 + 0.193743i
\(226\) 4.34265 0.288869
\(227\) 24.3045i 1.61314i 0.591137 + 0.806572i \(0.298679\pi\)
−0.591137 + 0.806572i \(0.701321\pi\)
\(228\) −6.52820 + 5.06655i −0.432341 + 0.335540i
\(229\) 16.4436i 1.08662i 0.839532 + 0.543311i \(0.182829\pi\)
−0.839532 + 0.543311i \(0.817171\pi\)
\(230\) 2.51663 0.165941
\(231\) 0.688878 0.534639i 0.0453249 0.0351767i
\(232\) 4.57705i 0.300498i
\(233\) 24.9298i 1.63320i 0.577202 + 0.816602i \(0.304145\pi\)
−0.577202 + 0.816602i \(0.695855\pi\)
\(234\) −3.60845 + 14.0848i −0.235892 + 0.920750i
\(235\) −0.834122 −0.0544121
\(236\) 5.86520i 0.381792i
\(237\) −6.50072 8.37612i −0.422267 0.544088i
\(238\) 8.36864i 0.542458i
\(239\) −8.26962 −0.534917 −0.267459 0.963569i \(-0.586184\pi\)
−0.267459 + 0.963569i \(0.586184\pi\)
\(240\) −1.06195 1.36831i −0.0685483 0.0883240i
\(241\) 12.4895i 0.804519i 0.915526 + 0.402259i \(0.131775\pi\)
−0.915526 + 0.402259i \(0.868225\pi\)
\(242\) 10.8458i 0.697192i
\(243\) 15.3933 2.45883i 0.987482 0.157734i
\(244\) 9.87755i 0.632345i
\(245\) 5.35668i 0.342226i
\(246\) −6.94384 + 5.38912i −0.442723 + 0.343598i
\(247\) 23.1229i 1.47128i
\(248\) −3.12935 4.60512i −0.198714 0.292426i
\(249\) 3.74454 2.90614i 0.237301 0.184169i
\(250\) 1.00000 0.0632456
\(251\) 25.1708 1.58877 0.794384 0.607416i \(-0.207794\pi\)
0.794384 + 0.607416i \(0.207794\pi\)
\(252\) −0.954441 + 3.72544i −0.0601241 + 0.234681i
\(253\) 0.988362 0.0621378
\(254\) 10.7481 0.674394
\(255\) 6.93260 + 8.93260i 0.434136 + 0.559381i
\(256\) 1.00000 0.0625000
\(257\) 23.3737i 1.45801i 0.684507 + 0.729007i \(0.260018\pi\)
−0.684507 + 0.729007i \(0.739982\pi\)
\(258\) −4.49610 + 3.48943i −0.279915 + 0.217242i
\(259\) 2.72266i 0.169178i
\(260\) 4.84655 0.300570
\(261\) −3.40780 + 13.3016i −0.210937 + 0.823346i
\(262\) −14.9782 −0.925354
\(263\) 10.4026 0.641451 0.320726 0.947172i \(-0.396073\pi\)
0.320726 + 0.947172i \(0.396073\pi\)
\(264\) −0.417061 0.537380i −0.0256683 0.0330735i
\(265\) 0.123231i 0.00757003i
\(266\) 6.11604i 0.374999i
\(267\) 15.1277 11.7406i 0.925799 0.718514i
\(268\) −10.9782 −0.670598
\(269\) −23.5925 −1.43846 −0.719230 0.694772i \(-0.755505\pi\)
−0.719230 + 0.694772i \(0.755505\pi\)
\(270\) −2.06741 4.76716i −0.125818 0.290120i
\(271\) 24.7707i 1.50471i 0.658757 + 0.752356i \(0.271083\pi\)
−0.658757 + 0.752356i \(0.728917\pi\)
\(272\) −6.52820 −0.395831
\(273\) −6.59776 8.50116i −0.399315 0.514514i
\(274\) 18.3592i 1.10912i
\(275\) 0.392733 0.0236827
\(276\) −3.44352 + 2.67252i −0.207276 + 0.160867i
\(277\) 20.0687i 1.20581i 0.797812 + 0.602906i \(0.205991\pi\)
−0.797812 + 0.602906i \(0.794009\pi\)
\(278\) 5.31671 0.318875
\(279\) −5.66564 15.7131i −0.339193 0.940717i
\(280\) 1.28192 0.0766094
\(281\) 10.6464i 0.635111i −0.948240 0.317556i \(-0.897138\pi\)
0.948240 0.317556i \(-0.102862\pi\)
\(282\) 1.14134 0.885793i 0.0679657 0.0527482i
\(283\) −16.3379 −0.971189 −0.485594 0.874184i \(-0.661397\pi\)
−0.485594 + 0.874184i \(0.661397\pi\)
\(284\) 9.33484i 0.553921i
\(285\) 5.06655 + 6.52820i 0.300116 + 0.386697i
\(286\) 1.90340 0.112550
\(287\) 6.50544i 0.384004i
\(288\) 2.90614 + 0.744540i 0.171246 + 0.0438725i
\(289\) 25.6175 1.50691
\(290\) 4.57705 0.268774
\(291\) 24.5175 19.0281i 1.43724 1.11545i
\(292\) 9.18740i 0.537652i
\(293\) 23.8799i 1.39508i −0.716546 0.697540i \(-0.754278\pi\)
0.716546 0.697540i \(-0.245722\pi\)
\(294\) 5.68851 + 7.32960i 0.331760 + 0.427471i
\(295\) −5.86520 −0.341485
\(296\) −2.12389 −0.123449
\(297\) −0.811938 1.87222i −0.0471134 0.108637i
\(298\) 5.26789 0.305160
\(299\) 12.1970i 0.705368i
\(300\) −1.36831 + 1.06195i −0.0789994 + 0.0613115i
\(301\) 4.21223i 0.242789i
\(302\) −4.12085 −0.237128
\(303\) −5.32209 6.85747i −0.305746 0.393951i
\(304\) −4.77100 −0.273636
\(305\) 9.87755 0.565587
\(306\) −18.9719 4.86051i −1.08455 0.277857i
\(307\) 8.71336 0.497298 0.248649 0.968594i \(-0.420013\pi\)
0.248649 + 0.968594i \(0.420013\pi\)
\(308\) 0.503452 0.0286869
\(309\) 9.53658 7.40135i 0.542517 0.421048i
\(310\) −4.60512 + 3.12935i −0.261553 + 0.177735i
\(311\) 6.24064i 0.353874i 0.984222 + 0.176937i \(0.0566189\pi\)
−0.984222 + 0.176937i \(0.943381\pi\)
\(312\) −6.63158 + 5.14678i −0.375440 + 0.291379i
\(313\) 7.88059i 0.445437i 0.974883 + 0.222719i \(0.0714931\pi\)
−0.974883 + 0.222719i \(0.928507\pi\)
\(314\) 2.19861i 0.124075i
\(315\) 3.72544 + 0.954441i 0.209905 + 0.0537767i
\(316\) 6.12151i 0.344362i
\(317\) 9.14329i 0.513538i 0.966473 + 0.256769i \(0.0826580\pi\)
−0.966473 + 0.256769i \(0.917342\pi\)
\(318\) 0.130865 + 0.168618i 0.00733854 + 0.00945565i
\(319\) 1.79756 0.100644
\(320\) 1.00000i 0.0559017i
\(321\) −14.5918 18.8014i −0.814434 1.04939i
\(322\) 3.22611i 0.179784i
\(323\) 31.1461 1.73301
\(324\) 7.89132 + 4.32748i 0.438407 + 0.240416i
\(325\) 4.84655i 0.268838i
\(326\) 12.1058i 0.670481i
\(327\) 12.1602 9.43756i 0.672462 0.521898i
\(328\) −5.07476 −0.280207
\(329\) 1.06928i 0.0589512i
\(330\) −0.537380 + 0.417061i −0.0295818 + 0.0229585i
\(331\) 23.9175i 1.31462i −0.753619 0.657311i \(-0.771694\pi\)
0.753619 0.657311i \(-0.228306\pi\)
\(332\) 2.73662 0.150191
\(333\) −6.17233 1.58132i −0.338242 0.0866560i
\(334\) 16.9254i 0.926118i
\(335\) 10.9782i 0.599801i
\(336\) −1.75406 + 1.36133i −0.0956920 + 0.0742667i
\(337\) 13.6435i 0.743207i −0.928391 0.371604i \(-0.878808\pi\)
0.928391 0.371604i \(-0.121192\pi\)
\(338\) 10.4891i 0.570531i
\(339\) 4.61166 + 5.94208i 0.250471 + 0.322730i
\(340\) 6.52820i 0.354042i
\(341\) −1.80858 + 1.22900i −0.0979403 + 0.0665540i
\(342\) −13.8652 3.55220i −0.749744 0.192081i
\(343\) −15.8403 −0.855295
\(344\) −3.28588 −0.177163
\(345\) 2.67252 + 3.44352i 0.143884 + 0.185393i
\(346\) −18.7522 −1.00813
\(347\) −15.0787 −0.809465 −0.404733 0.914435i \(-0.632635\pi\)
−0.404733 + 0.914435i \(0.632635\pi\)
\(348\) −6.26282 + 4.86058i −0.335723 + 0.260555i
\(349\) 13.1714 0.705047 0.352523 0.935803i \(-0.385324\pi\)
0.352523 + 0.935803i \(0.385324\pi\)
\(350\) 1.28192i 0.0685215i
\(351\) −23.1043 + 10.0198i −1.23322 + 0.534817i
\(352\) 0.392733i 0.0209327i
\(353\) −1.46704 −0.0780826 −0.0390413 0.999238i \(-0.512430\pi\)
−0.0390413 + 0.999238i \(0.512430\pi\)
\(354\) 8.02541 6.22853i 0.426546 0.331043i
\(355\) 9.33484 0.495442
\(356\) 11.0557 0.585953
\(357\) 11.4509 8.88704i 0.606045 0.470352i
\(358\) 2.59405i 0.137100i
\(359\) 4.42521i 0.233554i 0.993158 + 0.116777i \(0.0372562\pi\)
−0.993158 + 0.116777i \(0.962744\pi\)
\(360\) 0.744540 2.90614i 0.0392407 0.153167i
\(361\) 3.76245 0.198024
\(362\) −4.02779 −0.211696
\(363\) 14.8404 11.5176i 0.778917 0.604518i
\(364\) 6.21290i 0.325644i
\(365\) −9.18740 −0.480890
\(366\) −13.5155 + 10.4894i −0.706469 + 0.548291i
\(367\) 6.28174i 0.327904i 0.986468 + 0.163952i \(0.0524243\pi\)
−0.986468 + 0.163952i \(0.947576\pi\)
\(368\) −2.51663 −0.131188
\(369\) −14.7480 3.77836i −0.767749 0.196694i
\(370\) 2.12389i 0.110416i
\(371\) −0.157973 −0.00820152
\(372\) 2.97803 9.17231i 0.154404 0.475562i
\(373\) −30.4103 −1.57459 −0.787293 0.616580i \(-0.788518\pi\)
−0.787293 + 0.616580i \(0.788518\pi\)
\(374\) 2.56384i 0.132573i
\(375\) 1.06195 + 1.36831i 0.0548387 + 0.0706592i
\(376\) 0.834122 0.0430166
\(377\) 22.1829i 1.14248i
\(378\) −6.11112 + 2.65025i −0.314322 + 0.136314i
\(379\) 30.4929 1.56631 0.783156 0.621825i \(-0.213608\pi\)
0.783156 + 0.621825i \(0.213608\pi\)
\(380\) 4.77100i 0.244747i
\(381\) 11.4139 + 14.7067i 0.584751 + 0.753447i
\(382\) 7.48908 0.383175
\(383\) −34.4055 −1.75804 −0.879019 0.476787i \(-0.841801\pi\)
−0.879019 + 0.476787i \(0.841801\pi\)
\(384\) 1.06195 + 1.36831i 0.0541922 + 0.0698262i
\(385\) 0.503452i 0.0256583i
\(386\) 19.5334i 0.994226i
\(387\) −9.54923 2.44647i −0.485415 0.124361i
\(388\) 17.9181 0.909655
\(389\) −7.32763 −0.371525 −0.185763 0.982595i \(-0.559476\pi\)
−0.185763 + 0.982595i \(0.559476\pi\)
\(390\) 5.14678 + 6.63158i 0.260617 + 0.335803i
\(391\) 16.4290 0.830853
\(392\) 5.35668i 0.270553i
\(393\) −15.9060 20.4948i −0.802352 1.03382i
\(394\) 0.598768i 0.0301655i
\(395\) −6.12151 −0.308007
\(396\) 0.292405 1.14134i 0.0146939 0.0573544i
\(397\) 26.7188 1.34098 0.670488 0.741920i \(-0.266085\pi\)
0.670488 + 0.741920i \(0.266085\pi\)
\(398\) −12.0672 −0.604872
\(399\) 8.36864 6.49491i 0.418956 0.325152i
\(400\) −1.00000 −0.0500000
\(401\) 27.1300 1.35481 0.677403 0.735612i \(-0.263105\pi\)
0.677403 + 0.735612i \(0.263105\pi\)
\(402\) −11.6582 15.0215i −0.581459 0.749205i
\(403\) 15.1666 + 22.3190i 0.755501 + 1.11179i
\(404\) 5.01164i 0.249338i
\(405\) 4.32748 7.89132i 0.215034 0.392123i
\(406\) 5.86742i 0.291195i
\(407\) 0.834122i 0.0413459i
\(408\) −6.93260 8.93260i −0.343215 0.442230i
\(409\) 3.23637i 0.160028i −0.996794 0.0800141i \(-0.974503\pi\)
0.996794 0.0800141i \(-0.0254965\pi\)
\(410\) 5.07476i 0.250625i
\(411\) −25.1210 + 19.4964i −1.23913 + 0.961689i
\(412\) 6.96961 0.343368
\(413\) 7.51872i 0.369972i
\(414\) −7.31367 1.87373i −0.359447 0.0920888i
\(415\) 2.73662i 0.134335i
\(416\) −4.84655 −0.237622
\(417\) 5.64606 + 7.27490i 0.276489 + 0.356254i
\(418\) 1.87373i 0.0916471i
\(419\) 15.8496i 0.774303i −0.922016 0.387152i \(-0.873459\pi\)
0.922016 0.387152i \(-0.126541\pi\)
\(420\) 1.36133 + 1.75406i 0.0664261 + 0.0855895i
\(421\) 24.7086 1.20422 0.602111 0.798412i \(-0.294326\pi\)
0.602111 + 0.798412i \(0.294326\pi\)
\(422\) 15.3737i 0.748381i
\(423\) 2.42408 + 0.621038i 0.117863 + 0.0301959i
\(424\) 0.123231i 0.00598463i
\(425\) 6.52820 0.316664
\(426\) −12.7729 + 9.91310i −0.618851 + 0.480291i
\(427\) 12.6622i 0.612768i
\(428\) 13.7406i 0.664177i
\(429\) 2.02131 + 2.60444i 0.0975897 + 0.125744i
\(430\) 3.28588i 0.158459i
\(431\) 1.24844i 0.0601354i −0.999548 0.0300677i \(-0.990428\pi\)
0.999548 0.0300677i \(-0.00957229\pi\)
\(432\) 2.06741 + 4.76716i 0.0994681 + 0.229360i
\(433\) 23.2831i 1.11892i −0.828859 0.559458i \(-0.811009\pi\)
0.828859 0.559458i \(-0.188991\pi\)
\(434\) 4.01158 + 5.90340i 0.192562 + 0.283372i
\(435\) 4.86058 + 6.26282i 0.233047 + 0.300279i
\(436\) 8.88704 0.425612
\(437\) 12.0068 0.574364
\(438\) 12.5712 9.75652i 0.600675 0.466185i
\(439\) 37.2109 1.77598 0.887991 0.459862i \(-0.152101\pi\)
0.887991 + 0.459862i \(0.152101\pi\)
\(440\) −0.392733 −0.0187228
\(441\) −3.98826 + 15.5673i −0.189917 + 0.741299i
\(442\) 31.6393 1.50493
\(443\) 18.8683i 0.896460i 0.893918 + 0.448230i \(0.147945\pi\)
−0.893918 + 0.448230i \(0.852055\pi\)
\(444\) −2.25546 2.90614i −0.107039 0.137919i
\(445\) 11.0557i 0.524093i
\(446\) 18.0137 0.852973
\(447\) 5.59421 + 7.20810i 0.264597 + 0.340931i
\(448\) −1.28192 −0.0605650
\(449\) −30.0196 −1.41671 −0.708357 0.705854i \(-0.750563\pi\)
−0.708357 + 0.705854i \(0.750563\pi\)
\(450\) −2.90614 0.744540i −0.136997 0.0350980i
\(451\) 1.99303i 0.0938479i
\(452\) 4.34265i 0.204261i
\(453\) −4.37612 5.63860i −0.205608 0.264925i
\(454\) −24.3045 −1.14066
\(455\) −6.21290 −0.291265
\(456\) −5.06655 6.52820i −0.237263 0.305711i
\(457\) 16.6613i 0.779383i 0.920946 + 0.389691i \(0.127418\pi\)
−0.920946 + 0.389691i \(0.872582\pi\)
\(458\) −16.4436 −0.768357
\(459\) −13.4964 31.1210i −0.629960 1.45260i
\(460\) 2.51663i 0.117338i
\(461\) −25.1429 −1.17102 −0.585511 0.810664i \(-0.699106\pi\)
−0.585511 + 0.810664i \(0.699106\pi\)
\(462\) 0.534639 + 0.688878i 0.0248737 + 0.0320495i
\(463\) 10.9029i 0.506702i 0.967374 + 0.253351i \(0.0815327\pi\)
−0.967374 + 0.253351i \(0.918467\pi\)
\(464\) −4.57705 −0.212484
\(465\) −9.17231 2.97803i −0.425356 0.138103i
\(466\) −24.9298 −1.15485
\(467\) 38.5263i 1.78279i 0.453231 + 0.891393i \(0.350271\pi\)
−0.453231 + 0.891393i \(0.649729\pi\)
\(468\) −14.0848 3.60845i −0.651069 0.166801i
\(469\) 14.0731 0.649837
\(470\) 0.834122i 0.0384752i
\(471\) 3.00838 2.33480i 0.138619 0.107582i
\(472\) 5.86520 0.269968
\(473\) 1.29047i 0.0593360i
\(474\) 8.37612 6.50072i 0.384728 0.298588i
\(475\) 4.77100 0.218909
\(476\) 8.36864 0.383576
\(477\) −0.0917506 + 0.358127i −0.00420097 + 0.0163975i
\(478\) 8.26962i 0.378244i
\(479\) 0.704046i 0.0321687i −0.999871 0.0160843i \(-0.994880\pi\)
0.999871 0.0160843i \(-0.00512003\pi\)
\(480\) 1.36831 1.06195i 0.0624545 0.0484710i
\(481\) 10.2936 0.469346
\(482\) −12.4895 −0.568881
\(483\) 4.41432 3.42596i 0.200859 0.155887i
\(484\) 10.8458 0.492989
\(485\) 17.9181i 0.813620i
\(486\) 2.45883 + 15.3933i 0.111535 + 0.698255i
\(487\) 39.3676i 1.78392i −0.452117 0.891959i \(-0.649331\pi\)
0.452117 0.891959i \(-0.350669\pi\)
\(488\) −9.87755 −0.447136
\(489\) −16.5645 + 12.8558i −0.749074 + 0.581357i
\(490\) 5.35668 0.241990
\(491\) 24.0294 1.08443 0.542215 0.840240i \(-0.317586\pi\)
0.542215 + 0.840240i \(0.317586\pi\)
\(492\) −5.38912 6.94384i −0.242960 0.313053i
\(493\) 29.8799 1.34572
\(494\) 23.1229 1.04035
\(495\) −1.14134 0.292405i −0.0512993 0.0131426i
\(496\) 4.60512 3.12935i 0.206776 0.140512i
\(497\) 11.9665i 0.536772i
\(498\) 2.90614 + 3.74454i 0.130227 + 0.167797i
\(499\) 31.8208i 1.42450i −0.701928 0.712248i \(-0.747677\pi\)
0.701928 0.712248i \(-0.252323\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −23.1592 + 17.9739i −1.03468 + 0.803014i
\(502\) 25.1708i 1.12343i
\(503\) 18.8823i 0.841918i 0.907080 + 0.420959i \(0.138306\pi\)
−0.907080 + 0.420959i \(0.861694\pi\)
\(504\) −3.72544 0.954441i −0.165944 0.0425142i
\(505\) −5.01164 −0.223015
\(506\) 0.988362i 0.0439380i
\(507\) 14.3523 11.1388i 0.637408 0.494693i
\(508\) 10.7481i 0.476869i
\(509\) 24.1873 1.07208 0.536042 0.844191i \(-0.319919\pi\)
0.536042 + 0.844191i \(0.319919\pi\)
\(510\) −8.93260 + 6.93260i −0.395542 + 0.306981i
\(511\) 11.7775i 0.521007i
\(512\) 1.00000i 0.0441942i
\(513\) −9.86359 22.7441i −0.435488 1.00418i
\(514\) −23.3737 −1.03097
\(515\) 6.96961i 0.307118i
\(516\) −3.48943 4.49610i −0.153613 0.197930i
\(517\) 0.327587i 0.0144073i
\(518\) 2.72266 0.119627
\(519\) −19.9139 25.6589i −0.874122 1.12630i
\(520\) 4.84655i 0.212535i
\(521\) 0.707188i 0.0309825i 0.999880 + 0.0154912i \(0.00493121\pi\)
−0.999880 + 0.0154912i \(0.995069\pi\)
\(522\) −13.3016 3.40780i −0.582194 0.149155i
\(523\) 9.65100i 0.422009i −0.977485 0.211004i \(-0.932327\pi\)
0.977485 0.211004i \(-0.0676734\pi\)
\(524\) 14.9782i 0.654324i
\(525\) 1.75406 1.36133i 0.0765536 0.0594133i
\(526\) 10.4026i 0.453575i
\(527\) −30.0632 + 20.4290i −1.30957 + 0.889903i
\(528\) 0.537380 0.417061i 0.0233865 0.0181503i
\(529\) −16.6666 −0.724635
\(530\) 0.123231 0.00535282
\(531\) 17.0451 + 4.36688i 0.739695 + 0.189506i
\(532\) 6.11604 0.265164
\(533\) 24.5951 1.06533
\(534\) 11.7406 + 15.1277i 0.508066 + 0.654639i
\(535\) −13.7406 −0.594058
\(536\) 10.9782i 0.474184i
\(537\) 3.54946 2.75474i 0.153171 0.118876i
\(538\) 23.5925i 1.01714i
\(539\) 2.10374 0.0906147
\(540\) 4.76716 2.06741i 0.205146 0.0889669i
\(541\) 19.0755 0.820118 0.410059 0.912059i \(-0.365508\pi\)
0.410059 + 0.912059i \(0.365508\pi\)
\(542\) −24.7707 −1.06399
\(543\) −4.27730 5.51126i −0.183556 0.236511i
\(544\) 6.52820i 0.279894i
\(545\) 8.88704i 0.380679i
\(546\) 8.50116 6.59776i 0.363816 0.282358i
\(547\) −16.2881 −0.696428 −0.348214 0.937415i \(-0.613212\pi\)
−0.348214 + 0.937415i \(0.613212\pi\)
\(548\) −18.3592 −0.784265
\(549\) −28.7056 7.35423i −1.22512 0.313871i
\(550\) 0.392733i 0.0167462i
\(551\) 21.8371 0.930292
\(552\) −2.67252 3.44352i −0.113750 0.146566i
\(553\) 7.84729i 0.333701i
\(554\) −20.0687 −0.852639
\(555\) −2.90614 + 2.25546i −0.123359 + 0.0957389i
\(556\) 5.31671i 0.225479i
\(557\) −15.4857 −0.656151 −0.328075 0.944652i \(-0.606400\pi\)
−0.328075 + 0.944652i \(0.606400\pi\)
\(558\) 15.7131 5.66564i 0.665187 0.239846i
\(559\) 15.9252 0.673564
\(560\) 1.28192i 0.0541710i
\(561\) −3.50813 + 2.72266i −0.148113 + 0.114951i
\(562\) 10.6464 0.449092
\(563\) 16.5871i 0.699064i −0.936924 0.349532i \(-0.886341\pi\)
0.936924 0.349532i \(-0.113659\pi\)
\(564\) 0.885793 + 1.14134i 0.0372986 + 0.0480590i
\(565\) 4.34265 0.182697
\(566\) 16.3379i 0.686734i
\(567\) −10.1160 5.54748i −0.424834 0.232972i
\(568\) −9.33484 −0.391681
\(569\) −5.90748 −0.247654 −0.123827 0.992304i \(-0.539517\pi\)
−0.123827 + 0.992304i \(0.539517\pi\)
\(570\) −6.52820 + 5.06655i −0.273436 + 0.212214i
\(571\) 11.5683i 0.484118i −0.970262 0.242059i \(-0.922177\pi\)
0.970262 0.242059i \(-0.0778227\pi\)
\(572\) 1.90340i 0.0795852i
\(573\) 7.95300 + 10.2474i 0.332241 + 0.428090i
\(574\) 6.50544 0.271532
\(575\) 2.51663 0.104951
\(576\) −0.744540 + 2.90614i −0.0310225 + 0.121089i
\(577\) −33.5427 −1.39640 −0.698200 0.715902i \(-0.746016\pi\)
−0.698200 + 0.715902i \(0.746016\pi\)
\(578\) 25.6175i 1.06555i
\(579\) 26.7278 20.7435i 1.11077 0.862069i
\(580\) 4.57705i 0.190052i
\(581\) −3.50813 −0.145542
\(582\) 19.0281 + 24.5175i 0.788740 + 1.01628i
\(583\) 0.0483969 0.00200440
\(584\) 9.18740 0.380177
\(585\) −3.60845 + 14.0848i −0.149191 + 0.582334i
\(586\) 23.8799 0.986471
\(587\) −42.6221 −1.75920 −0.879601 0.475712i \(-0.842190\pi\)
−0.879601 + 0.475712i \(0.842190\pi\)
\(588\) −7.32960 + 5.68851i −0.302267 + 0.234590i
\(589\) −21.9710 + 14.9301i −0.905301 + 0.615186i
\(590\) 5.86520i 0.241467i
\(591\) −0.819300 + 0.635860i −0.0337015 + 0.0261558i
\(592\) 2.12389i 0.0872914i
\(593\) 30.3324i 1.24560i −0.782379 0.622802i \(-0.785994\pi\)
0.782379 0.622802i \(-0.214006\pi\)
\(594\) 1.87222 0.811938i 0.0768182 0.0333142i
\(595\) 8.36864i 0.343081i
\(596\) 5.26789i 0.215781i
\(597\) −12.8147 16.5116i −0.524470 0.675775i
\(598\) 12.1970 0.498771
\(599\) 39.2007i 1.60170i 0.598866 + 0.800849i \(0.295618\pi\)
−0.598866 + 0.800849i \(0.704382\pi\)
\(600\) −1.06195 1.36831i −0.0433538 0.0558610i
\(601\) 7.23029i 0.294930i −0.989067 0.147465i \(-0.952889\pi\)
0.989067 0.147465i \(-0.0471113\pi\)
\(602\) 4.21223 0.171678
\(603\) 8.17368 31.9041i 0.332858 1.29924i
\(604\) 4.12085i 0.167675i
\(605\) 10.8458i 0.440943i
\(606\) 6.85747 5.32209i 0.278566 0.216195i
\(607\) −6.11604 −0.248243 −0.124121 0.992267i \(-0.539611\pi\)
−0.124121 + 0.992267i \(0.539611\pi\)
\(608\) 4.77100i 0.193490i
\(609\) 8.02844 6.23088i 0.325329 0.252488i
\(610\) 9.87755i 0.399930i
\(611\) −4.04262 −0.163547
\(612\) 4.86051 18.9719i 0.196475 0.766893i
\(613\) 32.3900i 1.30822i 0.756400 + 0.654110i \(0.226957\pi\)
−0.756400 + 0.654110i \(0.773043\pi\)
\(614\) 8.71336i 0.351643i
\(615\) −6.94384 + 5.38912i −0.280003 + 0.217310i
\(616\) 0.503452i 0.0202847i
\(617\) 33.7250i 1.35772i −0.734269 0.678859i \(-0.762475\pi\)
0.734269 0.678859i \(-0.237525\pi\)
\(618\) 7.40135 + 9.53658i 0.297726 + 0.383618i
\(619\) 27.5804i 1.10855i −0.832333 0.554276i \(-0.812995\pi\)
0.832333 0.554276i \(-0.187005\pi\)
\(620\) −3.12935 4.60512i −0.125678 0.184946i
\(621\) −5.20288 11.9972i −0.208785 0.481430i
\(622\) −6.24064 −0.250227
\(623\) −14.1726 −0.567813
\(624\) −5.14678 6.63158i −0.206036 0.265476i
\(625\) 1.00000 0.0400000
\(626\) −7.88059 −0.314972
\(627\) −2.56384 + 1.98980i −0.102390 + 0.0794649i
\(628\) 2.19861 0.0877340
\(629\) 13.8652i 0.552842i
\(630\) −0.954441 + 3.72544i −0.0380259 + 0.148425i
\(631\) 49.0587i 1.95300i 0.215525 + 0.976498i \(0.430854\pi\)
−0.215525 + 0.976498i \(0.569146\pi\)
\(632\) 6.12151 0.243501
\(633\) 21.0360 16.3261i 0.836107 0.648903i
\(634\) −9.14329 −0.363127
\(635\) 10.7481 0.426524
\(636\) −0.168618 + 0.130865i −0.00668615 + 0.00518913i
\(637\) 25.9614i 1.02863i
\(638\) 1.79756i 0.0711660i
\(639\) −27.1284 6.95017i −1.07318 0.274944i
\(640\) 1.00000 0.0395285
\(641\) 18.5342 0.732055 0.366028 0.930604i \(-0.380718\pi\)
0.366028 + 0.930604i \(0.380718\pi\)
\(642\) 18.8014 14.5918i 0.742032 0.575892i
\(643\) 29.4769i 1.16246i −0.813741 0.581228i \(-0.802572\pi\)
0.813741 0.581228i \(-0.197428\pi\)
\(644\) 3.22611 0.127127
\(645\) −4.49610 + 3.48943i −0.177034 + 0.137396i
\(646\) 31.1461i 1.22543i
\(647\) −36.1460 −1.42105 −0.710523 0.703674i \(-0.751542\pi\)
−0.710523 + 0.703674i \(0.751542\pi\)
\(648\) −4.32748 + 7.89132i −0.169999 + 0.310000i
\(649\) 2.30346i 0.0904187i
\(650\) 4.84655 0.190097
\(651\) −3.81760 + 11.7582i −0.149623 + 0.460839i
\(652\) −12.1058 −0.474101
\(653\) 0.398710i 0.0156027i 0.999970 + 0.00780136i \(0.00248328\pi\)
−0.999970 + 0.00780136i \(0.997517\pi\)
\(654\) 9.43756 + 12.1602i 0.369038 + 0.475502i
\(655\) −14.9782 −0.585245
\(656\) 5.07476i 0.198136i
\(657\) 26.6999 + 6.84039i 1.04166 + 0.266869i
\(658\) −1.06928 −0.0416848
\(659\) 33.1277i 1.29047i −0.763984 0.645236i \(-0.776759\pi\)
0.763984 0.645236i \(-0.223241\pi\)
\(660\) −0.417061 0.537380i −0.0162341 0.0209175i
\(661\) −7.45088 −0.289806 −0.144903 0.989446i \(-0.546287\pi\)
−0.144903 + 0.989446i \(0.546287\pi\)
\(662\) 23.9175 0.929578
\(663\) 33.5992 + 43.2923i 1.30489 + 1.68133i
\(664\) 2.73662i 0.106201i
\(665\) 6.11604i 0.237170i
\(666\) 1.58132 6.17233i 0.0612750 0.239173i
\(667\) 11.5187 0.446007
\(668\) −16.9254 −0.654864
\(669\) 19.1296 + 24.6483i 0.739592 + 0.952958i
\(670\) −10.9782 −0.424123
\(671\) 3.87924i 0.149756i
\(672\) −1.36133 1.75406i −0.0525145 0.0676645i
\(673\) 46.6024i 1.79639i 0.439596 + 0.898196i \(0.355122\pi\)
−0.439596 + 0.898196i \(0.644878\pi\)
\(674\) 13.6435 0.525527
\(675\) −2.06741 4.76716i −0.0795745 0.183488i
\(676\) 10.4891 0.403426
\(677\) 14.1352 0.543261 0.271630 0.962402i \(-0.412437\pi\)
0.271630 + 0.962402i \(0.412437\pi\)
\(678\) −5.94208 + 4.61166i −0.228204 + 0.177110i
\(679\) −22.9696 −0.881493
\(680\) −6.52820 −0.250345
\(681\) −25.8100 33.2560i −0.989042 1.27437i
\(682\) −1.22900 1.80858i −0.0470608 0.0692542i
\(683\) 20.8246i 0.796832i 0.917205 + 0.398416i \(0.130440\pi\)
−0.917205 + 0.398416i \(0.869560\pi\)
\(684\) 3.55220 13.8652i 0.135822 0.530149i
\(685\) 18.3592i 0.701467i
\(686\) 15.8403i 0.604785i
\(687\) −17.4622 22.4999i −0.666224 0.858424i
\(688\) 3.28588i 0.125273i
\(689\) 0.597246i 0.0227533i
\(690\) −3.44352 + 2.67252i −0.131093 + 0.101741i
\(691\) −10.0491 −0.382285 −0.191143 0.981562i \(-0.561219\pi\)
−0.191143 + 0.981562i \(0.561219\pi\)
\(692\) 18.7522i 0.712854i
\(693\) −0.374840 + 1.46310i −0.0142390 + 0.0555787i
\(694\) 15.0787i 0.572378i
\(695\) 5.31671 0.201674
\(696\) −4.86058 6.26282i −0.184240 0.237392i
\(697\) 33.1291i 1.25485i
\(698\) 13.1714i 0.498543i
\(699\) −26.4741 34.1116i −1.00134 1.29022i
\(700\) 1.28192 0.0484520
\(701\) 5.98125i 0.225909i −0.993600 0.112954i \(-0.963969\pi\)
0.993600 0.112954i \(-0.0360314\pi\)
\(702\) −10.0198 23.1043i −0.378173 0.872016i
\(703\) 10.1331i 0.382177i
\(704\) 0.392733 0.0148017
\(705\) 1.14134 0.885793i 0.0429853 0.0333609i
\(706\) 1.46704i 0.0552127i
\(707\) 6.42452i 0.241619i
\(708\) 6.22853 + 8.02541i 0.234083 + 0.301614i
\(709\) 10.5995i 0.398074i −0.979992 0.199037i \(-0.936219\pi\)
0.979992 0.199037i \(-0.0637815\pi\)
\(710\) 9.33484i 0.350330i
\(711\) 17.7900 + 4.55771i 0.667177 + 0.170928i
\(712\) 11.0557i 0.414332i
\(713\) −11.5894 + 7.87541i −0.434025 + 0.294936i
\(714\) 8.88704 + 11.4509i 0.332589 + 0.428539i
\(715\) 1.90340 0.0711832
\(716\) 2.59405 0.0969442
\(717\) 11.3154 8.78189i 0.422581 0.327966i
\(718\) −4.42521 −0.165147
\(719\) 10.7883 0.402334 0.201167 0.979557i \(-0.435527\pi\)
0.201167 + 0.979557i \(0.435527\pi\)
\(720\) 2.90614 + 0.744540i 0.108306 + 0.0277474i
\(721\) −8.93448 −0.332738
\(722\) 3.76245i 0.140024i
\(723\) −13.2632 17.0895i −0.493263 0.635565i
\(724\) 4.02779i 0.149692i
\(725\) 4.57705 0.169987
\(726\) 11.5176 + 14.8404i 0.427459 + 0.550777i
\(727\) 24.6314 0.913529 0.456764 0.889588i \(-0.349008\pi\)
0.456764 + 0.889588i \(0.349008\pi\)
\(728\) 6.21290 0.230265
\(729\) −18.4517 + 19.7113i −0.683395 + 0.730049i
\(730\) 9.18740i 0.340041i
\(731\) 21.4509i 0.793390i
\(732\) −10.4894 13.5155i −0.387700 0.499549i
\(733\) 18.5871 0.686531 0.343265 0.939238i \(-0.388467\pi\)
0.343265 + 0.939238i \(0.388467\pi\)
\(734\) −6.28174 −0.231863
\(735\) 5.68851 + 7.32960i 0.209824 + 0.270356i
\(736\) 2.51663i 0.0927640i
\(737\) −4.31148 −0.158816
\(738\) 3.77836 14.7480i 0.139083 0.542880i
\(739\) 42.0629i 1.54731i 0.633607 + 0.773655i \(0.281574\pi\)
−0.633607 + 0.773655i \(0.718426\pi\)
\(740\) −2.12389 −0.0780758
\(741\) 24.5553 + 31.6393i 0.902061 + 1.16230i
\(742\) 0.157973i 0.00579935i
\(743\) −3.32260 −0.121895 −0.0609473 0.998141i \(-0.519412\pi\)
−0.0609473 + 0.998141i \(0.519412\pi\)
\(744\) 9.17231 + 2.97803i 0.336273 + 0.109180i
\(745\) 5.26789 0.193000
\(746\) 30.4103i 1.11340i
\(747\) −2.03752 + 7.95300i −0.0745491 + 0.290985i
\(748\) −2.56384 −0.0937433
\(749\) 17.6144i 0.643615i
\(750\) −1.36831 + 1.06195i −0.0499636 + 0.0387768i
\(751\) −39.1525 −1.42870 −0.714348 0.699790i \(-0.753277\pi\)
−0.714348 + 0.699790i \(0.753277\pi\)
\(752\) 0.834122i 0.0304173i
\(753\) −34.4415 + 26.7301i −1.25512 + 0.974098i
\(754\) 22.1829 0.807855
\(755\) −4.12085 −0.149973
\(756\) −2.65025 6.11112i −0.0963886 0.222259i
\(757\) 33.9683i 1.23460i 0.786728 + 0.617300i \(0.211773\pi\)
−0.786728 + 0.617300i \(0.788227\pi\)
\(758\) 30.4929i 1.10755i
\(759\) −1.35238 + 1.04959i −0.0490884 + 0.0380976i
\(760\) −4.77100 −0.173062
\(761\) 50.8630 1.84378 0.921891 0.387449i \(-0.126644\pi\)
0.921891 + 0.387449i \(0.126644\pi\)
\(762\) −14.7067 + 11.4139i −0.532767 + 0.413481i
\(763\) −11.3925 −0.412436
\(764\) 7.48908i 0.270945i
\(765\) −18.9719 4.86051i −0.685930 0.175732i
\(766\) 34.4055i 1.24312i
\(767\) −28.4260 −1.02640
\(768\) −1.36831 + 1.06195i −0.0493746 + 0.0383197i
\(769\) 37.4703 1.35121 0.675607 0.737262i \(-0.263882\pi\)
0.675607 + 0.737262i \(0.263882\pi\)
\(770\) 0.503452 0.0181432
\(771\) −24.8216 31.9825i −0.893930 1.15182i
\(772\) 19.5334 0.703024
\(773\) 43.2585 1.55590 0.777949 0.628327i \(-0.216260\pi\)
0.777949 + 0.628327i \(0.216260\pi\)
\(774\) 2.44647 9.54923i 0.0879365 0.343240i
\(775\) −4.60512 + 3.12935i −0.165421 + 0.112410i
\(776\) 17.9181i 0.643223i
\(777\) 2.89132 + 3.72544i 0.103726 + 0.133649i
\(778\) 7.32763i 0.262708i
\(779\) 24.2117i 0.867474i
\(780\) −6.63158 + 5.14678i −0.237449 + 0.184284i
\(781\) 3.66610i 0.131183i
\(782\) 16.4290i 0.587501i
\(783\) −9.46262 21.8195i −0.338166 0.779767i
\(784\) −5.35668 −0.191310
\(785\) 2.19861i 0.0784717i
\(786\) 20.4948 15.9060i 0.731024 0.567348i
\(787\) 15.8331i 0.564389i 0.959357 + 0.282194i \(0.0910623\pi\)
−0.959357 + 0.282194i \(0.908938\pi\)
\(788\) −0.598768 −0.0213302
\(789\) −14.2340 + 11.0470i −0.506743 + 0.393283i
\(790\) 6.12151i 0.217794i
\(791\) 5.56693i 0.197937i
\(792\) 1.14134 + 0.292405i 0.0405557 + 0.0103902i
\(793\) 47.8721 1.69999
\(794\) 26.7188i 0.948214i
\(795\) 0.130865 + 0.168618i 0.00464130 + 0.00598028i
\(796\) 12.0672i 0.427709i
\(797\) 19.1608 0.678712 0.339356 0.940658i \(-0.389791\pi\)
0.339356 + 0.940658i \(0.389791\pi\)
\(798\) 6.49491 + 8.36864i 0.229917 + 0.296247i
\(799\) 5.44532i 0.192642i
\(800\) 1.00000i 0.0353553i
\(801\) −8.23145 + 32.1296i −0.290844 + 1.13524i
\(802\) 27.1300i 0.957993i
\(803\) 3.60819i 0.127330i
\(804\) 15.0215 11.6582i 0.529768 0.411154i
\(805\) 3.22611i 0.113706i
\(806\) −22.3190 + 15.1666i −0.786152 + 0.534220i
\(807\) 32.2818 25.0540i 1.13637 0.881941i
\(808\) 5.01164 0.176309
\(809\) 13.6102 0.478508 0.239254 0.970957i \(-0.423097\pi\)
0.239254 + 0.970957i \(0.423097\pi\)
\(810\) 7.89132 + 4.32748i 0.277273 + 0.152052i
\(811\) 19.3201 0.678421 0.339211 0.940710i \(-0.389840\pi\)
0.339211 + 0.940710i \(0.389840\pi\)
\(812\) 5.86742 0.205906
\(813\) −26.3051 33.8940i −0.922562 1.18871i
\(814\) −0.834122 −0.0292360
\(815\) 12.1058i 0.424049i
\(816\) 8.93260 6.93260i 0.312704 0.242690i
\(817\) 15.6769i 0.548466i
\(818\) 3.23637 0.113157
\(819\) 18.0556 + 4.62575i 0.630912 + 0.161637i
\(820\) −5.07476 −0.177218
\(821\) −55.7366 −1.94522 −0.972610 0.232442i \(-0.925328\pi\)
−0.972610 + 0.232442i \(0.925328\pi\)
\(822\) −19.4964 25.1210i −0.680017 0.876196i
\(823\) 37.2577i 1.29872i −0.760481 0.649361i \(-0.775037\pi\)
0.760481 0.649361i \(-0.224963\pi\)
\(824\) 6.96961i 0.242798i
\(825\) −0.537380 + 0.417061i −0.0187092 + 0.0145202i
\(826\) −7.51872 −0.261610
\(827\) 16.8889 0.587286 0.293643 0.955915i \(-0.405132\pi\)
0.293643 + 0.955915i \(0.405132\pi\)
\(828\) 1.87373 7.31367i 0.0651166 0.254168i
\(829\) 17.3927i 0.604075i 0.953296 + 0.302037i \(0.0976668\pi\)
−0.953296 + 0.302037i \(0.902333\pi\)
\(830\) 2.73662 0.0949894
\(831\) −21.3119 27.4602i −0.739302 0.952585i
\(832\) 4.84655i 0.168024i
\(833\) 34.9695 1.21162
\(834\) −7.27490 + 5.64606i −0.251909 + 0.195507i
\(835\) 16.9254i 0.585728i
\(836\) −1.87373 −0.0648043
\(837\) 24.4388 + 15.4837i 0.844728 + 0.535196i
\(838\) 15.8496 0.547515
\(839\) 29.5325i 1.01957i −0.860300 0.509787i \(-0.829724\pi\)
0.860300 0.509787i \(-0.170276\pi\)
\(840\) −1.75406 + 1.36133i −0.0605209 + 0.0469704i
\(841\) −8.05060 −0.277607
\(842\) 24.7086i 0.851514i
\(843\) 11.3059 + 14.5676i 0.389396 + 0.501734i
\(844\) 15.3737 0.529186
\(845\) 10.4891i 0.360835i
\(846\) −0.621038 + 2.42408i −0.0213517 + 0.0833415i
\(847\) −13.9034 −0.477727
\(848\) −0.123231 −0.00423178
\(849\) 22.3553 17.3500i 0.767233 0.595451i
\(850\) 6.52820i 0.223916i
\(851\) 5.34504i 0.183226i
\(852\) −9.91310 12.7729i −0.339617 0.437594i
\(853\) 12.5693 0.430363 0.215181 0.976574i \(-0.430966\pi\)
0.215181 + 0.976574i \(0.430966\pi\)
\(854\) 12.6622 0.433293
\(855\) −13.8652 3.55220i −0.474180 0.121483i
\(856\) 13.7406 0.469644
\(857\) 3.29281i 0.112480i −0.998417 0.0562402i \(-0.982089\pi\)
0.998417 0.0562402i \(-0.0179112\pi\)
\(858\) −2.60444 + 2.02131i −0.0889142 + 0.0690064i
\(859\) 50.1085i 1.70968i −0.518891 0.854840i \(-0.673655\pi\)
0.518891 0.854840i \(-0.326345\pi\)
\(860\) −3.28588 −0.112048
\(861\) 6.90843 + 8.90145i 0.235439 + 0.303361i
\(862\) 1.24844 0.0425221
\(863\) −4.65899 −0.158594 −0.0792969 0.996851i \(-0.525268\pi\)
−0.0792969 + 0.996851i \(0.525268\pi\)
\(864\) −4.76716 + 2.06741i −0.162182 + 0.0703345i
\(865\) −18.7522 −0.637596
\(866\) 23.2831 0.791193
\(867\) −35.0526 + 27.2044i −1.19045 + 0.923908i
\(868\) −5.90340 + 4.01158i −0.200374 + 0.136162i
\(869\) 2.40412i 0.0815542i
\(870\) −6.26282 + 4.86058i −0.212330 + 0.164789i
\(871\) 53.2062i 1.80282i
\(872\) 8.88704i 0.300953i
\(873\) −13.3408 + 52.0726i −0.451517 + 1.76239i
\(874\) 12.0068i 0.406137i
\(875\) 1.28192i 0.0433368i
\(876\) 9.75652 + 12.5712i 0.329642 + 0.424742i
\(877\) −31.3987 −1.06026 −0.530129 0.847917i \(-0.677856\pi\)
−0.530129 + 0.847917i \(0.677856\pi\)
\(878\) 37.2109i 1.25581i
\(879\) 25.3592 + 32.6751i 0.855345 + 1.10210i
\(880\) 0.392733i 0.0132390i
\(881\) 0.742278 0.0250080 0.0125040 0.999922i \(-0.496020\pi\)
0.0125040 + 0.999922i \(0.496020\pi\)
\(882\) −15.5673 3.98826i −0.524177 0.134292i
\(883\) 34.0936i 1.14734i 0.819086 + 0.573670i \(0.194481\pi\)
−0.819086 + 0.573670i \(0.805519\pi\)
\(884\) 31.6393i 1.06414i
\(885\) 8.02541 6.22853i 0.269771 0.209370i
\(886\) −18.8683 −0.633893
\(887\) 7.22517i 0.242597i −0.992616 0.121299i \(-0.961294\pi\)
0.992616 0.121299i \(-0.0387059\pi\)
\(888\) 2.90614 2.25546i 0.0975237 0.0756883i
\(889\) 13.7782i 0.462105i
\(890\) 11.0557 0.370589
\(891\) 3.09918 + 1.69954i 0.103826 + 0.0569368i
\(892\) 18.0137i 0.603143i
\(893\) 3.97960i 0.133172i
\(894\) −7.20810 + 5.59421i −0.241075 + 0.187098i
\(895\) 2.59405i 0.0867095i
\(896\) 1.28192i 0.0428260i
\(897\) 12.9525 + 16.6892i 0.432472 + 0.557237i
\(898\) 30.0196i 1.00177i
\(899\) −21.0779 + 14.3232i −0.702987 + 0.477706i
\(900\) 0.744540 2.90614i 0.0248180 0.0968714i
\(901\) 0.804478 0.0268011
\(902\) −1.99303 −0.0663605
\(903\) 4.47317 + 5.76364i 0.148858 + 0.191802i
\(904\) −4.34265 −0.144434
\(905\) −4.02779 −0.133888
\(906\) 5.63860 4.37612i 0.187330 0.145387i
\(907\) 2.18703 0.0726190 0.0363095 0.999341i \(-0.488440\pi\)
0.0363095 + 0.999341i \(0.488440\pi\)
\(908\) 24.3045i 0.806572i
\(909\) 14.5645 + 3.73137i 0.483075 + 0.123762i
\(910\) 6.21290i 0.205955i
\(911\) 27.3383 0.905757 0.452879 0.891572i \(-0.350397\pi\)
0.452879 + 0.891572i \(0.350397\pi\)
\(912\) 6.52820 5.06655i 0.216170 0.167770i
\(913\) 1.07476 0.0355694
\(914\) −16.6613 −0.551107
\(915\) −13.5155 + 10.4894i −0.446810 + 0.346770i
\(916\) 16.4436i 0.543311i
\(917\) 19.2008i 0.634067i
\(918\) 31.1210 13.4964i 1.02715 0.445449i
\(919\) 36.8059 1.21411 0.607057 0.794659i \(-0.292350\pi\)
0.607057 + 0.794659i \(0.292350\pi\)
\(920\) −2.51663 −0.0829707
\(921\) −11.9226 + 9.25312i −0.392862 + 0.304901i
\(922\) 25.1429i 0.828038i
\(923\) 45.2418 1.48915
\(924\) −0.688878 + 0.534639i −0.0226624 + 0.0175883i
\(925\) 2.12389i 0.0698332i
\(926\) −10.9029 −0.358292
\(927\) −5.18915 + 20.2547i −0.170434 + 0.665251i
\(928\) 4.57705i 0.150249i
\(929\) −37.6751 −1.23608 −0.618041 0.786146i \(-0.712073\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(930\) 2.97803 9.17231i 0.0976534 0.300772i
\(931\) 25.5567 0.837588
\(932\) 24.9298i 0.816602i
\(933\) −6.62722 8.53912i −0.216966 0.279558i
\(934\) −38.5263 −1.26062
\(935\) 2.56384i 0.0838466i
\(936\) 3.60845 14.0848i 0.117946 0.460375i
\(937\) −45.9539 −1.50125 −0.750625 0.660729i \(-0.770247\pi\)
−0.750625 + 0.660729i \(0.770247\pi\)
\(938\) 14.0731i 0.459504i
\(939\) −8.36876 10.7831i −0.273104 0.351893i
\(940\) 0.834122 0.0272061
\(941\) −40.3651 −1.31586 −0.657932 0.753077i \(-0.728569\pi\)
−0.657932 + 0.753077i \(0.728569\pi\)
\(942\) 2.33480 + 3.00838i 0.0760720 + 0.0980182i
\(943\) 12.7713i 0.415890i
\(944\) 5.86520i 0.190896i
\(945\) −6.11112 + 2.65025i −0.198795 + 0.0862126i
\(946\) −1.29047 −0.0419569
\(947\) −52.5426 −1.70741 −0.853703 0.520760i \(-0.825649\pi\)
−0.853703 + 0.520760i \(0.825649\pi\)
\(948\) 6.50072 + 8.37612i 0.211134 + 0.272044i
\(949\) −44.5272 −1.44541
\(950\) 4.77100i 0.154792i
\(951\) −9.70968 12.5109i −0.314858 0.405692i
\(952\) 8.36864i 0.271229i
\(953\) −53.3751 −1.72899 −0.864495 0.502642i \(-0.832361\pi\)
−0.864495 + 0.502642i \(0.832361\pi\)
\(954\) −0.358127 0.0917506i −0.0115948 0.00297053i
\(955\) 7.48908 0.242341
\(956\) 8.26962 0.267459
\(957\) −2.45962 + 1.90891i −0.0795081 + 0.0617063i
\(958\) 0.704046 0.0227467
\(959\) 23.5350 0.759984
\(960\) 1.06195 + 1.36831i 0.0342742 + 0.0441620i
\(961\) 11.4143 28.8221i 0.368204 0.929745i
\(962\) 10.2936i 0.331878i
\(963\) 39.9322 + 10.2304i 1.28680 + 0.329671i
\(964\) 12.4895i 0.402259i
\(965\) 19.5334i 0.628804i
\(966\) 3.42596 + 4.41432i 0.110228 + 0.142028i
\(967\) 47.8830i 1.53981i 0.638157 + 0.769906i \(0.279697\pi\)
−0.638157 + 0.769906i \(0.720303\pi\)
\(968\) 10.8458i 0.348596i
\(969\) −42.6175 + 33.0755i −1.36907 + 1.06254i
\(970\) 17.9181 0.575316
\(971\) 17.2188i 0.552578i 0.961075 + 0.276289i \(0.0891046\pi\)
−0.961075 + 0.276289i \(0.910895\pi\)
\(972\) −15.3933 + 2.45883i −0.493741 + 0.0788669i
\(973\) 6.81560i 0.218498i
\(974\) 39.3676 1.26142
\(975\) 5.14678 + 6.63158i 0.164829 + 0.212381i
\(976\) 9.87755i 0.316173i
\(977\) 8.41194i 0.269122i −0.990905 0.134561i \(-0.957038\pi\)
0.990905 0.134561i \(-0.0429624\pi\)
\(978\) −12.8558 16.5645i −0.411082 0.529675i
\(979\) 4.34196 0.138770
\(980\) 5.35668i 0.171113i
\(981\) −6.61676 + 25.8270i −0.211257 + 0.824593i
\(982\) 24.0294i 0.766807i
\(983\) 3.47796 0.110930 0.0554648 0.998461i \(-0.482336\pi\)
0.0554648 + 0.998461i \(0.482336\pi\)
\(984\) 6.94384 5.38912i 0.221362 0.171799i
\(985\) 0.598768i 0.0190783i
\(986\) 29.8799i 0.951571i
\(987\) −1.13552 1.46310i −0.0361439 0.0465711i
\(988\) 23.1229i 0.735638i
\(989\) 8.26932i 0.262949i
\(990\) 0.292405 1.14134i 0.00929326 0.0362741i
\(991\) 6.14943i 0.195343i −0.995219 0.0976715i \(-0.968861\pi\)
0.995219 0.0976715i \(-0.0311395\pi\)
\(992\) 3.12935 + 4.60512i 0.0993570 + 0.146213i
\(993\) 25.3991 + 32.7265i 0.806015 + 1.03854i
\(994\) 11.9665 0.379555
\(995\) −12.0672 −0.382555
\(996\) −3.74454 + 2.90614i −0.118650 + 0.0920846i
\(997\) 0.524953 0.0166254 0.00831272 0.999965i \(-0.497354\pi\)
0.00831272 + 0.999965i \(0.497354\pi\)
\(998\) 31.8208 1.00727
\(999\) 10.1249 4.39095i 0.320339 0.138923i
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 930.2.h.c.371.10 yes 16
3.2 odd 2 inner 930.2.h.c.371.7 yes 16
31.30 odd 2 inner 930.2.h.c.371.15 yes 16
93.92 even 2 inner 930.2.h.c.371.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.h.c.371.2 16 93.92 even 2 inner
930.2.h.c.371.7 yes 16 3.2 odd 2 inner
930.2.h.c.371.10 yes 16 1.1 even 1 trivial
930.2.h.c.371.15 yes 16 31.30 odd 2 inner