Properties

Label 700.2.c.k.699.7
Level $700$
Weight $2$
Character 700.699
Analytic conductor $5.590$
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] = [700,2,Mod(699,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, 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("700.699");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: 16.0.29960650073923649536.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 699.7
Root \(1.32968 + 0.481610i\) of defining polynomial
Character \(\chi\) \(=\) 700.699
Dual form 700.2.c.k.699.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.736813 + 1.20711i) q^{2} -2.79793i q^{3} +(-0.914214 - 1.77882i) q^{4} +(3.37740 + 2.06155i) q^{6} +(2.51564 - 0.819496i) q^{7} +(2.82083 + 0.207107i) q^{8} -4.82843 q^{9} +O(q^{10})\) \(q+(-0.736813 + 1.20711i) q^{2} -2.79793i q^{3} +(-0.914214 - 1.77882i) q^{4} +(3.37740 + 2.06155i) q^{6} +(2.51564 - 0.819496i) q^{7} +(2.82083 + 0.207107i) q^{8} -4.82843 q^{9} -1.47363i q^{11} +(-4.97703 + 2.55791i) q^{12} +5.83095 q^{13} +(-0.864335 + 3.64046i) q^{14} +(-2.32843 + 3.25245i) q^{16} +4.12311 q^{17} +(3.55765 - 5.82843i) q^{18} +5.11582 q^{19} +(-2.29289 - 7.03858i) q^{21} +(1.77882 + 1.08579i) q^{22} -2.08402 q^{23} +(0.579471 - 7.89250i) q^{24} +(-4.29632 + 7.03858i) q^{26} +5.11582i q^{27} +(-3.75757 - 3.72568i) q^{28} -8.24264 q^{29} -3.95687 q^{31} +(-2.21044 - 5.20711i) q^{32} -4.12311 q^{33} +(-3.03796 + 4.97703i) q^{34} +(4.41421 + 8.58892i) q^{36} +2.24264i q^{37} +(-3.76940 + 6.17534i) q^{38} -16.3146i q^{39} -4.12311i q^{41} +(10.1858 + 2.41835i) q^{42} -2.94725 q^{43} +(-2.62132 + 1.34721i) q^{44} +(1.53553 - 2.51564i) q^{46} -11.8706i q^{47} +(9.10013 + 6.51478i) q^{48} +(5.65685 - 4.12311i) q^{49} -11.5362i q^{51} +(-5.33074 - 10.3722i) q^{52} +3.75736i q^{53} +(-6.17534 - 3.76940i) q^{54} +(7.26592 - 1.79066i) q^{56} -14.3137i q^{57} +(6.07328 - 9.94975i) q^{58} -5.59587 q^{59} +11.6619i q^{61} +(2.91548 - 4.77637i) q^{62} +(-12.1466 + 3.95687i) q^{63} +(7.91421 + 1.16843i) q^{64} +(3.03796 - 4.97703i) q^{66} +12.7570 q^{67} +(-3.76940 - 7.33428i) q^{68} +5.83095i q^{69} +7.97852i q^{71} +(-13.6202 - 1.00000i) q^{72} -12.3693 q^{73} +(-2.70711 - 1.65241i) q^{74} +(-4.67695 - 9.10013i) q^{76} +(-1.20763 - 3.70711i) q^{77} +(19.6935 + 12.0208i) q^{78} +4.16804i q^{79} -0.171573 q^{81} +(4.97703 + 3.03796i) q^{82} -2.79793i q^{83} +(-10.4242 + 10.5134i) q^{84} +(2.17157 - 3.55765i) q^{86} +23.0624i q^{87} +(0.305198 - 4.15685i) q^{88} -12.3693i q^{89} +(14.6686 - 4.77844i) q^{91} +(1.90524 + 3.70711i) q^{92} +11.0711i q^{93} +(14.3291 + 8.74643i) q^{94} +(-14.5691 + 6.18466i) q^{96} +8.24621 q^{97} +(0.808986 + 9.86638i) q^{98} +7.11529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 32 q^{9} - 24 q^{14} + 8 q^{16} - 48 q^{21} - 64 q^{29} + 48 q^{36} - 8 q^{44} - 32 q^{46} + 40 q^{56} + 104 q^{64} - 32 q^{74} - 48 q^{81} - 40 q^{84} + 80 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.736813 + 1.20711i −0.521005 + 0.853553i
\(3\) 2.79793i 1.61539i −0.589602 0.807694i \(-0.700716\pi\)
0.589602 0.807694i \(-0.299284\pi\)
\(4\) −0.914214 1.77882i −0.457107 0.889412i
\(5\) 0 0
\(6\) 3.37740 + 2.06155i 1.37882 + 0.841625i
\(7\) 2.51564 0.819496i 0.950821 0.309740i
\(8\) 2.82083 + 0.207107i 0.997316 + 0.0732233i
\(9\) −4.82843 −1.60948
\(10\) 0 0
\(11\) 1.47363i 0.444315i −0.975011 0.222157i \(-0.928690\pi\)
0.975011 0.222157i \(-0.0713099\pi\)
\(12\) −4.97703 + 2.55791i −1.43674 + 0.738404i
\(13\) 5.83095 1.61722 0.808608 0.588348i \(-0.200222\pi\)
0.808608 + 0.588348i \(0.200222\pi\)
\(14\) −0.864335 + 3.64046i −0.231003 + 0.972953i
\(15\) 0 0
\(16\) −2.32843 + 3.25245i −0.582107 + 0.813112i
\(17\) 4.12311 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 3.55765 5.82843i 0.838546 1.37377i
\(19\) 5.11582 1.17365 0.586824 0.809714i \(-0.300378\pi\)
0.586824 + 0.809714i \(0.300378\pi\)
\(20\) 0 0
\(21\) −2.29289 7.03858i −0.500350 1.53594i
\(22\) 1.77882 + 1.08579i 0.379246 + 0.231490i
\(23\) −2.08402 −0.434549 −0.217274 0.976111i \(-0.569717\pi\)
−0.217274 + 0.976111i \(0.569717\pi\)
\(24\) 0.579471 7.89250i 0.118284 1.61105i
\(25\) 0 0
\(26\) −4.29632 + 7.03858i −0.842578 + 1.38038i
\(27\) 5.11582i 0.984539i
\(28\) −3.75757 3.72568i −0.710113 0.704087i
\(29\) −8.24264 −1.53062 −0.765310 0.643662i \(-0.777414\pi\)
−0.765310 + 0.643662i \(0.777414\pi\)
\(30\) 0 0
\(31\) −3.95687 −0.710676 −0.355338 0.934738i \(-0.615634\pi\)
−0.355338 + 0.934738i \(0.615634\pi\)
\(32\) −2.21044 5.20711i −0.390754 0.920495i
\(33\) −4.12311 −0.717741
\(34\) −3.03796 + 4.97703i −0.521005 + 0.853553i
\(35\) 0 0
\(36\) 4.41421 + 8.58892i 0.735702 + 1.43149i
\(37\) 2.24264i 0.368688i 0.982862 + 0.184344i \(0.0590160\pi\)
−0.982862 + 0.184344i \(0.940984\pi\)
\(38\) −3.76940 + 6.17534i −0.611477 + 1.00177i
\(39\) 16.3146i 2.61243i
\(40\) 0 0
\(41\) 4.12311i 0.643921i −0.946753 0.321960i \(-0.895658\pi\)
0.946753 0.321960i \(-0.104342\pi\)
\(42\) 10.1858 + 2.41835i 1.57170 + 0.373160i
\(43\) −2.94725 −0.449452 −0.224726 0.974422i \(-0.572149\pi\)
−0.224726 + 0.974422i \(0.572149\pi\)
\(44\) −2.62132 + 1.34721i −0.395179 + 0.203099i
\(45\) 0 0
\(46\) 1.53553 2.51564i 0.226402 0.370910i
\(47\) 11.8706i 1.73151i −0.500470 0.865754i \(-0.666839\pi\)
0.500470 0.865754i \(-0.333161\pi\)
\(48\) 9.10013 + 6.51478i 1.31349 + 0.940328i
\(49\) 5.65685 4.12311i 0.808122 0.589015i
\(50\) 0 0
\(51\) 11.5362i 1.61539i
\(52\) −5.33074 10.3722i −0.739240 1.43837i
\(53\) 3.75736i 0.516113i 0.966130 + 0.258056i \(0.0830821\pi\)
−0.966130 + 0.258056i \(0.916918\pi\)
\(54\) −6.17534 3.76940i −0.840357 0.512950i
\(55\) 0 0
\(56\) 7.26592 1.79066i 0.970949 0.239286i
\(57\) 14.3137i 1.89590i
\(58\) 6.07328 9.94975i 0.797461 1.30647i
\(59\) −5.59587 −0.728520 −0.364260 0.931297i \(-0.618678\pi\)
−0.364260 + 0.931297i \(0.618678\pi\)
\(60\) 0 0
\(61\) 11.6619i 1.49315i 0.665299 + 0.746577i \(0.268304\pi\)
−0.665299 + 0.746577i \(0.731696\pi\)
\(62\) 2.91548 4.77637i 0.370266 0.606600i
\(63\) −12.1466 + 3.95687i −1.53032 + 0.498519i
\(64\) 7.91421 + 1.16843i 0.989277 + 0.146053i
\(65\) 0 0
\(66\) 3.03796 4.97703i 0.373947 0.612630i
\(67\) 12.7570 1.55851 0.779256 0.626706i \(-0.215597\pi\)
0.779256 + 0.626706i \(0.215597\pi\)
\(68\) −3.76940 7.33428i −0.457107 0.889412i
\(69\) 5.83095i 0.701964i
\(70\) 0 0
\(71\) 7.97852i 0.946877i 0.880827 + 0.473438i \(0.156987\pi\)
−0.880827 + 0.473438i \(0.843013\pi\)
\(72\) −13.6202 1.00000i −1.60516 0.117851i
\(73\) −12.3693 −1.44772 −0.723860 0.689947i \(-0.757634\pi\)
−0.723860 + 0.689947i \(0.757634\pi\)
\(74\) −2.70711 1.65241i −0.314695 0.192088i
\(75\) 0 0
\(76\) −4.67695 9.10013i −0.536483 1.04386i
\(77\) −1.20763 3.70711i −0.137622 0.422464i
\(78\) 19.6935 + 12.0208i 2.22985 + 1.36109i
\(79\) 4.16804i 0.468941i 0.972123 + 0.234471i \(0.0753357\pi\)
−0.972123 + 0.234471i \(0.924664\pi\)
\(80\) 0 0
\(81\) −0.171573 −0.0190637
\(82\) 4.97703 + 3.03796i 0.549621 + 0.335486i
\(83\) 2.79793i 0.307113i −0.988140 0.153557i \(-0.950927\pi\)
0.988140 0.153557i \(-0.0490727\pi\)
\(84\) −10.4242 + 10.5134i −1.13737 + 1.14711i
\(85\) 0 0
\(86\) 2.17157 3.55765i 0.234167 0.383631i
\(87\) 23.0624i 2.47254i
\(88\) 0.305198 4.15685i 0.0325342 0.443122i
\(89\) 12.3693i 1.31114i −0.755132 0.655572i \(-0.772427\pi\)
0.755132 0.655572i \(-0.227573\pi\)
\(90\) 0 0
\(91\) 14.6686 4.77844i 1.53768 0.500916i
\(92\) 1.90524 + 3.70711i 0.198635 + 0.386493i
\(93\) 11.0711i 1.14802i
\(94\) 14.3291 + 8.74643i 1.47793 + 0.902125i
\(95\) 0 0
\(96\) −14.5691 + 6.18466i −1.48696 + 0.631219i
\(97\) 8.24621 0.837276 0.418638 0.908153i \(-0.362508\pi\)
0.418638 + 0.908153i \(0.362508\pi\)
\(98\) 0.808986 + 9.86638i 0.0817199 + 0.996655i
\(99\) 7.11529i 0.715114i
\(100\) 0 0
\(101\) 14.0772i 1.40073i 0.713785 + 0.700365i \(0.246979\pi\)
−0.713785 + 0.700365i \(0.753021\pi\)
\(102\) 13.9254 + 8.50000i 1.37882 + 0.841625i
\(103\) 2.31788i 0.228388i −0.993458 0.114194i \(-0.963571\pi\)
0.993458 0.114194i \(-0.0364285\pi\)
\(104\) 16.4481 + 1.20763i 1.61287 + 0.118418i
\(105\) 0 0
\(106\) −4.53553 2.76847i −0.440530 0.268898i
\(107\) −9.80971 −0.948341 −0.474170 0.880433i \(-0.657252\pi\)
−0.474170 + 0.880433i \(0.657252\pi\)
\(108\) 9.10013 4.67695i 0.875661 0.450040i
\(109\) 2.82843 0.270914 0.135457 0.990783i \(-0.456750\pi\)
0.135457 + 0.990783i \(0.456750\pi\)
\(110\) 0 0
\(111\) 6.27476 0.595574
\(112\) −3.19211 + 10.0901i −0.301626 + 0.953426i
\(113\) 4.31371i 0.405800i 0.979200 + 0.202900i \(0.0650366\pi\)
−0.979200 + 0.202900i \(0.934963\pi\)
\(114\) 17.2782 + 10.5465i 1.61825 + 0.987773i
\(115\) 0 0
\(116\) 7.53553 + 14.6622i 0.699657 + 1.36135i
\(117\) −28.1543 −2.60287
\(118\) 4.12311 6.75481i 0.379563 0.621830i
\(119\) 10.3722 3.37887i 0.950821 0.309740i
\(120\) 0 0
\(121\) 8.82843 0.802584
\(122\) −14.0772 8.59264i −1.27449 0.777941i
\(123\) −11.5362 −1.04018
\(124\) 3.61743 + 7.03858i 0.324855 + 0.632083i
\(125\) 0 0
\(126\) 4.17338 17.5777i 0.371794 1.56594i
\(127\) −2.94725 −0.261526 −0.130763 0.991414i \(-0.541743\pi\)
−0.130763 + 0.991414i \(0.541743\pi\)
\(128\) −7.24171 + 8.69239i −0.640083 + 0.768306i
\(129\) 8.24621i 0.726038i
\(130\) 0 0
\(131\) 8.87385 0.775312 0.387656 0.921804i \(-0.373285\pi\)
0.387656 + 0.921804i \(0.373285\pi\)
\(132\) 3.76940 + 7.33428i 0.328084 + 0.638367i
\(133\) 12.8695 4.19239i 1.11593 0.363526i
\(134\) −9.39949 + 15.3990i −0.811993 + 1.33027i
\(135\) 0 0
\(136\) 11.6306 + 0.853923i 0.997316 + 0.0732233i
\(137\) 13.4853i 1.15213i 0.817406 + 0.576063i \(0.195412\pi\)
−0.817406 + 0.576063i \(0.804588\pi\)
\(138\) −7.03858 4.29632i −0.599164 0.365727i
\(139\) −10.7117 −0.908553 −0.454276 0.890861i \(-0.650102\pi\)
−0.454276 + 0.890861i \(0.650102\pi\)
\(140\) 0 0
\(141\) −33.2132 −2.79706
\(142\) −9.63093 5.87868i −0.808210 0.493328i
\(143\) 8.59264i 0.718553i
\(144\) 11.2426 15.7042i 0.936887 1.30868i
\(145\) 0 0
\(146\) 9.11387 14.9311i 0.754269 1.23571i
\(147\) −11.5362 15.8275i −0.951487 1.30543i
\(148\) 3.98926 2.05025i 0.327915 0.168530i
\(149\) −2.00000 −0.163846 −0.0819232 0.996639i \(-0.526106\pi\)
−0.0819232 + 0.996639i \(0.526106\pi\)
\(150\) 0 0
\(151\) 5.03127i 0.409439i −0.978821 0.204720i \(-0.934372\pi\)
0.978821 0.204720i \(-0.0656283\pi\)
\(152\) 14.4309 + 1.05952i 1.17050 + 0.0859384i
\(153\) −19.9081 −1.60948
\(154\) 5.36467 + 1.27371i 0.432297 + 0.102638i
\(155\) 0 0
\(156\) −29.0208 + 14.9150i −2.32352 + 1.19416i
\(157\) 10.6615 0.850878 0.425439 0.904987i \(-0.360120\pi\)
0.425439 + 0.904987i \(0.360120\pi\)
\(158\) −5.03127 3.07107i −0.400267 0.244321i
\(159\) 10.5128 0.833722
\(160\) 0 0
\(161\) −5.24264 + 1.70785i −0.413178 + 0.134597i
\(162\) 0.126417 0.207107i 0.00993227 0.0162718i
\(163\) 3.20009 0.250650 0.125325 0.992116i \(-0.460003\pi\)
0.125325 + 0.992116i \(0.460003\pi\)
\(164\) −7.33428 + 3.76940i −0.572711 + 0.294341i
\(165\) 0 0
\(166\) 3.37740 + 2.06155i 0.262137 + 0.160008i
\(167\) 0.960099i 0.0742947i 0.999310 + 0.0371473i \(0.0118271\pi\)
−0.999310 + 0.0371473i \(0.988173\pi\)
\(168\) −5.01013 20.3295i −0.386540 1.56846i
\(169\) 21.0000 1.61538
\(170\) 0 0
\(171\) −24.7013 −1.88896
\(172\) 2.69442 + 5.24264i 0.205447 + 0.399748i
\(173\) 2.41526 0.183629 0.0918144 0.995776i \(-0.470733\pi\)
0.0918144 + 0.995776i \(0.470733\pi\)
\(174\) −27.8387 16.9926i −2.11045 1.28821i
\(175\) 0 0
\(176\) 4.79289 + 3.43123i 0.361278 + 0.258639i
\(177\) 15.6569i 1.17684i
\(178\) 14.9311 + 9.11387i 1.11913 + 0.683114i
\(179\) 2.69442i 0.201390i −0.994917 0.100695i \(-0.967893\pi\)
0.994917 0.100695i \(-0.0321067\pi\)
\(180\) 0 0
\(181\) 3.41569i 0.253886i −0.991910 0.126943i \(-0.959483\pi\)
0.991910 0.126943i \(-0.0405166\pi\)
\(182\) −5.03989 + 21.2273i −0.373582 + 1.57347i
\(183\) 32.6292 2.41202
\(184\) −5.87868 0.431615i −0.433382 0.0318191i
\(185\) 0 0
\(186\) −13.3640 8.15731i −0.979893 0.598123i
\(187\) 6.07591i 0.444315i
\(188\) −21.1157 + 10.8523i −1.54002 + 0.791484i
\(189\) 4.19239 + 12.8695i 0.304951 + 0.936121i
\(190\) 0 0
\(191\) 4.67371i 0.338178i −0.985601 0.169089i \(-0.945917\pi\)
0.985601 0.169089i \(-0.0540825\pi\)
\(192\) 3.26918 22.1434i 0.235933 1.59806i
\(193\) 14.3137i 1.03032i −0.857093 0.515162i \(-0.827732\pi\)
0.857093 0.515162i \(-0.172268\pi\)
\(194\) −6.07591 + 9.95406i −0.436225 + 0.714660i
\(195\) 0 0
\(196\) −12.5059 6.29315i −0.893275 0.449511i
\(197\) 14.4853i 1.03203i 0.856578 + 0.516017i \(0.172586\pi\)
−0.856578 + 0.516017i \(0.827414\pi\)
\(198\) −8.58892 5.24264i −0.610388 0.372578i
\(199\) −22.1023 −1.56679 −0.783394 0.621526i \(-0.786513\pi\)
−0.783394 + 0.621526i \(0.786513\pi\)
\(200\) 0 0
\(201\) 35.6931i 2.51760i
\(202\) −16.9926 10.3722i −1.19560 0.729788i
\(203\) −20.7355 + 6.75481i −1.45535 + 0.474095i
\(204\) −20.5208 + 10.5465i −1.43674 + 0.738404i
\(205\) 0 0
\(206\) 2.79793 + 1.70785i 0.194941 + 0.118991i
\(207\) 10.0625 0.699395
\(208\) −13.5769 + 18.9649i −0.941392 + 1.31498i
\(209\) 7.53880i 0.521470i
\(210\) 0 0
\(211\) 25.7668i 1.77386i 0.461907 + 0.886928i \(0.347165\pi\)
−0.461907 + 0.886928i \(0.652835\pi\)
\(212\) 6.68368 3.43503i 0.459037 0.235919i
\(213\) 22.3234 1.52957
\(214\) 7.22792 11.8414i 0.494091 0.809459i
\(215\) 0 0
\(216\) −1.05952 + 14.4309i −0.0720912 + 0.981896i
\(217\) −9.95406 + 3.24264i −0.675725 + 0.220125i
\(218\) −2.08402 + 3.41421i −0.141148 + 0.231240i
\(219\) 34.6085i 2.33863i
\(220\) 0 0
\(221\) 24.0416 1.61722
\(222\) −4.62332 + 7.57430i −0.310297 + 0.508354i
\(223\) 9.55274i 0.639699i 0.947468 + 0.319849i \(0.103632\pi\)
−0.947468 + 0.319849i \(0.896368\pi\)
\(224\) −9.82786 11.2877i −0.656652 0.754194i
\(225\) 0 0
\(226\) −5.20711 3.17840i −0.346372 0.211424i
\(227\) 2.31788i 0.153843i 0.997037 + 0.0769217i \(0.0245091\pi\)
−0.997037 + 0.0769217i \(0.975491\pi\)
\(228\) −25.4616 + 13.0858i −1.68623 + 0.866627i
\(229\) 2.41526i 0.159605i 0.996811 + 0.0798024i \(0.0254289\pi\)
−0.996811 + 0.0798024i \(0.974571\pi\)
\(230\) 0 0
\(231\) −10.3722 + 3.37887i −0.682443 + 0.222313i
\(232\) −23.2511 1.70711i −1.52651 0.112077i
\(233\) 23.7990i 1.55912i 0.626325 + 0.779562i \(0.284558\pi\)
−0.626325 + 0.779562i \(0.715442\pi\)
\(234\) 20.7445 33.9853i 1.35611 2.22169i
\(235\) 0 0
\(236\) 5.11582 + 9.95406i 0.333011 + 0.647954i
\(237\) 11.6619 0.757522
\(238\) −3.56374 + 15.0100i −0.231003 + 0.972953i
\(239\) 8.84175i 0.571926i −0.958241 0.285963i \(-0.907687\pi\)
0.958241 0.285963i \(-0.0923134\pi\)
\(240\) 0 0
\(241\) 7.53880i 0.485617i −0.970074 0.242808i \(-0.921931\pi\)
0.970074 0.242808i \(-0.0780686\pi\)
\(242\) −6.50490 + 10.6569i −0.418151 + 0.685049i
\(243\) 15.8275i 1.01533i
\(244\) 20.7445 10.6615i 1.32803 0.682531i
\(245\) 0 0
\(246\) 8.50000 13.9254i 0.541940 0.887851i
\(247\) 29.8301 1.89804
\(248\) −11.1617 0.819496i −0.708768 0.0520380i
\(249\) −7.82843 −0.496106
\(250\) 0 0
\(251\) −20.9433 −1.32193 −0.660965 0.750417i \(-0.729853\pi\)
−0.660965 + 0.750417i \(0.729853\pi\)
\(252\) 18.1431 + 17.9892i 1.14291 + 1.13321i
\(253\) 3.07107i 0.193076i
\(254\) 2.17157 3.55765i 0.136257 0.223227i
\(255\) 0 0
\(256\) −5.15685 15.1462i −0.322303 0.946636i
\(257\) 23.3238 1.45490 0.727450 0.686161i \(-0.240706\pi\)
0.727450 + 0.686161i \(0.240706\pi\)
\(258\) −9.95406 6.07591i −0.619713 0.378270i
\(259\) 1.83783 + 5.64167i 0.114197 + 0.350556i
\(260\) 0 0
\(261\) 39.7990 2.46350
\(262\) −6.53836 + 10.7117i −0.403942 + 0.661770i
\(263\) 14.7363 0.908677 0.454338 0.890829i \(-0.349876\pi\)
0.454338 + 0.890829i \(0.349876\pi\)
\(264\) −11.6306 0.853923i −0.715814 0.0525553i
\(265\) 0 0
\(266\) −4.42178 + 18.6239i −0.271117 + 1.14190i
\(267\) −34.6085 −2.11801
\(268\) −11.6626 22.6924i −0.712406 1.38616i
\(269\) 14.0772i 0.858300i 0.903233 + 0.429150i \(0.141187\pi\)
−0.903233 + 0.429150i \(0.858813\pi\)
\(270\) 0 0
\(271\) −4.23808 −0.257445 −0.128723 0.991681i \(-0.541088\pi\)
−0.128723 + 0.991681i \(0.541088\pi\)
\(272\) −9.60035 + 13.4102i −0.582107 + 0.813112i
\(273\) −13.3698 41.0416i −0.809174 2.48395i
\(274\) −16.2782 9.93613i −0.983400 0.600264i
\(275\) 0 0
\(276\) 10.3722 5.33074i 0.624335 0.320873i
\(277\) 25.8995i 1.55615i −0.628171 0.778075i \(-0.716196\pi\)
0.628171 0.778075i \(-0.283804\pi\)
\(278\) 7.89250 12.9301i 0.473361 0.775498i
\(279\) 19.1055 1.14382
\(280\) 0 0
\(281\) −0.970563 −0.0578989 −0.0289495 0.999581i \(-0.509216\pi\)
−0.0289495 + 0.999581i \(0.509216\pi\)
\(282\) 24.4719 40.0919i 1.45728 2.38744i
\(283\) 12.6319i 0.750887i −0.926845 0.375444i \(-0.877490\pi\)
0.926845 0.375444i \(-0.122510\pi\)
\(284\) 14.1924 7.29408i 0.842163 0.432824i
\(285\) 0 0
\(286\) 10.3722 + 6.33117i 0.613323 + 0.374370i
\(287\) −3.37887 10.3722i −0.199448 0.612254i
\(288\) 10.6729 + 25.1421i 0.628909 + 1.48151i
\(289\) 0 0
\(290\) 0 0
\(291\) 23.0723i 1.35252i
\(292\) 11.3082 + 22.0028i 0.661762 + 1.28762i
\(293\) 16.4924 0.963498 0.481749 0.876309i \(-0.340002\pi\)
0.481749 + 0.876309i \(0.340002\pi\)
\(294\) 27.6055 2.26349i 1.60998 0.132009i
\(295\) 0 0
\(296\) −0.464466 + 6.32612i −0.0269965 + 0.367698i
\(297\) 7.53880 0.437445
\(298\) 1.47363 2.41421i 0.0853648 0.139852i
\(299\) −12.1518 −0.702758
\(300\) 0 0
\(301\) −7.41421 + 2.41526i −0.427348 + 0.139213i
\(302\) 6.07328 + 3.70711i 0.349478 + 0.213320i
\(303\) 39.3870 2.26272
\(304\) −11.9118 + 16.6389i −0.683189 + 0.954308i
\(305\) 0 0
\(306\) 14.6686 24.0312i 0.838546 1.37377i
\(307\) 3.75803i 0.214482i −0.994233 0.107241i \(-0.965798\pi\)
0.994233 0.107241i \(-0.0342017\pi\)
\(308\) −5.49026 + 5.53725i −0.312836 + 0.315514i
\(309\) −6.48528 −0.368935
\(310\) 0 0
\(311\) 22.3835 1.26925 0.634625 0.772820i \(-0.281155\pi\)
0.634625 + 0.772820i \(0.281155\pi\)
\(312\) 3.37887 46.0208i 0.191291 2.60542i
\(313\) 28.1543 1.59138 0.795688 0.605706i \(-0.207109\pi\)
0.795688 + 0.605706i \(0.207109\pi\)
\(314\) −7.85551 + 12.8695i −0.443312 + 0.726270i
\(315\) 0 0
\(316\) 7.41421 3.81048i 0.417082 0.214356i
\(317\) 14.3431i 0.805591i 0.915290 + 0.402796i \(0.131961\pi\)
−0.915290 + 0.402796i \(0.868039\pi\)
\(318\) −7.74599 + 12.6901i −0.434374 + 0.711627i
\(319\) 12.1466i 0.680077i
\(320\) 0 0
\(321\) 27.4469i 1.53194i
\(322\) 1.80129 7.58679i 0.100382 0.422795i
\(323\) 21.0930 1.17365
\(324\) 0.156854 + 0.305198i 0.00871412 + 0.0169554i
\(325\) 0 0
\(326\) −2.35786 + 3.86285i −0.130590 + 0.213943i
\(327\) 7.91375i 0.437631i
\(328\) 0.853923 11.6306i 0.0471500 0.642192i
\(329\) −9.72792 29.8622i −0.536318 1.64635i
\(330\) 0 0
\(331\) 18.1458i 0.997383i 0.866779 + 0.498692i \(0.166186\pi\)
−0.866779 + 0.498692i \(0.833814\pi\)
\(332\) −4.97703 + 2.55791i −0.273150 + 0.140383i
\(333\) 10.8284i 0.593394i
\(334\) −1.15894 0.707413i −0.0634145 0.0387079i
\(335\) 0 0
\(336\) 28.2315 + 8.93131i 1.54015 + 0.487243i
\(337\) 24.7990i 1.35089i −0.737412 0.675444i \(-0.763952\pi\)
0.737412 0.675444i \(-0.236048\pi\)
\(338\) −15.4731 + 25.3492i −0.841624 + 1.37882i
\(339\) 12.0695 0.655523
\(340\) 0 0
\(341\) 5.83095i 0.315764i
\(342\) 18.2003 29.8172i 0.984158 1.61233i
\(343\) 10.8517 15.0080i 0.585938 0.810356i
\(344\) −8.31371 0.610396i −0.448245 0.0329103i
\(345\) 0 0
\(346\) −1.77959 + 2.91548i −0.0956716 + 0.156737i
\(347\) −31.1556 −1.67252 −0.836260 0.548333i \(-0.815263\pi\)
−0.836260 + 0.548333i \(0.815263\pi\)
\(348\) 41.0239 21.0839i 2.19911 1.13022i
\(349\) 2.41526i 0.129286i 0.997908 + 0.0646429i \(0.0205908\pi\)
−0.997908 + 0.0646429i \(0.979409\pi\)
\(350\) 0 0
\(351\) 29.8301i 1.59221i
\(352\) −7.67333 + 3.25736i −0.408990 + 0.173618i
\(353\) −11.6619 −0.620701 −0.310350 0.950622i \(-0.600446\pi\)
−0.310350 + 0.950622i \(0.600446\pi\)
\(354\) −18.8995 11.5362i −1.00450 0.613141i
\(355\) 0 0
\(356\) −22.0028 + 11.3082i −1.16615 + 0.599333i
\(357\) −9.45384 29.0208i −0.500350 1.53594i
\(358\) 3.25245 + 1.98528i 0.171897 + 0.104925i
\(359\) 22.5667i 1.19102i −0.803347 0.595512i \(-0.796949\pi\)
0.803347 0.595512i \(-0.203051\pi\)
\(360\) 0 0
\(361\) 7.17157 0.377451
\(362\) 4.12311 + 2.51673i 0.216706 + 0.132276i
\(363\) 24.7013i 1.29648i
\(364\) −21.9102 21.7243i −1.14841 1.13866i
\(365\) 0 0
\(366\) −24.0416 + 39.3870i −1.25668 + 2.05879i
\(367\) 14.4697i 0.755313i 0.925946 + 0.377656i \(0.123270\pi\)
−0.925946 + 0.377656i \(0.876730\pi\)
\(368\) 4.85249 6.77817i 0.252954 0.353337i
\(369\) 19.9081i 1.03638i
\(370\) 0 0
\(371\) 3.07914 + 9.45215i 0.159861 + 0.490731i
\(372\) 19.6935 10.1213i 1.02106 0.524766i
\(373\) 10.5858i 0.548111i −0.961714 0.274056i \(-0.911635\pi\)
0.961714 0.274056i \(-0.0883652\pi\)
\(374\) 7.33428 + 4.47681i 0.379246 + 0.231490i
\(375\) 0 0
\(376\) 2.45849 33.4851i 0.126787 1.72686i
\(377\) −48.0624 −2.47534
\(378\) −18.6239 4.42178i −0.957910 0.227432i
\(379\) 22.8195i 1.17216i 0.810253 + 0.586080i \(0.199329\pi\)
−0.810253 + 0.586080i \(0.800671\pi\)
\(380\) 0 0
\(381\) 8.24621i 0.422466i
\(382\) 5.64167 + 3.44365i 0.288653 + 0.176193i
\(383\) 12.5495i 0.641250i 0.947206 + 0.320625i \(0.103893\pi\)
−0.947206 + 0.320625i \(0.896107\pi\)
\(384\) 24.3207 + 20.2618i 1.24111 + 1.03398i
\(385\) 0 0
\(386\) 17.2782 + 10.5465i 0.879436 + 0.536804i
\(387\) 14.2306 0.723382
\(388\) −7.53880 14.6686i −0.382724 0.744683i
\(389\) 15.5563 0.788738 0.394369 0.918952i \(-0.370963\pi\)
0.394369 + 0.918952i \(0.370963\pi\)
\(390\) 0 0
\(391\) −8.59264 −0.434549
\(392\) 16.8110 10.4590i 0.849082 0.528261i
\(393\) 24.8284i 1.25243i
\(394\) −17.4853 10.6729i −0.880896 0.537695i
\(395\) 0 0
\(396\) 12.6569 6.50490i 0.636031 0.326883i
\(397\) 30.5696 1.53424 0.767122 0.641502i \(-0.221688\pi\)
0.767122 + 0.641502i \(0.221688\pi\)
\(398\) 16.2852 26.6798i 0.816305 1.33734i
\(399\) −11.7300 36.0081i −0.587235 1.80266i
\(400\) 0 0
\(401\) 28.4558 1.42102 0.710509 0.703689i \(-0.248465\pi\)
0.710509 + 0.703689i \(0.248465\pi\)
\(402\) 43.0854 + 26.2992i 2.14891 + 1.31168i
\(403\) −23.0723 −1.14932
\(404\) 25.0408 12.8695i 1.24583 0.640283i
\(405\) 0 0
\(406\) 7.12440 30.0070i 0.353578 1.48922i
\(407\) 3.30481 0.163814
\(408\) 2.38922 32.5416i 0.118284 1.61105i
\(409\) 7.53880i 0.372770i −0.982477 0.186385i \(-0.940323\pi\)
0.982477 0.186385i \(-0.0596771\pi\)
\(410\) 0 0
\(411\) 37.7309 1.86113
\(412\) −4.12311 + 2.11904i −0.203131 + 0.104398i
\(413\) −14.0772 + 4.58579i −0.692692 + 0.225652i
\(414\) −7.41421 + 12.1466i −0.364389 + 0.596971i
\(415\) 0 0
\(416\) −12.8890 30.3624i −0.631933 1.48864i
\(417\) 29.9706i 1.46766i
\(418\) 9.10013 + 5.55468i 0.445102 + 0.271688i
\(419\) −14.9498 −0.730344 −0.365172 0.930940i \(-0.618990\pi\)
−0.365172 + 0.930940i \(0.618990\pi\)
\(420\) 0 0
\(421\) −23.3137 −1.13624 −0.568120 0.822946i \(-0.692329\pi\)
−0.568120 + 0.822946i \(0.692329\pi\)
\(422\) −31.1032 18.9853i −1.51408 0.924189i
\(423\) 57.3164i 2.78682i
\(424\) −0.778175 + 10.5989i −0.0377915 + 0.514728i
\(425\) 0 0
\(426\) −16.4481 + 26.9467i −0.796915 + 1.30557i
\(427\) 9.55688 + 29.3371i 0.462490 + 1.41972i
\(428\) 8.96817 + 17.4497i 0.433493 + 0.843465i
\(429\) −24.0416 −1.16074
\(430\) 0 0
\(431\) 25.1564i 1.21174i 0.795564 + 0.605870i \(0.207175\pi\)
−0.795564 + 0.605870i \(0.792825\pi\)
\(432\) −16.6389 11.9118i −0.800541 0.573107i
\(433\) 4.12311 0.198144 0.0990719 0.995080i \(-0.468413\pi\)
0.0990719 + 0.995080i \(0.468413\pi\)
\(434\) 3.42006 14.4048i 0.164168 0.691454i
\(435\) 0 0
\(436\) −2.58579 5.03127i −0.123837 0.240954i
\(437\) −10.6615 −0.510007
\(438\) −41.7762 25.5000i −1.99614 1.21844i
\(439\) 5.59587 0.267076 0.133538 0.991044i \(-0.457366\pi\)
0.133538 + 0.991044i \(0.457366\pi\)
\(440\) 0 0
\(441\) −27.3137 + 19.9081i −1.30065 + 0.948005i
\(442\) −17.7142 + 29.0208i −0.842578 + 1.38038i
\(443\) 15.7042 0.746130 0.373065 0.927805i \(-0.378307\pi\)
0.373065 + 0.927805i \(0.378307\pi\)
\(444\) −5.73647 11.1617i −0.272241 0.529710i
\(445\) 0 0
\(446\) −11.5312 7.03858i −0.546017 0.333286i
\(447\) 5.59587i 0.264675i
\(448\) 20.8668 3.54632i 0.985864 0.167548i
\(449\) 0.656854 0.0309989 0.0154994 0.999880i \(-0.495066\pi\)
0.0154994 + 0.999880i \(0.495066\pi\)
\(450\) 0 0
\(451\) −6.07591 −0.286104
\(452\) 7.67333 3.94365i 0.360923 0.185494i
\(453\) −14.0772 −0.661403
\(454\) −2.79793 1.70785i −0.131313 0.0801532i
\(455\) 0 0
\(456\) 2.96447 40.3766i 0.138824 1.89081i
\(457\) 12.5147i 0.585414i −0.956202 0.292707i \(-0.905444\pi\)
0.956202 0.292707i \(-0.0945560\pi\)
\(458\) −2.91548 1.77959i −0.136231 0.0831550i
\(459\) 21.0930i 0.984539i
\(460\) 0 0
\(461\) 14.0772i 0.655639i 0.944740 + 0.327819i \(0.106314\pi\)
−0.944740 + 0.327819i \(0.893686\pi\)
\(462\) 3.56374 15.0100i 0.165800 0.698328i
\(463\) −24.2931 −1.12900 −0.564499 0.825434i \(-0.690931\pi\)
−0.564499 + 0.825434i \(0.690931\pi\)
\(464\) 19.1924 26.8088i 0.890984 1.24457i
\(465\) 0 0
\(466\) −28.7279 17.5354i −1.33080 0.812312i
\(467\) 30.2972i 1.40199i 0.713167 + 0.700994i \(0.247260\pi\)
−0.713167 + 0.700994i \(0.752740\pi\)
\(468\) 25.7391 + 50.0816i 1.18979 + 2.31502i
\(469\) 32.0919 10.4543i 1.48187 0.482734i
\(470\) 0 0
\(471\) 29.8301i 1.37450i
\(472\) −15.7850 1.15894i −0.726564 0.0533446i
\(473\) 4.34315i 0.199698i
\(474\) −8.59264 + 14.0772i −0.394673 + 0.646586i
\(475\) 0 0
\(476\) −15.4928 15.3614i −0.710113 0.704087i
\(477\) 18.1421i 0.830671i
\(478\) 10.6729 + 6.51472i 0.488169 + 0.297976i
\(479\) 16.7876 0.767045 0.383522 0.923532i \(-0.374711\pi\)
0.383522 + 0.923532i \(0.374711\pi\)
\(480\) 0 0
\(481\) 13.0767i 0.596248i
\(482\) 9.10013 + 5.55468i 0.414500 + 0.253009i
\(483\) 4.77844 + 14.6686i 0.217426 + 0.667442i
\(484\) −8.07107 15.7042i −0.366867 0.713828i
\(485\) 0 0
\(486\) −19.1055 11.6619i −0.866642 0.528995i
\(487\) 31.4084 1.42325 0.711626 0.702559i \(-0.247959\pi\)
0.711626 + 0.702559i \(0.247959\pi\)
\(488\) −2.41526 + 32.8963i −0.109334 + 1.48915i
\(489\) 8.95362i 0.404897i
\(490\) 0 0
\(491\) 9.55688i 0.431296i −0.976471 0.215648i \(-0.930814\pi\)
0.976471 0.215648i \(-0.0691863\pi\)
\(492\) 10.5465 + 20.5208i 0.475474 + 0.925150i
\(493\) −33.9853 −1.53062
\(494\) −21.9792 + 36.0081i −0.988890 + 1.62008i
\(495\) 0 0
\(496\) 9.21329 12.8695i 0.413689 0.577859i
\(497\) 6.53836 + 20.0711i 0.293286 + 0.900310i
\(498\) 5.76809 9.44975i 0.258474 0.423453i
\(499\) 8.84175i 0.395811i 0.980221 + 0.197906i \(0.0634140\pi\)
−0.980221 + 0.197906i \(0.936586\pi\)
\(500\) 0 0
\(501\) 2.68629 0.120015
\(502\) 15.4313 25.2808i 0.688733 1.12834i
\(503\) 19.3867i 0.864410i 0.901775 + 0.432205i \(0.142264\pi\)
−0.901775 + 0.432205i \(0.857736\pi\)
\(504\) −35.0830 + 8.64605i −1.56272 + 0.385126i
\(505\) 0 0
\(506\) −3.70711 2.26280i −0.164801 0.100594i
\(507\) 58.7566i 2.60947i
\(508\) 2.69442 + 5.24264i 0.119545 + 0.232605i
\(509\) 8.24621i 0.365507i 0.983159 + 0.182753i \(0.0585010\pi\)
−0.983159 + 0.182753i \(0.941499\pi\)
\(510\) 0 0
\(511\) −31.1167 + 10.1366i −1.37652 + 0.448417i
\(512\) 22.0827 + 4.93503i 0.975927 + 0.218100i
\(513\) 26.1716i 1.15550i
\(514\) −17.1853 + 28.1543i −0.758010 + 1.24183i
\(515\) 0 0
\(516\) 14.6686 7.53880i 0.645747 0.331877i
\(517\) −17.4929 −0.769335
\(518\) −8.16424 1.93839i −0.358716 0.0851681i
\(519\) 6.75773i 0.296632i
\(520\) 0 0
\(521\) 28.8617i 1.26446i −0.774782 0.632228i \(-0.782141\pi\)
0.774782 0.632228i \(-0.217859\pi\)
\(522\) −29.3244 + 48.0416i −1.28349 + 2.10273i
\(523\) 8.39380i 0.367035i −0.983016 0.183518i \(-0.941252\pi\)
0.983016 0.183518i \(-0.0587484\pi\)
\(524\) −8.11259 15.7850i −0.354400 0.689571i
\(525\) 0 0
\(526\) −10.8579 + 17.7882i −0.473425 + 0.775604i
\(527\) −16.3146 −0.710676
\(528\) 9.60035 13.4102i 0.417802 0.583604i
\(529\) −18.6569 −0.811168
\(530\) 0 0
\(531\) 27.0192 1.17253
\(532\) −19.2230 19.0599i −0.833424 0.826351i
\(533\) 24.0416i 1.04136i
\(534\) 25.5000 41.7762i 1.10349 1.80783i
\(535\) 0 0
\(536\) 35.9853 + 2.64205i 1.55433 + 0.114119i
\(537\) −7.53880 −0.325323
\(538\) −16.9926 10.3722i −0.732605 0.447179i
\(539\) −6.07591 8.33609i −0.261708 0.359061i
\(540\) 0 0
\(541\) 1.75736 0.0755548 0.0377774 0.999286i \(-0.487972\pi\)
0.0377774 + 0.999286i \(0.487972\pi\)
\(542\) 3.12267 5.11582i 0.134130 0.219743i
\(543\) −9.55688 −0.410125
\(544\) −9.11387 21.4695i −0.390754 0.920495i
\(545\) 0 0
\(546\) 59.3926 + 14.1013i 2.54177 + 0.603479i
\(547\) −9.80971 −0.419433 −0.209716 0.977762i \(-0.567254\pi\)
−0.209716 + 0.977762i \(0.567254\pi\)
\(548\) 23.9879 12.3284i 1.02471 0.526644i
\(549\) 56.3087i 2.40319i
\(550\) 0 0
\(551\) −42.1678 −1.79641
\(552\) −1.20763 + 16.4481i −0.0514001 + 0.700080i
\(553\) 3.41569 + 10.4853i 0.145250 + 0.445880i
\(554\) 31.2635 + 19.0831i 1.32826 + 0.810762i
\(555\) 0 0
\(556\) 9.79276 + 19.0542i 0.415306 + 0.808078i
\(557\) 33.3137i 1.41155i 0.708437 + 0.705774i \(0.249400\pi\)
−0.708437 + 0.705774i \(0.750600\pi\)
\(558\) −14.0772 + 23.0624i −0.595934 + 0.976307i
\(559\) −17.1853 −0.726860
\(560\) 0 0
\(561\) −17.0000 −0.717741
\(562\) 0.715123 1.17157i 0.0301656 0.0494198i
\(563\) 37.2509i 1.56994i −0.619536 0.784968i \(-0.712679\pi\)
0.619536 0.784968i \(-0.287321\pi\)
\(564\) 30.3640 + 59.0804i 1.27855 + 2.48773i
\(565\) 0 0
\(566\) 15.2480 + 9.30733i 0.640922 + 0.391216i
\(567\) −0.431615 + 0.140603i −0.0181261 + 0.00590478i
\(568\) −1.65241 + 22.5061i −0.0693334 + 0.944335i
\(569\) −26.3137 −1.10313 −0.551564 0.834133i \(-0.685969\pi\)
−0.551564 + 0.834133i \(0.685969\pi\)
\(570\) 0 0
\(571\) 24.2931i 1.01664i −0.861169 0.508318i \(-0.830267\pi\)
0.861169 0.508318i \(-0.169733\pi\)
\(572\) −15.2848 + 7.85551i −0.639089 + 0.328455i
\(573\) −13.0767 −0.546288
\(574\) 15.0100 + 3.56374i 0.626505 + 0.148748i
\(575\) 0 0
\(576\) −38.2132 5.64167i −1.59222 0.235070i
\(577\) −15.7850 −0.657139 −0.328569 0.944480i \(-0.606566\pi\)
−0.328569 + 0.944480i \(0.606566\pi\)
\(578\) 0 0
\(579\) −40.0488 −1.66437
\(580\) 0 0
\(581\) −2.29289 7.03858i −0.0951252 0.292010i
\(582\) 27.8508 + 17.0000i 1.15445 + 0.704673i
\(583\) 5.53694 0.229317
\(584\) −34.8918 2.56177i −1.44383 0.106007i
\(585\) 0 0
\(586\) −12.1518 + 19.9081i −0.501987 + 0.822397i
\(587\) 29.8172i 1.23069i −0.788260 0.615343i \(-0.789018\pi\)
0.788260 0.615343i \(-0.210982\pi\)
\(588\) −17.6078 + 34.9905i −0.726133 + 1.44299i
\(589\) −20.2426 −0.834083
\(590\) 0 0
\(591\) 40.5288 1.66713
\(592\) −7.29408 5.22183i −0.299785 0.214616i
\(593\) −0.707413 −0.0290500 −0.0145250 0.999895i \(-0.504624\pi\)
−0.0145250 + 0.999895i \(0.504624\pi\)
\(594\) −5.55468 + 9.10013i −0.227911 + 0.373383i
\(595\) 0 0
\(596\) 1.82843 + 3.55765i 0.0748953 + 0.145727i
\(597\) 61.8406i 2.53097i
\(598\) 8.95362 14.6686i 0.366141 0.599842i
\(599\) 6.75773i 0.276113i −0.990424 0.138057i \(-0.955914\pi\)
0.990424 0.138057i \(-0.0440856\pi\)
\(600\) 0 0
\(601\) 7.53880i 0.307514i −0.988109 0.153757i \(-0.950863\pi\)
0.988109 0.153757i \(-0.0491373\pi\)
\(602\) 2.54741 10.7293i 0.103825 0.437295i
\(603\) −61.5961 −2.50839
\(604\) −8.94975 + 4.59966i −0.364160 + 0.187157i
\(605\) 0 0
\(606\) −29.0208 + 47.5443i −1.17889 + 1.93135i
\(607\) 31.6550i 1.28484i 0.766354 + 0.642418i \(0.222069\pi\)
−0.766354 + 0.642418i \(0.777931\pi\)
\(608\) −11.3082 26.6386i −0.458608 1.08034i
\(609\) 18.8995 + 58.0165i 0.765846 + 2.35095i
\(610\) 0 0
\(611\) 69.2170i 2.80022i
\(612\) 18.2003 + 35.4130i 0.735702 + 1.43149i
\(613\) 45.1127i 1.82208i 0.412313 + 0.911042i \(0.364721\pi\)
−0.412313 + 0.911042i \(0.635279\pi\)
\(614\) 4.53635 + 2.76897i 0.183072 + 0.111746i
\(615\) 0 0
\(616\) −2.63876 10.7072i −0.106319 0.431407i
\(617\) 22.0000i 0.885687i −0.896599 0.442843i \(-0.853970\pi\)
0.896599 0.442843i \(-0.146030\pi\)
\(618\) 4.77844 7.82843i 0.192217 0.314906i
\(619\) 20.0656 0.806504 0.403252 0.915089i \(-0.367880\pi\)
0.403252 + 0.915089i \(0.367880\pi\)
\(620\) 0 0
\(621\) 10.6615i 0.427830i
\(622\) −16.4924 + 27.0192i −0.661286 + 1.08337i
\(623\) −10.1366 31.1167i −0.406114 1.24666i
\(624\) 53.0624 + 37.9874i 2.12420 + 1.52071i
\(625\) 0 0
\(626\) −20.7445 + 33.9853i −0.829116 + 1.35832i
\(627\) −21.0930 −0.842375
\(628\) −9.74686 18.9649i −0.388942 0.756781i
\(629\) 9.24664i 0.368688i
\(630\) 0 0
\(631\) 6.25206i 0.248891i 0.992226 + 0.124445i \(0.0397152\pi\)
−0.992226 + 0.124445i \(0.960285\pi\)
\(632\) −0.863230 + 11.7574i −0.0343374 + 0.467683i
\(633\) 72.0937 2.86547
\(634\) −17.3137 10.5682i −0.687615 0.419717i
\(635\) 0 0
\(636\) −9.61098 18.7005i −0.381100 0.741522i
\(637\) 32.9848 24.0416i 1.30691 0.952564i
\(638\) −14.6622 8.94975i −0.580482 0.354324i
\(639\) 38.5237i 1.52397i
\(640\) 0 0
\(641\) −26.8284 −1.05966 −0.529830 0.848104i \(-0.677744\pi\)
−0.529830 + 0.848104i \(0.677744\pi\)
\(642\) −33.1314 20.2232i −1.30759 0.798148i
\(643\) 14.8674i 0.586313i 0.956064 + 0.293156i \(0.0947057\pi\)
−0.956064 + 0.293156i \(0.905294\pi\)
\(644\) 7.83085 + 7.76440i 0.308579 + 0.305960i
\(645\) 0 0
\(646\) −15.5416 + 25.4616i −0.611477 + 1.00177i
\(647\) 21.8210i 0.857874i −0.903334 0.428937i \(-0.858888\pi\)
0.903334 0.428937i \(-0.141112\pi\)
\(648\) −0.483979 0.0355339i −0.0190125 0.00139590i
\(649\) 8.24621i 0.323692i
\(650\) 0 0
\(651\) 9.07269 + 27.8508i 0.355587 + 1.09156i
\(652\) −2.92556 5.69239i −0.114574 0.222931i
\(653\) 1.55635i 0.0609047i 0.999536 + 0.0304523i \(0.00969477\pi\)
−0.999536 + 0.0304523i \(0.990305\pi\)
\(654\) 9.55274 + 5.83095i 0.373542 + 0.228008i
\(655\) 0 0
\(656\) 13.4102 + 9.60035i 0.523580 + 0.374831i
\(657\) 59.7243 2.33007
\(658\) 43.2145 + 10.2602i 1.68468 + 0.399984i
\(659\) 29.9348i 1.16609i 0.812438 + 0.583047i \(0.198140\pi\)
−0.812438 + 0.583047i \(0.801860\pi\)
\(660\) 0 0
\(661\) 38.8158i 1.50976i −0.655863 0.754880i \(-0.727695\pi\)
0.655863 0.754880i \(-0.272305\pi\)
\(662\) −21.9039 13.3701i −0.851320 0.519642i
\(663\) 67.2669i 2.61243i
\(664\) 0.579471 7.89250i 0.0224878 0.306289i
\(665\) 0 0
\(666\) 13.0711 + 7.97852i 0.506494 + 0.309162i
\(667\) 17.1778 0.665129
\(668\) 1.70785 0.877735i 0.0660786 0.0339606i
\(669\) 26.7279 1.03336
\(670\) 0 0
\(671\) 17.1853 0.663430
\(672\) −31.5823 + 27.4977i −1.21832 + 1.06075i
\(673\) 4.00000i 0.154189i 0.997024 + 0.0770943i \(0.0245643\pi\)
−0.997024 + 0.0770943i \(0.975436\pi\)
\(674\) 29.9350 + 18.2722i 1.15305 + 0.703819i
\(675\) 0 0
\(676\) −19.1985 37.3553i −0.738403 1.43674i
\(677\) −11.6619 −0.448203 −0.224102 0.974566i \(-0.571945\pi\)
−0.224102 + 0.974566i \(0.571945\pi\)
\(678\) −8.89294 + 14.5691i −0.341531 + 0.559524i
\(679\) 20.7445 6.75773i 0.796100 0.259338i
\(680\) 0 0
\(681\) 6.48528 0.248517
\(682\) −7.03858 4.29632i −0.269521 0.164515i
\(683\) −11.0305 −0.422070 −0.211035 0.977478i \(-0.567683\pi\)
−0.211035 + 0.977478i \(0.567683\pi\)
\(684\) 22.5823 + 43.9393i 0.863456 + 1.68006i
\(685\) 0 0
\(686\) 10.1206 + 24.1573i 0.386405 + 0.922329i
\(687\) 6.75773 0.257824
\(688\) 6.86246 9.58579i 0.261629 0.365455i
\(689\) 21.9090i 0.834666i
\(690\) 0 0
\(691\) −19.0231 −0.723673 −0.361837 0.932241i \(-0.617850\pi\)
−0.361837 + 0.932241i \(0.617850\pi\)
\(692\) −2.20806 4.29632i −0.0839380 0.163322i
\(693\) 5.83095 + 17.8995i 0.221500 + 0.679946i
\(694\) 22.9558 37.6081i 0.871392 1.42759i
\(695\) 0 0
\(696\) −4.77637 + 65.0551i −0.181048 + 2.46591i
\(697\) 17.0000i 0.643921i
\(698\) −2.91548 1.77959i −0.110352 0.0673586i
\(699\) 66.5880 2.51859
\(700\) 0 0
\(701\) −11.1716 −0.421944 −0.210972 0.977492i \(-0.567663\pi\)
−0.210972 + 0.977492i \(0.567663\pi\)
\(702\) −36.0081 21.9792i −1.35904 0.829551i
\(703\) 11.4729i 0.432710i
\(704\) 1.72183 11.6626i 0.0648937 0.439550i
\(705\) 0 0
\(706\) 8.59264 14.0772i 0.323388 0.529801i
\(707\) 11.5362 + 35.4130i 0.433862 + 1.33184i
\(708\) 27.8508 14.3137i 1.04670 0.537942i
\(709\) 28.0000 1.05156 0.525781 0.850620i \(-0.323773\pi\)
0.525781 + 0.850620i \(0.323773\pi\)
\(710\) 0 0
\(711\) 20.1251i 0.754750i
\(712\) 2.56177 34.8918i 0.0960064 1.30763i
\(713\) 8.24621 0.308823
\(714\) 41.9969 + 9.97111i 1.57170 + 0.373160i
\(715\) 0 0
\(716\) −4.79289 + 2.46327i −0.179119 + 0.0920568i
\(717\) −24.7386 −0.923881
\(718\) 27.2404 + 16.6274i 1.01660 + 0.620530i
\(719\) 30.5784 1.14038 0.570191 0.821512i \(-0.306869\pi\)
0.570191 + 0.821512i \(0.306869\pi\)
\(720\) 0 0
\(721\) −1.89949 5.83095i −0.0707409 0.217156i
\(722\) −5.28411 + 8.65685i −0.196654 + 0.322175i
\(723\) −21.0930 −0.784459
\(724\) −6.07591 + 3.12267i −0.225810 + 0.116053i
\(725\) 0 0
\(726\) 29.8172 + 18.2003i 1.10662 + 0.675475i
\(727\) 5.87707i 0.217969i 0.994043 + 0.108984i \(0.0347598\pi\)
−0.994043 + 0.108984i \(0.965240\pi\)
\(728\) 42.3672 10.4412i 1.57023 0.386978i
\(729\) 43.7696 1.62109
\(730\) 0 0
\(731\) −12.1518 −0.449452
\(732\) −29.8301 58.0416i −1.10255 2.14528i
\(733\) −24.7386 −0.913742 −0.456871 0.889533i \(-0.651030\pi\)
−0.456871 + 0.889533i \(0.651030\pi\)
\(734\) −17.4665 10.6615i −0.644700 0.393522i
\(735\) 0 0
\(736\) 4.60660 + 10.8517i 0.169802 + 0.400000i
\(737\) 18.7990i 0.692470i
\(738\) −24.0312 14.6686i −0.884601 0.539957i
\(739\) 43.1974i 1.58904i 0.607236 + 0.794522i \(0.292278\pi\)
−0.607236 + 0.794522i \(0.707722\pi\)
\(740\) 0 0
\(741\) 83.4625i 3.06607i
\(742\) −13.6785 3.24762i −0.502154 0.119224i
\(743\) −20.4827 −0.751436 −0.375718 0.926734i \(-0.622604\pi\)
−0.375718 + 0.926734i \(0.622604\pi\)
\(744\) −2.29289 + 31.2296i −0.0840615 + 1.14493i
\(745\) 0 0
\(746\) 12.7782 + 7.79974i 0.467842 + 0.285569i
\(747\) 13.5096i 0.494291i
\(748\) −10.8080 + 5.55468i −0.395179 + 0.203099i
\(749\) −24.6777 + 8.03901i −0.901702 + 0.293739i
\(750\) 0 0
\(751\) 34.7132i 1.26670i 0.773864 + 0.633352i \(0.218322\pi\)
−0.773864 + 0.633352i \(0.781678\pi\)
\(752\) 38.6086 + 27.6399i 1.40791 + 1.00792i
\(753\) 58.5980i 2.13543i
\(754\) 35.4130 58.0165i 1.28967 2.11284i
\(755\) 0 0
\(756\) 19.0599 19.2230i 0.693202 0.699135i
\(757\) 15.4142i 0.560239i −0.959965 0.280120i \(-0.909626\pi\)
0.959965 0.280120i \(-0.0903741\pi\)
\(758\) −27.5456 16.8137i −1.00050 0.610701i
\(759\) 8.59264 0.311893
\(760\) 0 0
\(761\) 30.8626i 1.11877i 0.828908 + 0.559384i \(0.188962\pi\)
−0.828908 + 0.559384i \(0.811038\pi\)
\(762\) −9.95406 6.07591i −0.360597 0.220107i
\(763\) 7.11529 2.31788i 0.257591 0.0839130i
\(764\) −8.31371 + 4.27277i −0.300779 + 0.154583i
\(765\) 0 0
\(766\) −15.1486 9.24664i −0.547341 0.334095i
\(767\) −32.6292 −1.17817
\(768\) −42.3780 + 14.4285i −1.52918 + 0.520645i
\(769\) 17.1998i 0.620242i 0.950697 + 0.310121i \(0.100370\pi\)
−0.950697 + 0.310121i \(0.899630\pi\)
\(770\) 0 0
\(771\) 65.2584i 2.35023i
\(772\) −25.4616 + 13.0858i −0.916382 + 0.470968i
\(773\) −13.0767 −0.470337 −0.235169 0.971955i \(-0.575564\pi\)
−0.235169 + 0.971955i \(0.575564\pi\)
\(774\) −10.4853 + 17.1778i −0.376886 + 0.617445i
\(775\) 0 0
\(776\) 23.2612 + 1.70785i 0.835028 + 0.0613081i
\(777\) 15.7850 5.14214i 0.566284 0.184473i
\(778\) −11.4621 + 18.7782i −0.410937 + 0.673230i
\(779\) 21.0930i 0.755737i
\(780\) 0 0
\(781\) 11.7574 0.420711
\(782\) 6.33117 10.3722i 0.226402 0.370910i
\(783\) 42.1678i 1.50696i
\(784\) 0.238620 + 27.9990i 0.00852213 + 0.999964i
\(785\) 0 0
\(786\) 29.9706 + 18.2939i 1.06901 + 0.652522i
\(787\) 39.1711i 1.39630i −0.715953 0.698149i \(-0.754007\pi\)
0.715953 0.698149i \(-0.245993\pi\)
\(788\) 25.7668 13.2426i 0.917903 0.471750i
\(789\) 41.2311i 1.46786i
\(790\) 0 0
\(791\) 3.53506 + 10.8517i 0.125692 + 0.385843i
\(792\) −1.47363 + 20.0711i −0.0523630 + 0.713194i
\(793\) 68.0000i 2.41475i
\(794\) −22.5241 + 36.9008i −0.799349 + 1.30956i
\(795\) 0 0
\(796\) 20.2062 + 39.3160i 0.716189 + 1.39352i
\(797\) 43.2319 1.53135 0.765677 0.643226i \(-0.222404\pi\)
0.765677 + 0.643226i \(0.222404\pi\)
\(798\) 52.1084 + 12.3718i 1.84462 + 0.437958i
\(799\) 48.9438i 1.73151i
\(800\) 0 0
\(801\) 59.7243i 2.11026i
\(802\) −20.9666 + 34.3492i −0.740358 + 1.21291i
\(803\) 18.2277i 0.643243i
\(804\) −63.4918 + 32.6311i −2.23918 + 1.15081i
\(805\) 0 0
\(806\) 17.0000 27.8508i 0.598799 0.981002i
\(807\) 39.3870 1.38649
\(808\) −2.91548 + 39.7093i −0.102566 + 1.39697i
\(809\) 6.82843 0.240075 0.120037 0.992769i \(-0.461699\pi\)
0.120037 + 0.992769i \(0.461699\pi\)
\(810\) 0 0
\(811\) −21.0257 −0.738311 −0.369156 0.929368i \(-0.620353\pi\)
−0.369156 + 0.929368i \(0.620353\pi\)
\(812\) 30.9723 + 30.7094i 1.08691 + 1.07769i
\(813\) 11.8579i 0.415873i
\(814\) −2.43503 + 3.98926i −0.0853477 + 0.139824i
\(815\) 0 0
\(816\) 37.5208 + 26.8611i 1.31349 + 0.940328i
\(817\) −15.0776 −0.527498
\(818\) 9.10013 + 5.55468i 0.318179 + 0.194215i
\(819\) −70.8261 + 23.0723i −2.47486 + 0.806213i
\(820\) 0 0
\(821\) 17.4142 0.607760 0.303880 0.952710i \(-0.401718\pi\)
0.303880 + 0.952710i \(0.401718\pi\)
\(822\) −27.8006 + 45.5452i −0.969658 + 1.58857i
\(823\) 19.9770 0.696354 0.348177 0.937429i \(-0.386801\pi\)
0.348177 + 0.937429i \(0.386801\pi\)
\(824\) 0.480049 6.53836i 0.0167233 0.227775i
\(825\) 0 0
\(826\) 4.83670 20.3715i 0.168290 0.708815i
\(827\) 33.5972 1.16829 0.584144 0.811650i \(-0.301430\pi\)
0.584144 + 0.811650i \(0.301430\pi\)
\(828\) −9.19932 17.8995i −0.319698 0.622050i
\(829\) 43.2319i 1.50151i 0.660583 + 0.750753i \(0.270309\pi\)
−0.660583 + 0.750753i \(0.729691\pi\)
\(830\) 0 0
\(831\) −72.4650 −2.51378
\(832\) 46.1474 + 6.81305i 1.59987 + 0.236200i
\(833\) 23.3238 17.0000i 0.808122 0.589015i
\(834\) −36.1777 22.0827i −1.25273 0.764661i
\(835\) 0 0
\(836\) −13.4102 + 6.89207i −0.463801 + 0.238367i
\(837\) 20.2426i 0.699688i
\(838\) 11.0152 18.0460i 0.380513 0.623387i
\(839\) −15.5463 −0.536718 −0.268359 0.963319i \(-0.586481\pi\)
−0.268359 + 0.963319i \(0.586481\pi\)
\(840\) 0 0
\(841\) 38.9411 1.34280
\(842\) 17.1778 28.1421i 0.591987 0.969842i
\(843\) 2.71557i 0.0935292i
\(844\) 45.8345 23.5563i 1.57769 0.810842i
\(845\) 0 0
\(846\) −69.1871 42.2315i −2.37870 1.45195i
\(847\) 22.2091 7.23486i 0.763114 0.248593i
\(848\) −12.2206 8.74874i −0.419658 0.300433i
\(849\) −35.3431 −1.21297
\(850\) 0 0
\(851\) 4.67371i 0.160213i
\(852\) −20.4083 39.7093i −0.699178 1.36042i
\(853\) −31.5700 −1.08094 −0.540468 0.841364i \(-0.681753\pi\)
−0.540468 + 0.841364i \(0.681753\pi\)
\(854\) −42.4547 10.0798i −1.45277 0.344923i
\(855\) 0 0
\(856\) −27.6716 2.03166i −0.945795 0.0694406i
\(857\) −52.1855 −1.78262 −0.891312 0.453390i \(-0.850214\pi\)
−0.891312 + 0.453390i \(0.850214\pi\)
\(858\) 17.7142 29.0208i 0.604752 0.990754i
\(859\) −37.3332 −1.27379 −0.636897 0.770949i \(-0.719782\pi\)
−0.636897 + 0.770949i \(0.719782\pi\)
\(860\) 0 0
\(861\) −29.0208 + 9.45384i −0.989027 + 0.322186i
\(862\) −30.3664 18.5355i −1.03428 0.631323i
\(863\) −23.0723 −0.785392 −0.392696 0.919668i \(-0.628457\pi\)
−0.392696 + 0.919668i \(0.628457\pi\)
\(864\) 26.6386 11.3082i 0.906264 0.384713i
\(865\) 0 0
\(866\) −3.03796 + 4.97703i −0.103234 + 0.169126i
\(867\) 0 0
\(868\) 14.8682 + 14.7420i 0.504660 + 0.500378i
\(869\) 6.14214 0.208358
\(870\) 0 0
\(871\) 74.3852 2.52045
\(872\) 7.97852 + 0.585786i 0.270187 + 0.0198372i
\(873\) −39.8162 −1.34758
\(874\) 7.85551 12.8695i 0.265717 0.435318i
\(875\) 0 0
\(876\) 61.5624 31.6396i 2.08000 1.06900i
\(877\) 28.9706i 0.978266i 0.872209 + 0.489133i \(0.162687\pi\)
−0.872209 + 0.489133i \(0.837313\pi\)
\(878\) −4.12311 + 6.75481i −0.139148 + 0.227964i
\(879\) 46.1447i 1.55642i
\(880\) 0 0
\(881\) 11.6619i 0.392900i −0.980514 0.196450i \(-0.937059\pi\)
0.980514 0.196450i \(-0.0629413\pi\)
\(882\) −3.90613 47.6391i −0.131526 1.60409i
\(883\) −45.8919 −1.54438 −0.772192 0.635389i \(-0.780840\pi\)
−0.772192 + 0.635389i \(0.780840\pi\)
\(884\) −21.9792 42.7658i −0.739240 1.43837i
\(885\) 0 0
\(886\) −11.5711 + 18.9567i −0.388738 + 0.636862i
\(887\) 12.8307i 0.430813i −0.976524 0.215407i \(-0.930892\pi\)
0.976524 0.215407i \(-0.0691077\pi\)
\(888\) 17.7001 + 1.29954i 0.593975 + 0.0436099i
\(889\) −7.41421 + 2.41526i −0.248665 + 0.0810052i
\(890\) 0 0
\(891\) 0.252834i 0.00847026i
\(892\) 16.9926 8.73324i 0.568956 0.292411i
\(893\) 60.7279i 2.03218i
\(894\) −6.75481 4.12311i −0.225915 0.137897i
\(895\) 0 0
\(896\) −11.0941 + 27.8014i −0.370629 + 0.928781i
\(897\) 34.0000i 1.13523i
\(898\) −0.483979 + 0.792893i −0.0161506 + 0.0264592i
\(899\) 32.6151 1.08777
\(900\) 0 0
\(901\) 15.4920i 0.516113i
\(902\) 4.47681 7.33428i 0.149062 0.244205i
\(903\) 6.75773 + 20.7445i 0.224883 + 0.690333i
\(904\) −0.893398 + 12.1683i −0.0297140 + 0.404710i
\(905\) 0 0
\(906\) 10.3722 16.9926i 0.344594 0.564543i
\(907\) 20.8402 0.691988 0.345994 0.938237i \(-0.387542\pi\)
0.345994 + 0.938237i \(0.387542\pi\)
\(908\) 4.12311 2.11904i 0.136830 0.0703228i
\(909\) 67.9706i 2.25444i
\(910\) 0 0
\(911\) 7.62096i 0.252494i 0.991999 + 0.126247i \(0.0402932\pi\)
−0.991999 + 0.126247i \(0.959707\pi\)
\(912\) 46.5546 + 33.3284i 1.54158 + 1.10361i
\(913\) −4.12311 −0.136455
\(914\) 15.1066 + 9.22101i 0.499682 + 0.305004i
\(915\) 0 0
\(916\) 4.29632 2.20806i 0.141954 0.0729565i
\(917\) 22.3234 7.27208i 0.737183 0.240145i
\(918\) −25.4616 15.5416i −0.840357 0.512950i
\(919\) 29.6820i 0.979118i 0.871970 + 0.489559i \(0.162842\pi\)
−0.871970 + 0.489559i \(0.837158\pi\)
\(920\) 0 0
\(921\) −10.5147 −0.346472
\(922\) −16.9926 10.3722i −0.559623 0.341591i
\(923\) 46.5224i 1.53130i
\(924\) 15.4928 + 15.3614i 0.509677 + 0.505352i
\(925\) 0 0
\(926\) 17.8995 29.3244i 0.588214 0.963660i
\(927\) 11.1917i 0.367585i
\(928\) 18.2199 + 42.9203i 0.598096 + 1.40893i
\(929\) 6.83139i 0.224130i −0.993701 0.112065i \(-0.964253\pi\)
0.993701 0.112065i \(-0.0357466\pi\)
\(930\) 0 0
\(931\) 28.9394 21.0930i 0.948451 0.691297i
\(932\) 42.3342 21.7574i 1.38670 0.712686i
\(933\) 62.6274i 2.05033i
\(934\) −36.5720 22.3234i −1.19667 0.730443i
\(935\) 0 0
\(936\) −79.4187 5.83095i −2.59588 0.190591i
\(937\) −35.6931 −1.16604 −0.583022 0.812457i \(-0.698130\pi\)
−0.583022 + 0.812457i \(0.698130\pi\)
\(938\) −11.0263 + 46.4412i −0.360021 + 1.51636i
\(939\) 78.7739i 2.57069i
\(940\) 0 0
\(941\) 24.7386i 0.806456i −0.915099 0.403228i \(-0.867888\pi\)
0.915099 0.403228i \(-0.132112\pi\)
\(942\) 36.0081 + 21.9792i 1.17321 + 0.716121i
\(943\) 8.59264i 0.279815i
\(944\) 13.0296 18.2003i 0.424076 0.592368i
\(945\) 0 0
\(946\) −5.24264 3.20009i −0.170453 0.104044i
\(947\) −39.7445 −1.29152 −0.645762 0.763539i \(-0.723460\pi\)
−0.645762 + 0.763539i \(0.723460\pi\)
\(948\) −10.6615 20.7445i −0.346268 0.673749i
\(949\) −72.1249 −2.34127
\(950\) 0 0
\(951\) 40.1312 1.30134
\(952\) 29.9581 7.38306i 0.970949 0.239286i
\(953\) 19.7696i 0.640399i −0.947350 0.320199i \(-0.896250\pi\)
0.947350 0.320199i \(-0.103750\pi\)
\(954\) 21.8995 + 13.3674i 0.709022 + 0.432784i
\(955\) 0 0
\(956\) −15.7279 + 8.08325i −0.508677 + 0.261431i
\(957\) 33.9853 1.09859
\(958\) −12.3693 + 20.2644i −0.399634 + 0.654714i
\(959\) 11.0511 + 33.9241i 0.356860 + 1.09547i
\(960\) 0 0
\(961\) −15.3431 −0.494940
\(962\) −15.7850 9.63510i −0.508929 0.310648i
\(963\) 47.3655 1.52633
\(964\) −13.4102 + 6.89207i −0.431913 + 0.221979i
\(965\) 0 0
\(966\) −21.2273 5.03989i −0.682978 0.162156i
\(967\) −0.863230 −0.0277596 −0.0138798 0.999904i \(-0.504418\pi\)
−0.0138798 + 0.999904i \(0.504418\pi\)
\(968\) 24.9035 + 1.82843i 0.800430 + 0.0587679i
\(969\) 59.0169i 1.89590i
\(970\) 0 0
\(971\) 41.0089 1.31604 0.658019 0.753001i \(-0.271395\pi\)
0.658019 + 0.753001i \(0.271395\pi\)
\(972\) 28.1543 14.4697i 0.903050 0.464116i
\(973\) −26.9467 + 8.77817i −0.863871 + 0.281415i
\(974\) −23.1421 + 37.9133i −0.741522 + 1.21482i
\(975\) 0 0
\(976\) −37.9298 27.1539i −1.21410 0.869175i
\(977\) 49.2843i 1.57674i −0.615199 0.788372i \(-0.710924\pi\)
0.615199 0.788372i \(-0.289076\pi\)
\(978\) 10.8080 + 6.59715i 0.345601 + 0.210953i
\(979\) −18.2277 −0.582561
\(980\) 0 0
\(981\) −13.6569 −0.436030
\(982\) 11.5362 + 7.04163i 0.368134 + 0.224707i
\(983\) 33.2940i 1.06191i 0.847399 + 0.530957i \(0.178167\pi\)
−0.847399 + 0.530957i \(0.821833\pi\)
\(984\) −32.5416 2.38922i −1.03739 0.0761655i
\(985\) 0 0
\(986\) 25.0408 41.0239i 0.797461 1.30647i
\(987\) −83.5523 + 27.2181i −2.65950 + 0.866361i
\(988\) −27.2711 53.0624i −0.867608 1.68814i
\(989\) 6.14214 0.195309
\(990\) 0 0
\(991\) 9.19932i 0.292226i −0.989268 0.146113i \(-0.953324\pi\)
0.989268 0.146113i \(-0.0466763\pi\)
\(992\) 8.74643 + 20.6039i 0.277699 + 0.654173i
\(993\) 50.7707 1.61116
\(994\) −29.0455 6.89612i −0.921266 0.218732i
\(995\) 0 0
\(996\) 7.15685 + 13.9254i 0.226774 + 0.441243i
\(997\) −14.0772 −0.445828 −0.222914 0.974838i \(-0.571557\pi\)
−0.222914 + 0.974838i \(0.571557\pi\)
\(998\) −10.6729 6.51472i −0.337846 0.206220i
\(999\) −11.4729 −0.362988
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 700.2.c.k.699.7 16
4.3 odd 2 inner 700.2.c.k.699.12 16
5.2 odd 4 700.2.g.i.251.1 8
5.3 odd 4 700.2.g.k.251.8 yes 8
5.4 even 2 inner 700.2.c.k.699.10 16
7.6 odd 2 inner 700.2.c.k.699.8 16
20.3 even 4 700.2.g.k.251.5 yes 8
20.7 even 4 700.2.g.i.251.4 yes 8
20.19 odd 2 inner 700.2.c.k.699.5 16
28.27 even 2 inner 700.2.c.k.699.11 16
35.13 even 4 700.2.g.k.251.7 yes 8
35.27 even 4 700.2.g.i.251.2 yes 8
35.34 odd 2 inner 700.2.c.k.699.9 16
140.27 odd 4 700.2.g.i.251.3 yes 8
140.83 odd 4 700.2.g.k.251.6 yes 8
140.139 even 2 inner 700.2.c.k.699.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.2.c.k.699.5 16 20.19 odd 2 inner
700.2.c.k.699.6 16 140.139 even 2 inner
700.2.c.k.699.7 16 1.1 even 1 trivial
700.2.c.k.699.8 16 7.6 odd 2 inner
700.2.c.k.699.9 16 35.34 odd 2 inner
700.2.c.k.699.10 16 5.4 even 2 inner
700.2.c.k.699.11 16 28.27 even 2 inner
700.2.c.k.699.12 16 4.3 odd 2 inner
700.2.g.i.251.1 8 5.2 odd 4
700.2.g.i.251.2 yes 8 35.27 even 4
700.2.g.i.251.3 yes 8 140.27 odd 4
700.2.g.i.251.4 yes 8 20.7 even 4
700.2.g.k.251.5 yes 8 20.3 even 4
700.2.g.k.251.6 yes 8 140.83 odd 4
700.2.g.k.251.7 yes 8 35.13 even 4
700.2.g.k.251.8 yes 8 5.3 odd 4