Properties

Label 702.2.bb.a.71.11
Level $702$
Weight $2$
Character 702.71
Analytic conductor $5.605$
Analytic rank $0$
Dimension $56$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [702,2,Mod(71,702)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(702, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("702.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 702.bb (of order \(12\), degree \(4\), 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: \(5.60549822189\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 234)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 71.11
Character \(\chi\) \(=\) 702.71
Dual form 702.2.bb.a.89.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.653109 + 0.175000i) q^{5} +(-3.90017 + 1.04505i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.653109 + 0.175000i) q^{5} +(-3.90017 + 1.04505i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.585562 - 0.338074i) q^{10} +(0.502310 - 0.502310i) q^{11} +(-2.29871 + 2.77775i) q^{13} +(-3.49679 - 2.01888i) q^{14} -1.00000 q^{16} +(-3.24443 - 5.61952i) q^{17} +(-0.253608 - 0.0679541i) q^{19} +(-0.175000 - 0.653109i) q^{20} +0.710373 q^{22} +(-0.860504 - 1.49044i) q^{23} +(-3.93420 + 2.27141i) q^{25} +(-3.58960 + 0.338733i) q^{26} +(-1.04505 - 3.90017i) q^{28} -1.28654i q^{29} +(1.04468 + 3.89881i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.67944 - 6.26776i) q^{34} +(2.36435 - 1.36506i) q^{35} +(-7.96159 + 2.13330i) q^{37} +(-0.131277 - 0.227379i) q^{38} +(0.338074 - 0.585562i) q^{40} +(-2.39802 + 8.94954i) q^{41} +(-5.67915 - 3.27886i) q^{43} +(0.502310 + 0.502310i) q^{44} +(0.445430 - 1.66237i) q^{46} +(9.07214 + 2.43087i) q^{47} +(8.05701 - 4.65172i) q^{49} +(-4.38803 - 1.17577i) q^{50} +(-2.77775 - 2.29871i) q^{52} +6.34328i q^{53} +(-0.240159 + 0.415967i) q^{55} +(2.01888 - 3.49679i) q^{56} +(0.909720 - 0.909720i) q^{58} +(3.52351 - 3.52351i) q^{59} +(-1.64932 + 2.85670i) q^{61} +(-2.01817 + 3.49557i) q^{62} -1.00000i q^{64} +(1.01520 - 2.21645i) q^{65} +(10.0909 + 2.70385i) q^{67} +(5.61952 - 3.24443i) q^{68} +(2.63709 + 0.706607i) q^{70} +(2.09577 - 7.82153i) q^{71} +(-1.40415 - 1.40415i) q^{73} +(-7.13817 - 4.12122i) q^{74} +(0.0679541 - 0.253608i) q^{76} +(-1.43416 + 2.48403i) q^{77} +(7.29283 + 12.6316i) q^{79} +(0.653109 - 0.175000i) q^{80} +(-8.02394 + 4.63262i) q^{82} +(-1.04760 + 3.90968i) q^{83} +(3.10238 + 3.10238i) q^{85} +(-1.69726 - 6.33427i) q^{86} +0.710373i q^{88} +(2.64065 + 9.85503i) q^{89} +(6.06248 - 13.2360i) q^{91} +(1.49044 - 0.860504i) q^{92} +(4.69609 + 8.13386i) q^{94} +0.177526 q^{95} +(0.520942 + 1.94418i) q^{97} +(8.98642 + 2.40791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/702\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) −0.653109 + 0.175000i −0.292079 + 0.0782624i −0.401883 0.915691i \(-0.631644\pi\)
0.109804 + 0.993953i \(0.464978\pi\)
\(6\) 0 0
\(7\) −3.90017 + 1.04505i −1.47412 + 0.394991i −0.904343 0.426806i \(-0.859639\pi\)
−0.569781 + 0.821796i \(0.692972\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) −0.585562 0.338074i −0.185171 0.106908i
\(11\) 0.502310 0.502310i 0.151452 0.151452i −0.627314 0.778766i \(-0.715846\pi\)
0.778766 + 0.627314i \(0.215846\pi\)
\(12\) 0 0
\(13\) −2.29871 + 2.77775i −0.637548 + 0.770410i
\(14\) −3.49679 2.01888i −0.934558 0.539567i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −3.24443 5.61952i −0.786890 1.36293i −0.927863 0.372920i \(-0.878356\pi\)
0.140973 0.990013i \(-0.454977\pi\)
\(18\) 0 0
\(19\) −0.253608 0.0679541i −0.0581817 0.0155897i 0.229611 0.973283i \(-0.426255\pi\)
−0.287792 + 0.957693i \(0.592921\pi\)
\(20\) −0.175000 0.653109i −0.0391312 0.146040i
\(21\) 0 0
\(22\) 0.710373 0.151452
\(23\) −0.860504 1.49044i −0.179427 0.310777i 0.762257 0.647274i \(-0.224091\pi\)
−0.941685 + 0.336497i \(0.890758\pi\)
\(24\) 0 0
\(25\) −3.93420 + 2.27141i −0.786840 + 0.454282i
\(26\) −3.58960 + 0.338733i −0.703979 + 0.0664310i
\(27\) 0 0
\(28\) −1.04505 3.90017i −0.197495 0.737062i
\(29\) 1.28654i 0.238904i −0.992840 0.119452i \(-0.961886\pi\)
0.992840 0.119452i \(-0.0381138\pi\)
\(30\) 0 0
\(31\) 1.04468 + 3.89881i 0.187630 + 0.700246i 0.994052 + 0.108905i \(0.0347346\pi\)
−0.806422 + 0.591341i \(0.798599\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 1.67944 6.26776i 0.288022 1.07491i
\(35\) 2.36435 1.36506i 0.399648 0.230737i
\(36\) 0 0
\(37\) −7.96159 + 2.13330i −1.30888 + 0.350713i −0.844800 0.535082i \(-0.820281\pi\)
−0.464077 + 0.885795i \(0.653614\pi\)
\(38\) −0.131277 0.227379i −0.0212960 0.0368857i
\(39\) 0 0
\(40\) 0.338074 0.585562i 0.0534542 0.0925854i
\(41\) −2.39802 + 8.94954i −0.374508 + 1.39768i 0.479554 + 0.877512i \(0.340798\pi\)
−0.854062 + 0.520171i \(0.825868\pi\)
\(42\) 0 0
\(43\) −5.67915 3.27886i −0.866062 0.500021i −2.44809e−5 1.00000i \(-0.500008\pi\)
−0.866038 + 0.499979i \(0.833341\pi\)
\(44\) 0.502310 + 0.502310i 0.0757261 + 0.0757261i
\(45\) 0 0
\(46\) 0.445430 1.66237i 0.0656750 0.245102i
\(47\) 9.07214 + 2.43087i 1.32331 + 0.354579i 0.850216 0.526434i \(-0.176471\pi\)
0.473092 + 0.881013i \(0.343138\pi\)
\(48\) 0 0
\(49\) 8.05701 4.65172i 1.15100 0.664531i
\(50\) −4.38803 1.17577i −0.620561 0.166279i
\(51\) 0 0
\(52\) −2.77775 2.29871i −0.385205 0.318774i
\(53\) 6.34328i 0.871317i 0.900112 + 0.435658i \(0.143484\pi\)
−0.900112 + 0.435658i \(0.856516\pi\)
\(54\) 0 0
\(55\) −0.240159 + 0.415967i −0.0323830 + 0.0560890i
\(56\) 2.01888 3.49679i 0.269784 0.467279i
\(57\) 0 0
\(58\) 0.909720 0.909720i 0.119452 0.119452i
\(59\) 3.52351 3.52351i 0.458722 0.458722i −0.439514 0.898236i \(-0.644849\pi\)
0.898236 + 0.439514i \(0.144849\pi\)
\(60\) 0 0
\(61\) −1.64932 + 2.85670i −0.211173 + 0.365763i −0.952082 0.305843i \(-0.901062\pi\)
0.740909 + 0.671606i \(0.234395\pi\)
\(62\) −2.01817 + 3.49557i −0.256308 + 0.443938i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 1.01520 2.21645i 0.125921 0.274917i
\(66\) 0 0
\(67\) 10.0909 + 2.70385i 1.23280 + 0.330327i 0.815669 0.578520i \(-0.196369\pi\)
0.417130 + 0.908847i \(0.363036\pi\)
\(68\) 5.61952 3.24443i 0.681467 0.393445i
\(69\) 0 0
\(70\) 2.63709 + 0.706607i 0.315193 + 0.0844556i
\(71\) 2.09577 7.82153i 0.248722 0.928245i −0.722753 0.691106i \(-0.757124\pi\)
0.971476 0.237139i \(-0.0762096\pi\)
\(72\) 0 0
\(73\) −1.40415 1.40415i −0.164343 0.164343i 0.620145 0.784488i \(-0.287074\pi\)
−0.784488 + 0.620145i \(0.787074\pi\)
\(74\) −7.13817 4.12122i −0.829795 0.479082i
\(75\) 0 0
\(76\) 0.0679541 0.253608i 0.00779487 0.0290909i
\(77\) −1.43416 + 2.48403i −0.163437 + 0.283081i
\(78\) 0 0
\(79\) 7.29283 + 12.6316i 0.820507 + 1.42116i 0.905305 + 0.424762i \(0.139642\pi\)
−0.0847976 + 0.996398i \(0.527024\pi\)
\(80\) 0.653109 0.175000i 0.0730198 0.0195656i
\(81\) 0 0
\(82\) −8.02394 + 4.63262i −0.886096 + 0.511588i
\(83\) −1.04760 + 3.90968i −0.114989 + 0.429144i −0.999286 0.0377806i \(-0.987971\pi\)
0.884297 + 0.466924i \(0.154638\pi\)
\(84\) 0 0
\(85\) 3.10238 + 3.10238i 0.336501 + 0.336501i
\(86\) −1.69726 6.33427i −0.183020 0.683042i
\(87\) 0 0
\(88\) 0.710373i 0.0757261i
\(89\) 2.64065 + 9.85503i 0.279908 + 1.04463i 0.952481 + 0.304600i \(0.0985226\pi\)
−0.672573 + 0.740031i \(0.734811\pi\)
\(90\) 0 0
\(91\) 6.06248 13.2360i 0.635521 1.38751i
\(92\) 1.49044 0.860504i 0.155389 0.0897137i
\(93\) 0 0
\(94\) 4.69609 + 8.13386i 0.484364 + 0.838944i
\(95\) 0.177526 0.0182138
\(96\) 0 0
\(97\) 0.520942 + 1.94418i 0.0528937 + 0.197402i 0.987317 0.158763i \(-0.0507507\pi\)
−0.934423 + 0.356165i \(0.884084\pi\)
\(98\) 8.98642 + 2.40791i 0.907766 + 0.243235i
\(99\) 0 0
\(100\) −2.27141 3.93420i −0.227141 0.393420i
\(101\) −14.5201 −1.44481 −0.722404 0.691472i \(-0.756963\pi\)
−0.722404 + 0.691472i \(0.756963\pi\)
\(102\) 0 0
\(103\) −16.7121 9.64874i −1.64669 0.950719i −0.978374 0.206844i \(-0.933681\pi\)
−0.668319 0.743874i \(-0.732986\pi\)
\(104\) −0.338733 3.58960i −0.0332155 0.351990i
\(105\) 0 0
\(106\) −4.48538 + 4.48538i −0.435658 + 0.435658i
\(107\) −11.5211 6.65169i −1.11378 0.643043i −0.173977 0.984750i \(-0.555662\pi\)
−0.939807 + 0.341706i \(0.888995\pi\)
\(108\) 0 0
\(109\) 7.63616 7.63616i 0.731412 0.731412i −0.239488 0.970899i \(-0.576979\pi\)
0.970899 + 0.239488i \(0.0769794\pi\)
\(110\) −0.463951 + 0.124315i −0.0442360 + 0.0118530i
\(111\) 0 0
\(112\) 3.90017 1.04505i 0.368531 0.0987476i
\(113\) 15.2122i 1.43105i −0.698588 0.715524i \(-0.746188\pi\)
0.698588 0.715524i \(-0.253812\pi\)
\(114\) 0 0
\(115\) 0.822829 + 0.822829i 0.0767292 + 0.0767292i
\(116\) 1.28654 0.119452
\(117\) 0 0
\(118\) 4.98300 0.458722
\(119\) 18.5265 + 18.5265i 1.69832 + 1.69832i
\(120\) 0 0
\(121\) 10.4954i 0.954125i
\(122\) −3.18623 + 0.853749i −0.288468 + 0.0772948i
\(123\) 0 0
\(124\) −3.89881 + 1.04468i −0.350123 + 0.0938152i
\(125\) 4.56251 4.56251i 0.408083 0.408083i
\(126\) 0 0
\(127\) 16.8933 + 9.75334i 1.49904 + 0.865469i 0.999999 0.00111133i \(-0.000353747\pi\)
0.499037 + 0.866581i \(0.333687\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 2.28513 0.849411i 0.200419 0.0744982i
\(131\) 4.87564 + 2.81495i 0.425986 + 0.245943i 0.697635 0.716453i \(-0.254236\pi\)
−0.271649 + 0.962396i \(0.587569\pi\)
\(132\) 0 0
\(133\) 1.06013 0.0919249
\(134\) 5.22343 + 9.04724i 0.451236 + 0.781563i
\(135\) 0 0
\(136\) 6.26776 + 1.67944i 0.537456 + 0.144011i
\(137\) −3.04445 11.3621i −0.260105 0.970726i −0.965179 0.261592i \(-0.915753\pi\)
0.705073 0.709134i \(-0.250914\pi\)
\(138\) 0 0
\(139\) 2.96212 0.251244 0.125622 0.992078i \(-0.459907\pi\)
0.125622 + 0.992078i \(0.459907\pi\)
\(140\) 1.36506 + 2.36435i 0.115369 + 0.199824i
\(141\) 0 0
\(142\) 7.01259 4.04872i 0.588484 0.339761i
\(143\) 0.240627 + 2.54996i 0.0201222 + 0.213238i
\(144\) 0 0
\(145\) 0.225144 + 0.840250i 0.0186972 + 0.0697790i
\(146\) 1.98576i 0.164343i
\(147\) 0 0
\(148\) −2.13330 7.96159i −0.175356 0.654439i
\(149\) 16.4140 + 16.4140i 1.34469 + 1.34469i 0.891329 + 0.453358i \(0.149774\pi\)
0.453358 + 0.891329i \(0.350226\pi\)
\(150\) 0 0
\(151\) −1.78383 + 6.65733i −0.145166 + 0.541766i 0.854582 + 0.519316i \(0.173813\pi\)
−0.999748 + 0.0224496i \(0.992853\pi\)
\(152\) 0.227379 0.131277i 0.0184429 0.0106480i
\(153\) 0 0
\(154\) −2.77058 + 0.742373i −0.223259 + 0.0598222i
\(155\) −1.36458 2.36353i −0.109606 0.189843i
\(156\) 0 0
\(157\) −5.48299 + 9.49681i −0.437590 + 0.757928i −0.997503 0.0706232i \(-0.977501\pi\)
0.559913 + 0.828551i \(0.310835\pi\)
\(158\) −3.77505 + 14.0887i −0.300327 + 1.12083i
\(159\) 0 0
\(160\) 0.585562 + 0.338074i 0.0462927 + 0.0267271i
\(161\) 4.91369 + 4.91369i 0.387253 + 0.387253i
\(162\) 0 0
\(163\) 3.31255 12.3626i 0.259459 0.968315i −0.706096 0.708116i \(-0.749545\pi\)
0.965555 0.260198i \(-0.0837880\pi\)
\(164\) −8.94954 2.39802i −0.698842 0.187254i
\(165\) 0 0
\(166\) −3.50533 + 2.02380i −0.272066 + 0.157077i
\(167\) 0.811408 + 0.217416i 0.0627886 + 0.0168242i 0.290077 0.957003i \(-0.406319\pi\)
−0.227288 + 0.973828i \(0.572986\pi\)
\(168\) 0 0
\(169\) −2.43183 12.7705i −0.187064 0.982348i
\(170\) 4.38743i 0.336501i
\(171\) 0 0
\(172\) 3.27886 5.67915i 0.250011 0.433031i
\(173\) −10.6585 + 18.4610i −0.810349 + 1.40356i 0.102272 + 0.994757i \(0.467389\pi\)
−0.912620 + 0.408808i \(0.865944\pi\)
\(174\) 0 0
\(175\) 12.9703 12.9703i 0.980463 0.980463i
\(176\) −0.502310 + 0.502310i −0.0378630 + 0.0378630i
\(177\) 0 0
\(178\) −5.10134 + 8.83578i −0.382361 + 0.662269i
\(179\) −0.120767 + 0.209175i −0.00902656 + 0.0156345i −0.870503 0.492162i \(-0.836207\pi\)
0.861477 + 0.507797i \(0.169540\pi\)
\(180\) 0 0
\(181\) 1.73952i 0.129298i 0.997908 + 0.0646488i \(0.0205927\pi\)
−0.997908 + 0.0646488i \(0.979407\pi\)
\(182\) 13.6461 5.07242i 1.01151 0.375993i
\(183\) 0 0
\(184\) 1.66237 + 0.445430i 0.122551 + 0.0328375i
\(185\) 4.82646 2.78656i 0.354848 0.204872i
\(186\) 0 0
\(187\) −4.45245 1.19303i −0.325595 0.0872430i
\(188\) −2.43087 + 9.07214i −0.177290 + 0.661654i
\(189\) 0 0
\(190\) 0.125530 + 0.125530i 0.00910688 + 0.00910688i
\(191\) −7.31652 4.22419i −0.529404 0.305652i 0.211369 0.977406i \(-0.432208\pi\)
−0.740774 + 0.671754i \(0.765541\pi\)
\(192\) 0 0
\(193\) 0.0138895 0.0518362i 0.000999786 0.00373125i −0.965424 0.260684i \(-0.916052\pi\)
0.966424 + 0.256953i \(0.0827185\pi\)
\(194\) −1.00638 + 1.74311i −0.0722541 + 0.125148i
\(195\) 0 0
\(196\) 4.65172 + 8.05701i 0.332265 + 0.575501i
\(197\) −2.56942 + 0.688475i −0.183064 + 0.0490518i −0.349186 0.937053i \(-0.613542\pi\)
0.166122 + 0.986105i \(0.446875\pi\)
\(198\) 0 0
\(199\) −1.51087 + 0.872302i −0.107103 + 0.0618359i −0.552595 0.833450i \(-0.686362\pi\)
0.445492 + 0.895286i \(0.353029\pi\)
\(200\) 1.17577 4.38803i 0.0831394 0.310281i
\(201\) 0 0
\(202\) −10.2673 10.2673i −0.722404 0.722404i
\(203\) 1.34449 + 5.01771i 0.0943649 + 0.352175i
\(204\) 0 0
\(205\) 6.26468i 0.437544i
\(206\) −4.99456 18.6399i −0.347987 1.29871i
\(207\) 0 0
\(208\) 2.29871 2.77775i 0.159387 0.192603i
\(209\) −0.161524 + 0.0932559i −0.0111728 + 0.00645064i
\(210\) 0 0
\(211\) 0.651117 + 1.12777i 0.0448248 + 0.0776388i 0.887567 0.460678i \(-0.152394\pi\)
−0.842743 + 0.538317i \(0.819060\pi\)
\(212\) −6.34328 −0.435658
\(213\) 0 0
\(214\) −3.44317 12.8501i −0.235370 0.878414i
\(215\) 4.28290 + 1.14760i 0.292092 + 0.0782657i
\(216\) 0 0
\(217\) −8.14887 14.1143i −0.553181 0.958138i
\(218\) 10.7992 0.731412
\(219\) 0 0
\(220\) −0.415967 0.240159i −0.0280445 0.0161915i
\(221\) 23.0677 + 3.90543i 1.55170 + 0.262708i
\(222\) 0 0
\(223\) −13.4964 + 13.4964i −0.903785 + 0.903785i −0.995761 0.0919766i \(-0.970682\pi\)
0.0919766 + 0.995761i \(0.470682\pi\)
\(224\) 3.49679 + 2.01888i 0.233639 + 0.134892i
\(225\) 0 0
\(226\) 10.7567 10.7567i 0.715524 0.715524i
\(227\) −15.8751 + 4.25372i −1.05367 + 0.282329i −0.743766 0.668440i \(-0.766963\pi\)
−0.309901 + 0.950769i \(0.600296\pi\)
\(228\) 0 0
\(229\) −13.1402 + 3.52092i −0.868332 + 0.232669i −0.665366 0.746517i \(-0.731725\pi\)
−0.202965 + 0.979186i \(0.565058\pi\)
\(230\) 1.16366i 0.0767292i
\(231\) 0 0
\(232\) 0.909720 + 0.909720i 0.0597260 + 0.0597260i
\(233\) −3.89618 −0.255247 −0.127623 0.991823i \(-0.540735\pi\)
−0.127623 + 0.991823i \(0.540735\pi\)
\(234\) 0 0
\(235\) −6.35050 −0.414261
\(236\) 3.52351 + 3.52351i 0.229361 + 0.229361i
\(237\) 0 0
\(238\) 26.2004i 1.69832i
\(239\) −1.52259 + 0.407977i −0.0984882 + 0.0263898i −0.307727 0.951475i \(-0.599568\pi\)
0.209238 + 0.977865i \(0.432902\pi\)
\(240\) 0 0
\(241\) −4.98879 + 1.33674i −0.321356 + 0.0861071i −0.415891 0.909414i \(-0.636530\pi\)
0.0945350 + 0.995522i \(0.469864\pi\)
\(242\) −7.42135 + 7.42135i −0.477062 + 0.477062i
\(243\) 0 0
\(244\) −2.85670 1.64932i −0.182881 0.105587i
\(245\) −4.44806 + 4.44806i −0.284176 + 0.284176i
\(246\) 0 0
\(247\) 0.771732 0.548254i 0.0491042 0.0348846i
\(248\) −3.49557 2.01817i −0.221969 0.128154i
\(249\) 0 0
\(250\) 6.45236 0.408083
\(251\) −3.50515 6.07109i −0.221243 0.383204i 0.733943 0.679211i \(-0.237678\pi\)
−0.955186 + 0.296007i \(0.904345\pi\)
\(252\) 0 0
\(253\) −1.18090 0.316421i −0.0742426 0.0198932i
\(254\) 5.04870 + 18.8420i 0.316784 + 1.18225i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −1.89609 3.28412i −0.118275 0.204858i 0.800809 0.598919i \(-0.204403\pi\)
−0.919084 + 0.394062i \(0.871070\pi\)
\(258\) 0 0
\(259\) 28.8221 16.6405i 1.79092 1.03399i
\(260\) 2.21645 + 1.01520i 0.137458 + 0.0629603i
\(261\) 0 0
\(262\) 1.45713 + 5.43807i 0.0900215 + 0.335965i
\(263\) 8.35425i 0.515145i −0.966259 0.257573i \(-0.917077\pi\)
0.966259 0.257573i \(-0.0829226\pi\)
\(264\) 0 0
\(265\) −1.11007 4.14286i −0.0681914 0.254494i
\(266\) 0.749625 + 0.749625i 0.0459625 + 0.0459625i
\(267\) 0 0
\(268\) −2.70385 + 10.0909i −0.165164 + 0.616399i
\(269\) −3.60032 + 2.07864i −0.219515 + 0.126737i −0.605726 0.795674i \(-0.707117\pi\)
0.386211 + 0.922411i \(0.373784\pi\)
\(270\) 0 0
\(271\) −20.1972 + 5.41182i −1.22689 + 0.328745i −0.813368 0.581749i \(-0.802369\pi\)
−0.413523 + 0.910494i \(0.635702\pi\)
\(272\) 3.24443 + 5.61952i 0.196723 + 0.340733i
\(273\) 0 0
\(274\) 5.88143 10.1869i 0.355310 0.615416i
\(275\) −0.835235 + 3.11714i −0.0503666 + 0.187971i
\(276\) 0 0
\(277\) 13.1496 + 7.59192i 0.790082 + 0.456154i 0.839991 0.542600i \(-0.182560\pi\)
−0.0499093 + 0.998754i \(0.515893\pi\)
\(278\) 2.09454 + 2.09454i 0.125622 + 0.125622i
\(279\) 0 0
\(280\) −0.706607 + 2.63709i −0.0422278 + 0.157596i
\(281\) −29.2088 7.82648i −1.74245 0.466889i −0.759463 0.650550i \(-0.774538\pi\)
−0.982990 + 0.183662i \(0.941205\pi\)
\(282\) 0 0
\(283\) 17.0472 9.84221i 1.01335 0.585059i 0.101180 0.994868i \(-0.467738\pi\)
0.912171 + 0.409810i \(0.134405\pi\)
\(284\) 7.82153 + 2.09577i 0.464122 + 0.124361i
\(285\) 0 0
\(286\) −1.63294 + 1.97324i −0.0965580 + 0.116680i
\(287\) 37.4107i 2.20829i
\(288\) 0 0
\(289\) −12.5527 + 21.7419i −0.738393 + 1.27893i
\(290\) −0.434945 + 0.753347i −0.0255409 + 0.0442381i
\(291\) 0 0
\(292\) 1.40415 1.40415i 0.0821715 0.0821715i
\(293\) −7.02611 + 7.02611i −0.410470 + 0.410470i −0.881902 0.471433i \(-0.843737\pi\)
0.471433 + 0.881902i \(0.343737\pi\)
\(294\) 0 0
\(295\) −1.68462 + 2.91785i −0.0980825 + 0.169884i
\(296\) 4.12122 7.13817i 0.239541 0.414897i
\(297\) 0 0
\(298\) 23.2129i 1.34469i
\(299\) 6.11812 + 1.03582i 0.353820 + 0.0599029i
\(300\) 0 0
\(301\) 25.5762 + 6.85312i 1.47419 + 0.395007i
\(302\) −5.96880 + 3.44609i −0.343466 + 0.198300i
\(303\) 0 0
\(304\) 0.253608 + 0.0679541i 0.0145454 + 0.00389744i
\(305\) 0.577261 2.15437i 0.0330539 0.123359i
\(306\) 0 0
\(307\) 14.4825 + 14.4825i 0.826560 + 0.826560i 0.987039 0.160479i \(-0.0513040\pi\)
−0.160479 + 0.987039i \(0.551304\pi\)
\(308\) −2.48403 1.43416i −0.141541 0.0817186i
\(309\) 0 0
\(310\) 0.706360 2.63617i 0.0401186 0.149724i
\(311\) 11.3091 19.5879i 0.641281 1.11073i −0.343866 0.939019i \(-0.611737\pi\)
0.985147 0.171712i \(-0.0549299\pi\)
\(312\) 0 0
\(313\) −9.43419 16.3405i −0.533252 0.923619i −0.999246 0.0388313i \(-0.987636\pi\)
0.465994 0.884788i \(-0.345697\pi\)
\(314\) −10.5923 + 2.83820i −0.597759 + 0.160169i
\(315\) 0 0
\(316\) −12.6316 + 7.29283i −0.710580 + 0.410254i
\(317\) 4.92071 18.3643i 0.276375 1.03144i −0.678540 0.734563i \(-0.737387\pi\)
0.954915 0.296881i \(-0.0959463\pi\)
\(318\) 0 0
\(319\) −0.646241 0.646241i −0.0361825 0.0361825i
\(320\) 0.175000 + 0.653109i 0.00978280 + 0.0365099i
\(321\) 0 0
\(322\) 6.94900i 0.387253i
\(323\) 0.440945 + 1.64563i 0.0245348 + 0.0915652i
\(324\) 0 0
\(325\) 2.73418 16.1496i 0.151665 0.895817i
\(326\) 11.0840 6.39936i 0.613887 0.354428i
\(327\) 0 0
\(328\) −4.63262 8.02394i −0.255794 0.443048i
\(329\) −37.9233 −2.09078
\(330\) 0 0
\(331\) −6.85161 25.5705i −0.376598 1.40548i −0.850995 0.525173i \(-0.824001\pi\)
0.474397 0.880311i \(-0.342666\pi\)
\(332\) −3.90968 1.04760i −0.214572 0.0574943i
\(333\) 0 0
\(334\) 0.420016 + 0.727488i 0.0229822 + 0.0398064i
\(335\) −7.06363 −0.385927
\(336\) 0 0
\(337\) −19.6500 11.3449i −1.07040 0.617996i −0.142110 0.989851i \(-0.545389\pi\)
−0.928291 + 0.371854i \(0.878722\pi\)
\(338\) 7.31055 10.7497i 0.397642 0.584706i
\(339\) 0 0
\(340\) −3.10238 + 3.10238i −0.168250 + 0.168250i
\(341\) 2.48316 + 1.43365i 0.134471 + 0.0776368i
\(342\) 0 0
\(343\) −6.57658 + 6.57658i −0.355102 + 0.355102i
\(344\) 6.33427 1.69726i 0.341521 0.0915102i
\(345\) 0 0
\(346\) −20.5906 + 5.51723i −1.10696 + 0.296608i
\(347\) 16.6116i 0.891759i −0.895093 0.445879i \(-0.852891\pi\)
0.895093 0.445879i \(-0.147109\pi\)
\(348\) 0 0
\(349\) −1.58754 1.58754i −0.0849789 0.0849789i 0.663340 0.748318i \(-0.269139\pi\)
−0.748318 + 0.663340i \(0.769139\pi\)
\(350\) 18.3428 0.980463
\(351\) 0 0
\(352\) −0.710373 −0.0378630
\(353\) 6.34497 + 6.34497i 0.337709 + 0.337709i 0.855504 0.517796i \(-0.173247\pi\)
−0.517796 + 0.855504i \(0.673247\pi\)
\(354\) 0 0
\(355\) 5.47507i 0.290587i
\(356\) −9.85503 + 2.64065i −0.522315 + 0.139954i
\(357\) 0 0
\(358\) −0.233304 + 0.0625136i −0.0123305 + 0.00330395i
\(359\) 25.1620 25.1620i 1.32800 1.32800i 0.420885 0.907114i \(-0.361720\pi\)
0.907114 0.420885i \(-0.138280\pi\)
\(360\) 0 0
\(361\) −16.3948 9.46553i −0.862883 0.498186i
\(362\) −1.23003 + 1.23003i −0.0646488 + 0.0646488i
\(363\) 0 0
\(364\) 13.2360 + 6.06248i 0.693753 + 0.317761i
\(365\) 1.16279 + 0.671335i 0.0608631 + 0.0351393i
\(366\) 0 0
\(367\) 23.1998 1.21102 0.605509 0.795839i \(-0.292970\pi\)
0.605509 + 0.795839i \(0.292970\pi\)
\(368\) 0.860504 + 1.49044i 0.0448569 + 0.0776944i
\(369\) 0 0
\(370\) 5.38322 + 1.44243i 0.279860 + 0.0749883i
\(371\) −6.62903 24.7399i −0.344162 1.28443i
\(372\) 0 0
\(373\) −30.0462 −1.55573 −0.777866 0.628430i \(-0.783698\pi\)
−0.777866 + 0.628430i \(0.783698\pi\)
\(374\) −2.30476 3.99196i −0.119176 0.206419i
\(375\) 0 0
\(376\) −8.13386 + 4.69609i −0.419472 + 0.242182i
\(377\) 3.57369 + 2.95738i 0.184054 + 0.152313i
\(378\) 0 0
\(379\) 7.34807 + 27.4234i 0.377445 + 1.40864i 0.849739 + 0.527203i \(0.176759\pi\)
−0.472294 + 0.881441i \(0.656574\pi\)
\(380\) 0.177526i 0.00910688i
\(381\) 0 0
\(382\) −2.18660 8.16051i −0.111876 0.417528i
\(383\) 2.62509 + 2.62509i 0.134136 + 0.134136i 0.770987 0.636851i \(-0.219763\pi\)
−0.636851 + 0.770987i \(0.719763\pi\)
\(384\) 0 0
\(385\) 0.501955 1.87332i 0.0255820 0.0954732i
\(386\) 0.0464751 0.0268324i 0.00236552 0.00136573i
\(387\) 0 0
\(388\) −1.94418 + 0.520942i −0.0987009 + 0.0264468i
\(389\) −1.01593 1.75965i −0.0515099 0.0892178i 0.839121 0.543945i \(-0.183070\pi\)
−0.890631 + 0.454727i \(0.849737\pi\)
\(390\) 0 0
\(391\) −5.58369 + 9.67124i −0.282379 + 0.489096i
\(392\) −2.40791 + 8.98642i −0.121618 + 0.453883i
\(393\) 0 0
\(394\) −2.30368 1.33003i −0.116058 0.0670060i
\(395\) −6.97354 6.97354i −0.350877 0.350877i
\(396\) 0 0
\(397\) −2.23806 + 8.35257i −0.112325 + 0.419203i −0.999073 0.0430503i \(-0.986292\pi\)
0.886748 + 0.462254i \(0.152959\pi\)
\(398\) −1.68516 0.451537i −0.0844694 0.0226335i
\(399\) 0 0
\(400\) 3.93420 2.27141i 0.196710 0.113571i
\(401\) −37.9864 10.1784i −1.89695 0.508286i −0.997450 0.0713636i \(-0.977265\pi\)
−0.899499 0.436923i \(-0.856068\pi\)
\(402\) 0 0
\(403\) −13.2313 6.06037i −0.659100 0.301888i
\(404\) 14.5201i 0.722404i
\(405\) 0 0
\(406\) −2.59736 + 4.49876i −0.128905 + 0.223270i
\(407\) −2.92761 + 5.07076i −0.145116 + 0.251348i
\(408\) 0 0
\(409\) −21.0344 + 21.0344i −1.04008 + 1.04008i −0.0409222 + 0.999162i \(0.513030\pi\)
−0.999162 + 0.0409222i \(0.986970\pi\)
\(410\) 4.42980 4.42980i 0.218772 0.218772i
\(411\) 0 0
\(412\) 9.64874 16.7121i 0.475359 0.823347i
\(413\) −10.0600 + 17.4245i −0.495023 + 0.857404i
\(414\) 0 0
\(415\) 2.73678i 0.134343i
\(416\) 3.58960 0.338733i 0.175995 0.0166077i
\(417\) 0 0
\(418\) −0.180157 0.0482728i −0.00881174 0.00236110i
\(419\) 12.1901 7.03797i 0.595527 0.343827i −0.171753 0.985140i \(-0.554943\pi\)
0.767280 + 0.641313i \(0.221610\pi\)
\(420\) 0 0
\(421\) 4.66713 + 1.25055i 0.227462 + 0.0609482i 0.370750 0.928733i \(-0.379101\pi\)
−0.143288 + 0.989681i \(0.545767\pi\)
\(422\) −0.337043 + 1.25786i −0.0164070 + 0.0612318i
\(423\) 0 0
\(424\) −4.48538 4.48538i −0.217829 0.217829i
\(425\) 25.5285 + 14.7389i 1.23831 + 0.714941i
\(426\) 0 0
\(427\) 3.44722 12.8652i 0.166823 0.622591i
\(428\) 6.65169 11.5211i 0.321522 0.556892i
\(429\) 0 0
\(430\) 2.21699 + 3.83995i 0.106913 + 0.185179i
\(431\) −16.0936 + 4.31228i −0.775203 + 0.207715i −0.624669 0.780890i \(-0.714766\pi\)
−0.150534 + 0.988605i \(0.548099\pi\)
\(432\) 0 0
\(433\) 5.53229 3.19407i 0.265865 0.153497i −0.361142 0.932511i \(-0.617613\pi\)
0.627007 + 0.779014i \(0.284280\pi\)
\(434\) 4.21817 15.7424i 0.202478 0.755660i
\(435\) 0 0
\(436\) 7.63616 + 7.63616i 0.365706 + 0.365706i
\(437\) 0.116950 + 0.436462i 0.00559446 + 0.0208788i
\(438\) 0 0
\(439\) 13.2838i 0.633999i −0.948426 0.317000i \(-0.897325\pi\)
0.948426 0.317000i \(-0.102675\pi\)
\(440\) −0.124315 0.463951i −0.00592650 0.0221180i
\(441\) 0 0
\(442\) 13.5497 + 19.0729i 0.644496 + 0.907203i
\(443\) −19.0340 + 10.9893i −0.904332 + 0.522117i −0.878603 0.477552i \(-0.841524\pi\)
−0.0257292 + 0.999669i \(0.508191\pi\)
\(444\) 0 0
\(445\) −3.44926 5.97429i −0.163511 0.283209i
\(446\) −19.0868 −0.903785
\(447\) 0 0
\(448\) 1.04505 + 3.90017i 0.0493738 + 0.184266i
\(449\) −8.04520 2.15570i −0.379676 0.101734i 0.0639330 0.997954i \(-0.479636\pi\)
−0.443609 + 0.896220i \(0.646302\pi\)
\(450\) 0 0
\(451\) 3.29089 + 5.69999i 0.154962 + 0.268402i
\(452\) 15.2122 0.715524
\(453\) 0 0
\(454\) −14.2332 8.21756i −0.667998 0.385669i
\(455\) −1.64317 + 9.70547i −0.0770329 + 0.454999i
\(456\) 0 0
\(457\) 9.62978 9.62978i 0.450462 0.450462i −0.445046 0.895508i \(-0.646813\pi\)
0.895508 + 0.445046i \(0.146813\pi\)
\(458\) −11.7812 6.80189i −0.550500 0.317831i
\(459\) 0 0
\(460\) −0.822829 + 0.822829i −0.0383646 + 0.0383646i
\(461\) 34.5408 9.25517i 1.60872 0.431056i 0.661062 0.750331i \(-0.270106\pi\)
0.947662 + 0.319275i \(0.103439\pi\)
\(462\) 0 0
\(463\) 12.0689 3.23386i 0.560891 0.150290i 0.0327754 0.999463i \(-0.489565\pi\)
0.528116 + 0.849172i \(0.322899\pi\)
\(464\) 1.28654i 0.0597260i
\(465\) 0 0
\(466\) −2.75501 2.75501i −0.127623 0.127623i
\(467\) −11.9847 −0.554587 −0.277293 0.960785i \(-0.589437\pi\)
−0.277293 + 0.960785i \(0.589437\pi\)
\(468\) 0 0
\(469\) −42.1818 −1.94777
\(470\) −4.49048 4.49048i −0.207131 0.207131i
\(471\) 0 0
\(472\) 4.98300i 0.229361i
\(473\) −4.49970 + 1.20569i −0.206896 + 0.0554377i
\(474\) 0 0
\(475\) 1.15210 0.308704i 0.0528618 0.0141643i
\(476\) −18.5265 + 18.5265i −0.849160 + 0.849160i
\(477\) 0 0
\(478\) −1.36512 0.788151i −0.0624390 0.0360492i
\(479\) −10.1637 + 10.1637i −0.464393 + 0.464393i −0.900092 0.435699i \(-0.856501\pi\)
0.435699 + 0.900092i \(0.356501\pi\)
\(480\) 0 0
\(481\) 12.3756 27.0192i 0.564280 1.23197i
\(482\) −4.47282 2.58239i −0.203732 0.117624i
\(483\) 0 0
\(484\) −10.4954 −0.477062
\(485\) −0.680464 1.17860i −0.0308983 0.0535174i
\(486\) 0 0
\(487\) 21.7160 + 5.81879i 0.984047 + 0.263675i 0.714748 0.699382i \(-0.246541\pi\)
0.269299 + 0.963057i \(0.413208\pi\)
\(488\) −0.853749 3.18623i −0.0386474 0.144234i
\(489\) 0 0
\(490\) −6.29050 −0.284176
\(491\) 21.6874 + 37.5637i 0.978738 + 1.69522i 0.667003 + 0.745055i \(0.267577\pi\)
0.311735 + 0.950169i \(0.399090\pi\)
\(492\) 0 0
\(493\) −7.22973 + 4.17409i −0.325611 + 0.187991i
\(494\) 0.933371 + 0.158023i 0.0419944 + 0.00710979i
\(495\) 0 0
\(496\) −1.04468 3.89881i −0.0469076 0.175062i
\(497\) 32.6955i 1.46659i
\(498\) 0 0
\(499\) 7.45370 + 27.8176i 0.333673 + 1.24529i 0.905300 + 0.424772i \(0.139646\pi\)
−0.571627 + 0.820514i \(0.693687\pi\)
\(500\) 4.56251 + 4.56251i 0.204042 + 0.204042i
\(501\) 0 0
\(502\) 1.81440 6.77143i 0.0809805 0.302224i
\(503\) −13.3453 + 7.70492i −0.595038 + 0.343545i −0.767087 0.641543i \(-0.778295\pi\)
0.172049 + 0.985088i \(0.444961\pi\)
\(504\) 0 0
\(505\) 9.48323 2.54102i 0.421998 0.113074i
\(506\) −0.611279 1.05877i −0.0271747 0.0470679i
\(507\) 0 0
\(508\) −9.75334 + 16.8933i −0.432735 + 0.749518i
\(509\) −1.81959 + 6.79081i −0.0806519 + 0.300997i −0.994455 0.105160i \(-0.966465\pi\)
0.913803 + 0.406157i \(0.133131\pi\)
\(510\) 0 0
\(511\) 6.94381 + 4.00901i 0.307176 + 0.177348i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 0.981486 3.66296i 0.0432915 0.161566i
\(515\) 12.6034 + 3.37706i 0.555371 + 0.148811i
\(516\) 0 0
\(517\) 5.77808 3.33598i 0.254120 0.146716i
\(518\) 32.1469 + 8.61374i 1.41245 + 0.378466i
\(519\) 0 0
\(520\) 0.849411 + 2.28513i 0.0372491 + 0.100209i
\(521\) 42.4222i 1.85855i 0.369391 + 0.929274i \(0.379566\pi\)
−0.369391 + 0.929274i \(0.620434\pi\)
\(522\) 0 0
\(523\) 1.58272 2.74135i 0.0692074 0.119871i −0.829345 0.558737i \(-0.811286\pi\)
0.898553 + 0.438866i \(0.144620\pi\)
\(524\) −2.81495 + 4.87564i −0.122972 + 0.212993i
\(525\) 0 0
\(526\) 5.90735 5.90735i 0.257573 0.257573i
\(527\) 18.5200 18.5200i 0.806745 0.806745i
\(528\) 0 0
\(529\) 10.0191 17.3535i 0.435612 0.754501i
\(530\) 2.14450 3.71438i 0.0931511 0.161342i
\(531\) 0 0
\(532\) 1.06013i 0.0459625i
\(533\) −19.3473 27.2335i −0.838023 1.17962i
\(534\) 0 0
\(535\) 8.68856 + 2.32809i 0.375639 + 0.100652i
\(536\) −9.04724 + 5.22343i −0.390781 + 0.225618i
\(537\) 0 0
\(538\) −4.01563 1.07599i −0.173126 0.0463890i
\(539\) 1.71051 6.38372i 0.0736770 0.274966i
\(540\) 0 0
\(541\) −5.91918 5.91918i −0.254486 0.254486i 0.568321 0.822807i \(-0.307593\pi\)
−0.822807 + 0.568321i \(0.807593\pi\)
\(542\) −18.1083 10.4548i −0.777818 0.449074i
\(543\) 0 0
\(544\) −1.67944 + 6.26776i −0.0720055 + 0.268728i
\(545\) −3.65092 + 6.32358i −0.156388 + 0.270872i
\(546\) 0 0
\(547\) 16.9449 + 29.3493i 0.724510 + 1.25489i 0.959176 + 0.282811i \(0.0912670\pi\)
−0.234666 + 0.972076i \(0.575400\pi\)
\(548\) 11.3621 3.04445i 0.485363 0.130053i
\(549\) 0 0
\(550\) −2.79475 + 1.61355i −0.119169 + 0.0688020i
\(551\) −0.0874256 + 0.326277i −0.00372445 + 0.0138999i
\(552\) 0 0
\(553\) −41.6438 41.6438i −1.77088 1.77088i
\(554\) 3.92987 + 14.6665i 0.166964 + 0.623118i
\(555\) 0 0
\(556\) 2.96212i 0.125622i
\(557\) 2.17805 + 8.12858i 0.0922868 + 0.344419i 0.996594 0.0824630i \(-0.0262786\pi\)
−0.904307 + 0.426882i \(0.859612\pi\)
\(558\) 0 0
\(559\) 22.1626 8.23812i 0.937378 0.348436i
\(560\) −2.36435 + 1.36506i −0.0999121 + 0.0576843i
\(561\) 0 0
\(562\) −15.1196 26.1879i −0.637782 1.10467i
\(563\) −31.8876 −1.34390 −0.671951 0.740596i \(-0.734543\pi\)
−0.671951 + 0.740596i \(0.734543\pi\)
\(564\) 0 0
\(565\) 2.66214 + 9.93526i 0.111997 + 0.417979i
\(566\) 19.0137 + 5.09470i 0.799205 + 0.214146i
\(567\) 0 0
\(568\) 4.04872 + 7.01259i 0.169881 + 0.294242i
\(569\) 32.4802 1.36164 0.680821 0.732450i \(-0.261623\pi\)
0.680821 + 0.732450i \(0.261623\pi\)
\(570\) 0 0
\(571\) −27.2576 15.7372i −1.14070 0.658582i −0.194094 0.980983i \(-0.562177\pi\)
−0.946603 + 0.322401i \(0.895510\pi\)
\(572\) −2.54996 + 0.240627i −0.106619 + 0.0100611i
\(573\) 0 0
\(574\) 26.4534 26.4534i 1.10414 1.10414i
\(575\) 6.77079 + 3.90912i 0.282361 + 0.163021i
\(576\) 0 0
\(577\) 3.78292 3.78292i 0.157485 0.157485i −0.623966 0.781451i \(-0.714480\pi\)
0.781451 + 0.623966i \(0.214480\pi\)
\(578\) −24.2499 + 6.49774i −1.00866 + 0.270270i
\(579\) 0 0
\(580\) −0.840250 + 0.225144i −0.0348895 + 0.00934861i
\(581\) 16.3432i 0.678031i
\(582\) 0 0
\(583\) 3.18629 + 3.18629i 0.131963 + 0.131963i
\(584\) 1.98576 0.0821715
\(585\) 0 0
\(586\) −9.93642 −0.410470
\(587\) 30.8578 + 30.8578i 1.27364 + 1.27364i 0.944165 + 0.329474i \(0.106871\pi\)
0.329474 + 0.944165i \(0.393129\pi\)
\(588\) 0 0
\(589\) 1.05976i 0.0436666i
\(590\) −3.25444 + 0.872025i −0.133983 + 0.0359007i
\(591\) 0 0
\(592\) 7.96159 2.13330i 0.327219 0.0876781i
\(593\) 3.43157 3.43157i 0.140918 0.140918i −0.633129 0.774047i \(-0.718230\pi\)
0.774047 + 0.633129i \(0.218230\pi\)
\(594\) 0 0
\(595\) −15.3420 8.85768i −0.628959 0.363130i
\(596\) −16.4140 + 16.4140i −0.672343 + 0.672343i
\(597\) 0 0
\(598\) 3.59373 + 5.05860i 0.146958 + 0.206861i
\(599\) −6.49912 3.75227i −0.265547 0.153313i 0.361315 0.932444i \(-0.382328\pi\)
−0.626862 + 0.779130i \(0.715661\pi\)
\(600\) 0 0
\(601\) 17.4262 0.710831 0.355416 0.934708i \(-0.384339\pi\)
0.355416 + 0.934708i \(0.384339\pi\)
\(602\) 13.2392 + 22.9310i 0.539590 + 0.934597i
\(603\) 0 0
\(604\) −6.65733 1.78383i −0.270883 0.0725828i
\(605\) −1.83669 6.85462i −0.0746721 0.278680i
\(606\) 0 0
\(607\) −30.9125 −1.25470 −0.627350 0.778737i \(-0.715861\pi\)
−0.627350 + 0.778737i \(0.715861\pi\)
\(608\) 0.131277 + 0.227379i 0.00532400 + 0.00922143i
\(609\) 0 0
\(610\) 1.93155 1.11518i 0.0782063 0.0451524i
\(611\) −27.6066 + 19.6123i −1.11684 + 0.793429i
\(612\) 0 0
\(613\) 11.1528 + 41.6227i 0.450456 + 1.68113i 0.701113 + 0.713050i \(0.252687\pi\)
−0.250657 + 0.968076i \(0.580646\pi\)
\(614\) 20.4813i 0.826560i
\(615\) 0 0
\(616\) −0.742373 2.77058i −0.0299111 0.111630i
\(617\) 8.95150 + 8.95150i 0.360374 + 0.360374i 0.863950 0.503577i \(-0.167983\pi\)
−0.503577 + 0.863950i \(0.667983\pi\)
\(618\) 0 0
\(619\) 0.291078 1.08632i 0.0116994 0.0436628i −0.959829 0.280584i \(-0.909472\pi\)
0.971529 + 0.236922i \(0.0761384\pi\)
\(620\) 2.36353 1.36458i 0.0949215 0.0548030i
\(621\) 0 0
\(622\) 21.8475 5.85403i 0.876006 0.234725i
\(623\) −20.5979 35.6767i −0.825239 1.42936i
\(624\) 0 0
\(625\) 9.17568 15.8927i 0.367027 0.635710i
\(626\) 4.88349 18.2255i 0.195184 0.728436i
\(627\) 0 0
\(628\) −9.49681 5.48299i −0.378964 0.218795i
\(629\) 37.8190 + 37.8190i 1.50794 + 1.50794i
\(630\) 0 0
\(631\) −3.51015 + 13.1000i −0.139737 + 0.521505i 0.860197 + 0.509962i \(0.170341\pi\)
−0.999933 + 0.0115421i \(0.996326\pi\)
\(632\) −14.0887 3.77505i −0.560417 0.150163i
\(633\) 0 0
\(634\) 16.4650 9.50608i 0.653909 0.377535i
\(635\) −12.7400 3.41367i −0.505571 0.135467i
\(636\) 0 0
\(637\) −5.59943 + 33.0733i −0.221857 + 1.31041i
\(638\) 0.913923i 0.0361825i
\(639\) 0 0
\(640\) −0.338074 + 0.585562i −0.0133636 + 0.0231464i
\(641\) 23.6580 40.9769i 0.934436 1.61849i 0.158801 0.987311i \(-0.449237\pi\)
0.775636 0.631181i \(-0.217429\pi\)
\(642\) 0 0
\(643\) 6.73860 6.73860i 0.265745 0.265745i −0.561638 0.827383i \(-0.689829\pi\)
0.827383 + 0.561638i \(0.189829\pi\)
\(644\) −4.91369 + 4.91369i −0.193626 + 0.193626i
\(645\) 0 0
\(646\) −0.851840 + 1.47543i −0.0335152 + 0.0580500i
\(647\) 8.42061 14.5849i 0.331048 0.573392i −0.651669 0.758503i \(-0.725931\pi\)
0.982718 + 0.185111i \(0.0592644\pi\)
\(648\) 0 0
\(649\) 3.53979i 0.138949i
\(650\) 13.3528 9.48611i 0.523741 0.372076i
\(651\) 0 0
\(652\) 12.3626 + 3.31255i 0.484157 + 0.129730i
\(653\) 25.2989 14.6063i 0.990022 0.571589i 0.0847408 0.996403i \(-0.472994\pi\)
0.905281 + 0.424814i \(0.139660\pi\)
\(654\) 0 0
\(655\) −3.67694 0.985233i −0.143670 0.0384962i
\(656\) 2.39802 8.94954i 0.0936270 0.349421i
\(657\) 0 0
\(658\) −26.8158 26.8158i −1.04539 1.04539i
\(659\) 12.4412 + 7.18293i 0.484641 + 0.279807i 0.722348 0.691529i \(-0.243063\pi\)
−0.237708 + 0.971337i \(0.576396\pi\)
\(660\) 0 0
\(661\) −10.7255 + 40.0282i −0.417174 + 1.55692i 0.363267 + 0.931685i \(0.381661\pi\)
−0.780441 + 0.625230i \(0.785005\pi\)
\(662\) 13.2363 22.9259i 0.514443 0.891041i
\(663\) 0 0
\(664\) −2.02380 3.50533i −0.0785387 0.136033i
\(665\) −0.692380 + 0.185523i −0.0268494 + 0.00719426i
\(666\) 0 0
\(667\) −1.91750 + 1.10707i −0.0742460 + 0.0428660i
\(668\) −0.217416 + 0.811408i −0.00841208 + 0.0313943i
\(669\) 0 0
\(670\) −4.99474 4.99474i −0.192964 0.192964i
\(671\) 0.606480 + 2.26342i 0.0234129 + 0.0873782i
\(672\) 0 0
\(673\) 39.4913i 1.52228i 0.648588 + 0.761140i \(0.275360\pi\)
−0.648588 + 0.761140i \(0.724640\pi\)
\(674\) −5.87256 21.9167i −0.226202 0.844199i
\(675\) 0 0
\(676\) 12.7705 2.43183i 0.491174 0.0935321i
\(677\) −14.7062 + 8.49064i −0.565206 + 0.326322i −0.755232 0.655457i \(-0.772476\pi\)
0.190026 + 0.981779i \(0.439143\pi\)
\(678\) 0 0
\(679\) −4.06352 7.03823i −0.155944 0.270103i
\(680\) −4.38743 −0.168250
\(681\) 0 0
\(682\) 0.742114 + 2.76961i 0.0284170 + 0.106054i
\(683\) 1.34228 + 0.359662i 0.0513607 + 0.0137621i 0.284408 0.958703i \(-0.408203\pi\)
−0.233047 + 0.972465i \(0.574870\pi\)
\(684\) 0 0
\(685\) 3.97672 + 6.88788i 0.151943 + 0.263173i
\(686\) −9.30068 −0.355102
\(687\) 0 0
\(688\) 5.67915 + 3.27886i 0.216516 + 0.125005i
\(689\) −17.6201 14.5814i −0.671272 0.555507i
\(690\) 0 0
\(691\) −7.28822 + 7.28822i −0.277257 + 0.277257i −0.832013 0.554756i \(-0.812812\pi\)
0.554756 + 0.832013i \(0.312812\pi\)
\(692\) −18.4610 10.6585i −0.701782 0.405174i
\(693\) 0 0
\(694\) 11.7462 11.7462i 0.445879 0.445879i
\(695\) −1.93459 + 0.518372i −0.0733832 + 0.0196630i
\(696\) 0 0
\(697\) 58.0723 15.5604i 2.19965 0.589393i
\(698\) 2.24512i 0.0849789i
\(699\) 0 0
\(700\) 12.9703 + 12.9703i 0.490232 + 0.490232i
\(701\) 26.3023 0.993423 0.496712 0.867916i \(-0.334541\pi\)
0.496712 + 0.867916i \(0.334541\pi\)
\(702\) 0 0
\(703\) 2.16409 0.0816202
\(704\) −0.502310 0.502310i −0.0189315 0.0189315i
\(705\) 0 0
\(706\) 8.97314i 0.337709i
\(707\) 56.6310 15.1742i 2.12983 0.570685i
\(708\) 0 0
\(709\) 31.3179 8.39161i 1.17617 0.315154i 0.382763 0.923846i \(-0.374972\pi\)
0.793406 + 0.608693i \(0.208306\pi\)
\(710\) −3.87146 + 3.87146i −0.145293 + 0.145293i
\(711\) 0 0
\(712\) −8.83578 5.10134i −0.331135 0.191181i
\(713\) 4.91197 4.91197i 0.183955 0.183955i
\(714\) 0 0
\(715\) −0.603399 1.62329i −0.0225658 0.0607077i
\(716\) −0.209175 0.120767i −0.00781723 0.00451328i
\(717\) 0 0
\(718\) 35.5844 1.32800
\(719\) −8.65353 14.9884i −0.322722 0.558971i 0.658326 0.752733i \(-0.271265\pi\)
−0.981049 + 0.193761i \(0.937931\pi\)
\(720\) 0 0
\(721\) 75.2634 + 20.1668i 2.80296 + 0.751050i
\(722\) −4.89972 18.2860i −0.182349 0.680535i
\(723\) 0 0
\(724\) −1.73952 −0.0646488
\(725\) 2.92226 + 5.06150i 0.108530 + 0.187979i
\(726\) 0 0
\(727\) 8.04825 4.64666i 0.298493 0.172335i −0.343273 0.939236i \(-0.611536\pi\)
0.641766 + 0.766901i \(0.278202\pi\)
\(728\) 5.07242 + 13.6461i 0.187996 + 0.505757i
\(729\) 0 0
\(730\) 0.347509 + 1.29692i 0.0128619 + 0.0480012i
\(731\) 42.5521i 1.57385i
\(732\) 0 0
\(733\) 9.12426 + 34.0522i 0.337012 + 1.25775i 0.901671 + 0.432422i \(0.142341\pi\)
−0.564659 + 0.825324i \(0.690992\pi\)
\(734\) 16.4047 + 16.4047i 0.605509 + 0.605509i
\(735\) 0 0
\(736\) −0.445430 + 1.66237i −0.0164188 + 0.0612756i
\(737\) 6.42692 3.71058i 0.236739 0.136681i
\(738\) 0 0
\(739\) 32.7392 8.77244i 1.20433 0.322699i 0.399795 0.916604i \(-0.369081\pi\)
0.804535 + 0.593905i \(0.202415\pi\)
\(740\) 2.78656 + 4.82646i 0.102436 + 0.177424i
\(741\) 0 0
\(742\) 12.8063 22.1812i 0.470134 0.814296i
\(743\) 2.77031 10.3389i 0.101633 0.379299i −0.896309 0.443431i \(-0.853761\pi\)
0.997941 + 0.0641321i \(0.0204279\pi\)
\(744\) 0 0
\(745\) −13.5926 7.84768i −0.497993 0.287517i
\(746\) −21.2459 21.2459i −0.777866 0.777866i
\(747\) 0 0
\(748\) 1.19303 4.45245i 0.0436215 0.162798i
\(749\) 51.8854 + 13.9027i 1.89585 + 0.507992i
\(750\) 0 0
\(751\) −12.1245 + 7.00006i −0.442428 + 0.255436i −0.704627 0.709578i \(-0.748886\pi\)
0.262199 + 0.965014i \(0.415552\pi\)
\(752\) −9.07214 2.43087i −0.330827 0.0886448i
\(753\) 0 0
\(754\) 0.435793 + 4.61816i 0.0158706 + 0.168184i
\(755\) 4.66013i 0.169600i
\(756\) 0 0
\(757\) −4.20269 + 7.27928i −0.152749 + 0.264570i −0.932237 0.361848i \(-0.882146\pi\)
0.779488 + 0.626417i \(0.215479\pi\)
\(758\) −14.1954 + 24.5871i −0.515600 + 0.893045i
\(759\) 0 0
\(760\) −0.125530 + 0.125530i −0.00455344 + 0.00455344i
\(761\) −20.7884 + 20.7884i −0.753578 + 0.753578i −0.975145 0.221567i \(-0.928883\pi\)
0.221567 + 0.975145i \(0.428883\pi\)
\(762\) 0 0
\(763\) −21.8022 + 37.7625i −0.789292 + 1.36709i
\(764\) 4.22419 7.31652i 0.152826 0.264702i
\(765\) 0 0
\(766\) 3.71244i 0.134136i
\(767\) 1.68790 + 17.8870i 0.0609467 + 0.645862i
\(768\) 0 0
\(769\) 35.1291 + 9.41282i 1.26679 + 0.339435i 0.828800 0.559545i \(-0.189024\pi\)
0.437989 + 0.898980i \(0.355691\pi\)
\(770\) 1.67957 0.969702i 0.0605276 0.0349456i
\(771\) 0 0
\(772\) 0.0518362 + 0.0138895i 0.00186563 + 0.000499893i
\(773\) 1.91671 7.15325i 0.0689391 0.257284i −0.922852 0.385156i \(-0.874148\pi\)
0.991791 + 0.127871i \(0.0408144\pi\)
\(774\) 0 0
\(775\) −12.9658 12.9658i −0.465745 0.465745i
\(776\) −1.74311 1.00638i −0.0625739 0.0361271i
\(777\) 0 0
\(778\) 0.525886 1.96263i 0.0188539 0.0703638i
\(779\) 1.21632 2.10672i 0.0435790 0.0754811i
\(780\) 0 0
\(781\) −2.87610 4.98156i −0.102915 0.178254i
\(782\) −10.7869 + 2.89033i −0.385738 + 0.103358i
\(783\) 0 0
\(784\) −8.05701 + 4.65172i −0.287750